TGD diary

Giant rings as the most recent evidence for the notion of cosmic string

2026-06-08T04:27:51.431-07:00

Sabine Hossenfelder's Youtube video (see this) about the observation of a giant ring (GR) having a diameter of 3 billion ly with a statistical significance is 4.1 σ (1/20,000) in constellation Bo tes at a distance of 7 billion light years. The article "Giant Ring in the Sky" by Lopez and Clowes (see this) reports the discovery.

GR has clusters of galaxies behind it. The light arriving from the galaxies is absorbed as it travels through the gas. There is an enhanced absorption at the ring. GR has as its part Giant Arc (GA) (see this) having northern and southern parts and encloses Big Ring (BR) (see this) having 4.5± .6 σ evidence. BR has diameter ∼ 400 Mpc.

Here is the abstract of the article:

We present the discovery of "A Giant Ring on the Sky" (GR); a ring-like, ultra-large-scale structure at z ∼ 0.8, located in the same field that contains the previously-documented Giant Arc (GA) and Big Ring (BR). The GR was predicted from the presence of a Northern Arc (NA) filament (noted in previous work), which looked like it could, with more or enhanced data, connect with the GA to form a giant ring that encompasses the BR.

There is now much evidence to support the reality of a GR. There appear to be two overlapping versions of the GR which differ by only the left-hand-side trajectory; this branching in the LHS of the GR was identified with the FilFinder algorithm and appears to correspond to both the GR prediction (the extended, elliptical, GR from the GA+NA ellipse), and the visually-identified ellipse (the visually-impressive, almost contiguous, roughly circular, GR which is enhanced by a tilted viewing angle). The branching in the GR seems to be hinting at multiple, overlapping ring features. The GR consists of a thin, filamentary northern region, a clustered, ambiguous southern region (including the members of the GA), and filamentary branching towards the LHS.

Statistical assessment with elliptical shells, and optimum elliptical-shell-matching, identified two ≥ 4σ ellipse features corresponding to the GR prediction and to the visually-identified GR. Additionally, the 2D Power Spectrum Analysis identified significant (3.5σ ) clustering on scales ∼ 320 Mpc. We also applied our statistical assessments to random data and to FLAMINGO-10K simulated data. The results demonstrate that, while superficially "significant" elliptical shells can be reproduced in random data with the optimum ellipse-matching method (many trials giving the "look-elsewhere" effect), with 2D PSA all of the random fields, and FLAMINGO-10K fields, were found to be entirely consistent with random.

The structures cannot have gravitational origin since the formation of bound states of this size by gravitational condensation is impossible in ΛCDM scenario. Some new interaction is needed. In TGD, space-times are 4-D surfaces in H=M⁴× CP₂ satisfying holography = holomorphy principle predicting that, apart from 3-D singularities representing edges of the space-time, space-time surfaces minimal surfaces obeying generalized holography satisfy the field equations for any general coordinate invariant variational principle constructible in terms of the induced geometry. Cosmic strings, which can thicken to monopole flux tubes, are fundamental structures predicted by TGD. They appear in all scales from cosmology to hadron physics and even down to CP₂ scale (see this and this). The natural identification of Giant Ring and Big Ring is as closed cosmic strings, whose immense gravitational field attracts gas around them.

See the article About the recent TGD based view concerning cosmology and astrophysics 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.

How did metabolism emerge?: breathing soil as a guideline

2026-06-05T20:00:40.963-07:00

This finding relates in an interesting way to the TGD inspired view that life and even genetic code are universal. Even quartz crystals (see this) could be living in a primitive sense and the basic quantum mechanism would be the same as for ordinary life. Pollack effect (see this, this this, this, this, this) in which protons are kicked to the magnetic body and generate in this way negatively charged exclusion zone (EZ) would be fundamental for metabolism. The dropping of dark protons from the magnetic body in the reverse Pollack effect would liberate the metabolic energy.

The findings of Fontaine's Lab suggest that in soil a hugely simplified variant of Krebs cycle and electron transport chain (ETC) make possible breathing producing CO₂ originates basically from the COOH groups of proteins. Consider first how the process occurs in biology.

The function of the Krebs cycle is to strip high energy electrons of the fuel and feed them to the electron transport chain (ETC) liberating the energy of electrons. According to the standard view, this creates electrochemical gradient pumping hydrogen ions across the mitochondrial membrane.
Krebs cycle strips electrons from the 2-carbon compounds obtained from the pyruvates combining with vitamin A to form Co-A involving citrate with 6 C atoms. Krebs cycle has as wastes CO₂ and water as the end product of ETC. The electrons striped from the counterpart provide the needed energy to kick the H⁺ ions to the magnetic body.
Krebs cycle is preceded by the splitting of glucose C₆H₁₂ O₆ with 6 carbon atoms to two pyruvate molecules C₃H₃O₃^- with 3 C atoms plus 2 net ATP molecules and NADH moleculefeeding high energy electrons into electron transport chain (ETC). Before entering the Krebs cycle, the 3-carbon molecule pyruvate is transferred into the mitochondrial matrix. Here, the enzyme complex pyruvate dehydrogenase removes a carbon atom from pyruvate to release the first molecule of CO₂. The outcome is H₂C=(CH)-O^- with two C atoms, which is attached to Coenzyme A to form Acetyl-CoA.
First glucose molecule with 6 C atoms and serving as a fuel is decomposed to two pyruvate molecules. Before entering the Krebs cycle, the 3-carbon molecule pyruvate is transported into the mitochondrial matrix. Here, the enzyme complex pyruvate dehydrogenase removes a carbon atom from pyruvate to release the first molecule of CO₂.
The remaining 2-carbon fragment -(C=O)-CH₃, acetyl group, is fused to Coenzyme-A to form Acetyl-Co-A (Co-A is a complex molecule derived from vitamin B₅). Acetyl-Co-A is transported to the mitochondrial matrix and meets oxaloacetate with 4 C atoms to form citric acid with 6 C atoms. Citric acid flows through the cycle and comes back as C0-A ready to take to the process a new -(C=O)-CH₃ molecule.

Could TGD explain what happens in breathing without enzymes? The findings of Fontaine's Lab suggest that in soil a hugely simplified analogs of the process leading from glucose to two pyruvates, Krebs cycle and ETC make possible breathing producing CO₂ originates basically from the COOH groups of proteins.

In the case of the soil there are no enzymes, so that the splitting of glucose to pyruvates, the Krebs cycle and ETC should be replaced with something dramatically simpler.

Already in the splitting of glucose to pyruvate generates ATP and therefore also dark protons. What comes to mind is that the Pollack effect for some 6 -OH groups of glucose C₆H₁₂O₆ could transform them to O^- plus dark protons at the magnetic body. 2 pyruvate molecules would be obtained if only a single H⁺ per pyruvate ion is transformed to a dark proton.
In the TGD framework, the transfer of H⁺ ions from the interior of the mitochondria to their exteriors during ETC is replaced by their transfer to the magnetic body of the system. The transfer makes the system negatively charged and this provides the interior of EZ with additional negative charge. In fact, cells are always negatively charged: this can be explained by the charges of DNA and RNA strands carrying constant charge density which is 3 unit charges per codon. In this case, the units of 3 dark protons representing dark codons are stable against the reverse Pollack effect.
The energy liberated by the stripped electrons in ETC would be used to transfer ordinary H⁺ ions to dark protons at the magnetic body of mitochondria rather than to the exterior of the mitochondria. The dark protons would be attached to ADP to form ATP acting as a shuttle carrying dark protons to the user molecule. The metabolic energy would be used as the dark proton becomes an ordinary proton in the reverse Pollack effect.

One can also imagine a more effective option for metabolism.

All 6 -OH groups of the glucose transformed to O^- plus a dark proton. This would lead to 2 C₃H₃(O^-)₃ molecules with 3 dark protons at their magnetic bodies, which could liberate metabolic energy in the reverse Pollack effect.
Remarkably, each molecule has 3 dark protons and in the TGD view of genetic code they would define dark codons. Large values of h_eff mean algebraic complexity and intelligence. Could these dark codons give for the system the IQ needed to drive the process further on?
The splitting of C₃ H₃(O^-)₃ to CO₂ and acetyl molecule (C-O^-)-CH₃, involving the dropping of 2 further dark protons back to oxygen ions to form -OH groups, would generate CO₂ and the acetyl group. This process could be an ultra simplified version of the steps preceding ETC. The further dropping of the third dark proton to acetyl ion would be the counterpart of ETC and would also liberate metabolic energy.

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.

A model for the variation of Newton's constant based on dark gravitation radiation pressure

2026-06-04T00:26:42.964-07:00

The proposal (see this is that the radiation pressure of the dark gravitational radiation from the Sun and perhaps also from the Earth can produce effects comparable to the gravitational force of the Sun. This radiation is extremely weak. Could quantum coherence in the length scale defined by gravitational-Compton wavelength enhance the intensity of the gravitational radiation?

1. General description of the model

The first guess was that the gravitational radiation at energy range 1-10⁵ eV assumed to be produced by Sun could somehow transform to dark gravitons with Compton length equal to gravitational wavelength Λ= Λ_gr= r_S(Sun)/2β₀(Sun ∼ 3000) km ∼ R_E/2, which does not depend at all on the energy of the graviton. This would guarantee the quantum coherence in the Earth scale making possible large effects. In microscopic scales the gravitational radiation is generated by thermal collisions in solar plasma and in macroscopic scales by hydrodynamic fluctuations. The macroscopic mechanism is more plausible as a candidate for producing the gravitational dark gravitation.

