Stephen Hawking's chronological protection conjecture holds that the laws of physics disallow time machines. However, lets think for a moment before jumping to a hasty conclusion.
There have been some toy experiments in which, at just the moment that the time machine is actuated, the universe conspires to blow it up, which has led Hawking and others to conclude that nature will contrive it so that time travel never in fact occurs. But NO ONE actually knows that this is the case, and it cannot be known until we have a FULL theory of quantum gravity, which we do not seem to be on the verge of yet.
One of Hawking's arguments in the conjecture is that we are not awash in thousands of time travelers from the future, and therefore time travel is impossible. This argument I find very dubious, and it reminds me very much of the argument that there cannot be intelligences elsewhere in space, because otherwise the Earth would be awash in aliens. I can think half a dozen ways in which we could not be awash in time travelers, and still time travel is possible.
First of all, it might be that you can build a time machine to go into the future, but not into the past, and we don't know about it because we haven't yet invented that time machine. Secondly, it might be that time travel into the past is possible, but they haven't gotten to our time yet, they're very far in the future and the further back in time you go, the more expensive it is. Thirdly, maybe backward time travel is possible, but only up to the moment that time travel is invented. We haven't invented it yet, so they can't come to us. They can come to as far back as whatever it would be, say A.D. 2300, but not further back in time.
Then there's the possibility that they're here alright, but we don't see them. They have perfect invisibility cloaks or something. If they have such highly developed technology, then why not? Then there's the possibility that they're here and we do see them, but we call them something else—UFOs or ghosts or hobgoblins or fairies or something like that. Finally, there's the possibility that time travel is perfectly possible, but it requires a great advance in our technology, and human civilization will destroy itself before time travelers invent it.
I'm sure there are other possibilities as well, but if you just think of that range of possibilities, I don't think the fact that we're not obviously being visited by time travelers shows that time travel is impossible.
A profound consequence of Einstein's special theory of relativity is that no material object can travel as fast as light. It is forbidden. There is a commandment: Thou shalt not travel at the speed of light, and there's nothing we can do to travel that fast.
The reason this is connected with time travel is because another consequence of special relativity is that time, as measured by the speeding space traveler, slows down compared to time as measured by a friend left home on Earth. This is sometimes described as the "twin paradox": two identical twins, one of whom goes off on a voyage close to the speed of light, and the other one stays home. When the space-traveling twin returns home, he or she has aged only a little, while the twin who has remained at home has aged at the regular pace. So we have two identical twins who may be decades apart in age. Or maybe the traveling twin returns in the far future, if you go close enough to the speed of light, and everybody he knows, everybody he ever heard of has died, and it's a very different civilization.
It's an intriguing idea, and it underscores the fact that time travel into the indefinite future is consistent with the laws of nature. It's only travel backwards in time that is the source of the debate and the tingling sensations that physicists and science-fiction readers delight in.
I don't know that my answer to what I hope was a somewhat sincere question has brought time travel a step closer. But maybe the joint effort of all those involved in this debate has at least increased the respectability of serious consideration of the possibility of time travel. As a youngster who was fascinated by the possibility of time travel in the science-fiction novels of H.G. Wells, Robert Heinlein, and others, to be in any way involved in the possible actualization of time travel is very exciting. Of course we're not really at that stage; we don't know that time travel is even possible, and if it is, we certainly haven't developed the time machine. But it's a stunning fact that we have now reached a stage in our understanding of nature where this is even a bare possibility...