Proposal for a twistorial description of generalized Feynman graphs

Listening of the lectures of Nima Arkani-Hamed is always an inspiring experience and so also at this time. The first recorded lectures was mostly about the basic "philosophical" ideas behind the approach and the second lecture continued discussion of the key points about twistor kinematics which I should already have in my backbone but do not. The lectures stimulated again the feeling that the generalized Feynman diagrammatics has all the needed elements to allow a twistorial description. It should be possible t to interpret the diagrams as the analogs of twistorial diagrams.

A couple of new ideas emerged as a result of concentrate effort to build bridge to the twistorial approach.

1. Generalized Feynman diagrams involve only massless states at wormhole throats so that twistorial description makes sense for the kinematical variables. One should identify the counterparts of the lines and vertices of the twistor diagrams constructed from planar polygons and counterparts of the region momenta.

2. M²⊂ M⁴ appears as a central element of TGD based Feynman diagrammatics and M² projection of the four momentum appears in propagator and also in the modified Dirac equation. I realized that p-adic mass calculations must give the thermal expectation value of the M² mass squared. Since the throats are massless this means that the transversal momentum squared equal to CP₂ contribution plus conformal weight contribution to mass squared.

3. It is not too surprising that a very beautiful interpretation in terms of the analogs of twistorial diagrams becomes possible. The idea is to interpret wormhole contacts as pairs of lines of twistor diagrams carrying on mass shell momenta. In this manner triangles with truncated apexes with double line representing the wormhole throats become the basic objects in generalized Feynman diagrammatics. The somewhat mysterious region momenta of twistor approach correspond to momentum exchanges at the wormhole contacts defining the vertices. A reasonable expectation is that the Yangian invariants used to construct the amplitudes of N=4 SUSY can be used as basic building bricks also now.

4. Renormalization group is not understood in the usual twistor approach and p-adic considerations and quantization of the size of causal diamond (CD) suggests that the old proposal about discretization of coupling constant evolution to p-adic length scale evolution makes sense. A very concrete realization of the evolution indeed suggest itself and would mean the replacement of each triangle with the quantum superposition of amplitudes associated with triangles with smaller size scale and contained with the original triangle characterized by the size scale of corresponding CD containing it. In fact the incoming and outgoing particles of of vertex could be located at the light-like boundaries of CD.

5. The approach should be also number theoretically universal and this suggests that the amplitudes should be expressible in terms of quantum rationals and rational functions having quantum rationals as coefficients of powers of the arguments. Quantum rationals are characterized by p-adic prime p and p-adic momentum with mass squared interpreted as p-adic integer appears in the propagator. This means that the propagator proportional to 1/P² is proportional to 1/p when mass squared is divisible by p, which means that one has pole like contribution. The real counterpart of propagator in canonical identification is proportional to p. This would select the all CD characterized by n divisible by p as analogs of poles.

What generalized Feynman diagrams could be?

Let us first list briefly what these generalized Feynman diagrams emerge and what they should be.

1. Zero energy ontology and the closely related notion of causal diamond (CD are absolutely essential for the whole approach. U-matrix between zero energy states is unitary but does not correspond to the S-matrix. Rather, U-matrix has as its orthonormal rows M-matrices which are "complex" square roots of density matrices representable as a product of a Hermitian square root of density matrix and unitary and universal S-matrix commuting with it so that the Lie algebra of these Hermitian matrices acts as symmetries of S-matrix. One can allow all M-matrices obtained by allowing integer powers of S-matrix and obtains the analog of Kac-Moody algebra. The powers of S correspond to CD with temporal distance between its tips coming as integer multiple of CP₂ size scale. The goal is to construct M-matrices and these could be non-unitary because of the presence of the hermitian square root of density matrix.

2. If is assumed that M-matrix elements can be constructed in terms of generalized Feynman diagrams. What generalized Feynman diagrams strictly speaking are is left open. The basic properties of generalized Feynman diagrams - in particular the property that only massless on mass shell states but with both signs of energy appear- however suggest strongly that they are much more like twistor diagrams and that twistorial method used to sum up Feynman diagrams apply.

The lines of the generalized Feynman diagrams

Generalized Feynman diagrams are constructed using solely diagrams containing on mass shell massless particles in both external and internal lines. Massless-ness could mean also massless-ness in M⁴× CP₂ sense, and p-adic thermodynamics indeed suggests that this is true in some sense.

1. For massless-ness in M⁴× CP₂ sense the standard twistor description should fail for massive excitations having mass scale of order 10⁴ Planck masses. At external lines massless states form massive on mass shell particles. In the following this possible difficulty will be neglected. Stringy picture suggests that this problem cannot be fatal.

2. Second possibility is that massless states form composites which in the case of fermions have the mass spectrum determined by CP₂ Dirac operator and and that that physical states correspond to states of super-conformal representations with ground states weight determined by the sum of vacuum conformal weight and the contribution of CP₂ mass squared. In this case, one would have massless-ness in M⁴ sense but composite would be massless in M⁴× CP₂ sense. In this case twistorial description would work.

3. The third and the most attractive option is based on the fact that its is M² momentum that appears in the propagators. The picture behind p-adic mass calculations is string picture inspired by hadronic string model and in hadron physics one can assign M² to longitudinal parts of the parton momenta.

   One can therefore consider the possibility that M² momentum square obeys p-adic thermodynamics. M² momentum appears also in the solutions of the modified Dirac equation so that this identification looks physically very natural. M² momentum characterizes naturally also massless extremals (topological light rays) and is in this case massless. Therefore throats could be massless but M² momentum identifiable as the physical momentum would be predicted by p-adic thermodynamics and its p-adic norm could correspond to the scale of CD.

   Mathematically this option is certainly the most attractive one and it might be also physically acceptable since integration over moduli characterizing M² is performed to get the full amplitude so that there is no breaking of Poincare invariance.

There are also other complications.

1. Massless wormhole throats carry magnetic charges bind to form magnetically neutral composite particles consisting of wormholes connected by magnetic flux tubes. The wormhole throat at the other end of the wormhole carries opposite magnetic charge and neutrino pair canceling the electro-weak isospin of the physical particle. This complication is completely analogous to the appearance of the color magnetic flux tubes in TGD description of hadrons and will be neglected for a moment.

2. Free fermions correspond to single wormhole throats and the ground state is massless for them. Topologically condensed fermions carry mass and the ground states has developed mass by p-adic thermodynamics. Above considerations suggests that the correct interpretation of p-adic thermal mass squared is as M² mass squared and that the free fermions are still massless! Bosons are always pairs of wormhole throats. It is convenient to denote bosons and topologically condensed fermions by a pair of parallel lines very close to each other and free fermion by single line.

3. Each wormhole throat carries a braid and braid strands are carriers of four-momentum.
   1. The four momenta are parallel and only the M² projection of the momentum appears in the fermionic propagator. To obtain Lorentz invariance one must integrate over boosts of M² and this corresponds to integrating over the moduli space of causal diamond (CD) inside which the generalized Feynman diagrams reside.

   2. Each line gives rise to a propagator. The sign of the energy for the wormhole throat can be negative so that one obtains also space-like momentum exchanges.

   3. It is not quite clear whether one can allow also purely bosonic braid strands. The dependence of the over all propagator factor on longitudinal momentum is 1/p²ⁿ so that throats carrying 1 or 2 fermionic strands (or single purely bosonic strand) are in preferred position and braid strand numbers larger than 2 give rise to something different than ordinary elementary particle. It is probably not an accident that quantum phases q=exp(i2π/n) give rise to bosonic and fermionic statistics for n=1,2 and to braid statistics for n>2. States with n≥ 3 are expected to be anyonic. This also reduces the large super symmetry generated by fermionic oscillator operators at the partonic 2-surfaces effectively to N=1 SUSY.

In the following It will be assume that all braid strands appearing in the lines are massless and have parallel four-momenta and that M² momentum squared is given by p-adic thermodynamics and actually mass squared vanishes. It is also assumed that M² momenta of the throats of the wormhole throats are paralleI in accordance with the classical idea that wormhole throats move in parallel. It is convenient to denote graphically the wormhole throat by a pair of parallel lines very close to each other.

Vertices

The following proposal for vertices neglects the fact that physical elementary particles are constructed from wormhole throat pairs connected by magnetic flux tubes. It is however easy to generalizes the proposal to that case.

1. Conservation of momentum holds in each vertex but only for the total momentum assignable to the wormhole contact rather than for each throat. The latter condition would force all partons to have parallel massless four-momenta and the S-matrix would be more or less trivial. Conservation of four-momentum, the massless on mass shell conditions for 4-momenta of wormhole throatas and on mass shell conditions M² momentum squared given by stringy mass squared spectrum are extremely powerful and it is quite possible that one obtains in a given resolution defined by the largest and smallest causal diamonds finite number of diagrams.

