Are Both Twins Equivalent in a Torus Universe with the Twin Paradox?

[jcsd]

Certainly the two observers have different planes of simultaneity, that is why they record different times, however they can pass each time sufficiently close that the problem of synchronizing clocks is negligible compared to the time of passage around the universe.

Yes I don't dispute that.

One of them will record the longer elapsed time, but which one?

I don't dispute that one observer will meausre time a longer time, infact I don't dispute (that their exist situations in which) their is one single observer out of the class of all possible observers who are locally inertial who experinces a maximal time.

Each has remained in an inertial frame of reference. The principle of relativity would have it that each observer is equivalent.

In GR though all obsrevers are equivalent, so when considering the equivaelnce principle why shouldn't we consider all the other obsrevers whose worldlines are coincidental to the two events? The only inetersting thing about our observers is that they travel along geodesics; clearly in GR are there are locally-length minimizing paths hich can be regarded as soem sense special, but I do not see the fact that under some topolgies more than one of these paths can pass through the same two points as a violation of GR! Surely you recognize that GR does assert absolute equiavalence in all ways for all observers (if that were the case we wouldn't get different measuremnts in different frames), only the equvalance of the laws of physics in each frame.

Obviously we have to consider the rest of the universe in deciding which one is the stationary observer, the question is does this then violate the principles of GR?

The universe can be regarded as geometrically different for each observer and the source of that geomertical difference can be traced to the different arrangement (caused by relative motion) of the matter in that universe (though of course both observers still inhabit the same spacetime).

 

[JesseM]

It's me again!

The only measurements made in this paradox are the local neighbourhood measurement of time made by both observers as the pass close by each other twice, with one of them circumnavigating the universe in the meantime. One of them will record a longer elapsed time, but which one?

You don't have to worry about constructing a cosmological coordinate system, just a local one.

How is the 'older' 'twin' selected?


Garth

If neither one's frame extends beyond their local neighborhood, and they don't have any type of global coordinate system, then neither one has any way to predict how fast the other one's clock is ticking while they're apart, so they can't predict how old the other will be when they meet again. You might as well imagine two twins that separate, one flies close to a black hole, then they reunite (both having traveled along geodesics, so locally they always observe the laws of physics working the same way as in SR), and the one that flew close to the black hole is younger thanks to gravitational time dilation...do you think this violates the SR principle that the laws of physics should work the same in all reference frames as well?

 

[yogi]

Garth - actually have several questions that relate to varying G - will send private message. Thanks Yogi