According to the popular article (see this) the model does not require explicit specification of intelligent behavior and the intelligent behavior relies on "causal entropic forces" (here one can counter argue that the selection process is necessary if one wants information gain). The theory requires that the system is able to collect information and predict future histories very quickly.

The prediction of future histories is one of the basic characters of life in TGD Universe made possible by zero energy ontology (ZEO) predicting that the thermodynamical arrow of geometric time is opposite for the quantum jumps reducing the zero energy state at upper and lower boundaries of causal diamond (CD) respectively. This prediction means quite a dramatic deviation from standard thermodynamics but is consistent with the notion of syntropy introduced by Italian theoretical physicist Fantappie already for more than half a century ago as well as with the reversed time arrow of dissipation appearing often in living matter.

The hierarchy of Planck constants makes possible negentropic entanglement and genuine information represented as negentropic entanglement in which superposed state pairs have interpretation as incidences a_{i}↔ b_{i} of a rule A↔ B: apart from possible phase the entanglement coefficients have same value 1/n^{1/2}, where n=h_{eff}/h define the value of effective Planck constant and dimension for the effective covering of imbedding space. This picture generalizes also to the case of multipartite entanglement but predicts similar entanglement for all divisions of the system to two parts. There are however still some questions which are not completely settled and leave some room for imagination.

- Negentropic entanglement is possible in the discrete degrees of freedom assignable to the n-fold covering of imbedding space allowing to describe situation formally. For h
_{eff}/h=n one can introduce SU(n) as dynamical symmetry group and require that n-particle states are singlets under SU(n). This gives rise to n-particle states constructed by contracting n-dimensional permutation symbol contracted with many particle states assignable to the m factors. Spin-statistics connection might produce problems - at least it is non-trivial - since one possible interpretation is that the states carry fractional quantum numbers- in particular fractional fermion number and charges.

- Is negentropic entanglement possible only in the new covering degrees of freedom or is it possible in more familiar angular momentum, electroweak, and color degrees of freedom?

- One can imagine that also states that are singlets with respect to rotation group SO(3) and its covering SU(2) (2-particle singlet states constructed from two spin 1 states and spin singlet constructed from two fermions) could carry negentropic entanglement. The latter states are especially interesting biologically.

- In TGD framework all space-time surfaces can be seen at least 2-fold coverings of M
^{4}locally since boundary conditions do not seem to allow 3-surfaces with spatial boundaries so that finiteness of the space-time sheet requires covering structure in M^{4}. This forces to ask whether this double covering could provide a geometric correlate for fermionic spin 1/2 suggested by quantum classical correspondence taken to extreme. Fermions are indeed fundamental particles in TGD framework and it would be nice if also 2-sheeted coverings would define fundamental building bricks of space-time.

- Color group SU(3) for which color triplets defines singlets can be also considered. I have been even wondering whether quark color could actually correspond to 3-fold or 6-fold (color isospin corresponds to SU(2)) covering so that quarks would be dark leptons, which correspond n=3 coverings of CP
_{2}and to fractionization of hypercharge and electromagnetic charge. The motivation came from the inclusions of hyper-finite factors of type II_{1}labelled by integer n≥ 3. If this were the case then only second H-chirality would be realized and leptonic spinors would be enough. What this would mean from the point of view of separate B and L conservation remains an open and interesting question. This kind of picture would allow to consider extremely simple genesis of matter from right-handed neutrinos only (see .

There are two objections against this naive picture. The fractionazion associated with h

_{eff}should be same for all quantum numbers so that different fractionizations for color isospin and color hyper charge does not seem to be possible. One can of course ask whether the different quantum numbers could be fractionized independently and what this could mean geometrically. Second, really lethal looking objection is that fractional quark charges involve also shift of em charge so that neutrino does not remain neutral it becomes counterpart of u quark.

- One can imagine that also states that are singlets with respect to rotation group SO(3) and its covering SU(2) (2-particle singlet states constructed from two spin 1 states and spin singlet constructed from two fermions) could carry negentropic entanglement. The latter states are especially interesting biologically.

Negentropy Maximization Principle (NMP) resolves also the above mentioned almost paradox related to entropy contra intelligence. I have proposed analogous principle but relying on generation of negentropic entanglement and replacing entropy with number theoretic negentropy obeying modification of Shannon formula involving p-adic norm in the logarithm log(|p|

_{p}) of probability. The formula makes sense for probabilities which are rational or in algebraic extension of rational numbers and requires that the system is in the intersection of real and p-adic worlds. The dark matter matter with integer value of Planck constant and h

_{eff}=nh predicts rational entanglement probabilities: their values are simply p

_{i}=1/n since the entanglement coefficients define a diagonal matrix proportional to unit matrix. Negentropic entanglement makes sense also for n-particle systems.

