### Pollack's findings and quantum model of cell membrane using square root of thermodynamics

Zero energy ontology (ZEO) is one of the basic differences between TGD and standard quantum theory based on positive energy ontology. One can say that TGD is as quantum theory square root of thermodynamics. Density matrix is replaced with its hermitian square root multiplied by unitary S-matrix same for all states. The general formalism is very beautiful but application has been lacking.I have now first real life application of TGD as square root of thermodynamics.

The existing model of cell membrane is thermodynamical: Coulomb energy differences and chemical potentials over the cell membrane play a key role in the description of osmosis, which is essential element but regarded as the "dirty" part of biophysics. I remember when I was something 20 +something and read in library about osmosis and felt disgust. Osmosis is however a real phenomenon: only its description is ugly, not the phenomenon.

Osmosis means the presence of pumps and channels - various transmembrane proteins. Pollack's findings about fourth gel-like phase of water and many other discoveries challenge this model, and it is not consistent with macroscopic quantum coherence. For instance, the description of metabolism requires that the chemical potential - a purely thermodynamical notion - is considerably larger than Coulomb energy for proton and dominates in metabolic energy of about .5 eV to be compared with Coulomb energy which is smaller by a factor .1-.2. This makes the skeptic inside me very alert.

Could it be that chemical potential could correspond to genuine energy: say cyclotron energy difference as suggested by TGD inspired quantum biology?

Even more, could one see osmosis as a gate to a new physics - maybe that involving magnetic body, dark matter and hierarchy of Planck constants, ZEO, etc... In TGD framework the thermodynamical description of cell membrane should be replaced with a quantal description using square root of thermodynamics. It would go roughly like follows.

- Transmembrane proteins become generalized Josephson junctions. What is new is that chemical potential, which dominates over the Coulomb energy for proton in the model for production of ATP from ADP, is replaced with the difference of cyclotron energies over the Josephson junction. Therefore the purely thermodynamical notions of proton gradient and protonmotive force become more concrete.

- Thermodynamical distibutions are replaced with their complex square roots - essentially Schroedinger amplitudes but proportional to the square root of Boltzmann weight so that ensemble property becomes single particle property and temperature has quantum mechanical meaning at single particle level as in p-adic thermodynamics too (about which one must also take square root to be be consistent).

For details see the TGD inspired model for Pollack's findings about water which helped to end up with this model.

The model can be applied to improve the earlier model of EEG: the energy of dark Josephson photon identifiable as EEG photon (say) is replaced with generalized Josephson energy including the difference of cyclotron energies for flux tube portions outside and inside the cell membrane and arriving from DNA (this was assumed already in the model of model DNA as topological quantum computer). Also the model of nerve pulse will become more detailed: the phase transitions changing the Planck constant at either or both sides of membrane introduce change of ion distributions as happens in nerve pulse. The new physics model for life is becoming more and more detailed and quantitative.

I have now a CMAP representation of TGD at my homepage. It gives kind of cognitive maps about basic ideas, notions, and arguments appearing in TGD. My hope is that they might help to get an idea about what TGD really is.

## 13 Comments:

Dear Matti,

Suppose there are two electrons interacting with each other. The interaction is through massless extremal. In description of it by Feynman diagrams, one can say at first order approximation there are just 2 electrons interacting by one massless extremal(as a propagator between them). At second order approximation or higher orders, there are more vertices and more particles.

3 question:

1-Are there any misunderstanding above?

2-What is difference between photons and massless extrimals? Or what is problem of photons that the massless extremals haven’t the problem

3-Is there any misunderstanding in the following?

Let’s concentrate on the first order. At this order, space of states are all possible paths of the two electrons interacting by all possible paths of one massless extremal between them. At the process of reduction of wave function, the wave function of both electrons and massless extremal reduce to just one possible interaction. Reduction occurs over from past to future of the wave function and because of this, after the reduction, there are just two definite paths of electrons coming from past and interacts by a definite path of one massless extremal and go to future as the definite paths.

