About the interpretation of the parameter β0 and a view of the reduction of the oscillator frequency in Allais effect

There are several longstanding questions related to the parameter β₀ appearing in the formula ℏ_gr= GMm/β₀ introduced originally by Nottale.

1. Is the interpretation of β₀ as a velocity parameter necessary? The gravitational Compton length Λ_gr =r_s/2β₀ has no dependence on the small mass m, which conforms with the Equivalence Principle. Also the cyclotron frequencies at the monopole flux tubes of the gravitational field body are independent of m.
2. There are two preferred values for β₀: β₀∼ 1 assigned with the Earth's gravitational field body an and β₀∼ 2^-11 assigned with the field body of the Sun.
3. The velocity of the solar system with respect to the galaxy is of the same magnitude as β₀, which supports the interpretation as velocity. The interpretation of β₀=v₀/c∼ 1 as a velocity of a massive object does not however look sensible.

There might be a very simple solution to these interpretational problems, which I have failed to notice.

1. In the standard quantum theory two quantum lengths characterize a massive particle. The Compton length Λ_c= h/m and the de-Broglie wavelength Λ_de-B= h/mβ₀, where β₀=v₀/c is the velocity of particle using light velocity as a unit.
2. Could the gravitational Planck constant ℏ_gr(S) assigned to Sun and also planets in the Bohr model for planetary orbits corresponds to de-Broglie wave length and could β₀ correspond to a velocity 220-230 km/s giving β ∈ [(.73, .77) × 10^-3] of the solar system with respect to galactic center. The error is about 20 per cent. The gravitational Planck constant assigned with the Earth would correspond to the gravitational Compton length and the problem with β₀=1 would disappear.

There are however an objections against this proposal.

1. The problem is that the Bohr orbit quantization of the planetary system (see this) does not make sense for this interpretation. The quantum input in the quantization is the quantization of angular momentum and it would say that L_z/m equals to a multiple of the gravitational de-Broglie wavelength. This does not make sense in the framework of standard QM. This suggests that β₀ cannot have an interpretation as physical velocity of a massive object. Could it correspond to an analog of light velocity? Neither can the value β₀(E)∼ 1 for the Earth for cosmological scales be identified as a velocity for a massive object.
2. M⁸-H duality for the gravitational Planck constant leads to a fractal generalization of Hubble's law suggesting that Hubble tension might relate to two slightly different values of β₀∼1 in short and long length scales differing by 5-6 percent (see this). This interpretation is not consistent with the interpretation of Λ_gr for β₀=1 as gravitational Compton length.

   The problem disappears if one can interpret v₀≤ c as light velocity with c_#= g_tt^1/2c≤ c along the space-time surface in the formula for the gravitational Compton length.

3. This interpretation has non-trivial consequences. In the case of the Sun, the disappearance of the 1/β₀(S)∼ 2¹¹ from the formula h_gr reduces the gravitational Compton length and gives Λ_gr(S)= 3× 10⁵Λ_gr(E) rather than Λ_gr(S)∼ 2¹¹× 3× 10⁵× Λ_gr(E). The energy E= h_gr(S)f for a given frequency would be also reduced by β₀(S)∼ 2^-11. And as noticed, the Bohr quantization of the planetary system would not make sense anymore.
4. It seems that the only solution to the problem is that β₀ is quite generally identifiable as reduced light velocity c_#. The reduction of c_#=(g_tt)^1/2 to say c_# ∼ 2^-11 would however require huge gravitational fields: this does not make sense in general relativistic framework.

Warping of the space-time surfaces as a solution of the problems

A possible solution of the problem comes from a basic distinction between TGD and General Relativity noticed already during the first year of TGD.

1. TGD allows solutions of field equations, which are gravitational vacua in the sense of GRT and also gauge theory vacua for induced gauge fields. The solutions however allow warping possible only for surfaces. A thin metal plate or a sheet of paper are good examples of a system unstable against warping and therefore critical systems.
2. TGD indeed allows minimal surface solutions with a 1-D CP₂ projection belonging to geodesic circle S¹⊂ CP₂ for which M⁴ time coordinate in the rest system of the causal diamond CD is of form m^0= t- φ/ω. The induced metric of X⁴ given by ds²= (1-R²ω²)-dz²-dwdw is flat and has a deformation of the Poinca group as isometries. The interpretation c_#= (1-R²ω²)^1/2 as a reduced light velocity is natural: the path around a warped space-time surface is longer than along a non-warped one. There would be no gravitational force but the vacuum would be warped. This warping makes sense also for monopole flux tubes obtained as deformations of the Cartesian product M²⊂ Y²⊂ M⁴× CP₂. M² would be completely analogous to a metal plate and could be warped.
3. The warping can occur also at the level of the embedding space H=M⁴× CP₂ for the Hamilton-Jacobi structure (see this). Now M²⊂ M² and CP₂ degrees would mix. An analogy is provided by a cylinder surface for which the coordinates (z,φ) are replaced with coordinates z-kφ,z+kφ for which coordinate lines are dual helices. The hypercomplex coordinates (u,v)→ (t-z,t+z) would be replaced with (u=T-z,v=T+z) where T is defined as T= t-φ/ω. The canonical embedding of M²⊂ M⁴ with constant CP₂ coordinates would be tilted towards the direction of S¹⊂ CP₂. CP₂ complex coordinates would suffer a time dependent U(1) rotation φ→ φ-ω t, which is holomorphic transformation and gives rise to a twisted Hamilton-Jacobi structure.
4. Even more general twisted Hamilton-Jacobi structures can be imagined (see this). The TGD based model for the honeybee dance (see this) led to the proposal that there are preferred extremals as sphere bundles, which assign to a given point of the space-time surface a geodesic sphere, whose position in CP₂ depends on 2 M⁴ coordinates so that one speak of local SU(3) rotation of the geodesic sphere depending on two M⁴ coordinates. Could also these kinds of twistings define exotic Hamilton-Jacobi structures? Could also twistings depending on time coordinate and complex coordinate w define exotic exotic Hamilton-Jacobi structures?
5. The twisted Hamilton-Jacobi structures could be associated with monopole flux tubes serving as body parts of field bodies. This would give connection with ℏ_gr. Also space-time surfaces representable as graps M⁴× CP₂ could have a twisted Hamilton-Jacobi structure and the Hubble tension (see this) could be understood if the Hamilton structures differ by a small twist in long and short cosmological scales.

