archived as http://www.stealthskater.com/Documents/Pitkanen_38.doc (also …Pitkanen_38.pdf) => doc pdf URL-doc URL-pdf

more from Matti Pitkänen is on the /Pitkanen.htm page at doc pdf URL

note: because important websites are frequently "here today but gone tomorrow", the following was archived from http://matpitka.blogspot.com/2010/02/life-as-islands-of-rationalalgebraic.html on February 16, 2010. This is NOT an attempt to divert readers from the aforementioned website. Indeed, the reader should only read this back-up copy if the updated original cannot be found at the original author's site.

Life as islands of rational/algebraic numbers in the seas ofreal and p-adic continua

by Dr. Matti Pitkänen / February 15, 2010

Postal address:Köydenpunojankatu 2 D 1110940, Hanko, Finland

E-mail: matpitka@luukku.comURL-address: http://tgdtheory.com

(former address: http://www.helsinki.fi/~matpitka )"Blog" forum: http://matpitka.blogspot.com/

The possibility to define Entropy differently for rational/algebraic entanglement -- and the fact that number theoretic entanglement Entropy can be negative -- raises the question about which kind of systems can possess this kind of entanglement. I have considered several identifications. But the most elegant interpretation is based on the idea that living matter resides in the intersection of real and p-adic worlds -- somewhat like rational numbers live in the intersection of real and p-adic number fields.

The observation that Shannon entropy allows an infinite number of number theoretic variants for which the entropy can be negative in the case that probabilities are algebraic numbers leads to the idea that Living matter in a well-defined sense corresponds to the intersection of real and p-adic worlds.

This would mean that the mathematical expressions for the space-time surfaces (or at least 3-surfaces or partonic 2-surfaces and their 4-D tangent planes) make sense in both real and p-adic sense for some primes p. The same would apply to the expressions defining quantum states. In particular, entanglement probabilities would be rationals or algebraic numbers so that entanglement can be negentropic and the formation of bound states in the intersection of real and p-adic worlds generates information and is thus favored by NMP.

This picture has also a direct connection with Consciousness.

1. Algebraic entanglement is a prerequisite for the realization of intentions as transformations of p-adic space-time sheets to real space-time sheets representing actions. Essentially, a leakage between p-adic and real worlds is in question and makes sense only in Zero Energy Ontology since various quantum numbers in real and p-adic sectors are not, in general, comparable in positive energy ontology so that Conservation Laws would be broken.

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TGD

Algebraic entanglement could be also called cognitive. The transformation can occur if the partonic 2-surfaces and their 4-D tangent space-distributions are representable using rational functions with rational coefficients in preferred coordinates for the imbedding space dictated by symmetry considerations. Intentional systems must live in the intersection of real and p-adic worlds. For the minimal option, Life would be also effectively 2-dimensional phenomenon and essentially a boundary phenomenon as number theoretical criticality also suggests.

2. The generation of non-rational (non-algebraic) bound state entanglement between the system and external world means that the system loses consciousness during the state function reduction process following the U-process generating the entanglement. What happens is that the Universe corresponding to a given CD decomposes to 2 un-entangled subsystems which in turn decompose. The process continues until all subsystems have only entropic bound state entanglement or negentropic algebraic entanglement with the External World.

3. If the sub-system generates entropic bound state entanglement in the process, it loses consciousness. Note that the entanglement entropy of the sub-system is a sum over entanglement entropies over all subsystems involved. This hierarchy of subsystems corresponds to the hierarchy if sub-CDs so that the survival without a loss of consciousness depends on what happens at all levels below the highest level for a given self.

In more concrete terms, the ability to stay conscious depends on what happens at cellular level also. The stable evolution of systems having algebraic entanglement is expected to be a process proceeding from short to long length scales as the evolution of Life indeed is.

4. U-process generates a superposition of states in which any sub-system can have both real and algebraic entanglement with the External World. This would suggest that the choice of the type of entanglement is a volitional selection. A possible interpretation is as a choice between Good and Evil. The hedonistic complete freedom resulting as the entanglement entropy is reduced to zero on one hand and the algebraic bound state entanglement implying correlations with the External World and meaning giving up the maximal freedom on the other hand.

The hedonistic option is risky since it can lead to non-algebraic bound state entanglement implying a loss of consciousness. The second option means expansion of Consciousness -- a fusion to the ocean of consciousness as described by spiritual practices.

5. This formulation means a sharpening of the earlier statement "Everything is conscious and consciousness can be only lost" with the additional statement "This happens when non-algebraic bound state entanglement is generated and the system does not remain in the intersection of real and p-adic worlds anymore".

Clearly, the quantum criticality of the TGD Universe seems has very many aspects and Life as a critical phenomenon in the number theoretical sense is only one of them besides the criticality of the space-time dynamics and the criticality with respect to phase transitions changing the value of Planck constant and other more familiar criticalities. How closely these criticalities relate remains an open question.

