The story of Martin Eden

I have a habit of listening radio plays on sunday afternoons and monday evenings. Last time the play contained a short episode in which Kalle Holmberg, finnish director acting in the play, read a fragment of text from the end of a book by Jack London. London had imagined what it is to die by drowning and doing it by own decision. This piece of text was so impressive that I dediced to find the book from the local library. I found it, or actually half of it. The book was "Martin Eden" and it was chopped into two pieces as I realized when I was back at home with part II of the book.

I read what I had got and it struck my feelings very deeply at personal level. The book tells about Martin Eden living a period of life when he has realized that his mission is to become a writer. He devotes all his mental powers to this challenge and learns and works fanatically. He sends his texts to magazines and they are rejected again and again. In some rare occasions the text is published but he has to learn this is by no means a guarantee that he will get the promised royalty. At that time it was not really easy to become a writer in USA. There was no social security system and to become a writer meant readiness to literally starve for years. So did also Martin Eden.

Hunger was however not the worst enemy. The social humiliations were much more difficult to tolerate. At that time people had strong ties to their neighbours. Middle class people saw Martin as a person afraid of real work and wanting to spend his time in leisury pretending that he was some sort of a writer.

Those who loved Martin produced him the deepest agony. His sister and beloved one could not but believe that his continual failure to get the texts published proved that he did not have the needed talent. They tried their best to persuade him to go to job just like anyone else in the neighbourhood did. He could only tell that he knew that he had the gift and could not do anything else. He of course saw that they could not believe him. He had to face their pity and to sense that they felt shame for him.

As a serious writer he of course soon learned that the texts published in literary journals were mostly horrible rubbish. The readers of these magazines wanted simple daydreams. He learned to use his evening time to produce these secondary texts using a simple format and this purposeful rubbish was the only text he got published for a long time.

The catastrophe in personal relationships had to come sooner or later. Martin Eden was a hard borne individualist in the style of Nietche but ironically got a label of communist: this was the final catastrophe. What happened that his friend took him to a meeting of socialist party. He spoke passoniately against socialistic ideas as a slave moral and this stimulated a furious debate between people who had built their world view with hard work and hard life experiences and knew what they were talking about. A local journalist happened to be in the occasion: a young and rather stupid man who did not have a slightest idea what he or anyone else in the meeting was arguing about. As a natural opportunist this young fellow deduced that Martin must be a socialist since all rational people participating in meetings of socialist party had to be socialists in his simple world. So he wrote to a local journal telling about Martin as a local leader of socialist party! Martin Eden had now a label of communist and it become impossible to even buy food from the local store. People did not want to have any contact with him. Also his beloved left him. He was completely alone.

And then suddenly the success came. For some reason impossible to explain one of his texts was accepted in a famous literary magazine and the snowball began to roll. The very same magazines which had not bothered to even respond to him during last years were suddenly fighting to get rights to publish his texts. They were ready to pay him incredible sums of money for just getting the title of his next work. His books were translated to other languages.

Martin Eden was suddenly a rich and famous man. The people who had refused to recognize him at street were now inviting him to lunch. These endless invitations to lunches were really funny: no one had suggested a lunch when he was starving. And nothing had changed. He was exactly the same Martin Eden as before. He had not written a single line of new text during this period of success. Suddenly all these people who had regarded him as a total failure and expressed their disgust openly, were reading his stories and expressing their admiration. Here realized that they were even afraid of him!

Martin Eden had perhaps seen too much to cheat himself. We must have some beliefs or at least illusions about our fellow human beings and society in order to survive but this period of "success" stripped even the last ones off without mercy. The bowl became full when his former beloved came to him and with a lot of tears confessed that she had only now learned to really love him. Martin Eden could not feel anything but embarrashed anymore and by an unlucky accident he had to learn that the tragic episode had been a pre-calculated scene. He was now rich, famous, and desperately alone. He could not hate nor love, his life was devoid of meaning. From this it was not very many paragraphs to the impressive piece of text which I heard from the radio play.

There are many manners to interpret "Martin Eden". It could be seen as a failure of Nietche's idea about Superman. It could be seen as a story about how it is possible to get rid of social illusions to the extent that one is able to resist the basic biological trait to survive and is ready to leave the cycle of Karma. The story could be seen as teaching how mission can help human being to tolerate almost every imaginable humiliation, and how the sudden loss of reason for existence drives a man swimming in money and social wellfare to such a deep depression that the only way out is a suicide.

To me this story was to a surprising degree a story of my life. For me the courage to think with my own brain and express my thoughts was what mission to write was for Martin. How painful it was to receive a label of crackpot as a prize for working years seven days a week and with five hours of sleep per day and going through all the social humiliations that Martin also experienced. How painful it was to realize that the real motivation of my academic destroyers was envy, and that it was useless to try to tell this to anyone because everyone of us wants to live in the world in which professors can be trusted. The complete inability to defend oneself against brutal social violence: it is impossible to tell how paralyzing this experience can be.

I did not of course starve physically but I was starving socially. I had become an academic Zombie. It is quite a feeling to realize that colleagues do not want to sit at your table, that you are not wellcome to any academic party, that you are not invited to speak in any seminar, that people seem to be even afraid of being seen in your company, that you simply cease to exist in academic sense. After this kind of experience, you begin to ask what really distinguishes these people regarded as highly civilized human beings from primitive savages living in a world of taboos.

With a deep pain I remember also the well-meaning attempts of people closest to me to persuade me to take an ordinary job. How painful it was to see that they regarded me as a loser who for a sheer personal vanity could not admit it. My mother dreamed that his son could some day enjoy human rights in this country famous for its social security. Her dream was not filled: she died this summer at the age of ninety four years. I feel that I could forgive these academic bastards all that they have done to me but not what they did to these good and honest people who believe that also professors are good and honest people.

Martin Eden experienced also "success". It seems that also I have now to face the "success" since the tide is now definitely turning in the academic stock market. For slightly more than decade ago two young finnish professors stated publicly that my work fails to safisfy every requirement that anyone can imagine scientific work should satisfy. Now I am listed as a candidate to a category "Phycicists" in Wikipedia. As Martin Eden did, I definitely know that I am the same person now as I was a decade ago and what I have done after that relies on what I had done before this time! Some people were lying for more than decade ago and this meant a professional murder in practice. Elsewhere in society these people would be responsible for what they have done but not in the world of science.

There are also definite social signals that the people who previously did not literally see me are experiencing strange metamorphosis. It has begun with friendly smiles and taps to the shoulder; Nice to see; How it is going..;... If this trend continues, I might be invited sooner or later to give a seminar in Physics Department about my life work! You never know about academic stock markets!

The most amusing piece of social commedy was the appearence of a link to my homepage at the homepage of some young finnish physicist. Certainly one of the first such links since my colleagues are well aware of the dangers of their profession. This fellow obviously knew that this is risky business and had decided to be cautious. He added the link under the title "Hörhöt" ("Nuts") to send a positive signal to the community. To give a positive signal to my direction he divided "Nuts" section into two clearly separate pieces and added a strong intendation to the lower section to create the impression about a separate section whose title had somehow disappeared (I would recommend "Controversially Nuts" as the lost title;-))! My name was the lowest one in the lower list to maximize the spatial distance to "Nuts" . I admit that I had never thought that social calculation could manifest itself as a precise geometric variational principle: maximize the spatial distance between the expressions of two opposite opinions you are forced to have simultaneously!

Despite all this and knowing the fate of Martin Eden, I would love to believe that these people in this corner of Universe have suddenly become human beings in a deeper sense of the word than the social games usually allow. I confess that this is not easy after these 28 years. I try to tell for myself the story about the commendant of a concentration camp with deep admiration for the music of Bach and living a happy family life. I try to tell me that the same human beings who are charming, humorous, and genuinely warmhearted individuals can become monsters as members of a collective. Martin Eden did not have this view about humans to help him over his crisis and this was fatal but I try to have so that I have good reasons to be optimistic.

How to not build theories of everything

I have decided to avoid writing about the situation in string models. After all, anyone with a little bit of intellectual honesty admits at least privately that this theory is dead and the basic reason that we still talk about it as the only known (or even possible!) theory of everything is that very few string theoretician has the moral strength to say "Sorry, this what I am doing has become a waste of money and time so that I do not want to receive my salary anymore!".

Now I however decided to make a few paragraph exception to my blogging habits. There will be a semester long program on string phenomenology taking place in Kavli Institute for Theoretical Physics. Wati Taylor had inaugural talk for the program with the title String Vacua and the Quest for Predictions. The main points of the talk are summarized in Not-Even Wrong. What made me optimistic was that the recent situation in string theory was openly admitted and difficulties analyzed. It is really remarkable that a leading theoretician does this and in this kind of context.

