Gravity ~ Acceleration ~ Centrifuge & GR

[gonegahgah]

Let's two centrifuges, They have different length arms, and spun such that a clock at the end experiences each feels 1g. The clock on the centrifuge on the longer arm will run slower, even though it feels the same g-force as the other clock. Or you could arrange it so that the speed of the ends of the arms are the same for each centrifuge. In this case both clocks will run at the same rate, even though one will feel a greater g0force than the other.

Thanks Janus. Just reiterating what I think you've explained. Correct me if wrong.
Are you saying that the time dilation for an object in a centrifuge is based purely on the speed it is traveling (SR) and that there is no gravitational (GR) time dilation to be counted?
And so the time dilation is independent of the radius of the centrifuge?

 

[Jonathan Scott]

Thanks Janus. Just reiterating what I think you've explained. Correct me if wrong.
Are you saying that the time dilation for an object in a centrifuge is based purely on the speed it is traveling (SR) and that there is no gravitational (GR) time dilation to be counted?
And so the time dilation is independent of the radius of the centrifuge?

That's one correct way of looking at it.

An alternative way of reaching the same mathematical result is to integrate the centripetal acceleration as if it were a gravitational field, from the center out to the relevant radius, giving the equivalent gravitational potential difference between those points, and hence derive the corresponding time dilation.

Regardless of whether you're using the SR velocity or the equivalent gravitational potential, the time dilation does not depend on the acceleration. As Janus pointed out, you can have the same time dilation for different accelerations, or different time dilations for the same acceleration.