A good guess is that algebraic entanglement is essential for quantum computation which therefore might correspond to a conscious process. Hence, cognition could be seen as a quantum computation like process (a more appropriate term being quantum problem solving). Living-Dead dichotomy could correspond to rational-irrational or to algebraic-transcendental dichotomy. This at least when Life is

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interpreted as Intelligent Life. Life would in a well-defined sense correspond to islands of rationality/algebraicity in the seas of real and p-adic continua.

The view about the crucial role of rational and algebraic numbers (as far as Intelligent Life is considered) could have been guessed on very general grounds from the analogy with the orbits of a dynamical system. Rational numbers allow a predictable periodic decimal/pinary expansion and are analogous to one-dimensional periodic orbits. Algebraic numbers are related to rationals by a finite number of algebraic operations and are intermediate between periodic and chaotic orbits allowing an interpretation as an element in an algebraic extension of any p-adic number field.

The projections of the orbit to various coordinate directions of the algebraic extension represent now periodic orbits. The decimal/pinary expansions of transcendentals are un-predictable being analogous to chaotic orbits.

The special role of rational and algebraic numbers was realized already by Pythagoras. The fact that the ratios for the frequencies of the musical scale are rationals supports the special nature of rational and algebraic numbers. The special nature of the Golden Mean (which involves 51/2) conforms the view that algebraic numbers rather than only rationals are essential for Life.

For details, see for instance the article "TGD-inspired theory of Consciousness" and the chapter "Quantum Theory of Self-Organization" of Bio-Systems as Self-Organizing Systems.

Comments

1. At 3:27 AM, Matti Pitkanen said... The new territory will be the connection between Number Theory and Physics. The gist of my

posting is that the quantum physics of Intention, Cognition, and Life could be what one might call "number theoretical quantum field theories". Basic notion would be rational points and subset of algebraic points as intersection of partonic 2-surfaces. At these points, Intention and Action would meet.

This notion is certainly familiar for mathematicians but totally unknown land for physicists. Maybe this physics is standard stuff of theoretical physics seminars before year 2050;-).

2. At 3:46 AM, Matti Pitkanen said... Nuclear string model predicts a lot of new nuclear physics -- part of which has already shown itself

as anomalies. The essentially new element are color flux tubes with quark and anti-quark at their ends connecting nucleons. They can have charges 1,-1 besides vanishing charges. Charged color bonds imply almost degeneracy of nuclear ground states.

One can have bosonic counterparts of fermionic nuclei with almost same mass and giving rise to almost the same chemistry but playing a key role in the new dark matter chemistry since they can form Bose-Einstein condensates at the magnetic flux tubes.

The new secondary p-adic time scales assigned with elementary particles. In particular the 0.1 second timescale assignable with electron as timescale of corresponding "Causal Diamond" and defining fundamental biorhythm will mean a direct connection between living and dead matter.

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By the way, I received from Gabor an article published by Nobelist Szent-Györgyi as early as 1941 with the title "Towards a New Biochemistry" [included below]. The necessity for new Biochemistry has been realized by the greatest visioniaries for 70 years ago. But the mainstream of Big Science is still trying to make progress with textbook wisdom! Mediocricy has replaced democracy in science.

3. At 7:47 PM, Matti Pitkanen said... Entropy (that is, negative information) is the only thing that Physics today can offer. Shannon

entropy is non-negative so that Shannon negentropy as its negative defines negative information measure. In case of entanglement, this is easy to understand since we do not know with certainty whether Schrodinger's cat is dead or alive. The point is to find measure for the entanglement itself as carrier of information.

If entanglement probabilities are rational numbers (even algebraic numbers are allowed), one can define number theoretic (p-adic) variants of Shannon entropy satisfying the basic defining conditions. These entropies can be negative and one can find prime p for which the entropy is maximally negative. Rational (algebraic) entanglement carries information- even more: conscious information. Entangling in this manner does not lead to a loss of consciousness but expands it. Joining to the ocean of consciousness as meditators express it. Suddenly even this talk about "cosmic consciousness" begins to make sense.

What is remarkable that this condition is true if Life is in the intersection of p-adic and real worlds. Life and intelligent Consciousness mean a physical counterpart for number theoretical criticality. p-Adic Intention can transform to real Action.

Also my own great experience -- which took me to the road leading to Consciousness theory and about which I have told a lot at my homepage -- can be finally understood. I have really experienced what it feels when all this background noise in body disappears and the entire body (or is it the magnetic one?) goes in a flowing liquid-like state of well-being.