The generation of quantum coherence as transformation of ordinary gravitons to dark gravitions is however difficult to understand. One can also consider a purely TGD based mechanism in which dark gravitons are generated at the gravitational magnetic body of the Sun, i.e. monopole flux tube loops associated with the Sun and mediating the gravitational interaction. The scale of Sunspots is indeed given by Λ_gr (see this. The gravitational radiation would be generated by the acceleration of charged particles in the magnetic field of the gravitational flux tubes.

The observed relative variation of Newton's constant is between .01-.1 percent. The value of c_#/c= 2^-11= .5× 10^-3 is one 1/2 of the lower bound. This observation might help in the attempts to understand about what is involved.

It is good to start with the possible gravitonic pressure caused by the Sun. The gravitational force of the Sun on the Earth must be compared to the total momentum flux produced by dark gravitons directed at the Earth to see whether the hypothesis can make sense. One must also test the corresponding hypothesis for other planets also in the case of the Earth's gravitational field.

The Sun is estimated to produce energy with a power of P=1.3× 10⁸ W through graviton radiation by thermal collisions and hydrodynamic fluctuations. The energy of the gravitons would in the range 1 eV-10⁵ eV. Thermal collisions, hydrodynamic fluctuations, and photoproduction by the decay of photons to gravitons.
The generated total power is estimated to be P= 1.3× 10⁸ W and correspond to a single nuclear power plant. It would give to give rise to a total momentum flux of F= P/c = 1.3/ N which is extremely small
The gravitational force of the Sun on the Earth is
F_gr ∼ 1.5× 3.54 × 10²² N .
The order of magnitude difference between F_gr and the force caused by the ordinary gravitational radiation pressure is enormous.
In absence of quantum coherence, the radiated power is proportional to the number N of emitters. Quantum coherence should effectively replace N with N². At least for the thermal radiation with high energies, it is difficult to see how this could amplifty the momentum flux so that it would be comparable to the gravitational force between the Earth and the Sun.
It seems more likely that the mechanism is related to the acceleration of gravitionally dark charged particles in the magnetic field of dark gravitational flux tubes characterized by ℏ_gr.
Λ_gr is the same regardless of the energy of the graviton E. The origin of quantum coherence and large effect would be here. Λ_gr = 3000 km that would be a wavelength and about half the radius of the Earth and could lead to effect in the scale of the entire Earth. Also the emission rate of the radiation in constant magnetic field of the Sunspot is proportional go Gm²f_c², f_c= eB/m and is independent of the mass of the m charged particle so that the radiation power is proportional to the total number of charged particles.

2. A model for the emission of dark gravitons

Consider now a model for the emission mechanism of gravitationally dark gravitons from the monopole flux tubes mediating the gravitational interaction.

Dark charges at the gravitational flux tubes of radius Λ_gr and extending to the Earth would produce the force as radiation pressure F= P/c, where P is the emitted power.
For dark gravitons, quantum coherence is assumed to produce a momentum proportional to the square N² of the number of emitters in the emitting region rather than to N as in absence of coherence.
Emission power P and corresponding momentum transfer rate F=P/c due to the radiation pressure for gravitational waves in a magnetic field B. The force produced by radiation pressure should be about 10^-2-10^-3 times smaller than the gravitational force. The lower bound is one 1/2 of β₀ ∼ 2^-11.

2.1 Parameters of the model

Consider first the parameters of the model.

The flux tubes should extend to the Earth and therefore have the length L= 1 AU. Their thickness is
Λ_gr = r_S(Sun)/2β₀(Sun) ∼ 3× 10⁶ m ∼ R_E/2 for β₀(Sun)= c_#/c= 2^-11.
The volume of the flux tube is given by
V= (π/2)LΛ_gr² .
A geometrically natural simplifying assumption is that there is about 1 unit charge per volume determined by the magnetic length L_B giving rise to a number density d/dV= 1/L_B³, L_B= (ℏ/eB)^1/2 .
The total number N of unit charges at the flux tube would be
N= (dn/dV)× V = (1/L_B³)× (π/2) AU× Λ_gr²

2.2 Radiation power and force for the Earth-Sun system

There exists a formula for the power of the gravitational radiation in a constant magnetic field B prevailing inside the monopole flux tube. Since cyclotron frequency f_c is inversely proportional to the mass of the particle, the power does not depend on the mass m of the charge.

The power of the gravitational radiation emitted by the unit charge e in a constant magnetic field is given by
P= (4/3) (Ge²/c³) β² γ⁴× y²~ J/s .
Here one gas y=r× B/T, r= .2566∼ .26.
The total radiation force is
F_rad= N²F=b× y⁵ β² γ⁴ × 5× 10²² ~N & y= r(B/T), r=.25 .

The outcome of the calculation is that the magnetic field at the monopole flux tubes cannot be much smaller than .25 Tesla unless one allows relativistic velocities for the charges. The based model for the generation of solar wind and radiation in the decay of M₈₉ protons to ordinary hadrons at the surface of the Sun (see this) indeed predicts relativistic energies.

2.4 The situation for the other planets

One can consider the situation for other planets using scaling arguments applied to F_gr and F_rad. The F_gr/F_rad scales like

(R_P/AU)⁴ (M^P/ME) B_P²

and the scaling

B_P B_E= (AU/R_P)²(M^E/MP)^1/2

leaves F_gr/F_rad invariant. Apart from mass ratio the scaling is that of a monopole magnetic field.

2.4 What about the Earth itself?

One can also ask whether F_rad due to the Earth itself could be important. In this case F_gr for a mass of 1 kg is scaled down to about 10 N and Λ_gr is scaled down to 5 mm. For a density of 10³ kg/m³, the volume Λ_gr³ corresponds to mass of 1.25 × 10^-4 kg so that the F_gr would be at the surface of the Earth about 1.25 × 10^-3 N. For the length L= R_{E/sub> of a monopole flux tube the (emanating from the interior of the Earth?) there would be a scaling down of F_rad by (R_{E/sub>/AU) × (Λ_gr(E)/&Lambda_gr(S))²∼ 10^-5× 10^-16 ∼ 10^-21.}}

For F_rad= 3.5× 10¹⁹ N corresponding to the reduction factor 10^-3, one would have F_gr∼ 3.5 × 10^-2 N. F_gr would be by an order of magnitude larger than the naive estimate and corresponds to a reduction factor 10^-2, which corresponds to the upper bound for Δ G/G. Maybe the combined effects of the Sun and Earth could explain the fluctuations of G.

2.5. The upper bound for the strength of the magnetic field of monopole flux tube equals to the strength of the "endogenous" magnetic field

By using scaling arguments, one can deduce an upper bound for y_max for the Earth and therefore for the maximum value B_max of the Earth's magnetic field by starting from the Sun-Earth system with y_max(S,E)∼ .25 and from the proportionally y_max ∝ (F_gr/L²)^1/5, where L is the length of the monopole flux tube.

In the estimate the F_gr(Sun,Earth) is replaced with the force between Earth and a mass blob with the density of water ρ_w=10³ kg/m³ with a volume Λ_gr³(E) and having mass m(Λ_gr)=ρ_wΛ_gr(E)³ .
This gives m(Λ_gr)∼ .75× 10²³m_p. F_gr is scaled down by the factor M_S/m(Λ_gr). From M_S/m_p= 1.189× 10⁵⁷ one has M_S/m(Λ_gr)= 1.59× 10²⁴.
In the estimate F_rad(Sun) is replaced by that for the Earth. The radiation force satisfies F_rad ∝ L². Assume that L= R_E holds true at the surface of the Earth. The scaling factor for F_rad is (R_E/AU)², where one has AU/R_E∼ .235× 10⁵.
The overall scaling factor in y_max(S,E)→ y_max(E) is (M_S/m(Λ_gr))^-1/5× (AU/R_E)^2/5. The outcome is y_max= .72× 10^-3. This gives B_max= 1.87× 10^-4 Tesla which corresponds to .187 Gauss. The strength for the Earth's magnetic field varies in the range .25-.65 Gauss. Amazingly, the empirical estimate for the strength of the "endogenous" magnetic field at monopole flux tubes is .2 Gauss!
The upper y_max(P)/y_max(E) scales like (R_E/R_P)^4/5: there is no dependence on Λ_gr. The planetary Bohr model inspired by the model of Nottale predicts y_max(P)/y_max(E)∼ 2.3 for Mercury. For outer planets the prediction is y_max(P)/y_max(E)∼ (1/n)^8/5, n=1,2,.. so that the strength of the "endogenous" magnetic field would weaken.
Jupiter is the largest planet with equatorial radius R_P= 11.2 R_E. Its surface density is ρ∼ xρ_w, x=2× 10^-4. This gives y_max(P)/y_max(E)∼ (R_E/R_J)^4/5× x^1/5 ∼ .026 for the endogenous magnetic field of Jupiter. The strength of Jupiter's total magnetic field, expected to be stronger than the endogenous magnetic field, is 2× 10⁴ times that of the Earth: there is a difference of 6 orders of magnitude.

One can argue that the model involves numerical constants of order unity. Since y_max is expressible as a fifth root, they do not have any significance. It seems that by applying these arguments Sun-planet pairs and planets could give very powerful constraints on the endogneous magnetic field strengths involved.

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.

TGD based description of contactless friction in magnetic systems

2026-05-31T22:07:11.857-07:00

Science daily has a highly interesting article with the title "Friction without contact discovered as magnetic forces break a 300-year-old law" (see this"). I am grateful to Gary Ehlenberger for sending the link. There is an article by Hongri Gu, Anton L ders, Clemens Bechinger with title "Non-monotonic magnetic friction from collective rotor dynamics" published in Nature Materials, 2026; DOI: 10.1038/s41563-026-02538-1 (see this).

Researchers at the University of Konstanz have identified a completely new type of sliding friction. The figure of the popular article (see this") illustrates the phenomenon.

