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 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=.867. The different values of Hubble constant (10 per cent difference) in long and short scales can be understood in terms of different values of β₀ with 10 per cent difference.

The quantization of redshifts as integer multiples associated with so-called God's fingers, discovered by Halton Arp, could be understood in terms of the quantization rule β₀=1/n proposed here. This quantization is however excluded in cosmic scales by the existing bounds on total mass density but could apply in shorter scales such as Sun and Earth. An alternative TGD based explanation is in terms of H³ tessellation realized for astrophysical objects (see here).

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

With inspiration coming from the claim of Donut Lab of having constructed a battery with almost miraculous properties. There is very little publlished 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, 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 TGD and condensed matter.

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.

TGD counterpart of Feynman diagrammatics with application to QFT limit and CP violation

Concerning the construction of scattering amplitudes, the M⁸ approach provides a very nice picture (see this) about the scattering amplitudes in the momentum space representation in the fermionic sector involving only 2-vertices identifiable in terms of analog of Brownian motion. This representation is however restricted to scattering amplitudes for a fixed space-time surface. The full scattering amplitudes require a functional integral over the WCW and this gives rise to the counterparts of bosonic propagators. In this article this aspect will be discussed.

The QFT limit of TGD must exist and emerge naturally from the full theory. This gives strong hints. One should understand the TGD counterparts of various notions such as fermion lines, vertices, fermion pair creation, and loops. The basic idea is simple: n-point functions of QFT generalize to n-point functions for the WCW spinor field at points which correspond to the 3-D edges of the space-time defining the vertices. Edges are 3-D delta function singularities for the trace of the second fundamental form for space-time surface as minimal surface, vanishing elsewhere and having an interpretation as a generalized acceleration and generalized classical Higgs field. This is true for any general coordinate invariant action constructible in terms of the induced geometry and has interpretation as universality associated with 4-D quantum criticality.

A key role is played by the notion of exotic smooth structure (see this, this, and this), which are possible in TGD (see this, this, this, and this). Exotic smooth structure is realized in terms of edges of the space-time allowing V-shaped fermion lines. In time direction this corresponds to a creation of a fermion pair. Most importantly, it is also possible to have finite fermion loops in which the fermion turns backwards in time and returns back along the same line.

This picture is applied to CP violation, whose understanding relies on loops. TGD predicts an entire hierarchy of standard model physics. A given standard model physics corresponds to color multiplets associated with a given mode of the Dirac equation in H (see this and this). To each multiplet one can assign a p-adic mass scale. The local transition to a scaled variant of hadron physics with a larger p-adic mass scale contributes to the CP violation. The CP violation can be assigned to the instanton part of the Kähler action giving rise to Kähler-Chern-Simons term assignable to the light-like partonic orbit carrying the fermion line (see this and this).

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.