Magnetic body, biophotons, and prediction of scaled variant of EEG

The model for quantum biology relying on the notions of MB and dark matter as hierarchy of phases with h_eff =nh, and biophotons identified as decay produces of dark photons. The assumption h_gr ∝ m becomes highly predictable since cyclotron frequencies would be independent of the mass of the ion.

1. If dark photons with cyclotron frequencies decay to biophotons, one can conclude that biophoton spectrum reflects the spectrum of endogenous magnetic field strengths. In the model of EEG it has been indeed assumed that this kind spectrum is there: the inspiration came from music metaphors suggesting that musical scales are realized in terms of values of magnetic field strength. The new quantum physics associated with gravitation would also become key part of quantum biophysics in TGD Universe.
   
   
2. For the proposed value of h_gr 1 Hz cyclotron frequency associated to DNA sequences would correspond to ordinary photon frequency f=3.6× 10¹⁴ Hz and energy 1.2 eV just at the lower limit of visible frequencies. For 10 Hz alpha band the energy would be 12 eV in UV. This plus the fact that molecular energies are in eV range suggests very simple realization of biochemical control by MB. Each ion has its own cyclotron frequency but same energy for the corresponding biophoton.
   
   
3. Biophoton with a given energy would activate transitions in specific bio-molecules or atoms: ionization energies for atoms except hydrogen have lower bound about 5 eV (see this ). The energies of molecular bonds are in the range 2-10 eV (see this ). If one replaces v₀ with 2v₀ in the estimate, DNA corresponds to .62 eV photon with energy of order metabolic energy currency and alpha band corresponds to 6 eV energy in the molecular region and also in the region of ionization energies.
   

   Each ion at its specific magnetic flux tubes with characteristic palette of magnetic field strengths would resonantly excite some set of biomolecules.This conforms with the earlier vision about dark photon frequencies as passwords.
   

   It could be also that biologically important ions take care of their ionization self. This would be achieved if the magnetic field strength associated with their flux tubes is such that dark cyclotron energy equals to ionization energy. EEG bands labelled by magnetic field strengths could reflect ionization energies for these ions.
   
   

It must be made clear that TGD has had an interpretational problem related to the identification of biophotons as decay product of dark protons. The resolution of this problem leads to conclusion that both Earth's and galactic MBs control living matter with EEG related by scaling. This would be rather dramatic realization of non-locality.

The problem is following. If one wants bio-photon spectrum to be in visible-UV range assuming that bio-photons correspond to cyclotron photons, one must reduce the value of r=h_grB_end/mv₀ for Earth particle system by a factor of order k=2× 10^-4. r does not depend on the mass of the charged particle. One can replace B_end with some other magnetic field having value which is considerably smaller. One can also increase the value of v₀.

1. For h_gr determined by Earth's mass and v₀=v_rot, where v_rot≈ 1.55× 10^-6c is the rotation velocity of Earth around its axis and for B_end→ B_gal= 1 nT, where B_gal is typical strength of galactic magnetic field, the energy of dark cyclotron energy is 45 eV (UV extends to 124 eV). This is roughly by a factor 50 higher than the lower bound for the range of bio-photon energies. One possibility is that B_gal defines the upper limit of the dark photon energies and has variation range of at least 7 octaves with lower limit roughly 1/50 nT.
   

   One can also consider the possibility B_gal defines lower bound for the magnetic field strengths involved and one has v₀>v_rot. For sun the rotation velocity at Equator is v_rot= 2× 10^-5 m/s and v₀ is v₀≈ 5.8× 10^-4c. One has v₀/v_rot≈ 29.0. If same is true in case of Earth, the value of the energy comes down from 25 eV to 1.6 eV which corresponds to visible wave length.
   

   The assignment of B_gal to gravitational flux tubes is very natural. Now however the frequencies of dark variants of bio-photons would not be in EEG range: 10 Hz frequency would correspond to 5× -4 Hz with period of 42 min. The time scale of 42 min is however very natural concerning consciousness and could be involved with longer bio-rhythms. Scaled EEG spectrum with alpha band around 46 min naturally assignable to diurnal sub-rhythms could be a testable prediction. Natural time would be sidereal (galactic) time with slightly different length of day and this allows a clear test. Recall the mysterious looking finding of Spottiswoode that precognition seems to be enhanced at certain time of sidereal day. Cyclotron frequency 1 Hz would correspond to 7 hours. One can ask whether 12 hours (25) is the natural counterpart for the cyclotron frequency 1 Hz assignable to DNA. This would correspond to lower bound B_gal→ 7B_gal/12 ≈ .58 nT or to v₀→ 1.7v₀.
   
   

2. The idea has been that it is dark EEG photons, which correspond to bio-photons. Could one assign bio-photons also to dark EEG so that magnetic fields of Earth and galaxy would correspond to two different control levels? If B_end=.2 Gauss is assumed to determine the scale of the magnetic field associated with the flux tubes carrying gravitational flux tubes, one must reduce h_gr. The reduction could be due to M→ M_D=kM and due to the change of v₀. k could characterize the dark matter portion of Earth but this assumption is not necessary.
   

   This would require k=M_{dark, E}/M_E≈ 5× 10^-5 if one does not change the value of v₀. This value of k equals to the ratio of B_gal/B_end and would be 1/4:th of k=2× 10^-4. One might argue that it is indeed dark matter to which the gravitational flux tubes with large value of Planck constant connect biomatter.
   
   

3. Suppose that one does not give up the idea that also Earth mass gives rise to h_gr and scaled analog of EEG. Then M_D must correspond to some mass distinguishable from and thus outside Earth. The simplest hypothesis is that a spherical layer around Earth is in question. TGD based model for spherical objects indeed predict layered structures. There are two separate anomalies in the solar system supporting the existence of a spherical layer consisting of dark mass and with radius equal to the distance of Moon from Earth equal to 60.3 Earth radii. The first anomaly is so called Flyby anomaly and second one involves a periodic variation of both the value of the measured Newton's constant at the surface of Earth and of the length of the day. The period is about 6 years and TGD predicts it correctly.
   

   One can imagine that dark particles reside at the flux tubes connecting diametrically opposite points of the spherical layer. Particles would experience the sum of gravitational forces summing up to zero in the center of Earth. Although the layer would be almost invisible (or completely invisible by argument utilizing the analogy with conducting shell) gravitationally in its interior, h_gr=M_Dm/v₀ would make itself visible in the dynamics of dark particles! This layer could represent magnetic Mother Gaia and EEG would take care of communications to this layer.
   

   The rotation velocity v_rot,M≈ 2.1× v_rot,E of Moon around its axis is the first guess for the parameter v₀ identifiable perhaps as rotation velocity of the spherical layer. A better guess is that the ratio r=v₀/v_rot,M is the same as for Sun and as assumed above for Earth. This would give for the ratio of cyclotron frequency scales r= (B_end/B_gal)× 2.1. 66.7 min, which corresponds to B_gal= .63 nT, would correspond to .1 s. For this choice 1 Hz DNA cyclotron frequency would correspond 11.7 h rather near to 12 h. This encourages the hypothesis that 72 min is the counterpart of .1 s cyclotron time. The cyclotron time of DNA (very weakly dependent on the length of DNA double strand) in B_gal (or its minimum value) would be 12 h.
   
