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?