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Critical Acceleration andVacuum Structure

Johann RafelskiDepartment of Physics, The University of ArizonaCharles A Whitten Memorial Symposium Dec 15/16 2011

I discuss foundational ultra-high acceleration physics challenges arising in the contextof relativistic laser pulse interactions: pulse interaction with the quantum vacuum, theopportunity to improve understanding of inertia, quantum vacuum as modern dayaether, and the materialization of pulse energy directly into high energy particles.

Supported by US DoE Grant: DE-FG02-04ER41318

Overview

1 Introduction

2 Critical acceleration

3 Fundametal Interaction

4 Mach and Inertia, Aether Quantum Vacuum

5 High energy particles

graphics credit to: S.A. Bulanov, G. Mourou, T. Tajima

The 21st Century Foundational Physics Challenges• How does the structured quantum vacuum control inertia,

and many other laws of physics• Is there a deeper understanding of time?

Rôle of the Universe expansion in defining time?• What is the cosmological dark energy,

λ = (2.4meV)4~−3c−5 = 4.3keVc−2/cm3

Is this excited state quantum Vacuum with non-zero pointenergy? If so how can we induce vacuum decay? What isthe magnitude of causal velocity (‘velocity of light’) in thedifferent vacuum states?

• What is the origin of grand scales as expressed bya) the Planck mass: MP =

√

~c/GN = 1.3 1019mproton andb) Higgs VEV 〈h〉 = 254 GeV ≃ 1013mneutrino.

• Space-time: dimensionality (3+1) → (n + 1): n > 3?Fractal dimension n < 3? Lattice? (Mem)brane?

Discovery is driven by new tools: acceleration

1899:Planck units

“These scales retain their natural meaning as long as the law ofgravitation, the velocity of light in vacuum and the central equations ofthermodynamics remain valid, and therefore they must always arise,among different intelligences employing different means ofmeasuring.” M. Planck, “Über irreversible Strahlungsvorgänge.” Sitzungsberichte der Königlich Preußischen

Akademie der Wissenschaften zu Berlin 5, 440-480 (1899), (last page)

Critical ↔ ‘Planck’ accelerationIn presence of high acceleration we probe connection betweenforces (interactions) and the structure of space-time. In thatsense there is also a ‘limiting’ Planck acceleration, which toavoid misunderstanding we term ‘critical’ acceleration ac .

Einstein’s gravity is built upon EquivalencePrinciple: a relation of gravity to inertia(=theresistance to acceleration). Note that wheninteractions are ‘geometrized’ like gravity instring theories, we are doing away withacceleration. Thus current super-theoriesreally go in direction of removing force. It isquantum physics that allows us today tocreate devices that expose particles toacceleration.

Critical AccelerationCritical acceleration acting on an electron:

ac =mec3

~→ 2.331 × 1029m/s2

This critical acceleration can be imparted on an electron by thecritical ‘Schwinger’ (Vacuum Instability) field strength ofmagnitude:

Ec =m2

ec3

e~= 1.323 × 1018V/m

Truly dimensionless unit acceleration arises when we introducespecific acceleration

ℵ =ac

mc2 =c~

Specific unit acceleration arises in Newton gravity at Plancklength distance: ℵG ≡ G/L2

p = c/~ at Lp =√

~G/c. In presenceof sufficiently strong electric field Ec by virtue of the equivalenceprinciple, we probe electrons subject to Planck scale force.

Critical acceleration probably achieved at RHICTwo nuclei smashed into each other from twosides: components ‘partons’ can be stopped inCM frame within ∆τ ≃ 1 fm/c. Tracks showmultitude of particles produced, as observed atRHIC (BNL).

