Do galactic rotational spectra show a violation of Strong Equivalence Principle?

This comment was inspired by a popular article (see this) about a study of the effect of external gravitational fields to the rotation curves of galaxies. The title of the research article by Chae et al is "Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies". The claim is that the Strong Equivalence Principle (SEP) is slightly violated: the rotational velocities are slightly reduced in the region region of orbital radii, where they are predicted to be constant in CDM models.

SEP predicts that in the cold dark matter (CDM) scenario that the internal dynamics of the galaxy should not depend appreciably on even strong external gravitational fields so that rotational velocities should not change. The reason is that in CDM dark matter is concentrated around the galaxy: the only effects would be tidal forces plus the Newtonian acceleration of the galaxy which does not depend on its mass. The observations suggest that this is actually not the case, and this is seen as a support for MOND and in conflict with CDM and also with GRT if SEP is assumed.

In the TGD framework the flat velocity spectrum of distant stars around the galaxy is due to a long cosmic string carrying dark matter and energy containing tangles in which strings have thickened and partially decayed to ordinary matter. This also explains why galaxies form linear structures. These are not local objects so that SEP does not apply to them. Hence there need not be any actual violation of SEP. The long string as a non-local object would react to the external forces which its own mass and rotating stars would experience the net gravitational force caused by the environment as entities in empty space since there would be no cold dark matter present now.

There would be a strong dependence of the effects on the direction of external gravitational fields when they are caused by a single object rather than being an average effect of the environment. If the external gravitational field is in the direction of the string, there would be an acceleration to this direction since the cosmic string does not cause gravitational field in this direction. This would sharply distinguish between halo models and TGD predicting the possibility of free flows of matter along long strings. If the external gravitational field is transversal there would be smaller perturbation reducing the transverse radial gravitational force of the cosmic string and attracting it.

In the recent study, the effect of gravitational fields caused by the environment of the galaxy was studied. These fields represent the sum of environmental gravitational fields. The first estimate is that the gravitational attraction of the environment boils down to a radial central force transversal to the cosmic string weakening the gravitational force caused by the long string. This would give rise to the reduction of the effective value of string tension T and indeed reduce the rotational velocity (v² ∝ TG). What about CDM model? Due to the presence of dark matter halo, the effect of external fields would be a considerably weaker tidal effect in the CDM model at the distances considered (near the boundary of the visible galaxy).

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Are mistletoes quantum energy thieves?

There was a thought provoking article in Quanta Magazine with the title "The mystery of mistletoe's missing genes. Various research groups have observed that the mitochondria of mistletoe miss large parts of their respiratory complex. There is article "Miniaturized mitogenome of the parasitic plant Viscum scurruloideum is extremely divergent and dynamic and has lost all NAD genes" by Skippington et al, article "Absence of Complex I Implicates Rearrangement of the Respiratory Chain in European Mistletoe" by Senkler et al, and article "Absence of Complex I Is Associated with Diminished Respiratory Chain Function in European Mistletoe" by Maclean et al.

Mitochondria serve as energy plants of the cell. The mitochondria of plants known as mistletoes are very small and many of the genes coding for the needed proteins are missing so that it seems that they cannot produce ATP appreciably. Somehow mistletoes however manage to get their metabolic energy. Mistletoes are parasites: could they be also metabolic energy parasites?

The respiratory complex I, which is the first one in the chain in which ATP is produced, seems to be missing in the mitochondria of mistletoe. This large protein has two catalytic functions. It catalyzes the transfer of protons against a field gradient through the mitochondrial membrane and the transfer of electrons from NADH to coenzyme Q10. Protons fall back and give their potential energy to the rotating shaft of APTPase resembling a turbine of a power plant. ATPase gives the energy to phosphorylize ADP to ATP. ATP transfers it to the end user as quantized metabolic currence, one might say. The production of ATP requires energy provided by the electrons transferred along the respiratory chain to acceptors, whose electronegativity (abilities to receive electrons) increases along the chain. As the electrons propagate along the chain, they lose energy originating from metabolites.

The idea that mistletoes could survive with a very little metabolic energy does not look attractive. One proposal mentioned in the article is that they could produce ATP by a much less effective method than usually - by a glycolysis burning sugar outside the mitochondria. This requires sugar: could mistletoes steal it from the host plant? Or could mistletoes get their ATP somehow from the host somehow receive the energy needed to transform the ADP of mistletoe to ATP from the host. Or could they get their energy as radiation by some mechanism difficult to imagine in the standard physics framework.

TGD indeed inspires the question whether mistletoes be more advanced energy criminals. Could they steal the metabolic energy by a mechanism that I have proposed to be a general mechanism of metabolism and called it quantum credit card or remote metabolism. They would effectively send negative energy to some system able to receive it. For this instance, in the transformation of ADP to ATP to get positive energy as a recoil. The energies involved would be around .5 eV which corresponds to metabolic energy quantum and IR energy. The model involves two ingredients. Zero energy ontology (ZEO) (see this) and the hierarchy of dark matter as _eff=nh₀ phases of ordinary matter (see this), which is a prediction of the number theoretic vision about TGD.

1. In zero energy ontology (ZEO) quantum credit card mechanism would be possible by making a "big" state function reduction (BSFRs) changing the arrow of time for some part of the magnetic body (MB). This would mean dissipation with a reversed arrow of time. For a standard observer this looks like extracting energy from the environment. For instance, could the ATP of the host receive the negative energy signal sent by mistletoe ADP and transform to ADP. This would occur also normally but now in a much longer length scale. Could mistletoe send negative energy signals to the mitochondria of the host or even to the own leaves of mistletoe performing photosynthesis.

   ZEO solves the basic paradox of quantum measurement theory and has very profound implications for the understanding of living systems and self-organization in general. Dissipation with reversed arrow of time looks like self-organization and self-organized quantum criticality very difficult to understand in the standard ontology because criticality is by definition something unstable becomes possible since critical system as a repeller with a reversed arrow of time looks like an attractor for the observer with the standard arrow of time.

2. Dark matter hierarchy as phases of ordinary matter (also photons) identified as h_eff=nh₀ would make possible quantum coherence of dark photons in scale much longer than the wavelength of order 2 micrometers. Hence this process would be possible in scales considerably longer than cell length scales associated with the ordinary metabolism. The system needing energy would send a negative energy signal to ATP transforming it to ADP and get positive energy as a recoil. This could be like a ATP-ADP→ADP-ATP→... flip-flop transferring the energy of ATP over intercellular distances.

   If this picture is correct, something related to the ATP of the mistletoe should differ somehow from the ordinary ATP. The magnetic body (MB) of mistletoe MB might be this something. If it carries dark matter with a value of h_eff =nh₀ higher than in the case of ordinary APT, the negative dark photons would have longer coherence length and they could transform to ordinary photons received by the ATP of the host. Quite generally, TGD view suggests that the increase of h_eff serving as a kind of universal IQ is responsible for big evolutionary leaps. For instance, the emergence of language is known to involve only a few genes, and the increase of h_eff for their MBs could be responsible for the evolution of language (see this).

We have written together with Reza Rastmanesh an article about the use of this mechanism by shock proteins in ordinary biology. They could extract thermal energy from the environment to reduce the local temperature in the case of heat shock and heat basic biomolecules by acting as ovens in the case of cold shock. They could also serve as heat engines for molecular motors.

See the article Homeostasis as self-organized quantum criticality . For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

New evidence for zero energy ontology

There was an interesting popular article in Digital Journal with title "Scientists show future events decide what happens in the past". The research article by Truscott et al published in Nature Physics has the title "Wheeler's delayed-choice gedanken experiment with a single atom".

There were two grates - I would speak of gratings - A and B following A so that particles went through A first. B was removed and put back randomly. If both gratings were in place, the incoming He atoms chose one path through A and behaved like a particle. When only the grate A was in place, wave behaviour was observed.

What looks paradoxical is that the addition of B forced particle behavior although the incoming He atom was already gone through A and selected wave behavior. The geometric past of the particle was changed from wavelike to particle-like! As if state function reduction would change also the geometric past of particle and quantum states were superpositions of classical time evolutions rather than time=constant snapshots as in the ordinary ontology!

This is what zero energy ontology (ZEO) indeed postulates so that the findings can be seen as an additional experimental support for ZEO. In ZEO quantum states are superpositions of time evolutions and "big" (ordinary) state function reduction (BSFR) selects new superposition of classical histories with opposite arrow of time: the roles of cause and effect for classical time evolution are apparently changed. ZEO solves the basic paradox of the quantum measurement theory. Also the weird looking findings of Minev et al can be explained in terms of the time reversal occurring in BSFR(see this).

Effect precedes cause: here cone for instance explanation for the findings of Libet challenging free will: the neural activity preceding act of free will in geometric time will is caused by free will initiating a superposition of time reversed classical time evolutions in the geometric future of the brain! The geometric past is changed.

To avoid paradox, one must keep in mind that "small" state function reductions (SSFRs) give to the experienced time correlating but not identifiable with the geometric time. In the experiment, the BSFR corresponds to a removal or addition of a grating and changes what happened before the addition/removal of grate - "before" in the sense of geometric time. Removal/addition is in the sense of subjective time of the experimenter.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

About the implications of the revised form of M8-H duality

A critical re-examination of M⁸-H duality hypothesis led to what might be called a brealthrough in the understanding of M⁸-H duality. Several intuitive beliefs turned out to be wrong at the level of details as precise calculation became possible. The improved understanding led to a construction of scattering amplitudes at M⁸ level as counterpart for momentum space representations of scattering amplitudes wheteras the earlier breakthrough was related to their construction at the level of H=M⁴× CP₂ (see this).

