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Theory of Bivacuum, Particles Duality, Fields & Time.Free energy, Overunity Devices and Cold Fusion

Alex KaivarainenUniversity of Turku,

Vesilinnantie 5, FIN-20014, Turku, FinlandH2o@karelia.ru

http://www.karelia.ru/~alexk

CONTENTS

Extended SummaryAbbreviations and definitions, introduced in Unified theoryIntroduction1. New hierarchic model of Bivacuum, as a superfluid multi-cell structure1.1 Properties of Bivacuum dipoles - Bivacuum fermions and Bivacuum boson1.2 The basic (carrying)Virtual Pressure Waves (VPW) and Virtual spin waves(VirSW1/2 of Bivacuum1.3 Virtual Bose condensation (VirBC), as a base of Bivacuum nonlocality2. Virtual particles and antiparticles3. Three conservation rules for asymmetric Bivacuum fermions (BVFas andBivacuum bosons (BVBas4. The relation between the external and internal parameters of Bivacuum fermions &quantum roots of Golden mean4.1 The rest mass and charge origination4.2 Quantization of the rest mass/energy and charge of sub-elementary fermions4.3 The ratio of energies at Golden mean and Dead mean conditions4.4 The solution of Dirac monopole problem, following from Unified theory5 Fusion of elementary particles as a triplets of sub-elementary fermions at Goldenmean conditions5.1 Correlation between new model of hadrons and conventional quark model of protons,neutrons and mesons6 Total, potential and kinetic energies of elementary de Broglie waves7. The dynamic mechanism of Corpuscle -Wave duality7.1 The dynamic mechanism of pulsing photon7.2 The correlated dynamics of pairs of sub-elementary fermions and antifermionsof the opposite and similar spins7.3 Spatial images of sub-elementary particles in [C] and [W] phase8. The nature of electrostatic, magnetic and gravitational interaction, based on Unifiedtheory8.1 Electromagnetic dipole radiation as a consequence of charge oscillation8.2 The different kind of Bivacuum dipoles perturbation, induced by dynamics of elementaryparticles8.3 The new approach to quantum gravity and antigravity8.4 Possible nature of neutrino and antineutrino8.5 The background of energy conservation law8.6 The Bivacuum dipoles symmetry shift and linear and circular ordering,as a background of electrostatic and magnetic fields origination8.7 The factors, responsible for Coulomb interaction between elementary particles8.8 The magnetic field origination8.9 Interpretation of the Maxwell displacement current,based on Bivacuum model8.10 New kind of current in secondary Bivacuum,additional to displacement and conducting ones8.11 The mechanism, increasing the refraction index of Bivacuum8.12 Application of angular momentum conservation law for evaluationof curvatures of electric and gravitational potentials

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8.13 Curvatures of Bivacuum domains of nonlocality, corresponding tozero-point electromagnetic and gravitational potentials of elementary particles9. Pauli Principle: How it works ?9.1 Spatial compatibility of sub-elementary fermions of the same charge and opposite spins9.2 The double turn (7200 of magnetic field, as a condition of the fermions spin statereversibility9.3. Bosons as a coherent system of sub-elementary and elementary fermions10. The Mystery of Sri Yantra Diagram11. The Link Between the Maxwell’s Formalism and Unified Theory12. Possible Role of Golden Mean in Properties of Atoms12.1 New Interpretation of Compton effect12.2 The Bohr’s Model and the Alternative Duality Model of Hydrogen Atom13. Unified Theory (UT) and General Theory of Relativity13.1 The Difference and Correlation Between our Unified Theory (UT)and General Theory of Relativity13.2 The Red Shift of Photons in Unified Theory14. The Principle of least action, the Second and Third laws of Thermodynamics,as a consequence of Bivacuum Virtual Pressure Waves (VPW action on particles14.1 The quantum roots of Principle of least action14.2 Mechanism of particles acceleration by high-frequency Bivacuum virtual pressurewaves14.3 The quantum roots of 2nd and 3d laws of thermodynamics14.4 The new approach to problem of Time15. Virtual Replica (VR) of matter in Bivacuum15.1 Bivacuum perturbations, induced by the oscillation of the total energy of de Brogliewaves,accompanied by their thermal vibrations and recoil antirecoil effects15.2 Modulation of the basic Virtual Pressure Waves (VPWq

and Virtual Spin Waves(VirSWq

1/2of Bivacuum by molecular translations and librations15.3 The ”Ether”, ”Astral” and ”Mental” bodies, as a local, distant and nonlocalcomponents of VR15.4 Contributions of different kind of internal dynamics of matterto Virtual Replica of the object16 Possible mechanism of Quantum entanglement between distant elementaryparticles via Virtual Guides of spin, momentum and energy (VirGS,M,E16.1 The role of tuning force (FVPW of virtualpressure waves VPWq

of Bivacuum in entanglement17. New kind of Bivacuum mediated nonlocal interaction between macroscopic objects18. Experimental data, confirming the Unified theory (UT)18.1 Radiation of accelerating charges18.2 Artificial generation of unstable groups of virtual particles and antiparticles18.3 The experiments of N.A. Kozyrev and his group18.4 The idea of nonlocal signals transmitter and detector construction and testing18.5 Michelson-Morley experiment, as a possible evidence for the Virtual Replica of theEarth existing18.6 Interaction of particles with their Virtual Replicas, as a background of two slitexperiments explanation19 Theory of overunity devices19.1 The source of free energy in Bivacuum20 Possible explanation of Biefeld- Brown effect21 Possible explanation of Searl effect, based on Unified theory21.1 The variation of weight of rotating magnets21.2 The nature of magnetic shells around the convertor22 The Bearden Motionless Electromagnetic Generator (MEG)23 The Hydrosonic or Cavitational Overunity Devices24. Possible mechanism of cold nuclear fusion (CNF) and the excessive heat effectThe Main ConclusionsReferences

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EXTENDED SUMMARYNew concept of Bivacuum is elaborated, as a dynamic superfluid matrix of the Universe

with large domains of virtual Bose condensation, standing for their nonlocal properties.Bivacuum is represented by continuum of subquantum particles and antiparticles of theopposite energies, with properties of quantum liquids, separated by energy gap. Thecollective excitations of such quantum liquid, form the quantized vortical structures inBivacuum - strongly interrelated donuts: toruses V and antitoruses V of the oppositeenergies with Compton radiuses L0

i /m0i c of three electron’s generation (i e,, . The

pairs of these in-phase clockwise or anticlockwise rotating toruses and antitoruses(cell-dipoles), form Bivacuum fermions (BVF V V) i and antifermions(BVF V V) i of opposite spins. The intermediate state between Bivacuum fermions ofopposite spins, named Bivacuum bosons, has two possible polarization: (BVB V V) iand (BVB V V) i. Two Bivacuum fermions of opposite spins may form Cooper pair:[BVF BVF. The correlated actual torus (V and complementary antitorus (V havethe opposite quantized energy, mass, charges and magnetic moments, which compensateeach other in symmetric primordial Bivacuum (in the absence of matter and fields) and donot compensate in secondary Bivacuum.The dependence of the resulting actual inertial mass: mV

m0/ 1 v/c2 of torusV of asymmetric Bivacuum fermions (BVFas V V) and Bivacuum bosons, on theexternal translational group velocity v 0 follows relativistic mechanics, while theresulting complementary inertialess mass of antitorus V :|mV

| |i2mV | m0 1 v/c2 has the reverse dependence. For Bivacuum

antifermions of opposite symmetry shift between torus and antitorus the above relativisticdependencies are opposite. Corresponding symmetry shift in secondary Bivacuum take aplace in presence of matter and fields. The product of actual (inertial) and complementary(inertialess) mass is a constant, equal to the rest mass of particle of corresponding generationsquared: |mV

mV | m0

2 i. The difference of their total energies is equal to doubled kineticenergy of particle: mV

mV c2 mV

v2 2Tk.The opposite shift of symmetry between V and V of two Bivacuum fermions of opposite

spins occur due to relativistic effects, accompanied their rotation side-by-side as a Cooperpairs BVF BVFas around common axe. In this case the quantum beats between V

and V of BVF BVF can occur in the same phase.When the external velocity (v of the external rotation of pair BVF BVFas reach theGolden mean (GM) condition (v2/c2 0, 618, this results in origination of the restmass: m0 |mV

mV | and elementary charge: e |e e | of opposite sign for

sub-elementary fermion: BVFas F and sub-elementary antifermion BVFas

F

with spatial image of pair of truncated cone of opposite symmetry. The resultingmass/energy, charge and spin of Cooper pairs [F F is zero because of compensationeffects.On the other hand, two adjacent asymmetric Bivacuum fermions and antifermions of similar

direction of rotation and spin can not rotate ’side-by-side’ in opposite directionBVF BVFas, but only ’head-to-tail’ in the same: clockwise or anticlockwisedirections: N[BVF BVFas or NBVF BVFas. The Pauli allows spatialcompatibility of two BVF and BVF only in the case if quantum beats between V and Voccur in the counterphase manner. In such configuration, corresponding to integer spin, theuncompensated energy/ mass, charge and half-integer spin, provided by their V and Vsymmetry shift, are the additive values.The positive and negative energy, charge and integer spin of such pairs determines their

polarization. As far in primordial Bivacuum the average mass/energy, charge and spinshould be zero, it means that the number of ’head-to-tail’ pairs of Bivacuum fermions isequal to similar pairs of Bivacuum antifermions: N N.The fusion of sub-elementary fermions and antifermions to stable triplets F Fx,y F zi also becomes possible at the Golden mean velocity vrot c1/2

after the gyration radius of pair F Fx,y around common axe at GM conditionsdeclines to Compton radius:

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L0 mV

vrot2 m0c c

rot

i

1

where: mV m0/ is the actual mass of torus at GM conditions; vrot2 c2 is the

external group velocity at GM conditions. At this conditions, the triplets, representingelectrons, positrons, protons and anti protons, are stabilized by the resonance exchangeinteraction of unpaired sub-elementary fermion Fi and paired F

andF i withBivacuum Virtual Pressure Waves (VPWq

i with fundamental quantized frequency(VPWq q0

i. This interaction occur in the process of quantum beats between the actualand complementary states of sub-elementary fermions, representing theirCorpusleC WaveW pulsations with fundamental Compton frequency:

C W VPWq q0 qm0c2 / i 2

where: m0c2 is a rest-mass energy of sub-elementary fermion of i -generation.The 1st stage of matter creation in form of sub-elementary fermions or antifermions is a

result of cells-dipoles symmetry shift towards the positive or negative energy,correspondingly, accompanied by uncompensated mass and charge origination. The 2ndstage of matter formation is fusion of triplets F F F i from sub-elementaryfermions and antifermions. Both of stages occur at Golden mean (GM) conditions:(v/c)2 0. 618 and results in elementary particles and antiparticles (electrons, protons andneutrons) origination. We suppose, that regular electrons and positrons are the result offusion of three electrons/positrons and protons and antiprotons are resulted from fusionof three electrons/positrons.The fusion is accompanied by release of huge amount of kinetic energy and the electronic

(e gluons and hadronic h gluons origination (i.e. strong interaction, providingstability of triplets).It is shown, that the [corpuscle (C) wave (W)] duality represents modulation of quantum

beats between the asymmetric ’actual’ (torus) and ’complementary’ (antitorus) states ofsub-elementary fermions or antifermions by de Broglie wave frequency of these particles,equal to frequency of [C W pulsations of the ’anchor’ Bivacuum fermion BVFanc i ofunpaired F i . The [C] phase of each sub-elementary fermions of triplets F F F i exists as a mass, electric and magnetic asymmetric dipole. The[C W] transition is a result of two stages superposition. The total energy, charge and spinof particle, moving in space with velocity (v) is determined by the unpaired sub-elementaryfermion F z

, as far the paired ones in F Fx,y of triplets compensate each other.The 1st stage is a reversible dissociation of [C] phase to Cumulative virtual cloud CVCF

of subquantum particles and the ’anchor’ Bivacuum fermion BVFanc :

I: F C

Recoil/Antirecoil BVFanc CVCF W

i 2a

The 2nd stage of [C W transition is a reversible dissociation of the anchor Bivacuumfermion BVFanc i V Vanci to symmetric BVF i and the anchor cumulativevirtual cloud (CVCBVFanc , with frequency, equal to frequency of de Broglie wave ofparticle:

II : BVFanc

C

i

Recoil/Antirecoil BVF CVCBVFanc

Wi 2b

This second stage of reaction of transition of [C] phase to [W] phase determines theempirical parameters of wave B of elementary particle. The relativistic effects are providedby the increasing of symmetry shift of the ’anchor’ BVFanc with external translationalvelocity of particle.The recoil antirecoil effects, accompanied emission absorption of cumulative virtualclouds CVCF and CVCBVFanc on the 1st and 2nd stages of [C W pulsations standfor origination of electric, magnetic and spin/torsion fields.The absence of magnetic monopole - spatially localized magnetic charge, is one of theimportant consequences of our model of elementary particles, as far the magnetic momentssymmetry shift of BVFas is independent on velocity (v in,ext and always zero:

V V

0 3

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In the case of proton:p F Fx,y F z 3a

the sub-elementary fermions and antifermions, resulting from fusion of - electrons to stabletriplets, have a properties of quarks and antiquarks. In our model of hadrons we do not needthe hypothesis of fractional quark charge, because of compensation of integer charges ofpaired sub-elementary fermion and antifermion in triplets. The energy of 8 gluons is about50% of energy/mass of quarks and antiquarks ( sub-elementary fermions and antifermions).These gluons correspond to 8 different superposition of [CVC CVC in two spinstates (1/2 of triplets of (p), emitted and absorbed with in-phase C W pulsation ofpair of quark antiquark:

F FS0,1p qqS0,1 3b

of triplets (3a). The pairs of quark (q ~ and antiquark (q ~ , like (3b) representsmesons with neutral bosons properties.Thenewformulas for total energyofdeBrogliewave of sub-elementary fermion, equal in bothphase, taking into account the recoil and antirecoil energy, compensating each other in theprocess of [C W pulsation, is derived.Thesystemof these formulasunifies theextended inourwork theoryof relativitywithquantummechanics dualityandquantumfield theory.The empirical frequency of de Broglie wave of the electron, proton, atom or molecule (Bext

is demonstrated to be the modulation frequency of the internal Compton (reference)frequency of C W pulsation of their sub-elementary fermions (0

in) i, formingelementary particles, by the external particles translational dynamics. The C Wpulsations of unpaired F i are accompanied by the emission absorption ofCumulative Virtual Clouds (CVC) and the reversible recoil - antirecoil effects, generatingfields due to conversion of local corpuscular asymmetry to non-local one.The notion of metastable Virtual replica (VR) or virtual hologram of any material object in

Bivacuum is introduced. The VR is a result of interference of fundamental Virtual PressureWaves (VPW0

of Bivacuum (reference waves), with virtual ”object waves” (VPWm . The

latter represent whirls of superimposed [CVC CVCmi , generated by the in-phase C W pulsation of pairs F Fx,yi of triplets F Fx,y F zi , modulated bytranslational and librational de Broglie waves of the object’s atoms and molecules. It followsfrom Unified theory, that the Principle of least action is a consequence of VirtualPressure Waves (VPW of Bivacuum influence on pulsing particles, driving theproperties of matter to conditions of combinational resonance. Its ground frequency is equalto Compton one equal to Golden mean frequency (2).The dimensionless pace of time for any closed system is determined by the pace of its

kinetic energy change (anisotropic in general case), related to change of Bivacuum TuningEnergy: TEi |mV

c2 qm0c2 |i |CW q0i |, introduced in our work, as a difference

between the total energy of particle, related to frequency of its [C W pulsation andfundamental energy of Bivacuum (nm0c2:

dt/t d ln t d lnTkx,y,z d ln1 RTEi x,y,z d ln1 R|CW q0

i |x,y,z

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4awhere: R 1 v/c21/2 is relativistic factor; q 1,2,3. . . is quantization number ofVPW energy EVPW qm0

i c2 q0i and fundamental Compton frequency:

0i m0

i c2/The time for each selected closed system of particles is a parameter, characterizing theaverage velocity and acceleration of these particles, i.e. this system dynamics. The pace oftime is zero and time - infinitive, if kinetic energy of closed system is permanent. The paceof time and time itself are uncertain (dt/t 0/0; t 0/0), if the translational velocity ispermanent and equal to zero (v 0 const.A lot of experimental results, like Kozyrev’s ones, incompatible with existing paradigm,

find the explanations in terms of our theory, confirming the existence of new kind ofBivacuum mediated nonlocal interaction between distant systems, realized via nonlocalVirtual Guides (VirGSMEext of spin, momentum and kinetic energy between Sender(nonequilibrium system) and Receiver. The worm hole like structures VirGSMEext can beformed by Bivacuum bosons or Cooper pairs of Bivacuum fermions. Synchronization ofC W pulsation between remote elementary particles under the action of all-pervading

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Bivacuum virtual pressure waves (VPW is important factor in quantum entanglement.The main source of ’free’ energy of Bivacuum, used by overunity devices, is forced

combinational resonance of de Broglie waves of real elementary particles with fundamentalBivacuum virtual pressure waves (VPW of basic quantized frequency0i m0

i c2 / roti (see eq.2). The condition of combinational resonance is:VPW q0

i kCWor : EVPW nm0

i c2 kmV c2

5 5a

where: q and k are the integer numbers.The energy exchange between VPW VPW and real particles in the process of C Wpulsation of pairs F Fx,y of triplets F Fx,y F zi at pull-in -range stateaccelerate them, driving to resonant conditions (5 and 5a).In accordance to rules of combinational resonance of Bivacuum virtual pressure waves with

elementary particles, we have the following relation between quantized energy andfrequency of VPW and energy/frequency of triplets C W pulsation in resonanceconditions:

EVPW VPWi q0

i CWi R0 B R0 h2/2mV

B2

or : qm0i c2 Rm0

i c2 mVv2 Rm0

i c2 m0i c2v/c2

R

R 1 v/c2; q 1, 2, 3. . . integer numbers)

6

6a

where the angle frequency of de Broglie waves is: B 1,2,3 their length is: B 2LB2 h/mV

v and:B /2mV

LB2 mVv2/2 7

The relation between translational most probable velocity of particle and quantizationnumber (q, corresponding to resonant interaction of Bivacuum VPW with pulsingparticles, is:

v c q21q2

1/2 8

At the conditions of triplets fusion, when q 1, the translational velocity of particle iszero: vq1 0. When the quantized energy of VPWq

, corresponds to q 2, the resonanttranslational velocity of particle should be: vq2 c 0.866 2,6 1010cm/s. At q 3, wehave from (8): vq3 c 0.942 2,83 1010cm/s.It is anticipated, that at the velocity, corresponding to n 1,5, the interaction of pulsing

particles with basic VPWn1 after forcing of oscillation should slow down the their velocity,

driving translational mobility to resonant conditions: q 1, v 0. The 2nd and 3d laws ofthermodynamics, reflecting the ’spontaneous’ cooling of matter can be a consequence of justthis conditions.For the other hand, if velocity of particles corresponds to q 1,5, their pull-in rangeinteraction with VPWn2

can accelerate them up to conditions: q 2, v 2,6 1010cm/s.Virtual particles and antiparticles have mass mV

mV m0 and charge |e e | e0

symmetry shift smaller, than the rest mass and charge of real sub-elementary fermions andantifermions. The frequency of their CW pulsation is lower than fundamentalCompton’s one:

CWi 0

i m0i c2/. These reasons prevent the fusion of virtual

particles and antiparticles to triplets. The action of fundamental virtual pressure waves(VPW of Bivacuum with Compton frequency (0

i on groups of Cooper pairs of virtualparticles: NBVF BVFas N 1, forming big vortices with radiuses:R / mV

mV ic L0

i LL1/2 /m0c , can accelerate their rotation

around common axis, driving to Golden mean conditions from the lower limit: vrotext 1/2c.It is another - virtual source of superfluous energy of Bivacuum, standing for mechanism ofoverunity devices. This acceleration finally may transform the virtual particles to the realelementary particles. It may happen in strong enough fields, providing starting symmetryshift of Bivacuum fermions and corresponding external velocity and frequency of CWpulsation, necessary for forcing of oscillation and synchronization with VPW.Most technically simple example of propulsion, based on mechanism of the accelerated

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electron gas in the electrodes of capacitor as a result of forced resonance with VPWq2 , is

presented by Biefeld-Brown (B-B) effect. This effect is confirmed in many laboratoriesover the world (Naudin, http://members.aol.com/jnaudin509/, Bahder and Fazi, 2003).When a high voltage (~30 kV) is applied to a capacitor, whose electrodes have differentdimensions, the capacitor experiences a net force toward the smaller electrode, positive inmost cases. The B-B effect may have applications to vehicle propulsion in space. Thephysical basis for the Biefeld - Brown effect is not understood in the framework of existingparadigm. Using our Unified theory, we may explain this effect as a result of two process:1) acceleration of the translational dynamics of conductivity electrons in the volume ofelectrodes of capacitors in strong electric field, making the electrons most probabletranslational velocity in eq.7 close enough to resonant velocity v 2,6 1010cm/s at q 2and CW 20, when the additional acceleration under the influence of BivacuumPressure Waves (VPW in conditions of combinational resonance (6 and 8) becomeseffective. The corresponding excessive internal kinetic energy of the electrons at big enoughvoltage can be resulted in overcoming the auto-electron emission threshold and electricbreak of capacitor, following by thrust. In Searl machine such pull-in range energy exchangeof conductivity electrons with Bivacuum VPW induce the ’spontaneous’ acceleration ofrolls rotation around stator of machine;2) different pressure on positive and negative electrodes of capacitors, provided by virtual

negative sub-elementary fermions of ( and by virtual positive sub-elementary antifermionsof (e generation, correspondingly, acquiring the additional kinetic energy in the externalspace between electrodes under basic VPWq1

e, action and their spatial separation instrong electric field. The asymmetric internal and external pressure of real and virtualelementary particles, correspondingly, is exerted by their, hitting on the electrodes ofopposite charge of capacitor, creating thrust and capacitor propulsion.Some evidence are existing, that the difference in electrodes dimensions is more importantfactor of thrust direction, than their polarity. The geometrical asymmetry of capacitor mayprovide the ’focusing’ of collective momentums of real and virtual particles increasing theB-B effect.The collective and coherent properties of the conductivity electrons in the electrodes of

capacitor are the important factor, which should increase the B-B effect, if our explanation isright. For verification of given explanation, I propose to use for the positive and negativeelectrodes of capacitors the magnets from paramagnetic materials, where the electronsdynamics is ordered much more than in regular metals. The strong enhancement of B-Beffect is anticipated.The Searl overunity device is also considered from the positions of our Unified theory.

Two accompanied its action effects - decreasing or increasing of the effective mass ofMagnetic Energy Converter (MEC), depending on clockwise or anticlockwise direction ofrotor of MEC, and its self acceleration should be analyzed separately, as far they are basedon different physical mechanisms and are not directly dependent on each other:1. The increasing or decreasing of the effective mass of rotating magnetic system, named

Magnetic Energy Converter (MEC) in Searl effect can be a consequence of shift ofequilibrium between Bivacuum fermions of opposite spins BVF BVB BVF to theleft or right, depending on clockwise or anticlockwise direction of MEC rotor rotation. Thiseffect is accompanied by mass symmetry shift of the huge number of BVF, surroundingsystem and between MEC and the Earth surface, providing their circular rotation aroundMEC. The magnetic repulsion or attraction between the magnets of MEC of permanentpolarization and with two opposite magnetic polarization of Bivacuum dipoles, surroundingrotor and stator of MEC, display itself in change of their effective mass;2. For explanation of self-acceleration of MEC rotor we proceed from assumption, that

between the velocity of MEC paramagnetic rolls rotation around stator and most probabletranslational velocity of real ’free’ electrons in their coherent clusters near rolls surface anddynamics of ions of rolls lattice the strong correlation is existing.The additional acceleration of orchestrated coherent electrons in moving magnets occur due

to forced resonance of their C W pulsation with high frequency virtual pressure wavesof Bivacuum: VPWq2

: q 2, v 2,6 1010cm/s. This pull-in range acceleration becomespossible after acquiring by the surface electrons of rolling magnets the sufficient resultingvelocity for combinational resonance condition (6). This resulting velocity can be evaluatedapproximately, as a sum of the internal most probable velocity of ’free’ electron gas, usingMaxwell distribution:

8

v in 2kTme

~107 cm/s at room temperature 9

(which may be much higher on the right wing of distribution) and the additionaltranslational electrons velocity increment, induced by the rolls of MEC rotation aroundstator. After overcoming of the rolls surface electrons velocity threshold (aboutvext 3 104 cm/s the self-acceleration of MEC rotor starts. The velocity increment isinduced by the accelerated electrons coupling with ion lattice of paramagnetic rolls.The superfluous energy of space, extracted by Motionless Electromagnetic Generators

(MEG), constructed and patented in US by Patrick, Bearden, Hayes, Moore and Kenny(2002), also can be a result of acceleration of charged real and virtual fermions orantifermions, induced by resonant interaction with Bivacuum positive and negativeVPWq1,2,3

. In such a way the ’free’ potential energy of Bivacuum VPWq2,3 is converted

to additional kinetic energy of the coherent electrons in ’collectors’. This increment ofkinetic energy, like in B-B effect, increases the electrons flux in short - livingnonequilibrium states, realized in MEG. The role of magnetic field action in MEG and dePalma overunity machines, based on Faraday disk, is to increase the fraction of coherentelectrons and cumulative effect of their interaction with VPWq2,3

in conducting parts ofdevices. The excitation of high-frequency VPWq2,3

can be stimulated by alternating orpulsing EM fields. The latter is important for tuning of the electrons de Brpoglie wavefrequency to pull-in-range combinational resonance with VPWq2,3

.

In hydrosonic or cavitation overunity devices, using ultrasound induced cavitation, thecollapsing of bubbles is accompanied by high temperature jump about 6000 K, ionizationand dissociation of liquids molecules (i.e. H2O H HO, tearing off the electrons andvisible radiation (sonoluminescence). The additional accelerations of the electrons andprotons in their pull-in range conditions with VPWq1

provide the ratio of output to inputenergy (Coefficient of performance) in the range 1,5 - 7. Our theory predicts, that in strongpulsing magnetic fields, exciting high-frequency VPWq1

, this coefficient will be greater.

The excessive heating is revealed in collapsing bubbles, stimulated by ultrasound or smallholes on the surface of cathodes of electrolytic cells. The additional heating can be a resultof elementary particles acceleration, induced by forced resonance of C W pulsation ofpaired sub-elementary fermions with high frequency VPWq2,3...

. The tunneling throw theCoulomb barrier between two protons of deuterons can be realized in their in-phase Wave[W] phase state, when the distance between them become less than the length of theirCumulative Virtual Clouds (CVC), the charge density decreases, and CVC overlapped:CVCp1

CVCp2 . This condition may realized at the temperature of collapsing bubbles

in liquid ( 6000K.The mechanism of nuclear cold fusion and overheating in electrolytic cell with heavy water

is also proposed. Like in previous case, it is based on superposition of cumulative virtualclouds of two protons of neighboring deuterons in their wave phase, in conditions ofexcessive quantum pressure, when their de Broglie wave length exceeds few times theseparation between d in small voids/cracks of the cathode. Except the high virtual pressure,the overcoming of Coulomb threshold is facilitated by much lover charge density inCVCp1,2

volume of [W] phase, than that of [C] phase. The effective temperature in voids,heating and destroying the cathodes can be of tenth of thousands degrees. The dimensions ofcathode voids, their ability to absorb the deuterons and the rigidness of void wallsdetermines the probability of cold fusion in accordance to our theory.Keywords: vacuum, Bivacuum, torus, antitorus, virtual Bose condensation, nonlocality,virtual fermions and bosons, sub-elementary particles, symmetry shift, golden mean, mass,charge, fusion of elementary particles triplets, corpuscle - wave duality, de Broglie wave,electromagnetism, gravitation, quantum entanglement, principle of least action,harmonization force, time, virtual guides, Pauli principle, virtual replica, unification,overunity devices, Biefeld - Brown effect, Searl effect, Bearden Motionless electromagneticgenerator (MEG), hydrosonic devices, overheating, cold fusion.

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Abbreviations and Definitions, Introduced in Unified theory

- (V and (V are correlated actual torus and complementary antitorus of Bivacuum,formed by non mixing subquantum particles of the opposite energy, charge and magneticmoment;- (BVF V V i and (BVF V V i are virtual dipoles of three opposite poles:actual (inertial) and complementary (inertialess) mass, positive and negative charge, positiveand negative magnetic moments, separated by energetic gap, named Bivacuum fermions andBivacuum antifermions. The opposite half integer spin S 1

2 of BVF i, notated as( and , depends on direction of clockwise or anticlockwise in-phase rotation of pairs of[torus (V antitorus (V], forming them. The index: i e, , define the energy andCompton radiuses of BVF i of three electron generations;- (BVB V V i are Bivacuum bosons, representing the intermediate transition statebetween BVF and BVF;- (VC j,k ~ V jVk i and (VC j,k ~V jVk i are virtual clouds and anticlouds, composed fromsubquantum particles. Virtual clouds and anticlouds emission/absorption accompany thecorrelated transitions between different excitation states (j and k of torus (Vj,k i andantitorus (Vj,k i of Bivacuum dipoles: BVF i and BVB i;- VirP is virtual pressure, resulted from the process of subquantum particles densityoscillation, accompanied the virtual clouds (VC j,k emission and absorption in the process oftorus and antitorus transitions between their j and k states;- VPW and VPW are the positive and negative virtual pressure waves, related withoscillations of (VirP);- VirP |VirPVirP | ~ VPW VPW ~ VC j,k VC j,k S0

0 means theexcessive virtual pressure, being the consequence of Bivacuum dipoles asymmetry;- VirP |VirP VirP | ~ VPW VPW ~ VC j,k VC j,k S0

is the total virtualpressure;- F and F are sub-elementary fermions and antifermions of the opposite charge (/-) andenergy. They emerge due to stable symmetry shift between the actual (V andcomplementary (V torus of BVF dipoles [V V to the left or right, correspondingly.Their stabilization and fusion to triplets occur when the velocity of rotation of Cooper pairsBVF BVF around the common axis corresponds to Golden mean: (v/c)2 0. 618.This symmetry shift provides the rest mass and charge origination;- Hidden Harmony condition means the equality of the internal and external group and phasevelocities of Bivacuum fermions and Bivacuum bosons: vgrin vgrext; vphin vphext v. It isproved that this condition is a natural background of Goldenmean: v2/c2 ext, in 0. 6180339887;- F F Fe

,p is the coherent triplet of sub-elementary fermions and antifermion,representing the electron/positron or proton/antiproton. In the latter case a sub-elementaryfermions and antifermions corresponds to u and d quarks;- CVC and CVC are the cumulative virtual clouds of subquantum particles andantiparticles, standing for [W] phase of sub-elementary fermions and antifermions. Thereversible quantum beats C W between asymmetric torus and antitorus ofsub-elementary fermions are accompanied by [emission absorption] of CVC. Thestability of triplets of leptons and partons is determined by the resonant exchange interactionof sub-elementary fermions and antifermions by CVC in the process of[Corpuscle Wave pulsations. The virtual pairs CVC CVC display the gluonsproperties;- VirBC means virtual Bose condensation of Cooper - like pairs [BVF BVF and/or[BVB, providing the nonlocal properties of huge Bivacuum domains;- TE and TF are Tuning Energy and Tuning Force of Bivacuum, correspondingly, drivingthe matter to Golden Mean conditions and slowing down (cooling) the thermal dynamics ofparticles. Such Bivacuum - matter interaction is responsible for realization of principle ofLeast action;- VirSW1/2 are the Virtual spin waves, excited as a consequence of angular momentums ofcumulative virtual clouds (CVC) of sub-elementary particles in triplets F

F F

10

due to angular momentum conservation law. The VirSW1/2 are highly anisotropic,depending on orientation of triplets in space, being the physical background of torsion field;- VirGSMEi is the nonlocal virtual spin-momentum-energy guide (virtual microtubule withwormhole properties), formed primarily by standing VirSWS

S1/2 BVB VirSWR

S1/2 ofopposite spins and by accompanied self-assembled Bivacuum bosons BVB or Cooperpairs of [BVF BVF i, representing quasi one or two-dimensional Bose condensate.The VirGSMEi are connecting the remote coherent triplets F F F i : elementaryparticles, like protons and electrons - free or in composition of atoms with opposite spins;- (mBC means mesoscopic molecular Bose condensate in the volume of condensed matter,determined by 3D standing de Broglie waves of molecules, related to their librations only(in liquids) or librations and translations (in solids);- VR is the Virtual Replica (virtual hologram) of elementary, particles, atoms, molecules,macroscopic objects and their different forms, including living organisms. The complexhierarchical VR are, created as a result of interference of basic reference Bivacuum virtualpressure and virtual spin waves (VPWq1

and VirSWq11/2 with modulated by de Broglie

waves of the object atoms, similar kind of waves (VPWm and VirSWm

1/2;- BMI is a new fundamental Bivacuum Mediated Interaction due to superposition of Virtualreplicas of Sender and Receiver, extra to known electromagnetic, gravitational, weak andstrong interactions.**********************************************************************The abbreviations are not in alphabetic, but in logical order to make this glossary moreuseful for perception of new notions, introduced in Unified theory.

11

IntroductionThe Dirac’s equation points to equal probability of positive and negative energy (Dirac,

1947). In asymmetric Dirac’s vacuum its realm of negative energy is saturated withinfinitive number of electrons. However, it was assumed that these electrons, followingPauli principle, have not any gravitational or viscosity effects. Positrons and electron in hismodel represent the ’holes’, originated as a result of the electrons jumps in realm ofpositive energy over the energetic gap: 2m0c2. Currently it becomes clear, that theDirac type model of vacuum is not general enough to explain all known experimental data,for example, the bosons emergency. The model of Bivacuum, presented in this paper and inother works (Kaivarainen, 1995; 2000; 2004; 2005a,b) looks to be more advanced.However, it use the same starting point of equal probability of positive and negativeenergy, confined in each of Bivacuum cell-dipole in the absence of these dipoles symmetryshift.

Aspden (2003) introduced in his aether theory the basic unit, named Quon, as a pair ofvirtual muons of opposite charges, i.e. [muon antimuon]. This idea has some commonwith our model of Bivacuum dipoles of torus antitorus of opposite energy/mass, chargeand magnetic moments with Compton radiuses, corresponding to electron, muon and tauon(Kaivarainen, 2004, 2005).

Our notions of Bivacuum torus (V and antitorus (V have also some similarity with’phytons’, introduced by Akimov and Shipov for explanation of torsion field action. AfterAkimov (1995): "In non-polarised condition, physical vacuum contains in each of itselements a phyton, which is a kind of circle shape - two wave packets, which are rotating inopposite directions, corresponding to right and left spin. Primarily phytons arecompensated, as far the sum of their angular momentums is zero. This is a reason, why thevacuum does not manifest nonzero angular momentum. But, if in the vacuum the spinningobject appears, then the phytons, with axes of rotation, coinciding with that of the object,will keep the same rotation, and phytons which’ rotational axes were originally in theopposite direction, will be inverted partly under the influence of the spinning object.

However, in addition to Akimov and Shipov’s ’phytons’, our model of Bivacuumbosons (BVB and fermions (BVF assumes, that their torus V and antitorus V mayhave except similar or opposite angular momentums (spins), the opposite energies/masses,charges and magnetic moments, compensating each other in the absence of Bivacuumpolarization, i.e. when the Bivacuum triple dipoles symmetry shift is zero. The latter takes aplace in ’primordial’ Bivacuum, where the influence of matter and fields is absent. Themass and charge: positive or negative - originate in our model, as a result of BVB andBVF symmetry shift towards torus or antitorus, correspondingly.

The ability of Bivacuum dipoles, like BVB and virtual Cooper pairs [BVF BVFto form virtual Bose condensate from the bundles of quasi one-dimensional virtualmicrotubules is demonstrated in our theory. These bundles, forming in-turn, 3D nonlocaldomains, makes it possible to consider Bivacuum as a medium - aether with superfluidproperties. The superfluid model of vacuum, composed from pairs of fermions of oppositespins and charge where discussed earlier by Sinha et. al., (1976; 1976a; 1978) and also byBoldyreva and Sotina (1999).

David Bohm was the first one, who made an attempt to explain wholeness of theUniverse, without loosing the causality principle. Experimental discovery:”Aharonov-Bohm effect” (1950) pointing that electron is able to ”feel” the presence of amagnetic field even in a regions where the probability of field existing is zero, wasstimulating. For explanation of nonlocality Bohm introduced in 1952 the notion of quantumpotential, which pervaded all of space. But unlike gravitational and electromagnetic fields,

12

its influence did not decrease with distance. All the particles are interrelated by verysensitive to any perturbations quantum potential. This means that signal transmissionbetween particles may occur instantaneously. The idea of quantum potential or activeinformation is close to notion of pilot wave, proposed by de Broglie at the Solvay Congressin 1927. In fact, Bohm develops the de Broglie idea of pilot wave, applying it formany-body system.

In 1957 Bohm published a book: Causality and Chance in Modern Physics. Later hecomes to conclusion, that Universe has a properties of giant, flowing hologram. Taking intoaccount its dynamic nature, he prefer to use term: holomovement. In his book: Wholenessand the Implicate Order (1980) he develops an idea that our explicated unfolded reality is aproduct of enfolded (implicated) or hidden order of existence. He consider themanifestation of all forms in the universe, as a result of enfolding and unfolding exchangebetween two orders, determined by super quantum potential.

In book, written by D. Bohm and B. Hiley (1993): ”THE UNDIVIDED UNIVERSE.An ontological interpretation of quantum theory” the electron is considered, as a particlewith well- defined position and momentum which are, however, under influence of specialwave (quantum potential). Elementary particle, in accordance with these authors, is asequence of incoming and outgoing waves, which are very close to each other. However,particle itself does not have a wave nature. Interference pattern in double slit experimentafter Bohm is a result of periodically ”bunched” character of quantum potential.

After Bohm, the manifestation of corpuscle - wave duality of particle is dependent onthe way, which observer interacts with a system. He claims that both of this properties arealways enfolded in particle. It is a basic difference with our model, assuming that the waveand corpuscle phase are realized alternatively with high frequency during two differentsemiperiods of sub-elementary particles, forming particles in the process of quantum beatsbetween sublevels of positive (actual) and negative (complementary) energy. Thisfrequency is amplitude and phase modulated by experimentally revealed de Broglie wave ofparticles.

The important point of Bohmian philosophy, coinciding with our concept, is thateverything in the Universe is a part of dynamic continuum. Neurophysiologist Karl Pribramdoes made the next step in the same direction as Bohm: ”The brain is a hologram enfoldedin a holographic Universe”.

The good popular description of Bohm and Pribram ideas are presented in books: ”TheBell’s theorem and the curious quest for quantum reality” (1990) by David Peat and ”TheHolographic Universe” (1992) by Michael Talbot. Such original concepts are interestingand stimulating, indeed, but should be considered as a first attempts to transform intuitiveperception of duality and quantum wholeness into clear geometrical and mathematicalmodels.

Some common features with our and Bohm-Hiley models has a Unitary QuantumTheory (UQT), proposed by Sapogin (1982). In the UQT any elementary particle is not apoint and source of field like in the ordinary quantum mechanics, but represents a wavepacket of a certain unified field (Sapogin and Boichenko, 1991). The dispersion equation ofsuch a nonlinear field turned out to be such, that the wave packet (particle) during itsmovement periodically appears and disappears, and the envelope of this process coincideswith the de Broglie wave. Numerous particles during their periodic disappearance(spreading in the Universe) and repeated appearance represent vacuum fluctuations. Thecorresponding transversal self-focusing of the wave packet is possible only in conditions ifthe refraction index of space/vacuum is dependent of particle velocity. The square of wavepacket describes the oscillating charged particle mass and energy (Sapogin, et.al., 2002),following the conventional Newton equations. The essential in UQT is the absence of the

13

energy and the momentum conservation laws for single particles.In 1950 John Wheeler and Charles Misner published Geometrodynamics, a new

description of space-time properties, based on topology. Topology is more general thanEuclidean geometry and deeper than non-Euclidean, used by Einstein in his General theoryof relativity. Topology does not deal with distances, angles and shapes. Drawn on a sheet ofstretching rubber, a circle, triangle and square are indistinguishable. A ball, pyramid and acube also can be transformed into the other. However, objects with holes in them can neverbe transformed by stretching and deforming into objects without holes. For example blackhole can be described in terms of topology. It means that massive rotating body behave as aspace-time hole. Wheeler supposed that elementary particles and antiparticles, their spins,positive and negative charges can be presented as interconnected black and white holes.Positron and electron pair correspond to such model. The energy, directed to one of thehole, goes throw the connecting tube -”handle” and reappears at the other. The connectingtube exist in another space-time than holes itself. Such a tube is undetectable in normalspace and the process of energy transmission looks as instantaneous. In conventionalspace-time two ends of tube, termed ’wormholes’ can be a vast distant apart. It gives anexplanation of quantum nonlocality.

The same is true for introduced in our theory nonlocal Virtual spin-momentum-energyguides (VirGSME. The VirGSME, formed by Bivacuum bosons (BVB or Cooper pairs ofBivacuum fermions, may connect not only positrons and electrons or other type of particlesand antiparticles, but also the similar kind of particles with opposite spins with closefrequency of Corpuscle Wave pulsation.

Sidharth (1998, 1999) considered elementary particle as a relativistic vortex ofCompton radius, from which he recovered its mass and quantized spin. He pictured aparticle as a fluid vortex steadily circulating with light velocity along a 2D ring or spherical3D shell with radius

L 2mc 1

Inside such vortex the notions of negative energy, superluminal velocities and nonlocalityare acceptable without contradiction with conventional theory.

