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Motivation

I am pretty confused of why people are hopeful to find a version of the equivalence principle ("the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system") within QFT. I personally am of the position QM and the equivalence principle are compatible under proper formulation (and I am aware that this is controversial grounds).

Question

Within Special Relativity the definition of acceleration is limiting (to say the least). In light of this I was curious if there existed a version of the equivalence principle within Special Relativity? Personally if someone asked me this I would have just used GR and tried to find this approximation but please do not post this answer (see motivation).

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  • $\begingroup$ The equivalence of gravitational and inertial mass can be stated even in Newtonian physics. Why would it be different in SR? $\endgroup$ – Brick Sep 13 at 19:16
  • $\begingroup$ @Brick I mention the equivalence principle in the motivation. $\endgroup$ – More Anonymous Sep 14 at 8:18
  • $\begingroup$ Note that acceleration of the reference system is only equivalent to a uniform gravitational field. Otherwise, the equivalence is only local, due to tidal forces. $\endgroup$ – PM 2Ring Sep 14 at 10:56
  • $\begingroup$ @PM2Ring yes but if I only have a point available to me (say the size of my lift is a point) then I can truly say "the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system"? $\endgroup$ – More Anonymous Sep 14 at 11:05
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    $\begingroup$ @PM2Ring Infact, at risk of being non-rigorous (but acceptable by physics standard's) even say: "the laws of special relativity hold in an infinitesimal region around a freely-falling observer" is the equivalence principle $\endgroup$ – More Anonymous Sep 14 at 11:49
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Yes, I think you can use the equivalence principle within the realm of special relativity if, at least, the observer(s) is (are) inertial. In short, a person located at the center of a rotating disc, for a small compartment located a distance $r$ away from the center which orbits the observer, measures an anti-gravity (gravity outward the center). His measurements, using the equivalence principle, can be equal to those measured by a Schwarzschild observer for a small compartment located a distance $r$ away from a massive planet if the angular velocity of the disc as well as the mass of the planet are chosen in a way that the centrifugal acceleration in the orbiting compartment equals the gravitational acceleration in the compartment at rest with respect to the planet.

Applying the equivalence principle to special relativity, Newton's law of gravitation can be relativistically revised as a post-Newtonian theory.

P.S. In this regard, I published an article four years ago in a somehow offbeat journal. The article is accessible via this link. For a better edition, I refer you to the first chapter of my book.

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There is an unresolved problem with the equivalence principle. Acceleration thought experiments do not involve any curvature of spacetime. As far as I know all explanations of gravitational time dilation do.

This does not necessarily invalidate the equivalence principle. It merely says that something somewhere is not right.

The direct observation of gravitational time dilation matching that expected from Special Relativity thought experiments in flat spacetime suggests the 'something somewhere' might not be the equivalence principle.

Added:

The flat space acceleration thought experiments (accepting the clock hypothesis) say that clocks a chosen distance ahead (in the direction of acceleration, distance measured in a momentarily co-moving frame) are judged to have an absolute addition to their rate proportional to both the acceleration and the distance, without limit. Looking behind, they have an absolute subtraction, again without limit, so that beyond the clocks judged to be stopped there are further clocks judged to be running backwards. These additions and subtractions apply both to co-moving (accelerating) clocks and to clocks in any rest frame the momentarily co-moving inertial frame is compared with.

The equivalence principle can only be tested over a limited gravitational distance for practical reasons. There is an issue, however, since the gravitational effect is not proportional to distance without limit when the distant clock is in a distant rest frame.

It seems unlikely the issue is with the clock hypothesis or the equivalence principle. I suspect it is more fundamental. (the work is ongoing)

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