Since the article grew rather long, I decided to divide it into two parts. Below are the absracts of these articles.

A critical re-examination of M⁸-H duality hypothesis: part I

This article is the first part of an article representing a critical re-examination of M⁸-H duality, which is one of the cornerstones of Topological Geometrodynamics (TGD). The original version of M⁸-H duality assumed that space-time surfaces in M⁸ can be identified as associative or co-associative surfaces. If the surface has associative tangent or normal space and contains a complex or co-complex surface, it can be mapped to a 4-surface in H=M⁴× CP₂.

Later emerged the idea that octonionic analyticity realized in terms of real polynomials P algebraically continued to polynomials of complexified octonion could fulfill the dream. The vanishing of the real part Re_Q(P) (imaginary part Im_Q(P)) in the quaternionic sense would give rise to an associative (co-associative) space-time surface.

The realization of the general coordinate invariance motivated the notion of strong form of holography (SH) in H allowing realization of a weaker form of M⁸-H duality by assuming that associativity/co-associativity conditions are needed only at 2-D string world sheet and partonic 2-surfaces and possibly also at their light-like 3-orbits.

The outcome of the re-examination was a positive surprise. Although no interesting associative space-time surfaces are possible, every distribution of normal associative planes (co-associativity) is integrable. Another positive surprise was that Minkowski signature is the only possible option. Equivalently, the image of M⁴ as real co-associative sub-space of O_c (complex valued octonion norm squared is real valued for them) by an element of local G_2,c or its subgroup SU(3,c) gives a real co-associative space-time surface. The conjecture is that the polynomials P determine these surfaces as roots of Re_Q(P). These surfaces also possess co-complex 2-D sub-manifolds allowing the mapping to H to H by M⁸-H duality as a whole. SH would not be needed and would be replaced with number theoretic holography determining space-time surface from its roots and selection of real subspace of O_c characterizing the state of motion of a particle. The equations for Re_Q(P)=0 reduce to simultaneous roots of ordinary real polynomials defined by the odd and even parts of P having interpretation as complex values of mass squared mapped to light-cone proper time constant surfaces in H.

Octonionic Dirac equation as analog of momentum space variant of ordinary Dirac equation forces the interpretation of M⁸ as an analog of momentum space and Uncertainty Principle forces to modify the map M⁴⊂ M⁸→ M⁴⊂ H from identification to inversion. Contrary to the earlier expectations the space-time surface in M⁸ would be analogous to Fermi ball and mass squared sections would correspond to Fermi spheres. This leads to the idea that the formulation of scattering amplitudes at M⁸ levels provides the counterpart of momentum space description of scattering whereas the formulation at the level of H provides the counterpart of space-time description.

See the article A critical re-examination of M⁸-H duality hypothesis: part I.

A critical re-examination of M⁸-H duality hypothesis: part II

This article is the second part of an article representing a critical re-examination of M⁸-H duality. This re-examination has yielded several surprises. The first surprise was that space-time surfaces in M⁸ must and can be co-associative so that they can be constructed also as as images of a map defined by local G_2,c (octonionic automorphisms) transformation applied to co-associative sub-space M⁴ of complexified octonions O_c in which the complexified octonion norm squared reduces to the real M⁴ norm squared. An alternative manner to construct them would be as roots for the real part Re_Q(P) of an octonionic algebraic continuation of a real polynomial P.

The outcome was an explicit solution expressing space-time surfaces in terms of ordinary roots of the real polynomial defining the octonionic polynomials. The equations for Re_Q(P)=0 reduce to simultaneous roots of the real polynomials defined by the odd and even parts of P having interpretation as complex values of mass squared mapped to light-cone proper time constant surfaces in H.

The second surprise was that space-time surface in M⁸ can be mapped to H as a whole so that the strong form of holography (SH) is not needed at the level of H being replaced with much stronger number theoretic holography at the level of M⁸.

The third surprise was that octonionic Dirac equation as an analog of momentum space variant of ordinary Dirac equation forces the interpretation of M⁸ as an analog of momentum space and Uncertainty Principle forces to modify the map M⁴⊂ M⁸→ M⁴⊂ H from identification to inversion. One obtains both massless quarks and massive quarks corresponding to two different number-theoretically characterized phases.

This picture combined with zero energy ontology (ZEO) leads also to a view about the construction of the scattering amplitudes at the level of M⁸ as analog of momentum space description of scattering amplitudes in quantum field theories. Local G_2,c element has properties suggesting a Yangian symmetry assignable to string world sheets and possibly also partonic 2-surfaces. The representation of Yangian algebra using quark oscillator operators would allow to construct zero energy states at representing the scattering amplitudes. The physically allowed momenta would naturally correspond to algebraic integers in the extension of rationals defined by P. The co-associative space-time surfaces (unlike generic ones) allow infinite-cognitive representations making possible the realization of momentum conservation and on-mass-shell conditions.

The new view about M⁸-H duality differs from the earlier one rather dramatically so that a summary of the differences is added to the end of paper.

See the article A critical re-examination of M⁸-H duality hypothesis: part II.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Breakthrough in understanding of M8-H duality

M⁸-H duality plays a crucial role in quantum TGD and this motivated a critical study of the basic assumptions involved leading to a surprisingly precise view realizing the most optimistic original vision. The notion of associativity as a number theoretical dynamical principle was however replaced with co-associativity.

1. Re_Q(o)=0 and Im_Q(P)=0 allow M⁴ and its complement as associative/co-associative subspaces of O_c. The roots P=0 for the complexified octonionic polynomials satisfy two conditions X=0 and Y=0. They are 6-D brane-like entities X⁶_c having real projection X⁶_r ("real" means that the number theoretic complex valued octonion norm squared is real valued).

   Posing the condition Im_Q(P)=0 gives a complex surface X²_c at which the number theoretic norm squared defines complex norm squared, which is not physically acceptable. The real projection X²_r with real norm is 2-D.

   The condition Re_Q(P)=0 gives complex surface X³_c which has 3-D real projection X³_r, which should be completed to a real surface X⁴_r by holography- perhaps by giving up the condition Y=0 and taking real projection X⁴_r of the resulting 4-D surface X⁴_c.

2. The cold shower came as I learned that 4-D associative sub-manifolds of quaternion spaces are geodesic manifolds and thus trivial. Co-associativity is however possible since any distribution of associative normal spaces integrates to a sub-manifold. Typically these sub-manifolds are minimal surfaces, which conforms with the physical intuitions. Therefore the surface X⁴_r given by holography should be co-associative. By the same argument space-time surface contains string world sheets and partonic 2-surfaces as co-complex surfaces.
3. The key observation is that G₂ as the automorphism group of octonions respects the co-associativity of the 4-D real sub-basis of octonions. Therefore a local G₂ (or even G_2,c ) gauge transformation applied to a 4-D co-associative sub-space O_c gives a co-associative four-surface as a real projection if the boundary conditions stating that X⁴_r has as its ends surfaces X³_r at X⁶_r.

   An open question is whether this approach is equivalent to giving up Y=0 conditions so that octonion analyticity would correspond to G₂ gauge transformation: this would realize the original idea about octonion analyticity. If this surface contains a co-complex 2-surface as a string world sheet, the conditions making possible to map X⁴_r to H by M⁸-H duality are satisfied and there is no need for a separate holography in H. There is no objection against this option and it would replaces SH with much strong number theoretic holography fixing space-time region from the roots of a real polynomial. One could say that classical TGD is an exactly solvable theory.

4. Remarkably, the group SU(3)_c⊂ G_2,c has interpretation as a complexified color group and the map defining space-time surface defines a trivial gauge field in SU(3)_c wheras the connection in SU(3) is non-trivial. Color confinement could mean geometrically that SU(3)_c reduces to SU(3) at large distances: could it be simpler!

   This picture conforms with the H-picture in which gluon gauge potentials are identified as color gauge potentials. Note that at QFT limit the gauge potentials are replaced by their sums over parallel space-time sheets to give gauge fields as the space-time sheets are approximated with a single region of Minkowski space.

5. Minkowski signature turns out to be the only possible option for X⁴_r. Also the phenomenological picture based on co-assiative space-time sheets, light-like 3-surfaces, string world sheets and partonic 2-surfaces, and wormhole contacts carrying monopole flux emerges.

See the chapter Breakthrough in understanding of M⁸-H duality or the article with the same title.

Ageing as approach of magnetic body and biological body to thermal equilibrium

There was an interesting a HREF="https://scitechdaily.com/researchers-solve-anti-aging-mystery-identify-gene-responsible-for-cellular-aging">article in Scitechdaily about ageing. The claim of the title of the article was that the gene responsible for ageing has been found.

The title of the article is somewhat misleading. David Sinclair emphasizes in this book Life Span that there is no gene for ageing. Rather, ageing can be understood as an outcome of the second law leading to molecular chaos at the level of DNA related molecules. He also emphasizes that epigenesis correspond to informtion processing in continuous degrees of freedom related to DNA geometry. In TGD these degrees of freedom would be associated with the magnetic body (MB) carrying dark matter as h_eff=nh₀ phases of ordinary matter and responsible for control and induction of the coherence of the ordinary biomatter from its own long scale quantum coherence.

