Does the model of bioharmony explain the major and minor scales?

The details of the bioharmony model have remained unclear. Bioharmony model (see this and this) predicts that 64 genetic codons can be identified as 64 3-chords as faces of 3 copies of icosahedron and one tetrahedron. This structure emerges from icosa tetrahedral tessellation (ITT) (see this this). There is an intriguing correspondence with the TGD based model for the icosahedral supercluster of water molecules and the supercluster is proposed to be in 1-1 correspondence with the realization of ITT at the field body of the system in terms of dark DNA (see this). The recent finding that animals communicated in frequency range peaked around 2 Hz gives additional support for the model (see this).

There are however long standing objections against the bioharmony model. In particular, the model predicts 12-note scale and complex bio-harmonies with 64 3-chords but does it allow us to understand the simplest major and minor scales and corresponding 3-chords?

1. Quint cycle modulo octave equivalence gives the notes of 12-note scale. This scale can be deformed to well-tempered scales in which notes correspond to powers of 2^1/12 modulo octave equivalence. The cycle FCGDAEH gives the notes of the major scale. 3 + 1/2 octaves are involved. Note that the quint cycle spans the note-scale of classical guitar. Also the minor scale is obtained. What remains missing are the altered notes F_# and G_#.

   Interestingly, the recent findings about animal communications containing frequency range .5 Hz -4 Hz and also higher frequencies are consistent with the range of 3 and 1/2 octaves (see this).

   If the quint cycle is continued, notes which do not belong to the basic scale appear and eventually give the 12-note scale. One can say that the standard scale emerges naturally.

2. What about the icosahedral 3-chords assuming a quint cycle? The edges of a face (triangle) contained in the Hamilton cycle correspond to quints. The number of quints per triangle is n=0,1,2. 3 quints would mean that the cycle intersects itself. Also triangles sharing no edges with the Hamilton cycle are possible.

   The problem is that the icosahedral part of the bioharmony does not contain in a natural way major and minor chords containing minor third (e.g. CEG and ACE).

Could the tetrahedral part of the bioharmony come to rescue? One can consider several options for tetrahedral harmony. The basic condition is that one obtains the major and minor chords. This is true if the tetrahedral scale contains edges defining minor third, major third and quint.

1. For the first option the tetrahedron does not share faces with the icosahedron and the tetrahedral Hamilton cycle is closed and corresponds to an octave. The simplest assumption is that the edges of the cycle correspond to minor thirds but one can also consider other options. 2 edges do not belong to the cycle. The notes of the 4-note cycle starting from A correspond to ACE_bF_#A. This does not allow chords containing minor third and major third.

   It seems that one must give up the ACE_bF_#A scale. The tetrahedral cycle CGEAC however satisfies the constraints: the faces contain quint CG, major third CE, and minor thirds AC and EG. The 4 tetrahedral chords are CEG(major), ACE (minor), and AGC and EAG.

2. During years I have considered many proposals for how the icosahedral and tetrahedral harmonies could be fused together. Tetrahedron has only a single Hamilton cycle. The notion of key is however essential when the scale is not the full 12-note scale, especially so when no modified notes are involved. The key distinguishes between different tetrahedral harmonies differing by transposition. The key for the tetrahedral chords could be determined by assigning the tetrahedron to a single note of icosahedral 12-note scale. Does this have a geometric interpretation? For instance, do the icosahedron and tetrahedron share a single vertex? This would allow 64 chords.

See the article Universal rhythm for communications between animals? or the chapter The recent view of TGD inspired theory of consciousness and quantum biology.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Lagrange points and consciousness?

I received a highly interesting email from a person with the signature "Larry". It contained a lot of links to topics related to plasmoids. I have been talking for a couple of decades about plasmoids as primitive life forms preceding biological life. Ball lightning and "UFO"s would be plasmoids in the TGD framework. The empirical findings of NASA in the ionosphere provide support for the notion (see this). TGD strongly suggests a universal representation of genetic code (see for instance this and this). Even plasmoids could have this universal genetic code.

