Free fall acceleration in SR

[harrylin]

[..] the concept of "SR based theory of gravitation" is inherently ill-defined and counter-factual.

Yes, I think we all agreed on that, and for me this topic has sufficiently been discussed and so I will not comment further in this thread. What remains is possible spin-offs for other, related topics. For example:

[..] One can't really claim that an "SR based theory of gravitation" could not possibly satisfy (operationally) the strong equivalence principle. In fact, there is a field interpretation of general relativity in which the curved metric is just an "effective" metric, on top of the "true" (but unobservable) flat Minkowski metric of special relativity. (This is similar to how special relativity can be interpreted in a Lorentzian sense, by invoking a metaphysically defined sense of "truth", adding strictly unobservable elements to the theory.) So, according to this interpretation, general relativity is actually a "SR based theory of gravitation".

?? GR is developed on top of SR, but is incompatible with SR's second postulate (the one of Einstein, not of some textbooks). If he did not explain that clearly enough for everyone, then we should probably start it as a topic in which I am willing to participate (in that case, please put a link to it here). It's very straightforward really.

I'd say the persistent problem in this thread is the mistaken idea that there is a unique theory of gravity consistent with special relativity,

Hmm I did not see anyone suggest that idea... never mind, it's a non issue.

Again, thanks for all the comments!

 

[stevendaryl]

?? GR is developed on top of SR, but is incompatible with SR's second postulate (the one of Einstein, not of some textbooks). If he did not explain that clearly enough for everyone, then we should probably start it as a topic in which I am willing to participate (in that case, please put a link to it here). It's very straightforward really.

This is a semantic issue. The mathematical structure of SR is described by Minkowsky spacetime. In that spacetime, there is a universal speed, c. Whether this speed is the speed that light propagates is not a critical aspect of the theory, it seems to me. It follows from Maxwell's equations that light travels at speed c through vacuum, but in the tensor theory of gravity being described, Maxwell's equations become coupled to that tensor, and it's no longer clear that light will travel at speed c (at least in the original coordinate system--you can always transform to new local coordinates in which light has speed c).

 

[Samshorn]

?? GR is developed on top of SR, but is incompatible with SR's second postulate (the one of Einstein, not of some textbooks). If he did not explain that clearly enough for everyone, then we should probably start it as a topic... It is really quite straightforward.

That's what Einstein thought too - originally - but as he developed general relativity he came to the crucial realization that it was not as straightforward as he thought. As he said in 1949, he already had the equivalence principle and the idea of curved spacetime by 1908, on which general relativity is based, but he didn't arrive at the final theory for another 7 years. "Why were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that coordinates must have a direct metrical significance." Your comments indicate that you are still stuck in the mindset of thinking that coordinates must have direct metrical significance. That's the misconception that caused so much confusion in the early days over what "THE speed of light" is in a gravitational field. The answer (in both special and general relativity) depends on the choice of coordinates. (There's an unfortunate crackpot named Pentcho Valev who has devoted his life to mis-understanding this.) To test your understanding, try answering this question: According to general relativity, is the speed of light at a given location the same in every direction?

Again, there is a perfectly viable field interpretation of general relativity in which the curved metric is just an "effective" metric, on top of the "true" (but unobservable) flat Minkowski metric of special relativity, in terms of which the speed of light is always c. If you're not familiar with this non-geometrical interpretation of general relativity, you should read up on it.

Hmm I did not see anyone suggest that idea...

Exactly. That was the problem: you didn't see it - even though it was implicit in the very subject of the thread, and in everything you said.