Bohm’s hydrodynamic formulation and substitution

Re iS 2

where R and S are real function of r and t, transforms the Schrödinger equation to

t v 0

or : St

2

2m S2 V 2

2m 2R/R Q

3

4

where: R2; v 2m S and Q 2

2m 2R/R

Sidharth comes to conclusion that the energy of nonlocal quantum potential (Q) isdetermined by inertial mass (m) of particle:

Q 2

2m 2R/R mc2 5

He treated also a charged Dirac fermions, as a Kerr-Newman black holes. Within theregion of Compton vortex the superluminal velocity and negative energy are possible afterSidharth. If measurements are averaged over time t~mc2/ and over space L~/mc, the

14

imaginary part of particle’s position disappears and we are back in usual Physics (Sidharth,1998).

Barut and Bracken (1981) considered zitterbewegung - rapidly oscillating imaginarypart of particle position, leading from Dirac theory (1947), as a harmonic oscillator in theCompton wavelength region of particle. The Einstein (1971, 1982) and Shrödinger (1930)also spoke about oscillation of the electron with frequency: m0c2/h and the amplitude:max /2mc. It was demonstrated by Shrödinger, that position of free electron can bepresented as: x x , where x characterize the average position of the free electron, and its instant position, related to its oscillations. Hestness (1990) proposed, thatzitterbewegung arises from self-interaction, resulting from wave-particle duality.

This ideas are close to our explanation of elementary particles zero-point oscillations, asa consequence of their recoil antirecoil vibrations, accompanied corpuscle wavepulsations. Corresponding oscillations of each particle kinetic energy, in accordance to ourtheory of time (Kaivarainen, 2005), is related with oscillations of instant time for thisclosed system. We came here to concept of space-time-energy discreet trinity, generated bycorpuscle wave duality.

Serious attack on problem of quantum nonlocality was performed by Roger Penrose(1989) with his twister theory of space-time. After Penrose, quantum phenomena cangenerate space-time. The twisters, proposed by him, are lines of infinite extent, resemblingtwisting light rays. Interception or conjunction of twistors lead to origination of particles. Insuch a way the local and nonlocal properties and particle-wave duality are interrelated intwistors geometry. The analysis of main quantum paradoxes was presented by Asher Peres(1992) and Charles Bennett et. al., (1993).

In our Unified model the local properties, within the Compton region of Bivacuumdipoles, are resulted from local Bivacuum symmetry shift of sub-elementary particles,responsible for their inertial mass and charge origination. The nonlocal properties of two ormore particles in state of entanglement, are the consequence of Bivacuum gap symmetryoscillation between torus and antitorus of BVF, BVB and corresponding pulsation ofradiuses of BVB or Cooper pairs of Bivacuum fermions [BVF BVF. The quasione-dimensional Bose condensation of toruses and antitoruses equal to that of virtualspin-momentum-energy guide VirGSME, connecting these particles with coherent [C Wpulsations.

The quite different approach for computational derivation of quantum relativisticsystems with forward-backward space-time shifts, developed by Daniel Dubois (1999), ledto some results, similar to ours (Kaivarainen, 1995, 2001, 2003, 2004). For example, thegroup and phase masses, introduced by Dubois, related to internal group and phasevelocities, has analogy with actual and complementary masses, introduced in our Unifiedtheory (UT). In both approaches, the product of these masses is equal to the particle’s restmass squared. The notion of discrete time interval, used in Dubois approach, maycorrespond to PERIOD of [C W] pulsation of sub-elementary particles in UT. Thepositive internal time interval, in accordance to our model, corresponds to forwardC W transition and the negative one to the backwardW C transition.

Puthoff (2001) developed the idea of ’vacuum engineering’, using hypothesis ofpolarizable vacuum (PV). The electric permittivity (0 and magnetic permeability (0 isinterrelated in ’primordial’ symmetric vacuum, as: 00 1/c

2. It is shown that changing ofvacuum refraction index: n c/v 1/2 , for example in gravitational or electric potentials,is accompanied by variation of lot of space-time parameters.

Fock (1964) and Puthoff (2001), explained the bending of light beam, induced bygravitation near massive bodies also by vacuum refraction change, i.e. in another way, thanGeneral theory of relativity. However, the mechanism of vacuum polarization and

15

corresponding refraction index changes in electric and gravitational fields remains obscure.Our Unified theory (Kaivarainen, 2005) propose such mechanism.

The transformation of neutron after scattering on neutrino, to proton and electron, inaccordance to Electro - Weak (EW) theory, developed by Glashov (1961), Weinberg(1967) and Salam (1968), is mediated by negative W particle. The reverse reaction in EWtheory: proton neutron is mediated by positive massless W boson. Scattering of theelectron on neutrino, not accompanied by charge transferring, is mediated by third masslessneutral boson Z0. In (EW) theory for explanation of spontaneous symmetry violation ofintermediate vector bosons: charged W and neutral Z0 with spin 1, accompanied by bigmass of these exchange particles origination, the Higgs field was introduced. The EWtheory needs also the quantum of Higgs field, named Higgs bosons with big mass, zerocharge and integer spin. The fusion of Higgs bosons with W and Z0 particles isaccompanied by increasing of their mass up to 90 mass of protons. The experimentaldiscovery of heavy W and Z0 particles in 1983 after their separation due to getting thesystem a big external energy, was considered as a conformation of EW theory. However,the Higgs field and Higgs bosons are still not found.

The spontaneous symmetry violation of vacuum, in accordance to Goldstone theorem,turns two virtual particles with imaginary masses (im to one real particle with mass:M1 2m and one real particle with zero mass:M2 0.

In the approaches, described above, two parameters of W particles, like charge andmass are considered, as independent. The described in this paper Unified theory tries tounify these parameters with magnetic moment, spin and Bivacuum symmetry shift, inducedby external translational-rotational motion of Bivacuum dipoles (Kaivarainen, 2004;2005a,b and section 3 of this paper). This theory makes an attempt to unify corpuscle-waveduality, zero-point oscillations, electromagnetism and gravitation with vacuum properties.

Thomson, Heaviside and Searl supposed that mass is an electrical phenomena. In theoryof Haisch, Rueda and Puthoff (1994), Rueda and Haish (1998) it was proposed, that theinertia is a reaction force, originating in a course of dynamic interaction between theelectromagnetic zero-point field (ZPF) of vacuum and charge of elementary particles.However, it’s not clear, how the charge itself originates. In our approach, the resistance ofparticle to acceleration (i.e. inertia force), proportional to its mass (second Newton’s law) isa consequence of resistance of Bivacuum symmetry and virtual pressure wave energydensity to changing, accompanied variation of particle’s momentum and kinetic energy. Incontrast to nonlocal Mach’s principle, our theory of particle-Bivacuum interactionexplains the existence of inertial mass of even single particle in empty Universe. Inaccordance to formalism of our theory, the rest mass and charge of elementary fermionsorigination are both the result of Bivacuum fermions (BVF) symmetry shift, correspondingto Golden mean conditions, i.e. equality of the ratio of external velocity of BVF to lightvelocity squared to: v/c2 0.618.The main goals of our work can be formulated as follows:1. Development of superfluid Bivacuum model, as the dynamic matrix of symmetric

double cells-dipoles, formed by pairs of virtual torus and antitorus of the oppositeenergy/mass, charge and magnetic moments. The explanation of creation of the electrons,positrons, quarks and photons, as a triplets of asymmetric Bivacuum sub-elementaryfermions of tree lepton generation (e,,. The resulting external properties of suchelementary particles are still described by the existing formalism of quantum mechanicsand Maxwell equations;

2. Development of the dynamic model of wave-corpuscle duality of sub-elementaryparticles/antiparticles, forming elementary particles and antiparticles. Explanation of thenonlocal quantum entanglement, based on new theory;

16

3. Generalization of Einstein’s and Dirac’s formalism for free relativistic particles,introducing the notions of correlated pairs of inertial - actual torus and inertialess -complementary antitorus of sub-elementary fermions, forming elementary particles, as theasymmetric triple-pole dipoles, containing the opposite mass, charge and magneticmomentum poles;

4. Finding the analytical equations, relating the internal and external parameters ofsub-elementary particles and elucidation the quantum roots of Golden Mean, as a conditionof triplets of sub-elementary fermions fusion, the rest mass and elementary chargeorigination. Stabilization of triplets occur at certain threshold of sub-elementary fermionssymmetry shift, making possible the resonant energy exchange internal viaCVC CVC as gluons) and external - with Bivacuum virtual pressure waves;

5. Explanation of the absence of Dirac’s monopole in Nature;6. Evaluation of the velocities of zero-point oscillations, responsible for

electromagnetic and gravitational fields of the electron as a consequence elasticrecoilantirecoil effects, accompanied Corpuscle Wave pulsation of particles;

7. Unification of Principle of least action, time, 2nd and 3d laws of thermodynamicswith action of introduced in our theory Tuning energy of Bivacuum virtual pressure waves(VPW on elementary particles dynamics;

8. Elaboration a concept of Virtual Replica (VR) of any material object in Bivacuumwith hologram properties, as a consequence of superposition of the reference basicBivacuum virtual pressure waves (VPW0

and virtual spin waves (VirSW01/2 with the

object virtual waves (VPWm and (VirSWm

1/2, modulated by de Broglie waves ofparticles, forming this object;

9. Proposing a new mechanism of Bivacuum - mediated nonlocal spin (information),momentum and energy exchange between remote coherent microscopic and macroscopicsystems via introduced Virtual guides of spin, momentum and energy VirGS,M,E;

10. Explanation of Kozyrev’s type experiments and other phenomena, incompatiblewith mainstream paradigm, based on new kind of nonlocal Bivacuum mediated interactionbetween remote objects, following from our Unified theory;

11. Construction of the new dynamic Hydrogen atom model, alternative to the Bohr’sone;

12. Explanation of the Biefeld-Brown, Searl, Bearden and cavitational overunitydevises action, converting the potential energy of Bivacuum high-frequency virtualpressure waves (VPWq2,3

to acceleration of the electrons and protons. It happens due toforced combinational resonance between Corpuscle Wave pulsation of particles andthe excited in pulsing fields regime virtual pressure waves of Bivacuum.

13. Explanation of mechanism of cold nuclear fusion (CNF) in voids of electrolytic cellcathode and the overheating effect due to excessive quantum pressure of sub-quantumparticles in form of Cumulative Virtual Clouds and much lower charge density in the wave[W] phase of deuteron, as respect to that of corpuscular [C] phase.

1. New Hierarchical Model of Bivacuum, as a Superfluid Multi-Cell Structure1.1. Properties of Bivacuum dipoles - Bivacuum fermions and Bivacuum bosons

The Bivacuum concept is a result of new interpretation and development of Diractheory (Dirac, 1958), pointing to equal probability of positive and negative energy inNature.

The Bivacuum is introduced, as a dynamic superfluid matrix of the Universe, composedfrom non-mixing subquantum particles of opposite polarization and three nonquantizedspin values, separated by an energy gap. The hypothetical microscopic subquantumparticles and antiparticles have a dimensions about or less than the Plank length (1033 cm),

17

zero mass, spin and charge. They spontaneously form the infinite number of mesoscopicpaired vortices - Bivacuum dipoles of three generations with Compton radii, correspondingto electrons (e), muons ( and tauons (, corresponding to three different spin values.Only such mesoscopic collective excitations of subquantum particles in form of pairs ofrotating fast torus and antitorus are quantized. In turn, these Bivacuum ’molecules’compose the macroscopic superfluid ideal liquid, representing the infinitive Bivacuummatrix.

Each of two strongly correlated ’donuts’ of Bivacuum dipoles acquire the opposite masscharge and magnetic moments, compensating each other in the absence of symmetry shiftbetween them. The latter condition is valid only for symmetric primordial Bivacuum,where the influence of matter and fields on Bivacuum is negligible. The sub-elementaryfermion and antifermion origination is a result of the Bivacuum dipole symmetry shifttoward the torus or antitorus, correspondingly. The correlation between paired vorticalstructures in a liquid medium was theoretically proved by Kiehn (1998).

The infinite number of paired vortical structures: [torus (V antitorus (V] with thein-phase clockwise or anticlockwise rotation are named Bivacuum fermions(BVF V V)i and Bivacuum antifermions (BVF V V)i, correspondingly.Their intermediate - transition states are named Bivacuum bosons of two possiblepolarizations: (BVB V V)i and (BVB V V)i The positive and negativeenergies of torus and antitorus (EV of three lepton generations i e,,), interrelatedwith their radiuses (LV

n , are quantized as quantum harmonic oscillators of oppositeenergies:

EVn m0c2 1

2 n 012 ni n 0,1,2,3. . .

or : EVn c

LVn

i

where : LVn

m0c 12 n

L012 n

i

1.1

1.1a

where: L0 /m0ce,,

is a Compton radii of the electron of corresponding leptongeneration (i e,, and L0

e L0 L0

. The Bivacuum fermions BVF, withsmaller Compton radiuses can be located inside the bigger ones BVFe.

The absolute values of increments of torus and antitorus energies (EVi , interrelated

with increments of their radii (LVi in primordial Bivacuum (i.e. in the absence of matter

and field influence), resulting from in-phase symmetric fluctuations are equal:

EVi c

LVi 2 LV

i EVi LV

i

LVi or :

LVi

LVi 2

c EVi

SBVFi

2hc EVi LV

i EVi

EVi

1.2

1.2a

where: SBVFi LVi 2 is a square of the cross-section of torus and antitorus,

forming Bivacuum fermions (BVF and Bivacuum bosons (BVB.The virtual mass, charge and magnetic moments of torus and antitorus of BVF and

BVB are opposite and in symmetric primordial Bivacuum compensate each other in theirbasic n 0) and excited n 1,2,3. . . ) states.

The Bivacuum ’atoms’: BVF V Vi and BVB V Vi represent dipolesof three different poles - the mass (mV

|mV | m0 i, electric (e and e and magnetic

( and dipoles.

18

The torus and antitorus (V V i of Bivacuum fermions of opposite spins BVF andBVF are both rotating in the same direction: clockwise or anticlockwise. This determinesthe positive and negative spins (S 1/2 of Bivacuum fermions. Their opposite spinsmay compensate each other, forming virtual Cooper pairs: [BVF BVF with neutralboson properties. The rotation of adjacent BVF and BVF in Cooper pairs is side- by- sidein opposite directions, providing zero resulting spin of such pairs and ability to virtual Bosecondensation. The torus and antitorus of Bivacuum bosons BVB V Vi withresulting spin, equal to zero, are rotating in opposite directions.

The energy gap between the torus and antitorus of symmetric BVF i or BVB i is:

ABVF EV EV 01 2ni m0i c21 2n hc

[dVV]ni 1.3

where the characteristic distance between torus (V i and antitorus (V i of Bivacuumdipoles (gap dimension) is a quantized parameter:

[dVV]ni h

m0i c1 2n

1.4

From (1.2) and (1.2a) we can see, that at n 0, the energy gap ABVFi is decreasing till0 m0

i c2 and the spatial gap dimension [dVV]ni is increasing up to the Comptonlength 0

i h/m0i c. On the contrary, the infinitive symmetric excitation of torus and

antitorus is followed by tending the spatial gap between them to zero: [dVV]ni 0 atn . This means that the quantization of space and energy of Bivacuum elements areinterrelated and discreet.

1.2 The basic (carrying)Virtual Pressure Waves (VPWq) and

Virtual spin waves (VirSWq1/2 of Bivacuum

The emission and absorption of Virtual clouds (VCj,k i and anticlouds (VCj,k i inprimordial Bivacuum, i.e. in the absence of matter and fields or where their influence onsymmetry of Bivacuum is negligible, are the result of correlated transitions betweendifferent excitation states (j,k of torus (Vj,k i and antitoruses (Vj,k i, forming symmetricBVFi and BVB i, corresponding to three lepton generations (i e,, :

VCqi Vj Vk

i virtual cloud

VCqi Vj Vk

i virtual anticloud

1.5

1.5a

where: j k are the integer quantum numbers of torus and antitorus excitation states;q j k.

The virtual clouds: (VCq i and (VCq i exist in form of collective excitation ofsubquantum particles and antiparticles of opposite energies, correspondingly. They can beconsidered as ’drops’ of virtual Bose condensation of subquantum particles of positive andnegative energy and similar in case of [BVFi and opposite in case of BVBi angularmomentums.

The process of [emission absorption of virtual clouds should be accompanied byoscillation of virtual pressure (VirP) and excitation of positive and negative virtualpressure waves: VPWq

and VPWq. In primordial Bivacuum the energies of opposite

virtual pressure waves totally compensate each other: VPWq VPWq

0. However, inasymmetric secondary Bivacuum, in presence of matter and fields, the total compensationis absent and the resulting virtual pressure is nonzero (Kaivarainen, 2005):

19

VirP |VirP | |VirP | 0.In accordance with our model of Bivacuum, virtual particles and antiparticles represent

the asymmetric Bivacuum dipoles BVFas and BVBas of three electron generations(i e,, in unstable state, not corresponding to Golden mean conditions (see section2.1). Virtual particles and antiparticles are the result of correlated and opposite Bivacuumdipole symmetry fluctuations. Virtual particles, like the real sub-elementary particles, mayexist in Corpuscular and Wave phases (see section 5). The Corpuscular [C]- phase,represents strongly correlated pairs of asymmetric torus (V and antitorus (V of twodifferent by absolute values energies. The Wave [W]- phase, results from quantum beatsbetween these states, which are accompanied by emission or absorption of CumulativeVirtual Clouds (CVC or CVC, formed by subquantum particles.

Virtual particles have a mass, charge, spin, etc., but they differs from realsub-elementary ones by their lower stability (short life-time) and inability for fusion tostable triplets (see section 3). They are a singlets or very unstable triplets or other clustersof Bivacuum dipoles (BVF)as in contrast to real fermions-triplets.

For Virtual Clouds (VC and virtual pressure waves (VPW excited by them, therelativistic mechanics is not valid. Consequently, the causality principle also does not workin a system (interference pattern) of VPW.

The quantized energies of positive and negative VPWq and VPWq

and correspondingvirtual clouds and anticlouds, emitted absorbed by BVF i and BVB i, as a result oftheir transitions between n j and n k states can be presented as:

EVPWq

i 0i j k m0

i c2j k

EVPWq

i 0i j k m0

i c2j k

1.6

1.6a

The quantized fundamental Compton frequency of VPWq:

q0i qm0

i c2/ 1.7

where: q j k 1,2,3. . is the quantization number of VPWj,k energy;

In symmetric primordial Bivacuum the total compensation of positive and negativeVirtual Pressure Waves takes a place:

qEVPWj,k

i qEVPWj,k

i q0i 1.8

The density oscillation of VCj,k and VCj,k and virtual particles and antiparticlesrepresent positive and negative virtual pressure waves VPWj,k

and VPWj,k . The

symmetric excitation of positive and negative energies/masses of torus and antitorus meansincreasing of primordial Bivacuum potential energy, corresponding to increasing of energygap between them (see eq. 1.3):

ABVFn EVn EVn 01 2ni m0

i c21 2n 1.8a

where quantum number: n 0,1,2,3. . . is equal to both - the actual torus (Vn and

complementary antitorus (Vn).

The symmetric transitions/beats between the excited and basic states of torus andantitorus are accompanied by virtual pressure waves excitation of corresponding frequency(1.6 and 1.6a).

The correlated virtual Cooper pairs of adjacent Bivacuum fermions (BVFS1/2 ),

rotating in opposite direction with resulting spin, equal to zero and Boson properties, can bepresented as:

20

BVFS1/2 BVFS1/2

S0 V V V VS0 1.9

Such a pairs, as well as Bivacuum bosons (BVB) in conditions of ideal equilibrium,like the Goldstone bosons, have zero mass and spin: S 0. The virtual clouds (VCq,emitted and absorbed in a course of correlated transitions of BVF BVFS0

j,k between (j)and (k) sublevels: q j k, excite the virtual pressure waves VPWq

and VPWq, carrying

the opposite angular momentums. They compensate the energy and momentums of eachother totally in primordial Bivacuum and partly in secondary Bivacuum - in presence ofmatter and fields.The nonlocal virtual spin waves VirSWj,k

1/2, with properties of massless collectiveNambu-Goldstone modes, like a real spin waves, represent the oscillation of angularmomentum equilibrium of Bivacuum fermions with opposite spins via "flip-flop"mechanism, accompanied by origination of intermediate states - Bivacuum bosons (BVB:

VirSWj,k1/2 ~ BVFV V BVBV V BVFV V 1.10

The VirSWj,k1/2 and VirSWj,k

1/2 are excited by VCqS1/2 and VCqS1/2

of oppositeangular momentums, S1/2 1

2 12 L0m0c and frequency, equal to VPWq

(1.7):

qVirSW1/2i qVPW

i qm0i c2/ q0

i 1.10a

The most probable basic virtual pressure waves VPW0 and virtual spin waves

VirSW01/2 correspond to minimum quantum number q j k 1.

The VirSWj,k1/2, like so-called torsion field, can serve as a carrier of the phase/spin

(angular momentum) and information - qubits, but not the energy.The Bivacuum bosons (BVB, may have two polarizations (, determined by spin

state of their actual torus (V:

BVB V V, when BVF BVF

BVB V V, when BVF BVF 1.11

1.11a

The Bose-Einstein statistics of energy distribution, valid for system of weaklyinteracting bosons (ideal gas), do not work for Bivacuum due to strong coupling of pairsBVF BVFS0 and (BVB, forming virtual Bose condensate (VirBC) with nonlocalproperties. The Bivacuum nonlocal properties can be proved, using the Virial theorem(Kaivarainen, 2004, 2005).

1.3 Virtual Bose condensation (VirBC), as a base of Bivacuum nonlocalityIt follows from our model of Bivacuum, that the infinite number of Cooper pairs of

Bivacuum fermions BVF BVFS0i and their intermediate states - Bivacuum bosons

(BVB i, as elements of Bivacuum, have zero or very small (in presence of fields andmatter) translational momentum: pBVFBVFi pBVBi 0 and corresponding de Brogliewave length tending to infinity: VirBCi h/pBVFBVF,BVBi . It leads to origination of3D net of virtual adjacent pairs of virtual microtubules from Cooper pairsBVF BVFS0, rotating in opposite direction and (BVBS0, which may form singlemicrotubules, with resulting angular momentum, equal to zero. These twin and singlemicrotubules, termed Virtual Guides VirGBVF

BVF and VirGBVB, represent a quasione-dimensional Bose condensate with nonlocal properties close to that of ’wormholes’(see section 9). Their radiuses are determined by the Compton radiuses of the electrons,

21

muons and tauons and state of corresponding Bivacuum dipoles excitation. Their length islimited only by decoherence effects. In symmetric Bivacuum, unperturbed by matter andfields, the length of VirG with nonlocal properties may have the order of stars and galacticsseparation.Nonlocality, as the independence of potential on the distance from its source in the

volume or filaments of virtual or real Bose condensate, follows from application of theVirial theorem to systems of Cooper pairs of Bivacuum fermions BVF BVFS0 andBivacuum bosons BVB (Kaivarainen, 1995; 2004; 2005).

The Virial theorem in general form is correct not only for classical, but also forquantum systems. It relates the averaged kinetic T kv

i

mivi2/2 and potential Vr

energies of particles, composing these systems:

2T kv i

mivi2 i

riV/ri 1.12

If the potential energy Vr is a homogeneous order function like:

Vr r, then n 2TkVr

1.12a

For example, for a harmonic oscillator, when T k V,we have 2. For Coulombinteraction: 1 and T V /2.

The important consequence of the Virial theorem is that, if the average kinetic energyand momentum (p of particles in a certain volume of a Bose condensate (BC) tends tozero:

T k p 2/2m 0 1.13

the interaction between particles in the volume of BC, characterized by the radius:LBC /p 0, becomes nonlocal, as independent on distance between them:

Vr r 1 const at 2T k/Vr 0 1.14

Consequently, it is shown, that nonlocality, as independence of potential on the distancefrom potential source, is the inherent property of macroscopic Bose condensate. Theindividual particles (real, virtual or subquantum) in a state of Bose condensation arespatially indistinguishable due to the uncertainty principle. The Bivacuum dipolesBVF BVFS0 and (BVBS0 due to quasi one-dimensional Bose condensation aretending to self-assembly by ’head-to-tail’ principle. They compose very long virtualmicrotubules - Virtual Guides with wormhole properties. The 3D net of these two kind ofVirtual Guides (VirGBVFBVF and VirGBVB) represent the nonlocal fraction of superfluidBivacuum..

2. Virtual Particles and AntiparticlesGenerally accepted difference of virtual particles from the actual ones, is that the

former, in contrast to latter, does not follow the laws of relativistic mechanics:

m m0

1 v/c2 1/2 2.1

For actual free particle with rest mass m0 and relativistic mass (m, the formula,following from (2.1) is:

22

E2p 2c2 m02c4 2.2

where E2 mc22 is the total energy squared andp m

v is the momentum of

particle.In accordance to our model of Bivacuum, virtual particles represent asymmetric

Bivacuum dipoles (BVF)as and (BVBas of three electron’s generation (i e,, inunstable state far from Golden mean conditions. Virtual particles, like the realsub-elementary particles, may exist in two phase: Corpuscular [C]- phase, representingcorrelated pairs of asymmetric torus (V and antitorus (V of two different energy statesand Wave [W]- phase, resulting from quantum beats between these states. Correspondingtransitions are accompanied by emission absorption of Cumulative Virtual Cloud (CVC

or CVC, formed by subquantum particles and antiparticles. For virtual particles theequality (2.2) is invalid.

Virtual particles differs from real sub-elementary ones by their lower stability (shortand uncertain life-time) and inability for fusion to triplets, as far their symmetry shift,determined by their external velocity and corresponding relativistic effects are not bigenough to follow the Golden Mean condition (see section 5).

For Cumulative Virtual Clouds (CVC and excited by them periodic subquantumparticles and antiparticles density oscillation in Bivacuum - virtual pressure waves(VPW, the relativistic mechanics and equality (2.2) are not valid. Consequently, thecausality principle also do not works in a system of VPW, representing oscillations ofsubquantum particles density.

The [electron - proton] interaction is generally considered, as a result of virtual photonsexchange (the cumulative virtual clouds CVC exchange in terms of our theory- section13.2, when the electron and proton total energies do not change. Only the directions oftheir momentums are changed. In this case the energy of virtual photon in the equation(2.2) E 0 and:

E2 p 2c2 p 2c2 0 2.3

The measure of virtuality (Vir) is a measure of Dirac’s relation validity:

Vir m02c4E2p 2c2 0 2.4

In contrast to actual particles, the virtual ones have a more limited radius of action. Themore is the virtuality (Vir), the lesser is the action radius. Each of emitted virtual quantum(virtual cloud) must be absorbed by the same particle or another in a course of theirC W pulsations.

A lot of process in quantum electrodynamics can be illustrated by Feynman diagrams(Feynman, 1985). In these diagrams, actual particles are described as infinitive rays (lines)and virtual particles as stretches connecting these lines (Fig. 1).

Each peak (or angle) in Feynman diagrams means emission or absorption of quanta orparticles. The energy of each process (electromagnetic, weak, strong) is described usingcorrespondent fine structure constants.

23

Fig. 1. Feynman diagrams describing electron-proton scattering (interaction), mediated byvirtual photons: a) - annihilation of electron and positron by means of virtual electron evand virtual positron ev with origination of two and three actual photons : diagrams b) and c) correspondingly.

3 Three conservation rules for asymmetric Bivacuum fermions (BVFas andBivacuum bosons (BVBas

There are three basic postulates in our theory, interrelated with each other:I. The absolute values of internal rotational kinetic energies of torus and antitorus are

equal to each other and to the half of the rest mass energy of the electrons of correspondinglepton generation, independently on the external group velocity (v, turning the symmetricBivacuum fermions (BVF to asymmetric ones:

I : 12 mV

vgrin 2 12 |mV

|vphin 2 12 m0c2 const

in

i 3.1

where: mV andmV

are the ’actual’ - inertial and ’complementary’ - inertialess massesof torus (V and antitorus (V; the vgrin and vphin are the internal angular group and phasevelocities of subquantum particles and antiparticles, forming torus and antitorus,correspondingly. In symmetric conditions of primordial Bivacuum and its virtual dipoles,when the influence of matter and fields is absent: vgrin vphin c andmV

mV m0.

It will be proved in section (7.1) of this paper, that the above condition means theinfinitive life-time of torus and antitorus of BVF and BVB.II. The internal magnetic moments of torus (V and antitorus (V of asymmetric

Bivacuum fermions BVFas V V and antifermions: BVFas V V], when vgrin vphin , mV

|mV | and |e | |e |, are equal to each other and to that of Bohr magneton:

B 0 12 |e0 |

m0c , independently on their external translational velocity v 0 andsymmetry shift. In contrast to permanent magnetic moments of V and V, their actual andcomplementary massesmV

and |mV |, internal angular velocities (vgrin and vphin and electric

charges |e | and |e |, are dependent on (v, however, they compensate each other variations:

II :| | 1

2 |e | |||mV |vgrin rot

| | 12 |e | ||

|mV | vphin rot

0 12 |e0 |

m0c const

i

3.2

This postulate reflects the condition of the invariance of the spin value, with respect tothe external velocity of Bivacuum fermions.III. The equality of Coulomb interaction between torus and antitorus V V of

primordial Bivacuum dipoles of all three generations i e, , (electrons, muons andtauons), providing uniform electric energy density distribution in Bivacuum:

III : F0i e0

2

dVV2 n

e

e02

dVV2 n

e02

dVV2 n

3.2a

where: [dVV]ni hm0i c12n

is the separation between torus and antitorus of Bivacuumthree pole dipoles (1.4) at the same state of excitation (n). A similar condition is valid aswell for opposite magnetic poles interaction; |e | |e | e0

2.The important consequences of postulate III are the following equalities:

24

e0m0e e0m0 e0m0 |ee ||mVmV

| const 3.2b

It means that the toruses and antitoruses of symmetric Bivacuum dipoles of generationswith bigger mass: m0

206,7 m0e ; m0

3487,28 m0e have correspondingly smaller

charges:

e0 e0

em0e /m0

; e0 e0

em0e /m0

3.2c

As is shown in the next section, just these conditions provide the same charge symmetryshift of Bivacuum fermions of three generations (i e, at the different mass symmetryshift between corresponding torus and antitorus, determined by Golden mean.

It follows from second postulate, that the resulting magnetic moment of sub-elementaryfermion or antifermion (, equal to the Bohr’s magneton, is interrelated with the actualspin of Bivacuum fermion or antifermion as:

| || |1/2 B 12

e0m0c S e0

m0c 3.3

where: e0/m0c is gyromagnetic ratio of Bivacuum fermion, equal to that of the electron.One may see from (3.3), that the spin of the actual torus, equal to that of the resulting

spin of Bivacuum fermion (symmetric or asymmetric), is:

S 12 3.4

Consequently, the permanent absolute value of spin of torus and antitorus is aconsequence of 2nd postulate.

The dependence of the actual inertial mass (mV of torus V of asymmetric Bivacuum

fermions (BVFas V V) on the external translational group velocity (v) followsrelativistic mechanics:

mV m0/ 1 v/c2 m 3.5

while the complementary inertialess mass (mV of antitorus V has the reverse velocity

dependence:

mV i2mV

m0 1 v/c2 3.6

where i2 1; i 1 and complementary mass in terms of mathematics is theimaginary parameter.

For Bivacuum antifermions BVFas V V the relativistic dependences of positiveand negative mass are opposite to those described by (3.5) and (3.6) and the notions ofactual and complementary parameters change place.

The product of actual (inertial) and complementary (inertialess) mass is a constant,equal to the rest mass of particle squared and reflect the mass compensation principle. Itmeans, that increasing of mass/energy of the torus is compensated by in-phase decreasingof absolute values of these parameters for antitorus and vice versa:

|mV | |mV

| m02 3.7

Taking (3.7) and (3.1) into account, we get for the product of the internal group andphase velocities of positive and negative subquantum particles, forming torus and antitorus,correspondingly:

25

vgrin vphin c2 3.8

A similar symmetric relation is reflecting the charge compensation principle:

|e | |e | e02 3.9

For Bivacuum antifermions BVFas V V the relativistic dependences of positiveand negative charge, like the positive and negative masses of torus and antitorus areopposite to that of Bivacuum fermions BVFas V V (see eqs.3.13 and 3.13a). Thesymmetry of Bivacuum bosons BVB V V i of each electron’s generation(i e,, can be ideal and independent on external velocity, due to opposite relativisticeffects of their torus and antitorus, compensating each other.

The product of actual (inertial) and complementary (inertialess) mass is a constant,equal to the rest mass of particle squared and reflect the mass compensation principle. Itmeans, that increasing of mass/energy of the torus is compensated by in-phase decreasingof absolute values of these parameters for antitorus and vice versa.

The difference between absolute values of total actual and the complementary energies(3.5 and 3.6) is equal to doubled kinetic energy of asymmetric BVFas :

|mV |c2 |mV

|c2 mV mV

c2 mVv2 2Tk m0v2

1 v/c2 3.10

The fundamental Einstein equation for total energy of particle can be reformed andextended, using eqs. 3.10 and 3.7:

Etot mVc2 mc2 mV

c2 mVv2

or : Etot mVc2 m0

2

mV c2 mV

v2

or : Etot mVc2 1 v/c2 m0c2 2Tk

3.10a

3.10b

3.10c

The ratio of (3.6) to (3.5), taking into account (3.7), is:

|mV |

mV m0

2

mV 2 1 v

c2 3.11

It can easily be transformed to the important formula (3.10).The opposite shift of symmetry between V and V of two Bivacuum fermions of

opposite spins occur due to relativistic effects, accompanied their rotation side-by-side as aCooper pairs BVF BVFas around common axe. In this case the quantum beatsbetween V and V of BVF BVF can occur in the same phase.

When the external velocity (v of the external rotation of pair BVF BVFas reachthe Golden mean (GM) condition (v2/c2 0,618, this results in origination of therest mass: m0 |mV

mV | and elementary charge: e |e e | of opposite sign for

sub-elementary fermion: BVFas F and sub-elementary antifermion BVFas

F

with spatial image of pair of truncated cone of opposite symmetry. The resultingmass/energy, charge and spin of Cooper pairs [F F is zero because of compensationeffects.

On the other hand, two adjacent asymmetric Bivacuum fermions and antifermions ofsimilar direction of rotation and spin can not rotate ’side-by-side’ in opposite directionBVF BVFas, but only ’head-to-tail’ in the same: clockwise or anticlockwise

26

directions:

NBVF BVFasorNBVF BVFas 3.12

The Pauli allows a spatial compatibility of two BVF and BVF only in the case if quantumbeats between V and V occur in the counterphase manner. In such configuration,corresponding to integer spin, the uncompensated energy/ mass, charge and half-integerspin, provided by their V and V symmetry shift, are the additive values.

The positive and negative energy, charge and integer spin of such pairs determines theirpolarization. As far in primordial Bivacuum the average mass/energy, charge and spinshould be zero, it means that the number of ’head-to-tail’ pairs of Bivacuum fermions withboson properties is equal to similar pairs of Bivacuum antifermions: N N.

4 The relation between the external and internal parametersof Bivacuum fermions & quantum roots of Golden mean

The important formula, unifying a lot of internal and external (translational-rotational)parameters of BVFas , taking into account that the product of internal and external phaseand group velocities is equal to light velocity squared:

vphin vgrin vphextvgrext c2 4.1

can be derived from eqs. (3.1 - 3.11):

mV

mV

1/2 mV

c2

m0c2 vphin

vgrin c

vgrin2

LVLV

L02

LV 2 |e ||e | e

e0

2 11 v2/c2

ext1/2

4.2

4.2a

where:

LV /mVvgrin L01 v2/c2

ext1/4

LV /mVvphin

L02

LV L0

1 v2/c2ext1/4

L0 LVLV 1/2 /m0c Compton radius

4.3

4.3a

are the radii of torus (V, antitorus (V and the resulting radius of BVFas V V,equal to Compton radius, correspondingly.

The absolute external velocity, squared of Bivacuum dipoles (v of Bivacuum dipolescan be expressed, using 4.2 and 4.2a, as a criteria of parameters of torus and antitorussymmetry shift as:

v2 c2 1 mV

mV c2 1 e

2

e2 c2 1 SS

4.4

where: S LV 2 and S LV2 are the squares of cross-sections of torus andantitorus of Bivacuum dipoles.

The relativistic dependence of the actual charge e on velocity of Bivacuum dipole,following from (2.13a), is:

27

e e0

1 v2/c2ext1/4

4.5

The influence of relativistic dependence of real particles charge on the resulting chargeand electric field density of Bivacuum, which is known to be electrically quasi neutralvacuum/bivacuum, is negligible for two reasons:

1. Densities of positive and negative real charges (i.e. particles and antiparticles) arevery small and approximately equal. This quasi-equilibrium of opposite charges is Lorentzinvariant;

2. The remnant uncompensated by real antiparticles charges density at any velocitiescan be compensated totally by virtual antiparticles and asymmetric Bivacuum fermions(BVF) of opposite charges.

The ratio of the actual charge to the actual inertial mass, as it follows from (4.2 and4.3a), has also the relativistic dependence:

emV

e0m0

1 v2/c2ext1/4 4.6

The decreasing of this ratio with velocity increasing is weaker, than what follows fromthe generally accepted statement, that charge has no relativistic dependence in contrast tothe actual massmV

. The direct experimental study of relativistic dependence of this ratioon the external velocity (v) may confirm the validity of our formula (4.6).

From eqs. (3.10); (3.13) and (3.13a) we find for mass and charge symmetry shift:

m mV mV

mV v

c2

e e e e2e e

vc

2

4.7

4.7a

These mass and charge symmetry shifts determines the relativistic dependence of theeffective mass and charge of the fermions. In direct experiments only the actual mass (mV

and charge (e can be registered. It means that the complementary mass (mV

and chargeare hidden for observation.

The ratio of charge to mass symmetry shifts (the effective charge and mass ratio) is:

em

e2

mV e e

4.8

The mass symmetry shift can be expressed via the squared charges symmetry shift alsoin the following manner:

m mV mV

mV e2 e2

e2 4.8a

or using (3.11) this formula turns to:

e2 e2e2

v2

c2 4.9

When the mass and charge symmetry shifts of Bivacuum dipoles are small and|e | |e | 2e 2e0, we get from 4.7a for variation of charge shift:

28

e e e 12 e0

v2

c2 4.10

The formula, unifying the internal and external group and phase velocities ofasymmetric Bivacuum fermions (BVFas , derived from (4.2) and (4.2a), is:

vgrinc

4

1 vc

2 4.11

where: vgrext v is the external translational-rotational group velocity of BVFas .At the conditions of ”Hidden Harmony”, meaning the equality of the internal and

external rotational group and phase velocities of asymmetric Bivacuum fermions BVFas :

vgrin Vrot vgrext

tr v

vphin Vrot vphext

tr

4.12

4.12a

and introducing the notation:

vgrinc

2

vc

2

vgrin

vphin

vgrext

vphext 4.13

formula (4.11) turns to a simple quadratic equation:

2 1 0,

which has a few modes : 1 1 or :

1 1/2 1

or : 11 1/2 1

4.14

4.14a

4.14b

The solution of (4.14), is equal to Golden mean: v/c2 0.618. It is remarkable,that the Golden Mean, which plays so important role on different Hierarchic levels ofmatter organization: from elementary particles to galactics and even in our perception ofbeauty (i.e. our mentality), has so deep physical roots, corresponding to Hidden Harmonyconditions (4.12 and 4.12a). Our theory is the first one, elucidating these roots(Kaivarainen, 1995; 2000; 2005). This important fact points, that we are on the right track.

The overall shape of asymmetric BVFas V Viis a truncated cone (Fig.2)

with plane, parallel to the base with radiuses of torus (L and antitorus (L, defined byeq. (4.3).

4.1 The rest mass and charge originationUsing Golden Mean equation in the form (4.14b), we can see, that all the ratios (4.2 and

4.2a) at Golden Mean conditions turn to:

mV

mV

1/2 mV

m0vphin

vgrin LL |e |

|e | ee0

2

1

4.15

where the actual (e and complementary (e charges and corresponding mass at GMconditions are:

29

e e0/1/2; e e01/2

mV m0/; mV

m0

4.16

4.16a

using (4.16 and 4.16a) it is easy to see, that the difference between the actual andcomplementary mass at GM conditions is equal to the rest mass:

|mV | mV mV

m01/ m0e,, 4.17

This is an important result, pointing that just a symmetry shift, determined by theGolden mean conditions, is responsible for origination of the rest mass of sub-elementaryparticles of each of three generation (i e,,.The same is true for charge origination. The GM difference between actual and

complementary charges, using relation 1/ 1, determines corresponding minimumcharge of sub-elementary fermions or antifermions (at vtrext 0:

3/2e0 |e | |e e | |e|

where: |e ||e | e02

4.18 4.18a

The absolute values of charge symmetry shifts for electron, muon and tauon at GMconditions are the same. This result determines the equal absolute values of empirical restcharges of the electron, positron, proton and antiproton. However, the mass symmetryshifts at GM conditions, equal to the rest mass of electrons, muons and tauons are verydifferent.

The ratio of charge to mass symmetry shifts at Golden mean (GM) conditions (vtrext 0is a permanent value for all three electron generations (e, , . The different values oftheir rest mass are taken into account by postulate III and it consequences of their rest massand charge relations: e0

e0em0

e /m0; e0

e0em0

e /m0 (see 3.2c) :

|e |

|mV |

|e i |

m0e |e |

|mV |

e03/2

m0e03/2

m0,

e,,

4.19

where: mV m0/ is the actual mass of unpaired sub-elementary fermion in [C]

phase at Golden mean conditions (see next section); e0 e0e ; m0

e m0.Formula (4.19) can be considered as a background of permanent value of gyromagnetic

ratio, equal to ratio of magnetic moment of particle to its angular momentum (spin). For theelectron it is:

e02mec

4.20

A huge amount of information, pointing that Golden mean plays a crucial role inNature, extrapolating similar basic principles of matter formation on higher thanelementary particles hierarchical levels, starting from DNA level up to galactics spatialorganization, are collected and analyzed in the impressive web site of Dan Winter:http://www.soulinvitation.com/indexdw.html

4.2 Quantization of the rest mass/energy and charge of sub-elementary fermionsFormula (3.10), using (4.19), can be transformed to following shape:

30

n2 mV

m0

2 e

e03/2

2

v/c4

1 v/c2 4.21

Introducing the definition: v/c2 x, eq. 4.21 can be reduced to quadratic equation:

x2 n2x n2 0 4.22

The solution of this equation is:

x 12 n2 n4 4n2 4.23

It is easy to calculate, that at n 1, n2 1 and mV m0; e e03/2 we have

xn1 v/c2 0.618 .At n 2, n2 4 and mV

2m0; e 2e03/2 we have xn2 0.8284 1.339.At n 3, n2 9 and mV

3m0; e 3e03/2 we have xn3 0.9083 1.469At n 4, n2 16 and mV

4m0; e 4e03/2 we have xn4 0.9442 1.528

4.3 The ratio of energies at Golden mean and Dead mean conditionsThe known formula, unifying the ratio of phase and group velocity of relativistic de

Broglie wave (vph/v c2/v2 with ratio of its potential energy to kinetic one VB/Tk is:

2 vphv 1 VBTk

4.24

It is easy to see from (4.24), that at GM condition: (vph/v c2/v2 1/, the ratio:

VB/Tk 2.236 and Tk/Tk VB Tk/EB 0.309 4.25

The Golden mean (GM) conditions for sub-elementary particles, composing freeelementary particles are the result of their fast rotation at GM or Compton frequency(section 5):

0i m0

i c2/ 4.25a

Such spinning of sub-elementary particles in triplets around the common axis (Fig.2), atthe Hidden Harmony conditions, when their internal and external group and phasevelocities coincide (eq.4.12; 4.12a).

