How Do Rindler Coordinates Affect Time Dilation and Acceleration?

[harrylin]

Very interesting thread!

From post #66 by Boustrophedon (and elaborated in #110), I think that Einstein's 1935 formulation (of which I gave an abbreviated version) is exact: a uniformly accelerated reference system (thus not "Born rigid") has accelerometers measuring the same "g" value everywhere; and that is postulated to be indistinguishable from a homogeneous gravitational field.

Note that the EEP is non-local: Einstein admitted that it does not represent the whole Minkowski space; I suppose that he had something similar as Rindler's horizon in mind (but not exactly, as I first thought).

Sorry, I now compared the equations and found that my first impression was correct: the equations are identical. That means that Einstein also implied Born rigid motion. Apparently different people even mean different things with "homogeneous"!

 

[harrylin]

Yes, in that sense I suppose you could say that what physicists today call the "EEP" is mislabeled since it's not the exact principle Einstein stated. Unfortunately (if you think this kind of thing is unfortunate), this kind of mislabeling is rampant in physics, so there's not much we can do about it. "Maxwell's Equations" were not written in the form we know them by Maxwell. "Newton's Laws" were not written in the form we know them by Newton. And so on.

I don't mind much as long as the modification is merely a matter of presentation; I only wear the Anti Mislabeling Brigade hat when I think that it really matters. In this case I'm afraid that the "Coca Cola" label has been put on a pack of coffee.

 

[PeterDonis]

I don't mind much as long as the modification is merely a matter of presentation

At least in the case of Maxwell's Equations, I'm not sure Maxwell himself would have called the difference between his formulation and later ones a matter of presentation. Steven Weinberg, in one of the essays in his collection Facing Up, talks about a comment that Heaviside once made, that Maxwell "was only half a Maxwellian", and what it meant: Maxwell believed that EM fields were tensions in a physical medium (the "ether"), whereas the later formulation (which Heaviside played a major part in developing) viewed EM fields as physical entities in their own right, not requiring any medium to exist or propagate (and Weinberg makes it clear that this view is still the mainstream view of physics today).

 

[zonde]

Thus, while it's true that the acceleration is second order in time, it's not relevant to the point that the EP is trying to be made. There exists a set of cirumstances where the observation time is long enough that you can observe acceleration, but the tidal forces can be neglected, and in this set of circumstances, one can apply the equivalence principle.

With tidal forces we actually mean certain spatial profile of acceleration, right? So it's like acceleration gradient.

Acceleration on the other hand we view as intrinsic property of worldline, right? If I pick a single worldline one of it's properties is acceleration and we can somehow determine it without looking at context. Where tidal acceleration would require many worldlines.