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)\rightarrow 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!

   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.

To sum up, it seems that by applying these arguments Sun-planet pairs and planets could give very powerful constraints on the 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.

"Cold fusion" is now fashionable!

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!

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.

1. 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.

2. 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.  
3. 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.

1. 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.

2. 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

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.

1. 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.
2. In the absence of any other forces than the gravitation of Earth) paraconical pendulum can behave much like a conical or Foucault pendulum. The oscillation plane of the paraconical pendulum turned by 13,5 degrees during 14 minutes (see this). It is difficult to see how the gravitational fields of the Sun and Moon could explain this behaviour by changing the effective value of the Earth's gravitational acceleration.
3. Allais concludes from his experimental studies that the orbital plane approach always asymptotically to a limiting plane and the effect is only particularly spectacular during the eclipse. During solar eclipse the limiting plane contains the line connecting Earth, Moon, and Sun. Allais explains this in terms of what he calls the anisotropy of space.

4. Some experiments carried out during eclipse have reproduced the findings of Allais, some experiments not. In the experiment carried out by Jeverdan and collaborators in Romania it was found that the period of oscillation of the pendulum decreases by 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.
5. There is also the finding by Popescu and Olenici, which they interpret as a quantization of the plane of oscillation of paraconical pendulum during solar eclipse (see this).
6. There is also evidence that the effect is present also before and after the full eclipse. The time scale is 1 hour. Allais emphasized that the effect is a dynamic, not static, phenomenon, connected to the variation of weight or inertia in the space swept by the pendulum during the eclipse. The 10 per cent excessive bending of light is reported during some eclipses (the "residual arc").

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.

1. 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.
2. 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.
3. 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.

4. 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.
5. 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.
6. 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.