In contrast to Golden mean (4.25), we may introduce here the ”Dead mean”,corresponding to thermal equilibrium. At this conditions any system can be described bythe number of independent harmonic oscillators, unable to coupling and self-organization:

VTk

D 1; 2Tk

EBD Tk V

EBD 1 4.26

The deep natural roots of Golden mean, as a consequence of Hidden Harmonyconditions (4.12), leading from our theory, explain the universality of this number( 0.618).

It is demonstrated in our work, that any kind of selected system, able to self-assembly,self-organization and evolution: from atoms to living organisms and from galactics toUniverse - are tending to conditions of combinational resonance with virtual pressurewaves under the action Tuning Energy (TE) of Bivacuum (section 15).

The less is deviation of ratio of characteristic parameters (dynamic and spatial) ofsystem from [ Phi], the more advanced is evolution of this system. We have to keep in

31

mind that all forms of matter are composed from hierarchic systems of de Broglie waves.4.4 The solution of Dirac monopole problem, following from Unified theory

The Dirac theory, searching for elementary magnetic charges g and g, symmetric toelectric ones e and e, namedmonopoles, leads to following relation between themagnetic monopole and electric charge of the same signs:

ge n2 c or: g n2

ce n

2e

where : n 1,2,3 is the integer number

4.27

where e2/c is the electromagnetic fine structure constant.It follows from this definition, that minimal magnetic charge at n 1 is as big

as g 67.7e. The mass of monopole should be huge 1016GeV. All numerous attemptsto reveal such particles experimentally has failed.

Our theory explains this fact in such a way: in contrast to electric and mass dipolessymmetry shifts (see 4.17 and 4.18), the symmetry violation between the internal actual | |and complementary | | magnetic charges of elementary fermions is absent because oftheir postulated permanent values (3.2). The equality of the actual (torus) andcomplementary (antitorus) magnetic moments of sub-elementary fermions andantifermions:

| | | | | | 0 4.28

independent on their external velocity, explains the absence of magnetic monopoles inNature.

The elementary magnetic charge is not a monopole, like electric one () or (-). It is adipole, formed by pair F F of triplet F F F i .

5 Fusion of elementary particles, as a triplets of sub-elementary fermionsat Golden mean conditions

At the Golden Mean (GM) conditions: v/c2 0.618, the Cooper pairs ofasymmetric Bivacuum fermions, rotating in opposite direction around the common axis ofvorticity, turns to pair of sub-elementary fermion and antifermion with ratio of radiuses oftorus and antitorus: L/L L2/L0

2 S/S0 (see eq. 4.15):

F F BVFas BVFas 5.1

of opposite charge, spin and energy with common Compton radius. The spatial image ofpair F F is two identical truncated cones of the opposite orientation of planesrotating without slip around common rotation axis (Fig.2).

32

Fig. 2. Model of the electron, as a triplets F F F i , resulting from fusion ofthird sub-elementary antifermion F to sub-elementary antifermion F with oppositespin in rotating pair F F. The velocity of rotation of unpaired sub-elementary Faround the same axis of common rotation axis of pair provide the similar rest mass m0 andabsolute charge |e |, as have the paired F and F. Three effective anchorBVF V Vanc in the vicinity of sub-elementary particles base, participate in recoileffects, accompanied their C W pulsation and modulation of Bivacuum pressure waves(VPWq

. The recoil effects of paired F F totally compensate each other and therelativistic mass change of triplets is determined only by the anchor Bivacuum fermionBVF anc of the unpaired sub-elementary fermion F .

The fusion of asymmetric sub-elementary fermions and antifermions of and generations F BVFas

,(Fig.2) to triplets of electrons/positrons,

protons/antiprotons and neutrons/antineutrons

F Fx,y F ze,p 5.2

This becomes possible also at the Golden mean (GM) conditions. It is accompanied byenergy release and electronic and hadronic e,h gluons origination, equal in sum to themass defect. It was demonstrated theoretically, that the vortical structures at certainconditions self-organizes into vortex crystals (Jin and Dubin, 2000).

The fusion threshold overcoming is due to ’switching on’ the resonant exchangeinteraction of CVC with Bivacuum virtual pressure waves VPW of fundamentalfrequency (0 m0c2/e,, in the process of [corpuscleC waveW] transitions ofelementary particles. The triplets of elementary particles and antiparticles formation (Fig.2)is a result of conjugation of third sub-elementary fermion (antifermion) F to one ofsub-elementary fermion (antifermion) of rotating pair F F of the opposite spins. Theopposite spins means that their C W pulsations are counterphase and these twosub-elementary particles are spatially compatible (see section 9). The velocity of rotation ofunpaired sub-elementary fermion F around the same axis of common rotation axis ofpair (Fig.2) provide the similar mass and charge |e |, as have the paired F and Fbecause of similar symmetry shift.

33

Let us consider the rotational dynamics of unpaired F e,, V Vas in triplets

(Fig.2) just after fusion to triplet at GM conditions in the absence of the externaltranslational motion of triplet.

Its properties are the result of participation in two rotational process simultaneously:1) rotation of asymmetric F

e,, around its own axis (Fig.2) with spatial image oftruncated cone with resulting radius:

LBVFas /|mV

mV |c /m01/ c /2.236m0c L0/2.23 5.3

2) rolling of this truncated cone of F e,, around the another axis, common for pair of

sub-elementary particles F F (Fig.2) inside of a larger vorticity with bigger radius,equal to Compton radius:

LBVFas BVFas /|mV

mV |c /m0c L0 5.4

The ratio of radius of BVFas F to radius of pairs F F at GM

conditions is equal to the ratio of potential energy (V) to kinetic energy (Tk) of relativisticde Broglie wave (wave B) at GM conditions. This ratio is the same, as in known formulafor relativistic wave B V

Tk 2 vph

vgr 1 :

LBVFas BVFas

LBVFas |mV

mV |

|mV mV

| V

Tk 2 vph

vgr 1 2,236 5.5

This result is a good evidence in proof of our expressions for total energy ofsub-elementary particle, as sum of internal potential and rotational kinetic energies (seesection 7, eqs. 7.1 - 7.3).The triplets of the regular electrons and positrons of the same or opposite spin state are

the result of fusion of sub-elementary particles of leptons generation:

e F F F e

e F F F e 5.6

5.7

with mass, charge and spins, determined by uncompensated/unpaired sub-elementaryparticle: F e.

5.1 Correlation between new model of hadrons and conventional quark model ofprotons, neutrons and mesons

The proton (Z 1; S 1/2 is constructed by the same principle as the electron(Fig.2). It is a result of fusion of pair of sub-elementary fermion and antifermion of generation F FS0

p and one unpaired sub-elementary fermion F S1/2 ,

accompanied by huge energy release, corresponding to mass defect: E~ m mpc2.These three components of proton correspond to three quarks: F S1/2

p ~ q andantiquarks F S1/2

p ~q.The difference with quark model is that we do not need to use the notion of fractional

charge in our model of proton with spin S 1/2:

34

p F FS0 F S1/2

or : p ~ q qS0 qS1/2

or : p~ S0 S1/2

5.9

5.9a

5.9b

The charges, spins and mass/energy of sub-elementary particles and antiparticles in pairsF F compensate each other. The resulting properties of protons (p) are determinedby unpaired/uncompensated sub-elementary particle F of heavy electronsgeneration, taking into account the mass defect after fusion.

The neutron (Z 0; S 1/2 can be presented as:

n F FS0 F Fe S1/2

or : n~ q q S0 q0 S1/2

e

or : n~ S0

Fe

5.10

5.10a

5.10b

where: the neutral quark q0 S1/2

e is introduced, as a metastable complex of positivesub-elementary fermion F

with negative electron’s e F F F esub-elementary fermion of opposite charge Fe:

q0 S1/2

e q Fe 5.11

This means that the positive charge of unpaired heavy sub-elementary particle F inneutron (n) is compensated by the charge of the light sub-elementary fermion Fe. Incontrast to charge, the spin of unpaired F is not compensated (totally) by spin of Fe

in neutrons, because of strong mass and angular momentum difference in conditions of theFe confinement. The mass of - electron, equal to that of -positron is: m 17823MeV, the mass of the regular electron is: me 0,5110031 MeV and the mass of electron is: m 105,65952MeV.

For the other hand, the mass of proton and neutron are correspondingly:mp 938,2803 MeV and mn 939,573 (3) MeV. They are about two times less, thanthe mass of - electron, equal, in accordance to our model, to mass of its unpairedsub-elementary fermion F. This difference characterize the energy of neutral masslessgluons (exchange bosons), stabilizing the triplets of protons and neutrons. In the case ofneutrons this difference is a bit less (taking into account the mass of Fe, providingmuch shorter life-time of isolated neutrons (918 sec.), than that of protons (1031 years).

In accordance to our hadrons models, each of three quarks (sub-elementary fermions of generation) in protons and neutrons can exist in 3 states (red, green and blue), but notsimultaneously:

1. The red state of quark/antiquark means that it is in corpuscular [C] phase;2. The green state of quark/antiquark means that it is in wave [W] phase;3. The blue state means that quark/antiquark F

is in the transition [C][W] state.The 8 different combinations of the above defined states of 3 quarks of protons and

neutrons correspond to 8 gluons colors, stabilizing the these hadrons. The triplets of quarksare stabilized by the emission absorption of cumulative virtual clouds (CVC in theprocess of quarks C W pulsation.

The known experimental values of life-times of and electrons, corresponding inaccordance to our model, to monomeric asymmetric sub-elementary fermions BVFas

,,

35

are equal only to 2,19 106s and 3,4 1013s, respectively. We assume here, that stabilityof monomeric sub-elementary particles/antiparticles of e, and generations, stronglyincreases, as a result of their fusion in triplets, possible at Golden mean conditions.

The well known example of weak interaction, like decay of the neutron to proton,electron and e antineutrino:

n p e e

or : q q q0 S1/2

e q q q e e

5.12

5.12a

is in accordance with our model of elementary particles and theory of neutrino (section8.4).

The sub-elementary fermion of generation in composition of proton or neutron canbe considered, as a quark and the sub-elementary antifermion, as antiquark:

F~ q and F

~ q 5.13

In the process of decay of neutron (5.12 and 5.11) the unpaired negativesub-elementary fermion Fe in (5.11) forms a complex - triplet (electron) withcomplementary virtual Cooper pair F FS0

e from the vicinal to neutron polarizedBivacuum:

Fe F FS0e e 5.14

The energy of 8 gluons, corresponding to different superposition of[CVC CVCS0,1, emitted and absorbed with in-phase C W pulsation of pair[quark antiquark] in triplets (5.9 - 5.9b):

F FS0,1 qqS0,1 5.15

is about 50% of energy/mass of quarks and antiquarks ( sub-elementary fermions andantifermions).

These 8 gluons, responsible for strong interaction, can be presented as a followingcombinations of transitions states of sub-elementary fermions (quarks q2 and q3) andantifermion (antiquark q1, corresponding to two spin states of proton (S 1/2, equalto that of unpaired quark.

For the spin state: S 1/2 we have following 4 transition combinations of tripletstransition states (gluons):

1 C Wq1

S1/2 C Wq2S1/2 C Wq3

S1/2

2 C Wq1

S1/2 C Wq2S1/2 C Wq3

S1/2

3 C Wq1

S1/2 C Wq2S1/2 C Wq3

S1/2

4 C Wq1

S1/2 C Wq2S1/2 C Wq3

S1/2

5.16

5.16a

5.16b

5.16c

and for the opposite spin state: S 1/2 we have also 4 transition states combinations(gluons):

36

5 C Wq1

S1/2 C Wq2S1/2 C Wq3

S1/2

6 C Wq1

S1/2 C Wq2S1/2 C Wq3

S1/2

7 C Wq1

S1/2 C Wq2S1/2 C Wq3

S1/2

8 C Wq1

S1/2 C Wq2S1/2 C Wq3

S1/2

5.17

5.17a

5.17b

5.17c

The neutral symmetric pairs of or generations F FS0,1, (5.15), representing

part of triplets (5.9 - 5.10) have a properties of mesons, as a neutral [quark antiquark] pairwith integer spin. The coherent cluster of such pairs - from one to four pairs:n q q S0,1,2,3,4 can provide the experimentally revealed integer spins - from zero tofour. It looks that our model of elementary particles is compatible with existing data.

One of the versions of elementary particle fusion have some similarity withthermonuclear fusion and can be as follows. The rest mass of isolated sub-elementaryfermion/antifermion before fusion of the electron or proton, is equal to the rest mass ofunstable muon or tauon, correspondingly. The 200 times decrease of muons mass is a resultof mass defect, equal to the binding energy of triplets: electrons or positrons. It is providedby origination of electronic e-gluons and release of the huge amount of excessive kinetic(thermal) energy, for example in form of high energy photons or e-neutrino beams.

In protons, as a result of fusion of three electrons/positrons, the contribution ofhadron h-gluon energy to mass defect is only about 50% of their mass. However, theabsolute hadron fusion energy yield is higher, than that of the electrons and positrons.Our hypothesis of stable electron/positron and hadron fusion from short-living and

- electrons, as a precursor of electronic and hadronic quarks, correspondingly, can beverified using special collider.

In accordance to our Unified Theory, there are two different mechanisms ofstabilization of the electron and proton structures in form of triplets of sub-elementaryfermions/antifermions of the reduced and generations, correspondingly, preventingthem from exploding under the action of self-charge:

1. Each of sub-elementary fermion/antifermion, representing asymmetric pair of torus(V and antitorus (V, as a charge, magnetic and mass dipole, is stabilized by theCoulomb, magnetic and gravitational attraction between torus and antitorus;

2. The stability of triplet, as a whole, is provided by the exchange of Cumulative VirtualClouds (CVC and CVC between three sub-elementary fermions/antifermions in theprocess of their C W pulsation. In the case of proton and neutron, the 8 transitionstates corresponds to 8 h-gluons of hadrons, responsible for strong interaction. In the caseof the electron or positron, the stabilization of triplets is realized by 8 lighter e-gluons. Theprocess of internal exchange of pairs F FS0,1

e,p with unpaired sub-elementary fermionin triplets is accompanied by the external energy exchange with Bivacuum dipoles,modulating positive and negative virtual pressure waves [VPW VPW. The feedbackreaction between Bivacuum and elementary particles is also existing (Kaivarainen, 2005a).

6 Total, potential and kinetic energies of elementary de Broglie wavesThe total energy of sub-elementary particles of triplets of the electrons or protons

F FS0 F S1/2e,p we can present in three modes, as a sum of total potential

Vtot and kinetic Ttot energies, including the internal and external contributions:

37

Etot Vtot Ttot 12 mV

mVc2 1

2 mV mV

c2

Etot mVc2 1

2 mV2c2 v2 1

2 mVv2

Etot 2Tkv/c2 12 mV

c21 R2 12 mV

v2

6.1

6.1a

6.1b

where: R m0/mV 1 v/c2 is the dimensionless relativistic factor; v is

external translational - rotational velocity of particle;mV and mV

are the absolute massesof torus and antitorus of dipoles.

One may see, that Etot m0c2 at v 0 and mV m0.

Taking into account that the total kinetic energy of dipoles is

TtotW 12 mV

mVc2 1

2 mVv2 TtotC 6.1c

TtotW 12 mV

mVc2 TtotC 1

2 mVv2 and c2 vgrvph, where vgr v, then dividing the

left and right parts of (6.1 and 6.1a) by 12 mV

v2, we get:

2 c2

v2 1 2 vphvgr 1 mV mV

c2

mVv2 mV

mV

mV mV

6.2

Comparing formula (6.2) with known relation for relativistic de Broglie wave for ratioof its potential and kinetic energy (Grawford, 1973), we get the confirmation of ourdefinitions of potential and kinetic energies of elementary particle in (6.1):

2 vphvgr 1 VtotTtot

mV mV

c2

mV mV

c2 6.3

In Golden mean conditions, necessary for triplet fusion, the ratioVtot/Ttot 1/ 2.236.

In the case of symmetric primordial Bivacuum fermions BVF BVF] and bosonsBVB the absolute values of their energy/masses of their torus and antitorus are equal:mV

c2 mVc2 m0c2 1

2 n (eq.1.1). This means that their kinetic energy is zero andtotal energy is determined by the value of potential energy:

Etot Vtot 12 mV

mVc2 1

2 m0c21 2n 6.3a

It is a half of the energy gap between torus and antitorus of Bivacuum dipoles (eq.1.3).The bigger is the potential energy of Bivacuum, the bigger is frequency of virtual pressurewaves (VPWq1

. It will be shown in chapters 14 and 19 of this paper, that the forcedresonance of VPWq1

with corpuscleC waveW pulsation of elementary particlesaccelerate them and is a source of energy for overunity devices. The idea, that the potentialenergy of vacuum, as a sum of absolute values of its positive and negative energies, can beused as a source of ’free’ energy for overunity devices was discussed also by Frolov (2003)and much earlier by Gustav Naan (1964).

In general case the total potential (Vtot and kinetic (Ttot energies of sub-elementaryfermions and their increments can be presented as:

38

VtotW 12 mV

mV c2 Vtot

C 12 mV

2c2 v2 12

cLVtot

Vtot ;

Vtot mVc2 Ttot 1

2cLVtot

LVtotLVtot

VpLVtotLVtot

6.4

6.4a

where: the characteristic velocity of potential energy, squared, is related to the groupvelocity of particle (v, as vp2 c22 v2/c2 and the characteristic curvature of potentialenergy of elementary particles is:

LVtot mV

mV c L0

at vtotc

2 6.4b

The total kinetic energy of unpaired sub-elementary fermion of triplets includes theinternal vortical dynamics and external translational one, which determines their de Brogliewave length, (B 2LText :

Ttot 12 |mV

mV |c2 1

2 mVv2 1

2cLTtot

Ttot ;

Ttot Ttot 1 R2

R2vv Tk

LTtotLTtot

6.5

6.5a

where the characteristic curvature of kinetic energy of sub-elementary particles intriplets is:

LTtot mV

mV c L0

at vtotc

2 6.5b

It is important to note, that in compositions of triplets F FS0 F S1/2e,p

the minimum values of total potential and kinetic energies and the maximum values of theircharacteristic curvatures correspond to that, determined by Golden mean conditions (seeeqs. 5.3 and 5.4). In our formulas above it is reflected by corresponding inequalities. Inaccordance to our theory, the Golden mean conditions determine a threshold for tripletsfusion from sub-elementary fermions.

The increment of total energy of elementary particle is a sum of total potential andkinetic energies increments:

Etot Vtot Ttot VtotLVtotLVtot

TtotLTtotLTtot

6.6

In the process of corpuscle-wave pulsation C W (section 7) at the permanentvelocity v const, the total energy is also permanent and it its increment is zero:Etot 0. This means that the oscillation of potential and kinetic energy in (6.6),accompanied C W pulsation should be opposite by value and compensating eachother:

VtotLVtotLVtot

CW Ttot

LTtotLTtot

6.6a

The well known Dirac equation for energy of a free relativistic particle, following alsofrom Einstein relativistic formula (3.5), can be easily derived from (6.1a), multiplying itsleft and right part on mV

c2 and using introduced mass compensation principle (3.7):

Etot2 mVc22 m0c22 mV

2v2c2 6.6b

39

where: m02 mV

mV and the actual inertial mass of torus of unpaired

sub-elementary fermion in triplets is equal to regular mass of particle: mV m0.

Dividing the left and right parts of (6.6b) tomVc2, we may present the total energy of

an elementary de Broglie wave, as a difference between doubled kinetic energy,representing the Maupertuis function (2Tk and Lagrange function ( Tk V)contributions, in contrast to sum of total potential and kinetic energies (6.1):

Etot mVc2 mV

mVc4/v2

m0mV

m0c2rotin mV

v2

Etot V Tk Rm0c2rotin 1

2 mVv2 1

2 mVv2

Etot 2Tk , where V Tk Rm0c2rotin

Etot hCW Rm0c2rotin h2

mVB2

6.7

6.7a

6.8

6.8a

6.8b

where: R 1 v/c2 is relativistic factor, dependent on the external translationalvelocity v of sub-elementary fermion in composition of triplet; mV

m0/R m is theactual inertial mass of sub-elementary fermion; the external translational de Broglie wavelength is: B h

mV vand CW is the resulting frequency of corpuscle - wave pulsation (see

next section).We can easily transform formula (6.8) to a mode, including the internal rotational

parameters of sub-elementary fermion, necessary for the rest mass and charge origination:

Etot R m002L0

2rotin mV

mVc2 tr 6.9

where: L0 /m0c is the Compton radius of sub-elementary particle; 0 m0c2/ isthe angular Compton frequency of sub-elementary fermion rotation around the commonaxis in a triplet (Fig.2).

For potential energy of a sub-elementary fermion, we get from (6.8), taking intoaccount, that mV

v2 trext 2Tk and Etot V Tk :

V Etot 12 mV

v2 Rm0c2rotin 1

2 mVv2 tr 6.9a

The difference between potential and kinetic energies, as analog of Lagrange function,from (4.9a) is:

V Tk Vtot 12 mV

v2 tr Rm0c2rotin 6.9b

It follows from (6.9 - 6.9b), that at vtrext c, the total relativistic factor, involving boththe external and internal translational - rotational dynamics of sub-elementary fermions intriplets: R 1 vtr/c2 0 and the rest mass contribution to total energy ofsub-elementary particle also tends to zero: Rm0c2rot

in 0. Consequently, the totalpotential and kinetic energies tend to equality Vtot Ttot, and the Lagrangian to zero. Thisis a conditions for harmonic oscillations of the photon, propagating in unperturbedBivacuum.

The important formula for doubled external kinetic energy (Maupertuis function) can bederived from (4.8), taking into account that the relativistic relation between the actual andrest mass ismV

m0/R :

40

2Tk mVv2 mV

c2 Rm0c2 m0c2

R 12 R2 or :

2Tk m0c2

R 1 R1 R 1 RmVc2 m0c2

6.10

6.10a

This formula is a background of the introduced in section 9 notion of Tuning energy ofBivacuum Virtual Pressure Waves (VPW.

Our expressions (6.1 - 6.10a) are more general, than the well known (4.6b), as far theytake into account the properties of both poles (actual and complementary) of Bivacuumdipoles and subdivide the total energy of particle to the internal and external or to kineticand potential ones.

7. The dynamic mechanism of corpuscle-wave dualityIt is generally accepted, that the manifestation of corpuscle - wave duality of a particle

is dependent on the way in which the observer interacts with a system. However, themechanism of duality, as a background of quantum physics, is still obscure.

It follows from our theory, that the [corpuscle (C) wave (W)] duality representsmodulation of the internal (hidden) quantum beats frequency between the asymmetric’actual’ (torus) and ’complementary’ (antitorus) states of sub-elementary fermions orantifermions by the external - empirical de Broglie wave frequency of these particles(Kaivarainen, 2005). The [C] phase of each sub-elementary fermions of triplets F F F i of elementary particles, like electrons and protons, exists as a massand an electric and magnetic asymmetric dipole.

The [C W] transition of triplets with nonzero external translational velocity(vtrext 0, providing the asymmetry of the ’anchor’ Bivacuum fermion in C phaseBVFanc

C

eanc

, is a result of two stages superposition:The 1st stage of transition is a reversible dissociation of charged sub-elementary

fermion in [C] phase FCe to charged Cumulative Virtual Cloud CVCF

eeancof

subquantum particles and the ’anchor’ Bivacuum fermion with internal frequency in i(eq. 7.4c):

I: FCe Recoil/Antirecoil BVFanc

C

eanc

CVCFeeanc

i 7.1

where notations e, eanc and e eanc mean, correspondingly, the total charge, theanchor charge and their difference, pertinent to CVC. Between the uncompensated chargeand uncompensated mass of Bivacuum dipoles the direct correlation is existing (eq.4.6).The 2nd stage of [C W transition is a reversible dissociation of the anchor

Bivacuum fermion BVFanc i V Vanci to symmetric BVF i and the anchorcumulative virtual cloud (CVCBVFanc , with frequency (Bext tr, equal to the empiricalfrequency of de Broglie wave of particle (eq. 7.4):

II : BVFanc

C

eanc

Recoil/Antirecoil

BVF0 CVCBVFanceanc

W

i 7.2

The 2nd stage takes a place if BVFanc i is asymmetric only in the case of nonzeroexternal translational - rotational velocity of particle. The beats frequency of BVFanc e,p isequal to that of the empirical de Broglie wave frequency: B /mV

LB2 . The higher isthe external kinetic energy of fermion, the higher is frequency B. The frequency of thestage (II) oscillations modulates the internal frequency of C W pulsation:

41

in i R 0i R m0

i c2/, related to contribution of the rest mass energy to the totalenergy of the de Broglie wave (Kaivarainen, 2005; 2005a andhttp://arxiv.org/abs/physics/0103031).

The C W pulsations of unpaired sub-elementary fermion F , of triplets of theelectrons or protons F F F e,p are in counterphase with the in-phasepulsation of paired sub-elementary fermion and antifermion, modulating Bivacuum virtualpressure waves (VPW :

F FWe,p CVC

CVC F FCe,p 7.3

The basic frequency of C W pulsation of particle in the state of rest, correspondingto Golden mean conditions, vin/c2 0,618 , is equal to that of the 1st stage frequency(5.1) at zero external translational velocity (vtrext 0; R 1. This frequency is the sameas the basic Bivacuum virtual pressure waves (VPWq1

and virtual spin waves(VirSWq1

S1/2 frequency (1.7 and 1.10a): q1 m0c2/i.The empirical parameters of de Broglie wave of elementary particle are determined by

asymmetry of the torus and antitorus of the anchor Bivacuum fermionBVFanc e,p V Vance,p (Fig.2) and the frequency of its reversible dissociation tosymmetric BVF i and the anchor cumulative virtual cloud (CVCanc stage (II) ofduality mechanism (7.2). The dimensions of CVCanc , i.e. the Wave phase of BVFanc e,p

are determined by the empirical de Broglie wave length and can be much bigger thandimensions of the anchor Bivacuum fermion in Corpuscular phase.

The total energy, charge and spin of triplets - fermions, moving in space with externaltranslational velocity (vtrext) is determined by the unpaired sub-elementary fermion Fz, asfar the paired ones in F Fx,y of triplets compensate each other. From (6.9; 6.9a and6.9b) it is easy to get:

Etot mVc2 CW R0rot

in Bext tr Rm0c2rotin mV

vtr2 ext

Etot mVc2 2Tk Rm00

2L02rotin h2

mVB2

Etot V Tk Rm0c2rotin 1

2 mVvtr2 1

2 mVvtr2

or : Etot mVc2 V Tk 1

2 mV mV

c2 12 mV

mVc2

7.4

7.4a

7.4b

7.4c

where: R 1 v/c2 is the relativistic factor; v vtrext is the external translationalgroup velocity; B h/mV

v 2LB is the external translational de Broglie wave length;the actual inertial mass ismV

m m0/R; L0i /m0

i c is a Compton radius of theelementary particle.

It follows from our approach, that the fundamental phenomenon of corpuscle waveduality (Fig.3) is a result of modulation of the primary - carrying frequency of the internalC Win pulsation of individual sub-elementary fermions (1st stage):

in i R0i R 1 v/c2 m0

i c2/ 7.4d

by the frequency of the external empirical de Broglie wave of triplet:Bext mV

vext2 / 2vext/LB, equal to angular frequency of C Wanc pulsation of theanchor Bivacuum fermion BVFanc i (2nd stage).

The contribution of this external translational dynamics to the total one is determined

42

by asymmetry of the anchor BVFanc i V Vanci of particle, i.e. by second terms in(7.4) and (7.4a):

2Tk B tr h2

mVB2 tr

mV mV

c2 tr

mVv2 tr mV

B2LB2 rot pB2mV

7.5

7.5a

This contribution is increasing with particle acceleration and tending to light velocity.At v c, and R 0 :

2Tk mVv2 tr

ext mVc2 Etot V Tk

or V Tk 12 mV

c2 12 CW

7.5b

7.5c

For example, the equality of the averaged potential and kinetic energies ofsub-elementary fermions and antifermions should take a place for photon (fig.4).

The double kinetic energy of sub-elementary particle can be expressed viaelectromagnetic fine structure constant e2/c, electric charge squared, frequency ofC W pulsation CW mV

c2/ and de Broglie wave length, equal to that ofcumulative virtual cloud CVC : LB LCVC /mV

v :

2Tk 2c2

mVc2LCVC2 1

e2

LCVC2c

CW 1

e2

LCVC2 Lres 7.6

where the resulting curvature of de Broglie wave is: Lres cCW .

In contrast to external translational contribution of triplets, the internalrotational-translational contribution of individual unpaired sub-elementary fermions,described by the Lagrange function, is tending to zero at the same conditions:

V Tk R0rotin in Rm00L0

2rotin 0 at v c 7.6a

as far at v c, the R 1 v/c2 0.For a regular nonrelativistic electron the carrier frequency is

in R0e ~1021s1 Bext. However, for relativistic case at v c, the situation is

opposite: Bext in at in 0.

43

Fig.3. Dynamic model of [C W pulsation of triplets of sub-elementaryfermions/antifermions (the reduced by fusion to triplets and electrons composing,correspondingly, electron and proton F F F e,p . The pulsation of the pairF F, modulating virtual pressure waves of Bivacuum (VPW and VPW, is

counterphase to pulsation of unpaired sub-elementary fermion/antifermion F .

The properties of the anchor Bivacuum fermion BVFanc where analyzed (Kaivarainen,2005), at three conditions:

1. The external translational velocity (v is zero;2. The external translational velocity corresponds to Golden mean (v c1/2;3. The relativistic case, when v c.Under nonrelativistic conditions (v c, the de Broglie wave (modulation) frequency

is low: 2B tr in R0. However, in relativistic case (v ~c, the modulationfrequency of the ’anchor’ (BVFanc ), equal to that of de Broglie wave, can be higher, thanthe internal one : 2B tr in.

The paired sub-elementary fermion and antifermion of F FS0 also have the’anchor’ Bivacuum fermion and antifermion (BVFanc ), similar to that of unpaired.However, the opposite energies of their C W pulsation compensate each other inaccordance with proposed model.

If we proceed from the assumption that the total energy of the corpuscular and wavephase of each sub-elementary fermion do not change in the process of C W pulsationof sub-elementary fermions EtotC W 0 in the inertial system (v const), then, from (4.6and 4.6a) we get, that the oscillations of potential and kinetic energy should be oppositeand compensating each other:

EtotC W Vtot Ttot 0

or : VtotLVtotLVtot

CW Ttot

LTtotLTtot

7.7

7.7a

44

Let us analyze what happens with contributions of the Lagrange function and doubledkinetic energy (Maupertuis function) to the permanent total energy of particle in theprocess of C W pulsation in the rest state condition. When the external translationalvelocity of particle is zero (v 0 const and R 1) and symmetry shift ofsub-elementary fermions in [C] phase is determined only by the relative rotation of thepaired F

F around common axes with internal rotational-translational velocity,determined by Golden Mean (vin/c)2 0.618. For the opposite counterphaseincrements pulsation of the Lagrange function and doubled kinetic energy we get:

Rm0c2rotin RmV

mVc2 R m00

2L02

2Ttot h2

mVB2

mVCVC2 LCVC2 1

e2LCVC2

cCW

C W 2Ttot

p02

m0

7.8

7.8a

7.8b

where LCVC L0 /m0c is a radius cumulative virtual cloud with charge squared:e2 ee; CW mV

c2/ is the resulting frequency of C W pulsation; p0 m0c.The decreasing of to zero ( 0 as a result of C W transition, due

equalizing of torus and antitorus energies and masses: mV mV

m0, is accompanied bythe Cumulative Virtual Cloud (CVC emission and increasing of its energy from zero tomV

CVC2 LCVC2 1

e2

LCVC2c

CW .The linear dimension of [C] phase of the triplets is determined by their Compton radius.

For the Wave phase, the configuration of triplets may change and they ’jump’ from theCorpuscular spatial state to another one in form of Cumulative Virtual Cloud (CVC. Wenamed this jumping process from the one Bivacuum fermion to another as the ’Kangarooeffect’. These C W pulsation in the process of particle propagation in space occurwithout dissipation in superfluid matrix of Bivacuum in the absence of external fields ormatter.

The linear dimension of the Wave phase of the electron in nonrelativistic condition0 vtrext c B h/mV

vtrext can be much bigger, than that [C] phase, determined byCompton length of particle: 0 h/m0c (B 0.

The counterphase oscillations of momentum (p and dimensions (x in the process of[C W pulsation of elementary particles (fig.3) is reflected by the uncertainty principle:

p x /2 7.9

The decreasing of momentum uncertainty p 0 in the Wave [W] phase isaccompanied by the increasing of the effective de Broglie wave length: x B and viceverse.

Taking the differential of de Broglie wave length, it is easy to get:

B h/ptrext B

B pp 7.9a

In conditions, when B B we have p p. The de Broglie wave lengthcharacterize the dimension of cumulative virtual cloud, positive for particles or negative forantiparticles (CVC in their [W] phase and momentum p mV

vtrext characterize thecorpuscular [C] phase.

The other presentation of uncertainty principle reflects the counterphase oscillation ofthe kinetic energy and time for free particle in process of [C W pulsation:

45

Tk t /2 7.10

This kind of counterphase energy-time pulsation is in accordance with our theory oftime (section 7.1).

The wave function for de Broglie wave of particle, moving in direction x with certainmomentum:

p mVvtrext /B k 7.10a

is described by the wave function:

x, t Cexp ipx Et 7.11

where: C is a permanent complex number. The module of the wave function squared||2 const is independent on x. This means that the probability to find a particlewith permanent p is equal in any space volume (or it can be localized everywhere). Thiscontradicts the experimental data.

The Quantum Mechanics solve this contradiction assuming the idea of Shrödinger, thatparticle represents the ’wave packet’ with big number of de Broglie waves with differentp k, localized in a small interval p. The amplitude of all this number of de Brogliewaves in the packet with spatial dimension x B add to each other because of closephase. For the other hand, at the x B they damper out each other because of phasedifference.

The wave packet model can be explained, using eq.7.4 for nonrelativistic particles:v c and R 1 v/c2 ~ 1. For this case, the carrying internal frequency of C Wpulsation (5.4c) is much higher, than the external translational de Broglie wave modulationfrequency (7.5): in Bext. The wave packet, consequently, in this case, is formed by thewaves, generated by the internal C Win dynamics, corresponding to zitterbewegung(Shrödinger, 1930). However, the wave packet concept itself do not explain the mechanismof C W duality.

Our dynamic corpuscle - wave C W duality theory suggests another possibleexplanation of the uncertainty principle realization, as a counterphase pulsation ofmomentum and position, energy and time, described above by eqs. 7.9 and 7.9a. TheC W transition is accompanied by conversion of real mass to virtual one, presented bycumulative virtual cloud CVC. As far the energies of both phase C and W are equal, itmakes possible to apply the relativistic mechanics to both of them.

7.1 The dynamic model of pulsing photonThe model of a photon with integer spin (boson), resulting from fusion (annihilation) of

pairs of triplets: electron positron (see Fig.2), are presented by Fig.4:

F FS0 F FS1

F FS0 7.11a

Two side pairs represent a Cooper pairs with zero spin. The central pair F FS1have uncompensated spin and energy (Eph hph. It determines the properties of photon.

Such a structure can originate also, as a result of excitation and fusion of three pairs ofasymmetric Bivacuum fermions and antifermions, in the process of transition of the excitedstate of atom or molecule, i.e. systems:[electrons protons] to the ground state.

There are two possible ways to make the rotation of adjacent sub-elementary fermionand sub-elementary antifermion compatible. One of them is interaction ’side-by-side’, like

46

in the 1st and 3d pairs of (7.11a). In such a case of Cooper pairs, they are rotating inopposite directions and their angular momenta (spins) compensate each other, turning theresulting spin of such a pair to zero. The resulting energy and charge of such a pair ofsub-elementary particle and antiparticle is also zero, because their symmetry shifts withrespect to Bivacuum is exactly opposite, compensating each other.

The other way of compatibility is interaction ’head-to-tail’, like in a central pair ofsub-elementary fermions of 7.11a. In this configuration they rotate in the same directionand the sum of their spins is: s 1. The energy of this pair is a sum of the absolutevalues of the energies of sub-elementary fermion and antifermion, as far their resultingsymmetry shift is a sum of the symmetry shifts of each of them.

In such a case, pertinent for photon, its total energy is interrelated with photonfrequency (ph) can be presented as:

Eph hph mV mV

c2FFF |mV

|mV c2

FFF

or : Eph hph mV c2

FFF |mV

|c2 FFF 2 mV

c2FF

F

7.12

7.12a

In accordance to our theory (see eqs. 7.4 and 7.4a), the rest mass contribution to energyof sub-elementary fermion Rm0c2 FF

F and that of sub-elementary antifermion

Rm0c2c2FFF in symmetric pairs are tending to zero: R 1 vtr/c2 0, when

the external translational group velocity of the whole particle is tending to light velocityv c. At these conditions the masses/energies of complementary torus of sub-elementaryfermion mV

c2FFF m0 1 vtr/c2 and that of complementary sub-elementary

antifermion: mV c2

FFF m0 1 vtr/c2 are also close to zero;

ph 1h mV

c2 FFF |mV

|c2 FFF 7.12b

is the photon frequency, equal to frequency of quantum beats between the actual statesof asymmetric pair of F and F in photon.

The energy of photon in Corpuscular phase is a sum of energy of tori of asymmetricsub-elementary fermion and antifermion. Equal to this energy, the energy of the Wavephase EphW is determined by the energy of two corresponding cumulative virtual cloudsCVC CVC :

EphC mphc2 mV |mV

|c2 CFF

EphW CVC CVC h2/mV |mV

|ph2 ;

EphC EphW hph mphc2 2mV c2 2m0c2

1 LphC rotc

2

7.13

7.13a

7.13b

where: LphC ~ L0 /m0c is dimension of photon in corpuscular phase; rot is the anglefrequency of photon rotation around the direction of its propagation;

mph mV |mV

| 2mV 2|mV

| hph/c2 hcph

7.14

is the effective mass of photon; ph c/ph is the photon wave length.

47

The energy of photon can be presented as a sum of potential V mV |mV

|c2 andkinetic Tk mV

|mV |c2 energies of uncompensated central pair of sub-elementary

fermions:

EphW mphc2 V Tk mV |mV

|c2 mV |mV

|c2 7.14a

For photon, propagating in space (primordial symmetric Bivacuum) with translationallight velocity, the complementary mass (eq.3.6) is close to zero |mV

| 0 and potential andkinetic energies are determined by rotational/angle velocity of photon and its central pairs:v Lphph

V Tk mVc2 m0c2

1 LphC rotc

2 7.14b

where Lph ~ L0C /m0c is dimension of photon in corpuscular phase; rot is the angle

frequency of photon in [C] phase rotation around the direction of its propagation.We suppose that potential energy of photon or elementary fermion, like electron or

proton stands for electric component of photon and kinetic - for its magnetic potential.It follows from our model (fig.4), that the minimum value of the photon effective mass

and energy, necessary for splitting of photon to electron positron pair is equal to thesum of absolute values of rest mass/energy of central pair of sub-elementary fermion andantifermion: Eph 2m0c2 with positive or negative integer spins (1 : F FS1 orsub-elementary antifermions F FS1. This consequence of our model is inaccordance with available experimental data.

Fig.4 Model of photon 2F FS0 F FS1

, as result of fusion of electronand positron-like triplets F F F of sub-elementary fermions , presented onFig.2. The resulting symmetry shift of such structure is equal to zero, providing the absenceor very close to zero rest mass of photon and its propagation in primordial Bivacuum withlight velocity or very close to it in the asymmetric secondary Bivacuum.

We may see, that it has axially symmetric configurations in respect to the directions ofrotation and propagation, which are normal to each other. These configurations periodicallychange in the process of sub-elementary fermions and antifermions correlatedCorpuscle Wave pulsations in composition of photon (Fig.4). The volume of sextet ofsub-elementary fermions in Corpuscular [C] phase is equal to volume, occupied by 6

48

asymmetric pairs of torus (V and antitorus (V with geometry of truncated cones andbases: SV LV2 ; SV LV2 (Korn and Korn, 1968):

VC 6d LV2 LVLV LV2 7.15

where: d is the height of truncated cone (eq.1.4); the radiuses of Compton bases LVand LV and their squares SV and SV of the electron’s torus and antitorus can becalculated, using eqs. 4.3 and 4.3a.