Negentropic entanglement corresponds therefore always to n× n density matrix proportional to unit matrix: this means maximal entanglement and maximal number theoretic entanglement negentropy for two entangled systems with number n of entangled states. n corresponds to Planck constant h_{eff}= n×h so that a connection with hierarchy of Planck constants is also obtained. Power of p-adic prime defines the largest prime power divisor of n. Individually negentropically entangled systems would be very entropic since there would be n energy-degenerate states with the same Boltzmann weight. Negentropic entanglement changes the situation: thermodynamics of course does not apply anymore. Hence TGD produces same prediction as thermodynamical model but avoids the almost paradox.

For details and background see the section "Updates since 2012" of chapter "Negentropy Maximization Principle" of "TGD Inspired Theory of Consciousness".

## 19 comments:

Dear Matti,

Thanks for the new postings.

“bosonic emergence means that gauge bosons are identified as bound states of fermion and antifermion at opposite light-like throats of wormhole contact.”

I can’t imagine that. Opposite light-like throats of wormhole contact means intersection of light-like throats of wormhole contact with two opposite boundary of Causal diamond? But this is partonic 2-surface. Hence the two partonic 2-surface identified as Fermion and anti-fermion? There is Misunderstandings for me.

Dear Hamed,

there is misunderstanding. " Opposite" does not refer to opposite ends of causal diamond but to wormhole throats at two space-time sheets connected by wormhole contact.

*Imagine two space-time sheets very near to each other and wormhole contact connecting them.

*Fermion is at another throat and anifermion at another one. The stability of wormhole contact is guaranteed by monopole Kahler flux through it.

*Since flux lines must be closed, there must be second wormhole contact so that one obtains closed flux tube traversing from throat to another one along "upper" space-time sheet and returning along lower one. This is the minimal model of elementary particle and includes automatically also graviton.

Dear Matti,

Thanks, but as i understood, the Fermions and anti-fermions are only like the ordinary fermions and not equal to them.

i write an analogy and ask my questions:

special relativity say that velocity is relative because we measure only rate of changing of the position of an object with respect to ourselves as velocity and not absolute velocity.

Just like this, can one say that Kahler field is relative? because we can measure only difference in Kahler potential of some space time sheet with respect to our spacetime(by fixing gauge of Kahler potential equal to zero at our spacetime sheet). Hence Kahler field is not absolute like velocity.

another analogy: I saw at the articles that at high electric field, permittivity of matter vary. Hence by analogy between 1/2*m*v^2 and 1/2ε*E^2(ε is permittivity of matter), this is like mass vary at high speed. Hence just like 1/2*m*v^2 is not correct at high velocities And it is an approximation of m*c^2 - m_0*c^2 for low velocities. It seems 1/2ε*E^2 must be replaced with another relation maybe ε*E_max^2(like m*c^2) or some other relation.

L=J^mnuJ_munu is not exception so that it seems it is not correct at high density of kahler field and the Lagrangian must be replaced with another relation. how do you think?

Dear Hamed,

You are right about special relativity. All boils down to the statement that four-momentum is Lorentz vector. Also p-eA is four-vector in M^4 which is the more standard manner to say that Kahler potential is "relative". The representation of A indeed depends on what M^4 co-ordinates we use for the space-time sheet.

I would not use the analogy between kinetic term for particle and "kinetic term" for Kahler action. They are not so directly related. Maxwell (and Kaehler action are essentially uniquely determined from the condition that they do not involve dimensional parameters other than CP_2 size scale. This makes space-time dimension D=4 unique.

Note that in induced geometry Kahler action is extremely non-linear with respect to imbedding space coordinates. Much more nonlinear than Einstein action with respect to space-time metric.

The rapid variation of CP_2 coordinates leads to the change of the signature of induced metric to Eucldiian as is easy to understand by studying the expressions for the components of induced metric (in particular g_tt). These regions correspond to elementary particles so that the extreme non-linearity has easily understandable effects. Cosmic strings is another implication of non-linearity meaning "compactification" of two space-time dimensions.

Dear Matti,

You wrote that Kahler potential is relative.

Hence suppose there is two small 3-surface located in imbedding space, one has Kahler potential B1 and Kahler form J1 and another has kahler Potential B2 and Kahler form J2.