Instead of criticizing string theory and its sociology, I find is much more inspiring to report the growth and evolution of my own brain child TGD as the happy and unashamedly proud father. I hope that these often hastily written postings, besides giving an online documentation about the trial-and-mostly-error process what real scientific work always is, would also demonstrate that many important things have been forgotten during last 21 years.

• Sometimes a real progress in science requires dramatic paradigm shifts but these shifts must be inspired by solutions to the problems of existing theory rather than decision that the model which did not work as a theory of hadrons is the only known theory of everything. The basic idea of TGD was stimulated by a simple question. Could it be possible to solve the conceptual problems related to the definition of energy in general relativity by constructing a Poincare invariant theory of gravitation? The answer to this question stimulated a question-answer process which has yielded 16 online books: not too bad taking into account the miserable circumstances in which this work has done. This continual questioning has also forced me to leave the narrow confines of particle physics and to realize that theory of everything is unavoidably also a theory of consciousness. It is really sad to see the brilliant string theorists to continue beating their big-brained heads on the wall after having narrowed their focus on Planck length scale or to algebraic geometry.

• What it means when idea really works. What was achieved during early days of quantum theory when no computers were available looks completely mysterious unless one realizes that the basic idea was so full of life that it took care of itself. The evolution of TGD during last 28 years without a single coin of research money should also teach the same lesson. The string story in turn convincingly proves that all the king's horses and all the king's men are not enough to resuscitate an idea which is dead.

• Real progress in science is not a series of fads and fashions lasting for year or two but requires total life time long devotion. Group think is not the manner to achieve paradigm shifts. Real revolutions are not made at streets nor are they made in palaces.

• Sticking to hidden philosophical assumptions paralyzes even the brightest thinker. I have heard again and again the evergreen about how standard model works too well, that quantum theories of gravitation cannot be tested experimentally, etc., etc.. My experience is totally different. Having been forced to give up the reductionistic dogma and having developed a network of ideas that really predicts and explains, I have found myself literally swimming in a flood of well-reported anomalies and I find myself again and again wondering how it can be possible that these brilliant theoreticians can be unaware of all this. The biggest anomaly is of course the very phenomenon of life. If your TOE cannot say anything interesting about life and consciousness, it is better to return to the drawing board and start from the scratch again.

During this effusion the inhibitory circuits in my brain have started to counter act (very important for a theoretician to have also these trouble makers) and I hasten to admit that TGD is a zoo of interacting ideas in a vigorous competition for survival rather than a clean and polished theory. Some of these ideas will suffer extinction and it will require time and certainly a lot of collective effort before a precise formulation and construction of the calculational machinery is possible. I also admit that TGD is also an endless error correction process and as such a wonderful means to get rid of self importance and tendency to have very strong opinions (something which should be a first year course in theoretical physics). Returning again and again to texts written for the first time for almost two decades ago is often quite frustrating but always very rewarding process.

In any case, just this morning I feel optimistic. I feel that theoretical physics is not a completely dead discipline after all. As long there is life there is also hope.

Do nuclear reaction rates depend on environment?

Claus Rolfs and his group have found experimental evidence for the dependence of the rates of nuclear reactions on the condensed matter environment (see this and this). See also the comments of Lubos Motl about these findings whose tone is not too difficult to guess. For instance, the rates for the reactions ⁵⁰V(p,n)⁵⁰Cr and ¹⁷⁶Lu(p,n) are fastest in conductors. The model explaining the findings has been tested for elements covering a large portion of the periodic table.

1. Debye screening of nuclear charge by electrons as an explanation for the findings

The proposedd theoretical explanation is that conduction electrons screen the nuclear charge or equivalently that incoming proton gets additional acceleration in the attractive Coulomb field of electrons so that the effective collision energy increases so that reaction rates below Coulomb wall increase since the thickness of the Coulomb barrier is reduced.

The resulting Debye radius

R_D= 69(T/n_effρ_a)^1/2 ,

where ρ_a is the number of atoms per cubic meter and T is measured in Kelvins. R_D is of order .01 Angstroms for T=373 K for n_eff=1, a=1 Angstrom. The theoretical model predicts that the cross section below Coulomb barrier for X(p,n) collisions is enhanced by the factor

f(E)=(E/E+U_e)exp(πη U_e/E).

E is center of mass energy and η so called Sommerfeld parameter and

U_e= 2.09×10^-11(Z(Z+1))^1/2×(n_effρ_a/T)^1/2 eV

is the screening energy defined as the Coulomb interaction energy of electron cloud responsible for Debye screening and projectile nucleus. The idea is that at R_D nuclear charge is nearly completely screened so that the energy of projectile is E+U_e at this radius which means effectively higher collision energy.

The experimental findings from the study of 52 metals support the expression for the screening factor across the periodic table.

1. The linear dependence of U_e on Z and T^-1/2 dependence on temperature conforms with the prediction. Also the predicted dependence on energy has been tested.

2. The value of the effective number n_eff of screening electrons deduced from the experimental data is consistent with n_eff(Hall) deduced from quantum Hall effect.

The model suggests that also the decay rates of nuclei, say beta and alpha decay rates, could be affected by electron screening. There is already preliminary evidence for the reduction of beta decay rate of ²²Na β decay rate in Pd (see this), a metal which is utilized also in cold fusion experiments. This might have quite far reaching technological implications. For instance, the artificial reduction of half-lives of the radioactive nuclei could allow an effective treatment of radio-active wastes. An interesting question is whether screening effect could explain cold fusion and sono-fusion: I have proposed a different model for cold fusion based on large hbar here.

2. Could quantization of Planck constant explain why Debye model works?

The basic objection against the Debye model is that the thermodynamical treatment of electrons as classical particles below the atomic radius is in conflict with the basic assumptions of atomic physics. On the other hand, it is not trivial to invent models reproducing the predictions of the Debye model so that it makes sense to ask whether the quantization of Planck constant predicted by TGD could explain why Debye model works.

TGD predicts that Planck constant is quantized in integer multiples: hbar=nhbar₀, where hbar₀ is the minimal value of Planck constant identified tentatively as the ordinary Planck constant. The preferred values for the scaling factors n of hbar correspond to n-polygons constructible using ruler and compass. The values of n in question are given by

n_F= 2^k ∏_i F_si,

where the Fermat primes F_s=2^2s+1 appearing in the product are distinct. The lowest Fermat primes are 3,5,17,257,2¹⁶+1. In the TGD based model of living matter the especially favored values of hbar come as powers 2^k11.

It is not at all obvious that ordinary nuclear physics and atomic physics should correspond to the minimum value hbar₀ of Planck constant. The predictions for the favored values of n are not affected if one has hbar(stand)= 2^khbar₀, k≥ 0. The non-perturbative character of strong force suggests that the Planck constant for nuclear physics is not actually the minimal one. As a matter fact, TGD based model for nucleus implies that its "color magnetic body" has size of order electron Compton length. Also valence quarks inside hadrons have been proposed to correspond to non-minimal value of Planck constant since color confinement is definitely a non-perturbative effect. Since the lowest order classical predictions for the scattering cross sections in perturbative phase do not depend on the value of the Planck constant one can consider the testing of this issue is not trivial in the case of nuclear physics where perturbative approach does not really work.

Suppose that one has n=n₀=2^k₀ > 1 for nuclei so that their quantum sizes are of order electron Compton length or perhaps even larger. One could even consider the possibility that both nuclei and atomic electrons correspond to n=n₀, and that conduction electrons can make a transition to a state with n₁<n₀. This transition could actually explain how the electron conductivity is reduced to a finite value. In this state electrons would have Compton length scaled down by a factor n₀/n₁.

For instance, suppose that one has n₀=2^11k₀ as suggested by the model for quantum biology and by the TGD based explanation of the optical rotation of a laser beam in a magnetic field (hep-exp/0507107). The Compton length L_e=2.4×10^-12 m for electron would reduce in the transition k₀→ k₀-1 to L_e =2^-11L_e= 1.17 fm, which is rather near to the proton Compton length since one has m_p/m_e≈ .94×2¹¹. It is not too difficult to believe that electrons in this state could behave like classical particles with respect to their interaction with nuclei and atoms so that Debye model would work.

The basic objection against this model is that anyonic atoms should allow more states that ordinary atoms since very space-time sheet can carry up to n electrons with identical quantum numbers in conventional sense. This should have been seen.

3. Electron screening and Trojan horse mechanism

An alternative mechanism is based on Trojan horse mechanism suggested as a basic mechanism of cold fusion. The idea is that projectile nucleus enters the region of the target nucleus along a larger space-time sheet and in this manner avoids the Coulomb wall. The nuclear reaction itself occurs conventionally. In conductors the space-time sheet of conduction electrons is a natural candidate for the larger space-time sheet.