For the simple case, when the radiuses of torus of sub-elementary fermion and antitorusin paired sub-elementary antifermion in photons are close: LV LV L0

e , then 7.15turns to: VC0 18 d L0

2.The volume of Wave phase of photon in general case is much bigger, than that [C]

phase. It can be evaluated as a 3D standing wave:

VW 38 ph

3 38

cph

3 7.16

The energy density in [C] phase is much higher, than that of [W] phase as far thevolume is much less and the energies are equal:

C ECVC

mV

vgr2

18 d L02

8 hph3 ph3

EWVW

W 7.17

The expanded Wave phase in contrast to compact Corpuscular phase represents a bignumber (NBVF of Bivacuum fermions and antifermions in the volume of wave [W] phaseVW with resulting symmetry shift and uncompensated energy:

c2

mph

0

mV mV

WdmV mphcgr2 C hc2/phph

2 W hph 7.18

For photon in primordial symmetric Bivacuum its group and phase velocities are equal:vgr vph c. This means that the average kinetic and potential energies are also equal:Tk Vp. In the process of C W pulsation the rotational-translational local kineticenergy of photon: m00L0

2 m0 vgrvph in C phase turns to non-local symmetry shift ofBivacuum dipoles in volume of W phase.

The clockwise and counter clockwise rotation of photons in [C] phase around the z-axis(fig.2) stands for two possible polarizations of photon.

The asymmetric pair [actual torus (V complementary antitorus (V)] ofsub-elementary fermion has a spatial image of truncated cone (Fig.3 and Fig.4). Usingvector analysis, the energy of Cumulative Virtual Cloud (CVC, equal to energy ofquantum beats between the torus and antitorus, can be expressed via internal group andphase velocity fields of sub-quantum particles and antiparticles, composing torus andantitorus: vL and vL, where L and L are their radiuses:

ECVC EW n CW n V V 1

2 rot vL rot vL 7.18a

where: n is the unit-vector, common for both: torus and antitorus of sub-elementaryfermion (F; CW 2ph n V

V is a frequency of quantum beats betweenactual and complementary states of F.

It is assumed here, that all of subquantum particles/antiparticles, forming actual andcomplementary torus and antitorus of [C] phase of sub-elementary fermion have the same

49

angular frequency: V and V , correspondingly.7.2 The correlated dynamics of pairs of sub-elementary fermions and antifermions

of the opposite and similar spinsWe define the energy, as the ability of system to perform a work. In this definition the

energy of asymmetric Bivacuum fermions and antifermions are always positive,independently of sign of symmetry shift between the mass and charge of torus V andantitorus V, if they are spatially separated.

If the adjacent asymmetric Bivacuum fermions and antifermions of the opposite spins(i.e. rotating in opposite direction), contacting with each other ’side-by-side’, form Cooperpairs BVF BVFas, are pulsing in the same phase between the actual andcomplementary states, their energy, charge and spin compensate each other.

On the other hand, if the adjacent asymmetric Bivacuum fermion and antifermion of thesame spin (i.e. direction of rotation) form ’head-to-tail’ complexes, they are spatiallycompatible only in the case if their pulsation are not in-phase. It will be shown in section 9,that Pauli repulsion between fermions of the same spin due to superposition of theircumulative virtual clouds CVC and CVC is absent, if their emission absorption in theprocess of C W pulsation are counter-phase. It is true also for pair of sub-elementaryfermion and antifermion F FS1

, like in photon (fig.4). In case of this configurationand dynamics the total spin and energy of pair is a sum of spins and absolute energies ofF and F eqs.(7.13-7.13b).

7.3 Spatial images of sub-elementary particles in [C] and [W] phaseThe spatial images of torus V and antitorus V of asymmetric sub-elementary

fermion in [C] phase, reflecting the energy distribution of the actual and complementarystates of sub-elementary fermions, can be analyzed in terms of wave numbers. For this endwe analyze the basic equations for actual and complementary energy of Bivacuumfermions, squared, leading from (3.5 and 3.6):

EV 2 mV c2

2 m0c22 mV

v2c2

EV 2 mV c2

2 m0c22 m0v2c2

7.19

7.19a

These equations can be transformed to following combinations of wave numberssquared:

for actual torus V : mV c

2

mV v

2 m0 c

2

for complementary antitorus V : mV c

2 m0 v

2 m0 c

2

7.20

7.20a

The spatial image of energy distribution of the actual torus [V], defined by equation(7.20), is described by equilateral hyperbola (Fig.5a):

V : X2 Y2 a2 7.21

where: X kV tot mV c/; Y mV v/; a m0c/

The spatial image of complementary antitorus [V (7.20a) corresponds to circle (Fig.5b), described by equation:

50

V : X2 Y2 R2 7.22

where: X kV tot mV c/; Y k0kin m0v/.The radius of complementary circle: R k0 m0c/ is equal to the axis length of

equilateral hyperbola: R a of actual [V state. In fact this circle is a spatial image of thecomplementary torus of asymmetric BVF sub-elementary particle or antiparticle (F).A spatial image of sub-elementary fermion F in corpuscular [C] phase is a

correlated asymmetric pair: [actual torus complementary antitorus] with radiuses of theircross sections, defined, correspondingly, as (L and (L:

L mV vgrin

iand L

mV vphin

i

the resulting Compton radius of vorticity of F is : L0 L L1/2 m0c

i 7.23

where: mV and mV are actual (inertial) and complementary (inertialess) effective massof torus and antitorus of sub-elementary particle, correspondingly; m0 mVmV1/2 is therest mass of sub-elementary particle; vgrin and vphin are the internal group and phasevelocities, characterizing collective motion (circulation) of subquantum particles andantiparticles, forming actual vortex and complementary torus (Fig.5 a, b).

Fig. 5a. Equilateral hyperbola, describing the energy distribution for the actual toruscorpuscular [V of sub-elementary fermion (positive energy region) and sub-elementaryantifermion (negative energy region). This asymmetrically excited torus is responsible alsofor inertial mass (mV

, the internal actual magnetic moment (in and actual electric chargecomponent (e of sub-elementary fermion (Kaivarainen, 2001a; 2004);Fig. 5b. Circle, describing the energy distribution for the complementary state [Vofantitorus of sub-elementary fermion. This state is responsible for inertialess mass (mV

, theinternal complementary magnetic moment (in and complementary component (e ofelementary charge. Such antitorus is general for Bivacuum fermions (BVF

) and Bivacuumbosons (BVB.

The [Wave] phase of sub-elementary fermions in form of cumulative virtual cloud(CVC) is a result of quantum beats between the actual and complementary torus andantitorus of [Corpuscular] phase of elementary wave B. Consequently, the spatial image ofCVC energy distribution can be considered as a geometric difference between energeticsurfaces of the actual [V and complementary [V states of Fig 5a and Fig.5b.

After subtraction of left and right parts of (7.20 and 7.20a) and some reorganization, we

51

get the energetic spatial image of the Wave phase or CVC, as a geometricaldifference of equilateral hyperbolaand circle:

mV2

m02 mV2

m02

c2

v2 mV2

m02

c2

v2 1 7.24

This equation in dimensionless form describes the parted (two-cavity) hyperboloid(Fig.6):

x2

a2 y2

b2 z2

c2 1 7.25

The c is a real semi-axe; a and b the imaginary ones.A spatial image of the wave [W] phase (Fig.6), in form of cumulative virtual cloud

(CVC) of subquantum particles, is a parted hyperboloid (Kaivarainen, 2001a).

Fig. 6. The parted (two-cavity) hyperboloid is a spatial image of twin cumulative virtualcloud [CVC and CVC, corresponding to [Wave] phase of sub-elementary fermion(positive cavity) and sub-elementary antifermion (negative cavity). It may characterize alsothe twofold CVC and CVC of positive and negative energy, corresponding to [W] phaseof pair (sub-elementary fermion sub-elementary antifermion) pairs F F, as ageneral symmetric part of the triplets of electron, positron, photon, proton and neutron (seeFigs. 2 and 3).

For the external observer, the primordial Bivacuum looks like a isotropic system of 3Ddouble cells (Bivacuum fermions) with shape of pair of donuts of positive and negativeenergy, separated by energetic gap (see eq.1.4). There are three kinds of like virtual dipoleswith three Compton radiuses, corresponding to the rest mass of three electron’s generation:i e,,and the external group velocity, equal to zero (vgrext v 0. The absence oftranslational dynamics of Bivacuum dipoles provide their zero external momentum and theconditions of virtual Bose condensation, related directly to Bivacuum nonlocal properties(section 1.3). The dimensions of Bivacuum dipoles (radius of two donuts and gap betweenthem) are pulsing in a course of virtual clouds (VC emission absorption.

The following reversible energy oscillations of the positive actual torus (V andnegative complementary antitorus (V, accompanied the [Corpuscle Wave] transitionsof asymmetric sub-elementary fermions of elementary particles.

52

Fig. 7. The in-phase oscillation of the total energy E1 E0 of the actual state (upper fig.)

and the symmetry oscillation [|T V |C |T V |W of the complementary state (down)during C W transitions of [vortex torus] dipole of sub-elementary particles.

8. The nature of electrostatic, magnetic and gravitational interaction,based on Unified theory

8.1 Electromagnetic dipole radiation as a consequence ofcharge oscillation

The [emission absorption of photons in a course of elementary fermions - triplets F FS0 F

S1/2e, vibrations can be described by known mechanism of the

electric dipole radiation (EH, induced by charge acceleration (a), following from Maxwellequations (Berestetsky, et. al.,1989):

EH 2e2

3c3 a2 8.1

The resulting frequency of C W pulsation of each of three sub-elementary fermionsin triplets is a sum of internal frequency contribution (R0

in and the external frequency(B of de Broglie wave from (7.4):

CW R0in B

i 8.2

where: R 1 v/c2 is relativistic factor.The acceleration can be related only with external translational dynamics which

determines the empirical de Broglie wave parameters of particles. Acceleration is a resultof alternating change of the charge deviation from the position of equilibrium:Bt Bt 0 sin Bt with de Broglie wave frequency of triplets: B /mVLB2 ,where LB /mVv. It is accompanied by oscillation of the instant de Broglie wave length(Bt .

The acceleration of charge in the process of C W pulsation of the anchor BVFanc canbe expressed as:

a B2Bt 8.3

53

a B2 B0 sin Bt 8.4

where: Bt 2LB is the instant de Broglie wave length of the particle and 0 h/m0c isthe Compton length of triplet.

The intensity of dipole radiation of pulsing BVFanc from 8.2 and 8.4 is:

EM 23c3 B

4 dEt 2 8.5

where the oscillating electric dipole moment is: dEt eB0.Consequently, in accordance with our model of duality, the EM dipole radiation is due

to modulation of the anchor Bivacuum fermion BVFanc frequency of C W pulsation ofunpaired sub-elementary fermion by thermal vibrations of triplets.

The photon in out theory is a result of fusion/annihilation of two triplets: electron positron, turning two asymmetric fermions to quasi-symmetric boson. The electromagneticfield, is a result of Corpuscle - Wave pulsation of photon and its fast rotation with anglevelocity (rot), equal to pulsation frequency. The clockwise or anticlockwise direction ofphoton rotation (Fig.4 of this paper), as respect to direction of its propagation, correspondsto its two polarization.

8.2 The different kind of Bivacuum dipoles perturbation, induced by dynamics ofelementary particles

In the process of [C W] pulsation of sub-elementary particles in triplets F F F e,p the [local (internal) distant (external)] compensation effectsstand for the energy conservation law. The local effects are pertinent for the [C] phase ofparticles. They are confined in the volume of sub-elementary fermions and are determinedby gravitational attraction between opposite actual and complementary mass, the Coulombattraction between opposite electric charges and magnetic attraction between magneticmoments of asymmetric torus and antitorus of sub - elementary fermions. These threepotential attraction forces are balanced by the energy gap between torus (V and antitorus(V and centripetal force of the axial rotation of triplets. The axis of triplet rotation isstrictly related, in accordance to our model, with its spin and direction of its translationalpropagation. It is supposed, that like magnetic field force lines, this rotation follows theright hand screw rule and is responsible for magnetic field origination. The total energy oftriplet, the angular frequency of its rotation and the velocity of its translational propagationare interrelated.

The distant (external) effects, related with certain polarization and alignment ofBivacuum dipoles (circular and linear) are related with [C W transition of unpairedF e,p . It is accompanied by the recoil effect and and the distant elastic deformation ofBivacuum superfluid matrix, shifting correspondingly a symmetry of Bivacuum dipoles.The reverse W C transition represents the antirecoil effect. The latter is accompaniedby giving back the delocalized recoil energy and restoration of the unpaired sub-elementaryfermion and the whole triplet properties.

The recoil - antirecoil and polarization effects on surrounding Bivacuum dipoles (BVF

and BVF in form of spherical elastic waves, excited by C W pulsations of unpairedsub-elementary fermions F and antifermions F of triplets F F F e,p ,are opposite. This determines the opposite effects of positive and negative charged F onsymmetry of Bivacuum torus (V and antitorus (V of Bivacuum dipoles BVF,accompanied by their mass and charge polarization and acquiring the external momentum.Corresponding energy shift between torus and antitorus is dependent on distance R from

54

charge as ( r /R). The induced by such mechanism linear alignment of Bivacuum bosons(BVB or Cooper pairs BVF BVF with opposite direction of BVF and BVFrotation between remote F and F of different triplets, like bundles of virtualmicrotubules stands for electrostatic field and its ’force lines origination.

On the other hand, pulsations of each of paired sub-elementary fermions F Fhave similar and symmetric effect on excitation of (V and (V of BVF V V,independently on the charge of unpaired fermion and direction of triplets motion.Corresponding excitation of positive and negative virtual pressure waves (VPW andVPW is a background of gravitational attraction between different triplets, like betweenpulsing spheres in liquid medium. The influence of the in-phase recoil effect of pulsingF F on the external momentum and energy of torus (V and antitorus (V ofBivacuum dipoles BVF V V should be symmetric and equal by absolute value toincrement of energy of unpaired F .

The fast rotation of pairs of sub-elementary fermion and antifermion F F oftriplets with opposite charges and actual magnetic moments should induce a polarization ofBivacuum dipoles around the vector of triplets propagation, shifting the spin equilibriumBVF BVB BVF to the left or right and stimulate their ’head-to-tail’ circularstructures assembly in form of closed virtual microtubules. Our conjecture is thatcorresponding circular/axial ’polymerization’ of polarized Bivacuum dipoles arounddirection of current, coinciding with that of triplets propagation, stands for curledmagnetic field origination. The fast chaotic thermal motion of conducting electrons inmetals or charged particles in plasma became more ordered in electric current, increasingcorrespondingly the magnetic cumulative effects due to triplet fast rotation in the sameplane.It is possible to present the above explanation of field nature and origination in

more formal way. The total energies of [C W] and [W C] transitions of particles wepresent using general formula (6.1). However, here we take into account the correspondingrecoil antirecoil effects and the reversible conversion of the internal - local (Loc)gravitational, Coulomb and magnetic potentials to the external - distant (Dis) Bivacuummatrix perturbation, stimulated by these transitions. The [C W] transition, accompaniedby three kinds of recoil effects, can be described as:

ECW mVc2 Vtot EGRec

Loc EGRecDist

Ttot EERecLoc EERec

Dist tr

EHRecLoc EHRec

Dist rot

8.6

8.6a

8.6b

In the process of the reverse [W C] transition the unpaired sub-elementary fermionF of triplet F FS0 F S1/2

gets back the antirecoil (ARec) energy inform of relaxation of Bivacuum matrix, transforming back the Bivacuum matrix elasticdeformation and VPW excitation:

EWC mVc2 Vtot EGARec

Loc EGARecDist

Ttot EEARecLoc EEARec

Dist tr

EHARecLoc EHARec

Dist rot

8.7

8.7a

8.7b

where: VtotW 12 mV

mV c2 Vtot

C 12 mV

2c2 v2 is a total potential energy ofeach sub-elementary fermion of triplet (6.4) in the wave and corpuscular phase;

55

TtotW 12 mV

mV c2 Ttot

C 12 mV

v2 is its total kinetic energy (6.5).The reversible conversions of the local gravitational potential VGRec,ARec

Loc to thedistant one VGRec,ARec

Dist , accompanied the [C W pulsation of unpairedsub-elementary fermions of triplets, interrelated with paired ones F F. The latterexcite the positive VPW and negative VPW spherical virtual pressure waves,propagating in space with light velocity. They are a consequence of transitions of torus V

and antitorus V of surrounding Bivacuum dipoles BVF V V between the excitedand ground states.

The EERec, ArecLoc EERec, ARec

Dist are the local and distant electrostatic potentialoscillations, equal to each other; the EHRec,Arec

Loc EHRec,ARecDist are the local and distant

magnetic potentials oscillations, equal to each other.These local non-local reversible interconversions are the result of C W

pulsations and emission absorption of rotating CVC of sub-elementary fermions oftriplets.

Let us consider in more detail the interconversions of the internal - local and theexternal - distant gravitational, Coulomb and magnetic potentials of charged elementaryparticles, like electron or proton.

8.3 The new approach to quantum gravity and antigravityThe unified right parts of eqs. (8.6) and (8.7), describing the excitation of gravitational

waves, which represent superposition of positive and negative virtual pressure waves(VPW and VPW, are:

V totCW Vtot EGRec

Loc EGRecDist ~ 8.8

This formula reflects the fluctuations of potential energy, accompanied C W pulsationof unpaired sub-elementary fermions (7.1 and 7.2), interrelated with and paired ones (7.3),which are responsible for gravitational field.

The more detailed presentation of 8.8 is:

V totCW 1

2 mV mV

c2 rr G mVmV

LG

Loc m0

i

MPl

2mV

mV c2

Dis

8.9

The local internal gravitational interaction between the opposite mass poles of themass-dipoles of unpaired sub-elementary fermions (antifermions) F S1/2

turnsreversibly to the external distant one:

EGFF rr G |mV

mV |

LG FF

Loc CW

WC r

r imV

mV c2 FF

Dis 8.10

where: LG /mV mV

c is a characteristic curvature of potential energy (4.4b);MPl

2 c/G is a Plank mass; rr is ratio of unitary vector to distance from particle;

m02 |mV

mV | is a rest mass squared; i m0

i

MPl

2is the introduced earlier dimensionless

gravitational fine structure constant (Kaivarainen, 1995-2005). For the electrone 1.739 1045 and e m0

e

MPl 0.41 1022.

The effective gravitational velocity of particle squared vG2 eff, introduced from the

right part of (8.10) as mV c22 v2/c2 mV

vG2 eff can be presented as:

vG2 eff c22 v2/c2 8.10a

56

At the Golden mean conditions, when (v2/c2 0.618 , we get from 8.10a thereduced value of zero-point oscillation, related to gravitation:

vG2 eff

c2 1.382

In triplets F F F e,p the contribution of symmetric pair F Fpulsation to gravitation field energy is the additive function of energies of their cumulativevirtual clouds energies: CVC

F and CVCF :

EGFF rr G |mV

mV |

LG FF

Loc CW

WC r

r imV

mV c2 FF

Dis

or : EGFF hG i CVCF CVC

F ~ VPWq VPWq

G 8.10ab

The excitation of the external - distant spherical virtual pressure waves of positive andnegative energy: VPWq

and VPWq is a result of pair of torus and antitorus energy beats,

accompanied C W pulsation of paired sub-elementary fermions F FS0, strictlyequal by absolute values to fluctuation energy of the unpaired F S1/2

one. It isimportant to note, that the introduced gravitational field does not depend on charge oftriplet, determined by unpaired sub-elementary fermion F FS0 F S1/2

, incontrast to electrostatic and magnetic field.

It follows from our approach, that the gravitational energy is pertinent even for ’empty’primordial Bivacuum in the absence of matter and fields or when their influence isnegligible. This phenomena can be responsible for the ’cold dark matter’ of the Universe.The primordial Bivacuum dipoles are symmetric and their absolute mass/energies, chargesand magnetic moments are equal:

mV mV

m0

Consequently, the right part of (8.10ab), using (1.1 and 1.3) can be presented as:

EGFF rr

imV mV

ic2 rr

im0c21 2n

or : EGFF rr

i01 2n ~ VPWq VPWq

G

8.11

8.11a

Consequently, the cold dark matter phenomena can be a consequence of simultaneousexcitation of huge number of Bivacuum dipoles, symmetric as respect to positive andnegative energy, in virtual domains of nonlocality (see section 1.3). The energy,proportional to V ~ mV

mV c2 considered in our theory as the potential one, in contrast

to kinetic one: Tk ~ mV mV

c2. The bigger is quantum number of Bivacuum dipolesexcitation (n), the higher is frequency of virtual pressure waves VPWq

VPWq G,

responsible for gravitational field.From the proposed mechanism of gravitation and similar values of mV

in the left andright parts of eq. 8.10 it directly follows the equality of gravitational and inertial mass. Theinertia itself is a consequence of particles system symmetry and effective mass relativisticincreasing with acceleration. Consequently, inertia is proportional to the number ofparticles in this system and (i.e. total mass of the system) and a generalized Le Chatelier’sPrinciple, as a resistance of system to additional symmetry shift.

The mechanism of gravitational attraction and repulsion

57

In accordance to our hypothesis (Kaivarainen, 1995; 2000; 2005), themechanism ofgravitational attraction is similar to Bjerknes attraction between pulsing spheres inliquid medium - Bivacuum. The dependence of Bjerknes force on distance between centersof pulsing objects is quadratic: FBj ~ 1/r2:

FG FBj 1r2 GR1

2R22v2 cos 8.12

where G is density of liquid, i.e. virtual density of secondary Bivacuum. It isdetermined by Bivacuum dipoles (BVF and BVB symmetry shift; R1 and R2 radiuses ofpulsing/gravitating spheres; v is velocity of spheres surface oscillation (i.e. velocity ofVPWq

, excited by C W pulsation of elementary particles, which can be assumed to beequal to light velocity: v c); is a phase shift between pulsation of spheres.

It is important to note, that on the big enough distances the attraction may turn torepulsion. The latter effect, depending on the phase shift of coherent C W pulsation ofinteracting remote triplets (, can explain the revealed acceleration of the Universeexpansion. The corresponding antigravitation energy or negative pressure energy, is about70% of the total Universe energy.

The possibility of artificial phase shift of C W pulsation of coherent elementaryparticles of any object may (for example by magnetic field) may change its gravitationalattraction to repulsion. The volume and radius of pulsing spheres (R1 and R2 in suchapproach is determined by sum of volume of hadrons, composing gravitating systems insolid, liquid, gas or plasma state. The gravitational attraction or repulsion is a result ofincreasing or decreasing of virtual pressure of subquantum particles between interactingsystems as respect to its value outside them. This model can serve as a background for newquantum gravity theory.

The effective radiuses of gravitating objects R1 and R2 can be calculated from theeffective volumes of the objects:

V1,2 43 R1,2

3 N1,243 Lp,n

3 8.12a

where: N1,2 M1,2/mp,n is the number of protons and neutrons in gravitating bodieswith massM1,2; mp,n is the mass of proton and neutron; Lp,n /mp,nc is the Comptonradius of proton and neutron.

From (8.12a) we get for effective radiuses:

R1,2 M1,2mp,n

1/3Lp,n

M1,2mp,n

1/3 mp,nc 8.12b

Putting this to (8.12) we get for gravitational interaction between two macroscopicobjects, each of them formed by atoms with coherently pulsing protons and neutrons:

FG 1r2 Bv

M1M22/3

mp,n4/3

mp,n

4 1c2 8.13

Equalizing this formula with Newton’s one: FGN 1r2 GM1M2, we get the expression

for gravitational constant:

G G

3 M1M2

2/c2

3 mp,n16

8.14

The condition of gravitational constant permanency from (8.14), is the anticipated from

58

our theory interrelation between the mass of gravitating bodies 3 M1M2 and the virtualdensity G of secondary Bivacuum, determined by Bivacuum fermions symmetry shift andexcitation in gravitational field:

G const, ifG

3 M1M2 const 8.14a

where, taking into account (8.10):

3 M1M2 ~ G 12

m0MPl

2mV

mV

34 LG

3 23

m0MPl

2mV

2 v2/c2

LG3 8.15

assuming, that the radius of Bivacuum fermion is:

LG mV

mV c 8.16

we get for reduced gravitational density:

G 23

13

m0MPl

2mV

mV 4c3 8.16a

we may see from (8.16) that the bigger is potential energy of Bivacuum:V mV

mV c2 the bigger is gravitational density and interaction.

8.4 Possible nature of neutrino and antineutrinoWe put forward a conjecture, that neutrinos or antineutrinos represent a stable

nonelastic Bivacuum excitations in form of packet of positive and negative virtual pressurewaves, slightly unequal to each other:

, ~ VPW VPW, ~ VirP VirP , 8.17

The spatially delocalized asymmetry of neutrino and antineutrino compensates the localasymmetry in Bivacuum, accompanied origination of positrons or electrons. Thisasymmetry can be described as a small difference in energy of paired sub-elementaryfermion and antifermion F FS0 in triplets F F F . It can be positivefor electrons and negative for positrons and expressed as energy increment of elementaryde Broglie wave:

Ei mV

c2FFF mV

c2FFF i

or : mVc2 Rm0c2 mV

v2 i

8.18

8.18a

We suppose that this increment of opposite sign, corresponding to neutrino andantineutrino, can be defined by gravitational fine structure constant i m0

i

MPl

2different

for each lepton generation:

E,i imV

c2 iRm0c2 mVv2 8.19

8.5 The background of energy conservation lawThe law of energy conservation for elementary particles, as a sum of their kinetic and

59

potential energies in wave and corpuscular phase can be reformulated. The additivity ofdifferent forms of energy means the additivity of Bivacuum dipoles torus and antitorusenergy difference (i.e. forms of kinetic energy) and sum of their absolute values (forms ofpotential energy). These energy conservation quantum roots are illustrated for onesub-elementary particle case by eqs.(6.1 and 6.1a).

The compensation of the local symmetry shift, related to particles/matter dynamics byspatially delocalized/distant symmetry shifts in huge number of Bivacuum dipoles aroundthese particles eqs.(8.6-8.7b) - looks to be a general phenomena. This idea ofinterconversions between local-corpuscular and non-local/distant (fields) effects can beformulated as follows:

The total sum of local (corpuscular-matter) and non-local (wave-fields) kinetic and potential energie

responsible for Matter and Bivacuum interaction in the Universe is zero:

1Z

Pkc2 mV mV

mV

mV

k

P jv2 mV mV

2 c2

v2 1 j

0 8.20

where: Z

Pk

P j is the total partition function, i.e. sum of probabilities of alltransitions, conversions, fluctuations of energy in the Universe, including kineticincrements of fields and matter:

mV mV

kc2 ~mV

v2 j 8.20a

as well as potential increments of fields and matter:

mV mV

k ~ mV

2 c2

v2 1 j 8.20b

mV andmV

are the actual and complementary mass of torus (V and antitorus (V ofeach Bivacuum dipoles and elementary particle in the Universe.

Such matter - fields energy interconversions in the Universe can be considered, as abackground for the energy conservation law.

8.6 The Bivacuum dipoles symmetry shift and linear and circular ordering,as a background of electrostatic and magnetic fields origination

Let us consider now the origination of electrostatic and magnetic fields, as aconsequence of proposed models of elementary particles and their duality. The unifiedright parts of eqs. (8.6-8.6b) can be subdivided to translational (electrostatic) and rotational(magnetic) contributions, determined by corresponding degrees of freedom of CumulativeVirtual Cloud (CVCtr,rot :

T totCW Ttot EERec

Loc EERecDist tr EHRec

Loc EHRecDist rot 8.21

where the most probable total kinetic energy of particle can be expressed via its masssymmetry shift mV

mV or actual inertial mass (mV

) and external velocity (v:

Ttot 12 mV

mV c2 1

2 mV v2 8.21a

60

The comparison of (8.21a) with (8.10) prove that the inertial and gravitational mass arethe same physical parameters.

Formula (8.21) reflects the fluctuations of the most probable total kinetic energy,accompanied C W pulsation of unpaired sub-elementary fermion, responsible forlinear - electrostatic and curled - magnetic fields origination. In more detailed form the eq.(8.21) can be presented as:

T totCW 1

2 mV mV

c2 |ee |LT

Loc e2

c mV mV

c2tr

Dis

KH| |LT

Loc

KH0

2

c mV mV

c2rot

Dis

8.22

8.23a

The oscillation of electrostatic translational contribution, taking into account theobtained relation between mass and charge symmetry shifts (4.8a):mV

mV mV

e2e2

e2

can be expressed as:

|ee |LT

Loc CW

WC mV

c2 e2 e2e2 tr

Dis 8.24

where: LT /mV mV

c is a characteristic curvature of kinetic energy (6.5b);|ee | e0

2 is a rest charge squared; e2/c is the well known dimensionlesselectromagnetic fine structure constant.

The right part of (8.24) taking into account that: e2 e2 e ee echaracterizes the electric dipole moment of triplet, equal to that of unpaired sub-elementaryfermion F .

Like in the case of gravitational potential, it is assumed, that the local internal Coulombpotential between opposite charges of torus and antitorus of unpaired sub-elementaryfermions (antifermions) F S1/2

turn reversibly to the external distant (non-local) onedue to elastic recoilantirecoil effects, induced by C W pulsation of F S1/2

.

8.7 The factors, responsible for Coulomb interaction between elementary particlesThere are three factors, which determines the attraction or repulsion between opposite

or similar elementary charges, correspondingly. They are provided by the recoil antirecoil effects, induced by [C W pulsation and emission absorption of positive ornegative cumulative virtual clouds CVC or CVC of the unpaired sub-elementary fermionF S1/2

of triplets:1. The opposite (attraction) or similar (repulsion) Bivacuum dipoles symmetry shift and

polarization;2. Polymerization or depolymerization of Bivacuum dipoles of opposite or similar

symmetry/polarization shifts;3. The different kind of interference of virtual pressure waves of the opposite or similar

by sign energy:

VPW VPW or VPW VPW

excited by corresponding cumulative virtual clouds - opposite or similar by the energyand angular momentum:

61

CVC CVC or CVC CVC

These virtual clouds, composed from subquantum particles, in accordance to our modelof duality, are emitted absorbed by the unpaired sub-elementary fermions or/andsub-elementary antifermions in triplets of elementary particles F FS0 F S1/2

.The 1st factor is a basic one. The asymmetry of torus (V and antitorus (V of

Bivacuum dipoles means their ability to beats, accompanied by emissionabsorption ofVirtual Clouds (VC of the opposite or similar energy. The attraction between oppositecharges is a consequence of exchange interaction between Bivacuum fermions (BVFwith opposite by sign VC VC , following by decreasing of the resulting symmetryshift of Bivacuum. The less is separation between charges, the more is symmetry shift ofBVF in space between them and more effective is the exchange interaction, stimulatingthe attraction between opposite charges. This effect increases with distance decreasingbetween charges (R) as (r/R), where r is radius vector between charges.

The repulsion between similar charges also due to superposition of VC of similar signdecreases with distance increasing between charges. Both of these processes are theconsequence of energy conservation law, formulated as eq. 8.20, involving tendency of theBivacuum symmetry increments to zero.The 2nd factor is a consequence of the 1st one, i.e. exchange interaction by means of

VC between BVF and BVF in composition of virtual Cooper pairs:

BVF V V BVF V V 8.25

induced by the unpaired sub-elementary fermions of triplets. This counterphase symmetryshift of BVF and BVF provides the linear assembly of such pairs, meaning their "head totail" polymerization in space between F S1/2

of two distant opposite charges (i.e.electron and proton).

These quasi one-dimensional virtual microtubules, in fact, represents the linear VirtualGuides (VirG), described later in this paper (chapter 16). Such microtubules, composedfrom Cooper pairsBVF BVF are responsible for the ’force lines’ originationbetween the opposite distant charges. The energy of attraction, determined by the exchangeinteraction decreases with distance and has the following dependence on the length (R:r /R, where r is the unitary radius-vector.

On the hand, in space between similar charge the probability of virtual Cooper pairs(8.25) decreases and that of Bivacuum bosons: BVBV V of similar polarization(positive or negative) increases. We suppose that in this case the repulsion between similarcharges is due to superposition of VC of similar sign, [emitted .absorbed] in the processof the in-phase beats of BVB of the same polarization. This effect decreases with distanceincreasing between charges (R) as (r/R), where r is unitary radius vector.The 3d factor is determined by interaction of positive and negative subquantum

particles density oscillation, representing virtual pressure waves: VPW and VPW isdirectly interrelated with 2nd one. Its effect on attraction or repulsion of charges also canbe explained in terms of tending of system: Charges Bivacuum to minimum symmetryshift and energy density in space between charges in accordance to energy conservationlaw in form of eq. 8.20.The oscillation of magnetic dipole radiation contribution in the process of [C W

pulsations of sub-elementary fermions between local and distant modes is not accompanied

62

by magnetic moments symmetry shift, but only by the oscillation of separation betweentorus and antitorus of BVF and rotational energy of CVC emitted absorbed in theprocess of [C W pulsation. It can be described as:

KHi| |LT

Loc CW

WC KHi

02

c mV mV

c2rot

Dis

or : KHi| |LT

Loc CW

WC KHi

02

c mVT2 LT

2

rot

Dis

8.26

8.26a

where: 02

c is the magnetic fine structure constant, introduced in our theory. Themagnetic conversion coefficient KH we find from the equality of the electrostatic andmagnetic energy contributions:

EH EE Trec 12e2

c mV mV

c2 12 KH

i 02

c mVT2 LT

2 8.27

These equality is a consequence of equal probability of energy distribution betweentranslational (electrostatic) and rotational (magnetic) independent degrees of freedom of anunpaired sub-elementary fermion and its cumulative virtual cloud (CVC in conditions ofzero-point oscillation. This becomes evident for the limiting case of photon in vacuum. Thesum of these two contributions is equal to

EH EE mV vres2 mV

Lphph2 8.28

where vres is a resulting recoil-antirecoil vibration velocity; Lph ph/2 is a radius ofphoton gyration; ph is the angle frequency of gyration.

From the above conditions it follows, that:

KH0

2

c KHe0

2

4m02c3 e0

2

c 8.29

where 02 | | 1

2 e0m0c

2 is the Bohr magneton.Consequently, the introduced magnetic conversion coefficientt is:

KHe,p m0

e,pc/2

2 2

L0e,p

2

8.30

where L0e,p /m0

e,pc is the Compton radius of the electron or proton.8.8 The magnetic field origination

Origination of magnetic field is assumed to be a result of dynamic equilibrium

BVFS1/2 BVB BVFS1/2

8.31

shift between Bivacuum fermions and Bivacuum antifermions to the left or right,accompanied by corresponding shift of equilibrium between Bivacuum bosons of zero spinand magnetic moment of opposite polarization:

BVB V V V V BVB 8.32

and circulation in the plane, normal to direction of charged particles propagation in thecurrent.

63

In contrast to linear Virtual Guides (VirG), formed by Cooper pairs of Bivacuumfermions, responsible for electrostatic interaction, the magnetic field is determined bysystem of closed/circular VirG around the direction of moving charge, formed byindependent Bivacuum dipoles: BVFS1/2

and BVFS1/2 and difference between positive

(VirP) and negative (VirP virtual pressure:

VirPR rR |VirPVirP | ~ r

R nBVFS1/2 nBVFS1/2

or : VirP ~ rR |nVC nVC | r

R n VC nn VC

8.32a

where: r is the unitary vector; R is a distance from electric current; n and n are thedensities of BVFS1/2

and BVFS1/2 ; VC and VC are positive and negative virtual

clouds, emitted absorbed in the process of transitions between asymmetric BVFS1/2 and

BVFS1/2 , correspondingly; KBVFBVF

BVFS1/2

BVFS1/2 n

n is the equilibrium constant (eq.

8.33).This phenomena can be related to asymmetric properties of unpaired sub-elementary

fermion F S1/2 of moving triplets F FS0 F S1/2

and fast rotation ofpairs of charge and magnetic dipoles F FS0 in plane, normal to directed motion oftriplets, i.e. current. This statement is a consequence of the empirical fact, that the magneticfield can be exited only by the electric current: j n evj, i.e. directed motion of thecharged particles.

The resulting effect of rotation of uncompensated cumulative virtual clouds (CVC ofmany of the electrons of current in plane, normal to current direction and axis ofF S1/2

and CVC rotation is determined by the hand screw rule and induce the

circular structure formation around j in Bivacuum. These axisymmetric closed structuresare the result of ’head-to-tail’ vortical assembly of Bivacuum dipoles, i.e. by the sameprinciple as between opposite charges. The vortex - like motion of these axial circledstructures along the force lines of the magnetic field occur due to a small symmetry shiftbetween mass and charge of torus and antitorus of BVF in accordance with (3.11) and(4.2a). This asymmetry is produced by perturbation of Bivacuum dipoles, induced byCVC of the unpaired and paired sub-elementary fermions of triplets. It is dependent on thedistance (R) from current as ( r /R).

The unpaired sub-elementary fermions and antifermions have the opposite influence onsymmetry shift between torus and antitorus, interrelated with their opposite influence onthe direction of the BVFS1/2

BVB BVFS1/2 equilibrium shift.

The equilibrium constant between Bivacuum fermions of opposite spins, characterizingtheir uncompensated magnetic moment, we introduce, using (3.11), as function of theexternal translational velocity of BVF:

KBVFBVF BVFS1/2

BVFS1/2 exp

mV mV

mV

exp v2

c2 exp T2LT2

c2

8.33

The similar values of KBVFBVF have the axial distribution with respect to the currentvector (j of charges. The conversion of Bivacuum fermions or Bivacuum antifermions toBivacuum bosons (BVB V V with different probabilities (P and P:

64

BVFS1/2 P

BVB V V

BVFS1/2 P

BVB V V

may provide an increasing or decreasing of the equilibrium constant KBVFBVF . Thecorresponding sign of probability difference: P P P is dependent on the direction ofcurrent, related in-turn with direction of paired sub-elementary fermions F FS0circulation and rotation of CVC, emitted absorbed by unpaired sub-elementary fermionof triplet. The clockwise and anticlockwise circulation of Cooper pairs F FS0 oftriplets forming closed/circular virtual double microtubules affects in opposite way on theangular momentum of torus and antitorus: V and V , shifting equilibriumBVFS1/2

BVFS1/2 to the left or right.

The magnetic field tension can be presented as a gradient of the constant of equilibrium:

H gradKBVFBVF r /RKBVFBVF 8.34

The chaotic thermal velocity of the ’free’ conductivity electrons in metals and ions atroom temperature is very high even in the absence of current, as determined byMaxwell-Boltzmann distribution:

vT kTmV

~107 cm/s 8.35

It proves, that not the acceleration, but the ordering of the electron translational androtational dynamics in space, provided by current, is a main reason of the curled magneticfield excitation. In contrast to conventional view, the electric current itself is not a primary,but only a secondary reason of magnetic field origination, as the charges translational androtational dynamics ’vectorization factor’.

8.9 Interpretation of the Maxwell displacement current,based on Bivacuum model

The magnetic field origination in Bivacuum can be analyzed also from moreconventional point of view.

Let us analyze the 1st Maxwell equation, interrelating the circulation of vector ofmagnetic field tension H along the closed contour L with the conduction current (j) anddisplacement current jd 1

4Et through the surface, limited by L :

LHdl 4

c S j 1

4Et ds 8.36

where (s is the element of surface, limited with contour (l.The existence of the displacement current: jd 1

4Et is in accordance with our model

of Bivacuum, as the oscillating virtual dipoles (BVF and BVB continuum.In condition of primordial Bivacuum of the ideal virtual dipoles symmetry (i.e. in the

absence of matter and fields) these charges totally compensate each other.However, even in primordial symmetric Bivacuum the oscillations of distance and

energy gap between torus and antitorus of Bivacuum dipoles is responsible fordisplacement current. This alternating current generates corresponding displacementmagnetic field.

Corresponding virtual dipole oscillations are the consequence of the in-phase transitionsof V and V between the excited and ground states, compensating each other. These

65

transitions are accompanied by spontaneous emission and absorption of positive andnegative virtual pressure waves: VPW and VPW.

The primordial displacement current and corresponding displacement magnetic fieldcan be enhanced by presence of matter. It is a consequence of fluctuations of potentialenergy of sub-elementary fermions of triplets, accompanied by excitation of positive andnegative virtual pressure waves, which in accordance to our approach, is interrelated withgravitational field of particles (see 8.8 - 8.10).

8.10 New kind of current in secondary Bivacuum,additional to displacement and conducting ones

This additional current is a consequence of vibrations of BVF, induced byrecoil-antirecoil effects, accompanied [C W transitions of unpaired sub-elementaryfermion of triplets F FS0 F

S1/2e, It can be also a consequence of

Bivacuum dipoles perturbations, induced by relativistic translational propagation ofparticles in Bivacuum.

The corresponding elastic deformations of Bivacuum fermions BVF V Vare followed by small charge-dipole symmetry zero-point oscillations (vext 0 withamplitude, determined by the most probable resulting translational - rotational recoilvelocity (vrec. At conditions e e e0 and |e e | e0, i.e. at small perturbationsof torus and antitorus: V and V we have for the charge symmetry shift oscillationamplitude:

e e e 12 e0

vrec2

c2 8.37

The resulting most probable recoil velocity using (8.27 and 8.28) standing forelectromagnetism, can be defined as:

Trec 12 mV

mV c2 1

2 mV vres2

vrec2 vres2 8.38

8.38a

The minimum value of recoil velocity, corresponding to zero external translationalvelocity of triplets and internal velocity, determined by Golden mean conditionsvres/c2 0.61803398, can be considered as the velocity of zero-point oscillations:

vrec2 min v02HE

min c2

or : vrec2 min

c2

8.39

8.39a

where: e2/c 0,0072973506; vrec2 min/c2 4.51 103.The alternating recoil current (jrecEH, additional to that of Maxwell displacement current

(jd,) existing in presence of charged particles even in the absence of conducting current(j 0 is equal to product of (8.37) and square root of (8.39). At Golden mean conditions(v/c)2 this recoil current is:

jrec EH evrecmin 12

1/23/2 e0c 8.40

Corresponding gravitational contribution of recoil velocity, related to vibration ofpotential energy of particle (8.10) is much smaller, as far :

66

Vrec 12 mV

mV c2 1

2 mV c22 v2/c2 8.41

The zero-point characteristic potential recoil velocity squared at GM conditions(v2/c2 0.618 is:

v02G c22 ; v0

2G/c2 2

v0G c1/22 1/2 1,446 1012 cm/s

8.42

Consequently, the Maxwell equation (8.36) can be modified, taking into account the EHrecoil current, as

LHdl 4

c S j 1

4Et jrecEH ds Itot 8.43

where: Itot is total current throw the surface (S.We have to note, that jrecEH is nonzero not only in the vicinity of particles, but as well in

any remote space regions of Bivacuum, perturbed by electric and magnetic potentials. Thisconsequence of our theory coincides with the extended electromagnetic theory of BoLehnert (2004, 2004a), also considering current in vacuum, additional to displacement one.