Hence, the relativle Kahler potential is B1-B2. and one can concludes that relative Kahler form is J=J1-J2=d(B1-B2)

Hence Kahler form is relative too and not absolute. is this anything wrong in the argument?

Another question:

In special relativity, the distance between two point as (C^2t^2-X^2-Y^2-Z^2) is invariant under transformations of observer with different velocities.

in TGD, space-time sheets are hyperquaternionic subspace of hyperoctonion space. Suppose there is two observer approximating as two 1D light curve located in the hyperoctonion space.

What is invariant between them?

is the minimum distance between two point in hyperoctonionic space is invariant between the two observer?

(As i understood hyperoctonionic space is flat but M4*CP2 that is dual description is not flat.)

I said that Kahler gauge potential is "relative" and meant that it behaves as vector field and thus 4-vector just like four-momentum. This is all that is needed. You mean above relative in stronger sense.

This stronger sense holds true only in the sense that you can add to Kahler potential gradient of scalar without affective Kahler form. U(1) gauge invariance.

Concerning second question. Hyperquaternionicity is conjecture about preferred externals. It is difficult to imagine deeper fundamental dynamical principle than associativity but it could be wrong!

Suppose one has two light-like curves - say assignable to the two wormhole contacts or two particles: distances are of course defined in appropriate natural resolution.

If one restricts consideration to the either boundary of CD then the distance along fermionic string connecting the points at different throats would define natural distance. It could be calculated either in the induced metric or just considering the end points as points of imbedding space and calculating the distance along geodesics connecting them. This would give shorter distance. Hyper-octonionicty is not involved in any many in this definition of distance.

Dear Matti,

Thanks, sometimes analogies leads that i better see the things and ask the new questions about it from myself although it might be wrong.

Hence i am sorry if some of my words seem critics about some principles of TGD. In really it is not critics at all, but it is just for understanding better the Basis of TGD.

Dear Matti,

First a typo error in last comment: critics to critique :-)

this is as very last texts: “all 3-surfaces on the orbit of 3-surface X^3 must be physically equivalent so that one can effectively replace all 3-surfaces Z^3 on the orbit of X^3 with a suitably chosen surface Y^3 on the orbit of X^3. The Lorentz and Diff4 invariant choice of Y^3 is as the intersection of the 4-surface with the set delta M^4*CP2, where M^4 denotes the boundary of the light cone”

As I understand, X^3 and all 3-surfaces belong to it’s orbit like Y^3 beginning at either end of CD and ending to the other end of CD. The orbit of X^3 means a symplectic transformation of X^3 that leaves induced kahler form invariant. You noted that the 3-sufaces in the orbit are separated by a zero distance from each other in the configuration space metric. Why is there zero distance between them?

Dear Hamed,

nothing bad in critics. It is always well-come if it is based on content. I find however difficult to tolerate replacing arguments and content with names as happens in too many blogs today.

That the orbit of X^3 is dictated by a symplectic transformation is too strong a statement. It would be completely analogous to a statement that the orbit of particle is obtained by a translation: this would make sense only for three particle.

Symplectic transformations appear only as symmetries just as translations do in translationally invariant system (note that all particles are translated in the same manner!).

The action of symplectic transformation is most probably limited to just partonic 2-surfaces and their tangent space data at the ends of CD and the 4-D space-time surface is dictated by field equation. Stronger form would allow their action 3-surfaces at the ends of CD and to light-like orbits of partonic 2-surfaces. That symplectic transformations would act in this manner as symmetries is non-trivial.

The construction of WCW geometry favours strongly the minimal option. The point is that super-conformal invariance requires that induced metric does not appear in the expressions of WCW Hamiltonians as Kahler fluxes weighted by Hamiltoans restricted to partonic 2-surfaces. If 2-D flux integrals are replaced with 3-D integrals, one cannot avoid the presence of induced metric.

The third coordinate of X^3 would correspond to gauge conformal degree of freedom analogous to the z coordinate in case of strings and one could choose the value of light-like radial M^4 coordinate r_M of light-like CD boundary freely as function of other two coordinates of X^3. Analogous statement would hold true for light-like coordinate at the orbits of partonic 2-surface.

Note that this manner of action does not mean that Kahler action remains invariant and one obtains conserved charges. If this were the case WCW metric obtained in terms of second functional derivatives of Kahler action would be trivial in symplectic degrees of freedom!

Therefore symplectic transformations define isometries of WCW but do not act as symmetries of Kaehler action.

To be continued...

Dear Hamed,

still a little addition to previous answer.