At conduction electron space-time sheet there is a constant charged density consisting of n_eff electrons in the atomic volume V= 1/n_a. This creates harmonic oscillator potential in which incoming proton accelerates towards origin. The interaction energy at radius r is given by

V(r)= α n_effr²/2a³ ,

where a is atomic radius.

The proton ends up to this space-time sheet by a thermal kick compensating the harmonic oscillator energy. This occurs below with a high probability below radius R for which the thermal energy E=T/2 of electron corresponds to the energy in the harmonic oscillator potential. This gives the condition

R= (Ta/n_effα)^1/2 a .

This condition is exactly of the same form as the condition given by Debye model for electron screening but has a completely different physical interpretation.

Since the proton need not travel through the nuclear Coulomb potential, it effectively gains the energy

E_e= Zα/R= (Zα^3/2/a)×(n_eff/Ta)^1/2,

which would be otherwise lost in the repulsive nuclear Coulomb potential. Note that the contribution of the thermal energy to E_e is neglected. The dependence on the parameters involved is exactly the same as in the case of Debye model. For T=373 K in the ¹⁷⁶Lu experiment and n_eff(Lu)=2.2+/-1.2, and a=a₀=.52 Angstrom (Bohr radius of hydrogen as estimate for atomic radius), one has E_e=28.0 keV to be compared with U_e=21+/- 6 keV of Rolfs et al (a=1 Angstrom corresponds to 1.24× 10⁴ eV and 1 K to 10^-4 eV). A slightly larger atomic radius allows to achieve consistency. The value of hbar does not play any role in this model since the considerations are purely classical.

An interesting question is what the model says about the decay rates of nuclei in conductors. For instance, if the proton from the decaying nucleus can enter directly to the space-time sheet of the conduction electrons, the Coulomb wall corresponds to the Coulomb interaction energy of proton with conduction electrons at atomic radius and is equal to α n_eff/a so that the decay rate should be enhanced.

The chapter Does TGD Predict the Spectrum of Planck Constants? of "Towards S-Matrix" contains this piece of text too. See also the chapter TGD and Nuclear Physics of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy"

Some problems of TGD as almost-topological QFT and their resolution

There are some problems involved with the precise definition of the quantum TGD as an almost-topological QFT at the partonic level and the resolution of these problems leads to new insights about the relationship between gravitational and inertial mass and a more precise definition of quantum classical correspondence.

1. Three problems

The proposed view about partonic dynamics is plagued by three problems.

1. The definition of supercanonical and super-Kac-Moody charges in M⁴ degrees of freedom poses a problem. These charges are simply vanishing since M⁴ coordinates do not appear in field equations.

2. Classical field equations for the C-S action imply that this action vanishes identically which would suggest that the dynamics does not depend at all on the value of k. The central extension parameter k determines the over-all scaling of the eigenvalues of the modified Dirac operator. 1/k- scaling occurs for the eigenvalues so that Dirac determinant scales by a finite power k^N if the number N of the allowed eigenvalues is finite for the algebraic extension considered. A constant Nlog(k) is added to the Kähler function and its effect seems to disappear completely in the normalization of states.

3. The general picture about Jones inclusions and the possibility of separate Planck constants in M⁴ and CP₂ degrees of freedom suggests a close symmetry between M⁴ and CP₂ degrees of freedom at the partonic level. Also in the construction of the geometry for the world of classical worlds the symplectic and Kähler structures of both light-cone boundary and CP₂ are in a key role. This symmetry should be somehow coded by the Chern-Simons action.

The first thing to come in mind is the extension of the Kähler form defined at the light-cone boundary to the entire M⁴ as a self dual or antiself-dual instanton. This option looks at first unattractive for several reasons. The Maxwell field in question is not covariantly constant and does not define a generalization of the CP₂ Kähler form. A charged Dirac monopole would be in question. Although its action would vanish, the energy density given by the sum of electro-static and magnetostatic energies would break Lorentz invariance of the Robertson-Walker cosmologies unless one extends the configuration space by adding to it light cones with all Lorentz transforms of the instanton field. Something more elegant is perhaps needed. I will discuss this option in a separate posting and show that it it does not exclude the option discussed here and could form part of the full story.

2. A possible resolution of the problems

A possible cure to the above described problems is based on the modification of Kähler gauge potential by adding to it a gradient of a scalar function Φ with respect to M⁴ coordinates.

1. This implies that super-canonical and super Kac-Moody charges in M⁴ degrees of freedom are non-vanishing.

2. Chern-Simons action is non-vanishing if the induced CP₂ Kähler form is non-vanishing. If the imaginary exponent of C-S action multiplies the vacuum functional, the presence of the central extension parameter k is reflected in the properties of the physical states.

3. The function Φ could code for the value of k(M⁴) via a proportionality constant

   Φ= (k(M⁴)/k(CP₂))× Φ₀ ,

   Here k(CP₂) is the central extension parameter multiplying the Chern-Simons action for CP₂ Kähler gauge potential. This tricks does just what is needed since it multiplies the Noether currents and super currents associated with M⁴ degrees of freedom with k(M⁴) instead of k(CP₂).

The obvious breaking of U(1) gauge invariance looks strange at first but it conforms with the fact that in TGD framework the canonical transformations of CP₂ acting as U(1) gauge symmetries do not give to gauge degeneracy but to spin glass degeneracy since they act as symmetries of only vacuum extremals of Kähler action.

3. How to achieve Lorentz invariance?

Lorentz invariance fixes the form of function Φ uniquely as the following argument demonstrates.

1. Poincare invariance would be broken in any case for a given light-cone in the decomposition of the configuration space to sub-configuration spaces associated with light-cones at various locations of M⁴ but since the functions Φ associated with various light cones would be related by a translation, translation invariance would not be lost.

2. The selection of Φ should not break Lorentz invariance. If Φ depends on the Lorentz proper time a only, this is achieved. Momentum currents would be proportional to m^k and become light like at the boundary of the light-cone. This fits very nicely with the interpretation that the matter emanates from the tip of the light cone in Robertson-Walker cosmology.

Lorentz invariance poses even stronger conditions to Φ.

1. Partonic four-momentum defined as Chern-Simons Noether charge is definitely not conserved and must be identified as gravitational four-momentum whose time average corresponds to the conserved inertial four-momentum assignable to the Kähler action (see this and this). This identification is very elegant since also gravitational four-momentum is well-defined although not conserved.

2. Lorentz invariance implies that mass squared is constant of motion. It is interesting to look what expression for Φ results if the gravitational mass defined as Noether charge for C-S action is conserved. The components of four-momentum for Chern-Simons action are given by

   P^k=(∂ L_C-S/∂ (∂_αa)) m^kl∂_m^la .

   Chern-Simons action is proportional to A_α=A_a∂_αa so that one has

   P^k propto ∂_aΦ ∂_m^ka=∂_aΦ m^k/a.

   The conservation of gravitational mass would give Φ propto a. Since CP₂ projection must be 2-dimensional, M⁴ projection is 1-dimensional so that mass squared is indeed conserved.

   Thus one can write

   Φ= (k(M⁴)/k(CP₂))× x×a/R,

   where R the radius of geodesic sphere of CP₂ and x a numerical constant which could be fixed by quantum criticality of the theory. Chern-Simons action density does not depend on a for this choice.

3. A rather strong prediction is that only homologically charged partonic 3-surfaces can carry gravitational four-momentum. For CP₂ type extremals, ends of cosmic strings, and wormhole contacts the non-vanishing of homological charge looks natural. In fact, for wormhole contacts 3-D CP₂ projection suggests itself and is possible only if one allows also quantum fluctuations around light-like extremals of Chern-Simons action. The interpretation could be that for a vanishing homological charge boundary conditions force X⁴ to approach vacuum extremal at partonic 3-surfaces.

4. Comment about quantum classical correspondence

The proposed general picture allows to define the notion of quantum classical correspondence more precisely. The identification of the time average of the gravitational four-momentum for C-S action as a conserved inertial four-momentum associated with the Kähler action at a given space-time sheet of a finite temporal duration (recall that we work in the zero energy ontology) is the most natural definition of the quantum classical correspondence and generalizes to all charges.

In this framework the identification of gravitational four-momentum currents as those associated with 4-D curvature scalar for the induced metric of X⁴ could be seen as a phenomenological manner to approximate partonic gravitational four-momentum currents using macroscopic currents, and the challenge is to demonstrate rigorously that this description emerges from quantum TGD.

For instance, one could require that at a given moment of time the net gravitational four-momentum of Int(X⁴) defined by the combination of the Einstein tensor and metric tensor equals to that associated with the partonic 3-surfaces. This identification, if possible at all, would certainly fix the values of the gravitational and cosmological constants and it would not be surprising if cosmological constant would turn out to be non-vanishing.

The chapter Construction of Quantum Theory: Symmetries of "Towards S-Matrix" contains this piece of text too.

