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.

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.

DNA and time reversal

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).

This posting is the introduction of the first article devoted to the view about DNA inspired by zero energy ontology (ZEO) (see this and this) forming the basis of the quantum measurement theory of Topological Geometrodynamics (TGD) and by the notion of dark DNA (see this) inspired by the TGD view about dark matter as phases of the ordinary matter with effective Planck constant h_eff=nh₀>h (see this and this,this) at (magnetic body) MB (see this, this,this and this) - the third key notion distinguishing TGD from standard model. The basic prediction of ZEO is that "big" (ordinary) state function reduction (BSFR) changes the arrow of time meaning "death" and "reincarnation" with opposite arrow of time. For dark matter at the MB the periods with a given arrow of time would be long and induce the long-lasting effective change of the arrow of time for the ordinary matter.

This leads to a new view about self-organization (see this) involving in an essential manner time reversed dissipation looking like energy feed in the standard direction and quantum coherent MB as a master quantum controlling the ordinary matter. The energy feed is necessary since the increase of h_eff requires energy.

Time reversal and the dynamics of DNA

The time reversals of the basic processes like transcription and replication turn out to be possible only for the conjugate strand - this is basically due to the chiral selection and CPT theorem in TGD context. CPT C denotes harge conjugation, P spatial reflection, and T geometric time reflection to be distinguished from thermo-dynamical time reversal and time reversal occurring in BSFR. The triviality of C (matter-antimatter asymmetry) implies that T acts like P mapping molecules to their mirror images. By chiral selection enzymes can catalyze processes but not their time reversals. For instance, conjugate strand polymerizes in reverse time direction - this looks like depolymerization in standard time direction. Polymerization of the conjugate strand however occurs in standard time direction but in reverse direction along strand.

The recombination of DNA strands during meiosis is poorly understood. This could correspond to reconnections for the magnetic flux tubes associated with the active DNA strands. Time reversal would occur in BSFR and formerly passive conjugate DNA strands would depolymerize to "loose" codons (see this) (not independent letters) by the time reversed polymerization, the flux tubes associated with the formerly active strands would suffer reconnections inducing recombination without assistance of enzymes, second BSFR would occur, and be followed by the replication of recombined active strands.

Does DNA have longitudinal electric field with direction correlating with the arrow of time?

According to the findings of Becker the direction of the electric along the body axis field determines whether the system is awake or asleep. By the properties of electric field under time reflection, the arrow of time correlates also with the direction of the electric field. TGD predicts that consciousness is possible even at the level of DNA. Could also DNA have a longitudinal electric field with direction correlating with the arrow of time of DNA at the MB of DNA? Could there be a switch changing the direction of this electric field?

There is an inspiring analogy with microtubules, which are highly dynamical and carry a longitudinal electric field, whose strength correlates with the microtubule length (see this). Could sticky ends 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 TGD framework DNA strands are accompanied by the dark analog of DNA with codons realized as 3-proton units neutralizing the negative charge of the ordinary DNA except at sticky ends.

A simple proposal for the time switch based on the analog of Becker's DC currents emerges: proton flow of the dark protons between sticky ends would change the arrow of time. The model could generalize also to proteins known to be ferro-electrets and accompanied also by their dark analogs.

See the article "DNA and time reversal" at RG or at homepage, or the chapter ZEO, Adelic Physics, and Genes.

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

Articles and other material related to TGD.

Arrow of time in neuroscience: TGD based view

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 - the topic of this posting - and 2 articles related to the arrow of time at the level of DNA. 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 question that inspired tes article of arrow of time in neuroscience was whether memories about the future are possible. This requires retrocausality. The criticism of retrocausality relies on the assumption that time, in particular the thermo-dynamical time, has always the same arrow.

If one gives up this assumption, there is no reason forbidding retro-causality and phenomena like sensory perception of signals arriving from future giving rise to precognition. In fact, our ability to predict a lot about our future might be due to this kind of sensory perception rather than only due to computation using a neuronal model.

There is empirical evidence for non-standard arrow of time. Phase conjugate light rays (see this) obeying second law in wrong time direction, Fantappie's work (see this), self-organization in biology - the self-assembly of the tobacco mosaic virus is a classical example (see this). The latest finding that I learned of is that an isolated system can extract organized energy from its thermal energy (see this).