2. I have already earlier developed argments strongly suggesting that that only three-vertices are fundamental kenociteallb/elvafu. The three vertex at the level of wormhole throats means gluing of the ends of the generalized line along 2-D partonic two surface defining their ends so that diagrams are generalization of Feynman diagrams rather than 4-D generalizations of string diagrams so that a generalization of a a trouser diagram does not describe particle decay). The vertex can be BFF or BBB vertex or a variant of this kind of vertex obtained by replacing some B:s and F:s with their super-partners obtained by adding right handed neutrino or antineutrino on the wormhole throat carrying fermion number. Massless on mass shell conditions hold true for wormhole throats in internal lines but they are not on mass shell as a massive particles like external lines.

3. What happens in the vertex is momentum exchange between different wormhole throats regarded as braids with strands carrying parallel momenta. This momentum exchange in general corresponds to a non-vanishing mass squared and can be graphically described as a line connecting two vertices of a triangle defined by the particles emerging into the vertex. To each vertex of the triangle either massless fermion line or pair of lines describing topologically condensed fermion or boson enters. The lines connecting the vertices of the triangle carry the analogs of region momenta kenociteallb/Yangian, which are in general massive but the differences of two adjacent region momenta are massless. The outcome is nothing but the analog of the twistor diagram. 3- vertices are fundamental and one would obtain only 3-gons and the Feynman graph would be a collection of 3-gons such that from each line emerges an internal or external line.

4. A more detailed graphical description utilizes double lines. For FFB vertices with free fermions one would have 4-gon containing a pair of vertices very near to each other corresponding to the outgoing boson wormhole decribed by double line. This is obtained by truncating the bosonic vertex of 3-gon and attaching bosonic double line to it. For topologically condensed fermions and BBB vertex one would have 6-gon obtained by truncating all apices of a 3-gon.

Some comments about the diagrammatics is in order.

1. On mass shell conditions and momentum conservation conditions are extremely powerful so that one has excellent reasons to expect that in a given resolution defined by the largest and smallest CD involves the number of contributing diagrams is finite.

2. The resulting diagrams are very much like twistor diagrams in N=4 D=4 SYM for which also three-vertex and its conjugate are the fundamental building bricks from which tree amplitudes are constructed: from tree amplitudes one in turn obtains loop amplitudes by using the recursion formulas. Since all momenta are massless, one can indeed use twistor formalism. For topologically condensed fermions one just forms all possible diagrams consisting of 6-gons for which the truncated apices are connected by double lines and takes care that n lines are taken to be incoming lines.

3. The lines can cross, and this corresponds to the analog of non-planar diagram. I have proposed a knot-theoretic description of this situation based on the generalized braiding matrix appearing in integrable QFTs defined in M². By using a representation for the braiding operation which can be used to eliminate the crossings of the lines one could transform all diagrams to planar diagrams for which one could apply existing construction recipe.

4. The basic conjecture is that the basic building bricks are Yangian invariants. Not only for the conformal group of M⁴ but also for the super-conformal algebra should have an extension to Yangian. This Yangian should be related to the symmetry algebra generated by the M-matrices and analogous to Kac-Moody algebra. For this Yangian points as vertices of the momentum polygon are replaced with partonic 2-surfaces.

Generalization of the diagrammatics to apply to the physical particles

The previous discussion has neglected the fact that the physical particles are not wormhole contacts. Topologically condensed elementary fermions and bosons indeed correspond to magnetic flux pairs at different space-time sheets with wormhole contacts at the ends. How could one describe this situation in terms of the generalization Feynman diagrams?

The natural guess is that one just puts two copies of diagrams above each other so that the triangles are replaced with small cylinders with cross section given by the triangle and the edges of this triangular cylinder representing magnetic flux tubes. It is natural to allow momentum exchanges also at the other end of the cylinder: for ordinary elementary particle these ends carry only neutrino pairs so that the contribution to interactions is screening at small momenta. Also momentum exchanges long the direction of the cylinder should be allowed and would correspond to the non-perturbative low energy degrees of freedom in the case of hadrons. This momentum exchange assignable to flux tube would be between the truncated triangle rather than separately along the three vertical edges of the triangular cylinder.

Number theoretical universality and quantum arithmetics

The approach should be also number theoretically universal meaning that amplitudes should make sense also in p-adic number fields. Quantum arithmetics is characterized by p-adic prime and canonical identification mapping p-adic amplitudes to real amplitudes is expected to make the universality possible.

This is achieved if the amplitudes should be expressible in terms of quantum rationals and rational functions having quantum rationals as coefficients of powers of the arguments. This would be achieve by simply mapping ordinary rationals to quantum rationals if they appear as coefficients of polynomials appearing in rational functions.

Quantum rationals are characterized by p-adic prime p and p-adic momentum with mass squared interpreted as p-adic integer appears in the propagator. If M² mass square is proportional to this p-adic prime p, propagator behaves as 1/P²∝ 1/p, which means that one has pole like contribution for these on mass shell longitudinal masses. p-Adic mass calculations indeed give mass squared proportional to p. The real counterpart of propagator in canonical identification is proportional to p. This would select the all CD characterized by n divisible by p as analogs of poles.

It would seem that one must allow different p-adic primes in the generalized Feynman diagram since physical particles are in general characterized by different p-adic primes. This would require the analog of tensor product for different quantum rationals analogous to adeles. These numbers would be mapped to real (or complex) numbers by canonical identification.

How to understand renormalization flow in twistor context?

In twistor contex the notion of mass renormalization is not straightforward since everything is massless. In TGD framework p-adic mass scale hypothesis suggests a solution to the problem.

1. At the fundamental level all elementary particles are massless and only their composites forming physical particles are massive.

2. M² mass squared is given by p-adic mass calculations and should correspond to the mass squared of the physical particle. There are contributions from magnetic flux tubes and in the case of baryons this contribution dominates.

3. p-Adic physics discretizes coupling constant flow. Once the p-adic length scale of the particle is fixed its M² momentum squared is fixed and massless takes care of the rest.

Consider now how renormalization flow would emerge in this picture. At the level of generalized Feynman diagrams the change of the IR (UV) resolution scale means that the maximal size of the CDs involve increases (the minimal size of the sides decreases).

Concerning the question what CD scales should be allowed, the situation is not completely clear.

1. The most general assumption allows integer multiples and would guarantee that the products of hermitian matrices and powers of S-matrix commuting with them define Kac-Moody type algebra assignable to M-matrices. If one uses in renormalization group evolution equation CDs corresponding to integer multiples of CP₂ length scale, the equation would become a difference equation for integer valued variable.

2. p-Adicity would suggest that the scales of CDs come as prime multiples of CP₂ scale.

3. p-Adic length scale hypothesis would allow only p-adic length scales near powers of two. There are excellent reasons to expect that these scales are selected by a kind of evolutionary process favoring those scales for CDs for which particles are maximally stable.

Renormalization group equations are based on studying what happens in an infinitesimal reduction of UV resolution scale would mean. Now the change cannot be infinitesimal but must correspond to a change in the scale of CD by one unit defined by CP₂ size scale.

1. The decrease of UV cutoff means that the vertex amplitudes associated with smallest truncated 3-polygons in the diagram are replaced with the sum of all amplitudes in which smaller polygons down to the cutoff size and having 3-external legs appear. The change of the total amplitude in this replacements define renormalization group equation. Conservation of four-momentum and on mass shell conditions suggest that only finite number of terms are allowed.

2. The increase of UV cutoff means that the size of the largest CD increases. The physical interpretation would be in terms of the time scale in which one observes the process. If this time scale is too long, the process is not visible. For instances, the study of strong interactions between quarks requires short enough scale for CD. At long scales one only observes hadrons and in even longer scales atomic nuclei and atoms.

3. One tends to think that the diagrams are imbedded in M² allowing identification as 2-plane in Minkowski space-time. This in turn would suggest that the step increasing UV resolution corresponds of replacement of triangles with graphs consisting of smaller triangles contained by them and having no intersections. This interpretation is attractive but might not be needed. Essential conditions are momentum conservation and on mass shell conditions.

4. One could also allow the UV scale to depend on the particle. This scale should correspond to the p-adic mass scales assignable to the stable particle. In hadron physics this kind of renormalization is standard operation.

Reader interested in background can consult to the article Algebraic braids, sub-manifold braid theory, and generalized Feynman diagrams and the new chapter Generalized Feynman Diagrams as Generalized Braids of "Towards M-Matrix".

Standing waves in TGD

Four-wave mechanism is one of the basic mechanism encountered in laser physics. It is not obvious what the description of four-wave mechanism is at the basic level in TGD framework. In Maxwellian approach one introduces non-linear F⁴ term in the Lagrangian: here F is the electromagnetic field strength. This approach must be replaced by something else in TGD level if one wants a microscopic description.

