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 tentacles 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. The 2 Lagrange points for the Sun at the Sun-Earth axis have a distance about .01 AU from the Earth. Interestingly, this distance is approximately 4a_gr(S), where the Bohr radius a_gr(S) for the Sun is a_gr(S)∼ AU/25 =.04AU in Nottale's model in which the Earth corresponds to n=5 Bohr orbit around Sun for gravitational constant ℏ_gr= GM(S)/β₀, β₀(S)∼ 2^-11.

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?

Addition: The comment to the post inspired the following additional piece of text concerning Lagrange points.

The Moon feels the gravitational forces of the Earth and Sun and Earth dominates inside the Lagrange distance of the Sun (.01AU) since the average distance of the Moon from the Earth is .00257 AU and much smaller. In the region between .00257AU and .01AU must treat the system as a 3-body system instead of approximating it as a 2-body system.

Each planet forms a pair with the Sun and planets between it and Sun and one can assign to each planet-Sun pair Lagrange points (rotating with the planet around Sun). Same with respect to planets and their moons.

This inevitably brings in mind horoscopes. Could there be plasma life around the stable Lagrange points? Could the biosphere have gravitational monopole flux tube contacts with these plasma lifeforms? In fact, at Lagrange points the gravitational monopole flux tube pairs from the heavier mass (such as Sun) reconnect to separate U-shaped flux tubes.

Could it really be that horoscopes are not mere fiction at the level of conscious experience? For instance, could something special take place when the Earth and some planet are near to each other? Intriguingly, the dynamics of the planetary system correlates with stock markets (see this and this).

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.

The dark matter particle detected by LUX-ZEPLIN detector is identifiable as dark pion of M89 hadron physics predicted by TGD!

I just learned of a direct detection of dark matter. The news was published already towards the end of 2025 (see this. I glue part of the news here.

The LUX-ZEPLIN detector (see this) at the Sanford Underground Research Facility, located 1,500 meters beneath the former Homestake Gold Mine, recorded 8 candidate dark matter interaction events over 1,000 days of operation that carry statistical certainty of 5.2 sigma crossing the discovery threshold physicists require for particle physics announcements. The detector uses 10 tonnes of ultra-pure liquid xenon cooled to minus 108 degrees Celsius, surrounded by water tanks shielding against cosmic rays that would overwhelm the faint dark matter signal at shallower depths.

Dark matter particles theorized as Weakly Interacting Massive Particles with masses between 10 and 1,000 times the proton mass produce tiny flashes of scintillation light and ionization when they collide with xenon nuclei, distinguishable from radioactive background through their characteristic dual-signal fingerprint.

The detected events carry particle masses consistent with a 65 proton-mass dark matter candidate, within the theoretical range predicted by supersymmetric extensions of the standard model. Independent verification is already underway at the PandaX-4T detector in China and the XENONnT detector in Italy's Gran Sasso Laboratory, with results expected within six months.

What has TGD to say about the claimed 5 sigma discovery?

1. One of the most dramatic predictions of TGD is a scale hierarchy of standard model physics labelled by Mersenne primes and their Gaussian counterparts. This hierarchy would correspond to the hierarchy of color partial waves associated with the Dirac equation in H= M⁴× CP₂ in which space-times are 4-surfaces obeying a slightly non-deterministic holography.

   The mass scales of leptons and hadrons of a given standard model physics would be proportional to the inverse of the square root of the Mersenne or Gaussian Mersenne characterizing the scaled copy (for the most recent articles about p-adic thermodynamics, replacing Higgs mechanism see this and this). For instance, for electron one would correspond to Mersenne prime M₁₂₇ =2¹²⁷-1.

2. Ordinary hadrons would correspond Mersenne prime M₁₀₇= 2¹⁰⁷-1.The Mersenne prime M₈₉ would correspond to mass scale, which is 512 times the mass scale of ordinary hadron physics. During about 2 decades pieces of evidence for M₈₉ hadron physics at LHC have been accumulating (see for instance this, this and this). M₈₉ hadron physics would dramatically modify the model for the energy production in the Sun (see this).
3. TGD predicts a hierarchy of effective Planck constants h_eff coming as integer multiples of its minimal value considerably larger than ordinary Planck constant. The phases with non-standard value of Planck constant would behave like dark matter since vertices involving fermions with particles having different values of h_eff are not possible. The 2-vertex changing the value of h_eff is however possible and phase transitions changing h_eff are possible.
4. A TGD based explanation for the LUX-ZEPLIN events interpreted in terms of dark matter would be as a pion of M₈₉ hadron physics identifiable as a scaled up copy of ordinary M₁₀₇ hadron with a mass scale which is 512 times higher but having a non-standard value of effective Planck constant so that the M₈₉ hadrons would be like dark matter. The scaling of the mass .134 MeV of the ordinary pion by factor 512 gives mass of 67 GeV. This is exactly the reported mass if proton mass 940 MeV is approximated as 1 GeV (the error is 6 per cent)!

   M₈₉ hadrons would be created as a phase of ordinary matter with scaled up valued of effective Planck constant guaranteeing that at quantum criticality for the phase transition the Compton lengths of M₈₉ hadrons, scaled by factor h_eff/h are same as for ordinary hadrons. This requires that the ratio of h_eff/h equals to the ratio p-adic length scales associated with M₁₀₇ and M₈₉ equal to 2^(107-89)/2= 2⁹=512.

One can apply the scaling argument to estimate already mass of scaled variants of other quarks.