In the framework of Topological Geometrodynamics (TGD) zero energy ontology (ZEO) (see this) leads to a quantum measurement theory solving the basic problem of standard quantum measurement theory due to the conflict between determinism of Schrödinger equation and non-determinism of quantum jump. Key prediction is that the arrow of time changes in ordinary "big" state function reduction (BSFR) whereas in "small" state function reductions (SSFR) analogous to "weak" measurements the arrow of time is not changed.

This forces a generalization of thermodynamics and dissipation with opposite arrow of time allows to understand self-organization and also energy feed necessary for it in terms of generalized second law. A system dissipating in non-standard time direction seems from the point of view of the outsider to develop structures and extract energy from the environment. The non-standard arrow of time would be associated with the magnetic body (MB) carrying h_eff=nh₀ phases of ordinary matter identifiable as dark matter and making it a macroscopic quantum system for sufficiently large values of n. MB would act as master of the ordinary matter and induce effective time reversal at the level of ordinary matter in long time scales.

The TGD view about the neural system differs from the standard picture.

1. The first new element is the different role of nerve pulses: they create communication pathways along which dark photons can propagate.
2. Second new element is the presence of linear flux tube structures assignable to neural pathways assignable to linguistic cognition unstable against effective axonal splitting occurring in Alzheimer disease (AD) \citeAlz, and the presence of 2- and even 3-D flux tube structures assignable to geometric and holistic cognition: this would survive in AD (see this) and in states involving cognitive defects (idiot savants). Meridian system and glial cells could relate to this aspect.

   Communications in this system would be based on dark photons transforming to bio-photons and travelling along flux tubes with light velocity. This system would be the predecessor of the neural system and could be realized even in the case of plants. In the neural system the real communications would rely on dark photons - ordinary photons with effective Planck constant h_eff=nh₀>h.

   The communication lines would be dynamical consisting of axonal flux tubes connected by nerve pulse transmission to longer structures serving as wave guides along with dark photons signals would propagate. Metabolic economy could motivate this kind of realization as for electronic communications in modern society. Nerve pulses would only build the connection lines for communications inside the brain. They would however modulate the frequency of Josephson radiation from neuronal membrane to the MB of the brain and in this manner communicate sensory data from cell membrane to MB.

3. According to ZEO based theory of consciousness causal diamond (CD) identified as CD = cd × CP₂ ⊂ H = M⁴× CP₂, where H denotes 8-D imbedding space containing space-time as 4-surface, and cd is the intersection of future and past directed light-cones in 4-D Minkowski space M⁴ and CP₂ is 4-D complex projective space. The passive boundary would correspond to holistic, spatial, and the “timeless” component of conscious experience dominating in meditative states and active boundary to reductionistic, temporal part of conscious experience such as sensory perception and cognition. These components correspond to opposite arrows of time at certain layers of MB.
4. I have considered the realization of the holistic emotional intelligence in terms of the notion of bio-harmony (see this and this). Here one must however remember that emotions could be sensory percepts at the level of MB so that they should correspond to the dynamical aspects of consciousness rather than the permanent part. Music expresses and induces emotions and harmony codes for the emotional state. A model involving icosahedral and tetrahedral symmetries leads to a model that Pitkänen calls bio-harmony: the model predicts correctly the basic aspects of the vertebrate genetic code. The codons would correspond to 3-chords of bio-harmony. The realization of bio-harmony is assigned with magnetic bodies of the basic biomolecules including RNA and DNA.
5. EEG frequencies f>10 Hz assigned to wake-up consciousness could correspond to the effectively 1-D and "linguistic" neural system and frequencies f<10 Hz to the system responsible for holistic aspects. During sleep f<10 Hz dominates so that the consciousness should be holistic. Since we do not remember anything about this period, it could correspond to time reversed mode making possible precognition as sensory perception of signals from geometric future.
6. The effective change of the arrow of time in the neural system induced by its real change at the level of MB could mean the change of the direction of nerve pulse conduction. This reversal could explain phenomena like reverse writing and reverse speech discussed in (see this). There is evidence that AD patients have precognitive and prophetic dreams (for references see the article at Research Gate). Ordinary nerve pulse conduction is prevented in AD by axonal plaque and exponentially attenuated. In the reverse time direction there would be an exponential amplification with respect to standard direction of time. This suggests that AD neurons are dead in standard time direction but re-incarnated in the opposite time direction. Death would be a gradual process.