The gene expression changes since the epigenetic control mechanisms involving for instance methylation and acetylation cease to function properly. The number of non-expressed genes increases. A chaotic behavior in the conformational degrees of freedom of DNA paired with dark DNA at its MB.

One can of course argue that there could exist an ageing gene. If cells would not age it would not take a long time for metabolic resources to deplete. However, the second law can generously take care of ageing.

Living systems are however able to fight against ageing. This is a mystery from the point of view of standard physics. One could argue that metabolic energy feed is enough but living systems are also critical and even quantum critical systems able to remain so: this is like a ball getting again and again at the top of the needle. How is this possible?

Here the zero energy ontology, which is behind TGD based quantum theory comes at rescue: "big" (ordinary) state function (BSFR) for subsystems changes the arrow of time and dissipation looks like self-organization and self-organized quantum criticality becomes possible. Generalized thermodynamics also allows metabolism as an extraction of even thermal energy from surroundings. Stress proteins could do this and be near physiological temperature and also act as heaters of DNA and proteins in cold shock and as heat engines driving molecular motors. Time reversal would happen also in the de-differentiation to stem cells.

Ageing would be basically heat death in this framework. The MBs of information molecules like DNA controlling them must be at much lower temperature than the physiological temperature otherwise they would not be information molecules. Physiological temperature would be near the maximal temperature - Hagedorn temperature of the string-like flux tubes of MB. The MBs however approach thermal equilibrium with the environment. Eventually heat death results and leads to BSFR (death followed life in reversed time direction) at the level of the entire organism.

The shortening of telomeres is also related to ageing. In TGD framework, the sticky ends associated with them would correspond to the decrease of the electric field strength along DNA. The opposite charges would be associated with sticky ends at the ends of chromosome. This possible in TGD framework.

The strength of the longitudinal electric field would correlate with level of consciousness for DNA just as the electric field along body axis correlates with the level of consciousness for humans and animals - this was discovered by Becker long time ago. When the electric field weakens, the level of consciousness is reduced. When the direction of the field changes consciousness is lost.

Ageing would involve weakening of this electric field, the energy density of DNA (plus its magnetic body) would be reduced, and the DNA string would become "sloppy" and start to behave randomly. This is part of the ageing.

We wrote an article about this with Reza Rastmanesh: see this .

For background see the article The based view about dark matter at the level of molecular biology written together with Reza Rastmanesh.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Zero energy ontology, hierarchy of Planck constants, and Kaehler metric replacing unitary S-matrix: three pillars of new quantum theory

TGD predicts revolution in quantum theory based on three new principles.

1. ZEO solving the basic paradox of quantum measurement theory. Ordinary ("big") state function reduction involves time reversal forcing a generalization of thermodynamics and leading to a theory of quantum self-organization and self-organized quantum criticality (homeostasis in living matter).
2. Phases of ordinary matter labelled by effective Planck constant h_eff=nh₀ identified as dark matter and explaining the coherence of living matter in terms of dark matter at magnetic body serving as a master, and predicting quantum coherence in all scales at the level of magnetic bodies. h_eff/h₀=n has interpretation as the dimension for an extension of rationals and is a measure of algebraic complexity. Evolution corresponds to the increase of n.

   Extensions of rationals are associated with adelic physics providing description of sensory experience in terms of real physics and of cognition in terms of p-adic physics. Central notion is cognition representation providing unique discretization of X⁴ in terms of points with imbedding space coordinates in the extension of rationals considered M⁸-H duality realizes the hierarchy of rational extensions and assigns them to polynomials defining space-time regions at the level of M⁸ and mapped to minimal surfaces in H by M8-H duality.

3. The replacement of the unitary S-matrix with the Kähler metric of the Kähler space defined by WCW spinor fields satisfying the analog of unitarity and predicting positive definite transition probabilities defining matrix in Teichmueller space. Einstein's geometrization of classical physics extends to the level of state space, Equivalence Principle generalizes, and interactions are coded by the geometry of the state space rather than by an ad hoc unitary matrix. Kähler geometry for the spinor bundle of WCW has Riemann connection only for a maximal group of isometries identified as super-symplectic transformations (SS). This makes the theory unique and leads to explicit analogs of Feynman rules and to a proof that theory is free of divergences.

In this article the third principle, which is new, is formulated and some of its consequences are discussed. The detailed formulation allows understanding of how normal ordering divergences and other divergences cancel.

See the article Zero energy ontology, hierarchy of Planck constants, and Kähler metric replacing unitary S-matrix: three pillars of new quantum theory or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

The analog of unitary S-matrix from a curved K\"ahler geometry of the space of WCW spinor fields

The understanding of the unitarity of the S-matrix has remained a major challenge of TGD for 4 decades. It has become clear that some basic principle is missing. Assigning S-matrix to a unitary evolution works in non-relativistic theory but fails already in generic QFT. The solution of the problem turned out to be extremely simple. Einstein's great vision was to geometrize gravitation by reducing it to the curvature of space-time. Could the same recipe work for quantum theory? Could the replacement of the flat Kähler metric of Hilbert space with a non-flat one allow to identify unitary S-matrix as a geometric property of Hilbert space?

An amazingly simple argument demonstrates that one can construct scattering probabilities from the matrix elements of Kähler metric and assign to the Kähler metric a unitary S-matrix assuming that some additional conditions guaranteeing that the probabilities are real and non-negative are satisfied. If the probabilities correspond to the real part of the complex analogs of probabilities, it is enough to require that they are non-negative: complex analogs of probabilities would define the analog of Teichmueller matrix. Teichmueller space parameterizes the complex structures of space: could the allowed WCW K\"ahler metrics- or rather the associated complex probability matrices - correspond to complex structures for some space? By the strong from of holography, the most natural candidate would be Cartesian product of Teichmueller spaces of partonic 2 surfaces with punctures and string world sheets.

Under some additional conditions one can assign to Kähler metric a unitary S-matrix but this does not seem necessary. The experience with loop spaces suggests that for infinite-D Hilbert spaces the existence of non-flat Kähler metric requires a maximal group of isometries. Hence one expects that the counterpart of S-matrix is highly unique.

In the TGD framework the world of classical worlds (WCW) has Kähler geometry allowing spinor structure. WCW spinors correspond to Fock states for second quantized spinors at space-time surface and induced from second quantized spinors of the imbedding space. Scattering amplitudes would correspond to the Kähler metric for the Hilbert space bundle of WCW spinor fields realized in zero energy ontology and satisfying Teichmueller condition guaranteeing non-negative probabilities.

Equivalence Principle generalizes to level of WCW and its spinor bundle. In ZEO one can assign also to the Kähler space of zero energy states spinor structure and this suggests strongly an infinite hierarchy of second quantizations starting from space-time level, continuing at the level of WCW, and continuing further at the level of the space of zero energy states. This would give an interpretation for an old idea about infinite primes asan infinite hierarchy of second quantizations of an arithmetic QFT.

See the article The analog of unitary S-matrix from a curved K\"ahler geometry of the space of WCW spinor fields or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

26 second pulsation of Earth: analog for 8:th period doubling of EEG alpha rhythm?

The pulsations of Earth - kind of mini earthquakes - occurring with a period of 26 s represent a mysterious phenomenon. In TGD framework the interpretation would rely on the notions of magnetic body (MB) controlling ordinary matter, and dark matter as phases of ordinary matter labelled by h_eff=nh₀ and giving rise to quantum coherence at MBs in all scales. The strange findings about earthquakes suggest that they correspond to macroscopic quantum jumps ("big" state function reductions (BSRs)) changing the arrow of time. Also classically the earthquake corresponds to a discontinuous process in which tectonic plates slide with respect to each other so that the identification as a macroscopic BSFR is natural in TGD framework. Could the periodic mini earthquakes correspond to a sequence of BSFRs?

Deep ocean waves hitting the shore should somehow induce this periodic microseism as a sliding of the tectonic plates with respect to each other. If there is a lattice like structure of incompressible cylindrical plates, the compression by sea waves arriving at shore induces a volume preserving vertical stretching of these cylinders inducing the detected Rayleigh wave.

Cyclotron periods of ions at MB are quantized and 26 s could be understood as a resonance period for the coupling between the tectonic dynamics and that of MB. The problem is that the periods associated with the deep ocean waves are below 20 s so that a linear coupling preserving frequency does not allow understanding of the 26 s period. However, non-linear coupling allows period doubling at the limit of chaos. Could 26 s period be seen as 8:th period doubling of

T=.1 s which corresponds to alpha rhythm in EEG and fundamental biorhythm, the secondary p-adic time scale of electron, and the cyclotron frequency of iron ion in the endogenous magnetic field B_end=(2/5)B_E identified as monopole flux part of Earth's magnetic field B_E and playing a key role in TGD inspired quantum biology?

See the article 26 second pulsation of Earth: analog for 8^th period doubling of EEG alpha rhythm?.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Homeostasis as self-organized quantum criticality?

I attach below the introduction of the article "Homeostasis as self-organized quantum criticality" written together with Reza Rastmanesh. I have dropped references. They can be found from the article which I shall add to Research Gate soon.