   

Magnetic body of Earth controlling bio-dynamics would be a dramatic manifestation of non-locality to say nothing about the control performed by galactic magnetic body. M_D would be associated with the magnetic Mother Gaia making life possible at Earth together with magnetic Mother Galactica. Both MBs would be in continual contact with biomolecules like ATP and the molecules for which ATP attaches or provides the phospate. Metabolic energy would be used to this process. These MBs would be Goddesses directing its attention to tiny bio-molecules. If this picture is correct, the ideas about consciousness independent on material substrate and assignable to a running computer program can be safely forgotten.

See the new chapter Non-locality in quantum theory, in biology and neuroscience, and in remote mental interactions: TGD perspective or article with the same title.

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

Further pieces of evidence for the notion of magnetic body

Evidence for the notion of magnetic body (MB) is accumulating. For instance, the recently observed synchrony between hemispheres in absence of corpus callosum (see this) could be understood in terms of MB serving as a "boss" and forcing the two disconnected hemispheres to march in same pace.

Today I learned that humans seem to have sixth sense: kind of sub-conscious magnetic sense of directions (see this) possessed by many animals lower in the evolutionary tree - in particular birds and fishes and also many mammals. There is evidence that also humans but not all of us and not always - seem to respond to magnetic field.

The name of geophysisicist Joe Kirschwink working at CalTech as professor of geobiology iwas already familiar to me. For instance, Kirscwink has introduced the term "snowball Earth". Kirscwink claims that he has proven that also humans have magnetic sense serving as a kind of compass. The experiment involves a slowly rotating constant magnetic field with strength between .25-.6 Gauss (Earth's magnetic field has nominal value of .5 Gauss and the "endogenous" magnetic field appearing in TGD inspired quantum biology has value about .2 Gauss). The field is created by coils located at the walls of a cube so that its direction is under control and it can be also cancelled. The subject person sits in the middle of a Faraday cage eliminating electromagnetic perturbations from environment. EEG of subject person is measured. The explanation for why the earlier experiments often failed is that external perturbations cancelled the effect.

What was found that when the applied field rotates counterclockwise there is a response: the intensity in EEG alpha band drops down. The response however appears few hundred milliseconds later than one would expect if the response is passive response due to the electric currents induced by the applied field in brain. The signal appeared for up-down direction and counter-clockwise rotation but not the opposite. It also appeared when the direction of the field "yawed into the floor". I take "yaw" to mean the orientation angle of magnetic field with respect to the vertical axis.

A slow counterclock-wise rotation of the applied field was necessary. The period of this rotation was not mentioned. The rotation of the applied field could have mimicked the effect produced by the rotation of head with respect to the magnetic field of Earth in good approximation non-rotating in the inertial frame of person. In TGD framework one can ask whether parity breaking effect in macroscopic length scales is involved. What comes in mind is the rotation of the water going down to drain taking always in clocwise direction. Magnetic field obeys same equation as incompressible hydrodyamic flow. Could it be that the magnetic field associated with magnetite sensors in magnetic receptor neurons rotates in clockwise direction much like water going into drain and the response is maximal when the rotation directions are opposite?

One can probably invent purely neuroscientific explanations for the time lag of few hundred milliseconds for EEG response (EEG consists of quasistationary pieces of duration about .3 seconds possibly identifiable as correlates of mental images). In TGD framework the lag could be understood as being due to the fact that the percept is communicated to MB responding by reducing the alpha wave responsible synchronization of the brain. This response could be kind of wake-up from synchrony.

A further piece of evidence for MB comes from NASA (see this). MIT scientists have found what the article calls mysterious "invisible" force field protecting planet's atmosphere by preventing cosmic ray radiation entering to the lower atsmosphere. The field was first noticed by two NASA spacecrafts orbiting in van Allen radiation belt at height of 11,000 km (Earth radius is 6,371 km). The field blocks highly radioactive higher energy electrons. These electrons are attracted towards Earth by the magnetic field of Earth but cannot approach planet closer than 13,300 km - slightly more than twice the Earth radius.

Low frequency electromagnetic fields are involved as with dark matter at magnetic bodies. My guess is that the guardian angel is the magnetic body of Earth carrying dark matter to which one can assign magnetic field strength of .2 Gauss (2/5 of the nominal value of the Earth's magnetic field): actually entire spectrum of values is expected. The flux tubes or sheets carry dark matter and it could absorb the cosmic rays and tame them to Bose-Einstein condensates. For large h_eff=n× h the high energy E of cosmic ray corresponds to very low frequency f= E/h_eff and very long wavelength of order Earth size scale. Ordinary cosmic ray would be transformed to dark cosmic ray with very long wave length. The effect of ordinary cosmic ray is in scale of wavelength and highly local and disastreous for biomolecules like DNA. Now the affect would be absent. Dark magnetic body would act like mattress.

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

Comparing TGD view about quantum biology with McFadden's views

McFadden has very original view about quantum biology: I have written about his work for the first time for years ago, much before the emergence of ZEO, of the recent view about self as generalized Zeno effect, and of the understanding the role of magnetic body containing dark matter (see this). The pleasant surprise was that I now understand McFadden's views much better from TGD viewpoint.

1. McFadden sees decoherence as crucial in biological evolution: here TGD view is diametric opposite although decoherence is a basic phenomenon also in TGD.
   
   
2. McFadden assumes quantum superpositions of different DNAs. To me this looks an unrealistic assumption in the framework of PEO. In ZEO it is quite possible option.
   
   
3. McFadden emphasizes the importance of Zeno effect (in PEO). In TGD the ZEO variant of Zeno effect is central for TGD inspired theory of consciousness and quantum biology. Mc Fadden suggests that quantum effects and Zeno effect are central in bio-catalysis: the repeated measurement keeping reactants in the same position can lead to an increase of reaction rate by factors of order billion. McFadden describe enzymes as quantum mousetraps catching the reactants and forcing them to stay in same position. The above description for how catalysis catches the reactants using U-shaped flux tube conforms with mousetrap picture.
   

   McFadden discusses the action of enzymes in a nice manner and his view conforms with TGD view. In ZEO the system formed by catalyst plus reactants could be described as a negentropically entangled sub-self, and self indeed corresponds to a generalized Zeno effect. The reactions can proceed in shorter scales although the situation is fixed in longer scales (hierarchy of CDs): this would increase the length of the period of time during which reactions can proceed and lead to catalytic effect. Zeno effect in ZEO plus hierarchies of selves and CDs would be essentially for the local aspects of enzyme action.
   
   

4. Protons associated with hydrogen bonds and electronic Cooper pairs play a universal role in McFadden's view and the localization of proton in quantum measurement of its position to hydrogen bond is the key step of enzyme catalysis. Also TGD dark protons at magnetic flux tubes giving rise to dark nuclear strings play a key role. For instance, McFadden models enzyme catalysis as injection of proton to a very special hydrogen bond of substrate. In TGD one has dark protons at magnetic flux tubes and their injection to a properly chosen hydrogen bond and transformation to ordinary proton is crucial for the catalysis. Typical places for reactions to occur are C=O type bonds, where the transition to C-OH can occur and would involve transformation of dark proton to ordinary proton. The transformation of dark proton to ordinary one or vice versa in hydrogen bonds would serve as a biological quantum switch allowing magnetic body to control biochemistry very effectively.
   

   What about electronic Cooper pairs assumed also by McFadden? They would flow along the flux tube pairs. Can Cooper pairs of electrons and dark protons reside at same flux tubes? In principle this is possible although I have considered the possibility that particles with different masses (cyclotron frequencies) reside at different flux tubes. For h_gr =h_eff this would make possible both frequency and energy resonance for cyclotron transitions.
   