To end up with this description by making first the question how to understand amplitude modulation. Even this is not enough. One must ask what is the first principle description for the linear superposition of fields in TGD framework. I have described this description in the earlier posting. The basis idea is that superposition does not occur for fields: only for their quantal effects. Some of the implications are discussed here, here, and here.

Also the phenomena of amplitude modulation and four-wave interaction would be effects appearing as quantal reactions of charged particles to the presence of space-time sheets carrying fields. They need not be present for the induced gauge fields. One might perhaps even say that these effects appear only at the level of conscious perception involving quantum jumps but not at the level of classical fields. This would be a direct evidence for the quantal character of conscious experience.

The summation of effects of em fields can induce amplitude modulation. If charged particles have topological sum contacts to the two space-time sheets carrying classical fields with different frequencies, the rate for quantum jumps is proportional to the modulus squared for the sum of the forces caused by these fields, and one obtains amplitude modulation visible as different and sum of the frequencies involved. In the case of massless extremals the sum and difference of frequencies appear only if MEs corresponding to opposite directions of 3-momentum are present. This leads to an effect that would be regarded as being caused by a standing electromagnetic wave. MEs correspond to waves propagating in single direction for a given sign of frequency, and in TGD framework it is highly implausible that standing waves could be realized as classical gauge fields. Probably I have not been the only child who has experienced standing wave in a rope as mysterious and somehow otherworldly phenomenon.

Similar description applies to four-wave mechanism. Four space-time sheets can give rise to the sums of four frequencies appearing with both signs in the sum and the temporally constant effect is obtained when the sum of the frequencies vanishes.

Quantum view about metabolism

After the writing of the first version of the chapter discussing quantum view about metabolism for about decade ago several new ideas have emerged. Since 2007 the evidence that photosynthesis involves quantum coherence in electronic degrees of freedom in the cell scale has been accumulating: this discovery is in blatant conflict with the predictions of standard quantum theory but conforms nicely with one of the oldest TGD based proposal that living matter is high T_c electronic super-conductor and with the identification of dark matter as phases with large value of Planck constant.

Both the new ideas and the new experimental results motivated rewriting of the chapter. Below is a brief summary about the new ideas that have emerged during last years, and questions raised by them, and how they affect the quantum model of metabolism at the basic level. Especially interesting new result is a concrete and testable proposal for how living matter acts as a high T superconductor bound to have practical implications. This proposal allows also to understand the basic aspects of bio-chemistry (why the number of valence bonds per molecule is maximized). Also a unification of three different views about high living matter manages to be macroscopic quantum system emerges. This unification is only one example of amazing convergence of the basic ideas of TGD that has taken place during the last years.

1. Three different views about living matter as a macroscopic quantum system

There are three different views about how living system manages to be a macroscopic quantum system.

1. The first vision is based on various kinds of super-conductivities. Electronic super-conductivity is assigned with the cell membrane and plays a key role in the model of cell membrane as a Josephson junction. Furthermore, the effects of ELF em fields on vertebrate brain (see this) suggest that biologically important ions form macroscopic quantum states and cyclotron Bose-Einstein condensates of bosonic ions have been suggested. The TGD based view about atomic nuclei (see this) predicts exotic nuclei chemically equivalent with ordinary ones but being bosons rather than fermions. Also these exotic ions could also form cyclotron Bose-Einstein condensates. Large value of Planck constant would guarantee that cycloctron energies proportional to hbar are above thermal energy.

2. A more precise view about hierarchy of Planck constants as an implication of the enormous vacuum degeneracy of Kähler action has emerged (see this). According to this view non-standard values of Planck constant are only effective.

   As the idea about the hierarchy of Planck constants emerged, I proposed that favored values of Planck constant could comes are powers of 2¹¹. This was just a first guess inspired partially by the observation that the mass ratio of proton and electron is 940/.5= 1880 ∼ 2¹¹. I managed to find indications supporting this hierarchy and also this chapter contains traces of this idea. I became later skeptic but one could actually imagine a mechanism implying this kind of hierarchy. Dark protons with say r=hbar/hbar₀= 1836=4× 3³× × 17 would correspond to approximately same Compton length as ordinary electrons. It is natural to assign this value of hbar also to electrons and this gives Compton length 44.6 Angstroms not far from the p-adic length scale L(149)≈ 50 Angstroms assigned with the lipid layer of cell membrane. The condition that dark proton corresponds to this Compton length gives r= 1836²: the electron Compton length comes now 8.1 μm, which corresponds to cell size scale. One could continue the resulting hierarchy of Planck constants indefinitely.

3. The notion of negentropic entanglement making sense for rational and even algebraic entanglement probabilities has emerged as a possible characterizer of living matter emerged (see this). Quantum arithmetics allows to generalize the notion of rational so that p-adic real correspondence mediated by canonical identification is fixed uniquely and is both continuous and respects symmetries. One implication is an explanation for Shnoll effect , which could be important also in living matter.

This raises several questions.

1. How high T_c super conductivity based on dark electron pairs and negentropic entanglement relate?

2. Could it be that electron pairs in valence bonds are the carriers of negentropic entanglement and that they generate the magnetic flux tubes as parts of their magnetic bodies and in this manner space-time correlates for macroscopic quantum coherence? This makes sense only if the valence electron pairs in living matter have spin 1. The Cooper pairs of high T_c super-conductors are ineed known to have spin 1 (see this). If this view is correct, biological evolution would favor the maximization of covalent electron pairs and this indeed seems to be the case (carbohydrates, fundamental biomolecules, phosphates having as many as 8 valence bonds!) .

3. Why large hbar would make possible negentropic entanglement or even force it? Is there some purely number theoretic reason for this? For instance, could the p-adic prime p characterizing quantum arithmetics divide the integer n characterizing the Planck constant or could prime valued integers n be favored?

2. Genetic code and dark nucleon states

New realization of the genetic code in terms of dark proton sequences identified as dark nucleons was discovered (see this and this).

1. The states of dark proton are in natural one-one correspondence with DNA, RNA, tRNA, and amino-acids and vertebrate genetic code is realized in a natural manner. Dark nucleons realized DNA codons as entangled quark triplets. The effective chemical formula H_1.5O for water in atto-second time scale supports this view (see this). How the notion of dark nucleon relates to negentropic entanglement of electrons? Could dark electron pairs and dark nucleons correspond to the same value of Planck constant? Could both dark protons and dark electrons play a key role in metabolism.

2. The simplest guess is that DNA strands are accompanied by dark nuclei with one dark proton per DNA nucleotide. The resulting positive charged would stabilize the system by partially neutralizing the negative charge density due to the phosphorylation (2 negative charges per nucleotide). Dark proton sequences could be associated also with other important bio-polymers. If the spins of the dark protons are parallel the dipole magnetic fields give rise to flux tubes connecting the protons and one can assign to the large hbar protons a macroscopically quantum coherent phase.

3. The natural guess would be that dark nucleus realization of the genetic code induces the biological realization as evolution assigns to dark nucleon sequences DNA, RNA, and aminoacid sequences with 1-1 correlation between dark nucleon state and basic unit of the sequence. The dark realization of genetic code suggest a totally new view about biological evolution as a process, which is analogous to R&D in high tech industry rather than being completely random (see this). The candidates for new genes could be tested at dark matter level and in the case that they work they would be transcribed to their chemical equivalents.

3. New ideas related to metabolism

Also new ideas related to metabolism have emerged at the same time when evidence for quantal aspects of photosynthesis has been emerging (see this, this, this, and this).

1. Negentropic entanglement leads also to the idea about energy metabolism and negentropy transfer as different sides of the same coin. The model for DNA as topological in turn suggest that ADP → ATP and its reverse can be interpreted as a standardized reconnection process re-organizing connections between distant molecules connected by magnetic flux tubes by the relay defined by ATP molecule. Metabolic energy would - or at least could - go to the re-organization of the flux tube connections and therefore of the negentropic quantum entanglement. The question is how to fuse this vision with the hypothesis about metabolic currencies as differences of zero point kinetic energies for space-time sheets.

2. The radiation from Sun defines the fundamental metabolic currency. Solar radiation cannot be said to negentropic since negentropic entanglement is a 2-particle property. Solar photons could possess a large value of hbar or - more plausibly - suffer at the magnetic body of the living system a phase transition increasing the value of hbar. Could the absorption of large hbar photons arriving from Sun or from magnetic body by electrons generate spin 1 valence electron pairs pairs or provide the metabolic energy needed to re-arrange the flux tube connections between distant molecules by ADP+P_i → ATP process?

