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

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Discussion Overview

The discussion centers on the implications of the twin paradox within the context of a toroidal universe. Participants explore whether both twins can be considered equivalent when one travels through a compact space, examining the effects of spacetime curvature and topology on their relative aging. The conversation touches on theoretical aspects, potential inconsistencies with general relativity, and the nature of preferred frames in cosmological models.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that in a toroidal universe, the moving twin may not experience acceleration and can return to compare times with the stationary twin, suggesting equivalence.
  • Others argue that the curvature of spacetime due to mass complicates the situation, leading to a non-symmetrical outcome where one twin may age differently based on their relative motion to mass.
  • A later reply references a paper discussing the twin paradox in compact spaces, suggesting that both twins could be in inertial frames, yet still perceive each other as aging differently, raising questions about the resolution of the paradox.
  • Some participants challenge the idea of a preferred frame introduced by the topology of the universe, questioning its compatibility with the principles of general relativity.
  • There are discussions about the implications of Mach's Principle and the equivalence principle, with some asserting that introducing matter and curvature leads to a preferred frame, while others maintain that the equivalence principle should hold even in curved spacetime.
  • One participant suggests that practical observations, such as the movement of galaxies, could help determine which twin is traveling, countering the notion of indistinguishability in a uniform universe.
  • Another participant emphasizes the historical context of Einstein's theories, arguing that the foundations of special relativity were built on the concept of no preferred frames, which may conflict with the implications of general relativity in cosmological scenarios.

Areas of Agreement / Disagreement

Participants express a range of views, with no consensus on whether the twins can be considered equivalent in a toroidal universe. Disagreements persist regarding the implications of general relativity, the nature of preferred frames, and the validity of Mach's Principle in this context.

Contextual Notes

The discussion highlights limitations in understanding the implications of compact spaces and the potential inconsistencies that arise when applying general relativity to cosmological models. The assumptions regarding the nature of spacetime curvature and the role of mass in determining reference frames remain unresolved.

  • #31
Garth said:
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).
 
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  • #32
Garth said:
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?
 
  • #33
Garth - actually have several questions that relate to varying G - will send private message. Thanks Yogi
 

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