• The acceleration a achieved to stop some/any of the components ofthe colliding nuclei in CM: a ≃ ∆y

Mi∆τ . Full stopping: ∆ySPS = 2.9, and∆yRHIC = 5.4. Considering constituent quark massesMi ≃ MN/3 ≃ 310 MeV we need ∆τSPS < 1.8 fm/c and ∆τRHIC < 3.4fm/c to exceed ac .• Observed unexplained soft electromagnetic radiation in hadronreactions A. Belognni et al. [WA91 Collaboration], “Confirmation of asoft photon signal in excess of QED expectations in π–p interactionsat 280-GeV/c,” Phys. Lett. B 408, 487 (1997). • Recent suggestions that thermal hadron radiation due to Unruhtype phenomena P. Castorina, D. Kharzeev and H. Satz, “ThermalHadronization and Hawking-Unruh Radiation in QCD,” Eur. Phys. J. C52, 187 (2007), also Biro, Gyulassy [arXiv:1111.4817]

Other path towards super-critical (Planck) accelerationa = 1(= mec3/~ → 2.331 × 1029m/s2)

Directly accelerated electrons at rest in lab by ultra intenselaser pulse: requires Schwinger scale fieldPresent laser pulse intensity technology misses several ordersof magnitude, further development needed. Shortcut: we canLorentz-boost: to reach the critical acceleration scale today: wecollide a counter-propagating electron with a laser pulse.

Laser pulse in electron’s rest frame

Figure shows boost (from left to right) of the force applied by aGaussian photon pulse to an electron, on left counter propagatingwith γ/ cos θ = 2000. Pulse narrowed by (γ cos θ)−1 in thelongitudinal and (γ sin θ)−1 in the transverse direction. Correspondsto Doppler-shift:

ω → ω′ = γ(ω + ~v · nk)

as applied to different frequencies making up the pulse.

SLAC’95 experiment near to critical acceleration

p0e = 46.6 GeV; in 1996/7 a0 = 0.4,

∣

∣

∣

∣

duα

dτ

∣

∣

∣

∣

= .073[me] (Peak)

Multi-photon processes observed:• Nonlinear Compton scattering• Breit-Wheeler electron-positron pairs

• D. L. Burke et al., “Positron production in multiphoton light-by-light scattering,” Phys.Rev. Lett. 79, 1626 (1997)

• C. Bamber et al., “Studies of nonlinear QED in collisions of 46.6 GeV electrons with

intense laser pulses” Phys. Rev. D 60, 092004 (1999).

EM Probe of critical acceleration possible todayIZEST, or SLAC,CEBAF: experimentspossible in principle

CEBAF: There is a 12 GeV(γ = 2400) electron beamThere is a laser teamThere is appropriate highradiation shieldedexperimental hall

Mach, Acceleration → Inertia• To measure acceleration we need to refer to aninertial frame of reference. Once we know one iner-tial observer, the class of inertial observers is defined.

• Before Einstein’s relativity, Mach posited, as an alternative toNewton’s absolute space, a) that inertia (resistance to acceleration)could be due to the background mass in the Universe, and b) that thereference inertial frame must be inertial with respect to the Universemass rest frame. The latter postulate Einstein called ‘Mach’s principle’.

• Any observer inertial wrt CMB frame qualifies: “Mach’s fixed stars".

• GR and later Cosmology motivated by Machs ideas, yet Einsteinnearly eliminated acceleration: geometrization of gravity means thatdust of GR point masses is in free fall.

• Inertia, the resistance to acceleration requires presence ofnon-geometric forces and/or extended quantum matter leading torigid extended material body.

• QFT provides the quantum vacuum, the Aether, as Mach’s frame.

Maxwell, Lorentz and Inertia: ad-hoc combination

The action I comprises three elements: (Fαβ ≡ ∂αAβ − ∂βAα)

I = −14

∫

d4x F 2 + q∫

pathdτ

dxdτ

· A +mc2

∫

pathdτ(u2 − 1).

Path is fixed at the end points assuring gauge-invariance.

• The two first terms upon variation with respect to the field, produceMaxwell equation including radiation emission in presence ofaccelerated charges.

• The second and third term, when varied with respect to the form ofthe material particle world line, produce the Lorentz force equation:particle dynamics in presence of fields.

Maxwell and Lorentz equations which arise NEED NOT BECONSISTENT, the form of I dictated by gauge- andrelativistic-invariance. Many modifications are possible. There is noreference to Mach’s inertial frame allowing definition of acceleration.

Gravity and other interactions not truly unified

J = I√−g +1

8πG

∫

d4x√−g R

There are acceleration paradoxes arising combining gravity andelectromagnetism:

• Charged electron in orbit around the Earth will not radiate ifbound by gravitational field, but it will radiate had it been bendinto orbit by magnets.