4. DNA as a topological quantum computer vision

The vision about DNA as topological quantum computer (see this) has turned out to be very general allowing to imagine several concrete realizations. The essential element is the coding of DNA nucleotides and one can imagine several options.

1. The original proposal for the realization of DNA as topological quantum computer is based on the representation of DNA nucleotides A, T, C, G as quarks u, d and their antiquarks and requires scaled up version of QCD (see this). This idea looks rather outlandish but could be justified by the strange findings of mathematician Barbara Shipman about honeybee dance (see this) and also by the p-adic length scale hierarchy and the hierarchy of Planck constants suggesting scaled variants of QCD like physics also in the length scale range relevant to the living cell.

2. The question whether one could one use spin 1 triplet and spin 0 singlet of dark electron pair instead of quarks and their antiquarks to represent codons, is rather obvious. The problem is that S= 0 state for electron pair however gives rise to vanishing dipole field so that flux tube structure would not be possible. The generation of flux tube structure along which supra currents can flow is however an essential element of the proposed mechanism of super-conductivity.

3. DNA as topological quantum computer hypothesis lead to the hypothesis that it is O= :s to which one must assign the flux tube pair responsible for the representation of the genetic code. Why O= would be in special role? And why should one have a pair of flux tubes? Could this relate to the coding of nucleotides by electron pairs? If there are two parallel flux tubes, one obtains tensor product 3× 3= 5+3+1 of electron triplets at the ends of the flux tubes. Could it be that A,T,C, and G are represented in terms of 3 and 1 and that the breaking of rotational invariance implies mixing of singlet and S_z=0 state of triplet so that nucleotides and their conjugates could correspond to the resulting two pairs related by reflection.

4. ATP→ ADP+P_i would correspond to the reconnection of the flux tubes of the flux tube pair with hydrogen bonds associated with two water molecules. The flux tubes would split and end to water molecules containing valence electron pair so the negentropic entanglement might not be totally lost. The reverse process would create flux tube connection labelled by the spin state equivalent of A,T,C, or G.

5. Pessimistic generalization of the second law of thermodynamics

The possibility of negentropic entanglement raises the question about the fate of the second law of thermodynamics. The proposal for a generalization of the second law of thermodynamics (see this) based on the most pessimistic vision is that entropy indeed increases also when negentropic entanglement is generated in state function reduction. If the generation of negentropic entanglement is accompanied by a compensating entropic entanglement, how it is generated? Or is the maximally pessimistic generalization really necessary? Is it implied automatically in time scales longer than the characteristic time scale associated with the causal diamonds serving as the basic correlates for conscious selves. One must apply ensemble description in these time scales: does the non-determinism of quantum jump imply second law at the level of ensemble automatically. If this argument is correct, second law would cease to hold in time scales than that characterizing the relevant CD. One might be able to anwer these quesetion by trying to understand the situation in the case of metabolism.

During writing I realized that the old chapter must be split to two pieces. The chapter of "Biosystems as Conscious Holograms" contains the updated material.

Is it really a Higgs?

Peter Woit tells in This Week's rumour that CMS has found that the signal for what could be Higgs in gamma-gamma decay channel is two times higher than it should be. The optimistic interpretation is that both ATLAS and CMS have been a little bit lucky. But can we believe this? Statistics has been improving: how it is possible that also CMS is getting "lucky"!

If the good luck continues, one is forced to challenge the idea that the signal represents standard model Higgs. SUSY Higgs cannot help since standard SUSY itself is in deep difficulties experimentally. We cannot forget that there are also Higgs like signals at higher masses but these were "forgotten" in the midst of the Higgs hysteria - at least by bloggers who seem to suffer from rather short span of long term memory. Some of us even experienced a sudden conversion from a phanatic no-fairiest to an equally phanatic believer-in-Higgs;-).

In the zero energy ontology of TGD Higgs is not needed at all. A scaled up variant of ordinary hadron physics characterized by Mersenne prime M₈₉ is however "almost-predicted" (better to be cautious!) with mass scale 512 higher than that for ordinary hadron physics. This hadron physics can be said to replace Higgs.

The mesons of this hadron physics should be detected first at LHC. In particular, M₈₉ pion and spion (obtained by replacing quark and antiquark of pion with squark and antiquark) should be there if TGD SUSY is realized in the simplest possible manner meaning the same p-adic mass scale for both quarks and squarks. The few year old discovery of exotic satellite states of ordinary pion supports this radically new view about SUSY as also the mysterious X and Y mesons which in many respects look like charmonium states but are not charmonium states. I have told about all this in the earlier postings. Here is the most recent one.

The generalization of partially conserved axial current hypothesis (PCAC) allows to predict various decay rates and leads to very similar expressions for the decay rates of M₈₉ pseudoscalar mesons as standard model for those of Higgs. Higgs vacuum expectation is replaced with the decay constant f_π of pion-like (more generally meson-like) state which in sigma model corresponds to the vacuum expectation of sigma field. Sigma model is however not necessary except as a phenomenological description in which sigma field expectation would characterize the contribution of the classical color magnetic fields to the mass of M₈₉ baryons. Quark masses would follow from p-adic thermodynamics providing a microscopic description for particle massivation: also the need for this description has been forgotten by the main stream bloggers.

In particular, spion would have 1.5 times higher gamma-gamma decay rate if one extrapolates directly the PCAC for ordinary pion by the simplest possible scaling argument. Could it be that the Higgs candidate is actually spion and pion and other mesons are also there waiting to be discovered? This is the question.

My guess is that within year Higgs hypothesis is dead and one must begin serious work in trying to resolve the problems visible already now.

Tachyonic explanation of neutrino superluminality killed

New Scientist reported about the sad fate of the tachyonic explanation of neutrino superluminality. The argument is extremely simple.

1. You start by assuming that a tachyon having negative mass squared: m(ν)²<0 and assume that super-luminal velocity is in question. The point is that you know the value of the superluminal velocity v(1+ε)c, ε≈ 10^-5. You can calculate the energy of the neutrino as

   E= |m(ν)|[-1+ v²/(v²-1)]^1/2,

   |m(ν)|=(-m(ν)²)^1/2 is the absolute value of formally imaginary neutrino mass.

2. In good approximation you can write

   E= |m(ν)|[-1+ (2ε^-1/2]^1/2 ≈|m(ν)| (2ε)^-1/2.

   The order of magnitude of |m(ν)| is not far from one eV - this irrespective of whether neutrino is tachyonic or not. Therefore the energy of neutrino is very small: not larger than keV. This is in a grave contradiction whith what is known: the energy is measured using GeV as a natural unit so that there is discrepancy of 6 orders of magnitude at least. One can also apply energy conservation to the decay of pion to muon and neutrino and this implies that muon has gigantic energy: another contradiction.

What is amusing that this simple kinematic fact was not noticed from beginning. In any case, this finding kills all tachyonic models of neutrino super-luminality assuming energy conservation, and gives additional support for the TGD based explanation in terms of maximal signal velocity, which depends on pair of points of space-time sheet connected by signal and space-time sheet itself characterizing also particular kind of particle.

Even better, one can understand also the jitter in the spectrum of the arrival times which has width of about 50 ns in terms of an effect caused fluctuations in gravitational fields to the maximal signal velocity expressible in terms of the induced metric. The jitter could have interpretation in terms of gravitational waves inducing fluctuation of the maximal signal velocity c_#, which in static approximation equals to c_#=c(1+Φ_gr)^1/2, where Φ_gr is gravitational potential.

Suprisingly, effectively super-luminal neutrinos would make possible gravitational wave detector! The gravitational waves would be however gravitational waves in TGD sense having fractal structure since they would correspond to bursts of gravitons resulting from the decays of large hbar gravitons emitted primarily rather than to a continuous flow (see this). The ordinary detection criteria very probably exclude this kind of bursts as noise. The measurements of Witte attempting to detect absolute motion indeed observed this kind of motion identifiable as a motion of Earth with respect to the rest frame of galaxy but superposed with fractal fluctuations proposed to have interpretation in terms of gravitational turbulence - gravitational waves.

For details see the earlier posting, the little article Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity? or the chapter TGD and GRT of "Physics in Many-Sheeted Space-time".

The basic objection against TGD

The basic objection against TGD is that induced metrics for space-time surfaces in M⁴× CP₂ form an extremely limited set in the space of all space-time metrics appearing in the path integral formulation of General Relativity. Even special metrics like the metric of a rotating black hole fail to be imbeddable as an induced metric. For instance, one can argue that TGD cannot reproduce the post-Newtonian approximation to General Relativity since it involves linear superposition of gravitational fields of massive objects. As a matter fact, Holger B. Nielsen- one of the very few colleagues who has shown interest in my work - made this objection for at least two decades ago in some conference and I remember vividly the discussion in which I tried to defend TGD with my poor English.