At ordinary Quantum mechanics there is no reduction of wave function for the electric potential between the two electrons and this can be regard as a forbidden element in QM.

- After the reduction, there is the action of preparation for the definite paths of two electron (from past to future)and ME. The preparation evolves them to all possible paths.

Dear Hamed,

I answer first the two first questions.

Hamed: Suppose there are two electrons interacting with each other. The interaction is through massless extremal. In description of it by Feynman diagrams, one can say at first order approximation there are just 2 electrons interacting by one massless extremal(as a propagator between them). At second order approximation or higher orders, there are more vertices and more particles.

3 question:

1-Are there any misunderstanding above?

MP: Something is lacking. There are two space-time sheets associated with particle and connected by two wormhole contacts. The wormhole contacts are connected by magnetic flux tube at each sheet so that closed string like object carrying monopole flux is formed. Both of these space-time sheets are massless extremals (MEs) apart from deformation caused by flux tube. Each ME carries a light-like momentum and polarization and the interaction via wormhole contacts makes possible momentum exchange so that the momentum is not constant. Their sum is constant but can be time-like. This gives rise to massivation described by p-adic thermodynamics in TGD. The string like object with wormhole contacts at its "ends" (wormhole contacts) is the correlate for any elementary particle.

Hamed: 2-What is difference between photons and massless extrimals? Or what is problem of photons that the massless extremals haven’t the problem.

MP: The pair of massless extremal is a correlate for photon as space-time sheet of Minkowskian signature. The wormhole contact pair with wormhole contacts identified as deformations of CP_2 vacuum extremal define the Euclidian correlate for particle. One can also identify the correlate of particle in terms of the light-like 3-surfaces associated with wormhole contacts (parton picture).

Dear Hamed,

answer to you third question.

Hamed: 3-Is there any misunderstanding in the following?

Let’s concentrate on the first order. At this order, space of states are all possible paths of the two electrons interacting by all possible paths of one massless extremal between them.

MP: This is path integral description deduced from Schroedinger equation and applied in QFT. In TGD framework the sum over path is replaced as integral over 3-D surfaces in WCW. The failure of strict determinism of Kaehler action however implies kind of sum over paths with fixed ends. This might have something to do with path integral or it could be a space-time correlate for state function reduction. More probably so. I do not believe in path integral picture

since Schroedinger evolution is too simplistic notion in TGD. S-matrix is replaced with the triple of U-matrix, M-matrix and S-matrix in ZEO. One starts directly from holography like picture: 3-surfaces at the ends of CD and by strong form

of holography partonic 2-surfaces and their 4-D tangent space data.

For CP_2 type vacuum extremals the M^4 projection is random light-like curve

and this leads to Virasoro conditions and realization that super-conformal invariance generalizes. There is also non-determinism due to vacuume extremals in Minkowskian signature: induced Kahler form vanishes when CP_2 projection belongs to at most 2-D Lagrangian sub-manifold of CP_2.

At the process of reduction of wave function, the wave function of both electrons and massless extremal reduce to just one possible interaction. Reduction occurs over from past to future of the wave function and because of this, after the reduction, there are just two definite paths of electrons coming from past and interacts by a definite path of one massless extremal and go to future as the definite paths.

MP: Quantum superposition of space-time surfaces indeed changes and thus "quantum average past" too. Remember however the sum over electronic 3-surfaces: this is important CP_2 scale.

At ordinary Quantum mechanics there is no reduction of wave function for the electric potential between the two electrons and this can be regard as a forbidden element in QM.

MP: I am not sure whether I understand what you mean with this. Electric charge conservation holds true

in operator sense and concretely for spinorial quantum numbers for Feynman diagrams. This is true also in TGD

and this condition implies the restriction of spinor modes to 2-surfaces and string model becomes part of TGD.