Quantum model for Priore's machine

Theoretician encounters sometimes inventions which work but seem to defy all attempts to understand them. Even more, it seems a complete mystery how the inventor has ended up with his device, unless one accepts the idea that the inventor was working under the guidance of some higher level conscious entities. Priore's machine demonstrated to heal cancer certainly belongs to this category. Although the biological effects of the Priore's device are described in high detail, the construction of the machine, which is very complicated, is described in a very sketchy manner (see U.S. Office of Naval Research Report on the Priore Machine, 16. August 1978 here). This makes it difficult to see what is essential and what is not.

During years I have used Priore's machine as a kind of testing tool for TGD based quantum model of living matter. The frustrating experience has been that I have not been able to understand the real function of Priore's machine although I have identified which many of the most essential pieces in the puzzle. The most recent view about quantization of Planck constant and about hierarchy of dark magnetic bodies using hierarchy of EEGs to control biological body and to receive information from it motivated take a new look on Priore's machine.

And then the flash came! I realized that the microwave radiation with frequency 9.4 GHz corresponds to the frequency of Josephson radiation at k=1 level of dark matter hierarchy defined by the hierarchy hbar= 2^k11hbar₀ forming the basis for the TGD based model for hierarchy of scaled variants of eEG. The corresponding energy turned out to be exactly the Josephson energy 80 meV associated with the cell membrane resting potential! Thus the function of microwave radiation could be regeneration of Josephson radiation essential for the generation of scaled up variant of EEG.

The basic function of Priore's machine is to artificially regenerate a level in the control hierarchy involving scaled variants of EEG, which is not present in the cancer tissue so that quantum bio-control fails. Priore's machine would do a lot of things.

1. Priore's machine would create the magnetic body corresponding to this level, it would creat also the rotating plasmoids responsible for realization of quantum control and carrying magnetic fields with strengths 612 Gauss and 1224 Gauss used by Priore's machine, and also regenerate the scaled up variant of cell membrane with size scaled up by a factor n=2¹¹ characterizing the corresponding Planck constant hbar=2^k11hbar₀, k=1.

2. Priore's machine would establish scaled up variant of EEG including the needed cyclotron radiation and Josephson radiation, stimulate plasma wave patterns by microwave radiation at plasma frequency, and perhaps also generate temporal codewords representing control commands of the immune system by modulating microwave radiation.

3. Priore's machine would also provide the metabolic energy needed to achieve all this. In particular the highly energetic electrons and X rays with energies up to 300 keV would be needed to give for electrons their high cyclotron energies measured in tens of keV:s. Electrons could be also kicked to space-time sheets with sub-atomic size scale and their dropping would provide metabolic energy quanta up to 258 keV for k=131 space-time sheet.

The constraint that the generalized EEG is precisely scaled up version of the ordinary EEG fixes the model for the function of the Priore's machine essentially completely.

The chapter Homeopathy in Many-Sheeted Space-Time of "Universe as a Conscious Hologram" contains the model for Priore's machine.

Has dark matter been observed?

The group of G. Cantatore has reported an optical rotation of a laser beam in a magnetic field (hep-exp/0507107). The experimental arrangement involves a magnetic field of strength B=5 Tesla. Laser beam travels 22000 times forth and back in a direction orthogonal to the magnetic field travelling 1 m during each pass through the magnet. The wavelength of the laser light is 1064 nm. A rotation of (3.9+/-.5)× 10^-12 rad/pass is observed.

A possible interpretation for the rotation would be that the component of photon having polarization parallel to the magnetic field mixes with QCD axion, one of the many candidates for dark matter. The mass of the axion would be about 1 meV. Mixing would imply a reduction of the corresponding polarization component and thus in the generic case induce a rotation of the polarization direction. Note that the laser beam could partially transform to axions, travel through a non-transparent wall, and appear again as ordinary photons.

The disturbing finding is that the rate for the rotation is by a factor 2.8× 10⁴ higher than predicted. This would have catastrophic astrophysical implications since stars would rapidly lose their energy via axion radiation.

The motivation for introducing axion was the large CP breaking predicted by the standard QCD. No experimental evidence has been found has been found for this breaking. The idea is to introduce a new broken U(1) gauge symmetry such that is arranged to cancel the CP violating terms predicted by QCD. Because axions interact very weakly with the ordinary matter they have been also identified as candidates for dark matter particles.

In TGD framework there is special reason to expect large CP violation analogous to that in QCD although one cannot completely exclude it. Axions are however definitely excluded. TGD predicts a hierarchy of scaled up variants of QCD and entire standard model plus their dark variants corresponding to some preferred p-adic length scales, and these scaled up variants play a key role in TGD based view about nuclear strong force (see this and this), in the explanation of the anomalous production of e⁺e^- pairs in heavy nucleus collisions near Coulomb wall (this), high T_c superconductivity (see this, this, and this), and also in the TGD based model of EEG (see this). Therefore a natural question is whether the particle in question could be a pion of some scaled down variant of QCD having similar coupling to electromagnetic field. Also dark variants of this pion could be considered.

What raises optimism is that the Compton length of the scaled down quarks is of the same order as cyclotron wavelength of electron in the magnetic field in question. For the ordinary value of Planck constant this option however predicts quite too high mixing rate. This suggests that dark matter has been indeed observed in the sense that the pion corresponds to a large value of Planck constant. Here the encouraging observation is that the ratio λ_c/λ of wavelength of cyclotron photon and laser photon is n=2¹¹, which corresponds to the lowest level of the biological dark matter hierarchy with levels characterized the value hbar= 2^11khbar₀, k=1,2,....

The most plausible model is following.

1. Suppose that the photon transform first to a dark cyclotron photon associated with electron at the lowest n=2¹¹ level of the biological dark matter hierarchy. Suppose that the coupling of laser photon to dark photon can be modelled as a coefficient of the usual amplitude apart from a numerical factor of order one equal to α_em(n) propto 1/n.
2. Suppose that the coupling g_πNN for the scaled down hadrons is proportional to α_s⁴(n) propto 1/n⁴ as suggested by a simple model for what happens for the nucleon and pion at quark level in the emission of pion.

Under these assumptions one can understand why only an exotic pion with mass of 1 meV couples to laser photons with wavelength λ= 1 μm in magnetic field B=5 Tesla. The general prediction is that λ_c/λ must correspond to preferred values of n characterizing Fermat polygons constructible using only ruler and compass, and that the rate for the rotation of polarization depends on photon frequency and magnetic field strength in a manner not explained by the model based on the photon-axion mixing.

The chapter Does TGD Predict the Spectrum of Planck Constants? of "Towards S-Matrix" contains the detailed calculations.

Zero energy ontology, cognition, and intentionality

In TGD inspired theory of consciousness the space-time correlates for intentions are provided by p-adic space-time sheets whereas actions correspond to real space-time sheets. The transformation of intention to action corresponds to a quantum jump in which p-adic space-time sheet transforms to a real one: these two space-time sheets have exactly the same analytic representation. The larger the number of rational (algebraic points) in the intersection of the space-time sheets, the more probable the transition is expected to be.

One could however argue that conservation laws forbid p-adic-real phase transitions in practice so that cognitions (intentions) realized as real-to-padic (p-adic-to-real) transitions is not be possible. The situation changes if one accepts what might be called zero energy ontology (see this and this).

1. Zero energy ontology classically

In TGD inspired cosmology the imbeddings of Robertson-Walker cosmologies are vacuum extremals. Same applies to the imbeddings of Reissner-Nordström solution and in practice to all solutions of Einstein's equations imbeddable as extremals of Kähler action. Since four-momentum currents define a collection of vector fields rather than a tensor in TGD, both positive and negative signs for energy corresponding to two possible assignments of the arrow of the geometric time to a given space-time surface are possible. This leads to the view that all physical states have vanishing net energy classically and that physically acceptable universes are creatable from vacuum.

The result is highly desirable since one can avoid unpleasant questions such as "What are the net values of conserved quantities like rest mass, baryon number, lepton number, and electric charge for the entire universe?", "What were the initial conditions in the big bang?", "If only single solution of field equations is selected, isn't the notion of physical theory meaningless since in principle it is not possible to compare solutions of the theory?". This picture fits also nicely with the view that entire universe understood as quantum counterpart 4-D space-time is recreated in each quantum jump and allows to understand evolution as a process of continual re-creation.

2. Zero energy ontology at quantum level

Also the construction of S-matrix leads to the conclusion that all physical states possess vanishing conserved quantum numbers. Furthermore, the entanglement coefficients between positive and negative energy components of the state define a unitary S-matrix. S-matrix thus becomes a property of the zero energy state and physical states code by their structure what is usually identified as quantum dynamics.