The mail told about Kordylewski Plasma clouds appearing at two opposite sides of the Moon at the Lagrange points (see this) for the Moon-Earth gravitational field which are stationary and therefore minima of the gradient of the effective potential characterizing gravitational potential plus effective centrifugal force. There are 5 Lagrange points in any system involving a small mass in the gravitational field of two massive bodies with a sufficiently large mass ratio. Two of them are along the line connecting the massive bodies at opposite sides of the larger body. Small objects can form stationary orbits around the stable Lagrange points: Trojan asteroids are such objects. The properties of Lagrange points make them very special in the space technology.

I have not thought about Lagrange points in the TGD context earlier but Kordylewski Plasma clouds (this) associated with the Moon look forces this. The gravitational magnetic bodies of the Sun, Earth and Moon (at least them) and carrying dark phases of ordinary matter are key objects TGD inspired theory of quantum biology and consciousness. These field bodies consist of U-shaped monopole flux tubes forming kinds of tentacable and would control our biological body.

Our own personal field/magnetic bodies would be in contact with these gravitational field bodies also with each other: this would make possible the generation quantum entanglement (see for instance this). Because of the higher level of cognitive consciousness measured by the values gravitational and electric Planck constants, these life forms have a higher level of cognition: some people might even speak of "soul".

Both dark ions and ordinary matter in the plasma phase could form stationary gravitationally bound states around Lagrange points. I have proposed plasma life to be a predecessor of ordinary life. It could reside around Lagrange points. Could the Lagrange points for the Earth-Sun and Moon-Earth system be of special interest: could our gravitomagnetic "souls" reside there? Could one speak of "souls" assignable to the Lagrange points of the Earth-Sun and Earth-Moon system? Is this assignment either-or or are both components present in our gravitomagnetic body. Can either of these modes dominate some aspects of our behavior and conscious experience? What could distinguish between them? I must admit that I have difficulties to avoid the association to male-female dichotomy in this context.

During solar eclipses, the Lagrange points of the Earth-Moon and Earth-Sun system are along the same line. Could something strange happen then: could this relate to Allais anomaly (see this)? Does something special happen during the full Moon when the Earth is between Sun and Moon and the Moon has a solar eclipse?

See the article A possible TGD based narrative for how life might have evolved or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Could the "4-ghost" discovered at LHC provide support for the holography = holomorphy principle of TGD

A 4-D resonant magnetic anomaly, called "4- ghost" has been discovered at LHC (see this). There is article about the finding in Nature Physics (see this").

The popular article describes the finding as follows.

The Ghost," has been detected within the Large Hadron Collider, the world’s most advanced particle research facility. It is disrupting particle paths in a way that current physics models cannot explain. The force is producing measurable, reproducible disruptions that challenge our fundamental understanding of reality.

This does not tell much. H. Bartosik, G. Franchetti & F. Schmidt have published an article with title "Observation of fixed lines induced by a nonlinear resonance in the CERN Super Proton Synchrotron" in Nature Physics. The abstract of the article allows to get some idea of the mysterious 4-D force.

The motion of systems with linear restoring forces and recurring nonlinear perturbations is of central importance in physics. When a system’s natural oscillation frequencies and the frequency of the nonlinear restoring forces satisfy certain algebraic relations, the dynamics become resonant.

In accelerator physics, an understanding of resonances and nonlinear dynamics is crucial for avoiding the loss of beam particles. Here we confirm the theoretical prediction of the dynamics for a single two-dimensional coupled resonance by observing so-called fixed lines.

Specifically, we use the CERN Super Proton Synchrotron to measure the position of a particle beam at discrete locations around the accelerator. These measurements allow us to construct the Poincaré surface of section, which captures the main features of the dynamics in a periodic system.

In our setting, any resonant particle passing through the Poincaré surface of section lies on a curve embedded in a four-dimensional phase space, the fixed line. These findings are relevant for mitigating beam degradation and thus for achieving high-intensity and high-brightness beams, as required for both current and future accelerator projects.

