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I quote the part I don't quite understand:

If it is possible for a rocket traveling below the speed of light to get from event A (say, the final of the 100-meter race of the Olympic Games in 2012) to event B (say, the opening of 100,004th meeting of the Congress of Alpha Centauri), then all observers will agree that event A happened before event B according to their times. Suppose, however, that the spaceship would have to travel faster than light to carry the news of the race to the Congress. Then observers moving at different speeds can disagree about whether event A occurred before B or vice versa. According to the time of an observer who is at rest with respect to the earth, it may be that the Congress opened after the race. Thus this observer would think that a spaceship could get from A to B in time if only it could ignore the speed-of-light speed limit. However, to an observer at Alpha Centauri moving away from the earth at nearly the speed of light, it would appear that event B, the opening of the Congress, would occur before event A, the 100-meter race. Thus the moving observer would say that if faster-than-light travel is possible, it should be possible to get from event B, the opening of the Congress, to event A, the 100-meter race. If one went slightly faster, one could even get back before the race and place a bet on it in the sure knowledge that one would win.

I think I misunderstood, but Hawking seems to state in this last sentence that an event can take place (the race) and one can go back in time before it took place (via superluminal travel). That seems ridiculous, since even if one has a teleportation device, which can teleport one over large distances instantaneously, such a feat would not be possible since the event either did not take place or already took place, regardless of whether you're teleporting in or not. Then how would it be possible by going faster than light, which would seem less powerful than a teleportation device?

If I misunderstood, do correct me.

J. Schmidt
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1 Answers1

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Your teleportation device (which is an extreme form of superluminal travel) would indeed allow you to travel backward in time, assuming (a) special relativity is true and (b) you were able to use this device in any reference frame to teleport between any two points at the same time (with "at the same time" defined by the reference frame you are in).

It may seem counterintuitive in the sense that you might think that teleportation (instantaneous transportation through space), should have nothing to do with time travel (transportation through time). But the key insight of special relativity is that space and time are inseparably linked. The fact that you can't have "instantaneous teleportation" without also having "time travel" is one manifestation of this.

These q/a's have some more details:

Andrew
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  • I understand how time dilation works through large speeds, however I'm struggling with the part of actually rewinding time to relive an event as the last sentence seems to imply. So you go faster than light, big deal, you end up far away from the event and eventually the light of the event reaches you. In what way does this help to actually rewind time and relive the exact same moment? I get that the event hasn't happened yet far away due to light needing some time to get there, but the event has happened at its proper location, so how is it possible to go back to that place AND time? – J. Schmidt Jun 07 '21 at 22:23
  • @J.Schmidt Yeah so the key idea is assumption (b) in my answer. The idea is that you have to create a "triangle" in Minkowski space. This requires using your teleportation machine twice, in two different frames. [I] First you go from event $A$ to spacelike separated event $B$ at time $t=0$ in the unprimed frame. [II] Then you boost by a velocity $v$ such that $A$ occurs after $B$ (it's always possible to find a frame where this happens since $A$ and $B$ are spacelike separated). Then you go from $B$ to an event $C$, which is at the same spatial location as $A$ but an earlier time. (...) – Andrew Jun 07 '21 at 22:26
  • (Note that $A$ is at the same time as $B$ in the original frame, and $C$ is at the same time as $B$ in the boosted frame, and $C$ is always in $A$'s past light cone). Then you just "wait" to go from $C$ to $A$, completing the triangle. Now you have completed a closed time -like loop. You've been able to travel to the past light cone of event $A$ and can cause havoc like killing grandfather's, etc. – Andrew Jun 07 '21 at 22:28
  • I think this construction is called the "tachyonic antitelephone" in the first q/a I linked in my answer. – Andrew Jun 07 '21 at 22:30
  • Thanks for the explanations so far, but it seems I simply cannot wrap my head around this. I suppose I'll give up and continue the book, trying to not think about it. It just seems so illogical to me: even though events may happen simultaneously for one observer, this doesn't mean they actually do, e.g. an event could occur at a large distance from the observer, and so light needs some time to reach the observer, say a year. This doesn't mean the event "happens" when the light reaches the observer after a year, the event has happened a long time ago. – J. Schmidt Jun 08 '21 at 15:42
  • @J.Schmidt Yes, I think you are hitting on the key point, even though it is indeed very counterintuitive! There is no absolute definition of simultaneity. Events which are space-like separated can happen in any order. Or, more precisely, observers traveling at different speeds will disagree about the time ordering of space-like separated events. Even though it is weird, this does not cause any contradictions, so long as no one can travel faster than the speed of light, because then it is not possible to travel from one event to a space-like separated event. – Andrew Jun 09 '21 at 03:16