1. The mass of the neutral kaon is about 498 MeV. The mass of the strange quark would be from the additivity of mass squared equal to m_s= m_K/2²∼ 352 MeV. The mass of M₈₉ s quark would be 176 GeV, which is not far from top quark mass 173 GeV.

   The mass of M₈₉ s quark would be 176 GeV, which is not far from top quark mass m_t=173 GeV. I proposed recently (see this that the top quark corresponds to M₈₉ u quark. I did not realize that the scaling argument allows only the interpretation as M₈₉ s quark.

2. The mass of c quark is estimated to be 1.5 GeV or 1.275 GeV. The M₈₉ c quark is estimated to have mass of 750 GeV or 63.75 GeV.
3. The mass of b quark is estimated to in the range 4.2-4.7 GeV M₈₉ b is estimated to have mass in the range 2400 GeV-2350 GeV.
4. I proposed recently in an article discussing toponium (see this top quark that it actually corresponds to a quark of M₈₉ hadron physics and the real top corresponds to the mass of 28 GeV or 30 GeV assignable explaining the Aleph anomaly this would predict that the mass of M₈₉ t quark is about 1400 or 1500 GeV.

This kind of estimates can be made also for leptons and baryons and M₈₉ electron would have mass about 250 GeV. The naive scaling of proton mass would give the mass of 512 GeV for M₈₉ nucleon. Needless to say, these predictions mean an entire scaled hadron physics to be tested at LHC.

See the article Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD 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.

Empirical evidence for two arrows of time

https://www.facebook.com/profile.php?id=61579273676681 Source: Perimeter Institute for Theoretical Physics Canada, European Space Agency Planck Collaboration, Physical Review D, 2025 \subsection{Evidence that the Universe has two arrows of time} The scientists in Perimeter Institute for Theoretical Physics Canada and European Space Agency Planck Collaboration have published in Physical Review D, 2025 evidence that the Universe has two arrows of time. The presence of two arrows of time is claimed to correspond to hemispherical asymmetry of the CMB. It is not obvious to me why the presence of two arrows of time would reflect itself via this asymmetry.

Could these findings be interpreted as a support for the zero energy ontology (ZEO) of TGD predicting that two arrows of geometric time are possible and that roughly one half of the Universe has both arrows of time?

1. In TGD, the view about the arrow of geometric time is more complex than in the framework of standard cosmology. The arrow of geometric time is associated with a given causal diamond (CD), which is analogous to a sub-cosmology in a Russian doll cosmology defined by a hierarchy of CDs with increasing size scales. A given CD can have both arrows of time and the arrow of time changes in the TGD counterpart of ordinary quantum measurement. The hierarchy of effective Planck constants labelling an infinite hierarchy of quantum coherence scales, which correspond to the size scales of the space-time surfaces and of CDs, is essential.
2. The meaning of the arrow of time used by the researchers is based on CPT as a symmetry. The proposal is that CPT would relate the two Universes with an opposite arrow of time: CPT would not be a trivial operation anymore. On the other hand, the time reversal in the sense of TGD inspired theory of consciousness does not reduce to time reversal as a discrete symmetry although one cannot exclude the possibility CPT - and TGD based views are closely related. It is assumed that the two arrows of time correspond to two half-cones of the light-cone. In the TGD framework, they would correspond to the two halves of a causal diamond CD as an intersection of future and past directed light-cones.

The TGD view of the arrow of time means roughly the following.

1. In quantum field theories there are two vacua as states annihilated by annihilation resp. creation operators. In the original picture of Dirac, all positive/negative energy states of fermions would be filled for these two vacua. In the standard QFT only the second vacuum is selected.
2. In TGD, a new quantum ontology, zero energy ontology (ZEO), solving the basic problem of quantum measurement theory, is forced because the classical time evolutions fail to be strictly deterministic. This non-determinism is absolutely essential for the non-triviality of quantum TGD and also for the TGD inspired view of consciousness. The mild non-determinism forces us to introduce additional discrete degrees of freedom implying that one must allow 3-D seats of classical non-determinism as carriers of quantum numbers in the interior the 4-D space-time surface obeying almost deterministic holography identified as cognitive degrees of freedom not present in standard physics.
3. In ZEO 3-D quantum states are replaced by zero energy states. In fermionic degrees of freedom, zero energy states in fermionic degrees of freedom correspond to pairs of 3-D many-fermion states assignable to the intersections of space-time surfaces with the opposite light-like boundaries of causal diamonds (CDs). These 3-D quantum states could be interpreted as initial and final states of a slightly non-deterministic time evolution. At the level of space-time surfaces, zero energy states are quantum superpositions of Bohr orbit-like space-time surfaces satisfying holography = holomorphy principle.
4. The states at the passive boundary of CD are unaffected by time evolution as small state function reductions (SSFRs). SSFRs define a generalization for a sequence of measurements of fixed observables. In standard QM these sequences leave the quantum state invariant meaning Zeno effect. In TGD, the Zeno effect is replaced with a sequence of SSFRs defining a flow of consciousness, self. In SSFR, the active boundary of CD is shifted, CD increases in statistical sense and the passive boundary suffers only a scaling leaving the 3-D quantum states at it invariant.
5. "Big" state function reduction (BSFR) is the counterpart of ordinary state function reduction. BSFR changes the roles of passive and active boundaries of CD so that the arrow of time is changed. At the level of conscious experience BSFR means death/falling asleep of self at a given level of self hierarchy.
6. In the TGD Universe, quantum coherence is possible in arbitrarily long scales. In cosmic scales stars older than the Universe can be explained by ZEO. Stars older than the Universe is an example of possible consequences of ZEO in cosmic scales.