The proposed hypothesis is testable. To hold true, manipulation of the level of acetylcholinesterase inhibitors (AChEIs) should reduce the formation of past event memory and increase the formation of future oriented precognitive memory traces. Indeed, there is evidence that Rivastigmine, a reversible ACEI used in the treatment of AD, increases memory and rapid eye movement sleep, and has been suggested that aside form those normal properties it could be implicated in retrograde dream formation, i.e., precognitive dreaming (for references see the article at Research Gate). Similar pilot study has yielded same results before (for references see the article at Research Gate).

Further support comes from the bidirectional relationship between AD and sleep disorders through a model of brain rhythm attractor breakdown (for reference see the article at Research Gate). In fact, individual differences were found in prophetic dream belief and experience, with a high frequency of prophetic dream experiences associated with disordered sleep patterns and sleep medication use (for references see the article at Research Gate).

In the sequel this picture is discussed in more detail. In particular, the question how the possibility of non-standard arrow of time could make possible precognition as sensory perception of signals from geometric future, is considered. Our ability to predict our future is usually regarded as trivial. Computationalists explain it by assuming that the brain is a computer predicting the future. This ability could involve this sensory perception in an essential manner.

See the article "Arrow of Time and Neuroscience: TGD Based View" at RG or at homepage , 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.

TGD based view about dark matter at the level of molecular biology

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 - the topic of this posting - and a 2-part article about a model of language.

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 basic idea of the TGD based vision about living matter is that dark matter having effective Planck constant h_eff=nh₀ (h=6h₀) located at the flux tubes of magnetic body controls ordinary matter: MB would be the boss and biological body the slave. This hypothesis can be justified by number theoretic vision about TGD, which unifies ordinary physics as physics of sensory experience described by real number based physics and the physics of cognition based on p-adic number fields: real and various p-adic number fields are fused to adele.

Physical motivations for the TGD notion of dark matter

The notion of dark matter as control of biomatter emerged before its number theoretic justification.

1. The findings of Blackman et al about the effects of ELF radiation (in EEG (electroencephalogram) frequency range) on vertebrate brain led to the hypothesis that besides protons also ions have dark variants having h_eff=nh₀ with h_eff=h_gr.
2. Also electrons could have these phases but now the value of h_eff would be much smaller and satisfy generalized Nottale hypothesis h_eff=h_em, where h_em is the electromagnetic analogue of h_gr assignable to flux tubes assigned with valence bonds. This leads to a model of valence bond (see this) predicting that the value of h_eff/h₀=n=h_em increases along the rows of the periodic table. This would explain why the molecules such as proteins containing atoms towards the right end of the rows serve as carriers of metabolic energy and why biologically important ions like C⁺⁺ are towards the left end of the rows.

   The energy scale of dark variants of valence electrons is proportional to 1/heff² so that the orbital radii are scaled up and the identification as a Rydberg atom is the only possibility in the standard physics picture: could dark valence electrons be in question? There is empirical evidence known for decades for the mysterious disappearance of valence electrons of some rare earth metals. The article " Lifshitz transition from valence fluctuations in YbAl3 by Chatterjee et al published in Nature Communications (see this) discusses the phenomenon for Yb.

   The finding (see this) about misbehaving Ruthenium atoms supports the view that covalent bonds involve dark valence electrons. Pairs of Ru atoms were expected to transform to Ru dimers in thermo-dynamical equilibrium but this did not happen. This suggests that valence electrons associated with the valence bond of Ru dimers are dark in TGD sense and the valence bonded Ru dimer has a higher energy than a pair of free Ru atoms. TGD based explanation (see this) could be justified by a resonant coupling of the dark electron with an ordinary Rydberg state of the valence electron. In the lowest approximation dark valence electron has energies in the spectrum of ordinary valence electrons so that a resonant coupling with Rydberg states can be considered. The evidence found by Randell Mill (see this) for atoms with an abnormally large scale of binding energy suggests the formula h= 6h₀ (see this). Adelic physics (see this) predicts h_eff hierarchy and allows to understand the findings.