The popular article suggests new exotic physics and the Nature article suggests that standard physics is enough to understand the findings. Which source you should believe? This question emerges repeatedly during the period of science hype. The best answer is "Do not believe either source: think by yourself!".

In the TGD framework, one can ask whether the the finding could provide support for the slightly non-deterministic holography = holomorphy principle defining the basic dynamical principle of TGD (see for instance this and this). In TGD, space-time surfaces in 8-D M⁴×CP₂ as analogs of Bohr orbits for 3-D particles replace string world sheets of string models. Holography = holomorphy principle allows to solve field equations explicitly and reduce them to algebraic equations at the fundamental level at which the general relativistic space-time is replaced with space-time surfaces which quite concretely correspond to what we see around us.

The solutions of field equations are slightly non-deterministic and analogous to 4-D minimal surfaces. Already 2-D minimal surfaces (soap films) are slightly non-deterministic: sevel of them are spanned by the same frame.

This leads to a profound revision of the construction of scattering amplitudes (see this, this, this, this). There is no path integral and associated divergences. The motion of the 3-surfaces representing holographic data can be regarded as an analog of Brownian motion in H=M⁴×CP₂ and the edges of the Brownian curve define the counterparts of vertices.

Concerning the strange 4-D force: magnetic monopole flux tubes are key entities of the TGD Universe in all scales and magnetic fields are involved in these experiments. Could the discrete non-deterministic degrees of freedom make the basic system effectively 4-D and give rise to the mysterious 4-D force. Ironically, this mysterious 4-D force makes possible non-trivial scattering amplitudes in the TGD universe but only in space-time dimension D=4.

See for instance the article TGD counterpart of Feynman diagrammatics with application to QFT limit and CP violation.

Have we already observed the variants of Mk hadron physics for k>107?

TGD predicts besides M₈₉ hadron physics as a scaled up version of the ordinary hadron physics also k>107 hadron physics. Suppose that only Mersenne primes and their Gaussian counterparts correspond to these hadron physics (primes near prime powers two cannot be excluded). For k>107, only the Mersenne prime k=127 associated also with the electron defines a p-adic length scale, which is not super-astronomical. There are several Gaussian primes corresponding to k∈ {113,151,157,163,167}. k=113 corresponds to the nuclear length scale and k∈ {151,157,163,167} to 4 miracle length scales in the range 10 nm-2.5 μm, which in the TGD framework would be important for cell nucleus and DNA.

Could all these length scales correspond to scaled copies of hadron physics with k>107?

1. For TGD analog of quark gluon phase quarks are massless in the sense that they satisfy the massless induced Dirac equations at the space-time surface X⁴. In this phase the quarks do not "know" which p-adic length scale they correspond to. In hadronization they become fermions satisfying the Dirac equation either in the embedding space H=M⁴× CP₂ or inside the causal diamond CD= cd× CP₂ serving the role of quantization volume. It is not clear which of these options is correct.
2. In hadronization fundamental quarks transform to color partial waves in CP₂ and correspond to a color multiplet in CP₂. This process occurs also for leptons. Quarks form color triplets and these in turn combine to color singlets. This proves involves formation of tachyonic states reducing the mass scale from the CP₂ scale of fundamental quarks to the mass scale of the physical quarks in hadrons and to the hadronic mass scale.

   Hadronization can take place to any color multiplet (quark-like or leptonic) so that a hierarchy of scaled variants of hadron physics is predicted. M₈₉ hadron physics is the hadron physics for this there are indications at LHC and RHIC.

3. Dark M₈₉ hadrons are created in the TGD counterpart of quark-gluon plasma emerging at quantum criticality. The assumption that ratio h_eff(89)/h of the effective Planck constants equals the ratio of L(107)/L(89)= 2⁹ guarantees that the Compton lengths of M₈₉ and M₁₀₇ hadrons are identical. This is natural at quantum criticality.

The quarks of hadron physics with k>107 can also combine also to dark hadrons of M₁₀₇ hadron physics in such a way that they have Compton lengths of hadrons of M_k hadron physics for k>107 but have masses of ordinary hadrons. What kind of predictions does this give.