See for instance, this, this and this.

An objection against the notion of Pollack battery

The model of Pollack battery (see this) is now rather concrete. In the simplest situation the opposite electrodes could correspond to carbon nanotubes with modifications =C → -(C-OH) and =C→ -(C=O) respectively.

The model is very general. What is essential is that one has lattice type structure in =X- type units are replaced with -(X-OH)- and -(X=O)- type units for the two electrodes. For instance, carbon nanotubes could be replaced with silicon nanotubes (SiNT), which indeed do exist. Silicon nanotubes, the tubes are not smooth but wrinkled: this would increase the capacity to load charge.

Charging would take place by Pollack effect kicking protons to monopole flux tubes by the process -OH→ -O^-+ dark proton at monopole flux tube. The charging voltage would provide energy and the process could occur by tunnelling. The electrolyte would be a hydrophilic polymer acting as a catalyst for Pollack effect and possibly also as a storage of chemical energy generated in charging. During use O^- ions would provide electrons serving as charge carriers of Ohmic current running the load.

The objection against the proposal is that the energy difference between states -C-(C=O)-C + e^- and -(C-O^-)-C is large and of wrong sign so that e^- is tightly bound to -(C-O^-)-C and Ohmic current cannot be generated. I am not a chemist but I am able to use Google, which answers as follows.

"The energy difference between a neutral carbonyl group plus a free electron C-(C=O)-C + e^- and the resulting radical anion -C-(C-O-C^- is characterized by the electron affinity (EA) of the carbonyl compound. For simple aliphatic ketones like acetone, the energy difference is approximately in the range 0.0 to -0.5 eV. This indicates that the formation of the radical anion is typically isothermic or slightly endothermic in the gas phase."

This would suggest that the liberation of e^- to become a carrier of ohmic current does not require energy or occurs even spontaneously and is made possible so that the electric field of the battery generates ohmic current.

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.

Allais effect again

The Allais effect (see this and this) was first reported by Maurice Allais in 1954. It involves an abrupt change in the azimuth of a paraconical pendulum s oscillation plane during the solar eclipse, totaling up to 13.5 degrees.

Empirical findings

Consider first a brief summary of the findings of Allais and others (see this and this).

1. Paraconical pendulum consists of a rigid rod of ∼ 1 meter and a metal ball. The bob, that is the weight at the bottom, has lense like shape. Paraconical pendulum differs from the conical pendulum in that the suspension point of the pendulum is not fixed but is a metal sphere able to roll without sliding in plane. Therefore it has 2 degrees of freedom rather than only one: both swinging and rotation around the vertical axis are possible.
2. In the absence of any other forces than the gravitation of Earth) paraconical pendulum can behave much like a conical or Foucault pendulum. The oscillation plane of the paraconical pendulum turned by 13,5 degrees during 14 minutes (see this). It is difficult to see how the gravitational fields of the Sun and Moon could explain this behaviour by changing the effective value of the Earth's gravitational acceleration.
3. Allais concludes from his experimental studies that the orbital plane approach always asymptotically to a limiting plane and the effect is only particularly spectacular during the eclipse. During solar eclipse the limiting plane contains the line connecting Earth, Moon, and Sun. Allais explains this in terms of what he calls the anisotropy of space.
4. Some experiments carried out during eclipse have reproduced the findings of Allais, some experiments not. In the experiment carried out by Jeverdan and collaborators in Romania it was found that the period of oscillation of the pendulum decreases by Δf/f∼ 5× 10^-4 (see this), which happens to correspond to the constant β₀=2^-11 appearing in the formula of the gravitational Planck constant for the Sun. It must be however emphasized that the overall magnitude of Δ f/f varies by five orders of magnitude. Even the sign of Δf/f varies from experiment to experiment.
5. There is also the finding by Popescu and Olenici, which they interpret as a quantization of the plane of oscillation of paraconical pendulum during solar eclipse (see this).
6. There is also evidence that the effect is present also before and after the full eclipse. The time scale is 1 hour. Allais emphasized that the effect is a dynamic, not static, phenomenon, connected to the variation of weight or inertia in the space swept by the pendulum during the eclipse. The 10 per cent excessive bending of light is reported during some eclipses (the "residual arc") is also reported.

While many attempts to confirm it have met with varied or ambiguous results, several observations indicated anomalous behavior that cannot be easily explained by general relativity (GR) or standard Newtonian mechanics.

The TGD view of Allais effect briefly

The TGD view of Allais effect involves quantum physics based on TGD based quantum ontology. One can consider several different levels for how quantum physics appears in the description.

1. One can start from a harmonic oscillator model for the gravitational pendulum and perform a quantization using the gravitational Planck constants of the Sun or the Earth. The huge values of these Planck constants imply that small values of the harmonic oscillator quantum number are involved. The changes of this quantum number could explain the fluctuations at quantum criticality assignable to the transition to the eclipse. The effect would not be gravitational but quantum mechanical and due to the large value of ℏ_gr.

2. During a full eclipse, the screening of the solar gravitational field might explain the Allais effect. There is however evidence that the Allais effect appears also outside the regions of full eclipse and therefore in the scale of the Earth. This suggests that a description involving interference and diffraction effects besides screening is needed.

   In the TGD framework, models involving classical long range gravitational or Z⁰/Kähler fields cannot be excluded. These models do not however look promising: the standard physics based expectation is that the effects are quite too small.

3. The description in terms of wave functions identified as spinor fields of the "world of classical worlds" (WCW) is more promising. The argument of the WCW spinor field would be the space-time surface as analog of Bohr orbit for a particle as 3-surface. One would have essentially wave mechanics in WCW. Instead of a Bohr orbit one would have a wave in the space of Bohr orbits (WCW).