All evolution is basically spiritual in this framework. Just expansion of Consciousness experienced as well-being and love. The basic ethical value is here. Moral rules can provide means of achieving this depends on situation. The basic rule is that the rule should not cause violence (which means by definition reduction of consciousness). Krishnamurti said all this in different words. He was quite spiritual number theorists. Indians are!

4. At 5:32 AM, Matti Pitkanen said... I have now begun to understand how far reaching the implications of number theoretic Shannon

entropy are. The presence of the negentropic entanglement implies the directedness of the biological processes since the outcome of the state function reduction would be far from random. The behavior of negentropic bonds could be almost deterministic. In the case of time-like entanglement, this would select only particular initial final state pairs so that determinism would emerge also in this manner and could lead to almost deterministic irreversible cellular automaton behavior characteristic for the living matter and very different from the reversible determinism of Classical Physics and very difficult to understand in Quantum context.

This would provide a general explanation for the ability of the living matter to overcome the Second Law of Thermodynamics basically implied by quantum randomness of the standard Quantum Theory. Non-equilibrium thermodynamics and cellular automaton models could be seen as phenomenological descriptions for the actual breaking of the Second Law in the intersection of real and p-adic worlds.

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I reworked to today the model for ATP→ADP+Pi (the fundamental piece of Biology). The first basic elements of the model are the magnetic flux tubes forming an Indra's net. For instance, they would connect ATP to catalyst molecules to catalyst molecules so that reduction of hbar would contract the flux tubes and bring the molecules near to each other.

The second element is liberation of metabolic energy as electron or proton drops to a larger space-time sheet. The third element is the assumption that the O=:s of phosphates act as universal plugs to which flux tubes are connected.

The new element is the assumption that negentropic entanglement is associated with the flux tubes and is between the ends of flux tubes. The innermost flux O= is connected to catalyst molecule so that ATP and O= can find each other when needed by reducing the value of Planck constant.

This identifies high energy phosphate bond as a flux tube between outer O=:s of ATP and carrying negentropic entanglement and positive energy. No binding energy would be needed since Negentropy Maximization Principle would stabilize the system.

All flux tube connections can be regarded as high energy bonds made possible by NMP which allows to have correlated pairs without binding energy. This binding would be a free love affair whereas ordinary binding to the bottom of potential well would be like the jail of the organized marriage. Krishnamurti was a brilliant biologists too;-)!

It really becomes possible to understand ATP to ADP transformation and various related processes. I attached the first draft of pdf file [below] as an example.

5. At 1:42 AM, Matti Pitkanen said... from Ulla: "How is it then with free will in TGD if everything is deterministic?"'

I did not say that everything is deterministic. Only in the intersection of real and p-adic worlds it is possible to get rid of total randomness of the state function reduction process simply because negentropy maximization does not choose between entangled eigenstates of density matrix with vanishing entropy now but leads to highly unique state with minimum negative entanglement entropy.

Thermalization in ensemble can be seen as a consequence of the random outcome of ordinary state function reduction and this is avoided in the case of negentropic entanglement. Thermal noise disappears just as I directly experienced as a bodily sensation in my "big experience".

Second aspect: Every quantum jump involves as a first step unitary process and this makes means re-creation. Only the initial and final states of even (positive and negative energy parts of Zero Energy state) in this intersection tend to be strongly correlated (unlike in the case of ordinary state function reduction).

In any case, however, I am just beginning to realize how powerful a notion this number theoretic negentropy is.

6. At 11:41 PM, Matti Pitkanen said... All Zero Energy states are in well-defined sense morphic fields. It is a matter of convention at what

level one begins to speak about memory.5

For instance, electrons causal diamond corresponds to the time scale 0.1 seconds which defines the fundamental biorhythm. This suggests that the magnetic bodies of electrons are crucial for consciousness and life. The self-organization patterns assignable to self plus the hierarchy of its subselves resulting in quantum jump define the habits, memes. The feed of ordered energy is central in self organization and now it is replaced with the feed of energy assignable to negentropic entanglement. Dissipation serves still as the Darwinian selector.

The interpretation of feelings and emotions like pain is very natural if one assigns the fundamental emotions to the expansion or loss of consciousness at some level of hierarchy of subselves.

Negentropic entanglement would allow to understand emotions. Negentropy would be the basic measure. Unfortunately, the positive emotion resulting from negentropic entanglement has a finite duration in Geometric-Time since CD has finite size.

About the beginning of new era. Science is what determines our values (or rather the lack of them) at this moment. In reductionistic science, there are no values; there is no good or evil; there is no love. There is only a fight for survival or the universe as a dead machine. This kind of world view more than explains why society has become a jungle. Our civilization is really about destroying itself.