There are two parallel magnetic layers composed of permanent dipole magnets with magnetization parallel to the layer. The magnets in the upper layer are free to rotate, while those in the lower layer are fixed. For the general sliding motion the dipole magnets of the upper layer experience a torque forcing them to rotate. As a consequence, the upper magnets periodically reorient, dissipating energy and giving rise to contactless friction. What is new and unexpected is that by decreasing the distance between the layers, which controls the effective load, the friction does not increase monotonically, in contrast to the prediction of Amontons law.

Amontons' law was originally linked to mechanical friction describing how much force presses two surfaces together. Indeed heavier objects are harder to move along surfaces than lighter ones. The explanation for the mechanical friction is that surfaces deform slightly under pressure, creating more microscopic contact points that increase resistance. The generalization of Amonton's law for magnets characterizes contactless friction: the distance of magnets gives rise to the effective weight, which increases as the distance is reduced. This explains why magnets with opposite dipole directions stick together.
For a pair of magnetic layers, the observed new kind of resistance to motion arises from the collective behavior of magnetic elements: which is rather complex when the individual magnets can rotate. Friction does not always increase steadily with the load (now the distance between the layers) but can reach a clear peak when magnetic ordering inside the system becomes frustrated.
Frustration occurs in spin glasses (see this) consisting of dipoles which can have different orientations and makes them extremely complex systems with a large number of free energy minima. Frustration, appearing already for 3 magnetic dipoles, means that the interaction energy for a single pair can be minimized but this is not possible for all pairs. Two people can agree, but in a group of 3 people, the third person tends to remain the third wheel. As a consequence, there are several free energy minima, which are degenerate in energy and the system does not know which of them to choose.

The contactless friction has a nice description based on the TGD view of space-time and classical fields.

In TGD, the classical fields are associated with what I refer to as field body as a space-time surface associated with the space-time surface of H= M⁴×CP₂ defining what might be called the physical body. The field body carries geometrized classical fields having a complex topology involving for instance magnetic monopole flux tubes and sheets (see for instance this and this).
The physical contact would be present also now but between the field bodies and produce small "field body friction". Monopole flux tubes associated with two dipole magnets minimize interaction energy when the flux tubes have opposite direction: in the contact the magnetic fields of flux tubes would cancel and flux tubes would fuse. Frustration can occur since flux tube can be parallel only with single flux tube unless all are parallel (for the role of spin glasses in TGD see this). Only the minimization of the interaction energy when the flux tubes have opposite direction and fuse to a single flux tube.
This explains why two dipole magnets tend to stick to each other: their separation creates magnetic field energy as separate flux tubes with opposite direction of flux are created. When the flux tube directions vary, spin glass phase emerges and the motion forces the and friction occurs so that there are several minima of free energy. Energy and external force is needed to move the layers with respect to each other.

See the article TGD and condensed matter or the chapter 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.

Gravity goes quantum: really?

2026-05-31T03:25:23.481-07:00

Just for fun, I had a session about rather hypeish "How gravity goes quantum" of NASA (see this) with Google to revive what I remember of the model of Partanen and Tulkki from previous discussions with Tulkki and about the review of their model that I wrote (see blog post). I also proposed the role of the octonions then and they are indeed introduced in their recent article.

The core fields are the space-time dimension field and 8-D spinor field defined in empty Minkowski space.

The space-time dimension field is essentially the tetrad field of GR and allows us to construct the space-time metric formally. Tetrad components would transform in GR by local Lorentz transformations acting as non-compact gauge symmetry, which however is not used.
1. The space-time is the flat Minkowski space M⁴ globally. Non-trivial topologies are not possible. This is an extremely strong limitation and one loses most of GR. One has just gauge theory in M⁴.
2. Metric as gravitational field is defined purely algebraically as an analog of vierein field by standard rules. The dimension field. as tetrad is a quantum field in M⁴ and the metric is constructed in terms of it. The products of vielbein components involve singularities and normal ordering is required. The construction of Christoffel symbols and curvature leads to horrible non-linearities. Poincare symmetries are obtained. Equivalence Principle and general coordinate invariance are claimed but it is difficult to take this claim seriously. The reason is that the action of the general coordinate coordinate transformations is very different from the action of gauge symmetries although the physical content of these symmetries is the same.
  One should should show that general coordinate invariance emerges from their theory but the definition of the space-time metric and curvature tensor, Ricci tensor and Ricci tensor as its companions is extremely difficult since quantum fields are in question. The same problems are encountered as in general relativity.
3. 8-spinor field would naturally correspond to the spinors of the standard model having besides spin degrees of freedom naturally electroweak spin and em charge. Color quantum numbers missing. This would however lead to problems since M⁴ spinors have non-compact gauge group SL(2,C) if one wants the gravitational gauge symmetries of GR. Color quantum numbers are missing.
  Symmetry group is assumed to be SU(8) assigned with 8-spinors and it is compact. Gravitation is assigned with 4-D Cartan group U(1)⁴. The remaining 3-D Cartan algebra U(1)³ should represent standard model Cartan algebra which is however 4-D. It is assumed that electromagnetic U(1) is shared by the gravitational Cartan group and standard model gauge group.
  The identification of the symmetries as la arger symmetry group SU(8) is not consistent with the notion of internal symmetries in Minkowski space allowing SL(2,c)× SU(2)_R×SU(2)_L at most as symmetries. Color symmetries remain missing in standard interpretation.
4. Gauge theories contain no inherent scales. How does the gravitational constant emerge? The proposal is that the dimension field, vierbein, develops a vacuum expectation value, which in the first approximation gives M⁴ metric. The correction to this is identified as a gravitational field with a scale given by gravitational constant. Already Saharov proposed something like this. Einstein's equations for YM fields in question should emerge and constraint the theory. This is just a semiclassical approximation used also by GR and EYM to avoid the non-renormalizable divergences.
The authors have clearly picked several ideas from TGD (congratulations for a good taste!) and try to fuse them to their own theory.
1. Also in TGD empty Minkowski space plays a key role but space-times are surfaces in H=M⁴×CP₂ and the dynamics is purely geometric. Poincare symmetry is not lost as in GR. The space-time surfaces representable as graphs M⁴→ CP₂ represent only special solutions important in the long length scale limit.
  CP₂ type extremals, cosmic strings are not surfaces of this type and are essential for the description of particles and monopole flux tubes are central for physics in all scales. Without non-trivial space-time topologies TGD would predict only one fermion generation. This is actually the situation also in the model of Partanen and Tulkki.
2. In TGD, the induced metric is a genuine metric and also spinor connection and spinor structure of H is induced and gives rise to electroweak gauge potentials. Also spinors are induced to the space-time surface.
3. In TGD one does not quantize the induced geometry. Instead, one introduces the notion of "world of classical worlds" (WCW) consisting of space-time surfaces as analogs of 4-D Bohr orbit so that one has wave mechanics in WCW with fermions included. Fermion fields are free fields in H identifiable as leptonic and quark-like fields and there are no divergence problems. The geometry of WCW is unique from its existence and has maximal symmetries: this is true already for the loop spaces.
4. The color degrees of freedom correspond to isometries of CP₂ and here comes the most dramatic prediction: an entire hierarchy of standard model physics is predicted since color is now associated with the CP₂ isometries and corresponds to color multiplets for the partial waves. Electroweak symmetries correspond to holonomomies of CP₂ and one can identify electroweak interactions in fermion spin degrees of freedom as color interactions.
5. Infinities cancel since holography = holomorphy principle solving the field equations implies that there is no path integral. Radiative corrections are obtained but are manifestly finite. No renormalization as elimination of infinities is needed.
6. Number theoretic vision defines the second half of TGD, complementary to the physics as geometry view and all basic number theory, including octonions and quaternions, is involved. Octonions are mentioned also in the recent article. I suggested a possible role of octonions in their theory in a discussion with Mikko Partanen (see the earlier blog post).
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.

Quantum Cheshire cats do not exist in the TGD Universe

2026-05-28T22:57:15.819-07:00

The article Quantum Cheshire Cats of Aharonov, Popescu, Rohrlich, and Skrzypczyk published in New Journal of Physics (see this) claims that the particle can be separated from its properties relies on the notion of weak measurement (see this). The mathematical model of weak measurements is not taken seriously by the mainstream and there are good reasons for the skepticism.

The claimed apparent separation of the particle from its properties (the grin of Cheshire cat from the Cheshire cat) could be an illusion and have a more mundane interpretation. This strange separation actually occurs in the sensory perception: the object and its properties, say the state of motion, are represented separately and one can ask whether something like this could occur at quantum level. The hypothesis raises many questions.