   In the planetary system there are two options for the Bohr quantization. β₀∼ 2^-11 would be true for the inner planets. For outer planets there are two options. Either β₀∼ 2^-11 is true but the principal quantum number n comes as multiples of 5 or β₀=2^-11/5 is true and Earth corresponds to the principal quantum number n=1 for outer planets or n=5 for the inner planets. For the second option c_#=β₀ would be different at the gravitational monopole flux tubes.

A connection with the frequency reduction in Allais effect

There would be a connection with the TGD proposed model explaining the Allais effect.

1. There is a surprisingly large reduction of the value of the oscillation frequency having upper bound Δ f/f≤ 2^-11. This brings in mind β₀(S) and the proposal was that the quantum critical transitions involves fluctuations reducing the oscillator frequency satisfying the formula E= h_gr(E)f: now the mass of the pendulum would be in the role of the small mass.
2. The modification Δ c_#/c_# would be needed. The gravitational fluctuations required to produced the effect would be quite too large as compared to the reduction of the value of c from its maximal value by GM_S/AU =r_s(S)/2AU∼ 10^-9 and GM_E/R_E= r_s(E)/2R_E∼ 10^-9.

The physical mechanism causing this modification should be identified and explain the large value of Δ c_#/c_#.

1. Warping is a critical phenomenon. Space-time warping as a fundamental quantum critical phenomenon could accompany and even induce many kinds of quantum critical phenomena, in particular Allais effect.
2. The model for the Allais effect proposed that diffraction-like effect for the gravitational flux tubes meaning a deviation of the monopole flux tubes, analogous to the deviation of flow lines of a hydrodynamic flow past solid object, could produce reduction of the effective gravitational flux. This would reduce the effective gravitational mass M_S experienced by the pendulum.
3. But why should this reduction be Δ f/f≤ 2^-11? Could the change of the mass of the pendulum could affect the value of h_gr forcing the change of f if E is invariant? The reduction Δ m/m≤ 2^-11 for the mass of the pendulum is highly implausible.
4. What about the particle mass associated with the field body? Δ f/f≤ 2^-11 is not far from the electron-proton mass ratio m_e/m_p∼ 1/1880: the deviation is 9 per cent. If the field body contains hydrogen atoms, their ionization to protons and electrons transforming to ordinary electrons would reduce h_gr by the required amount.

   The hydrogen atoms should be Rydberg atoms with a very small binding energy and therefore with very large size: this is indeed possible at the field body. The dropped electrons should have smaller energy compensating for the energy needed for the energy needed for ionization. The transition could take place by tunnelling and therefore involve a pair of "big" state function reductions (BSFRs).

   This kind of phase transition should occur at quantum criticality assigned with the beginning of the solar eclipse? Why the turning of the monopole flux tubes meeting the Moon should induce a phase transition leading to the transformation of dark electrons to ordinary electrons? Are the electrons so near to ionization state the turning ionizes them?

How to test the proposal?

How could the proposal ℏ_gr= GMm/c_# implying the formulas for the gravitational Compton length and time and de-Broglie wavelength be tested?

1. For the dark cyclotron the transitions at the magnetic body, the dependendence of cyclotron energy on m disappears. For other frequencies this is not the case and one would have E=h_grf= (GMm/2πc_#)× f. A possible test is to look whether the energies for slightly different masses m differ. The second possibility is that c_{# varies for critical phenomena.}
2. Examples would be proton and hydrogen atom with a relative mass difference of order 2^-11 and proton and neutron with mass difference of .14 per cent. One can imagine an entire spectroscopy allowing to test the notion of gravitational Planck constant by using the effects caused by the transformation of gravitationally dark photons to ordinary ones. Biophotons could be products of this transformation (see this).

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.

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.