Time travel from classical to quantum mechanics

I would like to return to the time travel questions we posed on this entry. Basically, we want to understand Polchinski’s paradox, which we show in this pic So, imagine that you have a time machine. You launch a ball into it in such a way that it will come out of it one second before. And you are so evil that you prepare things so that the outcoming ball will collide with the incoming one, preventing it from entering the machine. The advantage of this paradox is that it does not involve free will, or people killing gradpas (the GPA, grandfathers protection association, has filed a complaint on the theoretical physics community, and for good reason).

No grandpas are killed, sure, but maybe the full idea of time-travel is killed by this paradox. Why should we worry? Because general relativity predicts the possibility of time-travel, and general relativity is a beautiful and well-tested physical theory. We’re worried that it might not be consistent…

There is a seminal paper by Kip Thorne and coworkers (PRD 44, 1077) which you can find here, which advances the possibility that there are no paradoxes at all… how come? In the machine described above we have focused on a trajectory which gives an inconsistent history. But there might be other similar trajectories which give consistent histories. In fact, there are infinite of them, so our problem is now which one to choose! But let us not go too fast, let us describe how would the “nice” trajectories come.

A possible alternate history: the ball travels towards the machine with speed v, but out of it comes, one second before the collision, a copy of itself with speed v’>v, in such a way that the collision does not change the direction of the initial ball (a glancing collision), but it also accelerates it… up to v’, thus closing the circle! There are no problems with conservation of energy and momentum, since the final result is a ball with speed v…

Thorne et al. described, for a case that was similar to our own, infinitely many consistent trajectories… And the question is left open: is there any configuration which gives no consistent trajectories at all? So far, none has been found, but also there is no proof for this.

And what happens when we have more than one possible consistent trajectory? My feeling is that we’re forced to go quantum! Classical physics is just an approximation. Nature, really, follows all paths, and make them interfere. But if there is a minimum action path, then it, under some conditions, may be the most important one. Quantum mechanics is happy with lots of consistent histories: they would just interfere… And a lot of funny things happen then, but let us leave that for another post…

So, what do you think? It will always be possible to find a consistent history, or not? Are there true paradoxes in time travel?


7 thoughts on “Time travel from classical to quantum mechanics

  1. You mean, then: “the machine won’t work”… so you’re jumping out of the rules we’ve given to ourselves. Or are you implying that time travel is impossible? :)

  2. Why, if I may ask? :) I mean: my thesis is “time-travel is still consistent”. As far as I know, there are no “catastrophic” paradoxes involved…

  3. It’s not a catastrophe issue. Its just that if time is a continuum everything must be on it. Every movement you make will be relative to everything else. If you speed up the puntual time of something you must slow down everything else to keep it on scope. atime travel will be against thermodynamics.

  4. First of all, when we discuss these topics, we must attach to a certain framework. I’m talking always from general relativity, which is a rather well tested theory. In it, there is no “time conservation”, so I don’t see the reason for your first point. About the second one, I agree: we have to discuss the thermodynamics of time travel. Again, there are no “true” paradoxes, only apparent ones, but I agree with you that they’re pretty interesting anyway! :)

  5. Ok, ok, you’re the expert here. But as far as i know time is a dimension as well as space. that said, either you move into the dimension or you need another one to “bypass” it.

    (By the way, what are you doing don’t replying my recent mail? :P)

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