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I saw a post on reddit regarding immortality and how it would never be possible due to entropy. That said, assuming time travel was possible, would it not be possible to never reach this state of entropy if you could keep traveling back in time? Say for instance that you couldn't travel back in time within your own time curve, but you could travel to other time curves. You would merely jump to another curve when your current universe was about to reach its end. Is it too big of an assumption to think that your own initial entropy (by this I mean your entropy from your first timeline) would not 'follow you' to other time curves? I may be totally off-base in my assumptions, as I know next to nothing about physics. Any feedback/criticism is welcomed.

Here is the link to the post in reddit.

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    $\begingroup$ Please link to the post on reddit. $\endgroup$ – Ben Crowell Aug 26 '13 at 22:58
  • $\begingroup$ related: physics.stackexchange.com/questions/74041/… $\endgroup$ – Ben Crowell Aug 26 '13 at 22:59
  • $\begingroup$ A general warning about extreme assumptions: If the universe deems the proposition which you begin ("time travel is possible") as untrue, but you use it anyway, at best your conclusions have nothing to do with the actual universe. Worse, if the falseness of your assumed-true proposition logically follows from your other physical/mathematical axioms, then you will likely find that everything explodes and your entire logical system falls apart. Physics often demands assumptions, but unlikely assumptions should undergo extreme scrutiny. $\endgroup$ – user10851 Aug 27 '13 at 0:28
  • $\begingroup$ @ChrisWhite: I agree with your analysis in terms of Aristotelian logic, but I wouldn't necessarily agree that it's an "extreme assumption" to say that time travel is possible. It really depends on what one means by "time travel is possible." It's definitely possible in the sense that GR admits solutions that have CTCs. It's definitely not possible in the Dr. Who sense where you have some human-scale box you step into -- the structure of the Einstein field equations pretty much guarantees that huge amounts of matter would be involved. $\endgroup$ – Ben Crowell Aug 27 '13 at 20:40
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The question of whether it's possible to do an infinite number of calculations has been fairly thoroughly studied, and depends on the cosmological model. Dyson 1979 (described in Baez 2004) shows that the answer is yes in an open universe with zero cosmological constant. Krauss 1999 shows that the answer is no in an open universe with nonzero cosmological constant. Neither of these cosmological models include closed, timelike curves (CTCs), i.e., there's no time travel. Since the answers depend on the cosmological parameters in ways that are complicated and not obvious even to experts, it seems unlikely to me that the answer can be answered in the form in which you presented it. To make it answerable, you would have to postulate some specific cosmological model that was compatible with current cosmological observations, but also included CTCs. The fact that the chronology protection conjecture seems to be valid suggests that you will have a hard time making any such model. There is also no reason to believe that such a model, if it did exist, would be uniquely determined by current observations.

General relativity is not generally compatible with the second law of thermodynamics. For example, there are spacetimes that are not time-orientable, and in such a spacetime there is not even any consistent way to state the second law. In a universe that was time-orientable but had CTCs, there would be no way to satisfy the second law along a CTC (since you can't keep increasing entropy forever while wrapping back around to your starting point) except in the special case where there is maximum entropy all along the CTC.

Baez, J., 2004, "The End of the Universe.", http://math.ucr.edu/home/baez/end.html

Dyson, Time without end: Physics and biology in an open universe, Reviews of Modern Physics 51 (1979), pp. 447–460, doi:10.1103/RevModPhys.51.447.

Krauss and Starkman, 1999, Life, The Universe, and Nothing: Life and Death in an Ever-Expanding Universe, http://arxiv.org/abs/astro-ph/9902189

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It's confusing whether you're referring to the entropy of the universe or the entropy of your body. First of all, even if you could 'travel through time' this would not prevent biological effects from happening so even if you were immortal your cells would eventually stop reproducing and die.

Assuming this is magically prevented, there are solutions to Einstein's field equations that would allow for time to 'flow backwards' in which case there would be no problem with you going back in time to a hospitable point in time and reliving it over and over again.

Entropy always increases, it's the 2nd law of thermodynamics, but that doesn't mean that an object put into a system will immediately reach equilibrium and no longer have the same characteristics. Eventually it'll reach equilibrium but something as structured as a human wouldn't suddenly cease to exist to conserve entropic equilibrium. It's all a matter of whether you choose to go back in time and exist in an environment that wouldn't destroy your body, like a star or vacuum would.

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