In a comment on my last post, elkement asked:
“What are exactly are the limits for having an object time-travel that is a bit larger than a single particle? Or what was the scope of your work? I am asking because papers as your thesis are very often hyped in popular media as `It has been proven that time-travel does work’ (Insert standard sci-fi picture of curved space here). As far as I can decode the underlying papers such models are mainly valid for single particles (?) but I have no feeling about numbers and dimensions, decoherence etc.”
Yep, that is pretty much THE question about time travel – can we do it with people or not? (Or even with rats, that would be good too). The bottom line is that we still don’t know, but I might as well give a longer answer, since it is just interesting enough to warrant its own blog post.
First of all, nobody has yet been able to prove that time travel is either possible or impossible according to the laws of physics. This is largely because we don’t yet know what laws govern time travel — for that we’d almost certainly need a theory of quantum gravity. In order for humans to time-travel, we would probably need to use a space-time wormhole, as proposed by Morris, Thorne and Yurtsever in the late eighties . Their paper originated the classic wormhole graphic that everyone is so fond of:
However, there are at least a couple of compelling arguments why it should be impossible to send people back in time, one of which is Stephen Hawking’s “Chronology Protection Conjecture”. This is commonly misrepresented as the argument “if time travel is possible, where are all the tourists from the future?”. While Stephen Hawking did make a comment along these lines, he was just joking around. Besides, there is a perfectly good reason why we might not have been visited by travellers from the future: according to the wormhole model, you can only go back in time as far as the moment when you first invented the time machine, or equivalently, the time at which the first wormhole mouth opens up. Since we haven’t found any wormhole entrances in space, nor have we created one artificially, it is no surprise that we haven’t received any visitors from the future.
The real Chronology Protection Conjecture involves a lot more mathematics and head-scratching. Basically, it says that matter and energy should accumulate near the wormhole entrance so quickly that the whole thing will collapse into a black hole before anybody has time to travel through it. The reason that it is still only a conjecture and has not been proven, is that it relies upon certain assumptions about quantum gravity that may or may not be true — we won’t know until we have such a theory. And then it might just turn out that the wormhole is somehow stable after all.
The other reason why time travel for large objects might be impossible is that, in order for the wormhole to be stable and not collapse in on itself Hawking-style, you need matter with certain quantum properties that can support the wormhole against collapse . But it might turn out that it is just impossible to create enough of this special matter in the vicinity of a wormhole to keep it open. This is a question that one could hope to answer without needing a full theory of quantum gravity, because it depends only on the shape of the space-time and certain properties of quantum fields within that space-time. However, the task of answering this question is so ridiculously difficult mathematically that nobody has yet been able to do it. So the door is still open to the possibility of time-travelling humans, at least in theory.
To my mind, though, the biggest reason is not theoretical but practical: how the heck do you create a wormhole? We can’t even create a black hole of any decent size (if any had shown up at the LHC they would have been microscopic and very short-lived). So how can we hope to be able to manipulate the vast amounts of matter and energy required to bend space-time into a loop (and a stable loop no less), without annihilating ourselves in the process? Even if we were lucky to find a big enough, ready-made wormhole somewhere out in space, it will almost certainly be so far away as to make it nearly impossible to get there, due to sheer demands on technology. It’s a bit like asking, could humans ever build a friendly hotel in the centre of the sun? Well, it might be technically possible, but there is no way it would ever happen; even if we could raise humungous venture capital for the Centre-of-the-Sun Hotel, it would just be too damn hard.
The good news is that it might be more feasible to create a cute, miniature wormhole that only exists for a short time. This would require much smaller energies that might not destroy us in the process, and might be easier to manipulate and control (assuming quantum gravity allows it at all). So, while there is as yet no damning proof that time-travel is impossible, I still suspect that the best we can ever hope to do is to be able to send an electron back in time by a very short amount, probably not more than one millisecond — which would be exciting for science nerds, but perhaps not the headline that the newspapers would have wanted.
 Fun fact: while working on the movie “Contact”, Carl Sagan consulted Kip Thorne about the physics of time-travel.
 For the nerds out there, you need matter that violates the averaged null energy condition (ANEC). You can look up what this means in any textbook on General Relativity — for example this one.