This article started as an attempt to understand the properties of cold shock proteins (CSPs) and heat shock proteins (HSPs) in TGD framework. As a matter of fact , these proteins have great deal of similarity and have much more general functions, so it is easier to talk about stress proteins (SPs) having two different modes of operation. time

As we proceed, it will be revealed that this issue is only one particular facet of a much bigger problem: how self-organized quantum criticality (SOQC) is possible? Criticality means by definition instability but SOQC is stable, which seems to be in conflict with the standard thermodynamics. In fact, living systems as a whole seem to be quantum criticalt and manage to stay near criticality, which means SOQC. Note that the self-organized criticality (SOC) is generalized to SOQC.

Topological Geometrodynamics (TGD) is a 43 year old proposal for a unification of fundamental interactions. Zero energy ontology (ZEO) is basic aspect of quantum TGD and allows to extend quantum measurement theory to a theory of consciousness and of living systems. ZEO also leads to a quantum theory of self-organization predicting both arrows of time. Could ZEO make SOQC possible as well?

Summary of the basic properties of CSPs and HSPs

Let's consider a summary of CSPs and HSPs or briefly SPs.

1. There is a large variety of cold shock proteins (CSP) and heat shock proteins (HSPs). CSPs and HSPs are essentially the same proteins and labelled by HSPX, where X denotes the molecular weight of the protein in kDaltons. The value range of X includes the values {22,60,70,90,104,110} and HSPs are classified into 6 families: small HSPs, HSPX, X ∈ {40,60,70,90,110}. At least HSP70 and HSP90 have ATPase at their end whereas HSP60 has ATP binding site. CSPs and HSPs consist of about 10³-10⁴ amino acids so that X varies by one order of magnitude.

   Their lengths in the un-folded active configuration are below 1 micrometer. CSPs/HSPs are expressed when the temperature of the organism is reduced /increased from the physiological temperature. CSPs possess cold-shock domains consisting of about 70-80 amino-acids thought to be crucial for their function. Part of the domain is similar to the so called RNP-1 RNA-binding motif. In fact, it has turned that CSP and HSP are essentially the same object and stress protein (SP) is a more appropriate term.

   Wikipedia article about cold shock domain mentions Escherichia Coli as an example. When the temperature is reduced from 37 C to 10 C, there is 4-5 hours lag phase after which growth is resumed at a reduced rate. During lag phase expression of around 13 proteins containing cold shock domains is increased 2-10 fold. CSPs are thought to help the cell to survive in temperatures lower than optimum growth temperature, by contrast with HSPs, which help the cell to survive in temperatures greater than the optimum, possibly by condensation of the chromosome and organization of the prokaryotic nucleoid. What is the mechanism behinds SP property is the main question.

2. SPs have a multitude of functions involved with the regulation, maintenance and healing of the system. They appear in stress situations like starvation, exposure to cold or heat or to UV light, during wound healing or tissue remodeling, and during the development of the embryo. SPs can act as chaperones and as ATPAses.

   SPs facilitate translation, and protein folding in these situations, which suggests that they are able to induce local heating/cooling of the molecules involved in these processes. CSPs could be considered like ovens and HSPs like coolants; systems with very large heat capacity acting as a heat bath and therefore able to perform temperature control. SPs serve as kind of molecular blacksmiths - or technical staff - stabilizing new proteins to facilitate correct folding and helping to refold damaged proteins. The blacksmith analogy suggests that this involves a local "melting" of proteins making it possible to modify them.

   What "melting" could mean in this context? One can distinguish between denaturation in which the folding ability is not lost and melting in which it is lost. Either local denaturation or even melting would be involved depending on how large the temperature increase is. In a aqueous environment the melting of water surrounding the protein as splitting of hydrogen bonds is also involved. One could also speak also about local unfolding of protein.

3. There is evidence for large change Δ C_p of heat capacity C_p (C_p= dE/dT for pressure changing feed of heat energy) for formation ion nucleotide-CSP fusion. This could be due to the high C_p of CSP. The value of heat capacity of SPs could be large only in vivo, not in vitro.
4. HSPs can appear even in hyper-thermophiles living in very hot places. This suggests that CSPs and HSPs are basically identical - more or less - but operate in different modes. CSPs must be able to extract metabolic energy and they indeed act as ATPases. HSPs must be able to extract thermal energy. If they are able to change their arrow of time as ZEO suggests, they can do this by dissipating with a reversed arrow of time.

To elucidate the topic from other angles, the following key questions should be answered:

1. Are CSPs and HSPs essentially identical?
2. Can one assign to SPs a high heat capacity (HHC) possibly explaining their ability to regulate temperature by acting as a heat bath? One can also ask whether HHC is present only in vivo that is in a aqueous environment and whether it is present only in the unfolded configuration of HP?

The notion of quantum criticality

The basic postulate of quantum TGD is that the TGD Universe is quantum critical. There is only a single parameter, Kähler coupling strength α_K mathematically analogous to a temperature and theory is unique by requiring that it is analogous to critical temperature. Kähler coupling strength has discrete spectrum labelled by the parameters of the extensions of rationals. Discrete p-adic coupling constant evolution replacing continuous coupling constant evolution is one aspect of quantum criticality.

What does quantum criticality mean?

1. Quite generally, critical states define higher-dimensional surfaces in the space of states labelled for instance by thermo-dynamical parameters like temperature, pressure, volume, and chemical potentials. Critical lines in the (P,T) plane is one example. Bringing in more variables one gets critical 2-surfaces, 3-surfaces, etc. For instance, in Thom's catastrophe theory cusp catastrophe corresponds to a V-shaped line, whose vertex is a critical point whereas butterflly catasrophe to 2-D critical surface. In thermodynamics the presence of additional thermodynamical variables like magnetization besides P and T leads to higher-dimensional critical surfaces.
2. There is a hierarchy of criticalities: there are criticalities inside criticalities. Critical point is the highest form of criticality for finite-D systems. Triple point, for instance, for water in which one cannot tell whether the phase is solid, liquid or gas. This applies completely generally irrespective of whether the system is a thermo-dynamical or quantal system. Also the catastrophe theory of Thom gives the same picture. The catastrophe graphs available in the Wikipedia article illustrate the situation for lower-dimensional catastrophes.
3. In TGD framework finite measurement resolution implies that the number of degrees of freedom (DFs) is effectively finite. Quantum criticality with finite measurement resolution is realized as an infinite number of hierarchies of inclusions of extensions of rationals. They correspond to inclusion hierarchies of hyperfinite factors of type II₁ (HFFs). The included HFF defines the DFs remaining below measurement resolution and it is possible to assign to the detected DFs dynamical symmetry groups, which are finite-dimensional. The symmetry group in never reachable ideal measurement resolution is infinite-D super-symplectic group of isometries of "world of classical worlds" (WCW) consisting of preferred extremals of Kähler action as analogs of Bohr orbits. Super-symplectic group extends the symmetries of superstring models.
4. Criticality in living systems is a special case of criticality - and as the work of Kauffman suggests - of quantum crticality as well. Living matter as we know, it most probably corresponds to extremely high level of criticality so that very many variables are nearly critical, not only temperature but also pressure. This relates directly to the high value of h_eff serving as IQ. The higher the value of h_eff, the higher the complexity of the system, and the larger the fluctuations and the scale of quantum coherence. There is a fractal hierarchy of increasingly quantum critical systems labelled by a hierarchy of increasing scales (also time scales).

   In ZEO classical physics is an exact part of quantum physics and quantum physics prevails in all scales. ZEO makes discontinuous macroscopic BSFRs to look like smooth deterministic time evolutions for the external observer with opposite arrow of time so that the illusion that physics is classical in long length scales is created.

Number theoretical physics or adelic physics is the cornerstone of TGD inspired theory of cognition and living matter and makes powerful predictions.

p-Adic length scale hypothesis deserves to be mentioned as an example of prediction since it has direct relevance for SPs.

1. p-Adic length scale hypothesis predicts that preferred p-adic length scales correspond to primes p≈ 2^k: L(k)= 2^(k-151)/2L(151), L(151)≈ 10 nm, thickness of neuronal membrane and a scale often appearing molecular biology.

2. TGD predicts 4 especially interesting p-adic length scales in the range 10 nm- 25 μ. One could speak of a number theoretical miracle. They correspond to Gaussian Mersenne primes M_G,k = (1+i)^k-1 with prime k ∈{151,157,163,167} and could define fundamental scales related with DNA coiling for instance.
3. The p-adic length scale L(k=167)= 2^(167-151)/2L(151)= 2.5 μ m so that SPs could correspond to k∈{165,167,169} . L(167) corresponds to the largest Gaussian Mersenne in the above series of 4 Gaussian Mersennes and to the size of cell nucleus. The size scale of a cold shock domain in turn corresponds to L(157), also associated with Gaussian Mersenne. Note that the wavelength defined by L(167) corresponds rather precisely to the metabolic currency .5 eV.
4. HSPX, X∈ {60,70,90} corresponds to a mass of X kDaltons (Dalton corresponds to proton mass). From the average mass 110 Dalton of amino acid and length of 1 nm one deduces that the straight HSP60, HSP70, and HSP90 have lengths about .55 μm, .64 μ, and .8 μm. The proportionality of the protein mass to length suggests that the energy scale assignable to HSPX is proportional to X. (HSP60, HSP70, HSP90) would have energy scales (2.27, 1.95,1.5 eV) for h_eff=h naturally assignable to biomolecules. The lower boundary of visible photon energies is a 1.7 eV.