- After the reduction, there is the action of preparation for the definite paths of two electron (from past to future)and ME. The preparation evolves them to all possible paths.

MP: I find that am a little bit confused about what state preparation is in TGD description.

*The original picture was that state function reductions take place alternately at the two boundaries of CD. In this picture preparation was reduction at opposite boundary.

*Then I realized that repeated state function reductions on same boundary must be possible and explain basic facts about the relationship between experienced and geometric time. In this picture I do not however understand clearly what preparation means.

*The earlier interpretation for prepation seems to be rather feasible. Does the arrow of time change in preparation in elementary particle scale?!. This would explain the difference between macroscopic irreversible physics and microscopic physics reversible in average sense since the alternation of arrow of time sums up to no arrow at all. Could this make sense?

Do I actually have the courage to make a comment in this forum, and dare I risk potentially being ripped to shreds? Actually, yes, I do! There is no doubt in my mind that you know the answer to the final question listed above MP. No doubt about it, you absolutely know the answer.

Dear Zoeanne,

comments are wellcome. No violence in this blog.

As I started the first sentence of last paragraph, I knew what state preparation means. After that I realised that in the new view about how arrow of time emerges, I actually do not! Then I realised that maybe I know after all: the two views - state function reduction occurring to opposite boundaries of CD alternately and state function reductions occurring very many times at same boundary are limiting cases of the general view.

Answering questions is very useful!

Usually because of simplicity, I think in terms of point like limit of 3-surfaces rather than 3-surfaces themselves and I use the simplicity in asking my questions from you. But I must be careful for this simplicity!

Does the ground states of conformal algebra representation correspond to first order of generalized Feynman diagrams?

So are the second order and others (containing more vertices) corresponds to higher states of conformal algebra?

Before the wave function reduction, there is superposition of the levels of (states of) conformal algebra representation. In other words, superposition of one vertex interactions and two vertex interactions and others. After the reduction, wave function reduces to just one of them.

My reason for this conclusion is analogy with finite dimensional algebra like spin: Before the wave function reduction, there is superposition of eigen states of spin operator and after the reduction, wave function reduces to just one of them.

Dear Matti,

I forgot to thanks for your before answer:)

Dear Hamed:

A little comment in passing which popped into my mind somehow when I was answering your previous comment. In TGD one has spinor fields at three levels: space-time, imbedding space, and WCW.

Imbedding space spinor fields characterize the ground states of conformal algebra representations and elementary particles and they are the counterparts of spinor fields in QFTs.

Induced spinor fields at space-time level couple to induced spinor connection and the prediction seems to be the presence of classical Z^0 and W forces in all scales.

Is this true? Or does one obtain only massive weak bosons at imbedding space level or does one obtain something new. The conservative option would roughly mean that correlation function for W and Z go to zero above weak scale. Same for the counterparts of classical color fields.

If one obtains hierarchy of Planck constants then one expects a hierarchy of dark weak and color physics in different scales.

Dear Hamed,

Now the answer to your question. I agree with your expectation. Stringy diagrammatics should result apart from modification due to the fact that strings live inside 4-D space-time surfaces. Twistorial counterpart of Feynman diagrammatics is expected to result in lowest order with wormhole contact pairs representing particles. The information about wormhole structure of course disappears.

The graphs provide a representation for the zero energy state, usually they represent the interactions of positive energy state and are taken between initial and final states. This is consistent with crossing symmetry. The twistorial counterparts of Feyman diagrams should result from consistency conditions: Yangian variant of basic symmetries might be enough for this.

I expect that after state function reduction each fermion corresponds to one particular ground state of WCW spinor characterised by imbedding space spinor field. "Ground state" of finite-D spinor (say right-handed neutrino in case of CP_2 spinor) goes to ground state of WCW spinor represented as mode of spinor fields at lower level.

One can ask whether there is analogous correspondence with imbedding space spinor and the induced (space-time) spinor at partonic 2-surface.

