Cosmology of twin universes (p. 7)
The invariance of the Schrödinger equation is ensured if:
(56)
The Boltzmann equation is invariant if:
(57)
The Poisson equation for gravitation raises no particular problem and simply becomes (58)
From the Maxwell equations, we obtain:
(59)
(60)
which is consistent with the definition of an electric field due to an electric charge.
From the Einstein equation, as mentioned earlier, we obtain:
(61)
G
»
c²
Otherwise, the equation is no longer divergenceless.
If the quantities:
(62)
h, m, c, G, R, T
obey these relations,
it will not be possible to detect their variations in any laboratory experiment.
So what?
From (57), we obtain immediately:
(63)
which is nothing but the characteristic Schwarzschild length, so that:
(64)
Rs
»
R
Let us now examine the Jeans length:
(65)
where:
(66)
(66b)
(66t)
(67)
By combining equations (56) and (57), we obtain:
(67b)
(68)
The Compton length varies like R:
(69)
The Planck length is:
(70)
(70b)
The Planck time is:
(71)
The Jeans time is:
(72)
By combining (61) and (63), we obtain:
(73)
The variation of the constants does not conserve the mass.
If we conserve the number of species, the mass density
ρ
is found to obey:
(74)
...
Same law for the contribution
ρᵣ
of the radiation to the density
ρ
. The conservation of the radiative energy gives:
(75)
pᵣ R³ = constant
Then:
(76)