   The Moon would act as an obstacle giving rise to quantum diffraction, which reduces to screening immediately behind the Moon. The diffraction would not be caused by the classical gravitational interaction but would be analogous to the diffraction of electrons in a double screen and a genuine quantum effect.

4. The observed reduction Δ f/f ∼ 2^-11 of the oscillation frequency of the pendulum is several orders of magnitude larger than the prediction and happens to be equal the velocity parameter appearing in the solar gravitational Planck constant. Quantum criticality for the transition to eclipse and zero energy ontology (ZEO) (see this and this) suggest a possible explanation for this finding. In particular, the notion of causal diamond (CD) as a geometric counterpart for the perceptive field (see this) would be involved and the reduction of the frequency would be mathematically analogous to that occurring is cosmological redshift.

The cautious conclusion would be that the Allais effect does not tell so much about new gravitational physics than about the new quantum ontology predicting the notion of WCW realizing holography = holomorphy vision, the hierarchy of Planck constants, and ZEO.

See the article Allais effect again 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.

What about the second electrode of the Pollack battery and what happens when the battery is used?

The notion of Pollack battery (see this) was inspired by the claim of the finnish DONUT Lab that it had developed a battery with very fast charging, very large energy density and very large number of cycles. The fast charging is indeed found to occur in the VTT tests.

The charging of the Pollack battery by Pollack effect is expected to be a very fast process. The discharging of the Pollack battery must however occur slowly in ordinary applications. The Pollack battery must therefore behave classically during its use (Ohmic currents) and quantally during its charging.

1. Assume that electrodes E1 and E2 are in the initial state nanotubes, that is single-layered hexagonal lattice such that given carbon as single valence bond to 2 neighbors and 1 double valence bond to the third neighbor. The electrons are assumed to be prepared by making different modifications of double bonds =C:

   E1 : =C → -(C-OH) : addition of OH

   E2: =C → -(C=O) : addition of double bonded O.

   The open question is whether the oxygenation is possible energetically without energy feed.

2. What happens in charging?
   1. Pollack effect for E1 ocurrs and inducing the modification

      -(C-OH) → -(C-O^-) + dark proton at flux tube

   2. Dark proton is transferred to E2 and suffers reverse Pollack effect. At E2 one has

      -(C=O) +p, where p is ordinary proton.

3. What happens when the battery is used?
   1. Pollack effect at E2 is not possible (no -OH groups)! The battery voltage generated in charging induces an ohmic electron current from E1 to E2. The Ohmic current is not quantal and the discharging is slow.
   2. Electron leaves E1 and the transition

      -(C-O^-)-C→-(C=O)-C

      occurs and e^- is transferred to E2 ohmically.

   3. At E2 e^- combines with a proton to form H. After that the H combines with C=O to give

      -(C=0)-C +H -→ -(C-OH)-C

      The roles of E1 and E2 are changed!

   The next charging must use an opposite loading voltage inducing Pollack effect at E2.

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.

M8-H duality, implies fractal generalization of Hubble's law, predicts correct mass density of the Universe and resolves Hubble tension

The article by Thomas Brown (I am grateful to Esa-Juhani Ruoho for the link and also for inspiring discussions) discusses critically the interpretation of the Pollack effect. The vertex figure of ITT (IVF) (see this and this) is rhombicosidodecahedron (RID). I have proposed that the ITT is behind the genetic code and to be associated also with the hydrogen bonded water molecule clusters. Surprisingly, RID is identical with the third shell of the so-called icosahedral supercluster (ISC). This inspired the proposal about the duality between sensory representations realized by ISC at the level of the water and ITT realized at the level of the field body of the ISC.

The challenge is to understand how the complement of IVF, which should be outside RID, can correspond to the first and second shell of the ISC which are below the third shell. The obvious guess is ITT-ISC correspondences stating that the ITT realized at the field body of the ISC is related by inversion to ISC. M⁸-H duality, as the TGD counterpart of the momentum position duality, involves inversion in M⁴⊂ M⁸, having interpretation as momentum space, mapping it to M⁴ × CP₂. Is M⁸-H duality involved?

This question led to completely unexpected developments suggesting deep connections between fundamental physics (M⁸-H duality and the notions of gravitational and electric Planck constant as implications of number theoretic vision), physics of water (hydrogen bonded water clusters), consciousness theory (field body as controller of biological body forming sensory representations of biological body), biology (ITT view of the genetic code) and cosmology (generalization of Hubble's law to all scales).

In turned out that M⁸-H duality for the gravitational Planck constant leads to a fractal generalization of Hubble's law holding for causal diamonds CDs (CD=cd×CP₂) interpreted as counterparts of perceptive fields and analogous to cosmologies with big bang followed by a big crunch. This reflects the Russian doll cosmology predicted by TGD. Hubble constant appears as a scale dependent parameter charactrerizing the size scale of the cd. There is a single velocity type parameter β₀ parameter involved. This leads to a prediction for the Hubble length identified as gravitational Compton length interpreted as gravitational quantum coherence length at the gravitational field body. The large mass M, appearing in the expression of gravitational Planck constant, corresponds to the mass of a larger region containing the the quantum coherene region.

1. The proposed picture predicts that the mass of the visible Universe inside CD using solar mass as a unit is given by

   M(CD₁)/M_Sun= 2β₀(CD)L_H(CD)/r_S(Sun).