Also the transitions between zero energy states are possible but general arguments lead to the conclusion that the corresponding S-matrix is almost trivial. This finding, which actually forced the new view about S-matrix, is highly desirable since it explains why positive energy ontology works so well if one forgets effects related to intentional action.

At space-time level this would mean that positive energy component and negative energy component are at a temporal distance characterized by an appropriate p-adic time scale and the integer characterizing the value of Planck constant for the state in question. The scale in question would also characterize the geometric duration of quantum jump and the size scale of space-time region contributing to the contents of conscious experience. The interpretation in terms of a mini bang followed by a mini crunch suggests itself also.

3. Hyper-finite factors of type II₁ and new view about S-matrix

The representation of S-matrix as unitary entanglement coefficients would not make sense in ordinary quantum theory but in TGD the von Neumann algebra in question is not a type I factor as for quantum mechanics or a type III factor as for quantum field theories, but what is called hyper-finite factor of type II₁. This algebra is an infinite-dimensional algebra with the almost defining, and at the first look very strange, property that the infinite-dimensional unit matrix has unit trace. The infinite dimensional Clifford algebra spanned by the configuration space gamma matrices (configuration space understood as the space of 3-surfaces, the "world of classical worlds") is indeed very naturally algebra of this kind since infinite-dimensional Clifford algebras provide a canonical representations for hyper-finite factors of type II₁.

4. The new view about quantum measurement theory

This mathematical framework leads to a new kind of quantum measurement theory. The basic assumption is that only a finite number of degrees of freedom can be quantum measured in a given measurement and the rest remain untouched. What is known as Jones inclusions N in M} of von Neumann algebras allow to realize mathematically this idea (see this). N characterizes measurement resolution and quantum measurement reduces the entanglement in the non-commutative quantum space M/N. The outcome of the quantum measurement is still represented by a unitary S-matrix but in the space characterized by N. It is not possible to end up with a pure state with a finite sequence of quantum measurements.

The obvious objection is that the replacement of a universal S-matrix coding entire physics with a state dependent unitary entanglement matrix is too heavy a price to be paid for the resolution of the above mentioned paradoxes. Situation could be saved if the S-matrices have fractal structure. The quantum criticality of TGD Universe indeed implies fractality. The possibility of an infinite sequence of Jones inclusions for hyperfinite type II₁ factors isomorphic as von Neumann algebras expresses this fractal character algebraically. Thus one can hope that the S-matrix appearing as entanglement coefficients is more or less universal in the same manner as Mandelbrot fractal looks more or less the same in all length scales and for all resolutions. Whether this kind of universality must be posed as an additional condition on entanglement coefficients or is an automatic consequence of unitarity in type II₁ sense is an open question.

5. The S-matrix for p-adic-real transitions makes sense

In zero energy ontology conservation laws do not forbid p-adic-real transitions and one can develop a relatively concrete vision about what happens in these kind of transitions. The starting point is the generalization of the number concept obtained by gluing p-adic number fields and real numbers along common rationals (expressing it very roughly). At the level of the imbedding space this means that p-adic and real space-time sheets intersect only along common rational points of the imbedding space and transcendental p-adic space-time points are infinite as real numbers so that they can be said to be infinite distant points so that intentionality and cognition become cosmic phenomena.

In this framework the long range correlations characterizing p-adic fractality can be interpreted as being due to a large number of common rational points of imbedding space for real space-time sheet and p-adic space-time sheet from which it resulted in the realization of intention in quantum jump. Thus real physics would carry direct signatures about the presence of intentionality. Intentional behavior is indeed characterized by short range randomness and long range correlations.

One can even develop a general vision about how to construct the S-matrix elements characterizing the process (see this). The basic guideline is the vision that real and various p-adic physics as well as their hybrids are continuable from the rational physics. This means that these S-matrix elements must be characterizable using data at rational points of the imbedding space shared by p-adic and real space-time sheets so that more or less same formulas describe all these S-matrix elements. Note that also p₁→ p₂ p-adic transitions are possible.

The interpretation of infinite primes leads to a detailed vision about space-time correlates of quantum states and cognition and intentionality. Intentions correspond to p-adic space-time sheets and actions to their real counterparts being related by a mere algebraic continuations of the exlicit analytic representsions as surfaces. Cognitions correspond to pairs of real space-time sheet and correspond p-adic space-time sheet obtained in the same manner providing also a representation for a state generated by appropriate generator of super algebra.

The discreteness of the intersection of the real space-time sheet and its p-adic variant obtained by algebraic continuation would be a completely universal phenomenon associated with all fermionic states. This suggests that also real-to-real S-matrix elements involve instead of an integral a sum with the arguments of an n-point function running over all possible combinations of the points in the intersection. S-matrix elements would have a universal form which does not depend on the number field at all and the algebraic continuation of the real S-matrix to its p-adic counterpart would trivialize. Note that also fermionic statistics favors strongly discretization unless one allows Dirac delta functions.

The chapter p-Adic Physics as Physics of Cognition and Intention of "TGD Inspired Theory of Consciousness" contains a more detailed text about this topic.

Infinite primes, cognition, and intentionality

Somehow it is obvious that infinite primes (see this) must have some very deep role to play in quantum TGD and TGD inspired theory of consciousness. What this role precisely is has remained an enigma although I have considered several detailed interpretations (see the link above).

In the following an interpretation allowing to unify the views about fermionic Fock states as a representation of Boolean cognition and p-adic space-time sheets as correlates of cognition is discussed. Very briefly, real and p-adic partonic 3-surfaces serve as space-time correlates for the bosonic super algebra generators, and pairs of real partonic 3-surfaces and their algebraically continued p-adic variants as space-time correlates for the fermionic super generators. Intentions/actions are represented by p-adic/real bosonic partons and cognitions by pairs of real partons and their p-adic variants and the geometric form of Fermi statistics guarantees the stability of cognitions against intentional action.

1. Infinite primes very briefly

Infinite primes have a decomposition to infinite and finite parts allowing an interpretation as a many-particle state of a super-symmetric arithmetic quantum field theory for which fermions and bosons are labeled by primes. There is actually an infinite hierarchy for which infinite primes of a given level define the building blocks of the infinite primes of the next level. One can map infinite primes to polynomials and these polynomials in turn could define space-time surfaces or at least light-like partonic 3-surfaces appearing as solutions of Chern-Simons action so that the classical dynamics would not pose too strong constraints.

The simplest infinite primes at the lowest level are of form m_BX/s_F + n_Bs_F, X=∏_i p_i (product of all finite primes). m_B, n_B, and s_F are defined as m_B= ∏_ip_i^m_i, n_B= ∏_iq_i^n_i, and s_F= ∏_iq_i, m_B and n_B have no common prime factors. The simplest interpretation is that X represents Dirac sea with all states filled and X/s_F + s_F represents a state obtained by creating holes in the Dirac sea. The integers m_B and n_B characterize the occupation numbers of bosons in modes labelled by p_i and q_i and s_F= ∏_iq_i characterizes the non-vanishing occupation numbers of fermions.

The simplest infinite primes at all levels of the hierarchy have this form. The notion of infinite prime generalizes to hyper-quaternionic and even hyper-octonionic context and one can consider the possibility that the quaternionic components represent some quantum numbers at least in the sense that one can map these quantum numbers to the quaternionic primes.

The obvious question is whether configuration space degrees of freedom and configuration space spinor (Fock state) of the quantum state could somehow correspond to the bosonic and fermionic parts of the hyper-quaternionic generalization of the infinite prime as proposed here. That hyper-quaternionic (or possibly hyper-octonionic) primes would define as such the quantum numbers of fermionic super generators does not make sense. It is however possible to have a map from the quantum numbers labelling super-generators to the finite primes. One must also remember that the infinite primes considered are only the simplest ones at the given level of the hierarchy and that the number of levels is infinite.

2. Precise space-time correlates of cognition and intention

The best manner to end up with the proposal about how p-adic cognitive representations relate bosonic representations of intentions and actions and to fermionic cognitive representations is through the following arguments.

1. In TGD inspired theory of consciousness Boolean cognition is assigned with fermionic states. Cognition is also assigned with p-adic space-time sheets. Hence quantum classical correspondence suggets that the decomposition of the space-time into p-adic and real space-time sheets should relate to the decomposition of the infinite prime to bosonic and fermionic parts in turn relating to the above mention decomposition of physical states to bosonic and fermionic parts.

   If infinite prime defines an association of real and p-adic space-time sheets this association could serve as a space-time correlate for the Fock state defined by configuration space spinor for given 3-surface. Also spinor field as a map from real partonic 3-surface would have as a space-time correlate a cognitive representation mapping real partonic 3-surfaces to p-adic 3-surfaces obtained by algebraic continuation.

