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Posted: 1/3/2012 7:44:40 AM EDT
Ive pretty much got the basics of both SR and GR time dilation.

There is a paradox involved with SR time dilation where each observer sees the other's clock as moving slower than its own. OK, fine so far. But is there a similar paradox with GR's gravitational time dilation? With 2 stationary observers under a gravitational field, where 1 observer was much closer, would each see the other's clock as moving slower?

My scenario doesn't involve rotation. Like say if one clock was on earth at the bottom of Mt everest, and the other was at the top.

But this 2 page thread on physicsforums seems to say that rotation matters. Now I do realize how the two clocks are rotating at the same rate, but moving through actual space at different rates due to the rotation with different altitudes, like on the 2nd page there where the dual airplanes on the string was described. But I thought SR was only concerned with RELATIVE motion?
Link Posted: 1/5/2012 4:36:57 AM EDT
Someone called JesseM answered with this:


As kev showed on that thread I linked to, the total time dilation for an object in a circular orbit is just the velocity-based time dilation (velocity measured relative to the center of the body it's orbiting) multiplied by the gravitational time dilation.


IIRC, that's incorrect. The time dilation for reduced gravity on a GPS satellite is +45 microseconds for the satellite's time and the effect of velocity is -7 microseconds, which are combined to get the 38 microsecond delay.
Link Posted: 1/5/2012 6:13:23 AM EDT
Originally Posted By sigp226:
Someone called JesseM answered with this:


As kev showed on that thread I linked to, the total time dilation for an object in a circular orbit is just the velocity-based time dilation (velocity measured relative to the center of the body it's orbiting) multiplied by the gravitational time dilation.


IIRC, that's incorrect. The time dilation for reduced gravity on a GPS satellite is +45 microseconds for the satellite's time and the effect of velocity is -7 microseconds, which are combined to get the 38 microsecond delay.


I got that too, and just ignored it as it was an obvious error. but apparently someone else was claiming that in the case I described, the clocks would run different
Link Posted: 1/6/2012 4:47:08 AM EDT
Are you looking for the difference between a rotating gravitational field and a stationary one?
Link Posted: 1/6/2012 5:53:51 AM EDT
Originally Posted By sigp226:
Are you looking for the difference between a rotating gravitational field and a stationary one?


not 100% sure, but i think maybe.

basically want to read about how clocks tick differently (but not due strictly to gravity differences with altitude differences) say, here on earth where the earth is rotating and clocks are at equator but one is right at sea level and the other is up on a mountian. So obviously GR and lorentz calculations are involved for the gravity differences, but apparently, because they are spinning, there is some other calculation to be made, but its not the SR relative motion one.
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