As it was described in section 8.8, such kind of additional polarization and externaldynamics of BVF can be accompanied by their polymerization and formation of circularclosed Virtual Guides, rotating around the direction of current.

In accordance with the known Helmholtz theorem, each kind of vector field (F),tending to zero at infinity, can be presented, as a sum of the gradient of some scalarpotential ( and a rotor of vector potential (A):

F grad rotA 8.43a

The scalar and vector potentials are convenient to use for description of electromagneticfield, i.e. photon properties. They are characterized by the interrelated translational androtational degrees of freedom, indeed.

To explain the ability of secondary Bivacuum to keep the average (macroscopic) massand charge equal to zero, we have to postulate, that the mass and charge symmetry shiftsoscillations of Bivacuum fermions and antifermions, forming virtual Cooper pairs:

BVFS1/2 V V V V BVFS1/2

8.44

are opposite by sign, but equal by the absolute value. Consequently, the polarizedsecondary Bivacuum (i.e. perturbed by matter and field) can be considered, as a plasma ofthe in-phase oscillating virtual dipoles (BVF) of opposite resulting charge and mass/energy.

8.11 The mechanism, increasing the refraction index of BivacuumBy definition, the torus is a figure, formed by rotation of a circle with maximum radius,

corresponding to minimum quantum number (n 0, see 1.1a) LVi 2

m0i c

, around the axis,shifted from the center of the circle at the distance LEH,G. The electromagnetic (EH andgravitational (G vibrations of positions LEH,GV of the big number of recoiledBVFrec, induced by the elastic recoilantirecoil deformations of Bivacuum matrix, areaccompanied by vibrations of square and volume of torus (V and antitorus (V ofperturbed Bivacuum dipoles: BVFrec i V Vreci . The electromagnetic andgravitational increments of square (SV

E,G) and volume (VVE,G of toruses and antitoruses

of BVFrec i, as a consequence of their center vibrations can be presented,

67

correspondingly, as:

SVEH,G 42|LEH,G |V

EH,G LV

VVEH,G 42|LEH,G |V

EH,G LV2

8.45

8.45a

At conditions of zero-point oscillations, corresponding to Golden Mean (GM), when theratio (v0/c2 and external translational velocity (v is zero, the maximum shifts of centerof secondary Bivacuum dipoles in vicinity of pulsing elementary particles due toelectromagnetic and gravitational recoil-antirecoil (zero-point) vibrations are,correspondingly:

LEHi V CW

vEH i

m0i c1/2 0,067 LV

i

LGi V CW

vG i

m0i c

1/22 1/2 3,27 1023 LVi

8.46

8.46a

where: the recoil antirecoil oscillation period is CW 1/CW

/m0i c2 i

; therecoilantirecoil most probable velocity of zero-point oscillations, which determines theelectrostatic and magnetic fields is: vEH

c1/2 0.201330447 108 m s1 and1/2 0,067 the corresponding zero-point velocity, which determines gravitationalfield is: vG

ce1/22 1/2 1,446 1012 m s1 and e

1/22 1/2 0,48 1022.The dielectric permittivity of Bivacuum and corresponding refraction index, using our

theory of refraction index of matter (Kaivarainen, 1995; 2001), can be presented as a ratioof volume of Bivacuum fermions and bosons in symmetric primordial Bivacuum (Vpr totheir volume in secondary Bivacuum: Vsec VBVF r/rVBVFrec

E,G , perturbed by matterand fields. The secondary Bivacuum is optically more dense, if we assume that the volume,occupied by Bivacuum fermion torus and antitorus, is excluded for photons. The Coulomband gravitational potentials and the related excluded volumes of perturbed Bivacuumfermions/antifermions decline with distance (r as:

r /rVBVFrecEH and

r /rVBVFrecG

where: (r) is a distance from the charged and/or gravitating particle andr is the unitary

radius vector. Taking all this into account, we get for permittivity of secondary Bivacuum:

n2 cvEH,G

2 N Vpr

N Vsec

VBVFVBVF r/rVBVFrec

EH,G 11r/rVBVFrec

EH,G /VBVF

8.47

n2 11 r/r 3|L|V

EH,G LV

8.47a

where: the velocity of light propagation in asymmetric secondary Bivacuum of highervirtual density, than in primordial one, is notated as: vEH,G cEH,G; the volume ofprimordial Bivacuum fermion is VBVF 4/3LV3 and its increment in secondaryBivacuum: VBVFrec

E,G VVE,G (8.45a).

r/r is a ratio of unitary radius-vector to distance between the source of C Wpulsations (elementary particle) and perturbed by the electrostatic, magnetic andgravitational potential BVFrecEH,G.

68

Putting (8.46) into formula (8.46a) we get for the refraction index of Bivacuum andrelativistic factor RE in the vicinity of charged elementary particle (electron, positron orproton, antiproton) the following expression:

n2 ccEH

2

E 1

1 r/r 31/2 2.71 8.48

where: 1 n2 2,71 is tending to 1 at r .The Coulomb relativistic factor:

REH 1 cEH2

c2 r/r 0,631 r/r1/2 0.794 8.49

0 RE 0,794 is tending to zero at r .In similar way, using (8.46a) and (8.47a), for the refraction index of Bivacuum and the

corresponding relativistic factor RG of gravitational vibrations of Bivacuum fermions(BVF in the vicinity of pulsing elementary particles at zero-point conditions, we get:

n2 cGc

2

G 1

1 r/r3e1/221/2 1 8.50

where e1/22 1/2 0.48 1022.The gravitational relativistic factor:

RG 1 cGc

2 r/r 0,48 1022 r/r1/2 0,69 1011 8.51

Like in previous case, the Bivacuum refraction index, increased by gravitationalpotential, is tending to its minimum value: n2 1 at the increasing distance from thesource: r .

The charge - induced refraction index increasing of secondary Bivacuum, in contrast tothe mass - induced one, is independent of lepton generations of Bivacuum dipoles (e,,.

The formulas (8.48) and (8.50) for Bivacuum dielectric permittivity and refractionindex near elementary particles, perturbed by their Coulomb and gravitational potentials,point out that bending and scattering probability of photons on charged particles is muchhigher, than that on neutral particles with similar mass.

We have to point out, that the light velocity in conditions:nEH,G

2 c/vEH,G c/cEH,G 1 is not longer a scalar, but a vector, determined by thegradient of Bivacuum fermion symmetry shift:

grad |mV mV

|EH,G c2 grad mVv2 8.52

and corresponding gradient of torus and antitorus equilibrium constant increment:KVV 1 mV

/mV cEH,G/v2:

gradKVV 1 mV /mV

grad cEH,Gc

2 grad 1

n2

8.53

8.53a

The other important consequence of: n2 E,G 1 is that the contributions of the restmass energy of photons and neutrino (Kaivarainen, 2005) to their total energy is not zero,as far the electromagnetic and gravitational relativistic factors (REH,G) are greater than zero.

69

It follows from the basic formula for the total energy of de Broglie wave (the photon in ourcase):

Etot mVc2 CW Rm0c2rot

in Bext tr 8.54

where the gravitational relativistic factor of electrically neutral objects:RG r/r3,08 1022 r/r1/2 1.75 1011.

This consequence is also consistent with a theory of the photon and neutrino, developedby Bo Lehnert (2004a).

We can see, that in conditions of primordial Bivacuum, when r , the nEH,G 1,REH,G 0 and the contribution of the rest mass energy Rm0c2rot

in tends to zero. At theselimiting conditions the frequency of photon Corpuscle Wave pulsation is equal to thefrequency of the photon as a wave:

Eph CW ph h cph

8.55

The results of our analysis explain the bending of light beams, under the influence ofstrong gravitational potential in another way, than by Einstein’s general theory of relativity.A similar idea of polarizable vacuum and it permittivity variations has been developed byDicke (1957), Fock (1964) and Puthoff (2001), as a background of ’vacuum engineering’.

For the spherically symmetric star or planet it was shown using Dicke model (Dicke,1957), that the dielectric constant K of polarizable vacuum is given by the exponentialform:

K exp2GM/rc2 8.56

where G is the gravitational constant,M is the mass, and r is the distance from the masscenter.

For comparison with expressions derived by conventional General Relativitytechniques, it is sufficient a following approximation of the formula above (Puthoff, 2001):

K 1 2GMrc2 1

22GMrc2

2 8.57

Our approach propose the concrete mechanism of Bivacuum optical density increasingnear charged and gravitating particles, inducing light beams bending.

8.12 Application of angular momentum conservation law for evaluationof curvatures of electric and gravitational potentials

From the formulas of total energy of W phase of unpaired sub-elementary fermion(8.17) of triplet F FS0 F S1/2

e, we can find out the relation between thesum of internal and external angular momentum of CVC, including the electric andgravitational increments of CVC of [W phase for the one side, and a sum of correspondingrecoil angular momentums, for the other.

For the end of convenience, this expression can be subdivided to the internal M0in

(zero-point) and external Mext contributions to the total angular momentum M tot:

M tot M0in M

ext 8.58

It follows from the law of angular momentum conservation, that the angularmomentums of Cumulative virtual cloud (CVC) and the recoil (rec) angular momentums,

70

accompanied C W transitions of sub-elementary fermions, should be equal:

M0in Rm0cLE0 Rm0cLG0 rec Rm0cL0 Rm0cL0 Rm0cL0 CVC 8.59

where the internal momentum of elementary particle at Golden mean (zero-point)conditions:

p0in m0c |mV

mV |c mV

v2/c

L0 /m0c Compton radius

8.60

8.60a

and the external contribution to angular momentum:

Mext mV

vLEext mVvLGext rec mV

vLB mVvLB mV

vLB CVC 8.61

where the external momentum of particle is directly related to its de Broglie wavelength (B 2LB h/mV

v:

pext mVv h/B

LB 8.62

The sum of zero-point and angular momentums is:

M tot Rm0cLE0 mVvLEextrec Rm0cLG0 mV

vLGextrec Rm0cL0 mV

vLB Rm0cL0 mVvLBCVC Rm0cL0 mV

vLBCVC

8.63

The minimum space curvatures, related to electromagnetism, corresponding tozero-point longitudinal recoil effects, accompanied C W pulsation, can be find outfrom (8.59), reflecting the angular momentum conservation law, as:

LE0 L0 1 2 L0

1 1 aB L0 136,036L0

0,0072973506 1/137

8.64

We can see, that the space curvature, characteristic for electric potential of the electronat Golden Mean (zero-point) conditions (LE0 is very close to the radius of the 1st Bohrorbit aB in hydrogen atom:

aB 1 L0 137,036L0 0.5291 1010m 8.65

In similar way we can find from (8.59) zero-point Bivacuum curvature, determined byelementary particle gravitational potential:

LG0 G0

2 L01 2 L0

e,p 8.66

where: e m0e /MPl2 1.7385 1045; p m0

p/MPl2 5.86 1039 areintroduced in our theory gravitational fine structure constant, different for electrons andprotons; MPl c/G1/2 2.17671 108 kg is a Plank mass; m0

e 9.109534 1031 kgis a rest mass of the electron; m0

p 1.6726485 1027 kg m0e 1.8361515 103 kg is a

rest mass of proton.The length of one light year is 9.46 1015m. The gravitational curvature radius of

proton from (8.66), equal to LG0 p aG

p 3.58 1022m. may have the same importance incosmology, like the electromagnetic curvature of the electron, equal to 1st orbit radius of

71

the hydrogen atom: aB 0.5291 1010m in atomic physics. For comparison with aGp , the

characteristic distance between galactics in their groups and clusters is in range:0.3 1.5 1022m. The radius of of Local group of galactics, like Milky way, Andromedagalaxy and Magellan clouds, equal approximately to 3 106 light years. The radius ofVigro cluster of galactics is also close to aG

p .Let us consider now the curvature of electric potential, determined by the external

dynamics of the charged particle and its de Broglie wave length from (8.61):

LEext LB 1 2 LB 1

1 136,036LB 136,036 B2 8.67

In most common nonrelativistic conditions the de Broglie wave length of elementaryparticle is much bigger than it its Compton length (LB B

2 12

hmv L0

m0c and,consequently, the effective external radius of Coulomb potential action is much bigger,than the minimum internal one: LEext LE0 .

Similar situation is valid for external gravitational potential curvature from (8.61):

LGext G2 LB

1 2 LB 1

2

1 LB

8.68

8.13 Curvatures of Bivacuum domains of nonlocality, corresponding tozero-point electromagnetic and gravitational potentials of elementary particles

Let us analyze the length of coherence (de Broglie waves), determined by zero-pointvibrations velocity, accompanied the recoil effects of unpaired and paired sub-elementaryfermions of triplets F FS0 F S1/2

e,p, equal to radius of Bivacuum domainof nonlocality. It is assumed that the translational external velocity of triplets is zerovtrext 0.

The corresponding curvatures are related to electromagnetic and gravitational potentialof pulsing elementary particle of any of (i) generation:

LE

VirBC

mBVF v0E

mBVF c1/2

LG

VirBC

mBVF v0G

mBVF c2 1/2

8.69

8.69a

where zero-point velocities: v0HE c1/2 and v0G c2 1/2 are defined

by (8.39) and (8.42).The uncompensated masses of BVF, due to mass symmetry shifts, induced by

electromagnetic and gravitational vibrations can be evaluated as:

mBVF

E |mV

| |mV |E

mVv/c2

E

m01

m0

mBVF

G mV

v/c2G

m02 1 2

m02

8.70

8.70a

Putting 8.70 and 8.70a into 8.69 and 8.69a, we get radiuses of vortices of BVF andBVF, determined by their recoil antirecoil longitudinal vibrations, induced byzero-point C W pulsations of unpaired sub-elementary fermions of triplets -elementary particles, like electrons, protons and neutrons:

72

LE

VirBC 1 m0c3/2 L0

3/2

LG

VirBC

1 2

m0c2 3/2 L0

2 3/2

8.71

8.71a

These vortices of two very different radiuses represent standing circular virtual waves.In accordance to our theory, they characterize the regions of virtual Bose condensation,representing the domains of nonlocality.

9. Pauli principle: How it works ?Let us consider the reason why the Pauli principle ”works” for fermions and do not

work for bosons. In accordance to our model of elementary particles, the numbers ofsub-elementary fermions and sub-elementary antifermions, forming bosons, like photons(Fig.3), are equal. Each of sub-elementary fermion and sub-elementary antifermion insymmetric pairs FF of bosons can pulsate between their [C] and [W] states in-phase(S 0 or counterphase (S 1.

In both cases the positive and negative subquantum particles, forming CVC andCVC do not overlap, as far they are in realms of opposite energy.

For the other hand, the numbers of sub-elementary particles and sub-elementaryantiparticles in composition of fermions (i.e. triplets F F F i ) are not equalto each other. Consequently, the CVC and CVC of sub-elementary fermions andantifermions in triplets do not compensated each other . It leads to asymmetric oscillationsof Bivacuum virtual quanta density and symmetry shift in the process of [C Wpulsation.

In the framework of our model, the Pauli repulsion effect between fermions with thesame spin states and energy, i.e. the same phase and frequency of C W pulsation, issimilar to effect of excluded volume. It is provided by spatial incompatibility of twocumulative virtual clouds: CVC1

and CVC2 in the same moment of time, if the distance

between them is equal or less, than dimensions of CVC, determined by de Broglie wavelength of triplets: B CVC h/mV

vext. Let us analyze this situation in more detail.The contribution of external translational dynamics of fermions F F F i to

their total energy in [W] phase from (8.6, 8.11a and 8.15), taking into account the recoileffects, is:

EWext mVv2 mV

v2 rec h2

mVB2

h2

mVB2

h2

mVB2 CVCB tr

ext

mVv2 rec

h2

mVB2

h2

mVB2 CVCB tr

ext

EEext ECVCBext

9.1

9.1a

The Pauli repulsion energy between nonrelativistic fermions of the same spin andenergy on the distances B L0 /m0c is determined by the externalnon-electromagnetic energy of CVC:

P ECVCBext h2

mVB2

1 9.2

For the other hand, the external electric potential of particle - by its externallongitudinal recoil energy:

73

E EEext h2

mVB2

9.2a

Their ratio is very close to the reversed value of electromagnetic fine structure constant:

P/E 1/ 1~136 9.3

It points how much the Pauli repulsion energy between fermions of the same energyand spin exceeds the Coulomb interaction.

The effective distance of realization of Pauli repulsion between similar fermions:

B CVC hmV

vext 9.4

tends to infinity at v 0 and B CVC . Such nonlocal repulsion effect, which couldbe responsible for repulsive ’dark energy’ in the Universe, may be realized via Virtualguides of spin, momentum and energy VirGSME, described in section 17. In suchconditions, the spins and phase of C W pulsation of remote unpaired sub-elementaryfermions of distant Sender and Receiver should be in-phase.

If the spins of two sub-elementary and elementary fermions are opposite, then theirC W oscillations are counterphase and their CVC are spatially compatible, becausethey do not exist in the same space volume in the same moment of time.

For example, such situation takes a place in system of two sub-elementary fermions: Fand F of the electron F F F i or two sub-elementary antifermions F andF of the positron F F F i , because their CVC do not overlap in in thesame space in the same time.

In another example of the internal C W dynamics of triplets, as a condition of theirstability, the in-phase pulsations of sub-elementary fermion and sub-elementaryantifermion (F and F, localized in opposite energetic realms of Bivacuum, are possible,because the CVC and CVC do not overlap again.

The latter conditions occur also in the process of C W pulsation of elementarybosons (photons), and complex bosons, (atoms). In these two situations the effect ofexcluded volume is absent and fermions are spatially compatible. The mechanism,proposed, explains the absence of the Pauli repulsion in systems of Bosons and Cooperpairs.

9.1 Spatial compatibility of sub-elementary fermionsof the same charge and opposite spins

We postulate in our model, that [C W] transitions of two sub-elementary antifermions(F 1 F 2 with opposite spins in composition of the electron F F F or two sub-elementary fermions F 1 F 2 of the positron F F F are counterphase (see the upper part of Fig. 8).

In the case of counterphase [C W] pulsations of F 1 and F 2 with opposite

spins - they are spatially compatible, as far their corpuscular [C] and wave [W] phase arerealized alternatively in different semi-periods and the Pauli repulsion, described above, isabsent.

The example of such compatible pairs in composition of the electron or positron ispresented on (Fig.8).

74

Fig. 8. Schematic representation of pair of a spatially compatible sub-elementaryantifermions, as a pair of (vortextorus) dipoles of the electron F F F , withthe opposite half-integer spins: F and F and the same charge (e, energy andfrequency of [C W] pulsation. At the counterphase [C W] transitions of twosub-elementary antifermions with opposite spins: F and F , following by quantum beatsbetween actual and complementary corpuscular states, the [C W] pulsation of secondpaired sub-elementary antifermion F occur in-phase with F. In the volume of triplets ofelectrons and positrons the spin-spin exchange interaction between [Fand F ofunipolar sub-elementary (i.e. Pauli attraction) is stronger, than electromagnetic repulsion.

In accordance to our model, in triplet F F F , representing the electron,the resulting spin and charge of the electron is determined by ”uncompensated” spin of oneof two [F, presented on Fig.8. The actual inertial mass (mV of the electron is determinedby this unpaired/uncompensated sub-elementary fermion also.

The dynamics of sub-elementary particles of positron F F F is similar tothat of electron, determined, however, by uncompensated sub-elementary antifermion. Themechanism of the triplets of sub-elementary fermions spin state inversion needs 7200 not3600. It will be explained in the next section.

The elementary particles with opposite spins in pairs, like [electron electron],[positron positron], [electron proton], [protons and neutrons of heavy nuclears], etc.also could be spatially compatible, if their C W pulsations are counterphase and thePauli repulsion is absent. Such particles systems have a properties of bosons with integerspin S 0,1. The Cooper pairs have the like properties.

9.2 The double turn (7200 of magnetic field, as a condition of the fermionsspin state reversibility

It is known fact, that the total rotating cycle for spin of the electrons or positrons is not3600, but 7200, i.e. double turn by external magnetic field of special configuration, isnecessary to return elementary fermions to starting state (Davies, 1985). The correctness ofany new model of elementary particles should be testified by its ability to explain thisnontrivial fact.

We may propose three possible explanations, using our model of the electrons,positrons, protons and antiprotons, as a triplets of sub-elementary fermions/antifermions:(see section 5 of this paper).

75

Let us analyze them on example of the electron:

F F F e 9.5

1. We may assume, that the direction of external magnetic field rotation acts only onunpaired sub-elementary fermion, as asymmetric [torus (V antitorus (V pair:F V Vas, if the resulting magnetic moment of pair F F is zero and thepair do not interact with external magnetic field at all. In such conditions the 1st 3600 turnof external H field change the direction of torus V rotation to the opposite onetransforming the sub-elementary fermion to sub-elementary boson:F V V

3600

B V V. One more 3600 turn of the external magneticfield bring this sub-elementary boson and the triplet (7.10) to starting condition. The totalcycle can be presented as:

I F V V3600

B V V3600

F V V 9.6

2. The second possible explanation of double 7200 turn may be a consequence offollowing two stages, involving origination of pair of sub-elementary bosons B Bfrom pair of sub-elementary fermions, as intermediate stage and two full turns (2 3600 ofunpaired sub-elementary fermion:

II F F F 3600

B B F 3600

F F F 9.7

Both of these mechanisms are not very probable, because they involve the action ofexternal magnetic field on sub-elementary bosons with zero spin and, consequently, zeromagnetic moment.3. The most probable third mechanism avoids such strong assumption. The external

rotating H field interact in two stage manner (2 3600 only with sub-elementaryfermions/antifermions, changing their spins. However this mechanism demands that theangle of spin rotation of sub-elementary particle and antiparticles of neutral pairsF F are the additive parameters. It means that turn of resulting spin of pair on 3600

includes reorientation spins of each F and F only on 1800. Consequently, the full spinturn of pair F F resembles that of Mobius transformation.

The spin of unpaired sub-elementary fermion F , in contrast to paired ones, makes afull turn each 3600, i.e. twice in 7200 cycle:

Fx Fy Fz

3600

Fx18001800

Fy Fz

3600

Fx Fy Fz

9.8

The difference between the intermediate - 2nd stage and the original one in (9.8) is inopposite spin states of paired sub-elementary particle and antiparticle:

Fx Fy3600

Fx18001800

Fy 9.9

It follows from our consideration, that the 3D spatial organization of the electron (positron)is asymmetric, and some difference Fx F

x and Fy Fy is existing. TheC W pulsation of unpaired sub-elementary fermion Fz is counterphase and spatiallycompatible in basic state of the electron triplet with Fy and in the intermediate state -

76

with its partner Fx in triplets (9.8).One more known ”strange” experimental result can be explained by our dynamic model

of triplets of elementary particles. The existence of two paired in-phase pulsatingsub-elementary fermions (9.9) with opposite parameters, exchanging by spin, charge andenergy in the process of their C W pulsation, can be responsible for the two timesstronger magnetic field, generated by electron, as compared with those, generated byrotating sphere with charge |e |.

9.3. Bosons as a coherent system of sub-elementary and elementary fermions

The spatial image of the main unit of elementary boson (Fig. 6) could be presented as asuperposition of two strongly correlated (vortex - torus) dipoles with opposite charges andspin states, representing pair [sub-elementary fermion sub-elementary antifermion]. Ingeneral case the elementary bosons are composed from the integer number of such pairs.

Bosons have a zero or integer spin 0,1,2 in the units, in contrast to the halfinteger spins of fermions. In general case, bosons with S 1 include: photons, gluons,mesons and boson resonances, phonons, pairs of elementary fermions with opposite spins(i.e. Cooper pairs under the conditions of Bose-condensation), atoms and molecules.We subdivide bosons into elementary and complex ones:1. Elementary bosons (like photons), composed from equal number of sub-elementary

fermions and antifermions, moving with light velocity in contrast to complex bosons;2. Complex bosons, represent a coherent system of elementary fermions (electrons and

nucleons), like neutral atoms and molecules.Formation of stable complex bosons from elementary fermions of opposite charge and

same spins with different actual masses: mC 1 mC 2 is possible due to theirelectromagnetic attraction. It may occur, if the length of their waves B are the same andequal to distance between them. This former condition may be achieved by difference intheir external group velocities, adjusting the momentums to the same value:

L1 /mVv1 L2 /mV

v2 Ln /mVvn

at : v1/vn mVn/mV

1

9.10

The mentioned above conditions are the base for assembly of complex bosons, unifiedin the volume of 3D standing waves of fermions of the opposite or same spins.

The hydrogen atom, composing from two fermions: electron and proton is an exampleof complex microscopic complex bosons. The heavier atoms also must follow the sameprinciple of self-organization.

In accordance with our model, the elementary boson, such as photon, representsdynamic superposition of two triplets of sub-elementary fermions and antifermions (Fig. 3),corresponding to electron and positron structures. Such composition determines theresulting external charge of photon, equal to zero and the value of photon’s spin: J 1, 0or -1.

Stability of all types of elementary particles: bosons and fermions (electrons, positronsetc.) is a result of superposition/exchange of cumulative virtual clouds (CVC and CVC),emitted and absorbed in the process of [C W pulsations of sub-elementary particles andsub-elementary antiparticles, forming coherent pairs F F (Fig.9).

77

Fig. 9. Schematic representation of symmetric pair of the in-phase pulsing sub-elementaryfermion and sub-elementary antifermion F F with boson properties. The F and F,pulsing in-phase between the corpuscle and wave states compensate the mass, spin andcharge of each other. Such a pair is a neutral component of elementary particles, likeelectrons, positrons, protons, neutrons, etc.Properties of symmetric pair of F

F: resulting electric charge is zero; resultingmagnetic charge is zero; resulting spin: SFF 1, 0.

The neutral symmetric pairs of or generations F FS0,1, , forming part of

triplets eqs.(5.9 - 5.10) have a properties of mesons, as a neutral [quark antiquark] pairwith integer spin. The coherent cluster of such pairs - from one to four pairs:n q q S0,1,2,3,4 can provide the experimentally revealed integer spins - from zero tofour (chapter 5).

It follows from our model of elementary particles and antiparticles, as a triplets ofsub-elementary particles: F F Fi, that just symmetric pairs F Fi in acourse of their in-phase [C W pulsation are responsible for interaction of particles withpositive and negative Virtual Pressure Waves (VPW and VPW, their modulation andorigination of Virtual Replicas (VR) of matter (Kaivarainen, 2004; 2004a,b).

The Matter Bivacuum interaction and VR (virtual hologram) formation has beenconsidered in detail in chapter 16 and our work: New approach to Entanglement andQuantum Psi phenomena, based on Unified Theory of Bivacuum, Matter, Fields & Time.Archives of Los-Alamos: http://arXiv.org/abs/physics/0103031.

10 The Mystery of Sri Yantra DiagramIn accordance to ancient archetypal ideas, geometry and numbers describe the

fundamental energies in course of their dance - dynamics, transitions. For more than tenmillenniums it was believed that the famous Tantric diagram-Sri Yantra contains in hiddenform the basic functions active in the Universe (Fig. 10).

78

Fig. 10. The Sri Yantra diagram is composed from nine triangles. Four of them are pointedup and five down. Author is grateful to P. Flanagan for submitting of Sri Yantra diagramwith precise coordinates of most important points, making it possible the quantitativeanalysis.

Triangle is a symbol of a three-fold Nature. The Christian trinity, the symbol of Godmay be represented by triangle. The symbol of trinity is coherent to our idea of triplets ofsub-elementary particles, as a background of particles, forming matter. In Buddhism-Hindutriangle with apex up is a symbol of God-male and that with apex down is a symbol ofGod-female.

Sri Yantra diagram can be considered like geometric language, containing informationabout the mechanism of corpuscle-wave duality, as a background of all kinds offundamental interaction. Each of pair of triangles [down up] in terms of our modelcorresponds to positive and negative parts of two-cavity hyperboloid (Fig. 6), describingspatial image of [W] phase of the pair of [sub-elementary fermions (F sub-elementaryantifermions (F] in triplets F

FW FC, composing elementary particles, like

electron, positron, quarks in different excitation states. The uncompensated sub-elementaryfermion F is always in counterphase with pair F

F, in accordance with our model.In another terms, Fig. 11a, as a part of Sri Yantra (Fig.10), contains information about

spatial image of wave B in form of pair of cumulative virtual clouds (CVC CVC),corresponding to the wave [W] phase of symmetric pair F

FW and quantization oftheir energy.

79

Fig. 11a. Parts of Sri Yantra, representing in accordance to our model a spatial images ofpair of [sub-elementary particle (F sub-elementary antiparticle (F] of different statesof excitation, corresponding to WAVE phase [W] as a parted, (double) hyperboloid (Fig.6);Fig. 11b. Corresponding to this phase of triplet [(F FW F C

the asymmetricBivacuum ground state. The numbers near the right side of pictures characterize the energyof positive and negative energy sublevels of Bivacuum excitation:EB n 1

2 , where : n 0, 1, 2. . .

Other important feature of Sri Yantra, compatible with our model of symmetric pair[(F FW] CVC CVC in composition of electron, is Bivacuum symmetry shift,corresponding to this phase of triplet F FW FC.

Asymmetry is obvious from position of central point of diagram, denoted on Figs. (10)and (11a), as an open circle (o) and diamond shape of its nuclei (11b), composed from twotriangles with common base and different height.

It is interesting to note, that spatial position of central point (o), localized in lowertriangle of Sri Yantra diamond-nuclei as respect to its base and apex - corresponds toGolden mean.

The degree of asymmetry of Sri Yantra decreases with increasing the distance from itscentral point (o). For example, the shifts of zero-point positive and negative vacuumsublevels, pointed on Fig. 11a:

12 n and 1

2 n at n 0 10.1

as respect to central point (o) of Sri Yantra are characterized by ratio: 1.77. It reflects theasymmetry of Bivacuum boson of secondary Bivacuum , perturbed by uncompensated

80

sub-elementary particles. The less asymmetric shifts of higher energetic sublevels withquantum number: n 1,2,3,... of Bivacuum excitation: (3/2); (5/2) and(7/2) are characterized by the following ratios of their distance from central point:1.19; 1.1 and 1.046 correspondingly. Such a tendency points that the closer is energy ofelementary particle to zero-point one, the bigger is asymmetry of its exchange interactionwith Bivacuum in a course of C W pulsation of pair (F F.

In terms of our model, asymmetry of pair in the wave phase(F FW CVC CVC is related with asymmetry of Bivacuum gap symmetryoscillation (BvSO) and Virtual Pressure Waves of positive and negative vacuum:VirP |VPW VPW |, as a consequence of [C W pulsation of pair. Theasymmetry is generated by uncompensated sub-elementary particle in composition oftriplets:

F FW F C F FC F W 10.2

The analogy between some features of ancient diagram and our wave-corpuscle dualitymodel is surprising, indeed. The kind of asymmetry described, is responsible forgravitation, as will be shown below.

11 The Link Between the Maxwell’s Formalism and Unified TheoryUsing (7.18a), the quantization rule for photons can be expressed as:

nEel nCW nVV nmV

mVc2 11.1

where: mV c2 nV and mV

c2 nV are the quantized energies of the actualvortex and complementary torus of sub-elementary particle.

From this formula one can see that the electromagnetic energy is a result of quantumbeats with frequency (CW) between the actual and complementary corpuscular states ofsubquantum particles and antiparticles of the fermions. Such a pulsation represent thereversible quantum jumps from corpuscular [C] phase to the wave [W] phase and back withemission absorption of cumulative virtual cloud (CVC).

The electromagnetic contribution to the total energy of wave B (11.1) is defined by thefine structure constant, as a factor:

EE ECW n B n V V

2 rotVVr rotVV

r 11.2

where: n is the unit-vector, common for both vortices; CVC V V is a beats

frequency between actual vortex and complementary torus.In this consideration it is assumed, that all of subquantum particles/antiparticles,

forming actual and complementary vortices of [C] phase of sub-elementary particles, havethe same angle frequency: V and V , correspondingly.

We can express the divergency of Pointing vector: P c/4EHvia difference ofcontributions, related to actual vortex and complementary toruses, using known relation ofvector analysis:

divEH 4c divP H rotE E rotH 11.3

where H and E are the magnetic and electric components of cumulative virtual cloudsof subquantum particles, radiated and absorbed in a course of correlated [C W pulsationof two triplets of subquantum particles and antiparticles of photon.

Two structure of photon, corresponding to its two polarization and spin S 1, we

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present as superposition of two: electron positron triplets (Fig.4):

2F F F F S 1

2F F F F S 1

11.4

11.4a

The analogy between (11.2) and (11.3), illustrating the dynamic [vortex torus]dipole, is evident, if we assume:

V H rotE~ 2 rotVV

r

V E rotH~ 2 rotVV

r

11.5

11.5a

Then, the divergence of Pointing vector will take a form:

4c divP 2 rotVV

r rotVV

r ~mV

mVc2 11.6

We can see from 11.5 and 11.5a, that the properties of both: magnetic and electric fieldsare implemented in each of our torus and antitorus of Bivacuum dipoles.

We may apply also the Green theorems, interrelating the volume and surface integrals,to our duality model. One of known Green theorems looks like:

V

2 2dV

S

dS dV 11.7

If we define the scalar functions, as the instant energies of the actual andcomplementary states of [C] phase of sub-elementary particles as mVc2 and mVc2, then, taking into account that

2 divgrad divgrad mC c2

2 divgrad divgrad mC c2

11.8 11.8a

formula (11.7) can be presented in form:

V

mVc22mVc2 mVc22mVc2dV

S

dS mVc2mVc2 mVc2mVc2dV

11.9

119a

The upper part of (11.9) represents the energy of sub-elementary particle in [C] phaseand the lower part - the energy of cumulative virtual cloud (CVC), corresponding to [W]phase of particle.

12. Possible Role of Golden Mean in the Properties of Atoms.12.1 New Interpretation of Compton effect

Analyzing the experimental scattering of X-rays on the carbon atoms of paraffin andgraphite target, formed by the carbon atoms only, Compton found that the X-rays wavelength increasing ( 0 after scattering on the electrons of carbon has thefollowing dependence on the scattering angle ( angle between the incident andscattered beam):

82

2 hm0c sin2 2C sin2 12.1

Compton got this formula from the laws of momentum and energy conservation of thesystem [X-photon electron in atom] before and after scattering, in form:

k k mv thewavenumbers : k /c and k /c

m0c2 mc2 m m0/1 v/c21/2

12.2

12.2a

However, Compton made a strong assumption, that the electron beforeenergy/momentum exchange with X-photon is in rest, i.e. his group velocity is zero: v 0.

We propose the new interpretation of the Compton experiments, assuming that onlytranslational group velocity of the electron is close to zero: vtr 0, but it is not true forrotational velocity vrot c of sub-elementary fermions around common axes, whenit follows Golden mean and determines the rest mass of particle.

At the conditions of Golden mean, providing by fast spinning of sub-elementaryparticles of triplets [F F F around common axis with frequency 0 m0c2/,when: mV mV mV e

m0, the resulting energy and momentum of the electron

turns to:

EC EW

mV mVc2 mVvrot2

m0c2 m002L0

2

P mV mVc m0c mVvrot2 /c

12.3

12.3a

The corresponding resulting de Broglie wave length is equal to Compton length of theelectron:

res C hm0c 24 1013m

the Compton radius :

Lres C/2 L0 m0c 3.82 1013m

12.4

12.4a

The Compton radius of the proton is equal to:

LP P2

mPc 2.1 1016m 12.5

The Compton radius of the electron is about 2000 bigger, than that of proton:

L0/LP mP/m0 1836.15 12.6

Scattering of photon on the electron or proton, change their momentum and kineticenergy related to translations only, not affecting the parameters of spinning.

New interpretation of the experimental data, obtained by Compton in 1923, confirmsthe consequence of our UT, that the rest mass and spin of elementary particles areinterrelated parameters, provided by Bivacuum dipoles symmetry shift.

12.2 The Bohr’s Model and the Alternative Duality Model of Hydrogen AtomThe radius of the Hydrogen atom after Bohr can be evaluated from the equality of

Coulomb attraction force between proton and electron and centripetal force, acting on the

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electron, rotating around proton:

e2

r2 mv2r 12.7

The Coulomb potentials of the electron and proton in hydrogen atom should be equal. Itmeans a condition:

mVv2e

mVv2p 12.7a

This relation is valid, when the difference in mass of the electron and proton in atom iscompensated by the difference in their velocities of longitudinal vibrations:

mV e

mV p

v2pv2e

12.7b

It leads from the quantization of the angular momentum, that

mvr nwhere n 1,2,3. . .

12.8

Excluding the velocity (v from eqs. 12.7 and 12.8, we get the quantized radius of thehydrogen orbit:

rn 2

me2 n2 12.9

For the 1st stationary orbit (n 1, assuming that the mass of the electron is equal to itsrest mass (m m0, formula (12.9) turns to the 1st Bohr orbit of the hydrogen atom (aB :

aB rn1 2

me2 L0

m0c 12.10

where the Compton radius of the electron is L0 m0c

The energy of the electron on the n orbit of the hydrogen atom, after Bohr is equal to:

En me4

21n2 12.11

In another form this energy can be presented as:

En 2m0c2 1n2 12.12

where the fine structure constant is:

e2/c 1/137 12.13

In accordance to our Unified theory, just the Golden Mean conditions of elementaryparticles gyration v/c2 0.618 stand for the rest mass and electric chargeorigination. The translational zero-point oscillation of the electron, accompanied C Wpulsation are responsible for its external electric potential.

One of conditions of hydrogen atom stability is the equality of the electron’s andproton’s electromagnetic potentials. This means that the kinetic energy of the proton inH-atom, determined by its zero-point oscillations, should be the same as that of electron.

84

For such a case we have the electromagnetic balance equation of H-atom:

E0el meve

2 EP mP vP2 12.14

where: me me0/ and mP mP0/ are the actual masses of the electronand proton, corresponding to GM conditions for hydrogen atom; ve c1/2 iszero-point velocity of the electron.

The most probable zero-point group velocity of the proton vibration in H-atom from(12.14) is:

vP ve me

mP1/2

c1/2 me

mP

1/2

12.15

From (12.14 and 12.15) we can get the following ratio of the effective de Broglieradiuses of zero-point oscillations for the electron and proton:

Le0LP0

mV P

vPmV e

ve0 ve

vP mP

me1/2

~42 12.16

The spatial image of the hydrogen atom at Golden mean conditions represents thepair of triplets from sub-elementary fermions of different lepton generation: the proton F F F p and the electron F F F e , each of them characterizingby the own rotational-translational dynamics and frequency of C W pulsation.The electron with resulting dimension in [C] phase, equal to Compton radius:

L0 /m0c LL1/2, participate in three dynamic process:a) fast gyroscopic spinning/rotation with Compton frequency, equal to Golden mean

one and to the fundamental frequency of Bivacuum: 0e m0

ec2/;b) zero-point vibrations with most probable velocity: ve c1/2, caused by

C W pulsation of the unpaired sub-elementary fermion F;c) rotation around the proton along the 1st orbit with Bohr radius (aB L0/ of the

atom with velocity (vB c, corresponding to its standing de Broglie wave condition.In [W] phase of the electron, the uncompensated subquantum particle of the electron

turns to pair [BVF cumulative virtual cloud (CVC].The most probable radius of CVC, as a carrier of EM potential is equal to

(Kaivarainen, 2004):

LWel 1/2/L0 0.786 L0 0.786 aB 12.17

which is about 108 times more than the Compton radius (L0, pertinent for [C] phase of theelectron.The proton, pulsating like the electron between [C] and [W] phase, participates only in

Golden mean (GM) spinning, providing his mass of rest (m0P origination and zero-pointoscillation, responsible for its electromagnetic potential.

The frequency of correlated [C W pulsation of triplets of sub-elementary particles of generation, forming proton, is much higher (about 1800 times), than that of the electron:

CWP P m0Pc2

CWe e m0ec2

12.18

There are no charge in [C] phase of the electron and proton and no EM interactionbetween them in hydrogen atom. So, the EM interaction in H-atom is switched on and off

85

in the process of the electron and proton C W pulsation.As far, the charge density is oscillating, as a consequence of C W pulsation of the

spinning electron and its rotation around nuclear, the interpretation of dispersiveVan-der-Waals attraction, as a consequence of coherently flickering charge of atoms andmolecules, remains valid in our model.In complex neutral atoms, containing the same number of the electrons and protons, the

C W cycles of each selected [electron proton] pair - are accompanied bycorresponding quantized 3D standing waves formation.

Standing waves, formed by pairs of electrons with opposite spins and counterphaseC W and [W C pulsation, are more symmetric and stable, than in atoms withunpaired electrons.

Formation of molecules from atoms in a different chemical reactions is a result ofunification of unpaired electrons and creation of additional symmetrical standing waves B.

In accordance to our model, the pulsations of all electrons with opposite spins arecounterphase in atoms and small molecules. This condition defines spatial compatibilityand stability of [electron-electron] and [electron-proton] pairs.

13. Unified Theory (UT) and General Theory of Relativity13.1 The Difference and Correlation Between

Unified Theory (UT) and General Theory of RelativityEinstein found out, that gravitational field changes the trajectory of probe body from

the straight-line to geodesic one due to curving of conventional two-dimensional surface.The Lobachevskian geometry on curved surface was used in Einstein’s classic theory ofgravitation. The criteria of surface curvature of sphere is a curvature radius (R), defined as:

R S 13.1

where S is a square of triangle on the flat surface; R is a sphere radius; is a sum ofangles in triangle.

The sum of angles in triangle ( on the flat surface is equal to 1800 and curvatureR . For the other hand, on curved surface of radius 0 R , the sum of angles is

S/R2 13.2

When 0, the curvature R 0 is positive; when 0, the curvatureis imaginary (iR.

