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?


Why can’t I kill my grandpa? (Time travel, part I)

So, this is the first post that we will dedicate to the question of time-travel in physics. We’ll start easy, but things may get pretty confusing soon, so behold!

Of course, we’re all time traveling, right now. We’re traveling towards the future, at a rate of one second per second. Strange speeds in our time travel appear as early as the Mahabharata, when king Kakudmi visits lord Brahma for some chat and, when he returns, many years have gone by. Yet, travel to the past appears later in stories, and mostly for the pleasure of anachronism. The time machine appears by the end of the XIX century in a short story from a Spanish writer, Enrique Gaspar y Rimbau, el “Anacronópete”, where the theory is exposed that it is the atmosphere causing the flow of time, as can be checked by the conservation of food in hermetic cans… His machine travels to the past much like Superman, flying against the rotation of the Earth.

The first story to deal with the problems of time travel to the past seems to be
Tourmalin’s Time Cheques, by Thomas A. Guthrie, under pseudonym in 1891, which I can’t discuss yet… (it’s in my reading list).

To the best of my knowledge, the first story which shows the problems and paradoxes of time travel to the past in its full glory is By his own bootstraps, by Robert A. Heinlein, in 1941. If you enjoy discussion about these topics, you really should read that short story.

The first and foremost paradox of time-travel is the grandfather murder case. I travel 50 years back in time and kill my grandfather before he meets my grandmother… so I can’t be born, and can’t kill my grandfather. So, if I do A, I force not-A, which forces A… what is the way out? Somehow, something should prevent you from killing your grandfather, so that history remains coherent.

We physicists love to give a name to everything, so we’ve baptized it as the Novikov principle. History should be coherent. Perhaps, after all, I do not have free will, I can’t choose to kill my grandpa… You see, the paradox with people gets somehow out of focus. Let us put it up simply will balls. This way, we call it Polchinski’s paradox:

We have a time-machine which has an input slot, an output slot and one dial. If you put something in the input slot, it will come out of the output slot some time before given by the mark in the dial. OK. Now, we put the dial to “1 second” and throw a ball towards the input slot. The same ball will come out of the output slot 1 second before the original one hits the input slot, OK? Now we can fix the geometry so that the second ball hits the first and puts it out of the way. So the output ball will prevent the input ball from entering the machine and, therefore… where did the second ball come from?

Polchinski's paradox

There are ways to overcome this paradox. Can you think of any?

It's my turn on the time machine!!!!!

It's my turn on the time machine!!!!