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I have read this question.

Gravitational redshift and Energy of a photon

In the answers and the comments it states that the redshift/blueshift has to be observed from the same single frame. It says that the emission and absorption energy has to be measured in the same frame.

Now this is where i get confused. How can we measure from the same frame the emission and absorption both, if the photon is emitted at a different gravitational zone (a different place in the gravitational field where the potential is different)? This is physically impossible, because the observer would have to move with the photon to both observe emission and absorption.

The Pound–Rebka experiment was an experiment in which gamma rays were emitted from the top of a tower and measured by a receiver at the bottom of the tower.

https://en.wikipedia.org/wiki/Pound%E2%80%93Rebka_experiment

This says that the emission and absorption was from two different frames, located at different points in the gravitational field each of them having different potential.

If we want to go very basic, if the photon is emitted from the top of the tower, if I stand at the bottom of the tower, then I can only observe the absorption. Of course, later, I can collect information from a device that was at the top of the tower and measured the emission (or I can have information because it is a stimulated emission at certain mono frequency), but that information is from a different frame then where I actually observe the absorption.

Question:

  1. Do we actually have to observe the photon emission and absorption from the same single frame to see gravitational red/blueshift?
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Energy is a frame-dependent quantity, in particular the projection of momentum onto some time axis. In context of the given discussion of gravitational frequency shifts, the relevant frames are the frames of emitter and absorber at time of emission and absorption, defined by their velocities, and the coordinate frame (or rather, frame field).

In terms of the frame defined by Schwarzschild coordinates, photon energy remains constant because Schwarzschild time defines a Killing vector field (cf Wikipedia). However, if you want to know how the frequency has changed from the perspective of emitter and absorber sitting at fixed spatial Schwarzschild coordinates, you have to take into account that the Schwarzschild time coordinate does not correspond to the eigentime of such observers, ie gravitational time dilation.

Now, on to your question:

The comments you linked to seem a bit confused to me, but the claim that you have to choose the "same reference frame" alludes to the Schwarzschild frame field. When evaluated at time of emission and absorption, it yields two distinct frames.

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  • $\begingroup$ Thank you, so I see correctly, that in the Pound Rebka experiment, the information about the emission and absorption frequency was from two different frames right? $\endgroup$ Jan 12, 2020 at 17:31
  • $\begingroup$ Yes, I would say so. $\endgroup$
    – Christoph
    Jan 12, 2020 at 17:34

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