What about the electric body of the Sun?

In the Zoom session, Ville Saari made a question related to the Sun as an astrophysical quantum system, and I realized that although I had estimated the electric Planck constant h_em for the Sun.

1. Recall, that the electric Planck constant h_em for the pair determined by a relatively small charge Z and the charged system with large charge Q, is as a generalization of the gravitational Planck constant determined by the formula h_em= Qe²/β₀, where β₀=v₀/c <1 is a velocity parameter.

   For the Earth, there are reasons to believe that β₀≈ 1 holds true in the gravitational case. This implies that h_em has minimal value. For the inner planets of the Sun, Mercury, Venus, and Earth, one has in a good approximation β_0,S= 2^-11 as was deduced by Nottale. For the outer planets, one would have β₀=2^-11/5.

2. The charge is identified as the electric flux over a surface containing the charge. In the case of a spherically symmetric charge density within a sphere of radius R one has

   Q = ε₀ ES= ε₀ × E(R)× 4π R²,

   where ε₀= 8.85× 10^-12 C/Vm is the dielectric constant of vacuum. Note that one has E(R) ∝ 1/R². One can restrict the consideration to the surface of the system so that E(R) is the electric field at the surface, S is the surface area of the sphere, and R is the radius of the sphere.

3. One can use the scaling law Q_S/Q_E= (E_S/E_E)× (R_S/R_E)² .

   to deduce Q_S for the Sun from Q_E. From the values R_S≈ 6.9 × 10⁸ m and R_E≈ 6.3× 10⁶ m, one has R_S/R_E ≈ 101.

   For the Earth one has E_E=.1-.3 keV/m. For the charge of Earth one obtains the estimate Q≈ 4.4x× 10⁶ C =27.5× 10²⁴e. To get some perspective, note that aluminium capacitors can have a maximum charge of about 10³ C whereas the maximal charge of a van de Graaff generator is about .14 C. From C= 6.24 × 10¹⁸e one obtains ℏ_em,E ≈ 2.75x × 10²⁵/β_0,E, x in the range [1,3].

   The value of the electric field at the surface of the Sun is E_S= 1.5 V/m: this gives E_S/E_E= x× 10^-2, x in the range [1,3] and

   Q_S/Q_E ≈eq x× 100, x in the range [1.3,.43] .

4. Using these data, one can estimate the ratio h_eff,S/h_eff,E. For the inner planets (Mercury, Venus, Earth), in the case of gravity, β_0,E=1 and β_0,S= 2^-11. If one assumes the same values in the electric case, one obtains the estimate

   h_eff,S>/h_eff,E= (Q_S/Q_E) × (β_0,E/β_0,S) .

   h_eff,E= E_E 4π R²/β_0,E has been already estimated and is much larger than the gravitational Planck constant.

Consider now the electrical Compton wavelengths for the Earth and the Sun and restrict the consideration to the proton.

1. In the case of the Earth, the electric Compton wavelength Λ_em= h_em/m for proton is Λ_em,p≈ x× 650 km, x in the range [.33.,1] for a proton (m=m_p). There are numerical factors of order 1 involved. The radius of the thermosphere is about 340-350 km, one half of the upper bound. This puts bells ringing since the thermosphere is the area where the terrestrial plasmoids live!

   The gravitational Compton length of the Earth is same for all particles and given by Λ_gr=.5 cm. One has

   Λ_em,p/Λ_gr≈ 1.3x × 10⁸ .

   In the number theoretic sense, the electric body would be considerably smarter than the gravitational body.

   For a capacitor with capacitance of 1 μF and at voltage 1 V, the charge would be 1 μ C. For β₀=1 would have Λ_em,p/Λ_gr≈ 2.9× 10^-3 so that one would have Λ_em,p ≈ 1.5 × 10^-5 m. Could electronic systems be intelligent and conscious at least on this scale?

2. The electric Compton wavelength of the proton for the Sun would be obtained from the scaling law

   Λ_em,S/Λ_em,E = h_em,S/h_em,E = (Q_S/Q_E) (β_0,E/β_0,S)

   from that for the Earth. This gives

   Λ_em,S/Λ_em,E ≈ 2× 10⁵/x, x in the range [.33,1].

   For the proton this would give Λ_em,S≈ 1.3x× 10⁸ km for β_0,S=2^-11. The astronomical unit AU, that is the distance of the Earth from the Sun is AU= 1.5 × 10⁸ km! The Earth would live on the outskirts of the thermosphere, assignable to the inner planets of the Sun? Could this be a mere coincidence?

   The interpretation would be in terms of a hierarchy of electric and magnetic bodies and the electric body for the Sun + inner planets would be near the top of the hierarchy.

3. What about the outer planets? Nottale noticed that for the outer planets β₀ scales by a factor of 1/5 to β₀= 2^-11/5 so that the electric Compton wavelength at the level of the entire planetary system would be about 5AU. The corresponding thermosphere can accommodate Mars, whose radius is roughly 4 times the radius of Earth, but no other outer planets. Mars and Sun living at the outer boundaries of two thermospheres of Sun would be very special in that the thermal gradients of plasma would be very strong: this is the prerequisite for self-organization as development of complexity. Mars and Sun would have a very special position in the planetary system.

See the article About long range electromagnetic quantum coherence in TGD Universe 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.