I have considered the possibility that the slicing of space-time surface to partonic 2-surfaces and string world sheets could define different choices of representations for partonic 2-surfaces and tangent space data and these choices would correspond Kahler functions differing by real part of analytic function of WCW complex coordinates. This does not affect WCW Kahler form as is easy to see and corresponds U(1) gauge transformation for Kahler gauge potential of WCW.

Dear Hamed,

concerning your question about zero distance between 3-surfaces in the orbit. I would guess that I have talked about light-like orbit of partonic 2-surface at which 4-metric changes signature. I would also guess that I have referred to the distance between partonic 2-surfaces at the orbit defined by induced metric: this is naturally zero just like the distance between spheres of expanding light-front vanishes. Light-like 3-surface is just like light-like geodesic but for extended object.

This statement made at the *level of WCW* is un-necessary strong. All that is needed to consider are the partonic 2-surfaces and tangent space data at the ends of CD. Saying something about partonic 2-surface between them seems un-necessary as far as scattering amplitudes are considered but could bring in flexibility. This is of course the essense of (strong form of) holography.

General coordinate invariance as almost free choice of differ related representatives for X^3 is probably possible only in some sufficienty small space-time region. In any case this inspires questions.

*Can one use any partonic 2-surface at its light-like orbit as representative. If so, how can one formulate construct elementary particle vacuum functionals if the conformal equivalence class described by moduli varies along the orbit? Restriction to boundaries of CD would solve these problems.

*Can one slice the space-time surface to partonic 2-surface parametrized by string world sheets as the structure of preferred externals suggests (decomposition to longitudinal and transverse degrees of freedom defined by local light-like momentum and orthogonal polarisation)? I tend to believe that this slicing can be true only in sufficiently small regions of space-time since the slicing must develop singularities.

*Partonic 2-surfaces assigned with CD boundaries is in certain sense maximal choice. Upper and lower space-like 3-surfaces have maximal time-like distance. Could one shift boundaries of CD by upwards and downwards to obtain a family of parallel light-cone boundaries? Could this slicing have physical meaning? What about its singularities?

Dear Matti,

So thanks, I understand now that I confused between X^3 that is space like 3-surface and X_l^3 that is light like 3-surface! Hence I thought your means of orbit is symplectic orbit of light like 3-surface(that WCW is space of symplectic orbits of light like 3-surfaces). but it was misunderstanding.

In QFT, between two electrons there are photons as propagators creating from one electron and annihilated at another. But in TGD photons are emerging from two wormhole throat at two space time sheet that connect through a wormhole contact.

1-Hence in my imagination of TGD, there are a lot of wormhole contacts going from one electron to the other electron?

2-It seems for me this makes photons heavier than electrons. Because electron is just one space time sheet glued to the larger one, but photon is two space time sheets.

3- in TGD the gauge fluxes going from of one wormhole throat to the other. But in QFT, gauge fluxes is quantized and appears as paths of gauge bosons in Feynman diagram and noting remain as gauge fluxes. Hence gauge fluxes in TGD is something different that not quantized. What are them?

Dear Hamed,

here are my answers.

1- The picture about Feynman graphics and its twistorial counterpart is very similar to stanard one but requires

imaginative muscles!

*If particles were just wormhole contacts then wormhole contacts would split in two when electron emits photon: electron would carry fermion number at second throat and photon fermion and antifermion at its two throats.

*The picture is actually more complex.

-Stable wormhole contacts must carry magnetic flux throught them and this reuqires that also second wormhole contact is present. The flux flows to second wormhole contact throat, throught that contact, and returns along second sheet to the original wormhole contact. You get closed flux loop as the absence of isolated magnetic charges requires (monopole flux is possible but due to topology of CP_2).

-Feynman/twistor diagrams are relaced by their stringy variants. The visualization would be in terms of open strings. Think of open string with finite length as incoming string. Then it is doubled to two travelling at different directions. I think that Witten actually proposed this kind of diagrams in his variant of string field theory based on generalization of Chern-Simons action. Now something this happens at both space-time sheets. Here my ability to imagine is meeting its limits but you have younger brain;-).

2- I do not seen why photon should be heavier than electrons. Also electron has second space-time sheet (at least interacting electron. The second throat need not however carry fermion number. It could however carry excitations generated by the superconformal algebra.

If mass comes from p-adic thermodynamics it is possible to understand why photon is very light (probably not however exactly massless). The second throat must carry neutrino-right handed neutrino pair to neutralize weak isospin above weak scales. It is also possible that right handed neutrino is opposite to fermion carrying electron quantum numbers.

