Inertial & non-inertial frames & the principle of equivalence

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Discussion Overview

The discussion revolves around the equivalence principle in the context of inertial and non-inertial frames, exploring its implications from both Newtonian and relativistic perspectives. Participants examine the indistinguishability of physical laws in freely falling frames within a gravitational field and uniformly accelerating frames in Minkowski spacetime.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that the equivalence principle indicates that the laws of physics for freely falling particles in a gravitational field are locally indistinguishable from those in a uniformly accelerating frame in Minkowski spacetime.
  • Others argue that this conclusion cannot be derived from a Newtonian perspective, as Newtonian physics lacks the concept of spacetime.
  • A participant questions the interpretation of free-fall frames as locally inertial frames, suggesting confusion regarding the distinctions made in the sources referenced.
  • Some participants clarify that a frame at rest with respect to a gravitational source is not a free fall frame, as free falling particles in this frame will experience acceleration.
  • It is suggested that the equivalence principle implies that locally, an observer cannot distinguish between being at rest in a gravitational field or in a uniformly accelerating frame by conducting experiments.
  • Further clarification is made that the laws of physics in a freely falling reference frame reduce to those of special relativity.

Areas of Agreement / Disagreement

Participants express both agreement and disagreement on various interpretations of the equivalence principle. While some aspects are accepted, there remains uncertainty and differing views on the implications and derivations related to Newtonian physics and the nature of gravitational forces.

Contextual Notes

Some participants note that the discussion involves complex interpretations of the equivalence principle and its relationship to different frames of reference, which may lead to misunderstandings regarding the distinctions between inertial and non-inertial frames.

  • #121
@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.
 
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  • #122
DAH said:
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".
 
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  • #123
PeterDonis said:
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.)
 
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