   Here r_S(Sun) equals 3 km. Assume that the radius of CD₁ can be expressed as L_H(CD₁)= xL_H(CD) so that one has V(CD₁)= x³V(CD).

2. This gives an estimate for the mass within the Hubble radius

   M(CD₁)∼ 2× 10²² × β₀⁴(CD)×x^-3 M_Sun .

   Here the mass M(CD₁) corresponds to the mass within CD₁. M_Sun∼ 1.88 × 10⁵⁷ m_p, where m_p is proton mass. This predicts the average density

   ρ ∼ β₀⁴x^-3× 12× 10² m_p/m³ .

3. The density of baryons is estimated to be 5.9-6 protons per cubic meter (see this). The density ρ_B of ordinary (baryonic) matter is believed to be about p= 1/20 that is 5 percent of the total density: ρ∼ ρ_B/p= 20ρ_B∼ 120×m_p/m³. This gives β₀⁴x^-3∼ 1/10.
4. p-Adic length scales are good candidates for the size scales of CDs and seem to correspond to octaves p∼ 2^2k so that minimal scaling relating the sizes of CD and CD₁ containing CD should correspond to x=2. For β₀=1 the Universe would be a blackhole-like object with L_H= r_s/2β₀=r_s/2. For (p= 1/20,x=2) would predict β₀∼ .95. (β₀=1,x=2) would predict p∼ 6.1 per cent.

Hubble tension means that the Hubble length in short scales is 5-10 percent shorter than in long scales.

1. This requires that in short scales β₀ is 5-10 per cent smaller than in long scales. By β₀≤ 1 β₀=1 cannot be true in long scales (β₀=1,x=2) could be true in short scales (the rough estimate for ℏ_gr,E gives β₀∼ 1) and (β₀=.95,x=2) in long scales would predict difference 7.5 per cent Δ H₀/H₀ and resolve the Hubble tension.
2. β₀=1 in short scales as opposed to β₀=.95 in long length scales would require the scaling of baryon fraction from 5 percent in short scales to 6.1 percent in long scales. One would have L_H= r_s/2 and the Universe could be seen as a blackhole-like system for which the quantum coherence region would have radius L_H=r_s/2. This would give a p-adic fractal hierarchy of blackhole-like objects, which are quantum coherence regions of blackhole-like objects.
3. Why should the fraction of baryons be smaller in short scales than in long scales? A possible explanation is the transfer of baryons to dark baryons at monopole flux tubes, reducing the fraction of baryons in short scales (recent universe) from 6.1 percent to 5 percent. The cosmic evolution as an unavoidable increase of algebraic complexity would generate large h_eff phases and would also manifest as the formation of gravitational bound states such as galaxies, stars and planets.

See the article Do the icosatedrahedral tessellation of H³ and icosahedral H₂O supercluster correspond to each other? 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.

Are the indications that Donut battery contains water consistent with the Pollack battery property

Donut Lab of claims of having constructed a battery with almost miraculous properties. Using Claude Cowork Deep Research, Marko Manninen has carried out an analysis (see this) about what the Donut battery could be.

I have developed a TGD inspired model for what I call Pollack battery (see this, this and the article ). The Pollack battery is inspired by the TGD based view of quantum biology and might have something to do with the Donut battery.

Pollack effect would explain the rapid charging reported also for Donut battery. The most recent test by VTT studied the Donut battery for which the plastic pouch containing the battery was degraded at temperature near 100 degrees Celsius (see this). According to the VTT raport, vacuum was lost in the high temperature test test and agglutinations have contained a hole or a hole has appeared during the test.

1. The expansion of the popped battery by 17 percent has been used as a counter argument to the claim that the counterpart of electrolyte is in a solid state.

   The temperature of 100 degrees indicates that water was present and evaporated at this temperature. Water expands dramatically in evaporation. During the preparation of the paste UV drying is applied and if this drying has failed to be complete, the battery could have contained water. In TGD framework one can ask whether water was somehow created by the Pollack effect.

2. Water, which has been traditionally considered a battery poison, was found a few years ago to increase the charge storage capacity by a factor of two. Did the boiling of the water present from the beginning or the water created in the system cause the pop? Could the water give an additional contribution to the Pollack effect and improve the Pollack battery in some aspects, at least at temperatures near the physiological temperature, which could be optimal for the Pollack effect? Or is the effect opposite?
3. How could water have been created if it was not present originally? Let's assume a Pollack battery based on nanotube electrodes. The addition of -OH groups induce the transformations C=C → C-(C-OH). This is necessary for the occurrence of the Pollack effect as a transition -OH→ O^- + dark proton at the flux tube. Did dehydration of the hydrated nanotube, resulting in the formation of H₂O molecules, occur? The water created in this way would have evaporated at 100 degrees and induced the expansion of the battery.
4. How would dehydration have occurred?
   1. Assuming that 2 -OH groups at adjacent hexagonal rings of nanotube (defects in the nanotube) have been transformed by the Pollack effect into the state -O^- + dark proton H⁺ on the magnetic body.
   2. Assume that two dark protons drop back from the magnetic body by the reverse Pollack effect and attach to the second O^- so that H₂O⁺ ion is formed. Suppose that after this the second O^- donates its electron for H₂O⁺ ion so that H₂O and =O are formed so that one -OH defect of the nanotube disappears. The reverse Pollack effect would therefore produce dehydration of the electrode. The rates for the Pollack effect and its reversal by the dropping of two dark protons would determine the fraction of water present in equilibrium state.

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.

Do the icosatedrahedral tessellation of H3 and icosahedral H2O supercluster correspond to each other?

