This question arose when I read the Rietdijk-Putnam argument or "Andromeda paradox". Let's arrange two inertial frames of referance like usually, S being considered stationary (could be you sitting in a chair) and one that moves with a relative velocity v with respect to S, S' (a guy walking past you, passing you at time t=t'=0). Let's suppose that the andromedans in frame S' choose to take off to earth at the time t' = 0, then the time in S can be found using the Lorentz-transformation t = gamma(t' + v*x'/c^2). For simplicy let's assume this velocity between the frames is a walking speed of something like 5 km/h, the gamma factor will be very close to 1 so t is approximately t = v*x'/c^2 which can become quite a significant size because of the distance to the andromeda galaxy (I believe I got something like 4,5 days). Now to the question, let us suppose the guy in S' who saw the event happen at t'=0 at some later time, like t'=0,5day decides to stop (he accelerates so the relative velocity between the frames is zero) since this observer is now in a frame which shares plane of simultaneity with S he must experience the event again at the earlier found time t = v*x'/c^2 and thereby experiencing the same event twice, and actually experiences time "going backwards" in the andromeda galaxy as he decelerates. Is this true? I searched a bit on the subject and found a paper http://arxiv.org/PS_cache/physics/pdf/0411/0411008v1.pdf which comments on a paper by Dolby and Gull. Dolby and Gull wrote "If Barbara's hypersurface of simultaneity at a certain time depend so sensitively on her instantaneous velocity as these diagrams suggest, then she would be forced to to conclude that the distant planets swept backwards and forwards in time whenever she went dancing" to which is replied "... As far as I can tell, their worry here is that, as Barbara's instantaneous velocity changes from moment to moment, she will be forced to conclude that some events that are in her current subjective future (i.e. that lie within the future light cone of some event on her current hypersurface of simultaneity) were, at some point on her past worldline, judged to be in the past (i.e. lying within the past light cone of some event on her past (then current) hypersurface of simultaneity). Of course, this is no absurdity: it has long been clear that the pretheoretical concepts of "past" and "future" do not mesh perfectly with their relativised versions" So is this true? I simply have to ask because I find it to be a quite incredible result that time can be observed to run backwards during acceleration.