The objection generalizes also to induced gauge fields expressible solely in terms of CP₂ coordinates and their gradients. This argument is not so strong as one might think first since in standard model only classical electromagnetic field plays an important role.

1. Any electromagnetic gauge potential has in principle a local imbedding in some region. Preferred extremal property poses strong additional constraints and the linear superposition of massless modes possible in Maxwell's electrodynamics is not possible.

2. There are also global constraints leading to topological quantization playing a central role in the interpretation of TGD and leads to the notions of field body and magnetic body having non-trivial application even in non-perturbative hadron physics. For a very large class of preferred extremals space-time sheets decompose into regions having interpretation as geometric counterparts for massless quanta characterized by local polarization and momentum directions. Therefore it seems that TGD space-time is very quantal. Is it possible to obtain from TGD what we have used to call classical physics at all?

The imbeddability constraint has actually highly desirable implications in cosmology. The enormously tight constraints from imbeddability imply that imbeddable Robertson-Walker cosmologies with infinite duration are sub-critical so that the most pressing problem of General Relativity disappears. Critical and over-critical cosmologies are unique apart from a parameter characterizing their duration and critical cosmology replaces both inflationary cosmology and cosmology characterized by accelerating expansion. In inflationary theories the situation is just the opposite of this: one ends up with fine tuning of inflaton potential in order to obtain recent day cosmology.

Despite these and many other nice implications of the induced field concept and of sub-manifold gravity the basic question remains. Is the imbeddability condition too strong physically? What about linear superposition of fields which is exact for Maxwell's electrodynamics in vacuum and a good approximation central also in gauge theories. Can one obtain linear superposition in some sense?

1. Linear superposition for small deformations of gauge fields makes sense also in TGD but for space-time sheets the field variables would be the deformations of CP₂ coordinates which are scalar fields. One could use preferred complex coordinates determined about SU(3) rotation to do perturbation theory but the idea about perturbations of metric and gauge fields would be lost. This does not look promising. Could linear superposition for fields be replaced with something more general but physically equivalent?

2. This is indeed possible. The basic observation is utterly simple: what we know is that the effects of gauge fields superpose. The assumption that fields superpose is un-necessary! This is a highly non-trivial lesson in what operationalism means for theoreticians tending to take these kind of considerations as mere "philosphy".

3. The hypothesis is that the superposition of effects of gauge fields occurs when the M⁴ projections of space-time sheets carrying gauge and gravitational fields intersect so that the sheets are extremely near to each other and can touch each other ( CP₂ size is the relevant scale).

A more detailed formulation goes as follows.

1. One can introduce common M⁴ coordinates for the space-time sheets. A test particle (or real particle) is identifiable as a wormhole contact and is therefore pointlike in excellent approximation. In the intersection region for M⁴ projections of space-time sheets the particle forms topological sum contacts with all the space-time sheets for which M⁴ projections intersect.

2. The test particle experiences the sum of various gauge potentials of space-time sheets involved. For Maxwellian gauge fields linear superposition is obtained. For non-Abelian gauge fields gauge fields contain interaction terms between gauge potentials associated with different space-time sheets. Also the quantum generalization is obvious. The sum of the fields induces quantum transitions for states of individual space time sheets in some sense stationary in their internal gauge potentials.

3. The linear superposition applies also in the case of gravitation. The induced metric for each space-time sheet can be expressed as a sum of Minkowski metric and CP₂ part having interpretation as gravitational field. The natural hypothesis that in the above kind of situation the effective metric is sum of Minkowski metric with the sum of the CP₂ contributions from various sheets. The effective metric for the system is well-defined and one can calculate a curvature tensor for it among other things and it contains naturally the interaction terms between different space-time sheets. At the Newtonian limit one obtains linear superposition of gravitational potentials. One can also postulate that test particles moving along geodesics in the effective metric. These geodesics are not geodesics in the metrics of the space-time sheets.

4. This picture makes it possible to interpret classical physics as the physics based on effective gauge and gravitational fields and applying in the regions where there are many space-time sheets which M⁴ intersections are non-empty. The loss of quantum coherence would be due to the effective superposition of very many modes having random phases.

The effective superposition of the CP₂ parts of the induced metrics gives rise to an effective metric which is not in general imbeddable to M⁴× CP₂. Therefore many-sheeted space-time makes possible a rather wide repertoire of 4-metrics realized as effective metrics as one might have expected and the basic objection can be circumvented In asymptotic regions where one can expect single sheetedness, only a rather narrow repertoire of "archetypal" field patterns of gauge fields and gravitational fields defined by topological field quanta is possible.

The skeptic can argue that this still need not make possible the imbedding of a rotating black hole metric as induced metric in any physically natural manner. This might be the case but need of course not be a catastrophe. We do not really know whether rotating blackhole metric is realized in Nature. I have indeed proposed that TGD predicts new physics new physics in rotating systems. Unfortunately, gravity probe B could not check whether this new physics is there since it was located at equator where the new effects vanish.

For background and more details see either the article Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity? or the chapter TGD and GRT of "Physics in Many-Sheeted Space-time".

Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity?

The history of the modern measurements of absolute motion has a long - more than century beginning from Michelson-Morley 1887. The reader can find in web a list of important publications giving an overall view about what has happened. The earliest measurements assumed aether hypothesis. Cahill identifies the velocity as a velocity with respect to some preferred rest frame and uses relativistic kinematics although he misleadingly uses the terms absolute velocity and aether. The preferred frame could galaxy, or the system defining rest system in cosmology. It would be easy to dismiss this kind of experiments as attempts to return to the days before Einstein but this is not the case. It might be possible to gain unexpected information by this kind of measurements. Already the analysis of CMB spectrum demonstrated that Earth is not at rest in the Robertson-Walker coordinate system used to analysis CMB data and similar motion with respect to galaxy is quite possible and might serve as a rich source of information also in GRT based theory.

In TGD framework the situation is especially interesting.

1. Sub-manifold gravity predicts that the effective light-velocity measured in terms of M⁴ time taken for a light signal to propagate from point A to B depends on space-time sheet, on points A and B, in particular the distance between A and B. The maximal signal velocity determined in terms of light-like geodesics has this dependence because light-like geodesics for the space-time surface are in general not light-like geodesics for M⁴ but light-like like curves. The maximal signal velocity is in general smaller than its absolute maximum obtained light-like geodesics of M⁴, depends on particle, and could be larger than for photon space-time sheets. This might explain neutrino super-luminality (see this).

2. Space-time sheets move with respect to larger space-time sheets and it makes sense to speak about the motion of solar system space-time sheet with respect to galactic space-time sheet and this velocity is in principle measurable. Maximal signal velocity can be defined operationally in terms of time needed to travel from point A to B using Minkowski coordinates of the imbedding space as preferred coordinates. It depends on pair of points involved: basically on the direction on and spatial distance along effectively light-like geodesic defined by the sum of the perturbations of the induced metric for the space-time sheets involved. The question is whether one could say something interesting about various experiments carried out to measure the absolute motion interpreted in terms of velocity of space-time sheet with respect to say galactic space-time-sheet.

Also in Special Relativity the motion relative to the rest system of a larger system is a natural notion. In General Relativistic framework situation should be the same but the mathematical description of the situation is somewhat problematic since Minkowski coordinates are not global due to the loss of Poincare invariance as a global symmetry. In practice one must however introduce linear Minkowski coordinates and this makes sense only if one interprets the general relativistic space-time as a perturbation of Minkowski space. This background dependence is in conflict with general coordinate invariance. For sub-manifold gravity the situation is different.

Could the measurements performed already by Michelson-Morley and followers could provide support for the sub-manifold gravity? This might indeed be the case as the purpose of the following arguments demonstrate. The basic results of this analysis are following.

1. The basic formulas for interferometer experiments using relativistic kinematics instead of Galilean one are same as the predictions of Cahill using different basic assumptions, and allow to conclude that already the data of Mickelson and Morley show the motion of Earth -not with respect to aether- but with galactic rest system.

2. The only difference is the appearance of the maximal signal velocity c_# for space-time sheet to which various gravitational fields contribute. In the static approximation sum of gravitational potentials contributes to c_#.

3. This allows to utilize the results of Cahill, who has carried out a re-analysis of experiments trying to detect what he calls absolute motion using these formulas. Cahill has also replicated the crucial experiments of Witte.

4. The value of the velocity as well as its direction can be determined and the results from various experiments are consistent with each other. The travel time data demonstrate a periodicity due to the rotation of Earth and motion with respect a preferred frame identifiable as a galactic rest frame. The tell-tale signature is the periodicity of sidereal day instead of exact 24 hour periodicity. The travel time for photons shows fluctuations which might be interpreted in terms of gravitational waves having fractal patterns. TGD view about gravitons would suggest that the emission takes place -not as a continuous stream- but in burst-wise manner producing fractal fluctuation spectrum. These fluctuations could show themselves as a jitter also in the neutrino travel times discovered by Opera collaboration.