The only manner to change the situation is through the fusion of Science and Spirituality. My sincere hope is that these ideas could be taken seriously despite the fact that they generate aggression and disgust in a typical colleague for whom science means a specialization to apply a particular algorithm to lengthen curriculum vitae.

http://tgdtheory.com/public_html/newbiochem.pdf

TOWARDS A NEW BIOCHEMISTRY? [1]by Professor A. Szent-Gygrgyi

University, Szeged, Hungary

The atom consists of a nucleus surrounded by a system of electrons. By sharing one-or-more electrons, atoms can join to form molecules. In such a molecule, as a rule every electron belongs to 1-or-2 atoms. This is our idea of a single small molecule. And this picture has hitherto unconsciously governed our thinking in Biochemistry.

The study of crystals and metals, however, has revealed the existence of a different state of matter. If a great number of atoms is arranged with regularity in close proximity (as for instance, in a crystal lattice), the terms of the single valency electrons may fuse into common bands. The electrons in this band cease to belong to 1-or-2 atoms only and belong to the whole system.

These bands (or energy levels) are separated from possibly higher levels by forbidden zones. Under ordinary conditions, all electrons are within the lowest band. If this lowest band contains the maximum number of electrons (21ń if the number-of-atoms is n) as is the case with insulators, the electrons will be unable to transport energy.

If, however, one of these electrons is raised by the absorption of energy to a higher level and comes to be in what we call an "excited state" where it will move and transport its energy freely, it will be

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impossible to say which is the atom to which the excited electron belongs and the whole system can be looked upon as "activated". By falling back to the lower level, the electron will give off its excess energy and perform work in a place more or less distant from that of the absorption of energy.

This is the case with certain phosphors, as has been shown lately by N. Rieh1 [2]. Here (as for instance in ZnS) the electron -- raised to a higher level by a collision with an α particle -- can travel relatively long distances and will fall back to a lower level, giving up its energy where it meets a Cu atom ( present as an impurity). Thus the absorption and emission of energy will proceed independently at different places.

The problem is whether this state of matter (i.e., common energy levels) exists also in living systems. If it does, it cannot fail to influence profoundly our biological thinking and open new approaches to research and understanding. Protein molecules are systems built up of a great number of atoms closely-packed with great regularity. So theoretically, the possibility exists that within these molecules analogous conditions to those in crystals prevail.

The first indication of the existence of such common energy levels was given by the study of photosynthesis (one of the most fundamental biological processes). Emerson and Arnold [3] found that 2,500 chlorophyll molecules form one functional unit. Warburg and Negelein [4] showed that 4 quanta are necessary for the reduction of one CO2 molecule. There are observations to indicate that these 4 quanta must reach the CO2 molecule simultaneously.

Gaffron and Woh1 [5] calculated how many chlorophyll molecules must interact to absorb 4 quanta simultaneously at the meekest optimal illumination. Their calculation showed that only 1,000 molecules are capable of doing this. These observations indicate that the electrons -- raised to a higher energy level by the absorbed light -- can move and transport their energy freely through the system of chlorophyll molecules.

Kubowitz and Haas [6] have measured the inactivation-spectrum of urease. And P. Jordan [7] has pointed out that their results are in agreement with the idea that common energy levels exist within this protein molecule. At present, K. Laki and M. Gerendas are engaged in my laboratory in the study of the inactivation-spectrum of fumarase crystallized by Laki. Their results also indicate that the energy absorbed may leave the place of its absorption and cause a break of links at a different place, thus traveling at some distance through the molecule [8].

The more interesting question, however, is not whether common energy levels exist within one molecule but whether protein molecules can join into more extended systems with common energy levels. It would be difficult to picture such a continuum built up of globular protein molecules. Protein molecules have hitherto -- with rare exceptions -- been found to be globular.

However, last year Banga and I [9] found that the proteins building up the solid structure of the cell are fibrous. And that these fibrous molecules -- as shown by their strong thixotropy -- are interconnected by intermolecular forces. Chloroplasts also contain fibrous proteins.

This finding allows us to tentatively suppose that a greater number of molecules may join to form such energy continua along which energy (viz. excited leetrons) may travel a certain distance. The study of gene-mutation introduced by x-rays and ultraviolet light also indicates such a possibility. It cannot be expected that any single observation will definitely solve this problem. Only the accumulation of a great mass of data will answer these questions.

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But even at this early stage, we are justified in reconsidering the biological problems in the light of these possibilities. My own biochemical research of 2 decades has yielded one or another insignificant result (the isolation of this or that). But whenever I was faced with a fundamental problem, I failed. When these problems are reconsidered in the light of common energy levels, an easy explanation offers itself. I will enumerate a few of these problems stort.ing with one which arose lately in collaboration with Ranga [9].

The contractile element in muscle is myosine (a protein built up of fibrous molecules). These molecules are arranged in small, primitive bundles. A great number of such primitive bundles forms one microscopic fibril. The energy of muscular contraction is derived from the splitting of adenosine triphosphate.