   Remark: One has h= h_eff=nh₀ for n=6. What if one assumes n=2 giving h_eff=h/3 for which the observations of Randel Mills give support? This scales down the energy scales by factor 1/3 to (.77,.65,0.5) eV not far from the nominal value of metabolic energy currency of about .5 eV.

   There are strong motivations to assign to HSPs the thermal energy E=T=.031 eV at physiological temperature: this is not the energy E_max= .084 eV at the maximum of the energy distribution, which is by a factor 2.82 higher than E. The energies above are however larger by more than one order of magnitude. This scale should be assigned with the MBs of SPs.

5. The wavelengths assignable to HSPs correspond to the "notes" represented by dark photon frequencies. There is an amusing co-incidence suggesting a connection with the model of bio-harmony: the ratios of energy scales of HSP60 and HSP70 to the HSP90 energy are 3/2 and 1.3, respectively. If HSP90 corresponds to note C, HSP60 corresponds to G and HSP70 to note E with ratio 1.33. This gives C major chord in a reasonable approximation! Probably this is an accident. Note also that the weights X of HSPXs are only nominal values.

Hagedorn temperature, HHC, and self-organized quantum criticality (SOC)

Self-organized criticality (SOC) is an empirically verified notion. For instance, sand piles are SOQC systems. The paradoxical property of SOQC is that although criticality suggests instability, these systems stay around criticality. In standard physics SOQC is not well-understood. TGD based model for SOQC involves two basic elements: ZEO and Hagedorn temperature.

1. ZEO predicts that quantum coherence is possible in all scales due to the hierarchy of effective Planck constants predicted by adelic physics. "Big" (ordinary) state function reductions (BSFRs) change the arrow of time. Dissipation in reversed arrow of time looks like generation of order and structures instead of their decay - that is self-organization. Hence SOQC could be made possible by the instability of quantum critical systems in non-standard time direction. The system paradoxically attracted by the critical manifold in standard time direction would be repelled from it in an opposite time direction as criticality indeed requires.
2. Surfaces are systems with infinite number of DFs. Strings satisfy this condition as also magnetic flux tubes idealizable as strings in reasonable approximation. The number of DFs is infinite and this implies that when one heats this kind of system, the temperature grows slowly since heat energy excites new DFs. The system's maximum temperature is known as Hagedorn temperature and it depends on string tension for strings.

   In the TGD framework, magnetic flux tubes can be approximated as strings characterized by a string tension decreasing in long p-adic length scales. This implies a very high value of heat capacity since very small change of temperature implies very large flow of energy between the system and environment.

   T_H could be a general property of MB in all scales (this does not yet imply SOQC property). An entire hierarchy of Hagedorn temperatures determined by the string tension of the flux tube, and naturally identifiable as critical temperatures is predicted. The temperature is equal to the thermal energy of massless excitations such as photons emitted by the flux tube modellable as a black body.

   Remark: If the condition h_eff=h_gr , where h_gr is gravitational Planck constant introduced originally by Nottale, holds true, the cyclotron energies of the dark photons do not depend on h_eff, which makes them an ideal tool of quantum control.

   Hagedorn temperature would make them SOQC systems by temperature regulation if CSP type systems are present they can serve as ovens by liberating heat energy and force the local temperature of environment to their own temperature near T_H. Their own temperature is reduced very little in the process. These systems can also act as HSP/CSP type systems by extracting heat energy from/providing it to the environment and in this manner reduce/increase the local temperature. System would be able to regulate its temperature.

A natural hypothesis is that T_H corresponds to quantum critical temperature and in living matter to the physiological temperature. The ability to regulate the local temperature so that it stays near T_H has interpretation as self-organized (quantum) criticality (SOC). In the TGD framework these notions are more or less equivalent since classical physics is an exact part of quantum physics and BSFRs create the illusion that the Universe is classical in long (actually all!) scales.

Homeostasis is a basic aspect of living systems. System tends to preserve its flow equilibrium and opposes the attempts to modify it. Homeostasis involves complex many-levels field back circuits involving excitatory and inhibitory elements. If living systems are indeed quantum critical systems, homeostasis could more or less reduce to SOQC as a basic property of the TGD Universe.

I will add the article "Homeostasis and self-organized quantum criticality" to Research Gate.

See either the article Homeostasis as self-organized quantum criticality or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Earth's pulsation rhythm of 26 seconds as an analog of EEG rhythm?

There is an interesting article in Discover Magazine with title "The Earth Is Pulsating Every 26 Seconds, and Seismologists Don't Agree Why" (see this). That mini earthquakes would appear with a period of 26 seconds is a rather fascinating possibility.

First some background.

1. TGD based quantum theory relies on zero energy ontology (see this). and predicts quantum coherence in all scales being assignable to the magnetic bodies of systems consisting of ordinary matter. MBs would carry dark matter as h_eff=n×h₀ macroscopically quantum coherent phases.
2. Ordinary ("big") state function reductions (BSFRs) would change the arrow of time and this implies that they look like deterministic smooth time evolutions leading to the final state of BSFR. The world would be quantum coherent but look lclassical in all scales! The change of the arrow of time leads to a radically new view about self-organization and about biology and also self-organized quantum criticality emerges naturally and leads to the emergence of "breathing systems" so that the applications to living systems are natural. In fact, evidence for very simple "breathing" systems is emerging (see this).

   Earthquakes have some strange features and this led to the proposal that earth quarks could involve BSFR in macroscopic scales at the level of MB of Earth (see this). Could also these mini earthquakes involve BSFRs? Could they be interpreted as a sequence of life cycles for a conscious entity with a life time of about 26 seconds assignable to Earth?

3. It is known that electromagnetic activity accompanies Earth quarks and this activity is such that the interpretation in terms of time reversal suggests itself. Could 26 seconds define a period for an analog of alpha rhythm in EEG? There is also another strange rhythm with a period of 160 minutes assignable to astrophysical systems and I have proposed an interpretation as a "cosmic" alpha rhythm (see this).

This picture leads to ask whether the p-adic length scale hierarchy predicted by TGD could provide some understanding concerning the period of T=26 seconds associated with the pulsations.

1. TGD predicts a hierarchy of p-adic length scales L_p ∝ p^1/2, p ≈2^k, k>0 preferred integer, coming as half octaves. TGD does not deny the possibility of scaled variants of various particles. For instance, electron could correspond to several integers k with masses proportional to 2^k/2).
2. Secondary p-adic length scales correspond to scales p^1/2L_p ∝ p. There also tertiary etc time scales forming a fractal hierarchy coming in powers of p^1/2 and by p-adic length scales as preferred half octaves.
3. Electron corresponds to p-adic prime p= 2¹²⁷-1 (the largest Mersenne prime, which does not yet correspond to super-astrophysical length scale). Secondary p-adic length scale corresponds to a period T_e≈ .1 seconds. This is a fundamental biorhythm appearing in alpha band of EEG. Also quarks correspond to secondary p-adic length scales which correspond to human time scales.
4. T= 26 seconds is rather precisely equal to 2⁸× T_e, T_e=.1 seconds: the relative error is 1/64 or about 2 per cent. A scaled version of electron with mass m= m_e/2⁴≈ 32 keV would correspond to 25.6 seconds. The p-adic prime p≈ 2^k, k= 127+8=135 defining p-adic scale about .4 Angstrom. This is not far from Bohr radius a_B= .53 Angstrom for hydrogen atom.

Of course, the new dark particle need not be electron. One can consider a more detailed attempt to understand the situation involving the notion of electropion (or more generally, leptopion, see this) for which there is empirical support and empirical evicence that ordinary pion allows p-adically scaled up variants.

1. The scenaro would be based on axion-like states proposed also as candidates for dark matter predicted by TGD. They would be indeed dark also in TGD but in TGD sense being particles having h_eff= n×h₀>h. This would explain why they are not seen in decay widths in particle accelerators (and excluding them).
2. There is evidence for electropion with mass 2× m_e (already from 1970's) decaying to an electron-positron pair but forgotten since it does not conform with the standard model (it would increase decay widths of weak bosons). TGD provides a model for this state and predicts similar states for muon and tau and evidence also for these states have been found but also forgotten.

TGD also suggest fractally scaled variants of pion states with different p-adic length scales p ∝ 2^k and there is empirical evidence for these states with masses both larger and smaller than pion mass.

1. One can also imagine scaled variants of electropion with different p-adic lengths scales. The primary p-adic time scale assignable to electropion scales corresponds to k≤127. How to estimate k?

   If the mass squared (conformal weight is additive in p-adic mass calculations then mass squared of electropion is m²= 2m_e² giving m=2^1/2× m_e for k=127. Correct mass requires k_e=127→126. Compton time of electropion would be T_c(126,e)/2, where T_c(126,e) is the Compton time of electron with k=126.

   The secondary p-adic time Compton time associated with the scaled variant of k= 126 electropion corresponds to T(electropion,126+Δ k)=2^{Δ k} T_e/2. One must have Δ k= 8+2=10 and k=137. Amusingly, k= 137 corresponds to atomic length scales and to fine structure. I have called this co-incidence as a cosmic joke.