2. Consider first the concrete interpretation of integers m_B and n_B. The most natural guess is that the primes dividing m_B=∏_ip^m_i characterize the effective p-adicities possible for the real 3-surface. m_i could define the numbers of disjoint partonic 3-surfaces with effective p_i-adic topology and associated with with the same real space-time sheet. These boundary conditions would force the corresponding real 4-surface to have all these effective p-adicities implying multi-p-adic fractality so that particle and wave pictures about multi-p-adic fractality would be mutually consistent. It seems natural to assume that also the integer n_i appearing in m_B=∏_iq_i^n_i code for the number of real partonic 3-surfaces with effective q_i-adic topology.

3. Fermionic statistics allows only single genuinely q_i-adic 3-surface possibly forming a pair with its real counterpart from which it is obtained by algebraic continuation. Pairing would conform with the fact that n_F appears both in the finite and infinite parts of the infinite prime (something absolutely essential concerning the consistency of interpretation!).

   The interpretation could be as follows.

   1. Cognitive representations must be stable against intentional action and fermionic statistics guarantees this. At space-time level this means that fermionic generators correspond to pairs of real effectively q_i-adic 3-surface and its algebraically continued q_i-adic counterpart. The quantum jump in which q_i-adic 3-surface is transformed to a real 3-surface is impossible since one would obtain two identical real 3-surfaces lying on top of each other, something very singular and not allowed by geometric exclusion principle for surfaces. The pairs of boson and fermion surfaces would thus form cognitive representations stable against intentional action.

   2. Physical states are created by products of super algebra generators Bosonic generators can have both real or p-adic partonic 3-surfaces as space-time correlates depending on whether they correspond to intention or action. More precisely, m_B and n_B code for collections of real and p-adic partonic 3-surfaces. What remains to be interpreted is why m_B and n_B cannot have common prime factors (this is possible if one allows also infinite integers obtained as products of finite integer and infinite primes).

   3. Fermionic generators to the pairs of a real partonic 3-surface and its p-adic counterpart obtained by algebraic continuation and the pictorial interpretation is as a pair of fermion and hole.

   4. This picture makes sense if the partonic 3-surfaces containing a state created by a product of super algebra generators are unstable against decay to this kind of 3-surfaces so that one could regard partonic 3-surfaces as a space-time representations for a configuration space spinor field.

4. Are alternative interpretations possible? For instance, could q=m_B/m_B code for the effective q-adic topology assignable to the space-time sheet as suggested here. That q-adic numbers form a ring but not a number field casts however doubts on this interpretation as does also the general physical picture.

3. Number theoretical universality of S-matrix

The discreteness of the intersection of the real space-time sheet and its p-adic variant obtained by algebraic continuation would be a completely universal phenomenon associated with all fermionic states. This suggests that also real-to-real S-matrix elements involve instead of an integral a sum with the arguments of an n-point function running over all possible combinations of the points in the intersection. S-matrix elements would have a universal form which does not depend on the number field at all and the algebraic continuation of the real S-matrix to its p-adic counterpart would trivialize. Note that also fermionic statistics favors strongly discretization unless one allows Dirac delta functions.

The chapter Fusion of p-Adic and Real Variants of Quantum TGD to a More General Theory and TGD as a Generalized Number Theory III: Infinite Primes of "TGD as a Generalized Number Theory", and the chapter Infinite Primes and Consciousness of "Mathematical Aspects of Consciousness Theory" contains this piece of text too.

The most recent view about p-adicization program

The generalization of the number concept obtained roughly by glueing reals and various p-adic numbers and their algebraic extensions together along common rationals and possibly also common algebraics is the starting point of TGD vision about fusion of real physics and various p-adic physics. I call the process of assigning to real physics p-adic physics p-adicization and the heuristic idea is that it corresponds to an algebraic continuation. I realized that the recent progress in the understanding of the formulation of quantum TGD at parton level leads also to a considerable progress in p-adicization.The following text gives a brief summary about the most recent view about what p-adicization might be. This view might be characterized as minimalism and would involve geometrization of only the reduced configuration space consisting of the maxima of Kähler function.

1. p-Adicization at the level of space-time

The minimum amount of p-adicization correspond to the p-adicization for the maxima of the Kähler function. The basic question is whether the equations characterizing real space-time sheet make sense also p-adically. Suppose that TGD indeed reduces to almost topological theory defined by Chern-Simons action for the light-like 3-surfaces interpreted as orbits of partonic 2-surfaces (see this, this, and this). If this is the case, then the starting point here would be the algebraic equations defining light-like partonic 3-surfaces via the condition that the determinant of the induced metric vanishes. If the coordinate functions appearing in the determinant are algebraic functions with algebraic coefficients, p-adicization should make sense. This of course, means the assumption of some preferred coordinates and the construction of solutions of equations leads naturally to such coordinates (see this).

If the corresponding 4-dimensional real space-time sheet is expressible as a hyper-quaternionic surface of hyper-octonionic variant of the imbedding space as number-theoretic vision suggests, it might be possible to construct also the p-adic variant of the space-time sheet by algebraic continuation in the case that the functions appearing in the definition of the space-time sheet are algebraic.

2. p-Adicization of second quantized induced spinor fields

Induction procedure makes it possible to geometrize the concept of a classical gauge fields and also of the spinor fields with internal quantum numbers. In the case of the electro-weak gauge fields induction means the projection of the H-spinor connection to a spinor connection on the space-time surface.

In the most recent formulation induced spinor fields appear only at the 3-dimensional light-like partonic 3-surfaces and the solutions of the modified Dirac equation can be written explicitly (see this, this, and this) as simple algebraic functions involving powers of the preferred coordinate variables very much like various operators in conformal theory can be expressed as Laurent series in powers of a complex variable z with operator valued coefficients. This means that the continuation of the second quantized induced spinor fields to various p-adic number fields is a straightforward procedure. The second quantization of these induced spinor fields as free fields is needed to construct configuration space geometry and anti-commutation relation between spinor fields are fixed from the requirement that configuration space gamma matrices correspond to super-canonical generators.

3. Should one p-adicize at the level of configuration space?

If Duistermaat-Heckman theorem holds true in TGD context, one could express configuration space functional integral in terms of exactly calculable Gaussian integrals around the maxima of the Kähler function defining what might be called reduced configuration space CH_red. The huge super-conformal symmetries raise the hope that the rest of S-matrix elements could be deduced using group theoretical considerations so that everything would become algebraic. If this optimistic scenario is realized, the p-adicization of CH_red might be enough to p-adicize all operations needed to construct the p-adic variant of S-matrix.

The optimal situation would be that S-matrix elements reduce to algebraic numbers for rational valued incoming momenta and that p-adicization trivializes in the sense that it corresponds only to different interpretations for the imbedding space coordinates (interpretation as real or p-adic numbers) appearing in the equations defining the 4-surfaces. For instance, space-time coordinates would correspond to preferred imbedding space coordinates and the remaining imbedding space coordinates could be rational functions of the latter with algebraic coefficients. Algebraic points in a given extension of rationals would thus be common to real and p-adic surfaces. It could also happen that there are no or very few common algebraic points. For instance, Fermat's theorem says that the surface xⁿ+yⁿ=zⁿ has no rational points for n>2..

This picture is probably too simple. The intuitive expectation is that ordinary S-matrix elements are proportional to a factor which in the real case involves an integration over the arguments of an n-point function of a conformal theory defined at a partonic 2-surface. For p-adic-real transitions the integration should reduce to a sum over the common rational or algebraic points of the p-adic and real surface. Same applies to p₁→ p₂ type transitions.

If this picture is correct, the p-adicization of the configuration space would mean p-adicization of CH_red consisting of the maxima of the Kähler function with respect to both fiber degrees of freedom and zero modes acting effectively as control parameters of the quantum dynamics. If CH_red is a discrete subset of CH ultrametric topology induced from finite-p p-adic norm is indeed natural for it. 'Discrete set in CH' need not mean a discrete set in the usual sense and the reduced configuration space could be even finite-dimensional continuum. Finite-p p-adicization as a cognitive model would suggest that p-adicization in given point of CH_red is possible for all p-adic primes associated with the corresponding space-time surface (maximum of Kähler function) and represents a particular cognitive representation about CH_red.

A basic technical problem is, whether the integral defining the Kähler action appearing in the exponent of Kähler function exists p-adically. Here the hypothesis that the exponent of the Kähler function is identifiable as a Dirac determinant of the modified Dirac operator defined at the light-like partonic 3-surfaces suggests a solution to the problem. By restricting the generalized eigen values of the modified Dirac operator to an appropriate algebraic extension of rationals one could obtain an algebraic number existing both in the real and p-adic sense if the number of the contributing eigenvalues is finite. The resulting hierarchy of algebraic extensions of R_p would have interpretation as a cognitive hierarchy. If the maxima of Kähler function assignable to the functional integral are such that the number of eigenvalues in a given algebraic extension is finite this hypothesis works.