One must answer several questions before one can make predictions.

1. The reduction of light velocity in the case that there are many space-time sheets whose M⁴ projections intersect, is described using common M⁴ coordinates for the space-time sheets. The induced metric for given space-time sheet is the sum of flat M⁴ metric and CP₂ contribution identified as classical gravitational field. The hypothesis is that in good approximation a linear superposition for the effects of the gravitational fields holds true in the sense that a test particle having wormhole throat contacts to these space-time sheets experiences the sum of the gravitational fields of various sheets. Similar description holds for induced gauge fields.

   From this one can identify the reduced light velocity in the static situation as c_#=(g_tt)^1/2. In a more realistic necessary non-local treatment one calculates the effective light-velocity by assuming that the orbit of massless state n geometric optics approximation is light-like geodesic for the sum of the metric perturbations: this line is not a light-like geodesic of any of the space-time sheets.

   In the general the effective metric defined in this manner is not imbeddable as induced metric. This description of linear super-position allows to circumvent the basic objection against TGD, which is that induced metric and gauge fields are extremely strongly correlated since they are expressible in terms of CP₂ coordinates and their gradients and that the variety of metrics representable as induced metrics is extremely restricted. Same of course applies to gauge fields. This resuls is extremely important and would deserve a separate blog posting.

2. How the reduced light-velocity c_# relates to the reduced light-velocity in medium which is usually described by introducing the notions of free and polarization charges and magnetization and magnetization currents. In the simple situation when polarization tensor is scalar, refractive index n characterizes the reduction of the light velocity: V=c_#/n. Since the reduction of maximal signal velocity due to sub-manifold is purely gravitational and its reduction in medium has an electromagnetic origin, one can argue that the two notions have nothing to do with each other. Hence c_# should be treated as a local concept possibly depending on direction of motion by taking the limit when light-like geodesic with respect to effective metric becomes infinitesimally short. This dependence can be deduced by comparing light-like geodesics emanating from a point and calculating the maximal signal velocity as a function of direction angles of the light-like geodesic and the spatial distance along it.

3. What happens to the boundary conditions between different media deduced from the structural equations of classical electrodynamics and Maxwell equations? For instance, does the refraction of light take place also when c_# changes? It might of course be that c_# changes only in astrophysical scales - maybe at the surfaces of astrophysical objects - and stays constant at the boundaries between two media in laboratory scale but nevertheless this issue should be understood. The safest guess is that at the level of kinematic local Lorentz invariance still holds true so that the tangential wave vectors identifiable in terms of massless momentum components are conserved at boundaries and one obtains law of refraction also now.

4. In TGD Universe space-time sheets can move with respect to each other and the larger space-time sheet defines the analog of absolute reference frame in this kind of situation. Also in cosmology one can assign to CMB radiation a specific frame and Earth indeed moves with respect to it rather than being at rest in the global Robertson-Walker coordinate system. For Earth solar system is one such frame. Galactic rest system is second such preferred reference frame. To both one can assign linear Minkowski coordinates, which play a special physical. The obvious question is whether this kind of motion could be detected and whether the measurements carried out to detect absolute motion could allow to deduce this kind of velocity with respect to galactic rest system.

5. The question is how photons in medium behave when this kind of motion is present. Assume that the medium is characterized by refractive index n so that one has V= c_#/n and that space-time sheet moves with respect to larger one by velocity v characterized by direction angles and magnitude. Here c_#<c₀ is the maximal signal velocity at the space-time sheet. For definiteness assume that the larger space-time sheet corresponds to galaxy.
   1. In the measurements of light velocity the light propagates in medium with velocity V<c_#<c₀, and the question is how to describe this mathematically. In his experiments Michelson assumed summation of velocities based on Galilean invariance. This is of course wrong and Special Relativity suggests summation of velocities according to the relativistic formula:

      V →V₁(v,u) == [V+ vu]/[1+ u(Vv/c_#²)] ,

      V= c_#/n , u=cos(θ) .

      Here θ is the direction of the light signal with respect to the velocity v. This formula might be justified in TGD framework: also photon has very small but non-vanishing mass and summation formula for velocities can be applied. This demands the assumption of local Lorentz invariance made routinely in General Relativity. Also it requires that the complex process of repeated absorption and emission of photons is described by a propagation of photon with the reduced velocity.

   2. This predicts two effects which might be seen in the experiments trying to measure absolute velocity and its direction. Both solar and galactic gravitational field and also its perturbations - even gravitational waves- can affect the signal velocity via fluctuations in c_# deduced from the superposition of the perturbative contributions of CP₂ to the effective induced metric. Second effect is due to the change of the propagation time. This change depends on the propagation direction. Note however that also c_# in general has the directional dependence and only in the situation when the components g_ti vanish, this dependence is trivial. In the Newtonian approximation the assumption g_ti≈ 0 is made and corresponds to the description of the situation in terms of gravitational potential.

For background and more details see either the article Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity? or the chapter TGD and GRT.

The TGD based interpretation of the God helmet experiments

In the previous posting I described the God helmet experiments of Persinger briefly and Persinger's own interpretation of the results. Anyone interested to understand what neurotheology is about should listen the inspiring talk God and the Brain - The Persinger 'God Helmet', The Brain, and visions of God by Todd Murphy.

In this posting I will discuss the TGD inspired interpretation of the results of Persinger's experiments. To put it in very concise manner: whereas Persinger interprets right brain as "visitor" explaining sense of presence experiences and even meeting of God, I identify the "visitor" of the visitor experiences as the personal magnetic body or in the case of enlightment experiences as the emergence of a new layer to its fractal structure. Magnetic body would be also responsible for the third person aspect of conscious experience, which means that we tend to see ourselves from bird's eye perspective. Magnetic bodies make as social animals, and are responsible for the cultural evolution and explain why we differ so much from our cousins although the genomes differ so little.

1. Frequency modulation as a "code of consciousness"

Maxwell's electrodynamics would suggest that a superposition of endogenous and external magnetic fields takes place in God helmet experimens and is partially responsible for the effects. This is clear from the fact that quite spesific magnetic stimulation is used (signals derived from EEG during the second stage). In TGD framework one should be able to interpret this.

1. In TGD Universe endogenous magnetic fields could form a fractal hierarchy: flux quanta inside flux quanta. Several critical values of magnetic field expected. Flux quanta could be flux tubes or sheets (DNA strands could be traversed by flux sheets and one could have hierarchy of genomes making possible collective gene expression at various levels).

2. There is a hierarchy of Planck constants so that one can assign to the cell membrane potential a Josephson frequency proportional to 1/hbar and to cyclotron frequencies photon energy proportional to hbar.

3. The code for the communications from biological body to various levels of the magnetic body relies on the modulation of the Josephson frequencies assignable to the cell membrane. Assuming that the value of Planck constant is integer multiple of its standard value these frequencies span an enormous range. In the case of EEG the Planck constant is of order 10¹³ in order to for photons with the energy of visible photon to have frequency about 10 Hz. Since Josephson frequency is proportional to the membrane potential, the modulations of the membrane potential induce modulations of Josephson frequency so that the signal sent to the magnetic body is modulated and this frequency modulation must define the "code of consciousness".

4. The frequencies involved with these communications are sums of harmonics of Josephson frequency and cyclotron frequency and also cyclotron frequencies can be modulated by modulating magnetic fields. The simplest possibility is that the external magnetic field induces modulation of the magnetic field. This modulation is small since the field strength is of order .01 Gauss and by a factor 1/20 smaller than the endogenous magnetic field B_end=.2 Gauss suggested by the effects of ELF em fields on vertebrate brain. Of course also other field values are expected to be present.

2. The basic philosophy behind the TGD based model

The basic philosophy behind the TGD based explanation of God helmet experiences differs in many respects from that behind the model of Persinger and Murphys. Therefore it is good to describe this philosophy first.

1. In the normal social consciousness based strongly on verbal communications the left brain self dominates and social interactions actually split the left brain self from right brain self so that right brain self remains a silent companion unable to express itself except throught intuitions. This raises some questions.

   Could just the need to communicate the experience verbally automatically project "me" to left brain me and cut if from "right brain self" so that only the memories of left brain self are communicated. What would happen if the subject person would communicate with external world by singing? Often persons who have lost their ability to speak and comprehend spoken language can communicate by singing. Would the the projection occur to left brain self and could the memories be different?

