Timeline for Symmetrical twin paradox in a closed universe
Current License: CC BY-SA 3.0
14 events
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| Nov 20, 2012 at 20:49 | comment | added | Zo the Relativist | @dmckee: I was imagining constructing the torus out of the plane, imagining that the plane is its universal covering space.Then, the line that you use to do the gluing is what I'm calling the 'boundary'. If you prefer a more geometric construction, imagine the spacetime as a cylinder, with the time axis being noncompactified. Draw two antipoidal lines, that represent observers at rest with respect to the spacetime.The perpendicular distance between those lines will be a minimum in exactly one reference frame, and an observer between them can think of them as the 'boundary' in this sense. | |
| Nov 20, 2012 at 14:19 | comment | added | dmckee --- ex-moderator kitten | What "boundary"? It's clear that you can tell when you have lapped the stuff that was at rest near your starting point, but not clear how you tell where the "boundary" is. How do you know you didn't start right by it? | |
| Nov 13, 2012 at 17:53 | comment | added | Zo the Relativist | @user1247: new edit. In this spacetime, the motion relative to the universe is measurable. Just wait for a light ray to go around the universe, and you have the diameter of the universe. This quantity will depend on the relative motion to the boundary. | |
| Nov 13, 2012 at 17:51 | history | edited | Zo the Relativist | CC BY-SA 3.0 |
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| Nov 13, 2012 at 8:38 | comment | added | user1247 | let's make this more explicit to avoid confusion. In the case that one twin "stays put" and the other "circumnavigates the universe", and given that neither twin has accelerated, you are saying that there is asymmetric aging, yes? And yet, by rotational symmetry, how do you know which is the twin that stayed put, and which is the twin that is doing the circumnavigation? | |
| Nov 12, 2012 at 16:48 | history | edited | Zo the Relativist | CC BY-SA 3.0 |
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| Nov 12, 2012 at 14:40 | history | edited | Zo the Relativist | CC BY-SA 3.0 |
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| Nov 12, 2012 at 14:31 | comment | added | Zo the Relativist | @user1247: (cot'd) these paths are topologically inequivalent and there is no paradox. In essence, you added symmetry back into the problem, while the papers linked consider the general case of motion in these spaces. | |
| Nov 12, 2012 at 14:30 | comment | added | Zo the Relativist | @user1247: the preferred frame is the one that is at rest with respect to the boundaries, in which ''the universe is at its maixmum diameter.'' If you have one observer at rest with respect to this frame, than the other one will be the one that ages more slowly. You have BOTH observers moving with respect to this frame, one in one direction and the other in the other direction. Thus, no asymmetric aging, by the argument above. (and in my description). The asymmetric aging happens when you have one stationary observer, and the other one doing a ''lap around the universe.'' | |
| Nov 12, 2012 at 8:30 | comment | added | user1247 | what do you mean "in my construction?" In the construction of the OP (to which you responded with an answer that makes it clear you did not read the paper), there is a preferred frame and asymmetric aging. The interesting thing that I am pointing out is that this is in spite of perfect geometric symmetry of the problem. Neither twin accelerates asymmetrically, and the space is compact and symmetric about the direction of motion. This, to me, represents a paradox that should be explained. | |
| Nov 11, 2012 at 22:56 | comment | added | Zo the Relativist | @user1247: in your construction, both observers are moving with respect to the preferred frame at the same relative velocity, and the problem is removed. | |
| Nov 10, 2012 at 9:05 | comment | added | user1247 | Both the referenced paper and this one too (ajp.aapt.org/resource/1/ajpias/v51/i9/p791_s1?isAuthorized=no) for example, arrive at a different conclusion, ie that the aging is indeed asymmetric and there is a preferred frame. I believe this understanding is canonical. My issue is that I have a hard time reconciling this asymmetry with the perfect symmetry of the problem. | |
| Nov 9, 2012 at 16:21 | history | edited | Zo the Relativist | CC BY-SA 3.0 |
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| Nov 9, 2012 at 16:05 | history | answered | Zo the Relativist | CC BY-SA 3.0 |