If Duistermaat-Heckman theorem generalizes, the p-adicization of the entire configuration space would be un-necessary and it certainly does not look a good idea in the light of preceding considerations.

1. For a generic 3-surface the number of the eigenvalues in a given algebraic extension of rationals need not be finite so that their product can fail to be an algebraic number.

2. The algebraic continuation of the exponent of the Kähler function from CH_red to the entire CH would be analogous to a continuation of a rational valued function from a discrete set to a real or p-adic valued function in a continuous set. It is difficult to see how the continuation could be unique in the p-adic case.

The chapter TGD as a Generalized Number Theory I: p-Adicization Program of the book "TGD as a Generalized Number Theory" contains the most recent view about p-adicization.

My countryman in Wikipedia

I learned from a comment of anonymous to previous posting that Lubos Motl has written something to Wikipedia about finnish physicist Matti Pitkanen whom I happen to know quite well. Knowing Lubos the text could have been much more nasty and I am proud that Lubos sees the trouble of writing something about my countryman who is probably not experienced as any threat for string hegenomy. The text below is the stub by Lubos.

Matti Pitkanen is a Finnish alternative theoretical physicist who has attempted to prove the Riemann hypothesis, worked with p-adic numbers, and proposes an unusual theory called TGD that no other physicist understands.

I would like to suggest a couple of corrections. Pitkanen proposed a "strategy for proving Riemann hypothesis" (as a matter fact a proposal for a sketchy proof based on the identification of zeros as the spectrum of conformal weights of certain conformally invariant physical system: I understand why he choose the cautious formulation). I happen to know that Pitkanen is still working intensively with p-adic numbers and has some strange ideas about how to generalize the notion of number by fusing reals and p-adics to a larger structure. He seems also to believe that p-adic physics could provide the physics of cognition and intentionality. I would like to complete the stub but better not. I still remember the bloodthirsty furor stimulated by my attempt to fill the stub about TGD inspired theory of consciousness which is also one of the great passions of my countryman but not mentioned in the stub.

Progress in the understanding of rotating magnetic systems

The collaboration with Samuli Penttinen has led to a considerable progress in the understanding of rotating magnetic systems (Searl device). His simple and elegant experiments using simple rotating magnets gave negative results and his proposal that nylon layer in the four-layered structure of cylindrical magnets might act as a charge reservoir led to the idea of constructing a concrete model for the current flow equilibrium in the system. As a consequence rather detailed picture about the electric fields and charge distribution in the system emerged. Also the idea about quantum criticality as explanation for why these experiments are so difficult to replicate became much more concrete. I attach below a brief summary of the model.

The basic hypothesis of Topological Geometro-Dynamics (TGD) is that space-time is representable as a 4-surface in 8-dimensional space M⁴× CP₂. The notion of many-sheeted space-time forced by this hypothesis implies numerous new physics effects including gravitational anomalies, the possibility of negative energy space-time sheets making possible over unity energy production and classical communications to the geometric past. An essential element is the new view about the relationship between inertial and gravitational energy. The geometrization of the classical gauge fields in turn predicts the existence of long range color and electro-weak gauge fields, in particular classical Z⁰ field, which gives rise to macroscopic effects resembling those assigned usually with torsion fields. These fields are assignable to dark matter hierarchy rather than ordinary matter. In this article the strange findings about the physics of rotating magnetic systems are discussed in order to illustrate the new physics predicted by TGD.

In the beginning of the year 2002 I learned about strange effects related to rotating magnetic systems, and the model for these effects has evolved (and is still evolving) gradually during the year 2002 via trial and error process. Several new physics effects seem to be involved.

1. Explanation for the effective weight loss

The rotating magnetic system develops em and Z⁰ charges and experiences the classical em and Z⁰ electric forces created by Earth so that the effective weight is reduced or increases (depending on the direction of rotation) as much as 35 per cent. The charging is due to the flow of electrons and possibly also exotic neutrinos from the rolling magnets to the surrounding air induced by the radial electric and Z⁰ electric fields generated by the Faraday effect inducing vacuum charge density (not possible in Maxwell's electrodynamics). The fact that critical frequencies are different for clockwise and counter clockwise spontaneous rotation implies that classical Z⁰ force and exotic neutrino currents could be present.

2. Spontaneous acceleration

The spontaneous accelerating rotation above critical frequency can be understood as being to a Lorentz torque acting on the radial Ohmic em and Z⁰ currents in rollers and roller ring. Above the critical frequency the Lorentz torque, which is proportional to rotation frequency, becomes larger than frictional torque, and spontaneous accelerating rotation becomes possible due to the positive feedback. Energetic constraints imply negative feed back and the modelling of this "back reaction" leads to a model of the system based on butterfly catastrophe in Thom's classification of elementary catastrophes and allowing also to understand the effect of the load. Rather precise estimates for the parameters result and allow to quantify the role of classical Z⁰ force.

3. Zero point kinetic energy of electrons as basic energy source

The radial ohmic current of electrons leaking from the atomic space-time sheets of rollers to the space-time sheet of environment explains the presence of plasma around the system. The ionization of the molecules could be caused by the electrons from rollers gaining keV energy as they drop from atomic space-time sheets of rollers to the space-time sheets of the environment. The associated liberation of zero point kinetic energy provides a possible source of energy allowing making the system an over unity device.

The transformation of the Lorentz torque on conduction electrons to a torque on roller can be understood if the zero point kinetic energy of the photon emitted in the dropping of electron is absorbed by the atom in the outmost layer of the rotating magnet: the energetics works for Fe and Ti layers.

The molecules of the surrounding air could make transitions to higher energy states and also ionize by emitting phase conjugate (negative energy) photons absorbed by the dropping conduction electrons. Also the dropped highly energetic electrons can cause this.

A remote metabolism based on the emission of negative energy (phase conjugate) microwave "dark" photons with large value of Planck constant absorbed by dropping electrons could be a further mechanism. The energy needed to generate magnetic walls and the kinetic energy of electronic Cooper pairs in collective cyclotron states at magnetic walls could come from the remote metabolism involving also an angular momentum transfer. The absorbed phase conjugate photons would have energy of order keV and would result by the de-coherence from dark cyclotron photons emitted from magnetic walls having the same energy but microwave wave length (this is possible because the value of hbar is large for dark photons). This would explain the cooling of the air around the system. Also a remote magnetization of J=2 electron Cooper pairs at the space-time sheets of magnetic walls could result in this manner.

4. The material composition of the Searl device

The latest progress relates to the understanding of the role of material decomposition of the Searl device (layered Nd-nylon-Fe-Ti structure. The model the current flow equilibrium for the 4-layered cylindrical structure gives detailed quantitative picture about how charge accumulates in the interiors of layers and to the layer-layer boundaries emerges. The key finding is that the small electrical conductivity of air requires in the flow equilibrium that the electric field at the outer boundary of titanium layer is amplified by a factor of order 10⁸ to a field which is by a factor of order 10³ higher than the critical field inducing di-electric breakdown in air so that the simple model fails. The huge increase of the electric field requires an accumulation of positive charge at Ti-air boundary and explains why the air must be ionized but not its mechanism based on the dropping of electrons to larger space-time sheets.

The four-layered structure is used also for the stator: this can be understood if the magnetic field of stator also rotates as is suggested by the fact that its return flux goes through the rollers. The rotation of the stator magnetic field leads to a simple model for the classical behavior of the roller system as a dynamical equilibrium in which the electrostatic torque generated by the rotation of the stator and roller charge distributions induced by Lorentz torque on conduction electrons vanishes as rollers rotate with the same velocity as the charge distribution in the stator. This picture does not however explain the spontaneous acceleration. Especially interesting phenomena are expected to occur in the small air gap between stator and roller, one such phenomenon being a formation of dark variants of ordinary atoms, so called N-atoms.

In flow equilibrium there must be an electron flow from the hollow air volume inside the stator to the air volumes inside rollers and the expectation is that a closed current circuit is formed in the flow equilibrium. This mechanism would guarantee that the positive charges associated with various magnetic layers do not grow without limit. The system however loses electrons as they drop to larger space-time sheets if the system accelerates spontaneously and the system develops a positive charge: this charge cannot grow indefinitely. One might hope that the diffusion of electrons from air could compensate for the losses so that the system could effectively act as a perpetuum mobile for some time.

5. Quantum criticality, replication, and optimization

The replication of the experiments of Godin and Roschin has turned out to be difficult. The formation of the magnetic walls means the emergence of long length scale fluctuations with coherence length much longer than the size of the system. Hence a quantum critical phenomenon seems to be in question and this could explain why the replication of the experimental findings has turned out to be so difficult. There are indeed many conditions to be satisfied. The distance between magnetic walls must correspond to the radius of the stator in resonance. This length scale also corresponds to the wavelength of dark microwave photons emitted in cyclotron transitions and the energy of these photons must also correspond to a zero point kinetic energy liberated as electron drops to larger space-time sheet.

