Questions related to language from the TGD point of view

I received from Taylor Reed Ramsey a set of 3 highly inspiring questions of how the TGD view of cognition might relate to the basic structures of language. Ramsey is an independent researcher working on a long-form project about how external symbolic systems writing, in particular restructure human cognition. The questions relate to adelic physics, the hierarchy of Planck constants, and the genetic code. In the sequel Q1:, Q2:,... and A1:, A2:,... to the corresponding answer.

1. A question related to language and adelic physics

Q1: In your adelic vision, cognition is p-adic and a system's cognitive complexity corresponds to the dimension of the extension of rationals it realizes, with evolution as the growth of that extension. Humans also install external encoding systems alphabets, numerals, calendars in childhood, and these measurably reorganize cognition within a single generation.

Could a writing system be modeled as a macroscopic, learning-heritable selection over p-adic cognitive representations a culturally fixed extension of rationals (or preferred Galois structure) governing which representations a brain's magnetic body can run? Would an alphabetic versus a logographic script differ at the level of the extension or the Galois group?

A1: Before answering the questions, I will discuss one of the key questions that I have been pondering is how the extensions of rationals defining cognitive hierarchies on one hand, and p-adic hierarchies relate to each other?

1. The extensions E of rationals appear as coefficients field for the functions (f₁,f₂): H=M⁴× CP₂→ C² and g=(g₁,g₂): C²→ C² appearing in the general solution of classical field equations. The solutions in turn can give rise to extensions of E so that the situation is very complex.
2. When the extension E of rationals is realized in terms of roots of polynomials, one can assign to it Galois group. This is not true for an abstract extension defining the coefficients of f and g. For polynomials of a single variable ordinary notion of Galois group can be applied and the situation can in some cases reduce to this. For the general case, the roots are not points but 4-D surfaces (f₁,f₂)=(0,0) of H for which roots correspond to different regions.
3. The maps f, which are prime in the sense that they do not have composition f= g_º f₁ could be interpreted as representing the substrate whereas the maps g would represent cognition giving information about f via the roots of g_º f which correspond to space-time surfaces f= (c₁,c₂) where (c₁,c₂) is a root of g. In computer science one speaks of substrate independence.
4. The Galois group as a group of flows transforming roots as different space-time regions to each other makes sense (see this). Note that also the space-time surfaces satisfying (f₁,f₂)=(c₁,c₂) are possible and correspond to the roots of (f₁-c₁,f₂-c₂). These surfaces emerges as roots of g_º f, where g: C²→ C² is a holomorphic map. One can say tha the hierarchy of maps g provides information of the map f=(f₁,f₂) as roots of g_º f.

   This generalized Galois group characterizes space-time surfaces. There is a temptation to assume that this kind of group characterizes space-time surfaces representing DNA and RNA. The description of pair creation in TGD is in terms of a particle turning backwards in time in a 3-D vertex acting as 3-D edge of space-time at which the arrow of geometric time changes.

   This inspires the proposal that the replication of space-time surfaces is also behind biological replication. If so, these cognitive structures would be inheritable and inherited via DNA replication. In particular, the abstract representation of the writing system would be realized already at the level of dark DNA at the level of the magnetic body, and it would be possible to learn the writing system. One could even see writing and speaking as expressions of the genetic code analogous to expression in terms of proteins.

Some comments concerning the question whether a writing system could be modelled as a macroscopic, learning-heritable selection over p-adic cognitive representations a culturally fixed extension of rationals (or preferred Galois structure) governing which representations a brain's magnetic body can run.

1. Genetic code would provide one realization for cognition and could be behind the written and spoken languages. The number of letters of language is typically somewhat larger than the number of amino-acids (20). On the other hand, the lower bound for the number of tRNAs is 32: could the phonemes correspond to tRNA coded by 64 genetic codons. Note that the analogy between the letters of language and 4 letters of the genetic code fails as a strict analogy.
2. If the genetic code is a cognitive representation based on functional composition of polynomials of degree 4 representing the code letters, the genetic inheritance would be behind the ability to learn language although the correspondence between the language and genetic code would be very flexible. The generalization of p-adic number fields to function fields would be involved and polynomials with degree 4 (not prime) would be prime polynomials in the Galois sense. One could say that the cognitive representations could be inherited. This could reduce quite concretely to gene replication as a replication of the corresponding space-time surfaces.

