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Suppose there is an object motionless behind me. Now suppose I (almost) instantly accelerate away from it. In my perspective, this causes the time of the object behind me to be set back. Now this is not a contradiction, as he cannot possibly know I've accelerated before the time on his watch (once again) reaches what it was in our mutual frame when I started the acceleration. Therefore, no problem if we think of acceleration simply as changing inertial frames.

However, if we think of me as being in an accelerated frame, then it must be that my acceleration caused his time to move backwards, i.e. that he underwent a time-reversed process. This got me to thinking, how would this work exactly, particularly with respect to gravity? One might be tempted to say that gravity would simply reverse, i.e. that things fall up instead of down. However, an object in orbit would simply reverse its orbit, but still be subject to normal gravity. This seems like a contradiction to me. So what gives?

Travis Kidd
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  • Wait, are you accelerating instantly to some constant speed, or are you continuing to accelerate? – probably_someone Apr 26 '20 at 19:25
  • Also, what do you mean when you say the time of the other object is "set back"? Objects don't ever appear to go backwards in time. – probably_someone Apr 26 '20 at 19:26
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    This is actually one my complaints about acceleration being used to explain the "missing Earth aging" in the Twin Paradox. While it works out nicely if space-twin accelerates towards Earth twin, should space twin decided to turn around and go back to Alpha Centauri at some point on the way home, said explanation means Earth twin is going backwards in time. – JEB Apr 26 '20 at 20:25
  • What is wrong with going back in time, provided no contradiction arises as a result? Certainly Earth twin will not know he has gone back in time. – Travis Kidd Apr 26 '20 at 21:15
  • As I understand it, if I am between A and B which are motionless with respect to me, and C is moving past me toward A, the time on B's watch in C's perspective will be behind the same watch's time from my perspective. If I magically (er, using some really cool scientific principles) accelerate to match C's motion, then my perspective will match his, i.e. the time on B's watch will be set back. – Travis Kidd Apr 26 '20 at 21:23
  • And how do you explain the Twin Paradox if not with acceleration? – Travis Kidd Apr 26 '20 at 21:29

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Upon further searching I found the answer to my question here. In fact things do not fall up in time-reversed gravity. They move up because they were moving down in normal time, but their upward motion slows in reverse time either because they were falling more slowly at first in normal time or ... because of normal gravity.

(As a quick answer to the comments: I assumed I accelerated to a certain point. And it may very well be that the object goes backwards in time, at least in an accelerated frame of reference. My (current) concern about this has been resolved.)

Travis Kidd
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