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.
- 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= 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 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.
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.
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 × 1025/β0,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] .
heff,S>/heff,E= (QS/QE) × (β0,E/β0,S) .
heff,E= EE 4π R2/β0,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.
- 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,p/Λgr≈ 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,p/Λgr≈ 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?
Λem,S/Λem,E = hem,S/hem,E = (QS/QE) (β0,E/β0,S)
from that for the Earth. This gives
Λem,S/Λem,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.
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.
Source: http://matpitka.blogspot.com/2024/02/what-about-electric-body-of-sun.html
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