Note 407(1): Thomas Precession in Planetary Orbits and the H Atom Orbitals
Many thanks to Dr Horst Eckardt for pointing out that Note 407(1) is a remarkable result that shows that the "non relativistic" solutions of the Schroedinger equation are inherently relativistic and that the gamma factor is obtained a priori from rotation of the ECE2 covariant line element. He also points out that the standard model uses the idea of the Lorentz boost as being purely linear. As shown in Note 407(2), the "Thomas half" comes out of the commutator of boost matrices. This is also a new development because usually, the commutator of boost generators of the Lorentz group is used to give rotation generators. That procedure does not make clear that the Thomas half is given by a commutator of boost matrices. The Schroedinger equation is the non relativistic limit of the ECE2 fermion equation (the ECE2 covariant development of the Dirac equation), so it is natural (in retrospect) that the Schroedinger equation should also be relativistic. When I first derived this result a few days ago, it was a complete surprise. The ECE2 fermion equation gives spin orbit interaction, and also gives the Thomas factor of a half. Eq. (38) of Note 407(1) shows that the Thomas half enters into the description of the energy levels of the H atom. This is completely new to quantum mechanics.
Note 407(1): Thomas Precession in Planetary Orbits and the H Atom Orbitals
This is a highly interesting result that the energy levels of the H atom are directly related to Thomas precession. This shows that even the "non-relativistic" Schrödinger solutions are inherently "relativistic". The appearance of the gamma factor is derived from rotation a priori, this is remarkable because special relativity is based on constant linear motion and is not valid for rotational systems (although it is often used as "relativistic mechanics" – one of the obvious contradictions in standard physics).
I eqs. (13,14) of the note and related equations I would prefer writing "a" instead of "r" because Delta_phi_T should be a constant value, but this is marginally.
Horst
Am 06.05.2018 um 13:08 schrieb Myron Evans:
Note 407(1): Thomas Precession in Planetary Orbits and the H Atom Orbitals
This note shows that the well known energy levels of the H atom are due to Thomas precession as given by Eq. (38). This is a very remarkable result not known hitherto. So the well known Schroedinger H atom can be developed in terms of the fine structure constant, the Einstein rest energy m c squared, and the electron rest frequency m c squared / h bar. These are all relativistic concepts. Here n is the principal quantum number. Choosing n = 1 shows that there is a Thomas precession of 4.14 degrees as given by Eq. (41). Also, for n = 1 in atomic H, (v / c) squared = alpha , where alpha is the fine structure constant, so v / c = 0.0854. Alpha is 1 / 137. This is one way of showing that Thomas precession is not a small effect in atoms and molecules. It is well known that it emerges from the ECE2 fermion equation, a development of the Dirac equation. The Thomas precession (1) from rotating the ECE2 covariant line element (1) looks completely different but the two effects are based on the same theory. The EGR has fallen apart completely, so the only thing that can be claimed theoretically now is that the Thomas precession of a nearly circular orbit, Eq. (46) is part of the observed precession. Thomas precession is numerically a third of the de Siitter or geodetic precession, but the latter is incorrectly calculated from a geometry without torsion. It is of key importance to note that the standard model always gives the result (40) from its own equations. The standard result (49) refutes the standard claim (51), and the entire structure of EGR collapses completely. It was bound to to so because its geometry is completely wrong. There are many schools of ECE thought building up in essentially all universities of any note that are interested in physics, and a vast amount of interest from various sources in up to 192 countries. This is clear from the scientometrics. The next note will deal with commutators of Lorentz boosts in order to find exactly how the Thomas precession emerges. A complete new theory is in place, based on vacuum fluctuations.