3. Nottale hypothesis (see this) introduces the notion of gravitational Planck constant hbar_gr= GMm/v₀ and is in the TGD framework identified as a particular value of h_eff assignable to gravitational flux tubes (see this). One trivial implication reflecting Equivalence Principle is that the cyclotron energy spectrum E_c= nhbar_greB/m= nGMeB/v₀ does not depend on the mass m of the charged particle and is thus universal. The energies involved are proposed to be in the range of biophoton energies (at least) suitable for control of the transitions of bio-molecule.

The difference between non-organic and in-organic matter would be the presence of dark protons and electrons. The notions of acids and bases would reduce to the presence of dark protons: pH would characterize the fraction of dark protons. The notion of reduction and oxidation (REDOX reaction) would reduce to dark electrons associated with valence bonds (see this).

In biochemistry the density of dark protons would be much stronger and Pollack effect it in which the irradiation of water in presence of gel phases generates exclusion zones (EZs) as negatively charged regions by transferring every 4^th proton to dark proton at flux tubes forming dark proton sequences as dark nuclei. Also dark ions become important in biochemistry, at least positively charged ions would have an important control role in TGD based view about biochemistry.

Realization of the vision about MB as controller of ordinary biomatter

M⁸-H duality (see this) concretizes the general vision. This duality states the representability of space- times as a 4-D surfaces in either complexified M⁸ or H=M⁴× CP₂. n=h_eff/h₀ has interpretation as dimetinsion of extension of rationals and would the degree of a polynomial determining the space-time surface in M⁸ as a root of polynomial of degree n. Roots would correspond to different sheets of n-sheeted space-time surface and Galois group of extension would permute the sheets with each other and act as a number theoretic symmetry group. Dark matter states at the flux tubes of B_end would be in representations of Galois group and Galois confinement (see this) forcing n-particle states to behave as single unis like hadrons as color confined states.

The model of bio-harmony (see this and this) based on the icosahedral and tetrahedral geometries in turn predicts that genetic codons correspond to dark photon triplets as 3-chords of lights. The representation of 12-note scale as a sequence of quints reduced by octave equivalence fixes the harmony for a given Hamiltonian cycle and realizes the symmetries of the harmony defined by some subgroup of the icosahedral group.

Combination of 3 icosahedral harmonies with 20 chords and having different symmetries with tetrahedral harmony with 4 chords gives bioharmony 20+20+20+4=64 chords assigned to DNA codons. Amino-acids are identified as orbits of 3-chords under the symmetries of a given harmony, and one obtains 20 amino acids. DNA codons coding for a given amino acid correspond to the chords at the corresponding orbit and the numbers of DNA codons coding for a given amino acid come out correctly.

Bio-harmony assigns the binary aspects of information to the 6 bits of codon and emotional aspects to the bio-harmony characterized by allowed chords fixed by a given Hamiltonian cycle at icosahedron and the unique tetrahedral cycle. The model of bio-harmony requires that the values of B_end correspond to those associated with Pythagorean scale and defined by quint cycle.These frequencies would correspond to energies that a molecule must have to serve as a candidate for a basic biomolecule.

In the model of genetic code (see this) identifying codons as dark proton triplets, the numbers of dark proton triplets correspond to numbers of DNA, RNA, tRNA codons and amino acids and one obtains correctly the numbers of DNA and RNA codons assignable to given amino-acid in the vertebrate genetic code. Genes would correspond to sequences of dark proton triplets. Dark proton triplet would be analogous to baryon and Galois confinement (see this) would force it to behave like a single quantum unit. Dark codons would in turn bind to Galois confined states of the Galois group of extension of the extension associated with the codons.

Galois confinement would be realized also for the dark photon triplets as representation of genetic codons and also for the sequences of N dark-photon representing genes as dark 3N-photon states. Genes would serve as addresses in the communications based on dark 3N-photon resonances. For communications between levels with the same value of h_eff there would be both energy and frequency resonance and for levels with different values of h_eff only energy resonance. It is an open question whether for dark-ordinary communications dark photon 3N-plets transforms to single ordinary biophoton.