1. Nuclei correspond to Gaussian Mersenne k=113 and have p-adic length scale about L(113)=8L(107)∼ 10^-8 m. Could the nucleons inside nuclei be dark nuclei with Compton length many particles states of dark nuclei?

   What does this predict? M₈₉ hadrons can decay to ordinary hadrons, say pions. In the same way, dark M₁₀₇ hadrons can decay to pions of M₈₉ hadron physics. The mass of M₈₉ pion is m(π)/8∼ 17.5 MeV. This is precisely the mass of the particle observed and interpreted in terms of the fifth force (see this). Also other M₈₉ mesons should be found.

2. The TGD based model for "cold fusion" as dark fusion leads to the proposal that the process occurs at quantum criticality in which phases with non-standard value of h_eff>h are formed. The Compton length scale of dark nucleons corresponds to M₁₂₇ defining the Compton length scale of electrons. Could this mean that dark fusion corresponds to the formation of dark hadrons assignable to M₁₂₇. This would make possible the overlap of nucleons and allow it to overcome the Coulomb wall and in this way make possible "cold fusion" (see this, this, this, and this). This process could occur also in ordinary nuclear reactions and make possible quantum tunnelling through the Coulomb wall. If so the standard model assuming that the energy production of the Sun occurs at hot core, could be wong and this model indeed has numerous anomalies. In the TGD framework this leads to a model of the Sun in which solar energy and solar wind are produced in a transformation of M₈₉ nuclei to ordinary nuclei which experience "cold fusion" to ordinary nuclei (see this).

   One particular testable signature of the model would be the production of M₁₂₇ pions decaying to gamma pairs with total energy of .14 MeV. Also other M₁₂₇ mesons are produced.

3. The TGD based quantum biology could rely on ordinary dark nuclei associated with the number theoretical miracle defined by the 4 closely spaced Gaussian Mersennes with k∈ {151,157,163,167}. The signature would be gamma pairs produced by the decays of the pions of the hadron physics in question with a total energy equal to the mass of the pion. Their masses are {8 keV, 1 keV, .25 keV, 3.125 eV} and it should be possible to test this prediction. There are indeed empirical indications that quarks play a role in biology. Topologist Barbara Shipman (see for instance this) developed a model of honeybee dance, which paradoxically suggested that quark color could play a key role in biology. This led to the TGD based model for what might be involved (see this and this). If his proposal is correct, all 4 dark variants of hadron physics would play a key role in the quantum physics of cell nucleus and DNA.

See the article TGD counterpart of Feynman diagrammatics with application to QFT limit and CP violation or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

An improved version of the dark genetic code

The condition that the dark protons are stably dark implies that they cannot represent analogs of topological qubits formed by the pair of states -OH and -O^- plus dark proton at the monopole flux tube. The formation of dark nuclei would make dark proton sequences energetically stable and explain the negative charge of DNA and RNA strands and predict an evolutionary hierachy of values of electric Planck constant h_em assignable to the genes (see this, this, this and this). This forces to ask whether -OH and -O^- plus dark proton state pair can define an analog of topological qubit. Pollack effect would however play key role in metabolism and biocatalysis.

This forces to reconsider the model of the dark variant of the genetic code. The basic condition is that the dark codons are in 1-1 correspondence with the ordinary codons.

1. Each nucleotide (letter of the codon) should give rise to 2 bits. In the case of DNA codons the problem is that the only obvious quantum number for proton is its spin (I have earlier considered also other options but with no obvious success). The large value of h_eff=h_em would make proton spin a qubit and make possible quantum computation like activities.

   How to get the additional bit? I have already earlier proposed that the dark base pairs represent the letters of the dark codons. If the spins of the dark protons for codon and its conjugate are independent, this gives two bits and 4 letters. This would give an additional reason for why two DNA strands are necessary although the second strand is passive.