Why this atomic length scale, or rather the corresponding secondary p-adic length scale of scaled electropion, would be associated with the Earth's pulsations? Electropions should be dark and perhaps form a coherent state as in the model for the production of anomalous electron-positron pairs based on electropion involving in an essential manner non-orthogonal electric and magnetic fields of colliding nuclei?

Second proposal is based on TGD inspired quantum biology involving Bose-Einstein condensates of Cooper pairs of electrons, protons, and fermionic ions and also of bosonic ions at magnetic flux tubes and characterized by effective Planck constant h_eff=nh₀, h= 6h₀, making possible quantum coherence in length scales longer than Compton length.

1. Consider the Bose-Einstein condensate of electron Cooper pairs. Electron Cooper pairs has Compton length equal to L_2e= L_e/2, L_e the electronic Compton length. Secondary Compton time equals to T²⁾_2e= 2^127/2T_e/2=.05 s. Superconductivity in longer length scales than Compton length requires h_eff>h. The scaled up Compton scale L_n,2e= nL_2e gives the coherence length of a superconductor and the secondary Compton time scales to nT²⁾_2e=.05n s. This time equals to T=25.6 s for n=2⁹.
2. The general hypothesis is that there is resonance between dark and p-adic length scales so that this dark scale would correspond to identical p-adic length scale which would correspond to L(k=127+18= 145) ∼ 1.25 nm equal to the transversal length scale for DNA.
3. TGD predicts that ordinary dark DNA in aqueous environment is accompanied by dark DNA realized as flux tubes carrying dark proton triplets realizing genetic code. Also amino-acids would be accompanied by these dark proton triplets and electrons would neutralize proteins charge which would be 3 proton charges per amino-acid. This would suggest that this scale relates to dark DNA, RNA, and proteins, which would involve space-time sheets which are electronic super conductors, and that the 26 second rhythm reflects the presence of water.

Could 26 second rhythm be kind of a bio-rhythm for Earth analogous to heart-beat or breathing? These two rhythms are highly varying and assignable to self-organization. EEG alpha rhythm is however universal. Could the Earthly bio-rhythm be analogous to the alpha band in the analog of EEG of Earth with frequencies scaled down by factor 1/256?

Each period would correspond to a mini earth quake. Also the ordinary EEG would involve similar BSFRs as an analog of sleep-awake rhythms and all bio-rhythms could be this kind of sleep-awake rhythms. One could of course check whether the 26 second rhythm has an electromagnetic analog?

There exists also another analogous rhythm, the 160 minute rhythm assignable to many astrophysical objects. I have proposed an interpretation as a kind of cosmic alpha rhythm.

1. 160 minute period is obtained from 26 second rhythm by scaling by a factor about 369 ≈ 2^8.5 with error of 2 per cent - half octave again.
2. For the electro-pion option, one can think that one scales electropion with k= 127 having mass 2^1/2× m_e to k=127→ 127+17 =144 to get secondary Compton time scale 2^16+1/2) T_e=154.5 minutes not too far from 160 seconds.
3. For the Cooper pair option one could argue that since h_eff is integer valued, one can allow a value of n near to 2^17.5≈ 185364: this would give p-adic length scale L(162). L(163), which corresponds to one of the miracle length scales k∈{151,157,163,167} defining scales assignable to DNA coiling, would have been a more desired outcome.

   See either the article TGD inspired solution to three cosmological and astrophysical anomalies, the article Earthquakes and volcanic eruptions as macroscopic quantum jumps in zero energy ontology, or the chapter a About the Nottale's formula for h_gr and the possibility that Planck length l_P and CP₂ length R are related.

   For a summary of earlier postings see Latest progress in TGD.

   Articles and other material related to TGD.

Blackhole information paradox solved!: Really?

There was a popular article in Quanta Magazine with title "The Most Famous Paradox in Physics Nears Its End" about the work related to the blackhole information paradox. The claim was that the authors had demonstrated by computation that the information paradox disappears in quantum gravity theory - a theory which has the regrettable property that it does not exist. What would happen that very old blachole (BH) would explode and send the conserved information to environment. The conservation of information would reflect the assumption that the time evolution of the BH is unitary.

Calculations of Ahmed Almheir and colleagues are inspired by string theory but are claimed to stand on their own. From the popular article one learns that besides various calculational tricks, the calculation involves a lot of fashionable stuff: wormholes, the holographic principle, emergent space-time, quantum entanglement, quantum computers. To my opinion, the calculation is a model for BHe evaporation rather than a real calculation starting from basic principles for the simple reason that no quantum theory of gravity exists.

The calculation is not able to tell exactly how the information leaks out from the blackhole, which would eventually shrink to a point. The entanglement entropy of BH with radiation would start from zero and increase and eventually return to zero as BH has disappeared.

From the beginning it has been clear that BHs represent the failure of general relativity. This was also clear for Einstein. Then came the theoreticians who believe that all problems - also those which would requirea profound modification of basic postulates - can be solved by computing. Then they compute and compute and .... and eventually proudly declare "Problem solved". Here is an excellent example of this phenomenon. Einstein would have asked what goes wrong with general relativity and developed a better theory. I choose the same approach: TGD leads also to a profound modification of quantum theory itself.

In TGD framework a new ontology of quantum theory - I call it zero energy ontology (ZEO) - predicts that ordinary ("big") state function reductions (BSFRs) change the arrow of time. There is a direct empirical and experimental evidence for this (experiments of Minev et al) and the new view leads to a general theory of self-organization, quantum criticality and self-organized quantum criticality (see this). For understanding of life this vision is especially relevant.

Number theoretic vision about TGD predicts also a hierarchy h_eff=n×h₀ of Planck constants and phases with large value of h_eff corresponding to dark matter. Therefore BSFRs occur in all scales and imply that physics looks for a standard observer classical in all scales although BSFRs are discontinuous they look like continuous deterministic time evolutions (their superpositions, to be precise) leading to the final state of BSFR. There would therefore no limit at which quantum mystically transforms to classical. Also the basic paradox of quantum measurement theory is solved.

The postulated unitary evolution of BH would be replaced by a sequence of unitary evolutions followed by TGD analogs of "weak" measurements, "small" state function reductions (SSFRs). This replacement would hold true for the time evolution of any system. SSFRs would break the unitary evolution to unitary pieces. In TGD inspired theory of consciousness the sequence of SSFRs would define the life cycle of a conscious entity ending with BSFR- death or falling a sleep - followed by a "reincarnation" with an opposite arrow of time.

TGD provides also a detailed model for blackhole like objects as tangled magnetic flux tubes filling the volume (see this). BSFRs are possible also for the TGD counterparts of blackholes and indeed, when BH-like objects become very old they make BSFR and the evolution leading to BH ccurs in reversed time direction! For instance, quasars are excellent candidates for time reversals of these analogs of BH-like objects and also analogous to whiteholes (see this).

The calculation involves many notions appearing also in TGD.

1. Holography (or rather, strong form of holography) follows from general coordinate invariance in TGD framework.
2. AdS/CFT is replaced with strong holography meaning that data at 2-D surfaces code determine space-time surface and evolution of induced spinor fields. The representability of space-time as surface in either M^8 or M^4xCP_2 (M^8-H duality) is a new element and an essential piece of TGD. These alternative but equivalent choices of the imbedding space are unique from the condition that the twistor lift of TGD exists.
3. Calculation involves also extremal surfaces which are minimal surfaces. In TGD framework space-time surfaces are preferred extremals satisfying infinite number additional conditions besides field equations. They are minimal surfaces which are also extremals of Kä:hler action. They contains as analogous of blackhole horizons light-like 3-surfaces at which the metric changes its signature from Minkowskian to Euclidian as 3-surfaces identifiable as carriers of quantum numbers of particles: the presence of Euclidian space-time regions identifiable as interiors of elementary particles is something totally new. There are also string world sheets and partonic 2-surfaces, which are also minimal surfaces.
4. The analogs of blacholes themselves are magnetic flux tubes carrying monopole flux filling the entire volume. The quantized thickness of the flux tube characterizes these objects and ordinary blackholes are only a special case. There is not blackhole singularity.

Since colleagues officially have never heard anything about the existence of TGD - thanks to the very effective censorship which has lasted since 1982 when I published my thesis - I cannot officially blame them for stealing their basic physical picture from TGD and trying to reproduce it by calculating - this of course looks much more "scientific" and is certainly publishable unlike a genuine theory inspired by the obvious deficiences of GRT, in particular the fact that notions of energy, momentum, and angulare momentum are ill-defined in GRT due to the loss of Poincare invariance.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Could I go to bed today and wake-up yesterday morning?

In zero energy ontology (ZEO) falling asleep (death at"my" level of self the hierarchy) corresponds to ordinary - or "big" - state function reduction (BSFR) and also means a reincarnation with opposite arrow of time. We would be therefore conscious during sleep and wake-up would correspond to falling sleep of that other, time reversed self.

When I fall asleep, I wake-up later tomorrow morning for instance, not yesterday morning. It is interesting to see what kind of conditions this implies and whether it is possible to satisfy this easily and even more interesting is to see whether a time travel to the geometric past - maybe the Golden Youth - could be possible.

The following assumptions are made about what happens in BSFR.

