Shrinkage of radius
This is a very interesting result, and well worth a follow up paper. The main result here could also go into Section 3 of UFT413. The spin connection is always present when there is frame rotation due to torsion. On a purely classical level there is no spin connection and no vacuum force, the orbit is Newtonian and does not precess or shrink with time. The Newtonian theory is classical and there is no torsion and no curvature. The frame is (r , phi) in plane polar coordinates. Torsion in an ECE2 covariant theory results in the frame (r, phi’), defined by Eq. (1) of Note 413(5). In general the hamiltonian, Eq (2), in the frame (r, phi’) is relativistic, but in the classical limit it is given by Eq. (2). It is a constant of motion and this produces Eqs. (4) and (5). The lagrangian method also produces Eqs. (4) and (5). Eq. (5) is equivalent to the fact that the angular momentum in frame (r, phi’) is a constant of motion. This results in the spin connection (15). You have made the all important discovery that this spin connection gives orbital shrinking and precession. This finding explains the Hulse Taylor binary pulsar in a far simpler way than the standard model, and explains it without the use of gravitational radiation. This is what we set out to achieve. When the spin connection is known the vacuum force can be calculated using methods similar to those used in Lamb shift theory. All our latest UFT papers are being read with great interest, this can be seen from the scientometrics. I think that your interpretation is valid and can be followed up in UFT414, in which the fully relativistic theory can be developed, with a relativistic hamiltonian and lagrangian. This theory can also be applied to the S2 star system in which EGR fails by an order of magnitude, i.e. fails completely. This total failure of EGR has not yet dawned on the general scientist, but it means that the entire structure of EGR collapses. We have already shown this theoretically in almost a hundred different ways inthe UFT series. The only plausible replacement is ECE and ECE2. So we are making major progress with a combination of analytical and numerical methods. We have a very large and permanent following which entirely rejects EGR. The censorious publishing methods of the standard model have become irrelevant and the entire theory is based on well known Cartan geometry and is irrefutable unless Carran geometry is refuted. That has not happened in almost a century. The rest is experimental testing, and that goes on indefinitely.
I did some more experiments with the Lagrange solver. It seems that the
angular characteristic of an orbit changes dramatically if the frame
rotation speed is changed non-constantly with significance. However the
min and max radii remain unchainged (although varying widely in
precession angle).
Alternatively I added the spin connectionterm (12) of note 413(5) to the
radial equation of motion, with the spin connection defined by (15).
Then the constant of motion gets additional terms but is preserved.
Interestingly, now a shrinking of orbits takes place. Contrary (?) to
the analytical results, the spin connection in the equations of motion
seems to be the essential term for producing shrinking orbits. A pure
frame rotation alone only gives precession.
I am not sure if we can accept this result. If yes, it would mean that
classical frame rotation is not sufficient for shrinking orbits. The
ECE2 spin connection is the reason. This is another proof that ECE2
covariant theory alone is able to explain th behaviour of the
Hulse-Taylor pulsar. My interpretation is, that the companion star
distorts spacetime significantly (and vice versa) so that this effect
appears. In central systems with M>>m this is nearly not the case. Also
radial models could be developed, I have already developed the equations
for these.
The question is how we cope with this result. Nonsense? New insight?
Worth a successive paper with this topic?
Horst