You also asked whether the alphabetic and logographic writing system correspond to different Galois groups. The basic question is what differentiates these writing systems.

1. The first view is that they could correspond to reductionistic ("western)"" and holistic ("eastern") views of genetic codons. In logographic writing codons and entangled triplets of letters represented as states of dark protons would not reduce to product states defined by letters. In the alphabetic writing system this would be the case. I will later return this.
2. In a model for the genetic code (see this) based on functional composites of maps g_i: C²→ C², i=1,...4 characterizing the 4 letters of the genetic code, codons as holistic entities would correspond to deformations of functional composites of 3 maps g_i, which do not reduce to functional composites of polynomials of lower degree with the same Galois group. They are primes in the Galois sense, which is weaker than the purely number theoretic characterization in terms of the polynomial degree. They would correspond to the logographic writing system. In absence of the small deformation they would however decompose. This would be the reductionistic representation and could correspond to the alphabetic writing system. The Galois groups would be indeed different.

2. Bioharmony model of the genetic code, Galois groups, in relation to alphabetic/logographic writing systems

Q2: Your bio-harmony model derives the genetic code from icosahedral (A5) and tetrahedral (A4) symmetries read as Galois groups, with codons as 3-chords. Is there a linguistic analog one tier up does a script's phoneme grapheme inventory carry a comparable harmonic/Galois structure, so that an alphabet stands to dark-photon/EEG communication roughly as the genetic code stands to dark-nucleon chemistry? Could different scripts then correspond to different harmonies, and so to different baseline cognitive or emotional 'moods' at the population scale?

A2: I am not quite sure what you mean with the notion of script so that the following might involve misunderstandings.

1. Genetic code at the bit level is the same for all variants of the realizations of the genetic code in terms of frequency triplets providing the codons as 3-chords with emotional tone and allowing representation of moods. This representation would be analogous to computer code: there are no emotions. Music would also express emotions.

   The frequency triplets are differences of frequencies for a dark proton triplet. The transition between two states of dark proton triplet induces the frequency triplet as 3-chord. A full 3N-resonance means that the sender and receiver make opposite transitions. Resonance could be also partial.

   In the icosa tetrahedral realization of the genetic code, dark proton triplets are located to the triangular faces of 3 icosahedra and a tetrahedron. The transition transforming codons to each other would correspond to the transfer of dark proton triplet between two triangles determined by the Hamiltonian cycle. I have not previously considered the meaning of the predicted correlation between the state of the dark proton triplet and its location to a particular triangle.

2. The dark codons are (quantum) dynamical unlike the chemical codons. A possible interpretation is that the dynamics of dark codons is free so that they form a kind of R&D unit and perform processes analogous to quantum computations whereas chemical codons are frozen and represent the analog of classical computer program code.

   Dark codons are proposed to control chemical codons by energy resonance. The chemical codon would receive the control signal a 3-resonance when the frequency differences for the transition of dark codon correspond to resonance energies for the letters of the chemical codon. For a gene one would have 3N-resonance. The ordinary codons could also react only to the sum of the cyclotron frequency differences. In both cases, it is possible to have 1-1 correspondence if the frequencies for the letters depend on the position of the letter in the dark codon. These two ways of the chemical codon to react to the control signal could correspond to the reductionistic and holistic views of codons at the level of ordinary codons.

3. The representation of codons as 3-chords would add to the representation of emotions and emotional intelligence. Human moods are a phenomenon involving short time scales and the bioharmony characterizing can change in short time scales. An interesting question is whether moods appear at the whole body level so that every cell would involve the same Hamiltonian cycles or whether the cycle depends on the body part.

   Moods are expressed by gestures and by art. Writing expresses emotions but only via the generated associations. Therefore I would not be the first one to assign a "cultural" mood to the writing system.

Cultures might express themselves in writing systems differently.