2. Persinger and Murphy seem to assume that right brain is God from the perspective of the left brain. Magnetic body is responsible for the third person aspect of consciousness and also for the ability to see the dying biological body from the bird's eye perspective during OBEs accompanying also NDEs, which accordingy to Murphy could be quite real. There is indeed evidence that a subject person unable to move from bed has been able to see objects which she should not have been able to see. If magnetic body is real it could also receive extra-sensory information.

   Could the magnetic body of right brain or of the entire brain be in some sense the God from the view point of the brain? The TGD based interpretation for the vision of Jaynes about bicameral consiousness as a predecessor of modern consciousness would conform with this. The God of old testament would be the personal magnetic body which would not have yet become a highly integrated part of self and could be experienced as an outsider. Jaynes also proposes that the consciousness of schizophrenic is much like bicameral consciousness.

3. It is not necessary to assume that the right amygdala is specialized to produce negatively colored motions and left amygdala positive emotions. Same applies also to the proposed roles of right and left hippocampi. In fact, according to Wikipedia article about lateralization of brain function depression is linked with hyperactive right hemisphere and selective involvement in "processing negative emotions, pessimistic thoughts and unconstructive thinking styles". A relatively hypoactive left hemisphere is said to be "specifically involved in processing pleasurable experiences" and "relatively more involved in decision-making processes". One can interpret this in many manners. The hyper-activity of right hemisphere could tend to cut its connection with its magnetic body and cause a depressive mood.

   Intense nerve pulse activity could cause this if nerve pulse generation breaks coherence of the EEG oscillation due to the oscillating membrane potentials inducing generation of signals to the magnetic body. The reduced neural activity of left hemisphere would mean a better connection to the magnetic flux tube and positive emotional coloring.

4. Note that this picture conforms with spiritual practices which teach that the manner to achieve piece of mind and bliss is to stop thinking, which indeed means reduce neural activity and more stable connection to the magnetic body. If one takes this conceptualization seriously, one could conclude that the modern hectic society tends to split the connections to the personal magnetic bodies. Since they represent higher levels in the hierarchy of conscious entities, this would lead to a loss of spirituality and also social regression if magnetic bodies are responsible for social structures and cultural evolution.

5. For about 26 years ago I had also a long-lasting "enlightment" experience - actually two of them. The general structure of these experiences fits with thde proposed general format. The first experience began with the experience of getting in contact with what I spontaneously called Great Mind. I started to make all kinds of questions which I imagined of writing to a monitor that I saw in front of me. Later I realized that the writing was not necessary. I also understood that our communication was severaly estricted by the fact that my language did not yet have words for to express the messages of this Great Mind so that the messages contained a lot of "blancos".

   I had an experience of profound understanding but did not know what I understood. I also felt that everything around me has extremely deep meaning. One of the first questions I did was "How long I will live?". From the humorous reply expressed as an endless rapid running of a counter containing a long sequence of digits I understood that there is no death. I also asked "Am I alone in this Universe?". The reply was enigmatic "You are a God!".

   Later it somehow became clear that this God like entity was actually in some sense me. A possible interpretation could be that a new higher layer to the hierarchy of layers of my personal magnetic body had emerged as this God like creature became a part of my personal magnetic body. Much later I realized that this paradoxical realization was the analog for Brahman=Atman identity of Eastern philosophies.

Consider now the more technical assumptions.

1. One can assume that right and left brain selves can entangle to form a single self and that magnetic flux tubes between brain hemispheres closely associated with the connecting nerve bundles serve as a correlate for this entanglement. In TGD framework the notion of negentropic entanglement makes sense and means entanglement entropy defined number theoretically is negative rather than being positive as usually. Negentropy Maximization Principle for quantum jumps guarantees the stability of negentropic entanglement. Entanglement probabilities must be rational or at most algebraic numbers or negentropic entanglement.

2. The basic mechanism would be reconnection of magnetic flux tubes. Typically two parallel connecting flux tubes would touch each other and reconnect to form U-shaped flux tubes representing flux tubes beginning and returning to left (right magnetic body). What is the role of the external magnetic field in this process? Could the closed flux tubes of the external magnetic fields reconnect with those connecting the right hemisphere to left hemisphere. Suppose that magnetic flux tubes indeed serve as geometric correlates for attention interpreted as negentropic entanglement.

   Could one say that the magnet creating chirp signal catches the attention of the right brain magnetic body directed to the right hemisphere? Could the splitting of the connection to the magnetic body create the negative emotions. It is enough that the magnet- magnetic body entanglement becomes entropic to destroy the entanglement in state function reduction if one believes in NMP and perhaps this occurs.

3. One an ask whether this kind of mechanism could explain also the effects of strong (or order 1 Tesla) fields on brain in transcranial magnetic stimulation or is the standard explanation in terms of eddy currents inducing nerve pulse patterns enough to explain the effects.

3. The model for God helmet experiences

Consider now a the general TGD inspired model explaining God helmet experiences.

1. The magnetic chirp during the first stage tends to decouple the right hemisphere from its magnetic body and possibly also from the magnetic body of left brain. This alone creates the negatively colored emotions- kind of feeling of being abandoned by God. This could be also general mechanism of depression and the manner to cure depression would be re-establishment of this connection.

   At quantum level the cutting of the magnetic connection would mean the desctruction of entanglement between parts of the two brain hemispheres or between part of right hemisphere and its magnetic body temporarily. This would lead to the splitting of self to right and left brain sub-selves or the loss of the right hemisphere magnetic body entanglement.

2. If one is ready to take seriously the notion of number theoretic entropy, the minimum condition would be that the magnetic chirp causes the entanglement probabilities become non-rational or even non-algebraic numbers so that the number theoretic entropy does not make sense. Ordinary entanglement entropy is always non-negative and state function reduction reduces the entanglement and self splits to two.

3. During the second stage the simultaneous activation of both hemispheres by artificial neuronal signals derived from the EEG of amygdala and hippocampus would fuse both hemispheres to single coherent unit so that the mental images of the right hemisphere would contribute to the conscious experience. The coherence could increase from what it is during ordinary wake-up consciousness dominated by verbal communications. "Being nearer to God" alone could give rise to highly positived colored emotions and to a direct experience of seeing the God/light being/magnetic body and explain the experience of meaningfulness and deep understanding without being able to express what one understands. This inability could be simply to the lack of appropriate language. There is no need to assign this experience to the right hippocampus.

For background and pdf version of the text see the new chapter TGD Based View about Classical Fields in Relation to Consciousness Theory and Quantum Biology of "TGD and EEG".

Persinger's work with God helmet

Anyone - atheist or believer - wanting to learn about Persinger's work and the basic insights of neuro-theology should listen the extremely inspiring talk God and the Brain - The Persinger 'God Helmet', The Brain, and visions of God by Todd Murphy. Persinger's work (for refereces to the articles by Persinger and collaborators see the Wikipedia article about God helmet) suggests that the temporal pattern of the modulation of magnetic field strength (FM would be in question for slow variations) is important. We do not however know the "code". Also the strength of the magnetic field can be important. Note that the effects of very weak ELF em fields on vertebrate brain take place in amplitude windows.

The modulation of magnetic field would probably induce FM of cyclotron frequencies. The model for hearing suggests this kind of modulation as a manner to represents the frequencies of the sound wave. Also phase information is very important: time reversed speech sounds very different as normal speech but has the same power spectrum. Modulations would be slow in the time scales defined by the audible frequency range. .1 seconds would represent lower limit for the variation rate of modulation. Audible frequencies above 20 Hz.

1. God helmet

God helmet or Koren helmet named after its inventor is the device used by Persinger and collaborators to study the effects of magnetic field on consciousness. Transcranial magnetic stimulation is not in question: TCMS uses fields of order Tesla whereas Persinger uses magnetic fields with strength of order .01 Gauss. This is 2 per cent of the nominal value of Earth's magnetic field. There is a coil above both temporal lobes and the active coil rotates counterclockwise.

1. At the first stage the coil above right temporal lobe rotates counterclockwise. A chirp sequence is used. Chirp means use of an oscillating magnetic field with maximum amplitude about 1 microTesla with oscillation frequency going gradually down. The interpretation is that right-brain self is activated and dominates conscious experiences. The experiences have negative emotional coloring and sometimes the subject person has even fearful experiences.

2. At second stage both coils rotate counterclockwise. The signal is derived from amygdala and hippocampal EEG. Faraday cage is used to eliminate external electromagnetic perturbations and also sensory deprivation is necessary (subject person is blind-folded and in an acoustic chamber). Earth's magnetic field is present, which might have relevance and is indeed used in experiments related to the hypothesis that the variations in Earth's magnetic field affect consciousness.

   A burst of left brain activity is reported to take place during second stage. Also visitor experience is reported to occur during this period. This can mean meeting of God/light being, of angels, of deceased or of group of "beings", or just sense the presence of some conscious entity. A strong sense of meaning can accompany the experience. 80 per cent of subjec persons experience at least the sense of presence.