For instance, what does one mean with the particle? Usually the particle is identified as a collection of its properties like spin, energy and momentum. Now one adds the notion of particle path and this is in conflict with the standard QM. Only if one accepts path as observable, one can speak of states |A⟩ and |B⟩.
The detection of the particle is taken to mean its absorption: not a measurement of any usual property. The measurement would mean a localization to path |A⟩ or |B⟩ in the space of paths but in standard QM only the localization to a point of 3-space makes sense.
The conclusion is that the particle and its spin, parallel to the plane defined by the paths A and B, travel through different paths. This claim follows from the observation that the addition of a very weak magnetic field, orthogonal to the quantization axis of spin, has effect only at the second path, call it B, whereas the addition of a very thin absorbing screen has effect on the different path, call it A. Therefore one concludes that the spin moves along B and the particle along A.
In reality, the experimental arrangement guarantees that the spin directions are opposite on path A and B so that the claim about Chesire cat property is misinterpretation if taken literally.
How the spin directions at paths A and B are fixed.i.e. what determines the quantization axis of the spin. Could there be a magnetic field B_q, parallel to the plane defined by paths A and B, determining the quantization axis. When one adds a weak magnetic field ΔB orthogonal to the plane of A and B and therefore to B_q, it produces a torque trying to change the spin direction.
If the direction of the spin at path B is opposite to that of B_q, it corresponds to the maximum of the dipole energy E=-μ ċB_q which is unstable against the torque caused by the addition of ΔB. Think of a particle at the top of a hill. At path A the dipole energy is negative and minimum: this gives rise to stability and the addition of B. The torque has a negligible effect. One has quantum criticality at path and stability at path A.
Is the addition of a very thin screen ΔS analogous to the addition of the weak magnetic field ΔB. Is path B stable and not affected by ΔS and is path A critical and affected by ΔS This would explain the experimental findings.
There is however still a question to be answered. Why are the criticalities with respect to ΔB and ΔS orrelated? Why the criticality with respect to addition of ΔB implies stability with respect to the addition of ΔS and vice versa.
Could one understand the findings in the TGD framework?
1. There are the notions of preselection and postselection. Preselection is defined as a formation of a state (|A⟩ + |B⟩)|0⟩ and post selection as use of filter at path B to create state |A⟩|0⟩ + |B⟩|1⟩. As noticed, there is no notion of particle path in wave mechanics. The notion of spin state makes sense.
2. In TGD, point-like particles are replaced by 3-surfaces. Holography = holomorphy principle (see this and this) implies that 3-surfaces are replaced by 4-surfaces as analogs of Bohr orbits of 3-surfaces. This eliminates path integral and the associated infinities. This also forces zero energy ontology (see as new quantum ontology (see this and this) solving the basic paradox of quantum measurement theory.
  In TGD the introduction of states |A⟩ and |B⟩ makes sense in TGD. Fermions are located at Bohr orbits and define the spin states |0⟩ and |1⟩.
3. In TGD the classical description in terms of paths as Bohr orbits of 3-surfaces is an exact part of quantum description. At this level one can speak of classical energy and the notions of stability and criticality as unstability make sense.
4. Suppose that Bohr orbit A is obtained from stable Bohr orbit B by a deformation which increases its classical energy. This would make A unstable against the addition of ΔS. The state in which the Bohr orbit A ends by absorption at the screen is the stable state. Bohr orbit |B⟩ is unstable against the addition of ΔS because it is not a minimum of classical energy.
  If the preselected spin state |0⟩ is minimum of the magnetic energy then the |1⟩ associated with |B⟩ has a higher energy and is unstable against the addition of ΔB.
5. These assumptions imply the correlation between the two kinds of criticalities and would explain the claimed findings without the Cheshire cat hypothesis.
See the article Some comments related to Zero Energy Ontology or the chapter Zero Energy Ontology.
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.

Warping of the space-time surface explains the variation of Newton's constant

2026-05-27T07:32:42.394-07:00

Esa Ruoho has been studying Allais effect and has sent excellent and very inspiring questions related to the Allais effect. His questions have led to rather detailed and highly predictive TGD based model for the Allais effect based on the notion of warping distinguishing between GRT and TGD.

One of the latest questions whether the predicted large reduction of the light velocity, which is due to warping made possible only for space-times identified as 4-surfaces, could reflect itself in the value of the gravitational constant G.

Indeed, in 2015 a team of researchers led by J. D. Anderson published a study in Europhysics Letters (see this) reporting that measurements of Newton’s gravitational constant G over several decades appear to oscillate with a period of 5.899 +/- 0.062 years. The periodicity in G measurements matches the approximately 5.9-year oscillation found in Length of Day (LOD) variations, which are fluctuations in Earth's rotation rate. This phenomenon would be analogous to the variation of the pendulum period in the Allais effect.

Could warping, which predicts that the speed of light can have values c_# ≤ c=1 (here the units with c=1 are used), relate to the far too large variation associated with G measurements? Warping indeed affects the measured value of G.

I looked more closely to see if warping, which predicts that the speed of light can have values c_#≤c, could explain the far too large variation associated with G measurements. The second possibility is that the variation of the effective value of G is induced by the pressure caused by dark graviton feed from the Sun.

Warping does not affect the gradient of the gravitational potential to which the gravitational force is proportional. However, it causes a small change in g_tt and therefore in g^tt.
The gravitational acceleration predicted by GRT is given by
(1- r_{s/r²) ×GM/r²}
g_tt= 1-GMR/c²r == c_#² and extremely close to value 1 for the solar system.
c_#² is transformed by warping:
g_tt=c_#²→ c_#² -R²×ω² .
The change of g_tt can be much larger than the very small deviation of g_tt from 1 predicted by GRT. The effect on the gravitational force is however trivial.

Could the radiation pressure of the graviton flux coming from the Sun or from the Earth itself affect the value G_eff of G? This pressure decreases like 1/r² just as the gravitational force does. For the Sun graviton flux would concentrate to the wavelength λ= Λ_gr= 3000 km and the energies of gravitons would vary in the range 1-10⁵ eV. For the Earth the wavelength would be λ=Λ_gr= 5 mm. The period for the variation of c_# should be equal to that for the variation of G is T∼ 5.9 years.

If the gravitons with a shared gravitational Compton length λ=Λ_gr∼ R_E/2 from the Sun induce a transversal gravitational force, the variation of G_eff would be basically due to the emission of gravitons. The intensity of the emission of gravitational waves should have T as a period. Sunspot cycle has a period T_S= 11 years (varying in wide limits) and is part of a 22 year cycle. T∼ T_S/2 suggests a chaonic period doubling dynamics.
In TGD, sunspots relate very closely to the magnetic monopole flux tubes. The monopole flux loops emitted by reconnection mechanism from the Sun carry solar wind, radiation and also gravitationally dark gravitons with λ=Λ_gr∼ R_E/2 so that frequency-/wavelength resonance amplifies the effect of gravitons. Therefore variation of G_eff would reflect the dynamics of the monopole flux tubes.
The receival of dark gravitons induces transversal gravitational force and therefore has an effect on the rotation period of the Earth and could explain the correlation with the variation of LOD.

There is a connection to the problem of Hubble tension. The volume action is for warped extremals proportional to c_# and the 14 percent difference of two measured values of Hubble constant.

In the case of the Sun there is a rather dramatic prediction. The value of c_#∼2^-11 for the solar system can apply to gravitational flux tubes. The killer prediction is that signals about various dynamical phenomena in the Sun should appear as doubled. The first signal as ordinary radiation would arrive after 8 min 20 sec and the second copy as dark gravitational radiation after 11 days 20 hours 19 minutes.

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.

"Cold fusion" is now fashionable!

2026-05-24T21:25:45.982-07:00

Cold fusion is in fashion again as Sabine Hossenfelder informs (see this) and makes it clear that the massive funding is waste of money. I added a slightly ironic comment. Although Sabine uses irony, she cannot tolerate ironic attitude to her views so that the post was removed. I tried twice. The removal might be also automatic.

Sabine is a hardcore skeptic and cannot tolerate approaches claiming that there is something in physics which we do not yet quite understand. Even worse: I use high level mathematics and this is something that Sabine for some reason sees as an explanation for the recent miserable situation in theoretical physics. Sabine refuses to realize that both advanced mathematics and physical thinking are absolutely necessary. Here the censored out post is.

The issue of "cold fusion" is complex. The arguments of Sabine assume standard physics and in this framework the only logical conclusion is that pseudo science is in question. Congratulatons to Sabine for solid logical thinking.

Situation changes if one accepts that there might be still something in physics, which remains to be understood: after all, only 500 years have passed since Newton. This skeptic hunch might have something in it. The standard nuclear physics has a lot of anomalies and its applications to understand the energy production in stars, what happens supernova explosions, the abundances of elements in cosmos, etc.. involve anomalies.

For anyone with this attitude, the work of Tohoku group represents a highly interesting study of LENR (see this).

During the last two decades or so I have tried to develop understanding of "cold fusion" - or LENR - in the framework of new physics predicted by TGD (see this). This framework is much more general than a model trying to explain some particular observations: entire new world view is in question and "cold fusion" is only one of the numerous applications.

See the article A new experimental demonstration for the occurrence of low energy nuclear reactions.

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 recent view of Pollack battery allows to understand the claims of Donut Lab at quantitative level!

2026-05-23T23:45:35.267-07:00

The model for the Pollack battery developed through many twists and turns and several breakthroughs in the understanding of the physical interpretation of TGD were required (see this). The recent view of the charging of the Pollack battery would be as follows.

So, let us take the claims of Donut Lab (see this) seriously and look for what follows.

The number N_p of Pollack protons can be estimated from the transferred charge of Q=10⁵ Coulombs as N_p=Q/e. The claimed value for the stored energy E= 400 Wh. That would be equivalent to a proton energy E_p=E/N_p= 13.8 eV. For a Pollack battery this energy would be the energy gained by the Pollack electron when accelerated at the monopole flux tube in a voltage =13.8 V without dissipation. In a normal battery, the energy is dissipated quite thoroughly in Ohmic conduction.
The energy transferred by the Pollack effect would be smaller by a factor of 1/8 if the voltage is assumed to be 1.5 Volts. 8 of these four-layer units would be needed.
Then comes an important observation without, which I would never have arrived at the recent model, which could be called a full quantum version of the Pollack battery. The claimed 13.8 eV per Pollack electron corresponds to the binding energy 13.7 eV of a hydrogen atom! Is this a mere coincidence? Could it be that it is hydrogen atoms, rather than protons, which are transferred to the magnetic body to dark,to form Rydberg-atom like states with avery small binding energy so that the transferred energy per transferred proton would very close to the hydrogen atom binding energy of 13.7 eV per Pollack proton! This is exactly what follows by taking the claims of Donut Lab seriously. The phase transition generating a dielectric would store the electrostatic energy during the charging. The charge separation in the Pollack effect would be between ordinary matter and the dark matter at the magnetic body rather than between electrodes. However, the wave functions for the proton and electron of the dark Rydberg-like hydrogen atom tend to localize near opposite electrodes.
There was also the problem of whether the accelerated Pollack protons give too much momentum to the target electrode. Would that explain the reported swelling, which was in the order of 4 per cent? It turned out that for the classical variant of the model a simple estimate gives a completely negligible force, which is as much as ten orders of magnitude smaller than the estimate of the swelling force given by Google LLM, which is of order 10⁵ N.
The situations simply cannot be compared. In a standard battery, the currents are ohmic and produce swelling and also heating through dissipation. For a Pollack battery, electrons travel in flux tubes and would transfer impulse and energy directly to the target electrode.