   

McFadden has proposed quantum superposition for ordinary codons: This does not seem to make sense in PEO since the chemistries of codons are different) but could make sense in ZEO. In TGD one could indeed imagine quantum entanglement (necessary negentropic in p-adic degrees of freedom) between dark codons. This NE could be either between additional degrees of freedom or between spin degrees of freedom determining the dark codons. In the latter case complete correlation between dark and ordinary DNA codons would imply also the superposition of their tensor products with ordinary codons.

The NE between dark codons could also have a useful function: it could determine physically gene as a union of disjoint mutually entangled portions of DNA. Genes are known to be highly dynamical units, and after pre-transcription splicing selects the portions of the transcript translated to protein. The codons in the complement of the real transcript are called introns and are spliced out from mRNA after the pre-transcription (see this).

What could be the physical criterion telling whether a given codon belongs to exonic or intronic portion of DNA? A possible criterion distinguish between exons and introns is that exons have NE between themselves and introns have no entanglement with exons (also exons could have NE between themselves). Introns would not be useless trash since the division into exonic and exonic region would be dynamical. The interpretation in terms of TGD inspired theory of consciousness is that exons correspond to single self.

An updated nuclear string variant is summarized and also its connection with the model of harmony is discussed in chapter Three new physics realizations of the genetic code and the role of dark matter in bio-systems and in the article About physical representations of genetic code in terms of dark nuclear strings.

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

What about quantum entanglement between codons?

One could also imagine quantum entanglement (necessary negentropic in p-adic degrees of freedom) between codons. This NE could be between additional degrees of freedom or between spin degrees of freedom determining the codons. In the latter case complete correlation between dark and ordinary DNA codons would imply superposition of their tensor products too. This does not seem to make sense in PEO since the chemistries of codons are different) but could make sense in ZEO. McFadden has actually proposed this kind of quantum superposition for ordinary codons: I have compared this vision with TGD views as they were for years ago (see this). Now these views are somewhat out-of-date .

The NE between dark codons could also have a useful function: it could determine physically gene as a union of disjoint mutually entangled portions of DNA. Genes are known to be highly dynamical units, and after pre-transcription splicing selects the portions of the transcript translated to protein. The codons in the complement of the real transcript are called introns and are spliced out from mRNA after the pre-transcription (see this).

What could be the physical criterion telling whether a given codon belongs to exonic or intronic portion of DNA? A possible criterion distinguish between exons and introns is that exons have NE between themselves and introns have no entanglement with exons (also exons could have NE between themselves). Introns would not be useless trash since the division into exonic and exonic region would be dynamical(one can imagine also other reasons for them not being trash). The interpretation in terms of TGD inspired theory of consciousness would be that exons correspond to single self.

An updated nuclear string variant is summarized and also its connection with the model of harmony is discussed in
chapter Three new physics realizations of the genetic code and the role of dark matter in bio-systems and in the article About physical representations of genetic code in terms of dark nuclear strings.

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

Is bio-catalysis a shadow of dark bio-catalysis based on generalization of genetic code?

Protein catalysis and reaction pathways look extremely complex (see this) as compared to replication, transcription, translation, and DNA repair. Could simplicity emerge if biomolecules are identified as chemical shadows of objects formed from dark nuclear strings consisting of dark nucleon triplets and their dynamics is shadow of dark stringy dynamics very much analogous to text processing?

What if bio-catalysis is induced by dark catalysis based on reconnection as recognition mechanism? What if contractions and expansions of U-shaped flux tubes by h_eff increasing phase transitions take that reactants find each other and change conformations as in the case of opening of DNA double strand? What if codes allowing only the dark nucleons with same dark nuclear spin and flux tubes spin to be connected by a pair of flux tubes?

This speculation might make sense! The recognition of reactants is one part of catalytic action. It has been found in vitro RNA selection experiments that RNA sequences are produced having high frequency for the codons which code for the amino-acid that these RNA molecules recognize (this). This is just what the proposal predicts!

Genetic codes DNA to RNA as 64→ 64 map, RNA to tRNA as 64→ 40, tRNA to amino-acids with 40→ 20 map are certainly not enough. One can however consider also additional codes allowed by projections of (4⊕ 2₁⊕ 2₂) ⊗ (5⊕ 3 (⊕ 1)) to lower-dimensional sub-spaces defined by projections preserving spins. One could also visualize bio-molecules as collections of pieces of text attaching to each other along conjugate texts. The properties of catalysts and reactants would also depend by what texts are "visible" to the catalysts. Could the most important biomolecules participating biochemical reactions (proteins, nucleic acids, carbohydrates, lipids, primary and secondary metabolites, and natural products, see this) have dark counterparts in these sub-spaces?

An updated nuclear string variant is summarized and also its connection with the model of harmony is discussed in
chapter Three new physics realizations of the genetic code and the role of dark matter in bio-systems and in the article About physical representations of genetic code in terms of dark nuclear strings.

The selection of bio-active molecules is one of the big mysteries of biology. The model for the chemical pathway leading to the selection of purines as nucleotides (see this) assumes that the predecessor of purine molecule can bind to dark proton without transforming it to ordinary proton. A possible explanation is that the binding energy of the resulting bound state is higher for dark proton than the ordinary one. Minimization of the bound state energy could be a completely general criterion dictating which bio-active molecules can pair with dark protons. The selection of bio-active molecules would not be random after all although it looks so. The proposal for DNA-nuclear/cell membrane as topological quantum computer with quantum computations coded by the braiding of magnetic flux tubes connecting nucleotides to the lipids wlead to the idea that flux tubes being at O=-bonds (see this).

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

Are sound-like bubbles whizzing around in DNA essential to life?

I got a link to a very interesting article about sound waves in DNA (see this). The article tells about THz de-localized modes claimed to propagate forth and back along DNA double strand somewhat like bullets. These modes involve collective motion of many atoms. These modes are interpreted as a change in the stiffness of the DNA double strand leading to the splitting of hydrogen bonds in turn leading to a splitting into single strands. The resulting gap is known as transcriptional bubble propagating along double strand is the outcome. I do not how sound the interpretation as sound wave is.

It has been proposed that sound waves along DNA give rise to the bubble. The local physical properties of DNA double strand such as helical structure and elasticity affect the propagation of the waves. Specific local sequences are proposed to favor a resonance with low frequency vibrational modes, promoting the temperary splitting of the DNA double strand. Inside the bubble the bases are exposed to the surrounding solvent, which has two effects.

Bubbles expose the nucleic acid to reactions of the bases with mutagens in the environment whereas so called molecular intercalators may insert themselves between the strands of DNA. On the other hand, bubbles allow proteins known as helicases to attach to DNA to stabilize the bubble, followed by the splitting the strands to start the transcription and replication process. The splitting would occur at certain portions of DNA double strand. For this reason, it is believed that DNA directs its own transcription.

The problem is that the strong interactions with the surrounding water are expected to damp the sound wave very rapidly. Authors study experimentally the situation and report that propagating bubbles indeed exist for frequencies in few THz region. Therefore the damping deo not seem to be effective. How this is possible? As an innocent layman I also wonder how this kind of mechanism can be selective: it would seem that the bullet like sound wave initiates transcription at many positions along DNA. The transcription should be localized to a region assignable to single gene. What could guarantee this?

Can TGD say anything interesting about the mechanism behind transcription and replication?