   I have also proposed that the dark codons make possible a kind of R\&D lab \cite{btart/evogene,icosacluster}. One can think that the spins of dark protons pairs can act as qubit pairs making possible quantum compution type activities. They would interact with the ordinary codons only when they correspond to the same codons. The interaction would be via dark cyclotron multi-photons transforming to ordinary photons and acting resonantly with the ordinary codons.

2. In the case of RNA one has only a single strand. Dark code would have only two letters so that the number of codons would be only 2³=8. I have proposed that the -OH group of the ribose ring distinguishes RNA from DNA transforms to -O^- plus a dark proton so that there would be two dark protons per letter.

   If the dark protons of mRNA letters are able to stay at the monopole flux during the transcription and translation, the needed two bits per letter are obtained for mRNA. The time scale of transcription is 2-3 minutes for a typical gene and 1 minute for translation. Could one think that in the case of ribozymes acting as catalysts the dark proton stays at the flux tube only the time necessary for the process to occur? Could metabolic energy feed induce Pollack effect kicking the dark protons of the first two RNA letters from the -OH group to the monopole flux tube?

   The first 2 2-bit RNA letters would have charge -2. The standard belief is that they have charge -1. It might be easy to test whether this is the case also during transcription and translation and ribozyme catalysis.

3. DNA codons have an almost symmetry. For most mRNA codons the codons for which the third letter is A or G code for the same amino acid. There is however a small violation of the A-G symmetry. In the standard code there are two exceptions. The AUA-AUG pair corresponds to an ile-met pair rather than an ile-ile pair. The UGA-UGG pair corresponds to stop-trp pair rather than a stop-stop pair.

   Met is exceptional in that it is coded by the start codon in the transcription. Also trp is considered as an exceptional, unique, and rare amino acid among the 20 standard amino acids. Trp is special due to its structural complexity, low abundance, high energy cost to synthesize, and its critical role as a precursor to vital bioactive compounds.

   Trp is found at critical locations in protein structures such as protein-protein interfaces and the lipid-water interface of membrane proteins. Could the additional dark proton serve as an additional bit informing about the existence of the interface?

See the article How the genetic code is realized at the level of the magnetic body of DNA double strand? or the chapter About honeycombs of hyperbolic 3-space and their relation to the genetic code .

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Universal rhythm for communications between animals

I learned about a fascinating finding discussed in Neuroscience News). The popular article discusses the findings reported in the article "A widespread animal communication tempo may resonate with the receiver's brain" by Guy Amichay, Vijay Balasubramanian, and Daniel M. Abrams in journal PLOS Biology (see this).

The study reveals that communication signals across wildly different species tend to repeat at a nearly universal tempo of 2 hertz (two beats per second). Researchers suggest this isn t a coincidence, but a biological resonance where animal brains are naturally tuned to process information most efficiently at this specific pace. This 2 Hz rule applies to social communications of animals from insects to large mammals and does not depend on the physical size of the animal. Neural circuits respond strongly to signals in the .5-4.0 Hz band. Also faster signalling is possible. What is interesting is that most popular music clusters around 2 Hz. This is remarkable since animal communications can look wildly different flashing lights, chirping calls, croaking songs and elaborate dances. It should be noticed that audible frequencies in the case of humans are above 20 Hz.

One of the basic predictions of TGD inspired quantum biology is magnetic bodies (counterparts of Maxwellian magnetic fields), carrying phases of ordinary matter with a large value of effective Planck constant and therefore behaving like dark matter, are central in biosystems. The cyclotron frequencies associated with the endogenous magnetic field B_end associated with the magnetic body are crucial in biocontrol and communications and for TGD inspired theory of consciousness (see for intance this and this).

