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I've heard it said that in an infinite universe if you could go far enough in one direction you would end up in a location identical in every aspect to the one you left. Same Earth, same culture, same night sky, same age, same laws, same everything.

Is there a way to tell that it is different locations rather than the same one, or would that require an absolute reference frame?

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    $\begingroup$ I've heard it said that in an infinite universe if you could go far enough in one direction you would end up in a location identical in every aspect to the one you left. Same Earth, same culture, same night sky, same age, same laws, same everything. Where have you heard this? It certainly is not mainstream. $\endgroup$ – Aaron Stevens Sep 22 '19 at 21:45
  • $\begingroup$ You probably heard about doppelgangers in the context of speculative-but-reasonably-respectable physics regarding a multiverse. For example, see this popular account. You can’t travel to the other universes where another Earth or another you is. $\endgroup$ – G. Smith Sep 22 '19 at 22:31
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    $\begingroup$ Possibly related to this question: physics.stackexchange.com/q/132661 $\endgroup$ – D. Halsey Sep 22 '19 at 22:35
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    $\begingroup$ in an infinity of time and an infinity of space all things will happen, if it does not just wait, but this is more philosophical than physics $\endgroup$ – Adrian Howard Sep 23 '19 at 2:44
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You're phrasing this in terms of physical travel, but that won't actually work. For example, if you travel 1 billion light years relative to the Milky Way galaxy, which is essentially at rest relative to the Hubble flow, then the universe will have aged at least 1 billion years. Cosmological conditions will have changed by then, e.g., the cosmic microwave background will have cooled by some appreciable amount.

Actually, in order to reach a near-twin Earth, you would probably have to travel some silly distance like $10^{10^n}$ light years, where $n$ is pretty big. In that time, the conditions in the universe will have changed drastically -- to the point where there is no longer any life or consciousness.

Is there a way to tell that it is different locations rather than the same one, or would that require an absolute reference frame?

This answer seems to me like a reasonable attempt to spell out the assumptions underlying this idea of dopplegangers elsewhere in an infinite universe. Subject to those assumptions, and getting rid of the idea of physical travel, then it does seem likely to me that you could find a doppleganger-Earth that matched ours to any desired precision. If your ability to measure things is worse than that precision, then I think your idea is right -- there is no way to tell that it's different, because we don't have any absolute frame of reference. I think this also requires the assumption that cosmological homogeneity holds to an extremely good level.

One thing to be careful about here is that this kind of discussion seems to go beyond the philosophical bounds of science in the sense that any statements we make are inherently untestable. The arguments about the inability to physically travel to the doppleganger-Earth can probably be expanded to show that we can't test its existence by any empirical means.

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