For a moment I believed that the dielectric property of the target electrode E2 could be relevant for energy storage. As a side product, it turned out that TGD could offer an elegant first principle description of dielectrics using spacetime surfaces.

While building a model for the Allais effect (see this), I realized that the universal solutions of field equations that I found 47 years ago come to the rescue. They correspond to "warped" embedding of Minkowski space as a surface of H=M⁴× CP₂, come to rescue.
They do not involve gravitational or gauge fields, but they are warped, which means that they are tilted to the direction of M⁴× S¹ ⊂ H. The angular coordinate of S¹ is given by Φ = ω t implying that the time component g_tt of the induced metric decreases from 1 to 1-R²ω². The speed of light reduces to c_#= (1-R²ω²)^1/2 <c.
The warped space-time surfaces are quantum critical against the change of c_#. A vibrating thin metal plate serves as a good analogy. The metal plate corresponds now to the M² ⊂ M⁴. Warping generalizes to Hamilton-Jacobi structure (see this) so that the notion applies also to non-vacuum extremals. The quantum criticality would be a geometric correlate for that of quantum phase transitions.
This has several applications:
1. c_#/c corresponds in a natural way to the velocity parameter β₀ of the gravitational Planck constant GMm/β₀, whose identification has been a long standing mystery. This can be applied to the Allais effect (see this), which General Relativity cannot explain.
2. The speed of light also decreases for insulators. Refractive index is given by n= c_#/c. Dielectric constant is given by ε_r= 1/n² = (c_#/c)². The transition c→ c_# would occur when the system becomes an insulator. Could the atoms of the insulator be on a different space-time sheet, characterized by c_#<c? Water would be the most important example of this.
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.

Summary of the TGD based model of Allais effect

2026-05-19T05:30:58.788-07:00

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.

Paraconical pendulum consists of a rigid rod of \sim 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.
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.
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.
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 Δ f/f∼ 5× 10^-4, 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 Δ f/f varies from experiment to experiment.
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).
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").

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.

Anomalies and their brief explanations

Allais effect raises several problems which do not seem to have answers in the Newtonian and Einsteinian frameworks. The key observations are as follows.

Allais effect does not seem to involve any modification of classical gravitation in the sense that a modification of the classical gravitational force is not involved. This allows modification of gravitational potential by an addition of constant and in general relativity the addition of constant to the expression of the time component of the space-time metric.
The effect seems to be due to a horizontal force. The orbital plane is changed abruptly, which suggests a new kind of force. If is gravitational, it could be a force caused by the scattering of gravitons from the pendulum. The huge value of gravitational Planck constant implying long length scale quantum coherence and possibility of Bose-Einstein condensates together with the independence of the gravitational Compton length of graviton energy could make this effect large.
The fluctuations during the transition are large. This suggests quantum criticality. Classical field equations allow warped space-time surfaces, which are gravitational and gauge vacua and have a flat Minkowski metric with a reduced light-velocity c_#= (1-R²ω²)^1/2.
This leads to the notion of twisted (or warped) Hamilton-Jacobi structure (see this and this) for which canonically embedded M⁴ is tilted toward M⁴× S¹⊂ H: this allows the generalization of warping to the case of general space-time surfaces as solutions of field equations obeying holography = holomorphy principle (see this and this).
A thin metal plate serves as an excellent analogy and is a critical system. Same is true for the deformations of canonically embedded M⁴. This universal criticality reflecting itself as fluctuations of c_# could be behind very many forms of quantum criticality.
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.
Gravitational Planck constant is expected to play a key role in the Allais effect. It is inversely proportional to a velocity parameter β₀. The identification of β₀ has remained a mystery. The identification β₀= c_# is highly suggestive. This implies that one can talk about reflection, and refraction of waves at the boundaries of two regions with different values of β₀.
There are also diffractive effects and also these could be understood if gravitational waves or gravitations cause the transversal effects on the pendulum. Gravitational waves are indeed transversal. The gravitational Compton length λ_gr =GM/β₀ is the same for all gravitons and would characterize the diffraction pattern. Irrespective of the energy of the gravitons (or of any particle). There are several alternative identifications of the large mass M and the value of β₀. Empirical findings suggest a wavelength of 44 m and this scale can be understood rather naturally.
By a dimensional argument, the force constant of the gravitational pendulum is proportional to c_#<c. The fluctuations of c_#<c could induce the fluctuations of the pendulum's oscillation frequency. A possible quantum phase transition explaining the upper bound for Δ f/f≤ 2^-11∼ m_e/m_p can identified.

Does gravitational pendulum behave as a harmonic oscillator at small quantum number limit?

In this article, the earlier model for the effect based on the replacement of the oscillator with its quantum counterpart with very large gravitational Planck constant is discussed. For ℏ_gr the oscillator corresponds to a small oscillator quantum number limit, and this can give rise to large quantum fluctuations of the amplitude as transitions which change this quantum number so that the reason would not be classical gravitation but TGD based quantum theory allowing large quantum gravitational effects.

Are reflection, refraction and diffraction of gravitational waves responsible for the Allais effect?

There is evidence that the Allais effect does not involve screening of classical gravitational force. This raises the question whether reflection, refraction and diffraction type effects assignable to gravitational waves or gravitons are involved and explain the transversality of the effect.

Also diffractive effects are involved and conform with the long wavelengths implied by ℏ_gr. A rather promising model relies on quantum diffraction in the "world of classical worlds" (WCW) consisting of space-time surfaces obeying holography = holomorphy principle and having interpretation as Bohr orbits. Monopole flux tubes can be also interpreted as analogs for flowlines of an incompressible hydrodynamic flow past an obstacle. They can be regarded as quantum particles meaning analogy with quantum diffraction for Schrödinger equation.

The velocity parameter of the gravitational Planck constant as reduced light velocity induced by warping

The pondering of this question led as a by-product to a solution of a longstanding problem concerning the interpretation of the velocity parameter β₀ appearing in the Notale's hypothesis. Field equations allow as solutions warped space-time surfaces, which are flat just like Minkowski space but have reduced light velocity c_#= (g_tt)^1/2= (1-R²ω²)^1/2<c. The identification β₀=c_# is natural. This motivates the notion of twisted (or warped) Hamilton-Jacobi structure allowing to generalize this phenomenon to non-vacuum extremals. Warping as a universal quantum critical phenomenon distinguishing between TGD and GRT, makes it possible to identify a mechanism for the fluctuations of the oscillator frequency in the Allais effect.

The warping only shifts the gravitational potential appearing in g_tt=1-2Φ_gr but the classical gravitational force is unaffected. The reduction of the light velocity caused by the warping resembles that appearing for dielectrics and suggests that the shadow of the Moon involves the reduction c→ c_#. The large value of ℏ_gr and c_#<c suggest that the reflection, refraction and also diffraction of dark gravitons from the pendulum could cause the transversal effects in the transition zones.

The shadow of the Moon would be analogous to a dielectric. This would imply reflection and refraction of dark gravitational radiation from the Sun. Reflection at the surface of the Earth would induce transversal gravitational force amplified by the huge value of gravitational Planck constant and by the fact that the gravitational Compton length for gravitons does not depend on the energy of the dark graviton. The pendulum would become an ideal detector of gravitons. The 10 per cent excessive bending of light is reported during some eclipses (the "residual arc") could be interpreted in terms of reflection for dark photons by the same mechanism.

The reason for huge size of the effect: dark gravitational radiation has always the same wavelength

Sun produces gravitational radiation in the energy range (1--10⁵) eV. The huge value of ℏ_gr scales the wavelength range and makes possible long scale quantum coherence at the gravitational magnetic body amplifying the effect.

Gravitational Planck constant for a massless particle with energy E is GME/β₀. By Equivalence Principle, the expression for the wavelength of the graviton is λ=Λ_gr = GM/β₀=r_S/2β₀ irrespective of graviton energy. All dark gravitons, in fact all dark particles, would have the same Compton wavelength! This could explain why the Allais effect is so huge. The gravitational pendulum could become a detector of gravitons.

For the Earth mass M=M_E and for β_0,E ∼ 1 this gives 5 mm. The replacement β_0,E → β_0,S ∼ 2^-11 assigned with the Sun would give λ=10 m to be compared with 44 m suggested by the experiments. β₀= 2^-13 would give a good fit. For M= M_Sun= 3× 10⁵M_E one has λ = λ_gr,S= 3× 10⁶ m ∼ R_E/2, which is solar gravitational Compton length characterizing Sunspot size scale.

Reduction of the oscillator frequency

From the point of view of General Relativity, the maximal value for the reduction r=Δ f/f∼ 2^-11 of the oscillator frequency is huge. The identification of the fluctuations as being due to the fluctuations of β₀=c_# is natural.

There are several intriguing co-incidences. r equals the velocity parameter β₀ appearing in the expression of the solar gravitational Planck constant and is also near to the electron-proton mass ratio m_e/m_p. Also the velocity of the solar system with respect to the galactic center is of this order of magnitude? Which option is nearer to the truth?