The adenosinetriphosphatase activity is bound up with myosine. But our measurements indicate that only a very small fraction of myosine molecules can be endowed with such activity. The problem is how the energy liberated by a molecule can be communicated to a great number of similar molecules. The common energy levels give an easy answer.

Another problem that troubled me for many years was why the enzymes involved in oxidation and fermentation can be separated so sharply into soluble and insoluble ones. The enzymes involved in lactic fermentation of muscle are soluble while the enzymes involved in oxidation are insoluble (i.e., bound to the insoluble fibrous proteins of the cell). This difference can be explained if we suppose that the latter are part of a system with common energy levels. In lactic fermentation, no such common levels are necessary because the single enzymes do not interact but react in series with soluble molecules.

Still another problem (closely connected with the former) is how the enzymes of oxidation interact. In part of the oxidation system, electrons wander directly from enzyme to enzyme. The enzymes -- being insoluble -- have no free molecular motion and must be arranged so that their small reactive groups are at atomic distances.

It is possible to arrange 2 large protein molecules in such a way. But it is geometrically impossible to so arrange a whole series. Even if we could devise such an arrangement, it would still be incomprehensible how the energy liberated by the passing of an electron from one substance to the other (viz., from one Fe atom to the other,) could do anything useful.

All this can be understood if we suppose that the single catalysts are connected with different, distinct energy levels and that the electrons do not pass directly from one substance to the other but travel within the corresponding energy band and can fall to a lower level and give off energy only at a place where they can do work (e.g., a synthesis), analogous to the ZnS phosphors of Riehl. If the cell and with it the energy levels are disturbed in some way, we can expect the electrons to fall freely to lower levels at any place. This might explain why catabolic processes prevail over anabolic ones in damaged tissues (and cancer?); why certain oxidations (catecholoxidase) are activated by damage; why chloroplasts refuse to build up carbohydrates; and why viruses refuse to multiply outside the cell.

In closing, I wish to mention 3 problems from outside the field of my own work. One of my difficulties with protein chemistry was that I could not imagine how such a protein molecule can “live”. Even the most involved protein structural formula looks “stupid” if I may say so. If the atomic structure is only the backbone underlying the common energy levels, the thing becomes more likely.

It is equally difficult to understand the great biological activity of certain molecules. R.Kuhn, F. Moewus, and D. Jerchell [10] have shown lately that one single crocin molecule is capable of inducing a

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sexual change in a whole alga. If the cell forms an energy continuum, any substance approaching at any point can upset the whole system making, so to say, a "hole" in the continuum.

Then we do not know what a “cell” really means. Or why the kidney, for instance, is subdivided into such wanted. Possibly the cell wall is the border line of the still missing.

Biochemistry is, at present, in a peculiar state. By means of our active substances, we can produce the most astounding biological reactions. But we fail wherever a real explanation of molecular mechanisms is wanted. It looks as if some basic fact about life were units still missing, without which any real understanding is impossible. It may be that the knowledge of common energy levels will start a new period in Biochemistry, taking this science into the realm of Quantum Mechanics..

References[1] Korbnpi Memorial Lecture given in Budapest on March 21, 1941.[2] N. Riehl, Naturwiss., 28: 601, 1940.[3] R. Emerson and W.I. Arnold, Jour. gen. Physiol., 16:191, 1930.[4] O. Warburg and E. Ncgelein, Naturwiss., 13: 985, 1925.[5] H. Gaffron and K. Wohl, Naturwiss., 24: 81, 1936.[6] F. Kubowitz and E. Haas, Biochem. Zeits. 257:337. 1933[7] P. Jordan, Natuwiss., 42: 693, 1938.[8] If common energy levels are present in native protein molecules, this cannot fail to contribute to

the stability of the molecule and influence its immunological behavior.[9] J. Banga and A. Szent-GyErgyi, Science, 92: 514, 1940; Enzymozogia, 9: 111, 1940.

[10] R. Kuhn, F. Moewus, and D. Jerchel, Ber. d. Chem. Ges., 71: 1541, 1938.

http://tgdtheory.com/public_html/phosphatebond.pdf

0.1 Could high energy phosphate bond be negentropic bond with negative binding energy?

Most people assign the word "Love" to the word "Life" as their first association. There is a notable exception to this: scientists (including biologists). The uneducated layman might, however, wonder whether one can understand Life without identifying any physical counterpart for this notion (which could be replaced with that of compassion, sex, the ability to act synergetically … or just "X" if some of these notions sounds less un-scientific).

Certainly, the word "Love" stimulates a deep feeling of disgust in a reductionistically-conditioned scientist. But isn't the duty of the scientist to win this kind of feeling and try to see whether this identification might be possible after all? The prize could be high. The understanding of what distinguishes between living and dead matter could change the entire culture. Who knows, maybe it could be possible to identify some poorly understood fundamental biological process allowing a quantitative model using a guess for what this physical correlate could be.