2. Persinger's experiments and cyclotron frequencies

A more quantitative description of the God helmet experiment assuming that cyclotron frequencies are essential goes as follows.

1. The field strength used by Persinger is of the order .01 Gauss and very weak and different from B_end=.2 Gauss which is .4B_E with B_E=.5 Gauss the nominal value of the Earth's magnetic field. Cyclotron frequencies are by a factor of order 1/20 smaller than for B_end. This gives .75 Hz for Ca⁺⁺.

   From this it is clear that the changes of cyclotron frequencies would be small in static external field in Persinger's experiments and could be treated as a small perturbation. External magnetic field could superpose with B_end=.2 Gauss and affect cyclotron states and induce transitions between them. This would induce effects on EEG visible as frequency modulations. It seems that the period for the oscillation of B must be longer than cyclotron period for this picture to make sense.

2. One expects a fractal hierarchy of field strengths for endogenous magnetic fields and B≈ .01 Gauss could correspond to higher levels of consciousness so that cyclotron frequencies for these fields would be important. In this case the external magnetic field would not be a small perturbation. The cyclotron frequencies of DNA strand carrying charge density of 2 elementary charges per nucleotide from the phosphates depend only weakly on the length of DNA strand and are about 1 Hz in B_end. Could the cyclotron radiation from cyclotron states associated with the external magnetic field induce interaction with DNA cyclotron states in field B_end=.2 Gauss?

3. Consider next the time scales. The stimulation of right brain lasts during the first stage last about half an hour. There are however many lacking bits of data.
   1. In what range are the values of the rotation frequency for the magnetic field? ELf frequencies are used. If EEG frequencies are in question the rotation should be slower what the lowest EEG frequency involved and below 1 turn per second.

   2. The rotated magnetic field is time dependent. Chirp sequences are used to stimulate temporal lobe. What is the duration of single chirp and the frequency range covered during chirp? A good guess is that the frequency range is that of EEG. The natural expectation is that the duration of chirp is much longer than the periods in the frequency range considered. This would mean that one scan entire frequency range and that it makes sense to say that the changes of frequency during chirp is slow as compared to the instantaneous frequency.

   3. EEG signals from left amygdala or hippocampus are used to stimulate both temporal lobes during the second stage. This means that their natural frequency scale should be in the range 1-100 Hz. These time scales would be shorter than the time scale of order 1 second assignal to Ca⁺⁺. This suggests that small aplitude modulation of the cyclotron frequencies in EEG range is in question. The signals sent to the magnetic body would be determined by this modulation and at least in the second stage this modification would carry information.

3. Persinger's explanation

Persinger's own explanation for the findings relies on what might be called neurotheology.

1. The basic claim of Persinger is that the experiences in question are produced by brain so that meeting of God would not be real. Todd Murphy emphasizesthat it is actually impossible to conclude anything about the existence or non-existence of God on basis of these experiments. He however claims that evolution would have developed for brain the ability to produce visions of God which often accompany near death experiences and make it easier to accept the unavoidablity of the biological death. The reader can decide whether these two statements are consistent or not.

2. The general idea is that both right and left amygdala, which are the most sensitive parts of the brain because the membrane potential is nearest to the threshold for nerve pulse generation. The right hippocampus is assumed to be responsible for non-verbal, "silent" thinking and left brain hemisphere to verbal thinking. This general picture is used by Todd Murphy to understand the conscious experiences accompanying death process about which near death experiences give a information. The experiences generated by God helmet during the first stage would be akin to the fearful emotions associated with near death experiences (NDE). The experiences during the second stage bring in mind the spiritual experiences accompanying death process and having strong positive emotional coloring.

3. Persinger and Murphy propose that left amygdala is specialized to produce positive emotions (happiness, bliss, and even experience of encountering God or almost synonymously light being). Right amygdala would be specialized to produce negative emotions (such as fear and horror) and one can assign with it also depressive mood. This is not a generally accepted theory. If one accepts it, the natural question is whether right amygdala could serve as a kind of entropic dump pit and left amygdala as as a highly negentropic structure. The empirical data does not force the poor right amygdala to be a whole-daily sufferer.

Consider now the explanation of the experiences induced by God helmet. The lecture by Todd Murphy helps considerably in attempts to understand the gist of the explanation and also helsp to see its problematic aspects.

1. The selves of right and left brain fuse in some sense to form single self normally. The nerve bundles connecting the brain hemispheres allowing communications between them are essential for this integration. Right brain self is assumed to be sub-ordinate for left brain self. Magnetic pulses during the first period decompose self to two pieces: one could call them right and left self.

2. During the first stage the mental images from the right brain self become dominating and fearful experiences are due to the fact that right brain amygdala, which is specialized to produce negative emotions, is hyper-active. This phase is believed to break the connection between left and right brain hemispheres. The anecdotal evidence by Todd Murphy suggests a correlation between non-verbal mood of consciousness and negative emotions. One must be however very cautious because extreme fear and horror alone might make impossible not only verbal communication but any coherent action.

3. During the second stage both left and right brain are stimulated and expected contribute to the mental images of self when the connection between the hemispheres is intact. If I have understood correctly, the proposal is that the splitting of self to separate selves induced during the first phase is present almost permanently during the second phase and that left brain self dominates.

4. The temporary "intrusion" of the right hemisphere self to the consciousness of left brain self would give rise to visitor experience. Intrusions would mean occasional re-establishment of the connection between hemispheres. One can question the assumption that God experience and the sensed presence represent instances of the same basic experience due to the intrusion. One could also argue that sensed presence is a signal for the breakdown of the connection and is created by the realization that there is also another self using the same biological body.

5. The model of Todd Murphy for near death experiences would be that right amygdala can give rise to extremely frightening experiences but that the flow of the information to left amygdala transforms this experience to its emotional opposite. The right hippocampus suggested to be responsible for "silent" thinking would be responsible to the experiences of deep meaningfulness and of understanding. To my opinion this picture is too complex and involves too many ad hoc assumptions.

Somehow my personal feeling is that this model is not quite correct. For instance, I do not understand the meaning "intrusion"? This could be of course be just my misunderstanding. Also the hypothesis about the specialization of left and right amygdala looks strange. In the next posting I will describe the TGD inspired interpretation of Persinger's findings.

For background and pdf version of the text see the new chapter TGD Based View about Classical Fields in Relation to Consciousness Theory and Quantum Biology of "TGD and EEG".

TGD based view about classical fields, consciousness theory, and quantum biology

In TGD Universe gauge fields are replaced with topological field quanta. Examples are topological light rays, magnetic/electric flux tubes and sheets, and flux quanta carrying both magnetic and electric fields. Flux quanta form a fractal hierarchy in the sense that there are flux quanta inside flux quanta. It is natural to assume quantization of Kähler magnetic flux. Braiding and reconnection are the basic topological operations for flux quanta.

The basic question is how the basic notions assigned with the classical gauge and gravitational fields understood in standard sense generalize in TGD framework.

1. Superposition and interference of the classical fields is very natural in Maxwell electrodynamics and certainly experimentally verified phenomena. Also the notion of hologram relies crucially on the notion of interference. How can one describe the effects explained in terms of superposition of fields in a situation in which the theory is extremely non-linear and all classical gauge fields are expressible in terms of CP₂ coordinates and their gradients? It is also rather clear that the preferred extremals for Kähler action decompose to space-time regions representing space-time correlates for quanta. The superposition of classical fields in Maxwellian sense is impossible.

   How can one cope with this situation? The answer is based on simple observation: only the effects of the classical fields superpose. There is no need for the fields to superpose. Together with the notion of many-sheeted space-time this leads to elegant description of interference effects without any need to assume that linearization is a good approximation.

2. Topological quantization brings in also braiding and reconnection of magnetic flux tubes as basic operations for classical fields. These operations for flux tubes have also Maxwellian counterparts at the level of field lines. Braiding and reconnection are in a central role in TGD Universe and especially so in in TGD inspired theory of consciousness and quantum biology. The challenge is to build a coherent overall phenomenological view about the role of topologically quantized classical fields in biology and neuroscience. For instance, one can ask what is the precise formulation for the notion of conscious hologram and whether magnetic flux tubes could serve as correlates of entanglement (or at least negentropic entanglement suggested by the number theoretic vision and identified as a basic signature of living matter).

3. Topological quantization and the notion of magnetic body are especially important in TGD inspired model of EEG. The attempt to understand the findings of Persinger from the study of what is known as God helmet leads to a considerable progress in the understanding the possible role of topologically quantized classical fields in biology and neuro-science.

I do not bother to type more and instead give a link to the article TGD based view about classical fields, consciousness theory, and quantum biology.