Dear Matti,

Thanks, I’m not sure that I understand your answer or not.

I asked about “Does the ground states of conformal algebra representations correspond to first order of generalized Feynman diagrams?

So are the second order and others (containing more vertices) corresponds to higher states of conformal algebra?”

You noted: ” In TGD one has spinor fields at three levels: space-time, imbedding space, and WCW.

Imbedding space spinor fields characterize the ground states of conformal algebra representations and elementary particles and they are the counterparts of spinor fields in QFTs. “

Are the “Imbedding space spinor fields” just the spinor fields of CP2? Because in M4*CP2,M4 has not spinor structure. And only spinor field contribution of imbedding space come from CP2.

Does “spinor fields in QFTs”in your sentences refers to just one vertex interactions of Feynman diagrams or higher orders contribute in your meaning of these spinor fields?

But what about higher states of conformal algebra representations?

You noted at other comment that “ Twistorial counterpart of Feynman diagrammatics is expected to result in lowest order”

I understand from it:

In Twistor formalism, there is no higher orders of Feynman diagrams. Hence twistor calculates just one vertex interactions of Feynman diagrams.

Because TGD use Twistor formalism, also in TGD one can only calculate one vertex interactions and leave higher orders.

But my intuition support strongly that it must be higher vertex interactions. What is my misunderstanding?

Also in state function reduction, you leave higher orders of Feynman diagrams: “I expect that after state function reduction each fermion corresponds to one particular ground state of WCW spinor characterised by imbedding space spinor field.”

Dear Hamed,

thanks for nice questions.

Imbedding space spinor fields are spinor fields in M^4xCP_2. Tensor products of spinor fields in M^4 and CP_2. Have 4x4= 8+8 components corresponding to quark and lepton numbers identified as different H-chiralities. Quantum

numbers are spin and electroweak quantum numbers. Color emerges as CP_2 partial wave and is angular momentum like quantum number.

Stringy variants of twistor diagrams for massless states (getting small mass by p-adic thermodynamics) are expected to reduce to QFT type diagrams when exchanges of particles with masses in p-adic mass scales are neglected.

Just as in string models higher states give additional corrections not present in QFT description. They also make the theory finite by saving from logarithmic divergences.

Ordinary twistor approach in QFT gives only planar diagrams including planar loops. Non-planar case is not understood. String model description does not contain other than planar diagrams so that twistorialization seems to be much more natural in twistor context.

Each wormhole throat corresponds to WCW spinor characterized by imbedding space spinor mode plus superconformal generators acting on it. Particles correspond to string like objects formed by magnetic flux tube pair with wormhole contacts at ends and wormhole throats carrying fermions.

I do not leave away higher order corrections. Since time-like entanglement coefficients of zero energy states correspond to scattering amplitudes then they by definition contain all higher order corrections. One must of course think carefully what one means with particle since there is always finite measurement resolution involved. Just string like objects with wormhole throats carrying fermionic quantum numbers or also radiative corrections? To me the natural basis for state function reduced states contains no radiative corrections at the reduced end of CD. The other end of CD of course contains states with arbitrarily high particle numbers generated by radiation. Twistorial construction would give them.

Dear Matti,

Thanks for the answer.

I become really happy to see the categorization of the subjects of TGD at http://www.tgdtheory.fi/cmaphtml.html

A question:

Can TGD explains why right handed electron or neutrino doesn't interact with electroweak interactions?

Dear Hamed,

I hope that cognitive maps could help those

who are seriously trying to understand TGD.

I am still adding files to it: something like forty

files are still needed. Quite a job.

CP_2 codes standard model coupling structure

in the couplings of spinor connection and induction preserves this structure for classical

fields. For given H-chirality M^4 chirality (quarks/leptons) correlates with CP_2 chirality and CP_2 geometry breaks chiral invariance. W bosons have only left handed couplings. Counterpart of gamma only vectorial and Z^0 partly axial and vectorial.

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