• A free falling electron near BH will not radiate but an electronresting on a surface of a table should (emissions outsideobserver’s horizon.

• A micro-BH will evaporate, but a free falling observer may notsee this. Is the BH still there?

One is tempted to conclude that we do not have a theoryincorporating acceleration. New Physics Opportunity if we cancreate unit strength (critical) acceleration.

Better foundational theory not around the corner

Old idea: geometrize EM theory: 5-d Kaluza-Klein.

• EM potential part of 5-metric. To lowest order in charge,Lorentz force arises from 5-d geodetic. Hilbert-Einstein 5-daction reduces to 4-d Einstein-Maxwell action.

Pro: Any geometric EM theory has ‘æther’ and is Machian justlike GR; charge is a property of the ‘æther; the missing degreesof freedom appear in 5th dimension.

Con: Lack of understandings of dynamics in 5-d extradimension, solutions arbitrary. No experiment showinggeneralized equivalence principle justifying use of 5-d geodetic.

Should the generalization of Maxwell-Lorentz be geometric,critical acceleration experiments will be capable to explore thisunification.

Einstein’s Aether as an inertial frame of referenceAlbert Einstein at first rejected æther as unobservable when formulatingspecial relativity, but eventually changed his initial position, re-introducingwhat is referred to as the ‘relativistically invariant’ æther. In a letter to H.A. Lorentz of

November 15, 1919, see page 2 in Einstein and the Æther, L. Kostro, Apeiron, Montreal (2000). he writes:It would have been more correct if I had limited myself, in my earlierpublications, to emphasizing only the non-existence of an æther velocity,instead of arguing the total non-existence of the æther, for I can see that withthe word æther we say nothing else than that space has to be viewed as acarrier of physical qualities.

In a lecture published in May 1920 (given on 27 October 1920

at Reichs-Universität zu Leiden, addressing H. Lorentz), published in Berlin by Julius

Springer, 1920, also in Einstein collected works: In conclusion:. . . space is endowed with physical qualities; in thissense, therefore, there exists an æther. . . . But thisæther may not be thought of as endowed with thequality characteristic of ponderable media, as (NOT)consisting of parts which may be tracked throughtime. The idea of motion may not be applied to it.

Importance of quantum theory

Without quantum theory we would not have extended bodies,without extended material bodies we cannot create criticalacceleration – acceleration due to interplay of quantum and EMtheories.

Quantum vacuum state is providing naturally a Machianreference frame lost in classical limit. Critical acceleration inquantum theory (critical fields) leads to new particle productionphenomena which have a good interpretation and no classicalanalog or obvious limit.

Laws of Physics and Quantum VacuumDevelopment of quantum physics leads to the recognition that vacuumfluctuations define laws of physics (Weinberg’s effective theory picture). Allthis is nonperturbative property of the vacuum.

• The ‘quantum æther’ is polarizable: Coulomb law is modified;E.A.Uehling, 1935

• New interactions (anomalies) such as light-light scattering ariseconsidering the electron, positron vacuum zero-point energy;Euler, Kockel, Heisenberg (1930-36);

• Casimir notices that the photon vacuum zero point energy also inducesa new force, referred today as Casimir force 1949

• Non-fundamental vacuum symmetry breaking particles possible:Goldstone Bosons ’60-s

• ‘Fundamental electro-weak theory is effective - model of EWinteractions, ‘current’ masses as VEV Weinberg-Salam ’70-s

• Color confinement and high-T deconfinementQuark-Gluon Plasma ’80-s

Quantum Vacuum Structure

The best known and widely accepted vacuum property is that itis a dielectric medium: a charge is screened by particle-hole(pair) excitations.

In Feynman language the real photon is decomposed into abare photon and a photon turning into a virtual pair. The resultis a renormalized electron charge smaller than bare, andslightly stronger Coulomb interaction (0.4% effect).