1. Blackman proposed on the basis of his findings about the effects of ELF radiation on vertebrate brains the existence of an endogenous magnetic field B_end about .2 Gauss, about 2/5 of the strength of the Earth's magnetic field. It would explain the quantal effects of ELF radiation fields in the EEG range on vertebrate brains.
2. In TGD this endogenous magnetic field is assigned to the magnetic monopole flux tubes distinguishing between the Maxwellian and TGD based views of electromagnetism. Also the octaves of B_end are predicted in the TGD based model for music experience leading also to a model for the genetic code in terms of bioharmony. The corresponding cyclotron frequencies would come as octaves.
3. The huge value of the cyclotron energy scale proportional to h_eff= h_gr(Earth) implies that the effects of ELF em fields are large and not masked by thermal noise. In the Earth's gravitational field, the value of h_gr(Earth)/h is about 10¹³ and implies that the energy of 10 Hz alpha frequency belongs to the energy range of visible light. The proposal is that biophotons are produced by the transformation of dark photons to ordinary photons such that energy is conserved but wavelength is reduced by factor h/h_gr(Earth) to ordinary photons.

This leads to a detailed quantitative model of quantum control and commutations in biomatter.

1. The cyclotron frequencies of basic ions appearing in biomatter as cold plasma are in a key role. The cyclotron frequencies of various ions and DNA would relate to the communications from the biological body to the magnetic body and the control of the biological body by the magnetic body. Organisms, even those belonging to different species, can communicate with each other via their personal magnetic bodies and by larger, shared magnetic bodies. I have proposed this as a basic mechanism of remote mental interactions and the communications at the level of DNA could be unconscious communications giving rise to remote mental interactions.
2. The cyclotron frequencies of various biologically important ions are in EEG range for B_end=.2 Gauss and would related to the communication of sensory information from the biological body to its magnetic body and to control of the biological body by the magnetic body. They would play a key role in neuroscience. For 10 Hz the wavelength would correspond to a scale defined by the circumference of the Earth.
3. The cyclotron frequencies of DNA strands depend rather weakly on the details of the DNA strand, since its total charge is proportional to its length and therefore to its mass (see this). The cyclotron frequencies are predicted to be around 1 Hz for B_end=.2 Gauss, which is the strength of the endogenous magnetic field explaining the findings of Blackman. The experiments suggest 2 Hz frequency and B_end=.4 Gauss. The communication frequencies belong to the range .5 Hz and 4 Hz, which makes 3 octaves. This suggests 3 values of B coming as octaves. Note that in the case of humans, the range of audible frequencies is about 10 octaves and ranges from 20 Hz to 20 kHz and can be assigned to cyclotron frequencies of various ions. 20 Hz would correspond for B_end=.2 Gauss and 10 Hz alpha frequency to B_end,min=.1 Gauss.

   What is fascinating is that the sum for the masses, using g/mol as a unit, for the base the pairs formed by A (331.2) and T (322.2) and C(347.2) and G(307.2) are the same and equal to 654.4! For the double DNA strand the base pairs would have the same cyclotron frequency so that identical cyclotron frequencies would not be a mere approximation! There would be fine tuning by chosing the masses of nucleotides and their conjugates suitably!

4. The membrane potential V of the cell membrane varies in the range which corresponds to Coulomb energy range 0.02-.2 eV. For neurons the range of V is 0.06-0.08 eV. The thermal energy per particle at room temperature is in the range .025-.026 eV. For ℏ_gr,E= GMm_p/β₀ and for f_c=.5 Hz, the energy E= h_grf_c of a dark photon would be be would be .02 eV.

   For ordinary cells the lower bound for V corresponds to .5 Hz and the lowest octave. For neurons the lower bound corresponds to f_c=1 Hz and second octave. The upper bound .08 eV for the neuronal V corresponds to cyclotron energy E_c for f_c=2 Hz frequency. To understand the range of the ordinary membrane potential, the inclusion of the highest octave .16-.32 eV is required. Interestingly, the frequency for the lower bound .06 eV for the neuronal V corresponds to the quint of the frequency for .04 eV. Quint cycle is essential for the model of the genetic code based on icosa tetrahedral tessellation of hyperbolic 3-space (see this and this).

