Do clocks remain synchronized forever according to the equivalence principle?

[Bob Walance]

I did do some searching on this site for an answer to this, but couldn't find exactly what I was looking for. So, here it goes:

First -- assume that the gravitational field that Jim experiences is "homogenous" (that is, constant magnitude and direction within his region of spacetime).


Jim is standing on the Earth and is holding a clock. Bill, who has a similar clock, is in a rocket ship that is accelerating at a constant 1g (as measured by the body weight scale that Bill is standing on).

1 - Since, according to Einstein, these two cases are "equivalent", then shouldn't Jim's and Bill's clocks remain synchronized forever?

If this is true, then what this website says about relative aging is misleading.

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

It seems, rather, that a clock in an inertial frame of reference, for example a clock on a satellite, would age differently than Jim's and Bill's clocks.

2 - In this case the satellite is in 0g and Bill and Jim are at 1g, then after 5 years have elapsed on Bill's and Jim's clocks the satellite's clock will have aged 83.7 years, correct?

Thanks for any insight into this.

Bob Walance

 

[JesseM]

1 - Since, according to Einstein, these two cases are "equivalent", then shouldn't Jim's and Bill's clocks remain synchronized forever?

The equivalence principle just says that if they each make local observations--observations in a very small patch of space around them, over a brief amount of time (technically the equivalence is only exact if the space and time are infinitesimally small)--then they will see the same results if they perform identical experiments. The equivalence principle does not imply that if they are observing each other over a large distance and a significant period of time, that they will each observe the other's clock to be ticking at the same rate...the rate each sees would depend on the geometry of the whole spacetime and their relative positions in it.

 

[Bob Walance]

The equivalence principle just says that if they each make local observations--observations in a very small patch of space around them, over a brief amount of time (technically the equivalence is only exact if the space and time are infinitesimally small)--then they will see the same results if they perform identical experiments. The equivalence principle does not imply that if they are observing each other over a large distance and a significant period of time, that they will each observe the other's clock to be ticking at the same rate...the rate each sees would depend on the geometry of the whole spacetime and their relative positions in it.

So, if the space traveler returns to Earth, and assuming he orients his spacecraft to maintain his 1g acceleration the entire time, will the two clocks read the same?

Thanks,
Bob

 

[Al68]

I did do some searching on this site for an answer to this, but couldn't find exactly what I was looking for. So, here it goes:

First -- assume that the gravitational field that Jim experiences is "homogenous" (that is, constant magnitude and direction within his region of spacetime).


Jim is standing on the Earth and is holding a clock. Bill, who has a similar clock, is in a rocket ship that is accelerating at a constant 1g (as measured by the body weight scale that Bill is standing on).

1 - Since, according to Einstein, these two cases are "equivalent", then shouldn't Jim's and Bill's clocks remain synchronized forever?

Yes, if the relative velocity between them is zero. If not, then you have to account for SR time dilation.

And the equivalence principle says that Jim and Bill will get the same results for any local experiment they each perform. It doesn't say that each one's clock will read the same as the other. That would only be true if they were stationary with respect to each other, like if the rocket were 10 ft off the ground accelerating to oppose gravity, and Jim is 10 ft off the ground on a ledge next to the ship. Then their clocks would stay in synch with each other.

 

[JesseM]

So, if the space traveler returns to Earth, and assuming he orients his spacecraft to maintain his 1g acceleration the entire time, will the two clocks read the same?

No, not necessarily. Again, the equivalence principle is only about experiments which take place entirely in one small piece of spacetime--an experiment that involves starting out with synchronized clocks, then moving apart some significant distance for a significant time, then coming together and comparing clocks again, is not an experiment confined to a tiny region of spacetime where the effects of spacetime curvature can be considered negligible.