1. At fundamental level genetic code would relate to the completely exceptional tessellation of hyperbolic 3-space (surface of M⁴ ⊂ H=M⁴× CP₂ with constant value of light-cone proper time analogous to cosmic time). The proposal is that it is completely universal and that the human language is only a special case appearing at a very high level.
2. The numbers for the letters of written language are consistent with the idea that they are basically coded by genetic codons: the most plausible interpretation as tRNA codons was already mentioned. It is important that the letters in western language do not have meaning, at least they do not have meaning at our level of self hierarchy.

   The time scale for the transcription is measured in a fraction of second and this is true also for speech. This supports the idea. Perhaps sequences of dark genetic codons realized as temporal patterns at the magnetic body are transformed to speech.

3. The following observation related to alphabetic and logographic writing systems might be highly relevant. There are languages such as China in which this composition of words to letters does not occur (correct me if I am wrong). To my understanding the letters are originally pictures representing words.

   Could this correspond to the use of 64 genetic codons as basic units without a decomposition to 3 letters? Codons correspond to entangled dark proton triplets rather than unentangled product states for protons. No (no state function-) reduction of codons to a product state would occur in Eastern languages!

   That I Ching has 64 symbols would support this intuition. Eastern philosophies are holistic, western philosophies are reductionistic. Could this difference make itself manifest already at the level of the basic symbol system of language.

3. Does the notion of cognitive qualia make sense?

Q3: Number-theoretical universality and the adele give an object holding the real (sensory) norm and all p-adic (cognitive) norms at once. If a self could realize an adelic rather than single-p-adic representation sensory and all cognitive views simultaneously available and self-consistent what would its qualia structure be? Would it coincide with the high-h_{eff, maximally negentropic states you associate with expanded consciousness? (Leibniz's characteristica universalis seems to gesture at the same object.)}

A3: Interesting questions. I cannot give a clearcut answer to them. I have spoken about sensory qualia. One can of course speak of cognitive qualia and ask how the two kinds of qualia correspond to each other. I would tend to see cognitive qualia as names for sensory qualia, as symbols representing them.

One thing is certain: p-adic number fields and its functional analogs define a hugely simplified picture of sensory reality. Cognition simplifies and abstracts the essential features.

Instead, I try to explain (and to understand at the same time!) what cognition, and in particular, linguistic cognition, in TGD might be. The general structure of TGD suggests 3 approaches to cognition. One approach is at the level of the space of space-time surfaces, "world of classical worlds" (WCW), the second approach is at the level of the 8-D imbedding space H=M⁴× CP₂ and the third approach is at the level of 4-D space-time surfaces. 3.1. WCW level

WCW is the space of space-time surfaces obeying holography = holomorphy principle and analogous to 4-D Bohr orbits for particles identified as 3-surfaces.

I have assigned p-adics and adeles with cognition. In the recent form of TGD a generalization of p-adic number fields and adeles to their functional counterparts emerges at the level of WCW.

1. Holography = holomorphy principle (H-H) (see this, this and this) dictates the classical dynamics of the TGD space-time surfaces as a universal dynamics independent of variational principle. Space-time surfaces with Minkowskian signature corresponds to roots for a pair of holomorphic (in generalized sense) complex valued functions f=(f₁,f₂): H=M⁴× CP₂→ C² are roots. To each solution one can assign an infinite hierarchy of new solutions g_º f where g is holomorphic map C²→ C². Here maps g allow functional composition and their iterates define analogs of Mandelbrot fractals and Julia sets as space-time surfaces.

   This brings in mind Turing's and Gödel's view of computation in which arithmetic operations involve a finite basis of primitive functions (see this). One can identify maps f which do not allow compotion to f=g_º f₁ as prime substrates. One can also decompose maps g: C²→ C² to "prime" g:s having no such composition.

   The space-time surfaces assignable to genes and genetic codons would provide examples of this kind of g:s.