5. One can wonder whether the minimum of the neuronal membrane potential correlates directly with the precise value of B_end,min and therefore with the thickness of the monopole flux tubes? If so, it would be possible to measure it from the membrane potential. The second option is that the membrane potential is analogous to the length of the string producing the note. Bio-harmony is defined by a Hamiltonian cycle. Icosahedron allows a large number of Hamiltonian cycles and dodecahedron a unique Hamilton cycle.
6. The cyclotron frequency 2 Hz for DNA would correspond to B= 2× B_end ∼ .4 Gauss, which is near the nominal value of the Earth's magnetic field. This raises questions. Could there be an, at least 3-level, hierarchy of monopole flux tubes with field strengths coming as octaves of the field strength about B_end,min∼ .1 Gauss? Do the sub-octaves of B_end correspond to evolutionary hierarchy such that B_end is reduced by factor 1/2 as a higher evolutionary level with a longer cyclotron time scale emerges? Could genes be classified according to what octave they correspond in the hierarchy?

One can consider the analog of membrane potential as a note in the framework of bioharmony (see this and this). The model for the bioharmony allows us to consider two options, realized in terms of icosahedral and dodecahedral Hamiltonian cycles. Icosahedron allows a large number of Hamiltonian cycles. For the dodecahedron the cycle is unique.

1. Could the membrane potential be quantized and correspond to 12-note icosahedral scale or dodecahedral 20-note scale? Neuronal membrane potential is indeed quantized with miniature potential appearing as a unit ΔV in the range .4-.5 meV. Could this allow the realization of the icosahedral 12-note scale of the Western music or of the dodecahedral 20-note scale appearing in the Eastern music? Note that the icosahedral scale allows the realization of the genetic code and different cycles are identified as correlates for molecular moods.
2. The ratio ΔV/V would be about 1/k, k= 12 resp. k=20 for these two scales. The 12-note scale gives too large a value of ΔV/V. The 20-note scale with ΔV/V= 1/20 for ΔV= .5 meV would require V= .01 eV and therefore one more sub-octave with f= .025 Hz. If Cooper pairs are charge carriers as proposed in the model for nerve pulse and EEG (see this), their Coulomb energies E=2eV would be very near to the thermal energy per particle at room temperature so that this might work.

The experimental findings relate to communications between animals. What about plants and other life forms? Also plant DNA is characterized by cyclotron frequencies proportional to the corresponding value of B_end. Are the communications present but is the scale of B_end different so that the communications occur at higher or lower frequencies. Plants can be said to have motor actions but they take place rather slowly. Could this mean that the value range for B_end is for plants considerably lower than for animals so that the cyclotron frequencies are considerably lower for plants.

1. Besides the gravitational magnetic body of the Earth, also the solar magnetic body is involved. The solar gravitational Planck constant would give cyclotron energies scaled up by the ratio of the gravitational Planck constants ℏ_gr(S))/ℏ_gr(E)= (β₀(E)/β₀(S))× M_S/M_E∼ 2¹¹× 3× 10⁵ ∼ 6× 10⁸ of the Sun and Earth. The cyclotron energies would be huge for B_end= .2 Gauss. For 1 Hz cyclotron frequency, these energies would be of the order of 100 MeV. This does not make sense.
2. Could the strength of the endogenous magnetic field at the solar magnetic body be the strength of the solar magnetic field at Earth, which is about 5 nT? The cyclotron time scale 1 s would be scaled up by a factor of (1/x) B_end/B_S to ∼ 11 hours. The longest cyclotron time scale of .5 seconds would scale up to 22 hours, not far from the length of the day. The cyclotron energy scale would be scaled up by the ratio xB_S/B_end∼ 1.3× 10⁵ and give cyclotron energy of order 10 keV belonging to the upper boundary of the energy range [.1,10] keV of the X ray spectrum.
3. Another option is that cyclotron energies are not changed and therefore belong to the range of biophoton energies. This requires that the magnetic field strengths are scaled down by the ratio (1/x)∼ 2^-11× 10^-5/3 ∼ 1.7× 10^-9. The cyclotron period range [.25,2] s would scale up to about the range [4.7,37.4] years. Interestingly, the age after which the children have memories is about 4 years: could solar gravitational magnetic body be involved withg long term memories? The upper bound brings in human lifetime B_end would be scaled down to 3.5× 10^-14 Tesla. The magnetic fields of EEG in the brain have strengths of the order of 10^-14 Tesla.