Δf/f≤ m_e/mp could be nearest to the correct interpretation for the maximal reduction of frequency. The mechanism could be the phase transition in which Rydberg atoms with very large size at the magnetic body decay to protons and electrons. The condition that ℏ_gr(H)= ℏ_gr(p) guarantees that H atoms and protons can reside in the same monopole flux tubes: this condition holds true in biology also for base pairs of DNA. This would give β₀(H)/β₀(p) = c_#(H)/c_#(p) =m_p/m_H. The values of Δ f/f< m_e/mp could mean that only a part of the H atoms decay to a proton and electron.

The cautious conclusion would be that the Allais effect does not tell so much about classical gravitational physics than about the new quantum ontology predicting the notion of WCW realizing holography = holomorphy vision, the hierarchy of Planck constants, in particular huge values of gravitational Planck constant, and ZEO. The warping phenomenon distinguishing between General Relativity and TGD would be the central element.

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.

Number theoretic aspects of holography = holomorphy principle

2026-05-16T23:48:56.945-07:00

In the sequel, some number theoretic aspects of the holography = holomorphy (H-H) principle are considered.

Holography = holomorphy principle

First some background is needed.

The holography = holomorphy (H-H) (see this, this, and this) principle implies that space-time surfaces are determined as roots of the pairs of holomorphic functions f=(f₁,f₂): H=M⁴× CP₂ → C². The function pairs f=(f₁,f₂) define an algebra with respect to element-wise sum and product of functions f_i. If f₁ or f₂ is not varied, one obtains a function field.
The maps g=(g₁,g₂): C²→ C² define symmetries via the composition f→ g_º f and give rise to hierarchies of space-time surfaces with exponentially increasing algebraic complexity in the case of polynomials.
In particular, one obtains function field analogs of p-adic number fields and of adeles with powers of the p-adic prime p replaced with powers of polynomials of prime degree having coefficient polynomials with degree smaller than p. If the polynomial primeness is realized in the sense that the Galois group is not affected in deformations, there are also prime polynomials with non-prime degree having no decomposition to the functional composite of polynomials of lower degree.
The holomorphic maps g: C²→ C² define infinite hierarchies of space-time surfaces. The interpretation is in terms of complexity hierarchies and cognitive hierarchies. In the general case the complexity increases exponentially.
Space-time surfaces are analogs of Bohr orbits for 3-surfaces replacing point-like particles and provide representations for the elements of function algebras and function fields. Space-time surfaces can also be interpreted as theorems: the slight failure of the classical determinism located at the singularities makes possible several analogs of theorems represented as Bohr orbits such that the 3-D holographic data at the boundary of CD provides the fixed premises of the theorem. The classical laws of physics would provide a physical representation for the axioms of mathematics.
The dynamics implied by the H-H principle is universal if the classical action is general coordinate invariant and constructible in terms of the induced geometry of the space-time surface. By holomorphy = holography (H-H) principle (see this, this, and this) the solutions of field equations are holographic minimal surfaces with 3-D singularities at which the minimal surface property and holography fail. At singularities the boundary conditions stating the conservation of classical isometry charges are satisfied and without additional symmetries the singularities, in particular their positions, depend on the classical action.
This suggests that classical action serves in the role of effective action so that the parameters appearing in it can vary. In particular, they could depend on the extension E of rationals appearing in the coefficients of the pairs holomorphic functions f=(f₁,f₂): H=M⁴× CP₂ → C².
WCW would define what might be called Platonia and by adding WCW spinor fields one obtains quantum Platonia and Boolean logic. By adding state function reductions, one obtains conscious Platonia, which remembers and learns more and more about itself. Number theoretic evolution as an increase of number theoretic complexity is unavoidable.

How do CP₂ type extremals emerge?

The proposed view seems to give only the Minkowskian regions of the space-time surface: also CP₂ type extremals with Euclidean signature are needed. The space-time surface is not affected if f₁ and f₂ are scaled by a non-vanishing analytic function. What happens if f₁ and f₂ are scaled with the same function which vanishes at some points? A good guess is that the allowance of this kind of scalings leads to the emergence of the CP₂ type regions with Euclidean induced metric and the geometry of CP₂.

The scaling invariance implies that in regions z₃≠ 0, the natural interpretation of C² is as a projective space CP₂ obtained from C³ by identifying the points (z₁,z₂,z₃) of C³ differing by complex scaling and one can take z₃=1 are identified so that for instance (ξ₁,ξ₂)=(z₁/z₃,z₂/z₃) serve as coordinates. The regions with z₂= 0 and (z₁,z₂)≠ (0,0) correspond (z₁,z₂)≠ (∞,∞) defining the homologically trivial geodesic sphere of CP₂ at infinity. By using (z₁/z₂,z₃/z₂) or (z₂/z₁,z₃/z₁) as coordinates one obtains the three coordinate patches of CP₂.
The points (z₁,z₂,z₃)=(0,0,0) however remain still problematic and they are indeed of fundamental importance since the condition (z₁=0,z₂=0) defines the space-time surface. At these points the ratios z_i/z_j are ill-defined and a blow-up takes place so that these kinds of points must be replaced with CP₂. Is this the mechanism for how CP₂ type extremals as Euclidian regions of the space-time surface emerges as a blow-up? I have indeed proposed the blow-up mechanism earlier.
The problem is that CP₂ type extremals have as an M⁴ projection a light-like curve of M⁴, which only in a special case is reduced to the standard embedding of CP₂ to H. This problem can be solved by replacing the notion of H-J structure (see this) with its twisted variant (see this). Twisting means that the canonical embedding of CP₂ is replaced with a twisted embedding for which the geometry of CP₂ induced from H is not affected but a geodesic line of CP₂ is stretched to a light-like curve as a coordinate line for the Hamilton-Jacobi coordinates such that the dual of the light-coordinate is constant along it.
The twisting as tilting of M⁴ to the direction of the geodesic circle S¹⊂ CP₂ has also an interpretation as warping of H-J structure. The induced metric of tilted M⁴ is modified but remains flat. A reduction c→ c_#<c of light-velocity however occurs. This leads to an elegant explanation of some aspects of the Allais effect impossible to understand in Newtonian and general relativistic views of gravitation (see this). Warping is indeed possible only for space-time surfaces, not for abstract 4-D Riemann spaces.
Warping also explains the reduction of light-velocity in electrodynamics for non-vacuum systems (see this). The notions of di-electric constant and refraction therefore reduce to the geometry of space-time surfaces. Warping is also a universal critical phenomenon allowing large numbers of almost vacuum extremals X⁴ with energy density determined by the volume term in the classical action proportional to the cosmological constant Λ, which has an extremely small value in long length scales. Therefore it could therefore be behind very many quantum critical phenomena. This view corresponds to the original view based on the huage vacuum degeneracy of Kähler action interpreted as 4-D spin glass degeneracy. The introduction of small cosmological constant associated with thge volume action leaves only the approximate vacuum degeneracy appearing as warping.

The outcome would be that by allowing scaling factors of (f₁,f₂), which vanish at a discrete set of points and twisted H-J structure, one obtains also CP₂ type extremals as solutions of field equations.

Could classical action have interpretation as a number theoretic invariant?

The generalized Langlands duality (see thisand this) and the universality of the classical dynamics suggest that the exponent of the classical action has interpretation as an effective action and can be regarded as a number theoretic invariant. This invariant would assign to the space-time surface a number, which is real, algebraic number or integer depending on how strong assumptions are made about the roots of (f₁-c₁,f₂-c₂)=(0,0) .

The guess motivated by the H-H hypothesis is that this number is an analog of a discriminant D for a polynomial of a single variable expressible as a product of the non-vanishing root differences. In the recent case, the roots of (f₁-c₁,f₂-c₂)=(0,0) are 4-D regions of space-time surfaces. One should be able to pick points of the space-time surface as ordinary roots in order to define D using the standard formula.

There are several kinds of sub-manifolds of the space-time surface.

The 3-D singularities X³ are physically in a preferred role since they define loci of non-determinism as memory seats. They also define generalized vertices.
The 3-D light-like partonic orbits Y³ are interfaces of regions of the space-time surface with Minkowskian and Euclidean signature. The induced metric is effectively 2-D at them.
2-D string worlds Z² sheets appear as 2-D self-intersections of space-time surfaces X⁴ obtained at the limit of the intersections of X⁴ when a small deformation X⁴ becomes trivial. The intersections Y¹=Z²∩ Y³ of string world sheets and partonic 3-surfaces are identified as fermion lines.
3-D light-like partonic orbits Y³ and singular surfaces X³ intersect along 2-D partonic 2-surfaces Y². The light-curves Y¹ defining the fermion lineas intersect these partonic 2-surfaces Y² at a discrete set of points for which the conditions (f₁,f₂)=(0,0) is true. By 2-dimensionality of Y² the roots are complex numbers. If f_i is polynomial, one can assign to the roots discriminant D_i. As a matter of fact, this is true even when f_i is not a polynomial.
One can assign to all intersections Y²_i,j of partonic orbits Y³_i and singular 3-surfaces X³_j discriminant D defined as the product D(i,j)=D₁D₂(Y²_i,j) of the discriminants for f₁ and f₂ at the partonic 2-surface Y²_ij=X³_iY³_i. The roots as points of the partonic surface with coordinate z would be loci for fermions and the idea that fermions code for the classical dynamics is highly attractive.
If the complex coordinate z for Y² is unique, the roots have general coordinate invariant meaning. Whether this kind of generalized complex coordinate can be identified, is not clear. A weaker condition would be that only the discriminant is a general coordinate invariant, say conformal invariant. The Hamilton-Jacobi structure poses strong conditions on the coordinates of M⁴.
The proposal has been that a power of the product D=∏_i,jD_i,j of the discriminants D_i,j be identified as the exponent of the classical action for X⁴. This would give strong constraints to the form of the action, in particular the parameters appearing in it so that the interpretation as an effective action would be appropriate. If one requires that the discriminants are rational numbers or in an extension E of rationals, the conditions are really strong: this kind of condition is not however necessary. The discriminant hypothesis would solve the theory in the sense that the calculations of the exponent of classical action defining the vacuum functional could be reduced to number theory.
How uniquely the value of D characterizes the space-time surface as a root of (f₁,f₂)? D depends on the choice of H-J structure but this conforms with the fact that also the space-time surface depends on this choice.
Could the value of D and the fermionic loci as complex roots fix the space-time surface for a given Hamilton-Jacobi structure and the choice of CD? This would mean a strong form of holography and might be unrealistic. For instance, symmetry related space-time surfaces would have the same value of action and D. Also quantum criticality implies a degeneracy so that there could be a large number of space-time surfaces with the same action exponential. The fermionic loci at the singularities would allow to distinguish between symmetry-related space-time surfaces.
One the other hand, if f_i are polynomials, there is a finite number N= N₁+N₂ of coefficients for both of them: fixing the values of f=(f₁,f₂) at N=N₁+N₂ points associated with the fermionic loci at the singularities could fix the coefficients.
The Gödelian dream would be that D is analogous to Gödel number fixing space-time surface and therefore the statement represented by the space-time surface.