1. In TGD magnetic body controls and coordinates the dynamics. The strongest hypothesis is that basic biochemical process are induced by those for dark variants of basic bio-molecules (dark variants of DNA, enzymes,...). The belief that DNA directs its own transcription translates to the statement that the dark DNA consisting most plausibly from sequences of dark proton triplets ppp at dark magnetic flux tubes controls the transcription: the transcription/replication at the level of dark DNA induces that at the level of ordinary DNA.
   
   
2. If the dark DNA codons represented as dark proton triplets (ppp) are connected by 3 flux tube pairs, the reverse of the reconnection should occur and transform flux tube pairs to two U-shaped flux tubes assignable to the two dark DNA strands. Dark proton sequences have positive charge +3e per dark codon giving rise to a repulsive Coulomb force between them. There would be also an attractive force due to magnetic tension of the flux tubes. These two forces would compensate each other in equilibrium (there also the classical forces due to the negatively charged phosphates associated with nucleotides but these would not be so important).
   

   If the flux tube pairs are split, the stabilizing magnetic force however vanishes and the dark flux tubes repel each other and force the negatively charged DNA strands to follow so that also ordinary DNA strand splits and bubble is formed. The primary wave could therefore be the splitting of the flux tube pairs: whether one can call it as a sound wave is not clear to me. Perhaps the induced propagating splitting of ordinary DNA double strand could be regarded as an analog of sound wave.
   

   The splitting of flux tube pairs for a segment of DNA would induces a further splitting of flux tubes since repulsive Coulomb force tends to drive the flux tubes further away. The process could be restricted to DNA if the "upper" end of the split DNA region has some dark DNA codons which are not connected by flux tubes pairs. This model reason why for dark proton sequences.
   
   

3. This model does not yet explain how the propagating splitting wave is initiated. Could a quantum phase transition increasing the value of h_eff associated with the flux tube pairs occur for some minimal portion of dark DNA "below the region associated with gene and lead to the propagating wave induced by the above classical mechanism? That the wave propagates in one direction only could be due to chirality of DNA double helix.

An interesting question is how the RNA world vision relates to this general picture.

1. There are strong conditions on the predecessor of DNA and RNA satisfies many of them: reverse transcription to DNA making possible transition to DNA dominated era is possible. Double stranded RNA exists in cells and makes possible RNA genome: this would however suggest that cell membrane came first. RNA is a catalyst. RNA has ability to conjugate an amino-acid to the 3' end of RNA and RNA catalyzes peptide bond formation essential for translation. RNA can self-replicate but only relatively short sequences are produced.
   
   
2. TGD picture allows to understand why only short sequences of RNA are obtained in replication. If the replication occurs at the level of dark ppn sequences as it would occur for DNA in TGD framework, long RNA sequences might be difficult to produce because of the stopping of the propagation of the primary wave splitting the flux tube pairs. This could be due to the neuron pairs to which there is associated no Coulomb repulsion essential for splitting.
   
   
3. In TGD framework RNA need not be the predecessor of DNA since the evolution would occur at the level of dark nucleon strings and DNA as the dark proton string is the simpest dark nucleon string and might have emerged first. Dark nuclear strings would have served as templates and biomolecules would have emerged naturally via the transcription of their dark counterparts to corresponding bio-polymers.
   
   

An updated nuclear string variant is summarized and also its connection with the model of harmony is discussed in chapter Three new physics realizations of the genetic code and the role of dark matter in bio-systems and in the article About physical representations of genetic code in terms of dark nuclear strings

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

Metabolic energy is not information but is needed to transfer negentropic entanglement

At deep level metabolic energy might correspond to negentropic entanglement (NE) and thus information. Conscious information would be thus the basic currency and the transfer of metabolic energy and metabolites would make possible transfer of NE. It could be transfer of systems consisting of negentropically entangled parts or it could be transfer of NE with larger system, even Earth. Negentropy Maximization Principle (NMP) would force the systems to fight for NE and this would lead to the fight for metabolic resources. The transfer of entanglement (NE) is basic mechanism in quantum computation and would mean in biology stealing of NE, the fundamental crime! Metabolism in TGD framework is discussed in more detail in the article Non-locality in quantum theory, in biology and neuroscience, and in remote mental interactions: TGD perspective.

I have considered three possible three possible identifications of NE.

1. NE could be small scale entanglement - say between parts of molecules. This option is not favored by the needed large values of h_gr and thus of mass M by h_eff= n×h = h_gr= GMm/v₀.
   
   
2. NE could be between nutrient and larger structure - say Earth, Sun, or some other large enough structure to give
   a value of h_gr= GMm/v₀ guaranteeing that dark cyclotron energies (no dependence on mass m) in the range of bio-photon energies (visible and UV) and guarantee that EEG frequencies correspond to these energies (see this). Nutrients would be carriers of both metabolic energy and NE. This option does not conform with the fact that even electrons can provide metabolic energy and in TGD framework therefore also NE for some bacteria (see this). This suggests that nutrients carry only the energy needed to transfer NE.
   
   
   
3. NE could be also between a larger structure and phosphate molecule added to ADP using metabolic energy. This option is the simplest one and would predict that phosphates are in unique role as standard entanglers to mass M. Any source of metabolic energy is in principle possible since metabolic energy is only needed to transfer the flux tube connecting phosphate to mass M to ADP so that ATP is obtained. The flux tube would represent the "high energy phosphate bond". ATP in turn attaches the flux tube to biomolecule, which becomes negentropically entangled. Metabolism would be make the transfer of NE possible. Metabolites would not contain information but it would be assignable to the flux tube between phosphate and mass M.
   
   

A good candidate for the larger structure could be a spherical layer at the distance of Moon from Earth would give correct value for h_eff= h_gr (see this). Magnetic Mother Gaia would have very concrete meaning.

See the new chapter Non-locality in quantum theory, in biology and neuroscience, and in remote mental interactions: TGD perspective or article with the same title.

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

Could dark DNA, RNA, tRNA and amino-acids correspond to different charge states of codons?

If dark codons correspond to dark nucleon triplets as assumed in the following considerations there are 4 basic types of dark nucleon triplets: ppp,ppn, pnn, nnn. Also dark nucleons could represent codons as uuu,uud,udd,ddd: the following discussion generalizes as such also to this case. If strong isospin/em charge decouples from spin the spin content is same independently of the nucleon content. One can consider the possibility of charge neuralization by the charges assignable to color flux tubes but this is not necessarily. In any case, one would have 4 types of nucleon triplets depending on the values of total charges.

Could different dark nucleon total charges correspond to DNA,RNA, tRNA and amino-acids? Already the group representation content - perhaps correlating with quark charges - could allow to distinguish between DNA, RNA, tRNA, and amino-acids. For amino-acids one would have only 4× 5 and ordinary statistics and color singlets. For DNA and RNA one would have full multiplet also color non-singlets and for tRNA one could consider (4⊕ 2₁⊕ 2₂)× 5 containing 40 states. 31 is the minimum number of tRNAs for the realization of the genetic code. The number of tRNA molecules is known to be between 30-40 in bacterial cells. The number is larger in animal cells but this could be due to different chemical representations of dark tRNA codons.

If the net charge of dark codon distinguishes between DNA,RNA, tRNA, and amino-acid sequences, the natural hypothesis to be tested is that dark ppp, ppn, pnn, and nnn sequences are accompanied by DNA,RNA, tRNA, and amino-acid sequences. The dark beta decays of dark protons proposed to play essential role in the model of cold fusion could transform dark protons to dark neurons. Peptide backbones are neutral so that dark nnn sequence could be also absent but the dark nnn option is more natural if the general vision is accepted.