I do not understand the details of p-adic massivation completely at this level. One challenge would be to perform p-adic mass calculations by bringing in detailed model of particle. I am too old and too lazy and not angry enough to start a project requiring so much adreline;-).

3-I am not quite sure what you mean. In TGD magnetic fluxes can be assigned to flux tube like structures with transversal cross section which is closed two-surface and obtained as a deformation of cosmic string with infinitely thing M^4 projection and CP_2 projection which is sphere in the simplest case but can have also higher genus. The fluxes are quantized! This gauge flux is exactly similar to a gauge flux \oint Adl in Abelian gauge theory allowing magnetic monopole: now of course the monopole is homological and relates to non-trivial CP_2 homology.

Dear Matii,

Thanks,

1- At the time of interaction, a lot of gauge bosons (maybe infinite number of them), interacts with the fermion at the same region of space time.

2- in other hand, there are space time sheets that these bosons and the fermion touch to them.

each of the space time sheets contributes in the momentum of the fermion at point like limit as p-->p-eA1-eA2-eA3..) where Ai is the induced spinor connection of CP2 to i-th space time sheet at the region. this is superposition of effects at this level.

in my imagination, the number one and the second are very separately. how it is relation between interactions of bosons with the fermion and Ai at space-time sheets?

Dear Hamed,

1. I did not understand what you mean with this statement. Picture is essentially similar to the ordinary one and at QFT limit (forgetting heavier string excitations) should be what one expects from QFT.

2. I think I understand the source of confusion here.

*Let us think in terms of QFT first. The Feynman diagrammatics or twistor diagrammatics gives the amplitudes in *absence of external classical fields*.

In practice on must however describe the presence of complex external systems (which might contain something like 10^23 particles as classical fields and add to the action corresponding source term.

This gives rise to additional terms in the perturbative expansion. Description of atom sis excellent example of using external classical em field of nucleus. Actually the only one really working!

Same happens now. One has the twistor Grassmann diagrammatics in absence of space-time sheets carrying the classical fields of various systems involved. These give rise to additional interaction vertices. Interactions are additive although the classical fields are not at the level of space-time sheets.

Brilliant. Enjoying the posts and the dialog between you and Hamed here. As I grab another bag of popcorn and soda....

Matti, what are your thoughts about how the Wheeler-deWitt equation relates to TGD?

Peace,

Crow- (Stephen)

Hi Stephen,

canonical quantisation is what leads to Wheeler-de-Witt equations. The procedure is formal application of what one does in wave mechanics and as such would be a huge extrapolation.

In GRT the problems in its application are due to general coordinate invariance (GCI) and one must somehow fix the space-time coordinates to build Schroedinger equation in the space of 3-geometries ("world of classical worlds" in TGD consisting of 3-surfaces - equivalently of space-time surfaces by holography realising general coordinate invariance).

As a consequence of GCI the action of Hamilton describing time evolution on physical states vanishes identically. The reason is that time translation is just one particular general coordinate transformation. This means that there is no unitary time evolution. One loses time. This is a big problem. Barboux has even proposed that time is illusion. The r problem is following: time translation acts as isometry in special relativity and the existence of Hamilton follows by Noether theorem. Now time translation is just a general coordinate transformation and "gauge transformation" so that Hamiltonian vanishes.

One should be able to realize translations as genuine isometries but they cannot be isometries of space-time. Here from this point the path to TGD is very short: space-time as a surface of M^4xS and translations as isometries of M^4!

As I started TGD I tried to apply canonical quantisation to TGD. It failed completely since time derivatives of imbedding space-coordinates were many-valued functions of canonical momentum densities and the relationship was hopelessly non-linear. Few years ago I realised that this many-valuedness might actually be behind the effective covering spaces associated with the hierarchy of Planck constants since this many-valuedness indeed can be described in terms of covering space.

Canonically imbedded M^4 represented the worst case: in this case Kahler action density was fourth order in the gradients of coordinates so that kinetic term was identically vanishing. For this reason also the path integral around M^4 failed: propagator was simply 1/0! I was forced to find totally new approach.

Around 1985 I discovered the idea of WCW geometry ("configuration space" at that time). It took about five years to finally discover how WCW Kahler geometry could be constructed and that WCW must have maximal isometries in order that this geometry even exists. Super-conformal invariance, generalisation of Kac-Moody symmetries, etc.. are necessary for WCW geometry to exist. Physics is unique from its mathematical existence.

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