See the article Universal rhythm for communications between animals? and the chapterThe recent view of TGD inspired theory of consciousness and quantum biology.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Objections against the notion of Pollack battery

The basic counter-arguments against the notion of Pollack battery relate to dynamics.

1. The number of dark protons matters. According to the findings of Pollack, every fourth proton in the water in the EZ region is transferred to the magnetic body. This is quite a large number. This provides an order of magnitude estimate of the maximum amount of charge transferred via quantum tunnelling followed by the reverse Pollack effect. If the electrodes are wrinkled, as would happen for the ase of SiNT, the area of the electrodes increases and so does the maximal number of dark protons.
2. The time scale for the lifetime of (H₃ O₂)^- phase is attosecond in water. The large fraction of dark protons would give reason for optimism. In the case of DNA, RNA, and cell membrane the region with negative charge is stable and formation of dark nuclei from dark protons should imply the stability against the reverse Pollack effect.
3. At what speed does the transfer to the opposite electrode by quantum tunnelling occur? The tunneling probability could be estimated based on the existing formula for quantum tunnelling by simply replacing Planck constant h with h_eff. The tunnelling rate is an exponent exp(-X) of a term X proportional to 1/ℏ.

   The intuitive expectation is that for ordinary Planck constant X is very large in the scales considered so that tunnelling probability is essentially zero. However, the replacement ℏ → ℏ_gr,E= GM_em_p/β₀ ∼ 10¹³ for a proton could make X∝ 1/ℏ_gr small enough. An additional parameter possibly needed as a multiplicative factor is the amplitude for OH → O^- + dark proton decay. The optimistic first guess is that this parameter is of order 1.

Consider now an estimate for the tunnelling amplitude A, whose modulus squared gives the tunnelling probability.

1. Apart from the numerical factor of order one, the amplitude A can be written as an exponent and represents the value of a wave function at point L at E₂. In the classically forbidden region 0<x<L the wave function is an exponentially decreasing function. ∫₀^yk(x)dx is analogous to a plane wave exp(iky) with imaginary momentum. By using the relationship k(x)= p(x)/ℏ and p(x)= (2m(E-V(x)) between wave vector and momentum, one obtains

   A= exp(-X)

   X= (1/h_eff) ∫₀^L p(x)dx .

   p(x)=(2m(E-V(x))^1/2.

   In the recent case, V(x) is Coulomb energy V(x)= eE₀x for the proton and m is proton mass. In the Earth's gravitational field one has h_eff =ℏ_gr,E = GM_Em_p/β₀= r_s(E)m_p/2β₀, r_s(E)∼ 1 cm. The velocity parameter β₀= v₀/c≤ 1 has a spectrum of values but there are arguments supporting β₀∼ 1 as the most plausible value for the Earth. For the Sun the value β₀∼ 2^-11 is favored.

2. The boundary condition is that the proton, kicked by Pollack effect from the electrode E₁, arrives at rest to the electrode E₂. This gives

   E= V(L) = eE₀L = eV₀

   where E₀ is a constant electric field of the battery and V₀ the voltage between E₁ and E₂. This gives

   p(x)= (2m_p(V(L)-V(x))^1/2 = (2m_pV₀)^1/2 (1-x/L)^1/2

   The integral appearing in the definition of X can be calculated analytically and one obtains

   X= [(4×2^1/2/3] (eV₀/m_p)^1/2× L/r_s(E) .

3. An order of magnitude estimate is obtained by assuming eV₀=1 eV implying eV₀/m_p∼ 10^-9, L=10 cm. For β₀=1, this gives

   X∼ 6× 10^-4 .

   The value happens to be quite near to the value of β₀∼ 2^-11 for the Sun. The value of X is so small that exp(-X) ∼ 1 is true in a good approximation.

The conclusion is that, unless the additional coefficient possibly present is very small, the tunnelling probability can be large enough.

See the article Are Pollack batteries possible? and the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.