Trivial Refutation of the de Sitter Precession
1) I first expressed the Coulomb potential (11) as U sub C = – alpha h bar c / r. Its expectation values are given by Eq. (15), <U sub C> = -(alpha / n) squared m c squared.
2) It follows that the gravitational potential is U sub g = 2mMG / r = 2 x alpha h bar c / r. its expectation value is <U sub g> = – 2 x <U sub C> = 2 x (alpha n) squared m c squared. The missing factor 2 has been reinstated here.
3) So the energy levels of the H atom are Eq. (21) with x replaced by 2 x. These are the energy levels in a gravitational field because the Thomas precession is replaced by a de Sitter precession in a gravitational field. This is of course the dogma of the standard model.
4) I worked out x with the data of Eq. (23). It is x = 1.5752 ten power ten, and this is very large and not observed. So the de Sitter theory is refuted, Q. E. D.
The electron of the H atom experiences the gravitational field of the proton and also the gravitational field of the earth, the moon, the sun and other planets. The gravitational pull of the proton is negligible because the proton mass is very small. I simply used eq. (18) to work out the expectation value of 2mMG / r. in Eq. (18) mMG is multiplied and divided by alpha h bar c. For the electron in the gravitatonal field of the earth:
x = mMG / (alpha h bar c) = 1.575 ten power ten.
So the Coulombic expectation value, Eq. (15), is multiplied by – 2x. The factor – 2x is much smaller for the proton / electron gravitational interaction, which is negligible compared with the proton / electron electrostatic interaction. For r I used the radius of the earth, i.e. l assumed that the H atom is in a laboratory on the earth’s surface. The main point is that the standard model’s rotating Schwarzschild metric (de Sitter precession) gives complete nonsense. However the rotating ECE2 metric (Thomas precession) gives a perfect and original description of the H atom as in Note 407(1).
There are some points unclear to me: How did you equate the gravitational term
< m M G / r > = x < alpha hbar c / r >
to
x (alpha/n)^2 m c^2 ?
The latter is from the Coulomb potential and does not appera in <U_grav>.
Another question: Why did you use the electron mass orbiting around the earth and not the proton mass of the H atom?
Inserting the constants (with the factor 2 which seems to be missing) gives
<U_grav> = 2 < m M G / r > = 
Joule.
With 1 Rydberg = 
Joule
This is a small correction of four orders of magneitude below the H ground state energy, comparable to spin-orbit splitting.
Horst
Am 11.05.2018 um 14:40 schrieb Myron Evans:
Trivial Refutation of the de Sitter Precession
Once it is realized that the H atom is a Thomas precession, the de Sitter precession is trivially refuted as attached, by considering an H atom in the Earth’s gravitational field. The spinning Schwarzschild line element used by de Sitter gives a very large correction to the H atom energy levels, and this is never observed experimentally.