The basic step of metabolism is at the core of Life and indeed poorly understood. I shall argue that the identification of the negentropic entanglement as the counterpart for the notion of "Love" could allow to model quantititatively what happens in this process.

0.1.1 Basic ideas9

Before continuing, general motivating comments about implications of negentropic entanglement are in order.

1. Ordinary bound states are stable because they have positive binding energy. One can visualize this kind of binding as a "jail". The second particle resides near the bottom of a potential well. "Organized marriage" is a social analogy for this situation. Negentropic entanglement makes bound states possible for which binding energy can have (and perhaps even has always has) the wrong sign. The state is not prevented from decaying to free particles in state function reduction by energy conservation. The Negentropy Maximization Principle (NMP) [H2] takes care that they remain correlated. The social analogy would be a voluntary marriage based on love. Partners are completely free to leave but do not want to do it. One implication could be explanation for the stability of highly charged basic molecules of life such as DNA and ATP.

2. The presence of the negentropic entanglement implies the directedness of the biological processes since the outcome of the state function reduction would be far from random since the behavior of negentropic bonds could be almost deterministic. In the case of time-like entanglement, this would select only particular initial final state pairs so that determinism would emerge also in this sense and could lead to almost deterministic irreversible cellular automaton behavior characteristic for the living matter very different from the reversible determinism of classical physics and very difficult to understand in Quantum context.

3. The determinism would of course be only partial and would allow volition not spoiled by randomness of quantum jump. This would provide a general explanation for the ability of the living matter to overcome the Second Law of Thermodynamics basically implied by quantum randomness predicted by the standard Quantum Theory. This would happen in time scales shorter than the timescale of the appropriate causal diamond (CD) only. But one would have hierarchy of CD meaning that in arbitrary long timescales there are levels of hierarchy at which the Second Law is broken.

The hierarchy of Planck constants would be also crucial since it would allow zooming up to arbitrarily an long timescale. Non-equilibrium thermodynamics and cellular automaton models could be seen as phenomenological descriptions for the actual breaking of the Second Law in the intersection of real and p-adic worlds.

0.1.2 General formulation of the model

Consider now the model. The high-energy phosphate bond [1] assigned with the 2 outer-most phosphates of ATP [3] is fundamental for the basic processes in living matter. The ATP → ADP + P i

liberates metabolic energy loaded to ATP in the cellular respiration process [5] or its equivalent and occurs again and again and defines a kind of Karma's cycle in living matter. The phosphate bond is assumed to have a high energy content liberated as ATP is hydrated to ADP [2] and phosphate ion Pi = PO3-

4 [4]. The notion of high-energy phosphate bond has been challenged, however, as being meaningless [6, 7, 8].

1. One can, of course, consider a high-energy bond for which potential looks like a well at the top of mountain. Spin glass degeneracy of Quantum-TGD would certainly allow to consider this kind of notion. I do not know whether models realizing this idea concretely have been really constructed.

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2. My earlier proposal for ATP → ADP + Pi process is inspired by the notion of many-sheeted space-time and p-adic length scale hypothesis making sense in the intersection of real and p-adic worlds and involves the dropping of protons to larger space-time sheets and driven back in oxidative metabolism. The energy liberated in this process corresponds to the Zero-Point kinetic energy of protons which is smaller at the larger space-time sheet. The maximum value of zero point kinetic energy is predicted to be E0 ≈ 0.5 eV for k = 137 in the case of the proton and for k = 148 in the case of the electron (for the electron, the energy would be by a factor 2-

11mp/me ≈ 0.94 smaller).

3. With an inspiration coming from DNA as a topological quantum computer model [L5], I have also proposed that the magnetic flux tubes connecting biomolecules to each other define kind of Indra's net plays a key role in the biological information processing analogous. For instance, topological quantum computation could be realized in terms of braids formed by flux tubes [L5, ?]. O=:s associated with phosphates would serve as universal plugs to which flux tubes could be connected. In particular, the innermost O = of ATP could be connected by a flux tube to any biomolecule needing metabolic energy (say, some catalyst or the F1 machine central for energy metabolism).

The reduction of Planck constant would bring ATP and the biomolecule near each other and lead to a formation of a weakly-bound state making catalytic processes possible. The outer O=:s of the ATP molecule could be connected by a flux tube to each other which could be rather long. This flux tube could provide the new physics realization of the high-energy phosphate bond.

4. ATP (Pi) has 4 [3] units of negative charge and at least the ordinary layman might wonder why this does not induce instability. A similar problem is encountered in the case of DNA which contains 2 units of negative charge per nucleotide. This particular problem is regarded as completely real. The idea about Life as something in the intersection of real and p-adic worlds [I1] raises the question whether these high-energy states could be made possible by the presence of negentropic bonds (most naturally associated with the flux tubes with large ђ). This love marriage would stabilize ATP, ADP, and DNA and other charged biomolecules.