At any field strength the conversion of field energy into pairspossible

Acceleration and temperature

• Unruh observes that an accelerated observers willperceive temperature

TU =a

2π

relation to Hawking radiation:strong acceleration = ?? strong gravity

• Properties of quantum vacuum ‘accelerated’ in a constantfield can be cast into a form displaying heat capacity attemperature

TE =aπ

, a = eE/m

resolution of factor 2 and of the related issue ofFermi-Bose statistics choice remain a challenge

Euler-Heisenberg Z. Physik 98, 714 (1936) evaluate Dirac zero-point energywith (constant on scale of ~/mc) EM- fields, transform to actionE(D, H) → L(E , B) = E − ED, E ≡ ∂E

∂D

L(E , B) = −1

8π2

Z

∞

iǫ

dss3

e−m2s»

sEtan sE

sBtanh sB

− 1 +13(E2 − B2)s2

–

.

E , B relativistic definition in terms of invariants

L(E , B) →2α2

45m4

»

“

~E 2 − ~B 2”2

+ 7(~E · ~B)2–

= light − light scattering

Schwinger 1951 studies in depth the imaginary part – see zeros in tan sE :

|〈0+|0−〉|2 = e−2Im L, 2Im L =

α2

π2

∞X

n=1

n−2e−nπm2/eE

is the vacuum persistence probability in adiabatic switching on/off the E-field.For E → 0 essential singularity.

Note: vacuum unstable for any finite value of E and there is no analyticE → 0 limit!. The light–light perturbative term is first term of semi convergentexpansion which fails in a subtle way.

Temperature for vacuum fluctuations at a =Const.Using identity [B.Müller, W.Greiner and JR, PLB63A (1977) 181]:x cos xsin x

= 1 − x2

3+

∑

k=1

1k2π2

2x4

x2 − k2π2

give after resummation a “statistical” form with T = eE/πm = a/π:

L(E) = −2sm2T8π2

∫

∞

0ρ(ω) ln(1−e−ω/T )dω, ρ = ln(ω2 − m2 + iǫ);

Same sign of pole residues source of Bose statistics. For scalar loop

particles we havex

sin x= 1 +

x2

6+

∑

k=1

(−1)k

k2π2

2x4

x2 − k2π2 which yields

same expression up to: 1) statistics turns from Bose into Fermi:− ln(1−e−ω/T ) → ln(1+e−ω/T ) and 2) factor 2s → 1. Note that thestatistics is reversed compared to expectations and temperature istwice larger compared to Hawking-Unruh observer. Potentialimprovements needed in the nonperturbative approach to constrainsymmetry of the vacuum state.

Materialization into Particles at ULTRA High EnergyTwo high energy photons colliding head on can make particle inlaboratory rest frame. Same is true for two coherent laserpulses. To produce particles at high rapidity we collide two (ormore) laser pulses in a different geometry. For nearly parallelbeams [L.Labun and J.R. Phys Rev D84,0330003 (2011)] pairsarise in a frame of reference that is moving with high PointingMomentum:

pµ := T µνuν , p0 = ε12(~E2 + ~B2) +

14

T µ

µpi = ε (~E × ~B)i = ~S

The mass density is

µ2 := p2 = ε2(S2+P2)+(T µ

µ/4)2 S =

12(~B2−~E2); P = ~E ·~B

Expressed in comoving rest frame

µ2 = ε2(

d2 + b2

2

)2

+ (T µ

µ/4)2

Where the covariant field definition is

d2 =√

S2 + P2 − S → |~E |2 b2 =√

S2 + P2 + S → |~B|2

Integration over all volume yields mass available formaterialization. Particles are produced with high CM framerapidity with respect to lab frame of reference

cosh2 yS =µ2 + ε2(~E × ~B)2

µ2 =(p0)2

µ2

and emerge depending on angle of collision and asymmetry ofintensity r with rapidity

cosh2 y =1 + r sin θ + r2/2

r2(sin2 θ + r sin θ sin φ + r2/4)+ O(α2r3)

Summary

New opportunity to study foundational physics involvingacceleration and search for generalization of laws of physics –motivated by need for better understanding of inertia, Mach’sprinciple, Einstein’s Aether, and the temperature of theaccelerated quantum vacuum .

Critical acceleration possible in electron-laser pulse collisions.Exploration of physical laws in a new domain possible

Experiments should help resolve the old riddle of EM theoryand radiation reactionRich field of applications follows

Application: Ultra high energy particle production withoutacceleration.