In our Gravitation theory instead space-time curvature [R], we introduce BivacuumSymmetry Curvature (LCur. It is defined, as a radius of sphere of virtual Bosecondensation (VirBC), equal to that of domain of nonlocality in secondary Bivacuum (seeeq. 8.71), generated by gravitating particle with mass (mV and reduced velocityv/c2 0.618 :

R~LCur LG

VirBC L0

2 v/c2 3/2 13.3

where L0 /m0c is the Compton length of particle.The Bivacuum curvatures, induced by particles with mass, equal to that of the electron

and proton where calculated in this work (chapter 8).The analogy between R and LCur is obvious. However, we have to mention, that in

accordance to 13.3 the Universe is not flat, but very close to such, even in the absence of

86

external motion of Bivacuum dipoles, when v 0. This phenomena can be responsible forgravitating cold dark matter, pertinent even for primordial Bivacuum, i.e. in the absence ofmatter and fields. For the other hand, the negative pressure energy in the Universe is aconsequence of antigravitation effect. Its possibility follows from our hydrodynamic modelof gravity, in conditions, when the phase of pulsing particles became opposite.

13.2 The explanation of Red Shift of Photons in Unified TheoryAs well, as General theory of relativity (GR), UT can explain the red shift of photons in

gravitational field. The known relation between the negative gravitational potential ( andthe light frequency in this field (, following from GR (Landau and Lifshitz, 1988) is: 01 /c2 can be expressed via gravitational field energy of elementary particle:EG mV

and the total energy of this particle: Etot mVc2 as:

0 1 mV

mVc2 0 1 EGEtot

13.4

We can see, that the frequency of light/photon is increasing with increasing thegravitational field energy.

Using (8.10) for energy of gravitational field and taking into account that mV

m0/ 1 v2/c2 we get for the ratio EGEtot

c2 :

EGFF /mVc2 /c2 r

r i 1 m02

mV 2

FF

Dis

or : /c2 rr

i2 v2/c2FFDis

13.5

13.5a

where: m02

mV 2 mV

mV; rr is a ratio of unitary vector to the distance from particle.

The known relation between the shift of light frequency ( 1 2 and thedifference in gravitational potentials in place of photon emission (1 and its registration(2 is: 112/c2. This formula,, can be easily expressed via difference incorresponding energies of gravitational fields, taking into account that the both potentialsare negative:

1 EG2 EG

1 13.6

If, for example, EG2 and EG

1 correspond to gravitational fields energies on the Earthand Sun, i.e. EG

2 EG1, the frequency shift: 1 2 will be negative. This

phenomena is named a red shift.The increasing of the photons frequency in stronger gravitational field, as compared to

weaker one, follows also from our Unified theory. The energy/frequency of photons in both- corpuscular and wave phase can be expressed from (7.13 and 7.13b) as:

Eph hph CVC CVC 2mV c2 2m0c2

1 LphC rotc

2 13.7

This relation for photon frequency has certain similarity with formula for gravitationalenergy/frequency (8.10a,b), also including a sum of energies of positive and negativecumulative virtual clouds: CVC CVC , emitted absorbed in the process of C Wpulsation of pairs of sub-elementary fermion and antifermion:

87

EGFF hG i CVCF CVC

F 13.8

We may see from comparison of 13.7 and 13.8 that the more is energy and frequency ofgravitational field EGFF hG, determined by energy of CVC and CVC,accompanied by excitation of positive and negative virtual pressure waves: VPWq

andVPWq

, the more is the positive increment to energy/frequency of photon.Consequently, the results of GR are reinforced and got a concrete physical mechanism

in the framework of our Unified Theory of Bivacuum, duality of matter and fields.

14. The Principle of least action, the Second and Third laws of Thermodynamics,as a consequence of Bivacuum Virtual Pressure Waves (VPWq

action on particles14.1 The quantum roots of Principle of least action

Let us analyze the formula of action in Maupertuis-Lagrange form:

Sextt1

t0

2Tkext dt 14.1

The action can be presented also using the Lagrange function, representing differencebetween the kinetic and potential energy: L Tk V. Using 6.8a, we can see, thatL 1 v/c2 m0c2 and the action in Hamilton form can be expressed as:

S m0c2t1

t0

1 v/c2 dt

or : S m0c2 1 v/c2 t

14.1a

14.1b

The principle of Least action, responsible for choosing one of number of possibleparticles trajectories from one configuration to another has a form:

Sext 0 14.2

This means, that the optimal trajectory of each particle corresponds to minimumvariations of its external kinetic energy and time.

The time interval: t t1 t2 ntB we take as a quantized period of the de Brogliewave of particle (tB 1/B:

t t1 t2 ntB n/Bn 1,2,3. . . .

14.3

Using eqs.(14.1 and 6.10a), we get for the dependence of action in Maupertuis-Lagrangeform on introduced Bivacuum tuning energy TE:

Sext 2Tkext t mV v2 t 1 RmV

c2 m0c2tor : Sext mV

v2 t 1 RTE t

where relativistic factor: R 1 v/c2

14.4 14.4a

14.4b

88

mV v2 2Tkext is the doubled kinetic energy of particle.

We introduce here the new notion of Bivacuum Tuning Energy (TE), dependent onenergy of Bivacuum virtual pressure waves (EVPWq as:

TE Etot EVPWq TE CW q0

mVc2 qm0c2 mV

v21 R

14.5

14.5a

where: q j k q 1,2,3. . . . is a quantum number, characterizing the excitation ofBivacuum Virtual Pressure Waves (VPWq

, interacting with paired sub-elementaryfermions of triplets F F in the process of [C W pulsation:

F FW F C F FC F W 14.5b

The frequency difference (TE of Bivacuum Tuning energy is:

TE mV qm0c2/ C W q0 14.6

where: mV m0 and C W 0.

Tending of TE and TE to zero due to influence of basic VPWq1 at q 1 on

triplets dynamics, minimizing their kinetic energy, means realization of principle ofLeast action.14.2 Mechanism of particles acceleration by high-frequency Bivacuum virtual pressure

wavesThe influence of Tuning energy (TE) of Bivacuum on matter is a result of forced

resonance, leading to synchronization between fundamental frequency(VPW q0 qm0c2/e,, of virtual pressure waves (VPWi

) of Bivacuum and[C W] pulsations of elementary particles.The main source of ’free’ energy of Bivacuum, acting on particles, is combinational

resonance of de Broglie waves of real elementary particles with fundamental Bivacuumvirtual pressure waves (VPWq

of basic quantized frequency q0i qm0

i c2/. Thecondition of combinational resonance is:

VPWq q0i CW

or : EVPW qm0i c2 mV

c2

14.7

14.7a

The energy exchange between VPW VPW and real particles in the process ofC W pulsation of pairs F Fx,y of triplets F Fx,y F zi at pull-in-range state accelerate them, driving to resonant conditions (14.7 and 14.7a) at q 2,3. . . ,i.e. bigger than q 1. This statement will be proved below.

In accordance to rules of combinational resonance of Bivacuum virtual pressure waveswith elementary particles, we have the following relation between quantized energy andfrequency of VPW and energy/frequency of triplets C W pulsation in resonanceconditions:

89

EVPW VPWi q0

i CWi R0 B

or : EVPW qm0i c2 Rm0

i c2 mVv2 Rm0

i c2 m0i c2v/c2

R

or : q R v/c2

R

R 1 v/c2; q 1,2,3. . . integer numbers)

14.8

14.8a

14.8b

where the angle frequency of de Broglie waves is: B1,2,3 and:

B /2mVLB2 mV

v2/2 14.9

The important relation between translational most probable velocity of particle (v) andquantization number (q, corresponding to resonant interaction of Bivacuum VPWq

withpulsing particles, derived from (14.8b) is:

v c q21q2

1/2

14.10

At the conditions of triplets fusion, when q 1, the translational velocity of particle iszero: vn1 0. When the quantized energy of VPWq

, corresponds to q 2, the resonanttranslational velocity of particle should be: vq2 c 0.866 2,6 1010cm/s. At q 3,wehave from (14.10): vq3 c 0.942 2,83 1010cm/s.

On the other hand, if velocity of particles is high enough and corresponds to q 1,5 in(3.11), their pull-in range interaction with excited VPWq2

can accelerate them up toconditions: q 2, v 2,6 1010cm/s. In turn, if the starting particles velocity correspondsto q 2,5, their forced resonance with even more excited VPWq3

should accelerate themup to conditions: q 3, corresponding to v 2,83 1010cm/s. The described mechanismof Bivacuum - Matter interaction, is a general physical background of all kinds of overunitydevices.

14.3 The quantum roots of 2nd and 3d laws of thermodynamicsAt the velocity of particles (v, corresponding to q 1,5, the interaction of these

pulsing particles with basic q 1 virtual pressure waves of Bivacuum (VPWn1 due to

forced resonance should slow down their velocity, driving translational mobility ofparticles to resonant conditions: q 1, v 0.The second law of thermodynamics, formulated as a spontaneous irreversible

transferring of the heat energy from the warm body to the cooler body or surroundingmedium, also means slowing down the kinetic energy of particles, composing this body.Consequently, the 2nd law of thermodynamics, as well as Principle of least action, can be aconsequence of Tuning energy (TE) minimization, slowing down particles thermaltranslational dynamics at pull-in range synchronization conditions:

TE C W 0v0 0

at 1,5 q v0 q 1

14.11

The third law of thermodynamics states, that the entropy of equilibrium system istending to zero at the absolute temperature close to zero. Again, this may be a consequenceof forced combinational resonance between basic VPWn1

and particles C W

90

pulsation, when translational velocity of particles v 0 and TE C W 0v0 0

at q 1,5 v0 q 1. At these conditions in accordance with Hierarchic theory of

condensed matter (Kaivarainen, 1995; 2001; 2001a) the de Broglie wave length of atoms istending to infinity and state of macroscopic Bose condensation of ultimate coherence andorder, i.e. minimum entropy.

This result of our Unified theory could explain the energy conservation law,independently of the Universe cooling. Decreasing of thermal kinetic energy in the processof cooling is compensated by increasing of potential energy of the matter particle-particleinteraction, accompanied Bose condensation. The energy of resonant interaction of matterwith Bivacuum virtual pressure waves of basic energy: EVPW q0 qm0c2 at q 1 isalso increasing at v 0, keeping the total energy of the Universe permanent.

14.4 The new approach to problem of TimeIt follows from the section above, that the Principle of least action is a consequence of

basic Tuning energy (TEq1) of Bivacuum influence on particles, driving the properties ofmatter on all hierarchical levels to Golden mean condition. It is shown, using the formulafor action (14.4a), that the introduced dimensionless internal pace of time for any closedcoherent system is determined by the pace of its kinetic energy change (anisotropic ingeneral case), related to changes of Tuning energy (eq.14.5):

dt/t d ln t d lnTkx,,y,z d ln1 RTEx,y,z 14.12

Using relations (14.12 and 14.5a), the pace of the internal time and time itself for closedsystem of particles can be presented via their acceleration and velocity:

dtt d ln t dv

v2 v/c2

1 v/c2x,y,z

14.13

t vdv /dt

1 v/c2

2 v/c2 1 RTEd 1 RTE/dt x,y,z

14.14

The pace of time and time itself are positive (t 0, if the particle motion is slowingdown (dv /dt 0 and dv 0 and negative, if particles are accelerating. For example, attemperature decreasing the time and its pace are positive. At temperature increasing theyare negative. Oscillations of atoms and molecules in condensed matter, like pendulums, areaccompanied by alternation the sign of acceleration and, consequently, sign of time. TheCorpuscle Wave transition, as it follows from our theory, is accompanied by decreasingof mass and kinetic energy of unpaired sub-elementary fermion and converting the kineticenergy of [C] phase to potential energy of CVC of [W] phase. Consequently, thissemiperiod of pulsation is characterized by positive course of time (14.12). On contrary, thereverse W C transition means the negative time course. The time oscillation frequencyof particles and its kinetic and total energy, in accordance to mechanism, described above,can be changed due to forced resonance of VPWq

with [C W pulsation of pairedsub-elementary fermions. For the other hand the energy of quasi-symmetric excitedBivacuum VPWq1

and VPWq1 is opposite and compensate each other. However, the

increasing of their absolute values can be a source of free energy of Bivacuum, foroverunity devices.

This consequence of our microscopic quantum approach for overunity theory (see alsosection 19), including mass and time oscillation, using partly the negative energy of

91

Bivacuum, have some common with ideas, developed by W. Alek (2005) for macroscopicsystems.

In the absence of particles acceleration (dv /dt 0 and dv 0, the time is infinitiveand its pace zero:

t and dtt 0

at dv /dt 0 and v const

The postulated principle [I] of conservation of internal kinetic energy of torus (V andantitorus (V of symmetric and asymmetric Bivacuum fermions/antifermions: BVFas

F (eq.2.1) in fact reflects the condition of infinitive life-time of Bivacuum dipoles insymmetric and asymmetric corpuscular states. The latter means a stability ofsub-elementary fermions and elementary particles, formed by them.

In scale of the Universe, the decreasing of all-pervading Tuning energy (TE in (14.14):

d 1 RTE/dt 0 t 0 14.15

means positive direction of ”TIME ARROW” t 0. This corresponds to tending of theactual energy of particles to the energy of rest mass: mV

c2 qm0c2 at v 0, meaningcooling of the Universe, if quantization number of virtual pressure waves (VPW) isminimum: q 1.

The presented approach to the TIME problem differs from the conventional one,following from relativistic theory, however, they do not contradict each other. For example,from (14.14) we can see, that in relativistic conditions, when as a result of accelerationdv /dt 0 and v c the negative internal time of closed system is tending to zero, likeit follows from Lorentz relations for the ’own’ time of system.

The internal time (14.14) turns to infinity and its pace (14.13) to zero in the absence ofacceleration and deceleration in a closed system dv /dt 0. The permanent (t collective motion of the electrons and atoms of 4He in superconductors and superfluidliquids, correspondingly, with constant velocity (v const in the absence of collisionsand accelerations are good examples.

In Bivacuum with superfluid properties the existence of stable excitations, likequantized toruses/antitoruses of Bivacuum dipoles and vortical filaments - virtual guides(VirG), described in section 16, are also in-line with out time theory.

Each closed real systems of virtual Cooper pairs: NBVF BVF , forming doubleVirG in Bivacuum, of elementary particles and macroscopic objects, rotating aroundcommon center with radius r on stable orbits, like in atoms, planetary systems, galactics,etc. is characterized by different centripetal acceleration:

dvdt v 2

r 2 r 14.16

where the velocity of rotation is related to the radius and angle frequency of rotation () as:

v 2r r 14.17

Putting 14.16 and 14.17 into 14.14, we get the dependence of time for rotating systemon its radius and angle frequency:

t 1

1 r/c2

2 r/c2 1

m0/mV 2

1 m0/mV 2 14.18

92

where from (3.11) we have:

1 r/c2 1 v/c2 mV /mV

m0/mV 2 14.19

From 4.19 and 4.18 we can see, that at the limit case of zero-point oscillation, whenr v 0 andmV

m0, the characteristic time of such system is tending to infinity:

t 12 r

2v 14.20

However, it follows from 14.18, that even in the ’empty’ secondary Bivacuum a lowfrequency rotation of virtual filaments/guides (VirG), composed from Cooper pairs ofBivacuum fermions, the characteristic time is not uncertain or infinitive, like in primordialBivacuum. The presence of dynamics in any system means presence of time. The rotationof VirG, connecting elementary particles, is due to asymmetry of Bivacuum fermions,forming them, induced by external fields.

The closed systems of virtual particles and virtual waves in Bivacuum do not follow thecausality principle and the notion of time for such a systems is uncertain. In conditions ofprimordial symmetric Bivacuum, when any external dynamics of Bivacuum dipoles isabsent, the time is absent also.

At conditions: [v c const, valid for the case of photons in primordial Bivacuum,we get from (14.14) the uncertainty for time, like: t 0/0. The similar result we get forstate of virtual Bose condensate (VirBC) in Bivacuum, when the external translationalvelocity of Bivacuum fermions (BVF and Bivacuum bosons (BVB is equal to zero(v 0 const. The latter condition corresponds to totally symmetric BVF and BVB, ofprimordial Bivacuum, when their torus (V and antitorus (V mass, charge and magneticmoments compensate each other (Kaivarainen, 2005). It follows from (14.14) that theinternal time for each selected closed system of particles is a parameter, characterizing theaverage velocity and acceleration of these particles, i.e. this system dynamics.

This new concept of time is extending that of relativistic theory. The advantage is thatour formula for time includes not only velocity, but also acceleration.

15. Virtual Replica (VR) of matter in BivacuumThe basically new concept of Virtual replica (VR) or virtual hologram of any material

object in Bivacuum, is introduced in our Unified theory (Kaivarainen, 2004, 2005). The VRis result of interference of all-pervading quantized Virtual Pressure Waves (VPWq

andVPWq

and Virtual Spin waves (VirSWqS1/2) of Bivacuum, working as the ”reference

waves” in hologram formation, and the same waves, modulated by de Broglie waves ofatoms and molecules, representing the ”object waves” VPWm

and VirSWm1/2.

The frequencies of basic reference virtual pressure waves (VPWq1 VPW0

andvirtual spin waves (VirSWq1

1/2 VirSW01/2 of Bivacuum are equal to Compton

frequencies of three electron generation, like the carrying frequencies of C Wpulsation of sub-elementary fermions of triplets at zero external translational velocity ofparticles v 0:

VPW0 VirSW0 0 CWv0 m0c2/ i

Two kinds of primary wave modulation (VPWm and VirSWm

1/2 are realized bycumulative virtual clouds (CVC), emitted/absorbed in the process of C W pulsationof pairs: F FC F FW of elementary triplets (electrons, protons, neutrons) F F F i , and the recoil angular momentum, generated by CVC1/2 ofunpaired sub-elementary fermion F i , correspondingly:

93

F FC F

WCVC Recoil

CVC Antirecoil F

FW FC 15.1

The in-phase C W pulsation of a sub-elementary fermion F and antifermion F ofpair F F, accompanied by reversible [emission absorption] of cumulative virtualclouds CVC and CVC and the ’object’ virtual pressure wave (VPWm

and VPWm

excitation. However, the recoil energy and the angular momenta of CVC and CVC of Fand F of pairs compensate each other and the resulting recoil energy of F F is zero.

Superposition of VPWm and VPWm

, excited by cumulative virtual clouds: CVC andCVC, emitted and absorbed in the process of the in-phase C W pulsation of pairsF F of rotating triplets, activate quantized magnetic whirls in Bivacuum. Thestability of VR of object, as a hierarchical system of quantized metastable torus-like andvortex filaments structures formed by VPWm

and by VirSWm1/2 excited by paired and

unpaired sub-elementary fermions, correspondingly, in superfluid Bivacuum, could beresponsible for so-called ”phantom effect” of object after its destroyment or removing toremote place.

15.1 Bivacuum perturbations, induced by the oscillation of the total energyof de Broglie waves, accompanied

by their thermal vibrations and recoil antirecoil effectsIn contrast to the situation with unpaired sub-elementary fermion F in triplets, the

recoil/antirecoil momenta and energy, accompanying the in-phase emission/absorption ofCVCS1/2 and CVCS1/2 by F and F of pair F F, totally compensate each otherin the process of their C W pulsation. Such pairs display the properties of neutralparticles with zero spin and zero rest mass:

F FCECVC ECVC VP

FF

ECVC ECVC VPFF

F FW 15.2

The total energy increment of elementary particle, equal to that of each ofsub-elementary fermions of triplet, generated in nonequilibrium processes, accompanied byentropy change, like melting, boiling, etc., can be presented in a few manners:

Etot mVc2 m0c2

1 v/c21/2

m0vR3 v p

R2 v h

BR2 v

or : Etot mV mV

c2c/v2 2TkR2

vv

or : Etot 2TkR2

vv Rm0c2rot

in mVv2 trext

15.3

15.4

15.4a

where: R 1 v/c2 is the relativistic factor; v is the increment of the externaltranslational velocity of particle; the actual inertial mass of sub-elementary particle is:mV

m0/R; p mV v h/B is the external translational momentum of unpaired

sub-elementary particle F i , equal to that of whole triplet F F F i ;B h/p is the de Broglie wave of particle; 2Tk mV

v2 is a doubled kinetic energy; lnv v/v.

94

The increments of internal rotational and external translational contributions to totalenergy of the de Broglie wave (see eq. 15.4a) are, correspondingly:

Rm0c2rotin 2Tkv/v

mVv2 trext 2Tk trext 2Tk

1R2

R2vv

15.5

15.5a

The time derivative of total energy of elementary de Broglie wave, following from 6.1 -6.1b is:

dEtotdt 2Tk

R2vdvdt

2TkR2

d lnvdt 15.5b

Between the increments of energy of triplets, equal to that of unpaired Etot EFand increments of modulated CVCm and CVCm , emitted by pair F F in the processof C W transition, the direct correlation is existing.

These cumulative virtual clouds modulated by particle’s de Broglie wave(B h/mV

v: CVCm and CVCm of paired sub-elementary fermions, superimposed withbasic virtual pressure waves (VPW0

of Bivacuum, turn them to the object wavesVPWm

, necessary for virtual hologram of the object formation:

EFFF h

BR2 v 2TkR2

lnv CVCm VPWm

EFFF CVCm VPWm

15.6

15.6a

The virtual pressure waves represent oscillations of corresponding virtual pressure(VirPm .

The increment of total energy of fermion or antifermion, equal to increment of itsunpaired sub-elementary fermion can be presented via increments of paired sub-elementaryfermions (15.5 and 15.5a), like:

Etot EF 12 EF

FF EFFF 1

2 EFFF EF

FF Tk V 15.7

where, the contributions of the kinetic and potential energy increments to the totalenergy increment, interrelated with increments of positive and negative virtual pressures(VirP, are, correspondingly:

Tk 12 EF

FF EFFF ~ 1

2 VirP VirP ~ mV

v2F

V 12 EF

FF EFFF ~ 1

2 VirP VirP ~ mV

mV cF

2

15.8

15.8a

The specific information of any object is imprinted in its Virtual Replica (VR), becausecumulative virtual clouds (CVCm ) of the object’s elementary particles and theirsuperposition with Bivacuum pressure waves and Virtual spin waves: VPWm

andVirSWm

1/2 are modulated by frequency, phase and amplitude of de Broglie waves ofmolecules, composing this object. Comparing eqs. 8.8a and 6.9 we may see, that themodulated gravitational virtual pressure waves form a part of VR.15.2 Modulation of the basic Virtual Pressure Waves (VPWq

and Virtual Spin Waves(VirSWq

1/2of Bivacuum by molecular translations and librations

95

The external translational/librational kinetic energy of particle (Tk tr,lb is directlyrelated to its de Broglie wave length (B, the group (v, phase velocity (vph andfrequency (B B/2:

B hmV

v h

2mVTk

vphB 2 vphB tr,lb

15.9

where the de Broglie wave frequency is related to its length and kinetic energy ofparticle as:

B B2 h

2mVB2

mVv2

2h tr,lb 15.10

It follows from our model, that zero-point frequency of [C W pulsation (0 i ofsub-elementary fermions and antifermions, forming triplets of elementary particles F F F i , accompanied by [emission absorbtion of cumulative virtualclouds CVC has has the same value, as a basic (reference) frequencyq1 0 m0c2/ i of Bivacuum.

The total energy of de Broglie wave and resulting frequency of pulsation (CW (seeeq. 7.4) is a result of modulation of the internal frequency, related to the rest mass ofparticle, by the empirical most probable frequency of de Broglie wave of the whole particle(B, determined by its most probable external momentum: p mV

v.In a composition of condensed matter this value is different for thermal librations and

translation of molecules. The corresponding most probable modulation frequencies oftranslational and librational de Broglie waves are possible to calculate, using newHierarchic theory of condensed matter and based on this theory computer program(Kaivarainen, 2001; 2003; 2004; 2005).

The interference between the basic q j k 1 reference virtual spin waves(VirSWq1

1/2 and virtual pressure waves VPWq1 of Bivacuum with virtual ’object waves’,

modulated by the librational and translational de Broglie waves (lb,tr h/mVv) of

molecules, produce the holographic-like image or Virtual Replicas (VR) of the object.The frequencies of virtual pressure waves (VPWm

and virtual spin waves (VirSWm1/2

are modulated by de Broglie waves of the object particles. Corresponding modulationfrequencies are related to frequencies of librational (lb and translational (tr de Brogliewaves of molecules of matter (8.10) in accordance to rules of combinational resonance:

VPWm

i R0i gtr rlb R0

i gtr

VirSWm1/2

i R0i rlb gtr R0

i rlb

R 1 v/c2; g,r 1,2,3. . . integer numbers)

15.11

15.11a

Each of 24 collective excitations of condensed matter, introduced in our Hierarchictheory (Kaivarainen, 1995; 2001, 2004), has his own characteristic frequency and can beimprinted in Virtual Replica of the object, as a corresponding pattern.

Three kinds of modulations: frequency, amplitude and phase of the object (VPWm

and (VirSWm1/2 by de Broglie waves of the object’s molecules may be described by

known relations (Prochorov, 1999):1. The frequencies of virtual pressure waves (

VPWM and spin waves (

VirSWM ,

modulated by translational and librational de Broglie waves of the object’s molecules, canbe presented as:

96

VPWmM R0

i Btr cosBtr t

VirSWm

1/2M R0

i Blb cosBlb t

15.12

15.12a

The Compton pulsation frequency of elementary particles (section 1.4; 1.5) is equal tobasic frequency of Bivacuum virtual waves at q j k 1:

0i m0

i c2/ VPWq1 ,ViSWq1

i 15.12b

Such kind of modulation is accompanied by two satellites with frequencies: (0i B

tr,lband (0

i Btr,lb tr,lbi . The latter is named frequency deviation. In our case:

0e ~1021s1 B

tr,lb ~ 1012s1 and tr,lb Btr,lb.The temperature of condensed matter and phase transitions may influence the

modulation frequencies of de Broglie waves of its molecules.

2. The amplitudes of virtual pressure waves (VPWm and virtual spin waves VirSWm

1/2

(informational waves) modulated by the object are dependent on translational andlibrational de Broglie waves frequencies as:

AVPWm A0 sinR0i t B

tr sin t cosBtr t

IVirSWm1/2 I0 sinR0i t B

lb sin t cosBlb t

15.13

15.13a

where: the informational/spin field amplitude is determined by the amplitude ofBivacuum fermions [BVF BVF equilibrium constant oscillation:IS IVirSW1/2 ~KBVFBVFt

The index of frequency modulation is defined as: tr,lb/Btr,lb. The carrying

zero-point pulsation frequency of particles is equal to the basic frequency of Bivacuumvirtual waves: VPW0

,ViSW0i 0

i . Such kind of modulation is accompanied by two satelliteswith frequencies: (0

i Btr,lb and (0

i Btr,lb tr,lb. In our case:

0e~1021s1 B

tr,lb~ 1012s1 and 1.The fraction of molecules in state of mesoscopic molecular Bose condensation (mBC),

representing, coherent clusters (Kaivarainen, 2001a,b; 2004) is a factor, influencing theamplitude (A0) and such kind of modulation of Virtual replica of the object.

3. The phase modulated VPWm and VirSWm

1/2 by de Broglie waves of molecules,related to their translations and librations, can be described like:

AVPWmM A0 sin R0t tr sinBtrt

IVirSWm1/2M I0 sin R0t lb sinBlbt

15.14

15.14a

The value of phase increment tr,lb of modulated virtual waves of Bivacuum (VPWm

and VirSWm1/2, contains the information about geometrical properties of the object.

The phase modulation takes place, if the phase increment tr,lb is independent on themodulation frequency Btr,lb.The virtual holographic image, resulting from interference pattern of the virtual object

waves: VPWm and VirSWm

1/2, modulated (scattered) by translations and librations ofmolecules, with similar reference waves of Bivacuum (VPWq

and VirSWq1/2 contains full

information about the object’s internal dynamic and spatial properties and may be named”Virtual Replica (VR)” of the object.

15.3 The ”Ether”, ”Astral” and ”Mental” bodies, as a local,

97

distant and nonlocal components of VRI. The superpositions of individual local micro VR of the electrons, protons, neutrons

and atoms/molecules, formed by interference of de Broglie waves of these elementaryparticles with basic virtual waves of Bivacuum, stands for the total internal macroscopicvirtual replica of the object (VRmacin , localized in the volume of this object. The overallshape of (VRmacin should be close to shape of the object itself, for example, such as thehuman’s body and it organs shape. The latter corresponds to notion of the ”ether body” inEastern philosophy:

Ether Body VRmacin VRin 15.15

The internal Virtual Replica (Ether Body) is composed from virtual vortical structuresaround each triplet of elementary particles (electrons, protons and neutrons). Thesemicroscopic vortical structures are the result of two factors combination:

1. The coherent [W] phase of paired sub-elementary fermions F F in form ofcorresponding pair of Cumulative Virtual Clouds CVC CVC;

2. The fast rotation of this pair with Compton frequency: 0 m0c2/ i, correspondingto the rest mass and charge origination at Golden mean conditions.Spatial stability of condensed systems means that a hologram - like virtual structure

(VRmacin , as a system of 3D standing waves in form of curls in superfluid Bivacuum,should have location of nodes, coinciding with the most probable positions of the atomsand molecules in condensed matter.

The superposition of coherent de Broglie waves of atoms and molecules in compositionof clusters (3D standing waves B, determined by their librations and translations) representsthe mesoscopic Bose condensate: [mBC (Kaivarainen, 2001b,c). In accordance to ourtheory, this means the coherent [C W pulsations of elementary particles of thesemolecules. The violation of this coherency is accompanied by density fluctuation anddefects origination in condensed matter.

Stability of hierarchic system of whirls, forming local Virtual Replica of object (etherbody), as a hierarchical system of curls in superfluid Bivacuum (like permanent circularcurrents and whirls in superfluid 4He), could be responsible for so-called ”phantom effect”of this object.II. The external macroscopic virtual replica: VRmacext can be subdivided on two

components - distant and nonlocal:1) the distant component of external macroscopic VRdisext is a result of replication of the

internal VRmacin outside the volume of the object, as a consequence of ability of internalvirtual replica to be reproducible in any external space regions, where the interference ofvirtual system of modulated by de Broglie waves of the ’object’ virtual pressure waves:VPWm

and nonlocal VirSWm1/2 with Bivacuum reference waves: VPWq

and VirSWq1/2

may exist. The basic Bivacuum reference waves: VPWq1 and VirSWq1

1/2, necessary forvirtual hologram (VRmacext formation, are most probable.

The VRdisext, spatially separated from he body/object, may correspond to Eastern ancientnotion of the ”astral body”:

Astral BodyVRdisext 15.16

The dielectric permittivity (0 and permeability (0 in the volume of Ether and Astralbodies may differ from their averaged values in Bivacuum because of small chargesymmetry shift in Bivacuum fermions (BVF): e |e e | 0, induced by

98

recoil antirecoil effects, accompanied C W pulsation of elementary particles.Consequently, the probability of atoms and molecules excitation and ionization (dependenton Coulomb interaction between electrons and nuclears), as a result of their thermalcollisions with excessive kinetic energy, may be higher in volumes of the Astral bodies,than outside of them. This may explain their special optical properties - a shining of someobjects phantoms (ghosts) in darkness, or their specific spectrogram, representing astralbodies;

2) the nonlocal macroscopic virtual replica (VRnlext), is formed by the interference ofmodulated by molecular de Broglie waves the recoil antirecoil effects the Bivacuumvirtual spin waves: VirSWm

1/2 object spin waves with corresponding reference spinwaves of Bivacuum (VirSWq

1/2.The Eastern notion of mental body may correspond to:

MentalBody VRnlext 15.17

Hierarchical superposition of huge number of MentalBodies of all human population onthe Earth can be responsible for Global Informational Field origination, like Noosphere,proposed by Russian scientist Vernadsky in the beginning of 20th century.

The Astral and Mental bodies may partly be overlapped with Ether body. This providetheir dynamic exchange interaction.A complex Hierarchical virtual replica (HVR) of Solar system, galactics, including

Noosphere, may be considered as Hierarchical quantum supercomputer orSuperconsciousness, able to simulate all probable situations of virtual future and past(Kaivarainen, 2000; 2004). It is possible in conditions of time uncertainty: t 0/0 whenthe translational velocity v 0 and accelerations dv/dt 0 in the volume of HVR arezero (14.14).

For the other hand, our theory admit a possibility of feedback reaction between VR andthe object properties. Consequently, the phenomena of most probable event anticipation byenough sensitive physical detectors and human beings is possible in principle. This mayexplain the reproducible results of unconsciousness response (by changes of human skinconductance) of future events (presponse), obtained by Dick Bierman and Dean Radin(2002). However, in these experiments the possibility of influence of intention ofparticipant on random events generator (REG), choosing next photo (calm or emotional),like in Bierman’s experiments, also should be taken into account. Such kind of weakinfluence of humans intention on REG was demonstrated in long term studies of Danne andJahn (2003).In contrast to virtual time, the reversibility of real time looks impossible, as far it needs

the reversibility of all dynamic process in Universe due to interrelations between closedsystems of different levels of hierarchy. It is evident that such ’play back’ of the Universehistory needs the immense amount of energy redistribution in the Universe.

All three described Virtual Replicas: Ether, Astral and Mental bodies are interrelatedwith each other and physical body. The experimental evidences are existing, that betweenproperties of the Ether bodies and corresponding physical bodies of living organisms orinorganic matter, the correlation takes a place. It is confirmed by the Kirlian effect,reflecting the ionization/excitation threshold of the air molecules in volume of Ether andastral bodies.

The perturbation of the ETHER body of one object (Receptor) by the astral or mentalbody of the other object (Sender) can be imprinted in properties of physical body(condensed matter) of Receptor for a long time in form of subtle, but stable structuralperturbations. The stability of such kind of informational ’taping’ is determined by specific

99

properties of material. For example water and aqueous systems, like biological ones, arevery good for stable imprinting of virtual information and energy via introduced VirtualGuides (see chapter 5).The Ghost phenomena could be explained by reproducing of such imprinted in walls,

cells and floor information in form of virtual hologram - astral virtual replica, as a resultof certain superposition of their ETHER bodies with variable astral and nonlocal (mental)Virtual replicas of the Earth, Moon and Sun.

The nonlocalMental - Informational body formation in living organisms and humans,in accordance to our theory (Kaivarainen, 2001; 2003), is related to equilibrium shift ofdynamic equilibrium of [assembly disassembly] of coherent water clusters inmicrotubules of the neurons, accompanied series of elementary acts of consciousness innonequilibrium processes of meditation, intention and braining. Corresponding variationsof kinetic energy and momentum of water molecules can be transmitted from Sender toremote Receiver via nonlocal virtual spin-momentum-energy guides (VirGSMEext ), describedin chapter 16.

The perception of nonlocal Virtual Replica of macroscopic inorganic objects, as a resultof superposition with hierarchic system of psychic (Receiver) Virtual Replicas can explainthe Remote Vision (RV) phenomena.

In this complex process, the 1st stage is a ’target searching’ by nonlocal [mental body]of psychic, then activation of psychic’s [astral body], influencing its [ether body] andfinally - the components of physical body, like dynamics of water in microtubules ofneurons ensembles, realizing elementary acts of perception and consciousness. Thepossible mechanism of entanglement between microscopic and macroscopic objects, basedon our Unified theory, will be described in Chapters 16 and 17.

15.4 Contributions of different kind of internal dynamics of matterto Virtual Replica of the object

For each of 24 selected collective excitation of condensed matter, considered in ourHierarchic theory of matter (Kaivarainen, 2000a), the averaged thermal vibrationscontribution to VR of the object can be evaluated, using special computer program, namedComprehensive Analyzer of Matter Properties - CAMP.

The most effective source of coherent Virtual pressure waves (VPW amplitudeoscillations are the [disassembly assembly] of coherent clusters, existing in liquids(librational primary effectons) and solids (librational and translational primary effectons).Such clusters are the result of the ambient temperature mesoscopic Bose condensation(mBC) and may contain from tens (in liquids) to thousands (in solids) of coherentmolecules. Primary convertons - transition states between primary librational andtranslational effectons in liquids represents assembly - disassembly of clusters. Theseprocesses are accompanied by oscillation of molecular de Broglie waves length andfrequency, modulating the carrying frequency of Bivacuum virtual pressure waves(VPW. In accordance to described in section (15.1) mechanism, such kind of modulationfollows by formation of hologram-like Virtual Replica of the object. Other kinds ofcollective excitations in condensed matter are not so coherent (Kaivarainen, 2001; 2003)and corresponding VR components are not stable. This means that variation of mBCfraction in the object influence on the life-time of its virtual replica.

The internal kinetic energy of collective excitations: primary effectons (Tkineff , transitons

(Tkint and convertons (Tkincon vary, as a result of temperature change or more strongly as aresult of nonequilibrium cooperative process, like melting. The values of thesecontributions and their changes may be calculated using Hierarchic theory of condensedmatter, based on CAMP computer program (Kaivarainen, 2000a). The translational

100

dynamics dynamics modulate virtual Pressure Waves VPWm and librational dynamics

modulate virtual spin waves VirSWm1/2), as was demonstrated in previous section:

2Tkintot 2 Tkineff Tkint tr,lb

Tkincon

V02Z

tr,lb

nefEa1,2,3

2

2Mefvpha 2 Pefa Pefb

eff

ntEt1,2,3

2

2Mtvsres2Pd

t

V0ncon

ZEac

2

6Mcvsres2Pac

Ebc2

6Mcvsres2Pbc

EcMd

2

6Mcvsres2

con

~ VPWm VPWm

tr VirSWm1/2 VirSWm

1/2lb~ VirPVirPtr,lb

15.18

15.18a

15.18b

15.18c

where: V0 molar volume of water; Z partition function; nef concentration of primaryeffectons; Ea energy of the (a) state of the effectons; Pefa and Pefb probabilities of (a) and (b)states of the effectons; Mef, Mt andMc are the masses of primary effectons, transitons andconvertons; vpha is phase velocity of the effecton in a- state; nt and Et are concentration andenergy of transitons; ncon is concentration of convertons; Eac and Ebc and EcMd are theenergies of (a), (b) [lb/tr] convertons and macroconvertons, correspondingly.

For more detailed description of these parameters see paper: Hierarchic Theory ofCondensed Matter and its Computerized Application to Water and Ice, available on-line:http://arXiv.org/abs/physics/0102086.

16 Possible Mechanism of Quantum entanglement between distantelementary particles via Virtual Guides of spin, momentum and energy (VirGS,M,E

In accordance to our theory, the instant nonlocal quantum entanglement between two ormore distant similar elementary particles (electrons, protons, neutrons, photons), named[Sender (S)] and [Receiver (R)], revealed in a lot of experiments, started by Aspect andGrangier (1983), involves a few stages:1. Superposition of their nonlocal and distant components of Virtual replicas (VR) or

Virtual hologram, formed by interference of modulated by de Broglie waves of objectVirtual spin waves (nonlocal): VirSWm

1/2S VirSWm1/2R and Virtual pressure

waves, propagating with light velocity: VPWm S VPWm

R with correspondingreference waves of Bivacuum VirSWq

1/2 and VPWq, described in section 15.2;

2. Tuning (frequency and phase synchronization) of de Broglie waves of remoteinteracting identical particles (like electrons, protons) and their complexes in form of atomsand molecules, as a condition of Virtual Guides of spin-momentum-energy (VirGSMEbetween [S] and [R] formation (see Fig.12).

Superpositions of counterphase (VirSWm1/2 of [S] and [R], exited by their unpaired

sub-elementary fermions F of triplets F F F i of opposite spins in form ofvirtual standing waves, may stimulate formation of two kinds of Virtual Guides:

a) single nonlocal virtual guides VirGSMEBVB i - virtual microtubules from Bivacuum

bosons (BVB i. In this case the VirGSMEBVB i is not rotating as a whole around its axis and

the resulting spin is zero.b) twin nonlocal virtual guides VirGSME

BVFBVFi from Cooper pairs of Bivacuumfermions BVF BVFi. In this case each of two adjacent microtubules rotate as respectto each other and around their own axes in opposite directions. The resulting angularmoment (spin) of such pair is also zero.

101

Two remote coherent triplets - elementary particles, like (electron - electron) or (proton- proton) with similar frequency of C We,p pulsation and opposite spins (phase) can beconnected by Virtual guides (VirGSMEi of spin (S), momentum (M) and energy (E) fromSender to Receiver of both kinds. The spin - information (qubits), momentum and kineticenergy instant transmission via such VirGSMEi from [S] and [R] is possible. The same is truefor two synchronized photons (bosons) of opposite spins.

The double VirGSMEBVFBVFi can be transformed to single VirGSME

BVB i by conversion ofopposite Bivacuum fermions: BVF V V and BVF V V to the pair ofBivacuum bosons of two possible alternatives of polarization:

BVB V V or BVB V V

Superposition of two nonlocal virtual spin waves excited by similar elementaryparticles (electrons or protons) of Sender VirSWm

S1/2S and Receiver VirSWmS1/2R of

the same pulsation frequency and opposite spins, i.e. opposite phase of C W pulsation,forms Virtual Guide of spin, momentum and energy (VirGSME i (Fig.12).:

F FC FW SVirSWS

BVB

BVB VirSWR FC F

FW Ri

nBVBV VnBVBV V i VirGSMEext i

16.1

16.1a

The spin exchange via VirGSMEi is accompanied either by the instant change ofBivacuum boson polarization: BVB BVB i or by instant spin state change of bothBivacuum fermions, forming virtual Cooper pairs in the double virtual microtubule:

BVF BVFiS1/2S1/2

BVF BVFi 16.2

The radius of virtual microtubules of VirGSMEi is dependent on generation of torus andantitorus (i e,,, forming them:

LVe /m0ec LV

/m0c LV /m0

c

The radius of VirGSMEe , connecting two remote electrons, is the biggest one (Le. Theradius of VirGSME , connecting two protons or neutrons (L is about 3.5103 timessmaller. The entanglement between similar atoms in pairs, like hydrogen, oxygen, carbonor nitrogen can be realized via complex virtual guides of atoms (VirGSMEat , representingmultishell constructions.