One of the oldest ideas of TGD inspired quantum biology and consciousness theory is that that sensory representations realized both at the level of the biological body and magnetic body and closely related to each other are central in the understanding of for instance EEG and nerve pulse (see this, this, this, this, and this).

Pollack effect (see this) is assumed to transform ordinary protons and also alkali ions to dark particles with a large value of effective Planck constant h_eff at the field body. The TGD inspired generalization of Pollack effect is in the central role in the realization of the representations at the level of the field body (see this, this this, this, this, this). The "dark" protons at the field body of DNA are assumed to give rise to a dark variant of the genetic code relying on icosa tetrahedral tessellation (ITT) of hyperbolic 3-space identified asw the light-cone proper time constant surface of causal diamond (cd).

The article by Thomas Brown (I am grateful to Esa-Juhani Ruoho for the link and also for inspiring discussions) discusses critically the interpretation of the Pollack effect. The vertex figure of ITT (IVF) (see this and this) is rhombicosidodecahedron (RID). I have proposed that the ITT is behind the genetic code and to be associated also with the hydrogen bonded water molecule clusters. Surprisingly, RID is identical with the third shell of the so-called icosahedral supercluster (ISC). This inspired the proposal about the duality between sensory representations realized by ISC at the level of the water and ITT realized at the level of the field body of the ISC.

The challenge is to understand how the complement of IVF, which should be outside RID, can correspond to the first and second shell of the ISC which are below the third shell. The obvious guess is ITT-ISC correspondences stating that the ITT realized at the field body of the ISC is related by inversion to ISC. M⁸-H duality, as the TGD counterpart of the momentum position duality, involves inversion in M⁴⊂ M⁸, having interpretation as momentum space, mapping it to M⁴ × CP₂. Is M⁸-H duality involved?

This question led to completely unexpected developments suggesting deep connections between fundamental physics (M⁸-H duality and the notions of gravitational and electric Planck constant as implications of number theoretic vision), physics of water (hydrogen bonded water clusters), consciousness theory (field body as controller of biological body forming sensory representations of biological body), biology (ITT view of the genetic code) and cosmology (generalization of Hubble's law to all scales).

In particular, a prediction for the ordinary Planck Hubble constant implies a predictions for the mass density of the Universe and prediction is consistent with the observed mass density including contributions of dark matter and energy if the value of the velocity parameter β₀≤ 1 appearing in the formula for the gravitational Planck constant is equal to β₀∼ 1 and the very large system containing observable Universe as quantum coherence region with Hubble radius L_H is a blackhole-like object with Schwartschild radius r_s= 2β₀L_H∼ 2L_H for β₀∼ 1. Hubble tension means that the value of the Hubble length L_H= 1/H₀ in short scales is roughly 10 percent smaller than its value in long length scales.

Since L_H is proportional to 1/β₀ this can be understood if β₀ in the early universe (long scales) is roughly 10 per cent larger than in the long scales. This would imply that β₀∼ .92 in long length scales β₀∼ 1 in short scales. The predictions for the fraction of baryons would be about 5 percent in short length scales and 6.1 percent in long length scales. The difference could perhaps be understood in terms of transfer of baryons to dark baryons with large h_eff predicted by the number theoretic vision of evolution.

The article by Brown summarizes basic information about the Pollack effect. Pollack effect requires only the presence of hydrophilic polymer as a catalyst at the boundary of the water. I had erratically assumed that the gel phase is necessary. Concerning the TGD based notion of Pollack battery (see here) this finding was good news. Brown discusses Pollack's interpretation of EZs critically and this led to a more precise TGD inspired view about the realization of EZs and the genetic code at the level of water clusters to be discussed in this article.

See the article Do the icosatedrahedral tessellation of H³ and icosahedral H₂O supercluster correspond to each other? 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.

It is enough that the polymer electrolyte appearing in the model of Pollack battery is hydrophilic

The inspiration for this post comes from the claim of Donut Lab of having constructed a battery with almost miraculous properties. There is very little published information about the chemistry and structure of Donut battery. Using Claude Cowork Deep Research, Marko Manninen has carried out an analysis (see this) about what the Donut battery could be.

I have developed a TGD inspired model for what I call Pollack battery (see the blog post and the article ). The Pollack battery is inspired by the TGD based view of quantum biology and might have something to do with the Donut battery.

Pollack effect would explain the rapid charging reported also for Donut battery. The assumption that the solid state electrolyte, acting as catalyst for Pollack effect should be in gel phase, is problematic. This assumption turned out to be too strong as I learned from Esa-Juhani Ruoho whose sent an excellent article by Thomas Brown (see this) discussing the relationship between Pollack effect and icosahedral geometry playing a key role in the TGD based model of genetic code. In the usual Pollack effect, it is actually enough to have a hydrophilic polymer instead of a gel, and there are many of these. Hydrophilic polymers are possible also in the solid state as Google says.

1. Hydrophilicity favors certain amino acids on the surface of the protein that borders on water. Roughly one half of the amino acids are hydrophilic. When proteins fold, proteins arrange themselves in water in such a way that hydrophobic amino acids border the cavities inside and hydrophilic amino acids face the water.
2. There are 11 key hydrophilic amino acids.
   • 6 polar uncharged: Serine (Ser, S), Threonine (Thr, T), Asparagine (Asn, N), Glutamine (Gln, Q), Tyrosine (Tyr, Y), and Cysteine (Cys, C).
   • 3 positively charged (basic) : Lysine (Lys, K), Arginine (Arg, R), Histidine (His, H).
   • 2 negatively charged (acidic): Aspartic acid (Asp, D), Glutamic acid (Glu, E).