1. Causal diamond (CD) is a correlate for self. CD is obtained by gluing together two identical half-cones along their bottoms. Moment "Now" corresponds to the largest hyperplane T_now=T (origin of time coordinate is at either (call it "lower") tip of CD) .
2. During the sequence of SSFRs defining self, the 3-surfaces at the passive boundary of self are fixed although their 4-D tangent space changes and corresponds to the unchanging part of selfhood - soul one might say. The opposite active boundary of CD and 3-surfaces at it change and shift towards geometric future.This gives rise to wake-up consciousness involving sensory input and thoughts, emotions etc. induced by it. Each SSFR is preceded by the analog of unitary time evolution.
3. BSFR means a death of self (subself) and its reincarnation with an opposite arrow of time. One can equally well speak about the analog of falling in sleep and waking up after that for some level of hierarchy of selves. The self born in the death of the self with an opposite arrow of time self has no direct memories about the state. Self can however have memories about dreams in which part of say brain is awake. These memories store information about what self experienced during the sleep.

   In BSFR the active boundary of the CD becomes passive and is frozen. The size of CD is scaled down so that CD becomes small: this implies that the reincarnated self has a childhood and much of the memories - often not pleasant - stored near the active boundary as subselves living forth and back as conscious entities disappear. The surviving memories of self become "silent wisdom" of the reincarnated self.

4. If CD belongs to a larger CD, call it CD_super representing a larger unit of consciousness, the sub-CDs must shift to the same direction as the active boundary of CD_super. Otherwise the sub-CDs would drop from the flow of consciousness. This is analogous to co-movement of matter in cosmology.

   Note that the mental images of self correspond to sub-CDs around T_now and shift towards geometric future as CD increases and new mental images emerges at T_now plane: by M⁸-H correspondence these special moments in the life of self correspond to roots of the polynomial defining space-time surface and reside are the upper half-cone of the CD. As CD increases, new roots pop up inside the upper half-cone near the T_now hyper-plane for some particular SSFRs. Completely counterintuitively, the mental images about past experiences are therefore in the geometric future of T_now hyperplane!

The proposed picture must be consistent with everyday experience. Call the two periods of self sleep wake-up and sleep label the two different BSFRs by "sleep" and "wake-up".

1. In each SSFR CD size increases - at least in statistical sense this implies that T grows. Each SSFR corresponds to a scaling for the CD shifting its active boundary towards the geometric future. During its life cycle CD experiences scaling Λ:

   T_now→ T_now,sleep1= Λ(SSFR) T_now , Λ(SSFR) >1 .

2. When the system falls in sleep the size of CD is scaled down so that also the value of T_now is scaled down by Λ_BSFR<1:

   T_now,sleep2= (1- Λ(BSFR)) 2T_now,sleep1 = (1- Λ(BSFR)) Λ(SSFR)2T_now , Λ(BSFR)<1 .

   After that the CD begins to increase in size by small scalings in SSFRs to opposite time direction and T_now begins to decrease from its value T_now,sleep begins to decrease.

3. If CD belongs to a bigger CD - call it super-CD - representing a larger unit of consciousness with a longer life cycle, one can argue that the CD must shift to the same direction as the larger CD increases. Otherwise the CD would drop from the flow of consciousness defined by super-CD. This is analogous to co-movement of matter in cosmology. Therefore a given life cycle corresponds also a shift Δ T of sub-CDs towards the growth direction of super-CD takes place and one has for the time coordinate T_super,now of the super-CD. Therefore one must perform shiftT→ T+ Δ T for T_now,sleep1 and T_now,sleep2 to take into account the drifting. This gives for the moments "Now" before ad after the shrinking of CD in BSFR (falling asleep):

   T_{super,now,sleep1} = T₀+ T_now,sleep1 +Δ T ,

   T_{super,now,sleep2} = T₀+ (1- Λ(BSFR)) 2T_now,sleep1 +Δ T .

4. Similar formula holds true for the moment of wake-up. In the previous formula T_now is replaced with T_now,sleep2 and one has

   T_{super,now,wakeup1} = T₀+ Λ¹⁾(SSFR) T_now,sleep2 +Δ T¹⁾ , T_{super,now,wakeup2} = T₀+ (1- Λ¹⁾(BSFR)) Λ¹⁾(SSFR)2T_now,sleep2 +Δ T¹⁾ .

   The parameter T₀ depends on the choice of the origin of time for super-CD but is irrelevant.

One can deduce a consistency condition for the parameters of the model.

1. During the sleep period the time coordinate T_super,now for moment "Now" in the coordinates of larger CD changes in the following manner:

   T_{super,now,sleep} =T₀+ T_now,sleep1 → T_{super,now,wakeup}

   =T₀ + Λ^{1)(BSFR) T_{super,now,sleep2} +Δ T1) .}

   T₀ is an irrelevant parameter associated with super-CD. Note that there is breaking of time reversal symmetry since self associated with CD_super has fixed arrow of time unlike CD. Hence Δ T has at least in a statistical sense the same sign irrespective of the arrow of time of self.

2. This picture should be consistent with what we observe. When the tired average self fall a sleep at the evening, it wakes wake-up at the morning and is full of energy. Quite generally, wake-up occurs after time Δ T(sleep) meaning that the value of time T_super has increased by

   T_{super,now,wakeup}= T_super,now(sleep₁)+ Δ T(sleep) .

   These two expressions for the value of T_super,now(wakeup) must be consistent and this gives a conditions on the parameters involved:

   (1- Λ¹⁾(BSFR)) Λ¹⁾(SSFR)2T_now,sleep1 +Δ T¹⁾

   = T_now,sleep1 +Δ T + Δ T(sleep) .

   Δ T(sleep) is given by

   Δ T(sleep) =[(1- Λ¹⁾(BSFR)) Λ¹⁾(SSFR)2-1]T_now,sleep1 +Δ T¹⁾ -Δ T .

   Intuitively it seems clear that for a given arrow of time it is not possible to wake-up before one falls asleep, and the condition Δ T(sleep)>0 for the standard arrow of time gives a constraint on the parameters. One cannot however exclude the possibility of time travel without dying or falling asleep first of the duration of time travel is much longer than that of wave-up period: Δ T¹⁾ -Δ T.

   A special solution corresponds to

   Δ T(sleep)= Δ T¹⁾- Δ T and (1- Λ¹⁾(BSFR)) 2Λ¹⁾(SSFR)=1

   giving

   T_now,sleep2=T_now.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

New Physics View about Language

We have written together with Reza Rastmanesh several articles related to biology, neuroscience, and TGD during this year. Language is indeed what distinguishes us from the other animals in a radical manner and therefore a challenge for any theory of consciousness and life. There are 3 articles related to the origin of language involving one preparatory article explaining the role of magnetic body (MB) in biochemistry and a 2-part article about a model of language - the topic of this posting.

I decided to put the introductions of the articles to blog. Articles can be found also in Research Gate and hopefully sooner or later also at my homepage (my communizations to homepage have been continually terrorized during the summer).

Human languages differ dramatically from their analogs for animals. Animal languages consist mainly of simple signals, warnings and threats for instance; emotional expression dominates and grammar is lacking. Birds can have impressive repertoire of different song patterns and monkeys have gesture language. There is a huge variety of human languages: speech and written language, sign languages based on gestures, the language of mathematics and computer languages in which emotional expression is absent. One can also regard music as a kind language expressing emotions and creating them. Also pictures define linguistic representations. Children and animals learn language by mimicry and also learn the grammar and syntax without conscious efforts. Adults can learn a foreign language by learning the vocabulary and the rules of grammar. Human language is also special in that it involves conceptualization, metaphors, and analogies representing abstract concepts in terms of objects and actions of the external world.

One might understand the semantic aspect of language in terms of association and conditioning. Language acquisition involves showing an object and uttering the word(s) describing it or assigned to it. This suggests that conditioning and association happens so that mere word generates an imagined percept of the object. Conditioning and formation of associations is a very general form of learning assumed to relate to the increase of synaptic strengths leading to a generation of association pathways. In computer science pattern recognition and completion models it mathematically. One one can ask whether learning of language and language understanding is something more than this.

For more detailed approaches of language theories, interested readers may be referred to references (see this and references in the article). The article of Kempe and Brooks (see this) and the review article "From Molecule to Metaphor: A neural theory of language" about the language theory of Jerome A. Feldman by Stefan Frank (see this) gives a deeper perspective to language theories. The notion of embodiment is in key role in these theories and will be in a key role also in the proposal to be discussed.

About language genes

Forkhead box protein P2 (FOXP2) encodes a transcription factor involved in language acquisition and speech (see this) . In addition to FOXP2 a limited number of genes are involved in speaking (see this) . All vertebrates possess FOXP2, however it is estimated that some 120,000-200,000 thousand years ago, some mutations occurred only in humans which aided humans to start initial forms of speaking (reference in article). Animals have their own primitive language; both voices and gestures with meaning make communications possible. They mainly recognize each other and communicate with pheromones. As for vocabulary, a short review of the Old Testament, cuneiform writings, glossary of old books, and hieroglyphs clearly shows that the number of entries was quite limited in the past. Therefore, a further progression of language could be mostly a matter of cultural communications and technological advances.