The basic hypothesis is that both DNA, RNA, tRNA, and amino acids are paired with their dark analogs, and that energy resonance mediates the interaction between the members of pairs. In this article the goal is to clarify the dark-ordinary pairing and the interaction between the members of the pairs. To achieve this, we first propose some questions below and then synthetize the answers to them.

Questions

In the sequel we will address the following questions about the roles of MB in the biochemistry of the basic biomolecules.

1. Do dark protons appear already in non-organic chemistry? Does acid/base tend to give/bind with a dark proton? The basic process is OH → O^- +H⁺. Water represents the basic example containing ions H₃O⁺ and OH^-: the dark proton from H₂O would bind to the second H₂O acting in the role of base. pH characterizes the fraction of protons equal to 10^-7 for pH=7.

   Does the transition to biochemistry mean Pollack effect (see this) in which the fraction of dark protons becomes 1/4 corresponding to pH= log₁₀(4). This would be the case for DNA, RNA, amino-acids, and tRNA also? Are the transitions between dark and ordinary states a key element of biochemistry. Could the gravitational flux tubes of MB take an active role in biochemistry?

2. Could the proton in hydrogen bond be dark? Could length of the hydrogen bond vary corresponding to different values of h_eff=h_gr. Could this explain the behavior of water below 100 C, in particular at physiological temperatures, challenging the standard thermo-dynamical model.
3. Do dark electrons play a role in chemistry as suggested (see this)? Does oxidation/reduction mean almost giving/receiving a dark valence electron in the valence bond? REDOX reactions are central also in biochemistry. The basic example is combustion in which O==O in presence of hydrocarbon such as sugar C_nH_2n gives rise to CO₂ and H₂O and C_n-1H_2n-2. O is reduced so that it almost receives valence electrons from C and H and C and H are in turn oxidized. The notion of electronegativity parametrizes the tendency to receive an electron. Is it possible to state that in inorganic and organic chemistry the electromagnetic part of MB is by far more important than the gravitational part of MB whereas in biochemistry also the gravitational part becomes important.

   Also ions are proposed to appear as dark variants and one can wonder whether the valence electrons of positively charged biologically important dark ions like Ca⁺⁺ are actually dark.

The following question can be asked about the role of MB in biochemistry of basic biomolecules.

1. Does the energy resonance for dark proton triplets and even for their sequences between biomolecules and their dark variants select the basic biomolecules like DNA, RNA, tRNA, and amino-acids having dark proton counterparts? Base pairs in DNA double strand involve also hydrogen bonds. Could these hydrogen bonds have also dark variants?
2. Dark proton triplets would neutralize the negative charges assignable to the phosphates of DNA and RNA nucleotides and could be imaged as coming from POH→ PO^- +H⁺ by a transformation of proton to dark proton by the analog of Pollack effect making DNA negatively charged.

   What about the cell membrane, whose lipids have also phosphate ions at their ends? Could this give a higher level representation of the genetic code and genes at cell membrane level making possible dark 3N-photon communications between genome and cell membrae? Or do the dark protons serve at least as an energy storage? In fact, it has been proposed that cell membranes could involve a genetic code (see this).

   Microtubules are accompanied by negatively charged GTP molecules possibly associated with tubulins. 6-bit code defined also by DNA codons has been proposed by Hameroff et al as a memory code (see this). Could it be associated with genetic code represented using dark proton triplets?

3. The amino-acids in proteins should pair with dark variants of amino-acids by energy resonance. Amino-acid backbone does not however carry negative charge. Are the dark protons coming from NH₂ and COOH neutralized by electrons so that one would have dark hydrogens?
4. Also the ATP molecule has a negative charge of 3 units. Is it neutralized by a dark proton triplet serving as a temporary storage of metabolic energy? Could this energy at least partially explain the somewhat questionable notion of the high energy phosphate bond (also dark valence electrons would contribute)? Could ATP→ ADP liberate metabolic energy by splitting one dark valence bond and transforming one dark proton to ordinary one? Do the dark protons assigned with the proteins serve as metabolic energy storage besides valence electrons, whose reduced Coulombic binding energies also give rise to higher than expected bond energies?

See the article "The based view about dark matter at the level of molecular biology" at RG or at homepage, 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.