So the fact is that Einstein only predicted 'time' would pass at different speeds in different strengths of gravitational field in his original theory. Not that resonating frequencies would vary relative to external forces. Any observed changes in resonant frequencies was never part of his original theory. Nor are later relativists attempt to appropriate these classical effects of resonance acceptable or legitimate.
In experiments like Pound Rebka or the observed variation of GPS clocks, the atoms resonant frequencies are observed to change with different strengths of gravity on the atom. What has been ignored is that the amount of gravitational potential energy of an object, essentially its weight, depends on the height of the object above the earths surface. If it is a well known classical effect that a resonating system reduces its natural resonant frequency when its mass increases, then its not unreasonable to assume that a change in the atoms weight or gravitational potential will also increase or decrease its natural resonant frequency.
Essentially any predicted relativistic time dilation is premature. Experiments like Pound Rebka or the observed variable GPS clock times can be modelled and are consistent with classical resonant effects only. No need for GR or SR
Hafele Keating : In the same way that the force of gravity at different heights effects the natural resonant frequencies of resonant systems, different forces acting on an object at the same level will also produce differing effects on that objects natural resonant frequency. By applying force to an object to move it horizontally through a gravitational field will be equivalent to the object being subjected to stronger gravitational fields, and thus lower the objects natural resonant frequency.
If one studies the P-R setup Notice that the detector setup is such
that it only measures emr in a narrow frequency band. Which happens to
be the same as the emitted radiation when both emitter and detector
are at the the same altitude. Both being a sample of Fe57.
But place the emitter and detector at opposite ends of the tower and
the lower detector sample , now being subjected to a greater
external force of g than the emitter at the top of the tower would have
it’s resonant frequency changed by a stronger g at the base of the tower.
It would not be able absorb the incoming wave radiation from the
sample at the top of the tower because it’s resonant frequency was changed
due to a different g between the two samples. In resonance we have observed
this effect for centuries. A resonating system will always absorb
any incoming wave energy that is only at the same frequency as its resonant frequency.
Apply an external force to any resonating system and it’s resonant frequency
changes. And it no longer will be able to absorb those incoming waves because
the incoming waves are no longer at the same frequency as the systems old
resonant f.
The same happens in P-R. The lower absorbing samples resonant f
is now in a stronger g potential. It’s resonant frequency is lower
than the emitting f of the sample on the top of the tower. Giving
the false impression that the emitting radiation is blue shifted!
To correct this the emitter is vibrated creating a range of higher
and lower Doppler shifted radiation. Some of which was then
at the right f again to be absorbed by the detector sample.