The increments of momentum p mVv tr,lb and kinetic (Tk tr,lb energy

transmission from [S] to [R] of selected generation of elementary particles is determinedby the translational and librational velocity variation (v of nuclei of (S). This means, thatenergy/momentum transition from [S] to [R] is possible, if they are in nonequilibrium state.

The variation of kinetic energy of atomic nuclei under external force application,induces nonequilibrium in a system S R and decoherence of C W pulsation ofprotons and neutrons of [S] and [R]. The nonlocal energy transmission from [S] to [R] ispossible, if the decoherence is not big enough for disassembly of the virtual microtubulesand their systems in the case of atoms. The electronic VirGSMEe , as more coherent (not sodependent on thermal vibrations), can be responsible for stabilization of the complexatomic Virtual GuidesVirGSMEe,p,n.

The values of the energy and velocity increments of free elementary particles areinterrelated by (15.3).

102

The instantaneous energy flux via (VirGSME)i, is mediated by pulsation of energy andradii of torus (V and antitorus (V of Bivacuum bosons: BVB V V.Corresponding energy increments of the actual torus and complementary antitorus ofBVB, forming (VirGSME)i, are directly related to increments of Sender particle externalvelocity v:

EV mVc2 p

R2 vFFF mV

c2 LVLV N,S

actual

EV mVc2 p

R2 vFFF mV

c2 LVLV N,S

complementary

16.3

16.4

where: p mVv; p mV

v are the actual and complementary momenta; LV /mVc

and LV /mVc are the radii of torus and antitorus of BVB V V, forming

VirGS,M,Ein,ext .

The nonlocal energy exchange between [S] and [R] is accompanied by the instantpulsation of radii of tori (V and antitori (V of BVF and BVB, accompanied bycorresponding pulsation |LV /LV | of the whole virtual microtubule VirGSME (Fig.12).

Most effectively the proposed mechanism of spin (information), momentum and energyexchange can work between Sender and Receiver, containing coherent molecular clusters -mesoscopic Bose condensate (mBC) (Kaivarainen, 2001, 2005).

The instantaneous angular momentum (spin) exchange between [S] and [R] does notneed the radius pulsation, but only the instantaneous polarization change of Bivacuumdipoles BVB BVB i or Cooper pairs [BVF BVF BVF BVF,forming VirGSME.

Fig. 12. The mechanism of nonlocal Bivacuum mediated interaction (entanglement) betweentwo distant unpaired sub-elementary fermions of ’tuned’ elementary triplets (particles) of theopposite spins F

F F Sender

i and F F F Receiver

i , with closefrequency of [C W pulsation and close de Broglie wave length (B h/mV

v ofparticles. The tunnelling of momentum and energy increments: |mV

c2 |~|VirP | |VirP | from Sender to Receiver and vice-verse via Virtualspin-momentum-energy Guide [VirGSMEi is accompanied by instantaneous pulsation of

103

diameter (2LV of this virtual microtubule, formed by Bivacuum bosons BVB or doublemicrotubule, formed by Cooper pairs of Bivacuum fermions: [BVF BVF. The spinstate exchange between [S] and [R] can be realized by the instantaneous change polarizationof Cooper pairs: [BVF BVF BVF BVF and Bivacuum bosons: BVB BVB.

In virtual microtubules (VirGSMEi )i the time and its ’pace’ are uncertain: t 0/0, if theexternal velocities (v) and accelerations (dv/dt) of Bivacuum dipoles, composing suchvirtual Bose condensate, are zero (see eqs. 14.13 and 14.14).

16.1 The role of tuning force (FVPW of virtualpressure waves VPWq

of Bivacuum in entanglement

The tuning between two similar elementary particles: ’sender (S)’ and ’receiver (R)’via VirGSMEi may be qualitatively described, using well known model of damped harmonicoscillators, interacting with all-pervading virtual pressure waves (VPW of Bivacuumwith fundamental frequency (0 m0c2/. The criteria of tuning - synchronization of [S]and [R] is the equality of the amplitude probability of resonant energy exchange of Senderand Receiver with virtual pressure waves (VPW0

: ACWS ACWR , resulting fromminimization of frequency difference (S 0 0 and R 0 0:

ACWS 1mV

S

FVPW

S2 02 Im S

ACWR x,y,z 1

mV R

FVPW

R2 02 Im R

16.5

16.5a

where the frequencies of C W pulsation of particles of Sender (S) and Receiver(R are:

R C W R0in BextR

S C W R0in BextS

16.6

16.6a

is a damping coefficient due to decoherence effects, generated by local fluctuations ofBivacuum deteriorating the phase/spin transmission via VirGSME; mV

S,R are the actualmass of (S) and (R); FVPW is a tuning force of virtual pressure waves VPW ofBivacuum with tuning energy EVPW qm0c2 and wave length LVPW /m0c

FVPW EVPWLVPW

qm0

2c3 16.7

The most probable Tuning Force (TF) has a minimum energy, corresponding toq j k 1.

The influence of virtual pressure force (FVPW stimulates the synchronization of [S]and [R] pulsations, i.e. R S 0. This fundamental frequency 0 m0c2/ is thesame in any space volume, including those of Sender and Receiver.

The VirGSME represent quasi 1D macroscopic virtual Bose condensate with aconfiguration of single microtubules, formed by Bivacuum bosons (BVB or withconfiguration of double microtubules, composed from Cooper pairs as described inprevious section.

The effectiveness of entanglement between two or more similar elementary particles isdependent on synchronization of their C W pulsation frequency and ’tuning’ the phaseof these pulsations via nonlocal virtual guide (VirGSME)S,R between Sender and Receiver

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under the action of the virtual pressure waves VPWq1 and Tuning energy of Bivacuum.

The mechanism proposed may explain the experimentally confirmed nonlocalinteraction between coherent elementary particles (Aspect and Gragier, 1983), atoms andbetween remote coherent clusters of molecules.

Our theory predicts that the same mechanism, involving a nonlocal net of VirGSME,may provide the entanglement even between macroscopic systems, including biologicalones. It is possible, if the frequency and phase of C W pulsations of clusters of theirparticles in state of mesoscopic Bose condensation (Kaivarainen,2001; 2004) are ’tuned’ toeach other.17 New kind of Bivacuum mediated nonlocal interaction between macroscopic objects

In accordance to our approach, the remote interaction between macroscopic Sender [S]and Receiver [R] can be realized, as a result of superposition of distant and nonlocalcomponents of their Virtual Replicas (VRS VRR), described in previous sections, viaexternal multiple virtual spin-momentum-energy guides VirGSMGext (Fig.12 and Fig.13).

The angular momentum (spin) and energy remote exchange between coherent clustersof molecules in state of mesoscopic Bose condensation (mBC) of [S] and [R] is possible, if[S] is open or closed system in non-equilibrium state, exchanging with surroundingmedium by energy and mass or by energy only. The asymmetry of Bivacuum fermions andBivacuum bosons (BVF and BVB, necessary for influence of Bivacuum on [R], can beinduced also by stable systems, like objects of asymmetric shape - pyramids and cones,creating strongly anisotropic distant Virtual replicas, perturbing symmetry of Bivacuum.

Nonequilibrium processes in [Sender], accompanied by acceleration of particles, likeevaporation, heating, cooling, melting, boiling etc. may stimulate the nonelastic effects inthe volume of [Receiver] and increments of modulated virtual pressure and spin waves(VPWm

and VirSWm1/2, accompanied [C W pulsation of triplets

F F F i , formed by sub-elementary fermions of different generation,representing electrons, protons and neutrons.

The following unconventional kinds of effects of nonelectromagnetic andnon-gravitational nature can be anticipated in the remote interaction betweenmacroscopicnonequilibrium [Sender] and sensitive detector [Receiver] via multiple Virtual spin andenergy guides VirGSME (Fig.12), if our Unified theory is right:I. Weak repulsion and attraction between ’tuned’ [S] and [R] and rotational momentum

in [R] induced by [S], as a result of transmission of momentum/kinetic energy and angularmomentum (spin) between elementary particles of [S] and [R]. The probability of such’tuned’ interaction between [S] and [R] is dependent on dimensions of coherent clusters ofatoms and molecules of condensed matter in state of mesoscopic Bose condensation (mBC)(Kaivarainen, 1995; 2001; 2003; 2004) and may be regulated in corresponding way. Thekinetic energy distant transmission from atoms of [S] to atoms of [R] may be accompaniedby the temperature and local pressure/sound effects in [R];II. Increasing the probability of thermal fluctuations in the volume of [R] due to

decreasing of Van der Waals interactions, because of charges screening effects, induced byoverlapping of distant virtual replicas of [S] and [R]. In water the variation of probability ofcavitational fluctuations should by accompanied by the in-phase variation of pH andelectric conductivity due to shifting the equilibrium: H2O H HO to the right or left;III. Small changing of mass of [R] in conditions, increasing the probability of the

inelastic recoil effects in the volume of [R] under influence of [S];IV. Registration of metastable virtual particles (photons, electrons, positrons), as a

result of Bivacuum symmetry perturbations;V. The nonlocal (instant) electromagnetic signals transmission from [S] to [R] via

105

VirGSME .The first kind (I) of new class of interactions between coherent fermions of [S] and [R]

is a result of huge number of correlated virtual spin-momentum-energy guidesVirGSME VirSWS

VirSWR formation by standing spin waves (VirSWS,R).

These guides can be responsible for:a) virtual signals (phase/spin), momentum and kinetic energy instant transmission

between [S] and [R], meaning the nonlocal information and energy exchange;b) the regulation of Pauli repulsion effects between fermions of [S] and [R] with

parallel spins;c) the transmission of macroscopic rotational momentum from [S] of [R]. The

macroscopic rotational momentum, exerted by VirSWS, is dependent on the differencebetween the external angular momentums of elementary fermions of [S] and [R];

d) the creation of macroscopic magnetic dipoles between [S] and [R].The second kind (II) of phenomena: influence of [S] on probability of thermal

fluctuations in [R], - is a consequence of the additional symmetry shift in Bivacuumfermions (BVF, induced by superposition of distant and nonlocal Virtual Replicas of [S]and [R]: VRS VRR, which is accompanied by increasing of Bivacuum fermions(BVF V V virtual charge: e eV eV e0 in the volume of [R].Corresponding increasing of Bivacuum permittivity (0 and decreasing magneticpermeability (0 : 0 1/0c2 is responsible for the charges screening effects involume of [R], induced by [S]. This weakens the electromagnetic Van der Waalsinteraction between molecules of [R] and increases the probability of defects originationand cavitational fluctuations in solid or liquid phase of Receiver.The third kind of phenomena (III): reversible decreasing of mass of rigid [R] can be a

result of reversible lost of energy of Corpuscular phase of particles, as a consequence ofinelastic recoil effects, following the in-phase C W transition of Ncoh coherentnucleons in the volume of [R].

The probability of recoil effects can be enhanced by heating the rigid object or bystriking it by another hard object. This effect can be registered directly - by the object massdecreasing. In conditions, close to equilibrium, the Matter - Bivacuum energy exchangerelaxation time, following the process of coherent C W pulsation of macroscopicfraction of atoms is very short and corresponding mass defect effect is undetectable. Suchcollective recoil effect of coherent particles could be big in superconducting or superfluidsystems of macroscopic Bose condensation or in good crystals, with big domains of atomsin state of Bose condensation.The fourth kind of the above listed phenomena - increasing the probability of virtual

particles and antiparticles origination in asymmetric Bivacuum will be discussed later insection 19.3.It was demonstrated (Kaivarainen, 2004 a,b), that listed nontrivial consequences of our

Unified theory (I - IV) are already confirmed experimentally by groups of Kozyrev (1984;1991) and Korotaev (1999; 2000). It is important to note, that all of them are incompatiblewith existing today paradigm. It means that the current paradigm is timed out and shouldbe replaced to the new one.

18. Experimental data, confirming the Unified theory (UT)18.1 Radiation of accelerating charges

It follows from our theory, that the charged particle, nonuniformly accelerating incyclotron, synchrotron or in ondulator, could be a source of photons and gravitationalwaves.

106

From eqs.(6.10, 6.10a) and eq.15.5 we get general expression for electromagnetic andgravitational radiation, dependent on the doubled kinetic energy increment:2Tk mV

v2 of alternately accelerated charged particle and related inelastic recoileffects, accompanied [C W pulsation:

E G 2Tk 1 RmVc2 m0c2 1 RTE

where : E G 2Tk |mVv2 mV

v2 |rec mVv2

ext

the translational factor: R 1 v/c2

18.1

18.1a

We can see from this formula, that the alternation of kinetic energy of charged particle,as a result of its alternating acceleration can be accompanied by electromagnetic radiation.This effect occur, if the jump of kinetic energy: 2Tk and corresponding inelastic recoilenergy jump: |mV

v2 mVv2 |rec exceeds the energetic threshold, necessary for photon

origination. The [C W pulsations of all three sub-elementary fermions of triplets ofcharged elementary particles: F FW FCp,e F FC FWp,e,modulated by external translational dynamics, participate in photons creation.

It is the Tuning energy (TE) of Bivacuum: TE mVc2 nm0c2, that induces the

transitions of the excited state of particle to its ground state, corresponding to n 1,accompanied by photons emission:

mVc2 TE

m0c2 at vtrext 0 18.2

The are huge number of experimental data, confirming this consequence of our theoryfor electromagnetic radiation. The gravitational radiation in form of neutrinos in similarconditions is also predictable by our Unified Theory (Kaivarainen, 2004 a,b).At the permanent (uniform) acceleration of the charged elementary particle, moving

along the hyperbolic trajectory, the radiation is absent. This nontrivial experimental factalso can be explained by our Unified theory. In accordance to UT, the recoil energy,following radiation of CVC at C W transitions, equal to deceleration of particle in [C]phase, activate the elastic longitudinal spherical waves in superfluid Bivacuum matrix. Ifthe energy of this activation energy is smaller than threshold of inelastic recoil energy,necessary for photons origination, there are no EM radiation of moving particle. Theuniform acceleration, in contrast to alternative one, do not provide the fulfilment ofcondition of overcoming of corresponding activation barrier and the EM radiation is absent.Consequently, the real photon radiation by charged particles and other dissipation inelasticprocess in Bivacuum matrix, are possible only in the conditions of nonuniform and bigenough jumps of particles acceleration.

Some similarity is existing between the mechanisms of inelastic phonons excitation insolids, detected by resonance spectroscopy, and photons excitation in Bivacuum byalternatively accelerated particle.The one more consequence of UT is that the radiation of photons, induced by

accelerations of charged elementary particle, should be strongly asymmetric and coincidewith direction of charged particle propagation in space. This is also well confirmed resultby analysis of synchrotron and ondulator radiation.

Most of energy, emitted by relativistic particle is located in direction, close to its instantvelocity (v vext c in narrow angles range, determined by semi-empirical expression(Ginsburg, 1987):

107

1 v/c21/2 m0c2

E 0 18.3

where: E mc2 mVc2 is a total relativistic energy of the charged particle.

Our theory leads to same result. Formulas (4.2 and 4.2a) for relativistic condition(v c, can be easily transformed to:

1 v/c21/2 mV

mV

1/2 m0c2

mVc2

L

L0

vc 0 18.4

where, the radius of the actual torus, taking into account (4.3), is:

LV /mVvgrin 0 at v c

as far: mV m m0

1 v/c2 at v c

18.4a

and the Compton radius of sub-elementary particle is L0 /m0c constTheir ratio determines the angle range of radiation of accelerating particle. As far, in

accordance to our approach, the actual energy of particle is determined by the inertial mass:E mV

c2 mc2, we can see that eq. 19.3 coincides with eq.19.4.

18.2 Artificial generation of unstable groups of virtual particles and antiparticlesLet us consider the possible results of correlated symmetry shift in groups of virtual

Cooper pairs BVF BVF S0

as F FVir of Bivacuum fermions (BVF andantifermions (BVF with opposite spins, acquiring the opposite uncompensated mass:m |mV | |mV | and charge: e |e | |e | spontaneously or, most probable, inthe local gravitational (G), electric (E), magnetic (H) and massless spin (S) fields.The first stage can be considered, as association/polymerization of virtual Cooper pairs

of asymmetric Bivacuum fermions, representing unstable pairs of correlated virtualsub-elementary particles and antiparticles nF

F Vir. This is accompanied by formationof unstable double Virtual Guides (VirG).

In primordial Bivacuum the symmetric Bivacuum dipoles of opposite polarizationnBVF

BVF S0s , may rotate as respect to each other in opposite direction, keeping

their resulting orientation in space permanent, because their external velocity is zerov 0. However, even small symmetry shift between properties of torus (V andantitorus (V, caused by the external fields, is accompanied by emergence of the externalcirculation velocity (v) around common axis v 0. It follows from (3.11) that:

v2 c2 1 |mV |

mV 0, if mV

|mV | 18.5

nBVFBVFS0s nV V V VS0

s Fields

2FF Vir 3F

F Vir nF F Vir

18.10 18.10a

The formation of VirG in symmetric primordial Bivacuum is self-organization processwithout consuming the external fields energy. However, the presence of fields, turningprimordial Bivacuum to secondary one, induce the symmetry shift in pairsBVFBVFS0

as and rotation of VirG, formed by them. The energy of relative rotation ofasymmetric pairs around common axis in VirG is dependent on the energy of external field,

108

inducing asymmetry.The second stage - is a result of disassembly of the big coherent vortices (18.10a) to

smaller ones, accompanied by violation of equilibrium between densities of virtual particlesnBVFas nFVir and antiparticles n(BVFas nFVir, (n n acquiring,consequently, uncompensated charge and mass:

nF nFVirgradG,E,H

n F iVir n F iVir 18.11

18.11a

where: i e,, are three electron’ generations and the total density of virtualsub-elementary fermions and antifermions is:

n n nn n

18.12 18.12a

The shift of equilibrium between densities of virtual particles and antiparticles ofopposite charges and mass-energy in strong anisotropic electric and gravitational fields isaccompanied by generation of non zero difference of positive and negative virtual pressureof Bivacuum:

VirP n mVv2 n mV

v2e

i 18.13

The metastable virtual fermions may fuse to stable real fermions - triplets and photons,if the value of BVFas symmetry shifts will increase to that, corresponding to Goldenmean condition under the influence of high frequency VPWq2,3

(see section 14).The dissociation of metastable neutral Virtual Guides to charged virtual fragments with

fermion properties is energetically much easier, than that of stable photons, and may occureven in weak fields gradients.

Synchronization of C W pulsation of such virtual unstable fermions, as a conditionof entanglement between them, provides their collective behavior even after big ViGdissociation to coherent groups (ne and ne, where n 10) and their spatialseparation.

The results, confirming our scenario of coherent groups of metastable charged particlesorigination from asymmetric VirG, has been obtained in works of Keith Fredericks (2002)and Sue Benford (2001). Fredericks analyzed the trucks on Kodak photo-emulsions, placedin vicinity of human hands during 5-30 minutes. The plastic isolator was used between thefingers and the photographic emulsion. The tracks in emulsions point to existing ofcorrelation in twisting of trajectories of big group of charged particles (about 20) in aweak magnetic field. The in-phase character of set of the irregular trajectories may reflectthe influence of geomagnetic flicker noise on groups of correlated charged particles.

In these experiments the Bivacuum symmetry shift, necessary for dissociation of virtualBivacuum dipoles clusters on charged virtual fermions, can be induced by the electric,magnetic fields and nonlocal spin/torsion field. These fields can be excited by ’flickering’water clusters in microtubules of the nerve cells bodies and axons of living organisms in theprocess of nerve excitation (Kaivarainen, 2002; 2003; 2004).

The corresponding [dissociation association] of coherent water cluster in state ofmesoscopic molecular Bose condensate (mBC) is accompanied by oscillation of the H20dipoles angular momentum vibration with the same frequency about 107 s1. If theflickering of water clusters in MTs of the same cell or between ’tuned’ group of cellsoccurs in-phase, then the cumulative effect of modulated VirSWm

1/2 and EM field

109

generation by human’s finger near photoemulsion can be strong enough for stimulation ofdissociation of virtual vortices (18.11a) to virtual electrons and positrons, producing theobserved tracks in photoemulsion or photofilm.

In work of Benford (2001) the special device - spin field generator was demonstrated toproduce a tracks on the dental film, placed on a distance of 2 cm from generator andexposed to its action for 7 min. The spin field generator represents rotating hollow cylinderor ring made of ferrite-magnetic material with the axis of rotation coinciding with thecylinder’s main symmetry axis. Four permanent (wedge-like) magnets are inserted into thecylinder. It rotates with velocity several thousand revolutions per minute.

The effect of this generator is decreasing with distance and becomes undetectable bythe dental films after the distance from the top of cylinder bigger than 8 cm. The dots andtracks on dental X-ray films were reproduced over 200 trials. They are close to the regularcharged particle tracks on surface emulsions. However, the more exact identification ofparticles failed. The uncommon features of these tracks may be a result of unusualproperties of short-living virtual electrons, positrons, protons and antiprotons and theircoherent clusters.

18.3 The experiments of N.A. Kozyrev and his groupThese unusual series of experiments performed during decades (Kozyrev, et al.,1984;

1991), are very important for following reasons:- They prove, that the existing today paradigm is not comprehensive enough;- They motivate strongly searching of new kinds of distant and nonlocal weak

interactions (nonelectromagnetic and nongravitational), responsible for such effects;- They represent a good test for verification of new physical theories, challenging their

ability to explain a mechanism of discovered by Kozyrev phenomena, reproduced last yearsin many independent laboratories.

We analyzed a number of Kozyrev’s most important and reliable experiments andresults (Kaivarainen, 2005a). It was demonstrated, that they are in total accordance withconsequences and predictions of our Unified theory (http://arXiv.org/abs/physics/0103031).The review of Levich (1994) of Kozyrev’s group works was used as a main source ofexperimental data.The important results, obtained by group of Korotaev, also pointing to existence of

unknown - nonelectromagnetic mechanism of all-penetrating physical interaction(Korotaev, et. al., 1999; 2000) and the existing of the advanced and delayed effects oncosmic scale also confirm the consequences of our Unified theory (Kaivarainen, 2004a).These results also can be explained, as a consequence of superposition of Bivacuum virtualreplicas (VR) of [S] and [R], exchanging the information and energy, taking into account,that the causality principle do not work in systems of virtual particles, in contrast to realones.

Very interesting data of Tiller, Dobble and Kohane (2001), confirming theunconventional remote interaction between Sender and Receiver, containing aqueoussolutions, were discussed in my paper (Kaivarainen, 2005). In all experiment, described,screening of the target [R] from electromagnetic fields by Faraday’s cage did not influenceon the distant interaction between [S] and [R].Consequently, there are a lot of experimental evidence already, confirming the

existence of Virtual Replica of macroscopic objects and existing of basically new nonlocalremote Bivacuum - Mediated Interaction between Sender and Receiver, following from ourUnified Theory.

The direct approach for evaluation of Bivacuum perturbation in the volume of Virtualreplica of nonequilibrium or spatially asymmetric system (like pyramid) is to make a

110

precise measurements of Casimir effect (Lamoreaux, 1997; Mohideen and Roy, 1998). Thedimensions and density of cavitational fluctuations in water and other liquids, directlyrelated to sonoluminescence, could be also a good test-system for Bivacuum properties.18.4 The idea of nonlocal signals transmitter and detector construction and testingThe simple constructions of artificial physical devices with functions of [Sender] and

one or more [Receiver] for verification of nonlocal mechanism of communication viaVirtual Guides of spin/information, momentum and energy, following from our Unifiedtheory, were suggested (Kaivarainen, 2004a; 2004b). They can represent two or moreidentical and ’tuned’ to each other superconducting or superfluid multi-rings ortorus/donuts systems.

The pair: [S] and [R] can be presented by two identical systems, composed from thesame number (5-10 or more) of superconducting or superfluid rings of decreasing radius -from meters to centimeters, following Fibonacci series, because of fundamental role ofGolden mean in Nature, enclosed in each other. The ”tuning” of Virtual Replicas of [S] and[R] constructions in state of macroscopic Bose condensation (superconducting orsuperfluid) can be realized by keeping them nearby with parallel orientation of two set ofrings during few hours until equalizing of their physical parameters, i.e. currents. Aftersuch tuning, they should be removed from each other, keeping theirsuperconducting/superfluid state on at the same temperature, pressure and other conditions,on the increasing distances from hundreds of meters to hundreds of kilometers and testedfor interaction in each equipped for such experiments laboratory.

The experiments for registration of nonlocal interactions could be performed, asfollows. At the precisely fixed time moment, the superfluid or superconducting properties ofone of rings of [S], should be switched off by heating, ultrasound or magnetic field. At thesame moment of time the superconducting or superfluid parameters of all rings of [R]should be registered. If the biggest changes will occur in the ring of [R]-system with thesame radius, as that in [S]-system and faster, than light velocity, it will be a confirmationof possibility of nonlocal Bivacuum mediated information and momentum exchange(entanglement), following from our theory and based on resonant principles. Thecorresponding remote signals exchange via proposed in our work Virtual Guides(VirGSME should not be shielded by any screen.

There are a number of laboratories over the World, capable to perform the proposedexperimental project. In the case of success, such Nonlocal Signals Detector/Transmitter(NSD/T) with variable parameters would be the invaluable tool for extraterrestrialcivilizations search in projects, like SETI and for distant cosmos exploration (NASA). Onthe Earth, the Internet, radio and TV - nets also will get a strong challenge.

18.5 Michelson-Morley experiment, as a possible evidencefor the Virtual Replica of the Earth existing

The experiments, performed in 1887 by Michelson-Morley and similar laterexperiments of higher precision, has been based on checking the difference of light velocityin the direction of Earth motion on its orbit around the Sun and in the direction normal oropposite to the this one. In the case of fixed aether (vacuum) with condensed matterproperties, independent of the Earth motion, one may anticipate that the difference in thesetwo light velocities should exist, if the value of refraction index of vacuum/aether isindependent on velocity and direction of the Earth propagation in space. The absence ofany difference was interpreted, as the absence of the Earth - independent fixed aether. Thisconclusion was used by Einstein in his postulate of permanency of light velocity, butdifferent time in different inertial systems, termed ’the relativity principle’.

The conjecture of virtual replica (VR), following from our corpuscle-wave duality and

111

Bivacuum models, allows the another interpretation of Michelson-Morley experiments. TheVR of the Earth or any other material object represents a standing Bivacuum virtualpressure waves (VPW and VPW, modulated by the object’s particles corpuscle - wavepulsation (see section 8).

The distant component of VR may have at least as big diameter, as the Earthatmosphere and it moves in space together with planet. It is obvious, that in such ’virtualshell’ of the Earth the light velocity could be the same in any directions.

I propose the experiment, which may confirm the existence of both: the VR and theAether/Bivacuum, as a superfluid medium with certain mechanical properties, likecompressibility providing the VPW existing. For this end we assume that the properties ofVR on distance of about few hundred kilometers from the planet surface differs from thaton the surface.

If we perform one series of the Michelson-Morley like experiments on the satellite,rotating with the same angle velocity as the Earth, i.e. fixed as respect to the Earth surfaceand another series of experiments on the surface, the existence of difference in results willconfirm our Virtual Replica theory and the Bivacuum model with Aether properties.

The absence of difference in light velocity in opposite direction as respect to Earthtrajectory can be explained in two ways:

1. As a result of equality of light velocity in any directions, independently on directionof Earth translational propagation in space (confirmation of the Einstein relativity principleand the absence of the Aether);

2. As a result of certain correlation between the translational velocity of the materialobject (Earth or satellite) and Bivacuum perturbation (Bivacuum dipoles symmetry shift) inthe same direction, increasing the refraction index of Bivacuum and light velocity (seesection 6.6). This explanation is compatible with the Aether concept.

Consequently, the absence of difference in light velocity in Michelson-Morley likeexperiments, in any case is not a strong evidence for the Aether absence.

18.6 Interaction of particles with their Virtual Replicas, as a backgroundof two slit experiments explanation

In accordance with our model, the electron and proton (Fig.2) are the tripletsF F Fe,, formed by two negatively charged sub-elementary fermions ofopposite spins (F and F and one uncompensated sub-elementary antifermion (F of and generation. The symmetric pair of sub-elementary fermion and antifermion:F F are pulsing between Corpuscular [C] and Wave [W] states in-phase,compensating the influence of energy, spin and charge of each other.

It follows from our model, that the charge, spin, energy and momentum of the electronand positron are determined just by uncompensated/unpaired sub-elementary fermion (F.The parameters of (F are correlated strictly with similar parameters of pair F F due to conservation of symmetry of properties of sub-elementary fermions and antifermionsin triplets. It means that energy/momentum and, consequently, de Broglie wave length andfrequency of uncompensated sub-elementary fermion (F determine the empirical deBroglie wave properties of the whole particle (electron, positron).

The frequency of de Broglie wave and its length can be expressed from eq.7.4 as:

B mV

v2 trext

h vB

CW R0

or : B mV

c2

h R0

18.14

18.14a

112

where: 0 m0c2/h 0/2; B h/mVv

In a nonrelativistic case, when v c and the relativistic factor R 1 v/c2 1,the energy of de Broglie wave is close to Tuning energy (TE) of Bivacuum (7.5):

EB hB mVc2 m0c2 TE 18.15

The fundamental phenomenon of de Broglie wave is a result of modulation of thecarrying internal frequency of C W pulsation (in R0 Rm0c2/ by the angularfrequency of the de Broglie wave: B mV

vtr2 / 2v/B, equal to the frequency of beatsbetween the actual and complementary torus and antitorus of the anchor Bivacuum fermion(BVFanc ) of unpaired F. The Broglie wave length B h/mV

v and mass symmetry shiftof BVFanc is determined by the external translational momentum of particle: p mV

v .For nonrelativistic particles B 0. For relativistic case, when v is close to c andR 0, the de Broglie wave frequency is close to resulting frequency of C Wpulsation: B CW.

In accordance with our model of duality, the reversible C W pulsations of F andBVFanc are accompanied by outgoing and incoming Cumulative Virtual Cloud (CVC),composed of subquantum particles of opposite energy. On this point, our understanding ofduality and wave properties of particle coincide with that of Bohm and Hiley (1993).

Introduced in our theory notion of Virtual replica (VR) or virtual hologram of anymaterial object in Bivacuum (Kaivarainen, 2004; 2005) is a result of interference of basicVirtual Pressure Waves (VPWq1

and Virtual Spin Waves (VirSWq11/2 of Bivacuum

(reference waves), with virtual ”object waves” (VPWm and (VirSWm

1/2, representingCVC and CVC of pair F F, modulated by de Broglie waves of the wholeparticles (section 15).

The feedback influence of Bivacuum Virtual replica of the triplet on its original andcorresponding momentum exchange may induce the wave - like behavior of even a singeseparated elementary fermion, antifermion F F Fe,p (Fig.2) or boson, like thephoton (Fig. 4).

The reason for periodical character of the electron’s trajectory in our model(self-interference) can also be a result of periodic momentum oscillation, produced byC W pulsation of the anchor BVFanc of unpaired sub-elementary fermion (F intriplet. In the case of photon, the momentum oscillation is equal to its frequency(p c/p, as far the relativistic factor R 1 v/c2 in (10.6) is zero or very close tozero near strongly gravitating objects. It is provided by the in-phase C W pulsation ofthe anchor BVFanc of central pair of sub-elementary fermions with similar spin orientations(Fig. 4). The momentums of two side pairs of sub-elementary fermions of photon withopposite spins compensate each other, because their C W pulsations are counterphase.

The duality properties of elementary particles can be understood, as far they can besimultaneously in the corpuscle C and wave W phase. Our theory is able to prove thiscondition in two different ways:

1. In each triplet of elementary particle F F F the C W pulsations ofthe pair F F is counterphase with unpaired sub-elementary fermion F. It means,that when F F is in the C phase, the F is in the [W phase and vise versa;

2. In the absence of particle accelerations, meaning its permanent kinetic energy, theinternal time of C and W phases is the same. Consequently, in the internal referencesystem, both phase of unpaired or paired sub-elementary fermions in different de Brogliewave semiperiods can be considered as simultaneous.

This statement follows from our notion of time and its pace for closed system (see

113

section 7.1).The formula for pace of time for any closed coherent system or free particle is

determined by the pace of its kinetic energy: (mVv2/2x,y,z m0v2/ 2 1 v/c2

x,y,zchange, which is anisotropic in a general case:

dtt dTk/Tkx,,y,z 18.16

For the internal time itself it follows from (18.16):

t vdv/dt

1 v/c2

2 v/c2x,y,z

18.17

We can see, that in the absence of acceleration (dv/dt 0 and dv 0, i.e.permanent kinetic energy, momentum and, consequently, permanent de Broglie wavefrequency and length, the time for such particle is infinitive and pace of time is zero:

t and dtt 0 18.18

These conditions mean that the C and W phases of triplets - elementary particles,moving with permanent velocity, may be considered, as simultaneous. The oscillation ofkinetic energy and velocity of triplets occur only in transition states C W or W C,accompanied by recoil antirecoil effects.

We can see from the above analysis, that our model does not need the Bohmian”quantum potential” (Bohm and Hiley, 1993) or de Broglie’s ”pilot wave” for explanationof wave-like behavior of elementary particles.

Scattering of the photon on a free electron will affect its velocity, momentum, mass,wave B frequency, length, its virtual replica (VR) and its feedback influence on theelectron, following by change of the interference picture.

Our theory predicts that, applying of the EM field to singe electrons with frequencyresonant to their de Broglie frequency, should be accompanied by alternative accelerationof the electrons, modulation of their internal time and Virtual Replica with the samefrequency, accompanied by ’washing out’ the interference pattern in two-slit experiment.This consequence of our explanation of two-slit experiment can be easily verified.

19 Theory of Overunity Devices19.1 The Source of Free Energy in Bivacuum

The influence of Tuning energy (TE) of Bivacuum on matter is a result of forcedresonance, leading to synchronization between fundamental frequency(VPW q0 qm0c2/e,, of virtual pressure waves (VPWi

) of Bivacuum and[C W] pulsations of elementary particles.The main source of ’free’ energy of Bivacuum, acting on particles, is combinational

resonance of de Broglie waves of real elementary particles with fundamental Bivacuumvirtual pressure waves (VPWq

of basic quantized frequency q0i qm0

i c2/. Thecondition of combinational resonance is:

VPWq q0i CW

or : EVPW qm0i c2 mV

c2

19.1

19.1a

The energy exchange between VPW VPW and real particles in the process of

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C W pulsation of pairs F Fx,y of triplets F Fx,y F zi at pull-in-range state accelerate them, driving to resonant conditions (19.1 and 19.1a) at q 2,3. . . ,i.e. bigger than q 1. This statement will be proved below.

In accordance to rules of combinational resonance of Bivacuum virtual pressure waveswith elementary particles, we have the following relation between quantized energy andfrequency of VPW and energy/frequency of triplets C W pulsation in resonanceconditions:

EVPW VPWi q0

i CWi R0 B

or : EVPW qm0i c2 Rm0

i c2 mVv2 Rm0

i c2 m0i c2v/c2

R

or : q R v/c2

R

R 1 v/c2; q 1,2,3. . . integer numbers)

19.2

19.2a

19.2b

where the angle frequency of de Broglie waves is: B1,2,3 and:

B /2mVLB2 mV

v2/2 19.3

The important relation between translational most probable velocity of particle (v) andquantization number (q, corresponding to resonant interaction of Bivacuum VPWq

withpulsing particles, derived from (14.8b) is:

v c q21q2

1/2

19.4

At the conditions of triplets fusion, when q 1, the translational velocity of particle iszero: vn1 0. When the quantized energy of VPWn

, corresponds to q 2, the resonanttranslational velocity of particle should be: vq2 c 0.866 2,6 1010cm/s. At q 3,wehave from (19.4): vq3 c 0.942 2,83 1010cm/s.

On the other hand, if velocity of particles is high enough and corresponds to q 1,5 in(19.4), their pull-in range interaction with excited VPWq2

can accelerate them up toconditions: q 2, v 2,6 1010cm/s. In turn, if the starting particles velocity correspondsto q 2,5, their forced resonance with even more excited VPWq3

should accelerate themup to conditions: q 3, corresponding to v 2,83 1010cm/s. The described mechanismof Bivacuum - Matter interaction, is a general physical background of all kinds of overunitydevices (Kaivarainen, 2004; http://arxiv.org/abs/physics/0207027).

Virtual particles and antiparticles have the mass mV mV

m0 and charge|e e | e0 symmetry shift smaller, than the rest mass and elementary charge of realsub-elementary fermions and antifermions. The frequency of their CW pulsation islower than fundamental Compton’s one:

CWi 0

i m0i c2/. These reasons prevent the

fusion of virtual particles and antiparticles to triplets, in accordance to our theory (seesection 1.5).

The assembly of Cooper pairs of virtual particles: N BVF BVFas N 1,where the asymmetric BVF and BVF, forming pairs can rotate in opposite directions(clockwise and anticlockwise) around common axis. They may compose long virtualmicrotubules, named Virtual Guides (VirG), described in next sections. The action offundamental virtual pressure waves (VPWq1

of Bivacuum with Compton frequency (0i

can accelerate this rotation in conditions, close enough to combinational resonance. Such

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acceleration may drive the pairs of BVF BVFas to Golden mean conditions:vVir 1/2c. It is another possible - virtual source of superfluous energy of Bivacuum. Thisacceleration finally may provide the fusion of virtual BVF and BVF to real elementaryparticles. It may happens in strong enough electric, magnetic or gravitational fields,inducing starting symmetry shift of Bivacuum fermions. It is accompanied by increasing ofcorresponding external velocity of pairs rotation around common axes and frequency oftheir CW pulsation, necessary for pull-in range condition with VPWq1

.The action of basic VPWq1

on virtual particles is opposite to that on real particles. Itincreases the velocity and kinetic energy of virtual particles.

The described mechanism of Bivacuum - Matter interaction, can be a general physicalbackground of all kinds of overunity devices (Kaivarainen, 2004;http://arxiv.org/abs/physics/0207027; see also Naudin’s web site "The Quest ForOverunity"). The coherent electrons and protons of hot enough plasma in stars and inartificial conditions also may get the additional energy from high-frequency virtualpressure waves of Bivacuum VPWq2,3..

, excited by strong gravitational and/or magneticfields.The mechanism of high-frequency VPWq2,3..

excitation can be similar to excitation ofacoustic waves in superfluid liquid (helium). It was shown theoretically, using Gross-Pitaevsky equation (Leadbeater, et.al. 2001), that recombination of two vortex ring(toruses) of the opposite direction of rotation in superfluid liquid is accompanied by soundemission. The reconnections produce two highly elongated rings and two sound pulses. Thestreched rings rapidly shrink into two smaller vibrating which move outwards.

In Bivacuum similar mechanism of virtual sound emission, meaning the excitation ofhigh-frequency VPWq2,3..

can be a result of Bivacuum dipoles collision, annihilation,recombination and interconversions between different lepton generation. On macroscopicscale the emission of VPWq2,3..

can be a consequence of the conversion of doubled/twinVirtual Guides, formed by virtual Cooper pairs of Bivacuum fermions [BVF BVFi tosingle VirGBVBi , formed by Bivacuum bosons BVB V V :

VirGBVF VirGBVFH,Gfield VirGBVB VPWq2,3..

19.5

Such virtual turbulence perturbation in superfluid Bivacuum may occur due toBVF BVF equilibrium shift to the left or right under the action of alternating magneticor gravitational fields.

The utilization of these excessive virtual sound energy by overunity devices can be apermanent process because of spontaneous tendency of Bivacuum dipoles to self-assemblyin form of doubled Virtual guides VirGBVF VirGBVF. So just this inherent tendencyof Bivacuum to self-organization, starting from Bivacuum dipoles to their huge filaments inform of doubled VirG and their ability to disassembly with VPWq2,3

energy releasingunder the influence of fields of lesser-triggering energy, can be a source of free energy foroverunity machines. Consequently Bivacuum can be considered as the active medium, ablefor self-exciting of the basic VPWq1

.The experimental approaches to reach the symmetry shift between torus and antitorus

of Bivacuum fermions, generating virtual fermions and antifermions are listed below:1) gravitational fields: natural, like that of the Earth, and the artificial, generated by

centripetal acceleration of rotating cylinder or disk;2) static electric fields, like in Biefeld-Brown effect -thrust of capacitors of high

voltage. The recursive arrays of capacitors of special geometry may provide cumulativeBiefeld-Brown thrust in direction, determined by orientation of the asymmetric electrodes.In general case this direction do not coincides with that of the Earth gravitational potential;

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3) rotation of magnets system, affecting the thrust of system and its effective mass(magneto-gravitational Searl effect);

4) combination of static and saw-shape magnetic fields (the Bearden motionlesselectromagnetic generator).

20 Possible explanation of Biefeld-Brown (B-B) effectWhen a high voltage (~30 kV) is applied to a capacitor, whose electrodes have different

dimensions, the capacitor experiences a net force toward the smaller electrode, positive inmost cases. The B-B effect may have applications to vehicle propulsion in space. Thephysical basis for the Biefeld - Brown effect is not understood in the framework of existingparadigm.

The confirmed experimentally Biefeld - Brown (B-B) thrust effect reflects theappearance of net force in asymmetric capacitors of unknown nature, increasing withvoltage. In early works of Brown and his patents the statement was done, that the sign ofthrust is dependent on relative position of the electrodes and is directed from biggernegative to smaller positive electrode. The corresponding net force of B-B effect mayincrease or decrease the effective mass of capacitor. This effect is existing in the air andsmaller in vacuum.

Later the data appears, that the B-B is independent of polarity of applied voltage toelectrodes (Bahder and Fazi, 2003) and the orientation of capacitor as respect to plane ofthe Earth surface. The latter points that B-B effect is not related to gravitational field of theEarth. In the same work it was demonstrated the existence of B-B effect even in the case ofone electrode capacitor - suspended thin wire from the hot electrode of the high-voltagepower supply. Once the voltage supply approaches 35 kV, the wire starts to deviate andoscillate around initial vertical suspended position.

The magnitude of the net force on the asymmetric capacitor was estimated in the samework, considering two different mechanisms of charge conduction between its electrodes:ballistic ionic wind and ionic drift. The calculations indicate that ionic wind is at least threeorders of magnitude too small to explain the magnitude of the observed force on thecapacitor. The ionic drift transport assumption leads to the correct order of magnitude forthe force, however, it is difficult to see how ionic drift enters into the theory (Bahder andFazi, 2003).