The maps g: C²→ C² as symmetries of H-H princple

The maps f=(f₁,f₂): H→ C²) define what might be called functional integers or rationals, depending on whether f_i are polynomials or rational functions. The coefficient field can be assumed to be an extension E of rationals. The functional numbers are fundamental and cognition made possible by the existence of symmetries g:C²→ C² and the slight failure of determinism should make possible the representation of these functional numbers in terms of space-time surfaces satisfying (f₁,f₂)=(c₁,c₂) . How to achieve this?

The value pairs (f₁,f₂)= (c₁,c₂) define a representation of the functional number f as space-time surfaces identified as roots of (f₁-c₁,f₂-c₂). A representation of the functional number as a many-particle system would be in question. Only a finite subset of values (c₁,c₂) can be realized in this way in practice.
If one is interested in representing only a subset {(c₁^k),c₂^k))} of the spectrum of f one can consider a map g: H→ C defined as F= ∏_k [(f₁-c₁^k))² +(f₂-c₂^k))²] as a representation for the surfaces. Now the polynomials are reducible. c_i should belong to an extension of E. This kind of representation is however rather tricky.
For E-rational functions, the roots of (f₁,f₂)=(0,0) (and (f₁-c₁,f₂-c₂)=0) can be solved by first solving from f₂=0 the the one of the 3 complex coordinates of H, say z₁ as an algebraic function z₁(z₂,z₃,u) of the remaining two complex coordinate and one hypercomplex coordinate. After that one has equation f₁(z₁(z₂,z₃,u)), z₂,z₃,u)=0 and for instance z₂ can be solved as algebraic function of z₂(z₃,u). Note that the second light-like coordinate v dual to u is a dummy variable so that one obtains a 4-D algebraic surface.
For an E-rational map g= (g₁,g₂): C²→ C² g_º (f₁,f₂)=(0,0) selects a set or parameters (c₁^k),c₂^k)) as the roots of g in turn defining surfaces (f₁,f₂)= (c₁^k),c₂^k)). A number theoretically motivated hypothesis is that the allowed values of (c₁^k),c₂^k)) belong to the extension E of rationals so that one obtains hierarchies of discretizations of WCW.

Some general comments about the role of the maps g are in order.

This picture allows to understand why the hierarchies of the compositions of maps g applied to a space-time surface defined by (f₁,f₂)=(0,0) which is prime in the sense that it does not allow a representation as a functional composite f= g_º h is so important. One can say that prime pairs f represent the substrate and the maps g represent the cognition for which the goal is to understand the substrate represented by f.
The degree d of rational function R=P₁/P₂, defined as the difference d(P₁)-d(P₂) of the polynomials appearing in it, is analogous to polynomial degree and is multiplicative in the functional composition. Therefore rational functions with prime degree are special. One could define the generalization of functional p-adic numbers. Functional p-adic would be a sum of powers of rational function with prime degree multiplied by coefficients, which are rational functions of a lower degree.
Galois groups are an important part of the TGD view of cognition. One can also ask whether one can assign a Galois group to the roots of g identifiable as space-time surfaces. Google LLM informs that the notion of Galois group is extremely general and this makes sense. The Galois group would act as a flow permuting the roots. In the same way, one could assign a Galois group to the roots of (f₁,f₂)=0 having identification as space-time regions. This interpretation was proposed in (see this and this) as an intuitive notion.

Could birational maps g: C²→ C² play a special role?

The roots of g: C²→ C² define the corresponding spectrum (f₁,f₂)=(c₁,c₂). One can argue that since the maps g relate to cognition, the maps g: C²→ C² for which roots can be solved analytically are cognitively very special and might be those, which appear first in the number theoretic evolution.

For birational maps g=(g₁,g₂): C²→ C² also the inverses g^-1 are rational maps. This allows us to solve the roots g analytically as (c₁^k), c₂^k))= g^-1(0,0).
The birational maps g: C²→ C² are known as Cremona transformations (see this) and have a very rich structure. Their functional composition is possible but they do not form a group unlike in the case of CP₁ (Möbius transformations). Note that Möbius transformations as linear transformations act as symmetries of C².
Cremona transformations are generated by projective transformations of CP₂ and the so-called standard quadratic transformation (z₁,z₂)→ (1/z₁,1/z₂), which is singular at the origin. Projective transformations correspond to the group SL(3,C) containing the isometry group SU(3) of CP₂ as a subgroup. The implication of fundamental importance for TGD is that Cremona transforms a spectrum generating algebra rather than acting as a mere symmetry group.
The so called polynomial automorphisms are birational maps, which are everywhere well-defined isomorphisms of C² to itself. The Jung-van der Kulk theorem states that every polynomial automorphism is a composition of affine maps and elementary maps of form (z₁,z₂)→ z₁,z₂)→ z₁,z₂+P(z₁), where P(z₁) is a composition of affine maps and polynomial. These transformations could be regarded as symmetries.
Every Cremona transformation can be factored into a sequence of point blow-ups followed by a finite sequence of point blow-downs. Geometrically this means blowing up a set of points where the map is undefined and then contracting the curves down to points to create the image surface.
At the blow-up points the Cremona transformation gives an indeterminate expression like 0/0 and the value of the expression depends on the direction from which the point is approached. In the case of Cremona transformation a single point as image or pre-image is substituted by an entire projective in CP₁.
A familiar analog is the Coulomb force of the point charge which has ill-defined direction at the charge. In the case of Coulomb force, the point is replaced by a sphere. By the argument already given, the blow-up means that C² is replaced by CP₂ by adding the sphere CP₁ at infinity.
A concrete example is provided by the standard Cremona transformation (z₁,z₂)→ (z₂/z₁z₂,z₂/z₁z₂). Origin is the problem point. The approach to origin along the line z₂= mz₁ gives in projective coordinates the point (1/m,1) which gives to CP₁ instead of a single point. Blow-up as the addition of CP₁ to infinity replacing C² with CP₂ is the solution of the problem.
For g this would produce a sphere as an image point. There is no problem with the inverse image of (0,0) since it does not belong to CP₁ at infinity so that g^-1(0,0) is well-defined.
For g^-1(0,0), (c₁,c₂) would be ill-defined. For projective coordinates there would be an entire CP₁ of points (c₁,c₂) defining space-time surfaces. One can solve the problem by concluding that the coordinates for CP₂ become ill-defined in this situation and one must use another coordinate patch: 3 patches are enough. In a new coordinate patch g^-1(0,0) is unique and obtains a single space-time surface.
One could also argue that the inverse image is a union of the space-time surfaces labelled by the points of CP₁ and therefore 6-dimensional rather than 4-dimensional. Space-time surfaces can be regarded as intersections of 6-D f₁=0 and f₂=0 surfaces having a twistor space interpretat and the singularity could mean that the intersecting 6-surfaces are identical in this case In the case of Coulomb force, point is replaced by a sphere. The M-theory analog would be 4-dimensional 3-brane.
The degree of the rational map g: C²→ C² defines the analog for the degree of a polynomial. For the iterations of many families of maps this degree behaves like d_n = 3d_n-1 - 2d_n-2. At the limit n→ ∞ the asymptotic behavior d_n+1-d_n → Δ is consistent with this condition and means that complexity as the increase of the degree increases but not exponentially as in the general case. If genuine symmetries were in question, the complexity would not increase. The behavior of d_n can also be periodic and even chaotic.

See the article M⁸-H duality viz. Hubble law, gravitational Planck constant viz. Allais effect and warping, and CP₂ type extremals from holography = holomorphy principle 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.

Warping of the space-time surfaces and dielectric constant

2026-05-14T04:42:46.111-07:00

The flat warped space-time surfaces are characterized by the reduced light-velocity β₀=c_#/c≤ 1. There is a criticality with respect to the variations of c_# (instability of metal plates illustrates this). Also the twisted Hamilton-Jacobi structures would be characterized by c_# (see this). The criticality of the warping could induce or accompany various kinds of quantum criticalities. In the case of the Allais effect, this kind of quantum criticality would explain the variation of the pendulum frequency cannot be explained in terms of gravitation. Quite generally, one can write f_#= c_#/λ = f/n, where n= c/c_# is analogous to the refractive index appearing in electrodynamics in presence of matter. In Maxwellian electrodynamics, refractive index relates to the relative dielectric constant ε_r via the formula n=c/c_#= (ε_r^1/2. Could reflective index and dielectric properties have a geometric description in terms of the warping of the space-time surface? If so, the warping of the space-time surface could be seen directly via the reflection of light! Refractive index depends on frequency. This can be understood in terms of quantum criticality implying the value of c_# associated with the massless extremal assignable to the photons depends on frequency. At resonance, at which ε_r diverges, the value c_# would in the ideal case vanish: there would be no propagation of signals. The standard interpretation would be in terms of absorption of the signal by atoms, which contribute to the resonance frequencies. How the criticality of warping could manifest itself in critical systems?

