twin universe cosmology Twin Universes cosmology (p 7)
The invariance of the Schrödinger equation is ensured if:
(56)
The Boltzmann equation is invariant if :
(57)
The Poisson equation for gravitation poses 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 evidence their variations in any laboratory experiment.
And then?
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)
Combining the 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)
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 r is found to obey :
(74)
...same law for the contribution rr of the radiation to the density r. The conservation of the radiative energy gives :
(75) pr R³ = constant
Then :
(76)