The B-B effect in vacuum was confirmed, using the NASA two dimensionalasymmetrical capacitor modules. Two corresponding patents where granted to authorJonathan Campbell:

1) NASA patent US 6,317,310 (November 13, 2001 ) Apparatus & Method forGenerating Thrust Using a Two Dimensional, Asymmetrical Capacitor and

2) NASA patent application US6411493 ” Apparatus and Method for generating athrust using a two dimensional asymmetrical capacitor module ” (June 25, 2002 );

The first conductive element of each of two capacitors on the opposite ends of rotatingin horizontal plane rod of module can be a hollow cylinder or a solid cylinder. The secondconductive element of capacitor can be a flat disk, a dome. A dielectric is disposed betweenthe first conductive element and the second conductive element. The system also includes ahigh voltage source having first and second terminals connected respectively to the firstand second conductive elements of two capacitors on the rod. Special test confirms that thethrust observed is not the result of the ejection of electrons backward.

All known theoretical explanations do not explain the existing of B-B effect in vacuum(see site of J-L Naudin: http://members.aol.com/jnaudin509/ ) and (Bahder and Fazi,2003).

Using our Unified theory, we may explain this effect as a result of two process:

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1) acceleration of the translational dynamics of conductivity electrons in the volume ofelectrodes of capacitors in strong electric field, making the electrons most probabletranslational velocity in eq.19.4 close enough to resonant velocity v 2,6 1010cm/s atn 2 and CW 20, when the additional acceleration under the influence of BivacuumPressure Waves (VPW in conditions of combinational resonance (19.2) becomeseffective. The corresponding excessive internal kinetic energy of the electrons at bigenough voltage can be resulted in overcoming the auto electron emission threshold andelectric break of capacitor, following by thrust;

2) different pressure on positive and negative electrodes of capacitors, provided byvirtual negative sub-elementary fermions of ( and by virtual positive sub-elementaryantifermions of (e generation, correspondingly, acquiring the additional kinetic energy inthe external space between electrodes under basic VPWq1

e, action and their spatialseparation in strong electric field. The asymmetric internal and external pressure of real andvirtual elementary particles, correspondingly, is exerted by their hitting to the electrodes ofopposite charge of capacitor, creating thrust and capacitor propulsion.

The acceleration and increasing of virtual particles and antiparticles kinetic energyunder VPWq1,2,3

action result in the excessive virtual pressure VirP, directed topositive electrode if:

The virtual pressure effect, generated by kinetic energy of negative virtualsub-elementary antifermions of heavy ( generation, is much bigger, than the positivevirtual positrons (e generation even at their equal density (n nand may provide thelifting effect of capacitors:

VirP ~Tres k 12 nmV

v2 nmVv2 EG 20.1

where: n and n are the densities of virtual antiparticles and virtual particles.When the resulting virtual energy of all coherent virtual particles, hitting the electrode

Tkres, overcome the energy of gravitational attraction of capacitor (mCap to the Earth (M:

Tres k EG G mCapMr 20.2

the lifting effect, confirmed by Naudin (http://members.aol.com/jnaudin509/) occur.It is natural to assume, that the surface ions of positive electrodes presumably stimulate

negative virtual antifermions of heavy generation and the electrons of negativeelectrodes stimulate positive virtual sub-elementary antifermions of light e generation.This may explains the reason why the thrust in B-B effect usually is directed toward thepositive electrode of capacitor.

The asymmetric geometry of capacitor is also important factor for creating of gradientsof virtual sub-elementary antifermions, increasing the propulsion effect of capacitor inspace towards smaller electrodes, where the density of virtual particles is higher. Someevidence are existing, that the difference in electrode dimensions is more important factorof thrust direction, than their polarity. The independence of B-B thrust direction on polarityof applied voltage to electrodes (Bahder and Fazi, 2003) and dependence of the net forcedirection on capacitor asymmetry: always from bigger electrode to smaller one, we mayexplain in following way. The electric field force lines connect the equal number ofpositive and negative charges on the surface of opposite electrodes of capacitor.

If the square of 1st electrode (negative or positive) is bigger, than that of 2nd (positiveor negative) this means that the density of force lines, creating virtual ions or anti-ions inspace between electrodes is decreasing in direction from the small electrode to big one.This happens, even if starting number and density of virtual anti sub-elementary fermions

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(e or near electrodes is equal. Corresponding gradient of virtual particles energy andmomentum density determines direction of thrust of asymmetric capacitors. Suchmechanism can work in vacuum and any dielectric medium between opposite electrodes.

However, the existence of B-B thrust effect even with one electrode capacitor,independent on sign of its charge, described above, points on difference of density ofvirtual particles and virtual antiparticles even just after their excitation. The negative singleelectrode induce the opposite Bivacuum asymmetric polarization. The thrust at high voltage(35 kV) was registered by deviation of the wire from vertical position and its pendulum likeoscillation, approximately 600 angle from vertical. The piece of tape on the end of wireincreases the effect (Bahder and Fazi, 2003; USA Army Research Laboratory, approved forpublic release).

As was mentioned already, the spatial separation between negative virtual anti-ions andpositive virtual ions, increasing their life-time, is due to Coulomb attraction induced motionto positively and negatively charged electrodes, correspondingly.

Propagation of virtual particles and antiparticles in the volume of capacitor and/oralternative polarization (symmetry shift) of Bivacuum dipoles - (BVF) in alternativeelectric field, can be considered as a Maxwell’s ’displacement current’, responsible forcorresponding magnetic field origination.

The proposed mechanism of B-B effect, mediated by virtual particles and antiparticles,can be verified using photo or dental films. Like in experiments of Sue Benford (2001) andFredericks (2002), discussed in section 18.2, we anticipate the correlated tracks onphotoemulsion, produced by coherent groups of charged virtual particles and antiparticles.

The collective and coherent properties of the conductivity electrons in the electrodes ofcapacitor are the important factor, which should increase the B-B effect, if our explanationis right. For its verification I propose to use for the positive and negative electrodes ofcapacitors the magnets from paramagnetic materials, where the electrons dynamics isordered and correlated much more than in regular metals. The optimal relation betweenthe sign of electrodes charge and their magnetic poles (N or S) in capacitors, providing themaximum of B-B effect is a matter of experimental research.The capacitors with specific shape, like two separated hemispheres, cones or pyramids,

may provide the asymmetric repulsion force between two opposite electrodes andcorresponding thrust. I named such capacitors Virtual Jet Generators (VJG), see[Kaivarainen, http://arXiv.org/abs/physics/0003001 (version 2000, section 10.2)].

21 Possible explanation of Searl Effect, based on Unified theoryThe Searl effect, confirmed recently in experiments of Roshin and Godin (2000),

displays itself in decreasing or increasing weight of rotating permanent magnets, dependingon direction of their rotation as respect to Earth gravity vector: clockwise or anticlockwiseand self-acceleration of rotation after overcoming of certain speed threshold.

The setup (convertor) of Roshin and Godin is comprised by immobile stator and rotor,carrying magnetic rollers and moving around the stator. The diameter of rotor is about 1 m.The stator (weight 110 kg) and magnetic rollers (total weight 115 kg) were manufacturedfrom separate magnetized segments with residual magnetization of 0.85 T, a coercive forceof [Hc] ~600 kA/m and a specific magnetic energy of [W] ~150 J/m3. The stator and rotorwere assembled on a single platform made of nonmagnetic material.

The Searl overunity device is also considered from the positions of our Unified theory.Two accompanied its action effects - decreasing or increasing of the effective mass ofMagnetic Energy Converter (MEC), depending on clockwise or anticlockwise direction ofrotor of MEC, and its self-acceleration should be considered separately, as far they arebased on different physical mechanisms and are not directly dependent on each other:

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1. The increasing or decreasing of the effective mass of rotating MEC in Searl effectcan be a consequence of shift of equilibrium between Bivacuum fermions of opposite spinsBVF BVB BVF to the left or right, depending on clockwise or anticlockwisedirection of MEC rotor rotation. The attraction and repulsion between macroscopicmagnetic moments of rotor and stator of MEC and polarized Bivacuum is dependent onshift of equilibrium between positive and negative magnetic moments nBVF nBVF ofhuge number of Bivacuum fermions between MEC and the Earth surface to the left or right.The sign of the internal mass/energy symmetry shift in Bivacuum dipoles:mV

mV c2 mV

v2, generated by MEC and responsible for magnetic walls aroundMEC, is also dependent on clockwise or anticlockwise magnets rotation;

2. For explanation of self-acceleration of MEC rotor we proceed from assumption, thatbetween the velocity of MEC paramagnetic rolls rotation around stator and most probabletranslational velocity of real ’free’ electrons in their coherent clusters near rolls surface anddynamics of ions of rolls lattice the strong coupling is existing.

The additional acceleration of orchestrated collectivized electrons in moving magnets,driving their translational velocity to resonant interaction with VPWq2,3

: q 2,v 2,6 1010cm/s. This induced by excited Bivacuum acceleration of rotor becomespossible after acquiring by the surface electrons of rolling magnets the sufficient resultingvelocity for combinational resonance condition (19.2). This resulting velocity can beevaluated approximately, as a sum of the internal most probable velocity of ’free’ electrongas, using Maxwell distribution:

vin 2kTme

~107 cm/s at room temperature 21.1

and the additional translational electrons velocity increment, induced by the rolls ofMEC rotation around stator. After the rolls surface electrons velocity threshold overcoming(about vext 3 104 cm/s the MEC rotor acceleration starts. At this condition the mostprobable resulting translational velocity of the conducting electrons in paramagnetic partsof rollers becomes close enough to resonant velocity at q 2 for pull-in range conditions:

v v in vext

v q2,3res 21.2

The faster circulation of the orchestrated electrons within the rolls of MEC is due totheir coupling with ion lattice of paramagnetic rolls.

Self-acceleration starts, if the pull-in range becomes effective for the small enoughvalue of frequency difference near the combinational resonance of the electrons pulsationwith quantized VPW:

res c2/qm0 mV 21.3

where: q 2,3, . . . q 1.The rolls accelerations is accompanied by enhancement of degree of its particles

C W pulsation coherency and improving the conditions for combinational resonanceof matter with VPW of Bivacuum.

21.1 The Variation of Weight of Rotating MagnetsThe increasing or decreasing of the effective mass of rotating magnetic system, named

Magnetic Energy Converter (MEC), based on Searl effect can be a consequence of shift ofequilibrium between Bivacuum fermions of opposite spins BVF BVB BVF to theleft or right, depending on clockwise or anticlockwise direction of MEC rotor rotation.

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Consequently, in the local space around MEC we get the decreasing/increasing of theeffective gravitational attraction of the MEC and Earth because of opposite or similar bysign magnetic interaction of MEC with surrounding polarized Bivacuum.

This effect, starting before self-acceleration of the magnets (rolls) of rotor, can beexplained by the influence of their magnetic field (H on dynamic equilibrium of Bivacuumfermions, as a dipoles with opposite charges, energy/mass and magnetic moments to the leftor right:

NBVFBVF NBVFBVF 21.4

The constant of this equilibrium KBVFBVFr we introduce as

KBVFBVFr NBVFNBVF

exp r0rHBVF BVFm0i c2 UEM

21.5

where: UEM is the increment of Bivacuum density energy, determined byelectromagnetic fields, generated by the rolls of rotor; r0 is the unitary radius vector; r is adistance between a source of magnetic field radiation and point of KBVFBVFrobservation.

For the case of alternating electromagnetic field, the volume density of its energy inBivacuum is

UEM W E2 H2/2 21.6

where and are Bivacuum permittivity and permeability, correspondingly, dependingon density of virtual charge in given point of space.

The experiments of Roshin and Godin (2000) show, that the weight of MEC increasesor decreases on 30-35%, depending on the direction of rotation.

21.2 The Nature of Magnetic Shells Around the ConvertorOne more unusual effect, discovered in work of Roshin and Godin (2000), is the

appearance of the vertical ’magnetic walls’ - zones of increased magnetic field strength, ascompared to field strength between them, arranged coaxially to the rotor center. We explainthis, as a result of ability of slowly moving under the influence of curled magnetic field theexcessive Bivacuum fermions (BVF or BVF to form the quantized virtual standingwaves around rotating magnets.

The shift of dynamic equilibrium (21.4) and corresponding Bivacuum symmetry,induced by rotating magnetic field, in accordance to our model, should be accompanied bycorresponding mass (mV mV mV and charge (e e e symmetry shift ofBivacuum double cells-dipoles, followed by activation of their external translationalmovement with group velocity (v 0.

The motion of charged particles, like asymmetric BVFas in electric and magneticfield turns their trajectory under the influence of Lorentz force:

F eE ec vH 21.7

In the absence of electric field E 0, the Lorentz force is:

F ec vH 21.8

As far the Lorentz force is normal to vectors v and H and do not produce a work, butonly change the trajectory of charged particle to screw curvature. This curvature is a result

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of superposition of movement with velocity (v, parallel to H and uniform rotationalmovement in direction normal to H with velocity (v.

The Lorentz force, acting on asymmetric Bivacuum fermions with uncompensatedcharge e |e | |e |, moving in magnetic field (H) with velocity (v) by screwcurvature, is:

|F| ec vH sin 21.9

where is the angle between vectors (v) and (F).The module of Lorentz force |F| at E 0 is maximum at 900 and is equal to zero

at 00.To quantify our explanation of magnetic walls origination, we proceed from the

assumption, that the constant of resulting equilibrium between the actual andcomplementary states of BVF, (Kmm

res , dependent on their external group velocity (v,is correlated with constant of equilibrium [KBVFBVFr between BVF or BVF ofopposite magnetic moments and spin.

Then formula (3.11) can be presented as:

Kmmres v |mV |c2

|mV |c2 1 v/c2 KBVFBVFr NBVFNBVF

21.10

From (21.10), we get:

|mV |c2 |mV |v2 |mV |c2 21.11

Putting (21.11) to (21.10) after simple transformation we get:

2|mV |2v2

2m02c2 L0

2

LVext2 1

KBVFBVFres EH 1 21.12

where the resulting quantized spatial ’thickness’ of BVF, equal to that ofsub-elementary fermion (see 1.4) is dependent on quantum number (n like:

L0n ~ dBVF

n m0c2n 1 21.13

and the radius of standing waves, formed by uncompensated/asymmetric BVF or BVF

with nonzero external group velocity (v 0 and |mV | |mV | :

LBVFext mVv

21.14

where: mV m0/ 1 v/c2 at v c, mV m0

As far:

1/KBVFBVFres EH KBVFBVFres EH 21.15

we get from (21.12) and (21.13; 21.15) the dependence of external radius of standingvirtual de Broglie wave of asymmetric BVF on quantum number (n:

LVextn mVv

m0c2n 1

1KBVFBVFres EH 11/2

21.16

The series of standing waves, formed by quantized L0n of asymmetric uncompensated

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Bivacuum fermions (BVF), corresponding to quantum numbers:n 0,1,2,3,4,5,6,7,8,9,10,11,12. . . , in accordance to our theory, is responsible forvertical magnetic walls around the rotor with increased magnetic field strength (0.05T) anddecreased temperature (6-8 C0, revealed experimentally by Roshin and Godin (2000).

The maximum of registered walls radius is about 1500 cm, however it leads from ourcalculations, that the ground L0

e ext radius at n 0 may be of LVext 7500 cm or evenbigger. Such a walls were not revealed in experiment due to technical difficulties.Assuming that m0 is a rest mass of most common e electron, it is possible to calculate thevalue of equilibrium constant KBVFBVFres EH, for the latter condition (n 0, LC 7500cm) from (21.12 and 21.15), as:

KBVFBVFres EH 1 L0LVext n0

2 1 21.17

It is obvious, that if L0LVext n0

2 1 then KBVFBVFres EH is very close to 1.

From (21.10), knowing the value of KBVFBVFres EH 1/KBVFBVFres EH it is easy tocalculate the external group velocity of asymmetric/uncompensated BVF, forming’magnetic walls around convertor under the Lorentz force action:

v c1 KBVFBVFres EH1/2 21.18

Corresponding external group velocity of asymmetric BVF, forming walls, evaluatedfrom (21.17) and (21.18), is very low: v 20 5 105cm/s.

The average experimental distance between 11 registered magnetic walls:

LCext LCextn 1 LCextn~ 50 80cm 21.19

calculated using (21.16) is about 50 cm, increasing from the center to periphery.The thickness of magnetic walls was about 5-8 cm and their height more than 500 cm.

The lower temperature inside the walls, as compared to temperature between them (i.e. thelower kinetic energy of the air molecules), may be a result of decreasing of kinetic energyof air molecules due to virtual standing waves of slightly asymmetric BVF formation andincreasing of Bivacuum electric permeability (0 in the volume of magnetic walls. The(0 increasing is a consequence of virtual charge density increasing, defined by enhanceddensity of asymmetric Bivacuum fermions with uncompensated charge in the volume oftheir standing waves around rotating magnets.

The additional increasing of the intermolecular interaction potential and decreasing ofionization potential in magnetic walls could be a consequence of the air moleculespolarizability elevation due to enhanced screening effect of Coulomb interaction betweenthe electrons and protons of the air molecules

Q qeqp0r 21.20

by charged asymmetric BVFas. The spontaneous [ionization recombination] of the airmolecules in magnetic walls, as a result of (0 increasing, may explain the visible photonsemission in the region around converter. It is important to note, that in this case theionization is not induced by collision of molecules or strong external electric potential, likeat corona discharge.

The development of technology, based on Searl effect, could be used in future forextraction of ’free energy’ of Bivacuum, converting the energy of virtual pressure waves

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(VPW to kinetic energy of elementary particles, and for creation of new principles ofspace propulsion.

22 The Bearden Motionless Electromagnetic Generator (MEG)Good descriptions of the Tom Bearden (2000 - 2002) free energy collector, as a part of

motionless electromagnetic generator (MEG) action principle, has been presented byNaudin (2001) and by Squires (2000).

The interesting attempt for theoretical background of extracting energy from vacuumhas been done in work of Myron Evans (2002), using Sachs theory of electrodynamics(Sachs, 2002), unifying the gravitational and electromagnetic fields. In this theory bothfields are their own sources of energy: the equivalent to mass and equivalent to 4-cuurrent,correspondingly. The electromagnetic field influence the gravitational field and vice versa.The Sachs theory cannot be reduced to the Maxwell - Heaviside theory. The Evans (2002)comes to conclusion that just because of existence of space-time curvature (alwayspertinent for our secondary Bivacuum), any kind of dipole (like our sub-elementaryfermions F) can be used for extracting of energy from space. The idea of dipole, as a freeenergy transmitter, has been used by Bearden (2000) for explanation of his MEG.

The superfluous energy of space, extracted by Motionless Electromagnetic Generators(MEG), constructed and patented in US by Patrick, Bearden, Hayes, Moore and Kenny(2002), also can be a result of acceleration of charged real and virtual fermions orantifermions, induced by resonant interaction with Bivacuum VPWq

, described in previoussections. In such a way the ’free’ energy of Bivacuum is converted to additional kineticenergy of the coherent electrons in ’collectors’. This increment of kinetic energy, like inB-B effect, increases the electrons flux in short - living nonequilibrium states, realized inMEG. The role of magnetic field action in MEG and de Palma overunity machines, basedon Faraday disk, is to increase the fraction of coherent electrons and cumulative effect oftheir interaction with VPWq2,3

in conducting parts of devices.In all kinds of known ’free energy’ generators, like in Kozyrev’s experiments, one or

both of interacting systems should be in nonequilibrium state. In capacitors, Searl machineand MEG it is nonequilibrium system, including virtual and real particles, tending toGolden mean conditions under Bivacuum Virtual Pressure Waves VPWq

action.

Let us analyze, how the ’self-acceleration’ of the electrons with Bivacuum VirtualPressure Waves (VPWq2

after achievement of threshold of pull-in range conditions,produced by the local permanent magnetic, electric and gravitational fields, can increasethe electric current:

1. By increasing the conducting electrons resulting group velocity (v vq2 and theirkinetic energy (mV

v2 under the VPWq2 action, as far:

EE mV c2 m0c2

1 v/c21/2tr

VPWn2

2m0c2 22.1

2. By increasing the actual electric charge (e, with resulting group velocity (v vq2increasing, as far from (4.2):

ee 1

1 v/c21/4 22.2

In MEG the activation of the conducting electronic ’gas’ in ’collector’ occur inshort-living nonequilibrium states, induced by periodic action of the ramp generator incombination with permanent magnetic field action. Such asymmetry of Bivacuum and

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starting acceleration of the electrons is necessary for initiation of synchronization processbetween C W pulsation of the conducting electrons and VPWq2,3

. In these conditionsthe MEG action get the overunity ratio of output to input energy (coefficient ofperformance: COP1) (Naudin, 2001; Bearden, 2002).

The MEG, like other overunity devices, works on the principle water-mill, using thepull-in range synchronization action of VPWq2,3

of Bivacuum, increasing the frequency ofthe electrons C W pulsation, related directly with their translational kinetic energy. TheCOP is not the same as efficiency, which is always less, than 100%. It means, that the ’freeenergy’ devices are not violating the law of energy conservation and have nothing commonwith perpetual mobile.

23. The hydrosonic or cavitational overunity devicesIn hydrosonic or cavitation overunity devices, using ultrasound induced cavitation, the

collapsing of bubbles is accompanied by high temperature jump about 6000 K, ionizationand dissociation of liquids molecules (i.e. H2O H HO, tearing off the electrons andvisible radiation (sonoluminescence). The additional accelerations of the electrons andprotons in their pull-in range conditions with VPWq1

provide the ratio of output to inputenergy (Coefficient of performance) in the range 1,5 - 7.

In all kinds of known ’free energy’ generators, like in Kozyrev’s experiments, one orboth of interacting systems should be in nonequilibrium state.

The same principle of conversion of Bivacuum virtual pressure energy of (VPWq1 to

additional kinetic energy of the electrons and protons in-pull in range conditions, closeenough to resonance ones CW q0, is working in all other known kinds of overunitydevices:

- plasma-type devices;- magnetic motors, like Faraday’s rotating disk;- cold fusion, etc.In all kinds of known ’free energy’ generators, one or both of interacting systems

should be in nonequilibrium dynamic state, necessary for achievement of quasi-resonantconditions of C W pulsations of elementary particles with the excited high-frequencyVirtual Pressure Waves of Bivacuum (VPWq1

.The excitation of high-frequency VPWq2,3

can be stimulated by alternating or pulsingEM fields. The latter is important for tuning of the electrons de Broglie wave frequency topull-in-range combinational resonance with VPWq2,3

.The ability of our Unified theory to explain most important features of the

unconventional phenomena, like Biefeld - Brown, Searl effect and cavitational devicesoverunity action, can be considered, as a criteria of theory validity.

24. Possible mechanism of cold nuclear fusion (CNF) and the excessive heat effectThe numerous experimental data on cold nuclear fusion and accompanied the

electrolysis exothermal effects have been discussed in paper of Sapogin, et.al., (2002). Theclassical view of electrolysis of a palladium cathode saturated with heavy hydrogen inheavy water identifies an anomalous quantity of heat energy (Fleischmann and Pons, 1989).Products of nuclear reaction, like tritium, neutrons and helium have also been found.Similar processes are observed in case of a gas discharge on a palladium cathode,irradiation of deuterium mixture with a powerful ultrasound, in cavitating microbubbles ofheavy water, in a tube with palladium powder saturated with heavy hydrogen under apressure of 10-15 atm., etc. In certain reactions the neutrons of 14 MeV are absent, andsuch a strange situation occurs in other cases too. Activity in reactions with heavy

125

hydrogen and protons failed to be discovered.The most intriguing fact of all these processes is the shortage of nuclear reaction

products for explanation of the emerging heat effects. Thus, in certain cases the number ofnuclear reaction products (tritium, helium, neutrons) should be millions of times greater inorder to explain the quantity of the generated heat. The well-known interaction dd goesalong three channels (Sapogin et. al., 2002):

d d — T(1.01) p(3.03) (Channel 1)d d — He (0.82) n(2.45) (Channel 2)d d — He (5.5) . (Channel 3)All these reactions are exothermal. It was experimentally confirmed, that they can occur

under very small energies.The main problem impeding the occurrence of the d d reaction lies in the existence of

a very high Coulomb barrier. Sapogin et. al., (2001) try to solved this problem, usingdeveloped Unitary Quantum Theory (UQT). The UQT show that the distance to whichdeuterons can approach each other is strongly dependent on the phase of the wave function.The critical review of about 25 theoretical models of cold nuclear fusion , performed byChechin and coauthors (1993) shows that they are unable to explain the CNF phenomena.

Many researchers (Notoya, et al., 1993; Swartz, 1996) discovered that the quantity ofheat generated in the process of electrolysis of ordinary water on nickel electrodes, wherethe nuclear reaction is impossible, is the same as in the electrolytic cell with heavy water.This confirms other measurements, which showed that the quantity of nuclear reactionproducts is millions times less than is required for such an amount of generated heat, and itsorigin remains a mystery.

The surprising experimental results where received independently by Samgin et. al.,(1994; 1995) and Mizuno et. al. (1993). They used special proton-conducting ceramics,which, when electric current runs through them, generate a thousand times more heatenergy than the electric energy consumed. In some experiments this value even exceeded70.000. No radiation or nuclear debris were found, and the nuclear processes are notresponsible for such energy generation. The origin of such an amount of excessive energyis absolutely incomprehensible in the framework of conventional science, for they cannotbe accounted for either by nuclear or chemical reactions, or by phase passages. At first theauthors of this experiment supposed nuclear fusion reactions of the d d type. ThenSamgin replaced heavy hydrogen (deuterium) during ceramics production with ordinaryhydrogen when the nuclear fusion is impossible. However, all the anomalous heat effectspersisted. After such a large quantity of energy was generated, the tablet disintegrated intopowder.

These effects can be explained by UQT from the point of view of the harmonicoscillator theory (Sapogin et. al., 2002). When the tablet is agglomerated, the cavities of asize of hundreds Angstroms remains. When direct or alternating current runs through it, theprotons and deuterons in their movement (there are few electrons in such ceramics) get intothese caverns. A particles oscillate in such a pit, accumulating energy, and finally theenergy will be sufficient both for heating and for destruction of the pit walls (tablet turninginto powder). The same processes seem to be taking place in a palladium electrolytic cellwith heavy water, and in a nickel electrolytic cell with ordinary water, which accounts foranomalously large heat generation, not related to nuclear processes.

The explanation of the excessive heating in electrolytic cells, following from ourUnified theory, is based on three factors:

1. The stimulation of cavitational fluctuation/microbubbles collapsing by thecavities/caverns in the volume of negative electrodes (cathodes), accompanied by strongtemperature fluctuations and a shock waves. The contributions of accelerations of nuclears,

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induced by high-frequency VPWq1 ;

2. The partially inelastic recoil antirecoil effects, accompanied Corpuscle Wavepulsation of the deuterons and protons and energy exchange with walls of cathode cavities;

3. Compensation by rigid walls of cathodes voids the cumulative virtual clouds:CVCd1 and CVCd2

repulsion, due to effect of excluded volume described in section 9,because of their spatial incompatibility in the same W phase of C W pulsation. Thecorresponding rising of the effective pressure and temperature occur when the length ofCVCd1,d2 , equal to de Broglie wave length of this ions exceeds the distance between theircenters of serotinal in cathode cavities and, in some conditions, the diameter of void itself.

One may say, that the source of energy, necessary for cold fusion, is the potentialenergy between atoms/ions, forming the walls of cathode voids, which determines theirrigidness and the excessive virtual pressure. Similar mechanism of heating due to excessive’quantum pressure’ of CVC should exist not only for deuterons, but as well for protons.This consequence of proposed mechanism is confirmed in experiments, mentioned above.

The cold nuclear fusion needs spatial compatibility of two deuterons in the same time,corresponding to wave [W] phase. It is possible, because deuterons are bosons with spins 1 due to similar/parallel orientation of two half-integer spins of proton and neutron,composing deuteron. In accordance to proposed mechanism of Pauli principle realization(see section 9), it means that C W pulsation of proton and neutron of deuteron arecounterphase, providing their exchange interaction. The probability of overcoming ofCoulomb repulsion threshold between positive deuterons and nuclear fusion of dd typein addition to above two factors can be increased by the tunnelling effect, when bothprotons of deuterons pp are simultaneously in the wave [W] phase in form ofsuperimposed cumulative virtual clouds of protons of two deuterons CVCp

CVCp. Forsingle protons (fermions) of hydrogen atoms the probability of simultaneous superpositionof two cumulative virtual clouds is much lower because of the Pauli repulsion of fermionsin the same [W] phase (see section 9).

The collapsing of superimposed wave states of protons of neighboring deuterons backto Corpuscular [C] phase in conditions, when their de Broglie wave length exceeds theseparation between them, may happen in the same space-time, overcoming their Coulombrepulsion. Other reason, facilitating overcoming the Coulomb barrier between twodeuterons in [W] phase, is the much lover electric charge density in CVC, because innonrelativistic conditions the volume of CVC is much bigger, than the volume ofcorpuscular [C] phase of d.

As a consequence, the fusion of two deuterons to helium occur. The coherentcounterphase pulsation of big number of protons and neutrons of deuterons in cavities ofcathode become possible in state of entanglement, stimulated by virtual pressure waves(VPWq

of Bivacuum.The proposed mechanism can be confirmed by following calculations. The most

probable velocity of particle with deuteron mass (md 3.33 1027 kg at the ambienttemperature T 298K in equilibrium state system (heavy water) in accordance withMaxwell distribution is:

v 2kTmd

1.6 105cm/s 24.1

This translational velocity correspond to de Broglie wave length of free deuterons,equal to:

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fr hmdv h 1

2mdkT 1.2 Å 24.2

The absorption of positive deuterons (d on the walls of voids of cathodes or due toincreasing of their density in voids, easily may decrease the translational velocity (24.1)about 10 times or more. For example, the group velocity of water molecule at 25C0 is about104 cm/s (Kaivarainen, 2001), i.e. 16 times less than that of free deuterons (16 104cm/s atthe same temperature.

From 24.2 we can see, that 10 times decreasing of translational group velocity of d(immobilization) is accompanied by increasing the de Broglie wave length of deuterons upto im 12 Å.

We may assume, that the distance between centers of sorption in palladium voids is thesame, as the bond length Pd Pd, equal to 2.75Å. It is less than the length of cumulativevirtual cloud of proton in deuteron CVCD , fixed in cavity in 12/2.75 4.36 times. In thecase of high density of d in voids the separation between them can be smaller.

Let us evaluated the reduced ’quantum pressure’ in voids increasing, provided bysuperposition of number of pairs of cumulative virtual clouds of coherent deuteronsnCVCp

CVCp. The coherency of C W pulsation of number of deuterons can beprovided by entanglement, stimulated by Bivacuum virtual pressure waves (VPW, inaccordance to mechanism, described in section 16.

At the constant temperature, the differential of Clapeyron equation PV RT, workingapproximately also for real systems in equilibrium conditions, can be presented as:

PV VP 0

or : PP VV

24.3

24.3a

where V is the volume expansion in equilibrium conditions, due to difference inexcluded volume of cumulative virtual clouds of free deuterons, as a standing wavesVfr

34 fr

3 with de Broglie wave length, described by (24.1) and in immobilized stateVim 3

4 im3 , corresponding to increasing of volume, occupied by [W] phase of

deuterons CVCp CVCp:

VV Vim Vfr/Vfr

im3 fr3

fr3 PP 122 1.22

1.22 99 24.4

As far the volume of voids in fact do not increase due rigidness of the walls, it meansthat periodic synchronized C W pulsation of number of deuterons in the voids isaccompanied by pulsation of virtual pressure with the same frequency. Assuming thevolume of void remaining permanent: V const, the differential of Clapeyron equation,leads to: VP RT. Dividing the left and right part of this equation to the left and rightparts of Clapeyron equation, we get for the effective increment of temperature in the wavephase of deuterons:

T T PP 298 K 99 30.000 K 24.5

This effective temperature is higher than that, necessary for thermal nuclear fusion(TNF). It means that the mechanisms of CNF and TNF can be the same. However, in TNFcase the function of temperature is replaced by function of virtual pressure in thesimultaneous wave phase of protons in deuterons in cathode voids.

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In a lot of existing experiments our explanation of cold fusion is confirmed by the effectof the excessive heating, almost the same in regular and heavy water and gradualdestruction of cathodes of electrolytic cells.

In the absence of entanglement between deuterons (d np, providing in-phasepulsations of protons, the probability of nuclear fusion increases with temperature. Thisexperimental fact is in accordance with our dynamic model of duality, as far the frequencyof C W pulsation of elementary particles increases with their kinetic energy.Consequently, the temperature increasing - enhance the probability of neighboringuncorrelated protons to occur in the wave phase in the same time moment, whencumulative virtual clouds become spatially superimposed CVCp

CVCp. In accordanceto mechanism, proposed above, it is a condition of cold nuclear fusion of two deuterons tohelium nuclear.

The dimensions of cathode voids, their ability to absorb the deuterons and the rigidnessof void walls determines the probability of cold nuclear fusion and overheating inaccordance to our theory.

The main Conclusions1. A new Bivacuum model, as the infinite dynamic superfluid matrix of virtual dipoles,

named Bivacuum fermions (BVF)i and Bivacuum bosons (BVB i, formed by correlatedtorus (V and antitorus (V, as a collective excitations of subquantum particles andantiparticles of opposite energy, charge and magnetic moments and separated by energygap, is developed. In primordial non polarized Bivacuum, i.e. in the absence of matter andfields, these parameters of torus and antitorus totally compensate each other. Their spatialand energetic properties correspond to three generations of electrons, muons and tauons(i e,,. The positive and negative Virtual Pressure Waves (VPWq

and Virtual SpinWaves (VirSWq

S1/2 are the result of emission and absorption of positive and negativeenergy Virtual Clouds (VC, resulting from transitions of V and V between differentstates of excitation, symmetrical in realms of positive and negative energy: j k q.

2. The symmetry shift between V and V actual and complementary mass and chargeto the left or right, opposite for Bivacuum fermions BVF and antifermions BVF has therelativistic and reverse to that dependence on these dipoles external rotational-translationalvelocity. This shift is accompanied by sub-elementary fermion and antifermion formation.The formation of sub-elementary fermions/antifermions and their fusion to stable triplets ofelementary fermions, like electrons or protons F F Fe,p, following by the restmass and charge origination, become possible at the certain rotation velocity (v) of Cooperpairs of BVF BVF around their common axis. It is shown, that thisrotational-translational velocity value is determined by Golden Mean condition:(v/c)2 0.618. The photon is a result of fusion (annihilation) of two triplets ofparticle and antiparticle: [electron positron] or [proton antiproton]. It represents arotating sextet of sub-elementary fermions and antifermions with axial structural symmetryand minimum energy 2m0

ec2.3. The fundamental physical roots of Golden Mean condition: (v/c)2 vgrext/vphext are

revealed, as the equality of internal and external group and phase velocities of torus andantitorus of sub-elementary fermions, correspondingly: vgrin vgrext; vphin vphext. Theseequalities are named ’Hidden Harmony Conditions’.

4. The new expressions for total, potential and kinetic energies of de Broglie waves ofelementary particles were obtained. The former represents the extended basic Einstein andDirac formula for free particle:

129

Etot mVc2 1 v/c2 m0c2 h2/mV

B2

The new formulas take into account the contributions of the actual mass/energy of torus(V and those of complementary antitorus (V, correspondingly, of asymmetricsub-elementary fermions to the total ones. The shift of symmetry between the mass andother parameters of torus and antitorus of sub-elementary fermions are dependent on theirinternal rotational-translational dynamics in triplets and the external translational velocityof the whole triplets. The latter determines the de Broglie wave frequency and length:B h/mV

v5. A dynamic mechanism of [corpuscle (C) wave (W)] duality is proposed. It

involves the modulation of the internal (hidden) quantum beats frequency between theasymmetric ’actual’ (torus) and ’complementary’ (antitorus) states of sub-elementaryfermions or antifermions by the external - empirical de Broglie wave frequency of thewhole particles (triplets). In nonrelativistic conditions such modulation stands for the wavepackets origination.

6. It is demonstrated, that the elastic deformations and collective excitations ofBivacuum matrix, providing the electric and magnetic fields origination, are a consequenceof reversible recoil antirecoil effects, generated by correlated Corpuscle Wavepulsation of sub-elementary fermions/antifermions of triplets and their fast rotation. Thelinear and circular alignment of Bivacuum dipoles and their dynamics are responsible forelectrostatic and magnetic field origination, correspondingly. The zero-point vibrations ofparticle and evaluated zero-point velocity of these vibrations are also the result ofrecoil antirecoil effects, accompanied by C W pulsation of triplets.

The photon in out theory is a result of fusion/annihilation of two triplets: electron positron, turning two asymmetric fermions to quasi-symmetric boson. The electromagneticfield, is a result of Corpuscle - Wave pulsation of photon and its fast rotation with anglevelocity (rot), equal to pulsation frequency. The clockwise or anticlockwise direction ofphoton rotation (see Fig.2), as respect to direction of its propagation, corresponds to its spinsign: s .

The gravitational waves and field are the result of positive and negative energy virtualpressure waves excitation (VPWq

and VPWq by the in-phase C W pulsation of pairs

F F of triplets F F F, counterphase to that of unpaired F. Such virtualwaves provide the attraction or repulsion between pulsing remote particles, depending onphase shift of pulsations, as in the case of hydrodynamic Bjerknes force interaction. Theantigravitation is responsible for so-called negative pressure energy. The potentialgravitational energy of huge number of symmetric Bivacuum dipoles is equal to sum of theabsolute values of energies of torus and antitorus:

EG0 N

mV mV

c2 N

m0c22n 1

This attraction gravitational energy of unperturbed Bivacuum, whenmV mV

m0determines the cold dark matter.

7. Maxwell’s displacement current and the additional instant currents are theconsequences of asymmetric Bivacuum dipoles (BVF and BVB) symmetric excitationsand vibrations, correspondingly. Their vibrations represent the elastic deformations ofsecondary Bivacuum matrix, induced by presence of matter and fields. The increasing ofthe excluded for photons volume of toruses and antitoruses due to their vibrations, enhancethe refraction index of Bivacuum and decrease the light velocity near strongly gravitatingand charged objects. The nonzero contribution of the rest mass energy to photons and

130

neutrino energy is a consequence of the enhanced refraction index of secondary Bivacuum.8. It is shown that the Principle of least action and realization of 2nd and 3d laws of

thermodynamics for closed systems - can be a result of slowing down the dynamics ofparticles and their kinetic energy decreasing, under the influence of the basic - lowerfrequency Virtual Pressure Waves (VPWq1

with minimum quantum numberq j k 1. This is a consequence of induced combinational resonance between[C W pulsation of particles and basic VPWq1

of Bivacuum. The new notion ofBivacuum Tuning Energy (TE), responsible for forcing of particles pulsation frequency toresonance conditions with VPWq1

, is introduced.9. It is demonstrated, that the dimensionless ’pace of time’ (dt/t dTk/Tk) and time

itself for each closed system are determined by the change of this system kinetic energy.They are positive, if the particles of the system are slowing down under the influence ofVPWq1

and Tuning energy of Bivacuum. The dt/t and t are negative in the oppositecase. This new concept of time is extending that of relativistic theory. Our formula for timeincludes not only velocity, but also acceleration.

10. The notion of Virtual Replica (VR) or virtual hologram of any material object isdeveloped. The VR is a result of interference of all-pervading quantized Virtual PressureWaves (VPWq

and VPWq and Virtual Spin waves (VirSWq

S1/2) of Bivacuum, workingas ”reference waves” in holograms formation, with modulated by de Broglie waves ofmatter atoms and molecules - ”object waves” VPWm

and VirSWm1/2. In our Unified

theory the virtual pressure waves energy is interrelated with gravitational attraction orrepulsion.

11. A possible Mechanism of Quantum entanglement between remote elementaryparticles via Virtual Guides of spin, momentum and energy (VirGS,M,E is proposed. TheVirGS,M,E, connecting similar and coherent electrons and nuclears of atoms of Sender(S)and Receiver(R). The single VirGS,M,E

BVB can be assembled from Bivacuum bosons BVB i.The doubled VirGS,M,E

BVFBVF from the adjacent microtubules, rotating in opposite directions,can be formed by Cooper pairs of Bivacuum fermions [BVF BVFi. Thespin/information transmission via Virtual Guides is accompanied by reorientation of spinsof tori and antitori of conjugated Bivacuum dipoles. The momentum and energytransmission from S to R is realized by the instant pulsation of diameter of such virtualmicrotubule. The Virtual Guides of both kinds represent the quasi 1D virtual Bosecondensate with nonlocal properties, similar to that of ’wormholes’.

12. It is demonstrated that the consequences of Unified theory (UT) of Bivacuum,matter and fields are in good accordance with known experimental data. Among them:electromagnetic radiation of nonuniformly accelerating charges; the double turn(2 360 7200 of the electron’s spin in external magnetic field, necessary for totalreversibility of spin state of fermion. The two slit experiment also get its explanation evenin a single particles case, as a consequence of interference of particle in the wave phasewith its own virtual replica (VR).

13. The mechanisms of antigravitational Biefield-Brown, overunity Searl effect,Bearden overunity generator, cavitational overunity device, cold nuclear fusion and theexcessive heat effect are proposed. It follows from our Unified theory, that the forcedresonance of high-frequency virtual pressure waves VPWq2,3...

of Bivacuum withC W pulsation of the electrons and protons, accelerating them, can be a general sourceof energy for overunity devices. The low frequency basic VPWq1

can accelerate virtualparticles, however, it slow down the velocity and energy of real elementary particles.

14. The mechanism of nuclear cold fusion and overheating in cathodes of electrolyticcell with heavy water is proposed. It is based on superposition of cumulative virtual cloudsof protons of two deuterons (d in their wave phase, in conditions of excessive quantum

131

pressure, corresponding to very high effective temperature, when their de Broglie wavelength exceeds few times a spatial separation between d on centers of absorption in smallvoids/cracks of cathode.

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