## Tuesday, February 06, 2024

### 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 hem for the Sun.
1. Recall, that the electric Planck constant hem 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 hem= Qe20, 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 hem has minimal value. For the inner planets of the Sun, Mercury, Venus, and Earth, one has in a good approximation β0,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 QS/QE= (ES/EE)× (RS/RE)2 .

to deduce QS for the Sun from QE. From the values RS≈ 6.9 × 108 m and RE≈ 6.3× 106 m, one has RS/RE ≈ 101.

For the Earth one has EE=.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 ℏem,E ≈ 2.75x × 10250,E, x in the range [1,3].

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

QS/QE ≈eq x× 100, x in the range [1.3,.43] .

4. Using these data, one can estimate the ratio heff,S/heff,E. For the inner planets (Mercury, Venus, Earth), in the case of gravity, β0,E=1 and β0,S= 2-11. If one assumes the same values in the electric case, one obtains the estimate

heff,S>/heff,E= (QS/QE) × (β0,E0,S) .

heff,E= EE 4π R20,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 Λem= hem/m for proton is Λem,p≈ x× 650 km, x in the range [.33.,1] for a proton (m=mp). 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 Λgr=.5 cm. One has

Λem,pgr≈ 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 Λem,pgr≈ 2.9× 10-3 so that one would have Λem,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

Λem,Sem,E = hem,S/hem,E = (QS/QE) (β0,E0,S)

from that for the Earth. This gives

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

For the proton this would give Λem,S≈ 1.3x× 108 km for β0,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.