3. Their key properties are as follows.
   • They are highly soluble in water because their side chains can form hydrogen bonds.
   • Protein Structure: They are typically found on the surface of globular proteins, interacting with the aqueous environment.
   • Catalysis: Charged hydrophilic amino acids (like His, Asp, Glu, Lys) are crucial in the active sites of enzymes, facilitating chemical reactions.
   • They are "water-loving" in contrast to hydrophobic amino acids (like Val, Leu, Ile, Phe, Trp) which prefer to be inside the protein, away from water.

Does a nanotube with -OH inserts at the defects of the nanotube at which C=C bond is transformed to a C-C bond make it a water-like compound as far as Pollack effect is considered? If so, the Pollack effect would correspond to a transition -OH →O^- + dark proton at the flux tube also in this case.

Could hydrogen bonds form between the hydrogens of the nanotube and some atoms of the solid state polymer? Hydrogen bonds form between a hydrogen atom covalently bonded to a highly electronegative atom (typically Nitrogen, Oxygen, or Fluorine) and another electronegative N, O, or F atom on a nearby molecule. This suggests that the solid state polymer should contain N, O or F. N and O look the most plausible. All earlier mentioned polymer candidates, i.e. polyethylene oxide polymer, LiCF₃SO₃ salt, and silane-treated Al₂O₃ (Al₂O₃-ST) ceramic filler) contain oxygen atoms.

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.

Official top quark and toponium as particles of M89 hadron physics rather than standard hadron physics?

I watched an excellent video about what we have learned at LHC (see this). Three runs RUN1, RUN2, and RUN3 have been completed and now we know where the limits for the applicability of the Standard Model are.

The immediate successor of LHC will be high-luminosity LHC operating from 2029- 2030 onwards for ten years. Future circular collider (FCC) will start to operate in the late 2040s. Electrons and positrons will collide and the collider (Higgs factory) will act as a high precision collider.

The philosophy is that high precision might allow us to develop a theory allowing us to solve the various anomalies of the standard model. In future, the experimentalists would not be merely testing whether a given extension of the standard model might solve some anomalies but trying to identify more general deviations from the standard model. But is this enough? What has been lacking from theoretical physics since the times of Einstein and his contemporaries, is philosophical thinking challenging the basic assumptions. Can one make progress by merely measuring more precisely?

What did we learn at LHC?

The video explains  the basic anomalies. The anomalies are also discussed in detail by Crivellin and Mellado (see this). The following  list defines the boundaries of the region of phenomena that the standard model can explain.

1. Toponium exists although it should not.
2. W mass deviates from the predicted mass.
3. g-2 anomaly of muon is claimed to disappear in lattice calculations using only quarks and gluons but does not disappear when hadronic data are used as an input.
4. Lepton universality is violated in some meson decays.
5. Penta and tetra quarks, whose existence is not denied but not predicted by the standard model.
6. There are anomalies associated with the CP violation of the CKM matrix.
7. The axions, proposed to solve the problem due to the strong CP violation predicted by QCD, have not been found and the strong CP violation is too weak to explain matter antimatter asymmetry.
8. Quark-gluon plasma predicted by QCD did not behave like gas but a perfect liquid and the transition to quark gluon plasma seems to occur at several energies rather than single phase transition point.
9. SUSY was believed to solve the hierarchy problem involving the fine tuning of the Higg couplings but no evidence for SUSY particles was found.
10. WIMPs as candidates for galactic dark matter have not been found.

Toponium anomaly as an indication for M₈₉ hadron physics

I have discussed various standard model anomalies from the TGD point of view in various articles. Here I will consider only the discovery of the toponium, which is one of the latest surprises. The Standard model does not deny toponium's existence but according to the standard intuition it should not exist.

1. The lifetime of the top quark is too short for the formation of toponium. There are of course proposals for solving this and also other anomalies but the problem is that these proposals typically solve only one anomaly. The lifetime of the standard top quark candidate with mass m\simeq 172.5 GeV is τ=5× 10^-25 s. This time is shorter than required for QCD hadronization processes (10^-23-10^-24 s). This is why it has been believed that toponium does not exist.
2. The toponium was however discovered both by LHC and ATLAS and its lifetime is estimated to be 2.5 × 10^-25 s. Toponium is suggested to be a quasi-bound state or a resonance appearing when top quarks are produced very near to the threshold energy (see this and this). Toponium decay is triggered by a weak decay of one of its constituents rather than being a strong decay. Both ATLAS and CMS verified the existence of this state with a resonance width of about 3 GeV.

Consider now the basic ideas of TGD view of hadron physics and standard model in general. TGD leads to almost inescapable conclusion that there must exist an entire hierarchy of standard model physics assignable to the triality +/-1 color representations defined by color partial waves of quarks and antiquarks in CP₂. Leptons would appear in triality 0 color partial waves (see this and this).

1. The color multiplets of quarks of a given standard model physics would combine to form color triplets, which would serve as building bricks of hadrons of a given hadron physics (see this, this, and this). These hadrons would correspond to a hierarchy of p-adic mass scales, proposed to be labelled by ordinary and Gaussian Mersenne primes. The longer the p-adic scale, the higher the dimension of the color multiplet.

   For the observed leptons, color representations would combine to form color singlets but also analogs of mesons as bound states of colored leptons might be possible (see this). Only at energies near CP₂ mass would color deconfinement for incoming and outgoing states be possible.