The presence of phosphates would be a clear-cut signature of this stabilization mechanism. Also, proteins involve phosphates playing a key role in the biocontrol. Typically phosphorylation activates or de-actives the protein and is also involved with the generation of signal pathways. Why this happens would be easy to understand in Indra's net model.

5. In ATP → ADP+Pi transformation the energy carried by the negentropic bonds would be liberated but leave the flux tube bonds negentropic. Cell respiration would take care of the loading of the batteries with negentropic metabolic energy. This would involve the kicking of protons back to the smaller space-time sheets. Also, the molecular lovers ADP and Pi would find each other again as the Planck constant for the flux tube connecting them would be reduced during the cellular respiration.

0.1.3 Quantitative estimates

Consider now a more detailed model for ATP → ADP + P i. The binding of ATP to the catalytic site involves several steps. I have described them in [L7] and in the following add to this template the interpretation suggested by the proposed picture.

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1. Step 1: The binding ATP + F1 →ATP → F1 to the catalyst site is a complex process involving the break-up of the hydrogen bonds between cellular water and ATP molecule and cell water and catalyst site and generation of hydrogen bonds between catalyst site and ATP molecule. In TGD framework, this means that protons can be kicked to and dropped back from atomic space-time sheets. Only the net number of protons dropped matters, however.

This process involves liberation of Gibbs free energy about ∆GATP = 0.42 eV. It was earlier believed that this energy is liberated instantaneously. But the findings about the behavior of the F1 motor coupled to dissipative load lead Oster and Wang to suggest that the process is more complex and starts from a loose binding and ending up to a strong binding [?].

Comment: One can question the assumption that strong binding is generated. The simplest interpretation in the proposed picture is that the negentropic flux tube connecting ATP and Fi molecule and behaving as high-energy phosphate bond associated with innermost O= is contracted via the reduction of Planck constant. Then a proton is dropped from k = 137 space-time sheet and liberates metabolic energy E(137) = 0.5 eV.

(a) The simplest interpretation in the proposed picture is that the negentropic flux tube connecting ATP and F1 molecule and behaving as a high-energy phosphate bond associated with the innermost O= is contracted via the reduction of Planck constant. Then a proton is dropped from the k=137 space-time sheet to a much larger space-time sheet and liberates metabolic energy quantum E(137) ≈ 0.5 eV.

Another possibility is that an electron at the k=148 space-time sheet is dropped. This process would replace the instantaneous generation of binding energy. In Zero Energy Ontology, the timescale for this process would correspond to the time scale of appropriate causal diamond (CD).

(b) Instead of single particle energy, Macroscopic Gibbs energy G = E + PV - TS is the useful notion now since Macroscopic quantities of matter are studied and pressures and temperature are typically constant in the situations considered (dG = -SdT + VdP). G is minimized for constant T and P prevailing in the situation considered.

(c) In the attachment of ATP to catatyst, S is reduced. A good guess is that the volume is not affected so that PV term does not change. From this, one can deduce that the liberated energy per catalyst particle (call it ∆e = ei - ef = ∆g - T∆s (i and f refer to initial and final states) satisfies ∆e > ∆g = 0.42 eV.

(d) One must estimate the value of ∆e. The attachment reduces the kinetic energy of relative motion of catalyst and ATP to zero. If it makes sense to speak about thermal equilibrium for ATP an catalyst in translational degrees-of-freedom, the reduction of kinetic energy is ∆eK = 3T/2. Which is of order 0.045 eV at room temperature. Whether this energy remains in the catalyst-ATP system or is it liberated in the process is not clear. The energy liberated in the dropping of the proton or electron gives a contribution ∆e = E0 = 0.5 eV. This gives the condition

∆g1 = E0 + 3T/2 - T∆s = 0.42 eV (1)

If the liberated kinetic energy remains in the system, the first guess is ∆e = E0 = 0.5 eV where E0 is the nominal value of Zero-Point kinetic energy. This would give for T∆s the estimate T∆s = 0.08 eV (about 3 times thermal energy corresponding to 3 translational degrees-of-freedom). This looks like a rather reasonable order of magnitude estimate.

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(e) NMP suggests (maybe even requires) that the bond remains negentropic. The binding energy associated with ATP- catalyst binding could be small (of the order of thermal energy about 0.045 eV).

2. Step 2: Hydrolysis: F1 ∙ ATP → F1 ∙ ADP ∙ Pi. The change of free energy is small during this step (∆G ~ 0).

Comment: The simplest option explaining the fact that the change of energy is small is that hydrolysis leaves the flux tube between outer O=s of ATP intract and removes only the P-O-P bond. This flux loop could have rather large ħ.

