A few questions about GR

alexbib

No, I think Janus is right, the inertial clock actually running faster has to be due to acceleration. Go read the GR explanation from the link you provided.

Ambitwistor

It's all well and good to work in a non-inertial frame, if you want. But if you actually compute the time dilation factor between the inertial and non-inertial clocks at any instant of time, you will find that it can be expressed solely in terms of their relative velocity (computed in a hypersurface of simultaneity), even in the GR explanation.

The "gravitational field" in the non-inertial frame is precisely arranged to have this property (i.e., the acceleration depends on the relative velocity in just such a way to make the time dilation depend only on relative velocity); it has to, in order to agree with the observations in an inertial frame.

The reason why the analysis goes differently in an accelerating frame is not because the time dilation factor depends directly on the proper acceleration or anything like that (if it doesn't in one frame, it doesn't in any frame) -- it's just because the acceleration changes the surfaces of simultaneity.

It is an empirical fact that SR time dilation depends only on velocity, not acceleration. That was the point of the clock postulate FAQ on the same site.

alexbib

I get your point. As you say, it depends only on the velocity, and the best way to calculate it is to do it with time distortion relative to the inertial frame.
However, I also think it is important to understand why you still get more elapsed time on the inertial clock from the non-inertial clock's point of view, which is (in my opinion) explained pretty well on the link you posted.

Thanks a lot for your answers guys.

GijXiXj

... ... or life, the twin paradox, and ... ?

I'm very dubious about accelerations not being a factor, or at least an easily discountable one.

Question: If you accelerate, does the Principle of Equivalence not include the idea that your time slows down as if you were in a gravitational field? I know (foggy memory) that at least your not supposed to be able to tell if your falling (gravity) or accelerating, at least by any 'internal' experiment.

Ambitwistor

Most of my posts in this thread, above yours, were aimed specifically at addressing the issue of time dilation in an accelerating frame and the equivalence principle. The "GR explanation" to which I refer is the equivalence principle.