The fact that continual di-electric breakdown is involved means second kind of criticality and the requirement that liberated zero point kinetic energy in the dropping of electron corresponds to the ionization energy of titanium atom for n=3 valence electron makes also the phenomenon quantum critical.

Perhaps the most important manner to optimize the functioning of the device would be based on the condition of quantum criticality some of whose aspects are now understood. Hall effect for the radial Ohmic current plays a key role in generating torque and this raises the question whether quantum Hall effect at low temperatures involving increases of conductivity by 13 orders of magnitude could maximize the torque.

The chapter The Notion of Free Energy and Many-Sheeted Space-Time Concept of the book "TGD and Fringe Physics" contains the newest version about the model for Searl device. See also the article About Strange Effects Related to Rotating Magnetic Systems.

TGD as almost topological QFT

I told in the previous posting about the formulation of TGD at fundamental level using Chern-Simons action for the induced Kähler gauge potential and the modified Dirac action associated with this action fixed by the requirement that super currents are conserved.

1. Exact solutions of the TGD counterpart of the Chern-Simons action

As I wrote the previous posting I had not yet realized that classical field equations can be solved exactly: the only solutions are those for which CP₂ projection of 3-dimensional light-like 3-surface is at most 2-dimensional. Thus the construction of theory at this level reduces to that of constructing light-like 3-surfaces of imbedding space as representation of partons.

2. Solutions of the modified Dirac equation and eigen modes of modified Dirac operator

Also the modified Dirac equation can be solved exactly and solutions can be added to the generalized eigen modes of the modified Dirac operator: this defines the super-conformal symmetries in TGD sense. The hypothesis is that the Dirac determinant defined by the product of the eigenvalues gives rise to the exponent of Kähler action. If true, it would allow to construct the theory solely from the data provided by the light-like partonic 3-surfaces.

The allowance of only the eigenvalues belonging to a particular algebraic extension of rationals defining the extension of p-adic number field could guarantee the finiteness by leaving only finite number of eigenvalues to the spectrum. One would obtain number theoretic hierarchy of physics serving as a correlate for a cognitive hierarchy if one accepts p-adic physics as a physics of cognition and intentionality.

The earlier hypothesis that the super-canonical conformal weights relate in a simple manner to the zeros of Riemann Zeta finds additional support from the more detailed structure of the spectrum of eigen values if the super-canonical conformal weights are identified as eigenvalues of the modified Dirac operator. According to earlier idea, the existence of p-adicization might quantize the eigenvalues rather than boundary conditions or finiteness requirement.

3. Super-conformal symmetries

The basic super-conformal symmetries follow trivially from the almost-topological character of the theory and actually generalize. The light-likeness condition brings in the metric of the imbedding space and manifests itself in eigenvalue spectrum of the modified Dirac operator inducing breaking of the super-conformal invariance and the loss of topological field theory property. Therefore TGD would be as near as possible to a topological quantum field theory and somewhat ironically, the breaking of the super-conformal invariance and the emergence of gauge and gravitational interactions as well as classical Kähler dynamics would follow from light-likeness condition.

4. TGD counterpart of super-space formalism

The precise relationship between super-conformal invariance of TGD and that of super-string models has been quite a stressor since the super-space formalism in the standard form breaks down in TGD. The reason is that Majorana spinors are replaced by Weyl spinors (quarks and leptons correspond to different H-chiralities). That super-conformal invariance makes sense has been clear for a long time but one cannot never exlude the possibility that some subtle error combined with overall optimism could have led to a self deception.

It is now however clear that the super-space formalism exists also in TGD framework but involves a different definition of the Grassmann integral measure. The formalism means the replacement of the radial lightlike coordinate of partonic 2-surface with its super-counter part involving second quantized spinor field consisting of eigenmodes of the modified Dirac operator behaving like Weyl spinors. Only the fermionic fields appear besides imbedding space coordinates as dynamical variables in this case. Super-space formalism gives the modified Dirac action as one integrates over the Grassmann parameters using a modified integration measure

dθ^* Γ^rdθ,

where Γ^r is the modified gamma matrix associated with the lightlike direction and ^* denotes Dirac conjugation (it would be nice to have also bar in html symbol repertoire). The modified gamma matrices associated with the other coordinates vanish identically so that super-symmetrization occurs only in the radial direction. Also super-symmetrized canonical and Kac-Moody symmetries are formal symmetries of the Chern-Simons action.

The generalization of the super-space formalism to a higher- dimensional case is obtained by the replacement of the product

∏_idθ _idθ^*_i

with the wedge product

dθ^* γ¹dθ ×_w dθ^*γ²dθ ×_w...

completely analogous to the bosonic volume element

dx¹ ×_w dx²×_w...

Here ×_w symbolizes wedge product. It would be interesting to whether this Grassmann integral allows to construct a physically acceptable super-symmetric field theories based on Weyl- rather than Majorana condition. The requirement that the number of Grassmann parameters given by 2D is the number of spinor components of definite chirality (counting also conjugates) given by 2×2^D/2-1 gives critical dimension D=8, which suggest that this kind of quantum field theory might exist and define the quantum field theory limit of TGD.

The last section of chapter Construction of Quantum Theory represents the detailed form of the argument above.

Super Kac-Moody symmetry and TGD as almost topological conformal field theory

I have discussed in previous postings how N=4 super-conformal invariance might emerge in TGD framework (at least in the leptonic sector) and suggested that TGD might reduce to an almost-topological super conformal field theory (SCFT). Superconformal symmetry involves two ingredients: super Kac-Moody and super-canonical invariance and in the following it is found that the super Kac-Moody symmetries acting as deformations of partonic boundary component allow N=4 super-conformal symmetry as a maximal super-conformal symmetry and that TGD indeed reduces to an almost topological SCFT with parton dynamics defined by the Chern-Simons action for the induced Kähler gauge potential.

1. Consider first the modified Dirac equation for the induced spinor fields. Ordinary Γ matrices are replaced with modified Γ matrices which are linear combinations of the imbedding space Γ matrices with coefficients which are canonical momentum densities defined by the action determining the dynamics of the surface. The divergence of the vector field of X³_l defined by the modified Γ matrices vanishes by classical field equations and this guarantees the vanishing of the mass term in the modified Dirac equation necessary for the existence of super currents identified as products of the modified Γ matrices with the solutions of the modified Dirac equation. The conjecture is that the Dirac determinant defined by the product of generalized eigenvalues of the modified Dirac operator equals to the exponent of Kähler function so that the action assignable to partonic 3-surfaces would determine the dynamics of quantum TGD completely.

2. The classical action is in general ill-defined for light-like 3-surfaces if it contains induced metric becoming degenerate to X³_l. The only possibility is that the action is Chern-Simons form for the induced Kähler gauge potential. This would indeed mean that TGD reduces to almost topological field theory in the sense that the induced metric would appear only implicitly via the condition that partonic 3-surface is light-like (I have however no intention to replace TGD with ATGD;-)

3. The Chern-Simons action involves only CP₂ Γ matrices so that SL(2,C) replaces the group SU(2) acting as rotations of spinors generating super-conformal symmetries. This would guarantee Lorentz invariance. Therefore the Kac-Moody algebra would be more general than for N=4 super-conformal invariance but would restrict naturally to SU(2) when one chooses rest frame at lightcone boundary.

4. Super Kac-Moody symmetries should correspond to solutions of the modified Dirac equation which are in some sense holomorphic. Holomorphy makes sense since light-like partonic 3-surfaces can be provided with coordinates z, z^*, r, where r is lightlike coordinate: one can speak about degenerate complex, Kähler, and symplectic, and metric structures at partonic 3-surface. The analyticity of spinors with respect to z is the obvious condition to be satisfied. The modified Γ matrix Γ^z must annihilate the solutions. Covariant constancy with respect to z^* and r are also natural conditions. The corresponding integrability conditions state that induce spinor curvature contracted with the modified Γ matrices annihilates the physical states (just as it annihilates right handed neutrinos). Each solution of the integrability conditions corresponds to a representation of N=4 super-conformal algebra. A breaking of super-conformal symmetry can occur and would mean that less than one half of the components of the induced spinor field satisfy the integrability conditions. In the leptonic sector N=4 supersymmetry associated with right handed neutrino is always present but super-conformal symmetries could be lost.

To sum up, it seems that it that almost-topological SCFT emerges from TGD framework in a natural manner and is the only possibility if one accepts the identification of the interior dynamics of the space-time surface in terms of the classical degrees of freedom postulated in quantum measurement theory.

The last section of chapter Construction of Quantum Theory of "Towards S-Matrix" represents the detailed form of the argument above.