However, today it is clear that crucial mutations occurred in the non-coding part of the genome controlling the expression of genes coding for proteins (see this) which lead to language evolution. Therefore, the evolutionary step was associated with control of existing genes. Humans are also distinguished from animals by their learning abilities.

Language acquisition must rely on conditioning/associations between language expressions and experiences. It seems that embodiment is the mechanism, which associates to a linguistic expression an imagined sensory perceipt and/or motor action making the emergence of meaning. What is needed is long term memory and also some kind of standardization of percepts so that they consist of standardized mental images. Pattern recognition and completion could give this standardization.

Since sensory and motor imagination could be seen as almost sensory experiences and motor actions, this suggests that new communications between auditory organs and sensory and motor areas emerged. Even more generally, this kind of communication could have emerged quite generally. This would be essentially a new form of conditioning and the same mechanism could apply to all kinds of conditionings.

How the mutation of only a few genes led to cultural evolution?

Amazingly, only a few mutations for relatively few genes seems so have led to human languages. Why few point mutations of relatively few genes could have transformed biological evolution to cultural evolution? What happened for these genes? In the biochemistry framework it is difficult to imagine an answer to this question. Here TGD could come in rescue.

Number theoretic physics is part of quantum TGD and essential for understanding evolution as an increase of algebraic complexity. Evolutionary hierarchies would correspond to hierarchies of algebraic extensions of rationals. The dimension n of extension defines effective Planck constant h_eff/h₀=n, the larger the dimension, the larger the scale of quantum coherence at corresponding level of magnetic body (MB) associated with the system. One can also say that n is analog of IQ. One can assign a value of h_eff characterizing their evolutionary level also to genes. The genes with larger h_eff would serve as control genes. The increase of h_eff for genes would mean an evolutionary step. Perhaps a dramatic increase of h_eff occurred to FOXP2 and some other genes as human language emerged.

Second mechanism could be energy resonance in the coupling of the analogs of DNA, RNA, tRNA, and amino acids consisting of dark proton triplet with their chemical counterparts. The coupling would be between the entire gene and its dark analog and codon sequence would play a role of address. In both cases small changes of the gene could spoil or produce an energy resonance. This sensitivity would make genes an ideal control tool but would also serve as a general mechanism also for genetic diseases. The increase of h_eff accompanied by a small mutation to guarantee energy resonance could be the mechanism explaining the importance of FOXP2 and similar control genes.

See the articles "TGD view about language: part I" at RG or at homepage, and "TGD view about language: part II" at RG or at homepage, or the chapter TGD view about language.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

About the role of possible longitudinal electric field of DNA

We have written together with Reza Rastmanesh several articles related to biology, neuroscience, and TGD during this year. There is an article related to the arrow of time and memory in neuroscience and 2 articles related to the arrow of time at the level of DNA- the topic of this posting. I decided to put the introductions of the articles to blog. Articles can be found also in Research Gate and hopefully sooner or later also at my homepage (my communizations to homepage have been continually terrorized during the summer).

The motivation for the second article discussing DNA and arrow of time was the question whether there could be a longitudinal electric field associated with DNA and whether the reduction of its strength could serve as a bioelectric marker of cancer, aging and death. This could be the case if the length of DNA correlates with the strength of this electric field. The natural question is whether the length of the negatively charged sticky end of DNA could determine the strength of this electric field.

Could DNA be a ferroelectret and could the length of sticky ends control the strength of the longitudinal electric field?

DNAs and RNAs are bioelectrets (see this and this) but the question whether they are bioferroelectrets (see this) possessing a constant longitudinal electric field in the absence of external electric field is an open question.

Telomeres are associated with the ends of DNA double strands. The lengths of telomeres (see this) are controlled by the telomerase enzyme. The shortening of telomeres is known to relate to aging. For cancer cells, germ cells and stem cells the length of the telomeres is not varying. In cancer their lengths are abnormally short. Telomeres could act as buffers shielding the part of DNA coding for proteins. Telomeres have "sticky ends" assignable only to the second DNA strand and carrying negative charge. What their function could be? Could telomere lengths correlate with the lengths of the sticky ends and what could control their lengths?

There is an analogy with microtubules, which are highly dynamical and carry a longitudinal electric field, whose strength correlates with the microtubule length. Could the sticky ends (see this) generate a longitudinal field along DNA double strand with strength determined by the lengths of the sticky ends? In the standard picture the flux of the longitudinal electric field would be proportional to the difference of the negative charges associated with the sticky ends. In a conceptual framework based on Topological Geometrodynamics (TGD), which is a proposal for a unification of fundamental interactions inspiring a vision about consciousness and quantum biology, DNA strands are accompanied by the dark analog of DNA with codons realized as 3-proton units neutralizing the negative charge of ordinary DNA except at sticky ends.

If the dark double strand accompanies also the sticky end, the total charge is positive. If not, it is negative. This allows to consider the possibility that opposite sticky ends have opposite charges so that there is a long dipole like entity carrying longitudinal electric flux proportional to the common length of sticky ends.

Experimental signatures

Also in standard physics based picture (no dark DNA), an external electric field created by the polarization of the nucleotides A, T, C, G in an external electric field is possible (see this). This would mean electrect property, not yet ferroelectricity. The model for the phenomenon suggests that ferro-electricity could result in the sense that the polarization is non-vanishing also in absence of the external electric field so that the nucleotide -rather than entire DNA strand - would be an electric analog of ferromagnet.

In this case the behavior in the external electric field is different from that for ferroelectric DNA double strand: DNA double strand itself would not experience a direct torque in the external electric field. The effective polarization per nucleotide predicted by TGD is at least by a factor 2.5-7.5 stronger than standard model polarizations so that the model can be tested. Furthermore, ferroelectricity of DNA in TGD sense requires DNA double strands and would be present for single DNA strand.

The secod testable prediction is the possibility of currents running along DNA double strand in the longitudinal electric field even without external electric field. External field would however add to the ferroelectric field of oriented DNA double strands and lead to an anomalously high conductivity. Another test would be based on the ferroelectret property of living tissues, which could be caused both by DNA and protein ferro-electricity. Living tissues are indeed known that be ferroelectres as the phenomena of pyroelectricity, piezoelectrity (studied first by Ahlenstaedt (see this) and the polarization in an external electric field demonstrate. Ahlenstaedt proposed that the permanent dipole like character (ferroelectricity) of the linear biomolecules gives rise to their bioferroelectricity.

Connection with consciousness

An analogy with the findings of Becker about the electric fields along the body axis emerges. Becker found that the direction of this field determines whether the organism is awake or in a sleep state. The weakening of these fields leads to aloss of consciousness. TGD inspired theory of consciousness predicts that even sysems like DNA can be conscious and the fractality of TGD Universe suggests that the physical correlates of consciousness are same in all scales.

Could the direction and strength of the electric field of DNA correlate with consciousness at this level? In TGD based quantum measurement theory extending to a theory of consciousness the arrow of time changes in "big" state function reductions (BSFRs), which mean "death" and "reincarnation" with opposite arrow of time (see this). By the tensorial properies of electromagnetic field tensor the arrow of time correlates also with the direction of the electric field. This leads to ask whether the change of the arrow of time in BSFR could change the direction of the DNA's bioelectric field, and one ends up with a simple mechanism for this based on the analog of Becker's DC currents along DNA as proton currents.

Telomore length, cancer, and DNA ferroelectricity

Compelling evidence suggest that there is an inverse relationship between telomere length and both different types of cancer incidence and mortality (references in article) suggesting that the control of telomere length by telomerase enzyme is impaired (references in article). Almost in all cancer cells, telomere length is shortened (references in article). Telomere shortening accompanies ageing (references in article)e. Even in stem cells, except for embryonic stem cells and cancer stem cells, there are overwhelming evidence that telomere shortening occurs during replicative ageing, though at a lower rate than that in normal somatic cells (references in article).

In this picture, the simplest possibility is that telomeres act as buffers, and the strength of the longitudinal electric field controlled by the length of sticky ends controls the length of telomeres and thus of DNA. Sticky ends would be the key control knobs used by telomerase enzyme, and magnetic body (MB) of the system would be the ultimate controller.

Apart from some exceptions, telomere length in DNA is shortened in almost all cell types during aging and some diseases, based on the level of telomerase activity or its absence. Ageing could be purposefully induced since eternal life would be a metabolic catastrophe from the perspective of population overgrowth and evolution (reference in article).

This motivated us to propose the hypothesis that DNA bioelectricity changes over time and depends on disease progression and severity. This provides an excellent opportunity to establish novel predictive, prognostic and therapeutic biomarkers differentially in different cell types or as a combined bioelectric marker for "whole-body" as a derivation of mathematical formulations. This hypothesis is necessary for designing tailor-made microelectrochemical impedance spectroscopy technologies, and consequently, pilot studies designed a priori are needed to test our hypothesis. Along with replication of well-designed pilot study with a more diverse population and larger sample size, it will be needed to address questions about cut-offs or personalized normal ranges for differential and mean whole-body DNA's bioelectric field in a longitudinal study in a prospective manner. With this brief background, the aim of this paper is to suggest DNA's bioelectric field as a novel bioelectric marker to be used for prognostic and diagnostic purposes in researches of cancer, aging, surgery grafts and rejuvenation, for the first time.

See the article DNA's bioelectric field an early bioelectric marker of cancer aging and death: a working hypothesis.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.