2. Ordinary hadrons would correspond to the Mersenne prime M₁₀₇. The nucleon of M₈₉ hadron physics would correspond to the mass scale 512 m_n and therefore to the LHC energy scale. The transition from M₁₀₇ hadron physics to M₈₉ hadron physics would take place at quantum criticality. The phase transition usually interpreted as a creation of the quark-gluon phase could correspond to this phase transition (see this). At quantum criticality the value h_eff/h would scale up the Compton length scale of M₈₉ hadrons. This would reflect long range quantum fluctuations. This re-interpretation of what has been identified as quark gluon-plasma would solve various anomalies associated with this identification mentioned already in the list of anomalies (see this). The existence of M₈₉ hadron physics can have dramatic implications. For instance, a dramatic modification of the model of the Sun (see this) can be considered.
3. The ratio of the p-adic length scales associated with M₁₀₇ and M₈₉, characterizing the Compton lengths and also defining the geometric size of nucleons as 3-surfaces, is 512. The assumption is that the geometric size of the M₈₉ hadron with a large h_eff is the same as for M₁₀₇ hadron at quantum criticality implies h_eff/h= 512. The sizes of M₈₉ hadrons would be the same as for ordinary hadrons at quantum criticality for the transition from M₈₉ hadron physics to M₁₀₇ hadron physics.
4. I have proposed the identification of various bumps observed at LHC, originally identified first as candidates for SUSY particles but then rejected, in terms of M₈₉ mesons (see this and this).

The large mass of the official top quark raises the question whether it could be M₈₉ quark created at quantum criticality.

1. A natural guess is that the lifetime of top quark at quantum criticality is scaled up h_eff/h= 512 to .25 × 10^-21 s. The corresponding distance scale would be .75× 10^-13 m, which is longer than the nuclear size scale!
2. A reasonable guess is that the hadronization time scale for M₈₉ is for h_eff/h scaled down by factor 1/512 due to decrease of the p-adic length scales. This p-adic length scale corresponds to the geometric size scale of the causal diamond CD= cd\times CP₂ assignable to the region in which the phase transition occurs. This local phase transition is discussed here. The increase h_eff→ 512h_eff keeps the geometric time scale associated for hadronization the same as it would be for ordinary hadrons and determined by the p-adic time scale L(107) assignable to ordinary hadrons.

   What happens to the rate of hadronization? The phase transition increasing the value of h_eff guarantees that the TGD counterpart of perturbative theory,, still applies. "Mother Nature loves her theoreticians" (see this) is one way to express this principle. Since the zeroth order term in the TGD counterpart of the perturbative expansion, giving the classical approximation, does not depend on h_eff, the classical approximation improves as h_eff increases.

   The rate for M₈₉ hadronization is proportional to the hadronic mass scale m(89)=512m(107). Since the geometric time scale is L(107) by quantum criticality, the short lifetime of top does not prevent the formation of toponium. Quantum criticality could quite generally increase the probabilities for the formation of bound states of very short-lived particles.

The basic objection is that the official top quark as M₈₉ quark would most naturally correspond to genus g=0 for the partonic 2-surface and serve as a counterpart of u quark. The actual g=2 U type quark should have a lower mass.

1. There is indeed evidence for a top quark-like state at much lower mass from Aleph. The mass is estimated to be about 30 GeV or 28 GeV (see this). This has motivated the question whether the two candidates for the top quark could correspond to a scaled variant of the top. In the TGD framework, the p-adic length scale hypothesis might allow this (see this and this).
2. What about the toponium in this case? There is an old anomaly reported by Aleph at 56 GeV (see this) and there is reference to an old paper: ALEPH Collaboration, D. Buskulic et al, CERN preprint PPE/96 052. What was observed was 4-jet events consisting of dijets with invariant mass around 55 GeV. What makes this interesting is that the mass of 28 GeV particle candidates would be one half of the mass of a particle with a mass of 56 GeV particle, quite near to 55 GeV. Could this state be the toponium as g=2 U quark (see this and this)?

If this picture is correct, the official top quark would more naturally correspond to the genus g=0 and therefore to M₈₉ u quark. Could the poor understanding of the family replication phenomenon and of the origin of the CKM mixing explain this mis-interpretation?

1. The CKM matrix V is empirically determined from charged currents (W decays). The matrix elements of type V^U_D, U ∈{u,c}, D ∈{d,s} reflect the CKM mixing of d and s quarks. Unitary conditions bring in the matrix elements V^t_D and dependence on top quark mass. Both beta decays and kaon decays provide information about V^U_D, U U ∈{u,c}, D ∈{d,s}. These two kinds of constraints lead to slightly different outcomes \cite{bpnu/partano} for V.
2. Could a wrong identification of the top quark mass cause the discrepancy? In TGD, the official top as the g=0 quark of "dark" M₈₉ hadron physics created in the transition to quark-gluon plasma would induce a leakage of probability inducing a genuine violation of the unitary for the CKM matrix.
3. In TGD, the description of family replication has topological explanation and CKM mixing reduces to topological mixing (see this and this). A model for the transition between M₁₀₇ and M₈₉ is needed to see whether the new interpretation can be consistent with what is known about creation of official top quarks.
4. The prediction is that the official top as an M₈₉ u quark is accompanied by an M₈₉ d quark so that toponium should be a member of an isospin triplet. The M₈₉ counterparts of π and ρ mesons should exist. The discovery of the M₈₉ d quark, perhaps through the discovery of an isospin triplet for toponium, with nearly the same mass as the official top quark, would force us to take the TGD view seriously.

See the article Official top quark and toponium as  particles of M₈₉ hadron physics?, the article The findings of RHIC about quark gluon plasma from the TGD point of view or the chapter Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD.

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.