Is this picture consistent with what is known about charges of amino-acids DNA,RNA, tRNA, and amino-acids?

1. DNA strand has one negative charge per nucleotide. Also RNA molecule has high negative charge. This conforms with the idea that dark nucleons accompany both DNA and RNA. DNA codons could be accompanied by dark ppp implying charge neutralization in some scale and RNA codons by dark ppn. The density of negative charge for RNA would be 2/3 for that for DNA.
   
   
2. Arg, His, and Lys have positively charged side chains and Asp,Glu negative side chains (see (see this). The charge state of amino-acid is sensitive to the pH value of solution and its conformation is sensitive to the counter ions present. Total charge for amino-acid in peptide however vanishes unless it is associated with the side chain: as in the case of DNA and RNA it is the backbone whose charge is expected to matter.
   
   
3. Amino-acid has central C atom to which side chain, NH₂, H and COOH are attached. For free amino-acids in solution water solution NH₂→ NH₃⁺ tends to occur pH=2.2 by receiving possibly dark proton whereas COOH tends to become negatively charged above pH= 9.4 by donating proton, which could become dark. In peptide OH attach to C and one H attached to N are replaced with peptide bond. In the pH range 2.2-9.4 amino-acid is zwitterion for which both COOH is negatively charged and NH₂ is replaced with NH₃⁺ so that the net charge vanishes. The simplest interpretation is that the ordinary proton from negatively ionized COOH attaches to NH₂ - maybe via intermediate dark proton state.
   
   
4. The backbones of peptide chains are neutral. This conforms with the idea that dark amino-acid sequence consists of dark neutron triplets. Also free amino-acids would be accompanied by dark neutron triplets. If the statistics is ordinary only 4 dark nnn states are possible as also 5 dark color flux tube spin states.
   
   
5. tRNA could involve dark pnn triplet associated with the codon. An attractive idea is secondary genetic code assigning RNA codons to tRNA-amino-acid complex and projecting 8⊗ (5⊕ 3) containing 64 dark RNA spin states to 8⊗ 5 containing 40 dark tRNA spin states with same total nucleon and flux tube spins. Dark tRNA codons would in turn be attached to dark amino-acids by a tertiary genetic code projecting spin states 8⊗ 5 to 4⊗ 5 by spin projection. In the transcription dark tRNA would attach to dark mRNA inducing attachment of dark amino-acid to the growing amino-acid sequence and tRNA having only dark tRNA codon would be left. The free amino-acids in the water solution would be mostly charged zwitterions in the pH range 2.2-9.4 and the negative charge of COO^- would be help in the attachement of the free amino-acid to the dark proton of tRNA codon. Therefore also the chemistry of free amino-acids would be important.
   

   An interesting question is why pnn triplets for tRNA would only 5 in flux tube degrees of freedom entire 8 in nucleon degrees of freedom. For RNA consisting of ppn triplets also 3 would be possible. What distinguishes between ppn and pnn?
   

An updated nuclear string variant is summarized and also its connection with the model of harmony is discussed in chapter Three new physics realizations of the genetic code and the role of dark matter in bio-systems and in the article About physical representations of genetic code in terms of dark nuclear strings.

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

Non-locality in quantum theory, in biology and neuroscience, and in remote mental interactions: TGD perspective

Non-locality seems to be a basic aspect of what it is to be living. Living system is elementary particle like coherent unit. The phenomenon of memory suggests temporal non-locality. Also remote mental interactions - if real - suggest non-locality. In fact, non-locality - both spatial and temporal - is the basic element of entire quantum TGD, and in particular, of its applications to quantum biology, neuroscience, theory of consciousness, and also of remote mental interactions.

In the sequel I make kind of pseudo deduction of the picture provided by Topological Geometrodynamics (TGD) by starting from empirical findings loosely related to non-locality rather than problems of General Relativity or of particle physics. The hope is that this could make the basic ideas of TGD easier to grasp. Also the mathematical framework and its interpretation as they are now are briefly discussed and the some applications to TGD inspired theory of consciousness and quantum biology are discussed.

See the new chapter Non-locality in quantum theory, in biology and neuroscience, and in remote mental interactions: TGD perspective or article with the same title.

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

Two proposals for physical realization of genetic code predicting correctly the numbers of codons coding given amino-acid

The view about evolution as a random process suggests that genetic code is pure accident. My own view is that something so fundamental as life cannot be based on pure randomness. TGD has led to several proposals for genetic code, its emergence, and various realizations based on purely mathematical considerations or inspired by physical ideas (see this). One can argue that genetic code is realized in several manners just like bits can be represented in very many manners. Two especially interesting proposals have emerged. The first one is based on geometric model of music harmony involving icosahedral and tetrahedral geometries. Second model having two variants is based on dark nuclear strings. Both models predict correctly the numbers of DNA codons coding for a given amino-acid.

For the successful options entire codons rather than letters are represented. The difference between letter-wise representation and codon-wise representations is analogous to that between spoken and written languages. In spoken languages words are not analyzed further to letters.

1. The geometric theory of harmony (see this) represents codons as 3-chords without assigning fixed notes to A,T,C,G and explains also DNA-amino-acid correspondence.
   
   
2. For the first variant of dark nuclear string serves as analog of DNA strand. The map of codons to the dark nucleon states of dark nucleon consisting of dark u and d type quarks does the same and also predicts the degeneracies successfully.
   

   This model can be modified by replacing u and d by dark nucleon states p and n without any change in predictions related to genetic code. The evidence that DNA codons indeed couple to dark nucleon states (see this) supports this option.
   
   

Geometric Theory of Harmony ond Genetic Code

The idea that the 12-note scale could allow mapping to a closed path going through all vertices of icosahedron having 12 vertices and not intersecting itself is attractive. Also the idea that the triangles defining the faces of the icosahedron could have interpretation as 3-chords defining the notion of harmony for a given chord deserves study. The paths in question are known as Hamiltonian cycles and there are 1024 of them (see this. There paths can be classified topologically by the numbers of triangles containing 0, 1, or 2 edges belonging to the cycle representing the scale. Each topology corresponds to particular notion of harmony and there are several topological equivalence classes.

In the article (see this) I introduced the notion of Hamiltonian cycle as a mathematical model for musical harmony and also proposed a connection with biology: motivations came from two observations. The number of icosahedral vertices is 12 and corresponds to the number of notes in 12-note system and the number of triangular faces of icosahedron is 20, the number of amino-acids. This led to a group theoretical model of genetic code and replacement of icosahedron with tetra-icosahedron to explain also the 21st and 22nd amino-acid and solve the problem of simplest model due to the fact that the required Hamilton's cycle does not exist. The outcome was the notion of bioharmony.

All icosahedral Hamilton cycles with symmetries(Z₆,Z₄, Z₂^rot, and Z₂^refl turned out to define harmonies consistent with the genetic code. In particular, it turned out that the symmetries of the Hamiltonian cycles allow to to predict the basic numbers of the genetic code and its extension to include also 21st and 22nd amino-acids Pyl and Sec: there are actually two alternative codes - maybe DNA and its conjugate are talking different dialects! One also ends up with a proposal for what harmony is leading to non-trivial predictions both at DNA and amino-acid level.

