Undergrad Inertial & non-inertial frames & the principle of equivalence

[PeterDonis]

@Sagittarius A-Star I'm going to have to take some time to look at the 2017 paper you linked to. I see what you're saying, but I need to reconcile it with other things I know about the Bell congruence.

 

[Sagittarius A-Star]

The Pound-Rebka experiment successfully detected a blueshift in light when photons were sent towards the surface of the Earth from a height of 22.6 m. The formula for the blueshift is given by: $$
z=-\frac{gh}{c^{2}}$$
However, I was thinking about how the blueshift would be observed over time in the accelerating frame, and i came across this paper: https://arxiv.org/abs/1907.06332
According to the paper above the blueshift would drift with time and if photons were sent in the other direction then the redshift will also drift with time. The formula for the blueshift drift is given by:
$$z=-\frac{aL}{\left ( c+at \right )^{2}}$$
So, I would like to know, if this is a flaw in EP and could this experiment be used to distinguish between gravity and an accelerating frame?

Please have a look at ...

TABLE I: Redshift $z_−$ and blueshift $z_+$ between co-moving objects in uniformly accelerated reference frames calculated with different approaches.

... on page 19 of that paper:

For your comparison, you must pick the first row "Møller coordinates" instead of the second row "Non-relativity".

 

[PeterDonis]

I see what you're saying, but I need to reconcile it with other things I know about the Bell congruence.

I think I have the reconciliation I was looking for.

The thing I needed to reconcile was that the Bell congruence has a positive expansion scalar, which means, heuristically, that each ship sees the other moving further away. (This is why the string stretches and finally breaks in the Bell spaceship paradox.) But if each ship sees the other moving further away, it seems like it should also see the other ship's light signals being redshifted.

What I forgot was that the ships are accelerating, so the rest frame of each ship is a Rindler frame, not an inertial frame. And in a Rindler frame, there is "gravitational" time dilation--clocks at higher "altitude" in the frame run faster. So in the rear ship's (non-inertial) rest frame, while the front ship is moving away, it is also at higher altitude, and in that frame, the gravitational blueshift outweighs the redshift due to moving away.

(In the front ship's non-inertial rest/Rindler frame, the rear ship is at lower altitude, so both effects--the altitude effect and the moving away effect--cause a redshift. So the front ship sees the rear ship's light signals redshifted, as expected.)