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.