3. Step 3: Ortophosphate is released from the catalyst site: F1 ∙ADP ∙Pi → F1 ∙ADP + Pi. Free energy ∆G ~ 0.31 eV is liberated at this step.

Comment: The simplest option is that the negentropic flux tube liberates its energy but remains negentropic. The increase of Planck constant might be involved.

(a) The value of ∆e is now smaller than ∆G which suggests that the metabolic energy quantum corresponds to E(139) ≈ 0.25 eV. The average change of kinetic energy can be assumed to be equal to thermal energy in final state and is same as above. This gives the condition

∆g2 = E0/2 - 3T/2 + T∆s = 0.32 eV .

(b) By adding this equation with the similar equation for Step 1 (see Eq. 1), one obtains the condition

∆g1 + ∆g2 = 3E0/2 = 0.74 eV .

This gives E0 = 0.49 eV so that the model seems to be internally consistent.

4. Step 4: ADP is released from the catalyst site: F1 ∙ ADP + Pi → F1 + ADP + Pi. ∆G ~ 0 holds true also for this process.

Comment: ђ increases back to the original value for the innermost flux tube which could it still have small positive energy and be negentropic.

The model would predict that ADP and Pi and remain highly correlated as do also AXP and Fi. These predictions should be testable by marking ADP and Pi of ATP with the same "color" (say radioactively) and finding whether the colors of ADP and Pi remain the same during the subsequent cycles or whether they mix immediately.

These love affairs at molecular level could be modified only by reconnections of flux tubes as also in human relationships. For instance, two ADPs could exchange their P is or F1s. Negentropic entanglement could guarantee the highly-organized and directed nature of basic biocatalytic processes.

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misc. remarks

A. If I had to find correlate for chi or subtle energies or various other analogous notions, it would be magnetic flux tubes with negentropic entanglement between their ends and no binding energy between their ends.

DNA is highly-charged and its stability is a well-known puzzle. If I remember correctly, 2 units of negative charge per nucleotide and the phosphates extending the system by bringing in negentropic flux tubes and negentropic entanglement could stabilize DNA. DNA as a topological quantum computer model assumes that flux tubes connect DNA and nuclear and cell membranes.

It is also known that DNA is stable against dehydration only inside the cell nucleus. Negentropic entanglement need not (but could) relate to this. An alternative explanation is that water inducing polymerization by hydration is in ordered ice-like state.

Large ђ for flux tubes increases the time period during which negentropic entanglement prevails. Recall that in Zero Energy Ontology, the basic structure is causal diamond, chronon, or event. The larger the bar, the longer the duration of this event. Breakdown of the Second Law is always below some timescale.

This comment of Mae about networks fits very nicely with the proposed mechanism of metabolism. The strong prediction is that ADP and Pi remain connected by long flux tube and find each other in the next event. Also, ADP remains connected with the system for which provided metabolic energy. These predictions should be testable by radioactively marking ADP and Pi of ATP with same "color" and finding whether the colors remains the same during the subsequent cycles or whether they mix immediately. Mixing of colors is possible, of course, by the reconnection of flux tubes in which two ADPs exchange their Pis.

Opening the meaning of the last paragraph would require some work. I am not a professional!

B. One must be careful with the meaning of "Life is quantum physical". Standard wave mechanics or quantum field theory is certainly not enough.

● p-Adic physics brings in negentropic entanglement.● Hierarchy of Planck scales brings in Macroscopic and even astroscopic quantum coherence

besides dark matter.● The new view about space-time brings in the notion of magnetic body among other things.● Zero-Energy Ontology brings in the new view about time, thermodynamics, and self-organization.

References[I1] The chapter "Quantum Theory of Self-Organization" of Biosystems as Self-Organizing

Quantum Systems.http://tgd.wippiespace.com/public_html/bioselforg/bioselforg.html#selforgac.

[L5] The chapter "DNA as Topological Quantum Computer" of Genes and Memes.http://tgd.wippiespace.com/public_html/genememe/genememe.html#dnatqc.

[L7] The chapter "Evolution in Many-Sheeted Space-Time" of Genes and Memes.http://tgd.wippiespace.com/public_html/genememe/genememe.html#prebio.

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[H2] The chapter "Negentropy Maximization Principle" of TGD-inspired theory of Consciousness.http://tgd.wippiespace.com/public_html/tgdconsc/tgdconsc.html#nmpc.

[1] High-energy phosphate, http://en.wikipedia.org/wiki/High-energy_phosphate .

[2] Adenosine di-phosphate. http://en.wikipedia.org/wiki/Adenosine_diphosphate .

[3] Adenosine tri-phosphate. http://en.wikipedia.org/wiki/Adenosine_triphosphate .

[4] Phosphate. http://en.wikipedia.org/wiki/Phosphate .

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