The conjecture is that DNA codons correspond to 3-chords perhaps realized in terms of dark photons or even ordinary sound. There are 256 different bio-harmonies and these harmonies would give additional degrees of freedom not reducing to biochemistry. Music expresses and creates emotions and a natural conjecture is that these bio-harmonies are correlates of emotions/moods at bio-molecular level serving as building bricks of more complex moods. Representations of codons as chords with frequencies realized as those of dark photons and also sound is what suggests itself naturally. This together with adelic physics involving hierarchy of algebraic extensions of rationals would explain the mysterious lookin connection between rational numbers defined by ratios of frequencies with emotions.

Mapping DNA and Amino-Acids to Dark Nucleon States

Could dark nuclear strings provide a representation of the genetic code. The answer was totally unexpected: the states of dark nucleons formed from three quarks can be grouped to multiplets in one-one correspondence with 64 DNAs, 64 RNAS, and 20 amino-acids and there is natural mapping of DNA and RNA type states to amino-acid type states such that the numbers of DNAs/RNAs mapped to given amino-acid are same as for the vertebrate genetic code.

The dark model emerged from the attempts to understand water memory (see this) . The outcome was a totally unexpected finding: the states of dark nucleons formed from three quarks connected by color bonds can be naturally grouped to multiplets in one-one correspondence with 64 DNAs, 64 RNAS, 20 amino-acids, and tRNA and there is natural mapping of DNA and RNA type states to amino-acid type states such that the numbers of DNAs/RNAs mapped to given amino-acid are same as for the vertebrate genetic code.

The basic idea is simple. The basic difference from the model of free nucleon is that the nucleons in question - maybe also nuclear nucleons - consist of 3 linearly ordered quarks - just as DNA codons consist of three nucleotides. One might therefore ask whether codons could correspond to dark nucleons obtained as open strings with 3 quarks connected by two color flux tubes or as closed triangles connected by 3 color flux tubes. Only the first option works without additional assumptions. The codons in turn would be connected by color flux tubes having quantum numbers of pion or η.

This representation of the genetic would be based on entanglement rather than letter sequences. Could dark nucleons constructed as string of 3 quarks using color flux tubes realize 64 DNA codons? Could 20 amino-acids be identified as equivalence classes of some equivalence relation between 64 fundamental codons in a natural manner? The codons would be not be anymore separable to letters but entangled states of 3 quarks.

If this picture is correct, genetic code would be realized already at the level of dark nuclear physics and maybe even in ordinary nuclear physics if the nucleons of ordinary nuclear physics are linear nucleons. Chemical realization of genetic code would be induced from the fundamental realization in terms of dark nucleon sequences and vertebrate code would be the most perfect one. Chemistry would be kind of shadow of the dynamics of positively charged dark nucleon strings accompanying the DNA strands and this could explain the stability of DNA strand having 2 units of negative charge per nucleotide. Biochemistry might be controlled by the dark matter at flux tubes.

The ability of the model to explain genetic code in terms of spin pairing is an impressive achievement, which I still find difficult to take seriously.

1. The original model mapping codons to dark nucleon states assumed the overall charge neutrality of the dark proton strings: the idea was that the charges of color bonds cancel the total charge of dark nucleon so that all states uuu, uud,udd, ddd can be considered. The charge itself would not affect the representation of codons. Neutrality assumption is however not necessary. The interpretation as dark nucleus resulting from dark proton string could quite well lead to the formation the analog of ordinary nucleus via dark beta decays (see this) so that the dark nucleus could have charge. Isospin symmetry breaking is assumed so that neither quarks nor flux tubes are assigned to representations of strong SU(2).
   

   There is a possible objection. For ordinary baryon the mass of Δ is much larger than that of proton. The mass splitting could be however much smaller for linear baryons if the mass scale of excitations scales as 1/h_eff as indeed assumed in the model of dark nuclear strings (see this and (see this).
   
   

2. The model assumes that the states of DNA can be described as tensor products of the four 3-quark states with spin content 2⊗ 2⊗ 2= 4⊕ 2₁⊕ 2₂ with the states formed with the 3 spin triplet states 3⊗ 3= 5⊕ 3⊕ 1 with singlet state dropped. The means that flux tubes are spin 1 objects and only spin 2 and spin 1 objects are accepted in the tensor product. One could consider interpretation in terms of ρ meson type bonding or gluon type bonding. With these assumptions the tensor product (2⊗ 2 ⊗ 2) ⊗ (5⊕ 3) contains 8× 8=64 states identified as analags of DNA codons.
   

   The rejection of spin 0 pionic bonds looks strange. These would however occur as bonds connecting dark codons and could correspond to different p-adic length scale as suggested by the successful model of X boson (see this) .
   

   One can also ask why not identify dark nucleon as as closed triangle so that there would be 3 color bonds. In this case 3⊗ 3⊗ 3 would give 27 states instead of 8 (⊕ 1). This option does not look promising.
   
   

3. The model assumes that amino-acids correspond to the states 4× 5 with 4 ∈{4⊕2⊕ 2} and 5∈{5⊕ 3}. One could tensor product of spin 3/2 quark states and spin 2 flux tube states giving 20 states, the number of amino-acids!
   
   
4. Genetic code would be defined by projecting DNA codons with the same total quark and color bond spin projections to the amino-acid with the same (or opposite) spin projections. The attractive force between parallel vortices rotating in opposite directions serves as a metaphor for the idea. This hypothesis allow immediately the calculation of the degeneracies of various spin states. The code projects the states in ( 4⊕ 2⊕ 2)⊗ (5⊕ 3) to the states of 4× 5 with same or opposite spin projection. This would give the degeneracies D(k) as products of numbers D_B∈ {1, 2, 3, 2} and D_b∈ {1, 2, 2, 2, 1} : D= D_B× D_b. Only the observed degeneracies D= 1, 2, 3, 4, 6 are predicted. The numbers N(k) of amino-acids coded by D codons would be
   

   [N(1), N(2), N(3), N(4), N(6)]=[2, 7, 2, 6, 3] .
   

   The correct numbers for vertebrate nuclear code are (N(1), N(2), N(3), N(4), N(6))= (2, 9, 1, 5, 3). Some kind of symmetry breaking must take place and should relate to the emergence of stopping codons. If one codon in second 3-plet becomes stopping codon, the 3-plet becomes doublet. If 2 codons in 4-plet become stopping codons it also becomes doublet and one obtains the correct result (2, 9, 1, 5, 3)!
   

   It is difficult to exaggerate the importance of this simple observation suggesting that genetic code is realized already at the level of dark or even ordinary nuclear physics and bio-chemistry is only a kind of shadow of dark matter physics.
   
   

Mapping DNA and Amino-Acids to Dark 3-Nucleon States

The assumption that entire codon rather than letter corresponds to a state of dark proton does not conform with the model for the origin of purines as DNA nucleotides (see this) assuming that purines and in fact all nucleotides are combined with dark proton unless one assumes that 3 nucleotides combine with the same dark proton. This looks somewhat artificial but cannot be excluded.

Amazingly, the arguments of the model involve only the representations of rotation group and since p and n have same spin as u and d, the arguments generalize to 3- nucleon states (ppp,ppn,pnn,nnn) connected by two color bounds and organized to linear structures. Concerning genetic code, exactly the same predictions follow in the recent formulation of the model. In this case quark color is not present. One could however use the 1-dimensionality and the ordering of dark nucleons as already described.

This variant has several nice features. The model is consistent with the model for dark nucleon strings consisting of nucleons and color bonds between them. There is no need to introduce Δ type nucleon states and colored states are not needed in fermionic sector. Color bonds must be colored if one wants ordinary bosonic statistics for flux tubes but here braid statistics might help. Colored bonds could of course have some important function.