For a harmonic oscillator, the frequency is given in terms of force constant and mass as ω=(k/m)^1/2. A reasonable dimensional guess is that the force constant k characterizing the electromagnetic force is proportional to (c_#/c)². For instance, cyclotron frequency would be proportional to c_#. More generally, the Coulomb force in a dielectric is scaled from its vacuum value by 1/ε_r= (c_#/c)². Also capaticance of a capacitor would be propoertional to (c_#/c)². The variation of c_# at quantum criticality would make it possible to change the contribution of the electromagnetic force.
Gravitational masses have always the same sign so that the notion of dielectret does not make sense and c_# is not expected to play any role: this conforms with the character of warping. For instance, the gravitational force created by a constant mass density ρ corresponds to potential energy proportional to Gmρ r², which is harmonic oscillator potential energy. The force constant k∝ Gmρ does not depend on c_#.
If the system is in an equilibrium involving electromagnetic and gravitational forces, the variation of c_# appearing in the electromagnetic component of force could make possible the loss of equilibrium. The tuning of c_# could allow the field body to change the equilibrium point of a physical system and even destroy or create the equilibrium. In biology the generation of nerve pulse, the splitting of DNA double strand preceding transcription and replication could serve as examples of this.

See the article M⁸ H duality viz. Hubble law, and gravitational Planck constant viz. Allais effect and warping 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.

M8 H duality viz. Hubble law, and gravitational Planck constant viz. Allais effect and warping

2026-05-13T04:51:34.001-07:00

In this article two developments in TGD are discussed. These developments emerged in a "wrong context".

The first discovery was the realization that M⁸-H duality in zero energy ontology implies a fractal generalization of Hubble's law. It emerged in a work related to TGD inspired quantum biology, where gravitational Planck constant h_gr= GMm/β₀ (M and m are masses and β₀ is velocity parameter) introduced by Nottale plays a key role. This already also led to a partial understanding of Hubble tension: the value of β in cosmic scales is very near to 1 but its values differ slightly in long and short cosmic scales.

The second discovery emerged while developing a TGD based model for Allais effect, which has no explanation in the context of general relativity or Newtonian gravitation. The work led to the question concerning the interpretation of the velocity parameter β₀ appearing in the formula of the gravitational Planck constant h_gr introduced already by Nottale. The gravitational field bodies of the Earth and structures of cosmological size scale are characterized by β₀=v₀/c∼ 1 and cannot correspond to a velocity of matter for a matter flow. Solar system characterized by β₀∼ 2^-11, which cannot correspond to light-velocity in the general relativistic framework.

The solution of the problem came from a prediction of TGD, which emerged already 47 years ago during the first year of TGD. TGD predicts warped space-time surfaces which are flat like Minkowski space M⁴ (no gravitation) and have vanishing gauge fields. They have Poincare symmetry but have reduced light-velocity due to the warping. Light-like geodesics of M⁴ are replaced by light-like geodesics of M⁴× S¹⊂ H=M⁴× CP₂. Warped space-time surface can explain the Allais effect, in particular the dramatic reduction of the parabolic oscillator frequency in terms of reduced light velocity. The notion of warping generalizes: one can speak of warped Hamilton-Jacobi (H-J) structures for which the hypercomplex structure of M⁴ and complex structure of CP₂ are mixed in the sense that M⁴ H-J structure is replaced with that of a warped space-time surface.

See the article M⁸ H duality viz. Hubble law, and gravitational Planck constant viz. Allais effect and warping 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.

Pollack effect and basic biosystems as analogs of semiconductors

2026-05-11T23:45:02.104-07:00

The idea that biological systems like cells, neurons and even DNA and mRNA could serve as role models for conscious computers is rather attractive. Base voltage/charge controls the voltage of the transistor output and the guess is that Pollack effect and its reversal could control the charge of the base of the transistor and therefore the value of the bit represented by the transistor. The base should be covered by a material containing -OH groups to make the Pollack effect possible and this is often done.

Could this picture be applied in a reverse direction at the level of basic biology?

Axon conducts in a preferred direction: in this sense the axon behaves like a semiconductor. This suggests that semiconductor analogy applies to neurons and axons and nerve pulse conduction. The transistor picture is however too simple as such. The incoming nerve pulses act as bits and determine whether the neuron fires by generating a bit as a nerve pulse. The charge for the counterpart of base would be affected by the incoming nerve pulses so that a single neuron would act as a gate, whose output as nerve impulse is determined by the incoming nerve pulses as bits.
Nerve pulse would correspond to the change for the direction of a bit conducted along the axon. This suggests that the axon and cell membrane can be regarded as collections of transistor-like systems defined by basic units, which have size scales of order 10^-8 meters, which is the size scale of ion channels. In the ground state, the state of all these transistors correspond to the same value of bit (note the analogy with fermionic ground state in the original Dirac model of fermion). Nerve pulse means a temporary change of the direction of the bit conducted along the axon.
This picture is supported by the model of the neuronal membrane as Josephson junction (see this) in which the ground state of the axon corresponds to a propagating soliton sequence with each soliton representing a single bit, say b=1. Soliton sequence fixes the values of axonal bits to say b=1. Nerve pulse means propagation of a perturbation in which the membrane potential has changed sign and corresponds to an opposite bit value. This is natural: only deviations from the equilibrium configuration carry relevant information.
The resting potential is negative, which means that the cell interior (exterior) is negatively (positively) charged. If the Pollack effect occurs in the neuronal exterior, membrane potential is reduced in magnitude. The same occurs if the reverse Pollack effect takes place in the neuronal interior.
This would suggest that the Pollack effect in the neuronal exterior and its reversal in the neuronal interior can temporarily change the sign of the membrane potential representing a bit and generate a nerve pulse. Since the stable ground states of neuronal and axonal membranes correspond to say b=1, the nerve pulse must have a finite duration. Physically the stability of the membrane potential would correspond to the fact that the generation of dark nuclear binding energy (much smaller than the ordinary binding energy) in the formation of dark nuclei from dark protons at the MB makes b=1 energetically favored.
The Pollack effect would correspond to the transition -OH \rightarrow O^- + dark proton at the monopole flux tube. The energy difference Δ E between these two states must be small enough and would be in the range 01-.05 eV (see this). Its sign determines whether the Pollack effect occurs spontaneously. The first guess is that either the resting potential or a voltage associated with either lipid layer serves in the role of the base potential in turn controlling the value of Δ E.
For small enough values of Δ E, the Pollack effect can take place. It is expected to be more probable at the positively charged exterior side of the membrane. When Δ E too large, the dark nuclei become energetically unstable and this induces reverse Pollack effect in the interior of the membrane reducing the membrane potential. The transfer of positive protonic charge from the exterior to the interior would be the net effect, reducing the magnitude of the membrane potential and even changing its sign.
Since the soliton sequence defines the stable value of the membrane potential, the duration of the nerve pulse must be finite. The stability of dark nuclei at the magnetic body would be the energetic reason for this.
Interestingly, the search of axon-like materials suitable for a more efficient computation is under away (see for instance this).

This picture inspires two questions.

Andrew Adamatsky (see this), who has studied sponges and found that they show electrical activity sequences consisting of analogs of action potentials ('spikes') (see this). The spikes have the same amplitude scale as miniature potentials appearing in neural systems. The semiconductor analogy, based on a cell membrane as Josephson junction with soliton sequence as a ground state and Pollack effect, is suggestive as a model for the generation of spikes.
The chirality of the DNA strand gives it a directionality analogous to the semiconductor type behavior. The bases of DNA base pairs A-T and C-G are connected by hydrogen bonds (see this), which suggests the possibility of Pollack effect suggested to be catalyzed by the presence of hydrogen bonds.
DNA transcription and translation are preceded by the splitting of the DNA double strand to separate strands is a process analogous to the opening of a zipper. Could the opening be induced by the analog of nerve pulse conduction along the double strand? Could also the DNA double strand be regarded as a Josepson junction, with ground state modellable as a Sine-Gordon soliton sequence? Could also now the Pollack effect and its reversal change the sign of the voltage between the members of the base pair temporarily and induce the analog of nerve pulse conduction?

See the article Quartz crystals as a life form and ordinary computers as an interface between quartz life and ordinary life? 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.

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

2026-05-07T04:34:26.462-07:00

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

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.
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.
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.

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.
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.

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.
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.
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.
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.

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.
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.
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.
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?
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.

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.
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_#.

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.
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.
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.
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?

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.}}
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?

2026-05-03T23:00:00.487-07:00

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?

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.
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.

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.
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?

2026-05-02T21:07:12.201-07:00

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

2026-05-01T21:51:02.774-07:00

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?

2026-04-23T20:53:54.038-07:00

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?

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.
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.
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.

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.
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.
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

2026-04-21T00:13:00.000-07:00

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.

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.
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.
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

2026-04-16T20:30:00.000-07:00

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).

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.
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.
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.

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.
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.
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!
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).
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.
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.

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.
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.

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.
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.
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

2026-04-11T05:27:00.000-07:00

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

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.
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.
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.

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.
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) .
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!

2026-04-09T22:06:00.000-07:00

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?

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.
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).
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.
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.

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.
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.
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.
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

2026-04-09T20:44:00.000-07:00

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?

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.
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.

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.
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.
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.
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.
"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.
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

2026-04-09T14:50:00.000-07:00

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.