   1. One could identify f as a "substrate" and the function g allowing functional composition would define a cognitive hierarchy. The "thoughts"/cognitions are assignable to the substrate. Substrate and cognition would be rather independent. Any system can cognize, which looks rather radical an idea. This brings in mind the substrate independence of computer science.
   2. For the functions g, one can generalize the notion of p-adicity and obtain function field counterparts of ordinary p-adics. The functional counterparts of p-adic number fields could relate to cognition. These p-adic function fields are mapped by category theoretical morphism to ordinary p-adics. Also the notion of functional adele makes sense. This generalization allows us to understand the p-adic length scale hypothesis.
   3. There is a proposal (see this) for how genetic codons and genes could correspond to slightly deformed compositions of maps g assignable to letters. Although the degree of the polynomials associated with the letters is d=4 and therefore not prime degree, they do not have functional compositions to lower degree polynomials (of degree 2). Codons would correspond to small deformations of 3-fold compositions of the letter polynomials having no functional compositions to lower degree polynomials with the same Galois group. The same would apply to genes.

   3.2. Embedding space level

   Icosa tetrahedral tessellation (see this and this) is a completely unique tessellation of the hyperbolic space H³ in the sense that 3 Platonic solids appear as its effective building bricks: octahedrons however define holes of this tessellation. This would make the genetic code universal. This realization would correspond to the level of embedding space H=M⁴× CP₂. There is evidence for its realization at the level of clustering of water molecules (see this).

   The sequences of codons and letters would define sequences of symbols giving rise to linguistic expressions. The proposal is that DNA/RNA gives rise to a representation of ordinary genetic code and a parallel quantal representation in terms of dark proton triplets associated with the magnetic body of DNA/RNA. Also temporal sequences as singularities at the level of space-time can be considered.

   3.3 Space-time level

   There is also an approach to the origin of language at space-time level. At space-time level it would basically relate to the small failure of classical determinism (no violation of field equations) for H-H principle (see this, this and this) exhibited already by 2-D minimal surfaces realized as soap films spanned by the frames: now space-time surfaces are holomorphic minimal surfaces: this irrespective of classical actions (see this).

   The loci of non-determinism correspond to the failure of classical non-determinism as 3-D edges of space-time. These edges define 3-D features characterizing the entire space-time surface information theoretically. They form temporal sequences analogous to expressions of language. An attractive idea is that a finite number of these edges determines a collection of symbols forming the basis of language for a given space-time surface. The space-time surfaces allowed by classical non-determinism would define a set of sentences as these symbol sequences. There would be a connection with the WCW level since the singularities as edges of space-time are the seats for failure of generalized holomorphy.

   What could be the counterparts of vowels and consonants in this framework?

   1. The consonants emerged to the written language first and the vowels came later. Consonants could correspond to features as 3-D edges at between two space-time regions serving as analogs of vowels.
   2. There would be an analogy with visual perception. At the lowest level boundaries define the basic features and the representation is analogous to a child's drawing. After that come colors and other visual attributes for the regions bounded by features. Vowels could be seen as analogs of colors.
   3. A further analogy relates to the sequence of "small" state function reductions (SSFRs) defining self as a sequence. Each SSFR would be analogous to a consonant and the period of subjective time between SSFR and the next SSFR, with qualia represented as quantum numbers, would be analogous to a particular vowel. In singing the notes could correspond to colors and vowels and the moments, when the note is replaced with a new one could be analogs of consonants as boundaries. The rhythm in music would define a regularly spaced sequence of 3-D space-time edges dividing it to constant periods. It would also provide a clock.

      One could see the written and spoken language as a representation for the time evolution of self as a sequence of SSFRs.

   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.

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

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

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.

1. 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.
2. 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.
3. 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.  
4. 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.
5. 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.

1. 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.
2. 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.
3. 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.

1. 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?

2. 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

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.

1. 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

2. 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.

3. 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.

1. 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.
2. 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.
3. 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.

1. 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 .

2. 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 .
3. 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.

1. 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.

2. 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 Frad by (RE/sub>/AU) × (Λgr(E)/&Lambdagr(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.

1. 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.

2. 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.
3. 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!
4. 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.
5. 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

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.

1. 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.
2. 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.
3. 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.

1. 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).
2. 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.
3. 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?

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.

1. 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

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.

1. 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⟩.
2. 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.
3. 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.

4. 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.

5. 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.
6. 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

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.

1. 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.
2. 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.

3. 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.

1. 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.
2. 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.