An updated nuclear string variant is summarized and also its connection with the model of harmony is discussed in chapter Three new physics realizations of the genetic code and the role of dark matter in bio-systems and in the article About physical representations of genetic code in terms of dark nuclear strings.

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

About physical representations of genetic code in terms of dark nuclear strings

The standard view about evolution as a random process suggests that genetic code is pure accident. My own view is that something so fundamental as life cannot be based on pure randomness. TGD has led to several proposals for genetic code, its emergence, and various realizations based on purely mathematical considerations or inspired by physical ideas. One can argue that genetic code is realized in several manners just like bits can be represented in very many manners. Two especially interesting proposals have emerged. The first one is based on geometric model of music harmony involving icosahedral and tetrahedral geometries. Second one having two variants is based on dark nuclear strings. Both models predict correctly the numbers of DNA codons coding for a given amino-acid.

An updated nuclear string variant is summarized and also its connection with the model of harmony is discussed in
chapter Three new physics realizations of the genetic code and the role of dark matter in bio-systems and in the article About Physical Representations of Genetic Code in Terms of Dark Nuclear Strings.

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

Is the sum of p-adic negentropies equal to real entropy?

I ended almost by accident to a fascinating and almost trivial theorem. Adelic theorem for information would state that conscious information represented as sum of p-adic negentropies (entropies, which are negative) is equal to real entropy. The more conscious information, the larger the chaos in the environment as everyone can verify by just looking around;-)

This looks bad! Luckily, it turned out that this statement is true for rational probabilities only. For algebraic extensions it cannot be true as is easy to see. That negentropic entanglement is possible only for algebraic extensions of rationals conforms with the vision that algebraic extensions of rationals characterize evolutionary hierarchy. The rationals represent the lowest level at which there either conscious information vanishes or if equal to p-adic contribution to negentropy is companied by equally large real entropy.

It is not completely obvious that the notion of p-adic negentropy indeed makes sense for algebraic extensions of rationals. A possible problem is caused by the fact that the decomposition of algebraic integer to primes is not unique. Simple argument however strongly suggests that the various p-adic norms of the factors do not depend on the factorization. Also a formula for the difference of the total p-adic negentropy and real entropy is deduced.

p-Adic contribution to negentropy equals to real entropy for rational probabilities but not for
algebraic probabilities

The following argument shows that p-adic negentropy equals to real entropy for rational probabilities.

1. The fusion of real physics and various p-adic physics (identified as correlates for cognition, imagination, and intentionality) to single coherent whole leads to what I call adelic physics. Adeles associated with given extension of rationals are Cartesian product of real number field with all p-adic number fields extended by the extension of rationals. Besides algebraic extensions also the extension by any root of e is possible since it induces finite-dimensional p-adic extension. One obtains hierarchy of adeles and of corresponding adelic physics interpreted as an evolutionary hierarchy.
   

   An important point is that p-adic Hilbert spaces exist only if one restricts the p-adic numbers to an algebraic extension of rationals having interpretation as numbers in any number field. This is due to the fact that sum of the p-adic valued probabilities can vanish for general p-adic numbers so that the norm of state can vanish. One can say that the Hilbert space of states is universal and is in the algebraic intersection of reality and various p-adicities.
   
   

2. Negentropy Maximization Principle (NMP) is the variational principle of consciousness in TGD framework reducing to quantum measurement theory in Zero Energy Ontology assuming adelic physics. One can define the p-adic counterparts of Shannon entropy for all finite-dimensional extensions of p-adic numbers, and the amazing fact is that these entropies can be negative and thus serve as measures for information rather than for lack of it. Furthermore, all non-vanishing p-adic negentropies are positive and the number of primes contributing to negentropy is finite since any algebraic number can be expressed using a generalization of prime number decomposition of rational number. These p-adic primes characterize given systen, say elementary particle.
   

   NMP states that the negentropy gain is maximal in the quantum jump defining state function reduction. How does one define the negentropy? As the sum of p-adic negentropies or as the sum of real negative negentropy plus the sum of p-adic negentropies? The latter option I proposed for some time ago without checking what one obtains.
   
   

3. The adelic theorem says that the norm of rational number is equal to the product of the inverses of its p-adic norms. The statement that the sum of real and p-adic negentropies is zero follows more or less as a statement that the logarithms of real norm and the product of p-adic norms for prime factors of rational sum up to zero.
   

   The core formula is adelic formula stating that the real norm of rational number is product of its p-adic norms. This implies that the logarithm of the rational number is sum over the logarithms of its p-adic norms. Since in p-adic entropy assigned to prime p logarithms of probabilities are replaced by their p-adic norms, this implies that for rational probabilities the real entropy equals to p-adic negentropy. If real entropy is counted as conscious information, the negentropy vanishes identically for rational probabilities.
   

   It would seem that the negentropy appearing in the definition of NMP must be the sum of p-adic negentropies and real entropy should have interpretation as a measure for ignorance about the state of either entangled system. The sum of p-adic negentropies would serve as a measure for the information carried by a rule with superposed state pairs representingt the instances of the rule. The information would be conscious information and carried by the negentropically entangled system.
   
   

4. What about probabilities in algebraic extensions? The probabilities are now algebraic numbers. Below
   an argument is develoed that the p-adic norms of of probabilities are uniquely defined and are always powers of primes so that the adelic formula cannot be true since on the real side one has logarithms of algebraic numbers and on the p-adic side only logarithms of primes.
   

   What could be the interpretation?
   
   

   1. If conscious information corresponds to N-P, it accompanies the emergence of algebraic extensions of rationals at the level of Hilbert space.
      
      
   2. If N corresponds to conscious information, then at the lowest level conscious information is necessary accompanied by entropy but for algebraic extensions N-P could be positive since N is maximized. This option looks more plausible.
      
      
   One however expects that the value of real entropy correlates strongly with the value of negentropy. One expects that the value of real entropy correlates strongly with the value ofp-adic total negentropy. This would conform with the observation that large entropy seems to be a prerequisite for life by providing large number of states with degenerate energies providing large representative capacity. For instance, Jeremy England has made this proposal: I have commented this proposal from TGD point of view.

Formula for the difference of total p-adic negentropy and real entanglement entropy

In the following some non-trivial details related to the definition of p-adic norms for the rationals in the algebraic extension of rationals are discussed.

The induced p-adic norm N_p(x) for n-dimensional extension of Q is defined as the determinant det(x) of the linear map defined by multiplication with x. det(x) is rational number. The corresponding p-adic norm is defined as the n:th root N_p(det(x))^1/n of the ordinary p-adic norm. Root guarantees that the norm co-incides with the ordinary p-adic norm for ordinary p-adic integers. One must perform now a factorization to algebraic primes. Below an argument is given that although the factorization to primes is not always unique, the product of p-adic norms for given algebraic rational defined as ratio of algebraic integers is unique.

Can one write an explicit formula the difference of total p-adic entanglement negentropy (positive) and real entanglement entropy using prime factorization in finite dimensional algebraic extension (note that for algebraic numbers defining infinite-dimensional extension of rationals factorization does not even exist since one can write a=a^1/2a^1/2=...)? This requires that total p-adic entropy is uniquely defined. There is a possible problem due to the non-uniqueness of the prime factorization.

1. For Dedekind rings, in particular rings of integers, there exists by definition a unique factorization of proper ideals to prime ideals (see this). In contrast, the prime factorization in the extensions of Q is not always unique. Already for Q((-5)^1/2) one has 6=2× 3= (1+(-5)^1/2)(1-(-5)^1/2) and the primes involved are not related by multiplication with units.
   

   Various factorizations are characterized by so called class group and class field theory is the branch of number theory studying factorizations in algebraic extensions of integer rings. Factorization is by definition unique for Euclidian domains. Euclidian domains allow by definition so called Euclidian function f(x) having values in R₊ with the property that for any a and b one has either a=qb or a= qb+r with f(r)<f(b). It seems that one cannot restrict to Euclidian domains in the recent situation.
   
   

2. Even when the factorization in the extension is not unique, one can hope that the product of various p-adic norms for the factors is same for all factorizations. Since the p-adic norm for the extensions of primes is induced by ordinary p-adic number this requires that the p-adic prime for which the induced p-adic norm differs from unity are same for all factorizations and that the products of p-adic norms differing from unity are same. This independence on the representative for factorization would be analogous to gauge invariance in physicist's conceptualization.
   

   The probabilities P_k belongs to a unique product of ideals labelled by primes of extension. The ideals are characterized by norms and if this norm is product of p-adic norms for any prime factorization as looks natural then the independence on the factorization follows. Number theorist can certainly immediately tell whether this is true. What is encouraging that for Q((-5)^1/2) z=x+(-5)^1/2y has determinant det(z)=x²+5y² and for z==1+/- (-5)^1/2 one has has det(z)=6 so that for the products of p-adic norms for the factorizations 6=2× 3 and (1+(-5)^1/2)(1-(-5)^1/2) are equal.
   
   

3. If this guess is true, one can write the the difference of total p-adic negentropy N and real entanglement entropy S as
   

   N-S= ∑ P_k log(P_k/∏_p N_p(P_k)) .
   

   Here ∏_p N_p(P_k) would not depend on particular factorization. The condition ∑ P_k=1 poses an additional condition. It would be nice to understand whether N-S≥ 0 holds true generally and if not, what are the conditions guaranteeing this. The p-adic numbers of numerators of rationals involved give positive contributions to N-S as the example P_k=1/N in rational case shows.
   
   

See the article Is the sum of p-adic negentropies equal to real entropy? or the chapter Negentropy Maximization Principle of "TGD Inspired Theory of Consciousness".

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

X boson anomaly and its relation to LHC anomalies

For more than week I have had no time to write blog posts. Preparing an article about X boson took most of my time but was an enjoyable process of discovery proceeding via trial and error as processes of discovery usually do.

1. The key observation was that the X boson (see this, this, this, and previous posting) has just the same mass of 17 MeV as the pion of hadron physics scaled down to nuclear p-adic length scale from hadronic scale (k=107) to nuclear scale (k=113). Recall that p-adic prime is near to 2^k, k positive integer with primes preferred and Mersenne primes especially preferred.
   
   
2. The problem was that I first believed the claim that X cannot be a pseudoscalar but is spin 1 particle. The claim was based on limits on its decay rate to gamma pair. I checked what the rate would be by scaling the decay rate of pion and found that the situation is indeed this. I had however made a stupid calculational blunder - probably under hypnotic suggestion of the X boson article - and only later realized that the decay rate to gamma pairs is below the upper limit. X is k=113 pion!
   
   
3. The decay rate of k=113 pion to e⁺e- pairs as predicted by the scaling of the standard model for the decays of ordinary pion assuming that the decay is mediated by creation of virtual gamma pair gave however too slow rate by a factor 1/100. As a matter of fact, also for ordinary pion the predicted rate is somewhat too low already order of magnitude comes out correctly and even leptoquarks have been discussed as an alternative decay mode since decay via axial coupling the intermediate Z boson has quite too low rate.
   
   
4. It took time to realize that here is the order for as p-adically scaled down variant of weak interactions. Pion couples to the axial current, which couples to Z boson, which decays to e⁺e^- pair. The decay of pion could correspond to the decay to virtual timelike Z boson decaying to e⁺ee^- pair! It turned out that if Z correspond to nuclear p-adic scale k=113 the rate is within the general experimental limits. If it corresponds to k=114 - still nuclear scale but does not correspond correspond to Gaussian Mersenne - a resonance takes place and the rate is in the middle of the interval defining stronger bounds proposed in the article proposing that X boson is prophobic spin 1 boson mediating fifth force. Also the dark variant of M₈₉ weak physics with Z effectively massless within the scaled up Compton length gives a rate within the weak bounds.
   
   
5. This also leads to a new understanding about semileptonic decays of hadrons since also ordinary mesons could decay to leptons via the same mechanism. p-Adically scaled down or dark weak interaction physics would be realized both in nuclear and hadronic scales! When I started to work with CP₂ for about 35 years ago, the frustrating observation was that classical weak boson fields and color gauge fields appear in all scales. This was in complete conflict with standard wisdom. Now it is becoming clear that these physics are there in preferred p-adic scales! Mandelbrot meets particle physics! Weak symmetries predict the decay rate ratios of charged and weak mesons and this together with p-adic scaling of weak boson and pion masses gives a powerful test for the scenario.
   
   
6. What is also nice that the picture conforms with the number theoretic vision about scattering amplitudes, which suggests that all scattering diagrams understood in topological sense for generalized Feynman diagrams having lines thickened to 4-manifolds should be transformable to tree diagrams and with quantum criticality plus number theoretic vision demanding that the functional integral over WCW gives vanishing loop correction and coupling constant evolution reduces to discrete p-adic coupling constant evolution with piecewise constant coupling constants. Indeed, I ended up with new mechanism of pion decay from the requirement that the diagram in question is tree diagram. The transformation of box diagrams involved with the CP breaking to non-loopy tree diagrams provides a killer test for this vision.
   
   
7. There is also consistency with M⁸-M⁴× CP₂ duality in the sense that color group acting in CP₂ is replaced with SO(4) group acting in M⁴× E⁴. M⁸ corresponds in twistor approach naturally to the tangent space of M⁴× CP₂ and 4-D momenta are replaced to M⁸, which naturally lead to M⁴ momenta and SO(4) quantum numbers as one forms partial wave in E⁴ degrees of freedom. Some particle physicist might still remember that SO(4) is the symmetry group of low energy hadron physics. One can understand conserved vector current hypothesis (CVC) and partially conserved axial current hypothesis (PCAC) in this framework and scaled variants of weak physics make the picture very concrete.
   
   

The incredible sounding conclusion is that three (3!) new p-adically scaled hadron physics - M₈₉ (most low-lying mesons including also ρ meson besides scalar mesons appear as bumps with 750 GeV state identified as eta type meson), M_G,79 (pion like bump around 2 GeV), and the nuclear M_G,113 (X boson as pion like state) are showing themselves besides the old M₁₀₇!

Event better, also scaled variants of weak physics are showing up. Ordinary k=89 weak physics scaled down to nuclear p-adic scale k=113 or k=114 makes itself visible via X boson decays to e⁺e- pairs and k=107 in the decays of the ordinary pion. There is also evidence for the Higgs associated with second generation weak bosons assignable to M_G,79 as bump at 4 GeV.

Clearly, the fractal TGD Universe is making itself visible in a spectacular manner. Colleagues have no other way than to give up and admit that committees cannot decide about world views. Theoretician could not hope a better prize for the work of almost four decades!

For details see the article X boson as evidence for nuclear string model or the chapter Nuclear string model of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy".

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