But the discussion has led scientists to divide into the two popular theories related to time travel which we have here found to be insufficient: the fixed time theory and the parallel dimension theory. Each camp has adduced what it incorrectly sees as "scientific proof" of its position, and I would like to address those "proofs" as well as the theories they support. But first I thought I'd take a moment to summarize the basic theory.
Blame it on Carl Sagan; everyone else does. When he was writing his book Contact, he needed a scientific theory which would carry his explorer across the universe and back again rapidly. The idea of flying into a black hole and out a "white hole" somewhere else in the universe was immediately rejected by his friends in the scientific community, but they did remember that Einstein's Theory of Relativity also predicted the possibility of "wormholes" which connected two points in space by a straight line through another, shorter, dimension. Thus Sagan had his solution, and scientific attention was directed toward the wormhole question for the first time.
Leading theoreticians in this field began to realize that the wormhole theory had some peculiar aspects. For one thing, it was possible for the ends of a wormhole to move, so that the same wormhole connected to new places. Second--and this is the tricky part--if you could move one end of the wormhole at a velocity approaching the speed of light, time for it would slow down, and since less time would pass for it than for the other end, it would be in the past relative to that other end: a traveler entering the stationary end would travel backwards in time, while one entering the end which moved would travel into the future. It was further determined that if one could collect strange matter in a planetary quantity (which has only been collected in atomic quantities at present), one could use that to create and move a wormhole.
If you understand the theory, you will immediately perceive (as is admitted by those who developed it) that it could not carry you into a past before the machine was created. The wormhole is created at time A, and one end is moved. But when that end has reached its resting place, it will be in the past relative to the fixed end, but in the future relative to time A. Still, it is genuine time travel.
That is the primary thesis; and while Hawking and his friends will not commit either way at this point, it is the most promising shot at time travel yet proposed.
Which brings us to the second phase of the discussion: what happens when you time travel?
Scientists, being expert at simplifying a question, have reduced the famed Grandfather Paradox to a problem involving billiard balls. In that form, the question is quite simple. Let us suppose that a ball travels in a straight line into a pocket which is actually the entrance to a wormhole with a temporal displacement. It then comes out the other end of the same wormhole, now in the past, and proceeds to collide with itself, knocking itself off its original trajectory such that it will not enter the wormhole. But obviously if it does not enter the wormhole, it will not exit the wormhole, and so will not interfere with its own path. The problem of the man who kills his own grandfather is reduced to its simplest terms.
Scientists working with this model have demonstrated that it is always possible to create a model in which the billiard ball coming out of the pocket in the past will in colliding with itself knock itself into the entry. They have further asserted that since such a solution always exists, it must be that this will always happen, for "nature" will not permit an uncaused result. Thus having demonstrated that it could happen, they assert that it must.
There are several logical fallacies here, but the most glaring one is the confusion of the possible with the necessary. One could as easily extrapolate that because the billiard ball entered the wormhole in the original timeline, when it exits the wormhole it will never collide with itself. This is as valid an assumption as the other, and any ninny can devise a thousand models in which the collision doesn't happen for every one in which it does. More to the point--and a problem I have with the fixed timeline theory generally--is that it begs the question of how this occurred in the first place. Basic Newtonian Mechanics will tell us that if the collision is necessary to drive the billiard ball into the wormhole, then if the collision does not occur there is no way that the ball will ever enter the wormhole. That is, if we have one entrance to the wormhole and one exit, and we adduce a model in which the ball coming out of the exit will collide with itself such that it will drive itself into the entrance, then we know intrinsically that if the collision does not happen, the billiard ball will never enter the wormhole initially, and so won't exit in the past. Occam's razor should alert us immediately that the solution to this problem is the billiard ball never enters the wormhole at all, because there is nothing to drive it that way. No, the fixed timeline theory fails because it is easier to suppose that time travel will not occur than to suppose that having occurred in the future it will cause itself in the past. If it must have happened in order to happen, it is easier to suppose that it never happened.
Grandfather paradox aside, let me make this clear: if the billiard ball is rolling toward the wormhole in the first place, but it collides with itself coming out of the wormhole, it will be deflected such that it will never enter the wormhole; but if it is not bound for the wormhole initially, there is no reason for us to assume that it will come out of the wormhole and deflect itself into it. The only thing that can be said is that a billiard ball coming out of a wormhole will not collide with itself under any scenario, and that patently requires an intervention of a divine level.
But at least the fixed timeline theory recognizes the vital premise that you cannot have uncaused effects in the universe. The competing theory, the Parallel Dimension theory, suggests that causes in one universe have effects in another.
The proof of the parallel dimension theory is much in doubt. The basic science involves unusual results in photon experiments. Single photons fired through a complex filter arrangement behave as if they are encountering interference from other photons theoretically not present. No one has a solid explanation for this phenomenon. However, it has been suggested that these photons are encountering interference from photons in a dimension so closely parallel to our own that the photons are in a sense existing in the same space. This, they say, proves the existence of parallel dimensions, and thus also proves that if you traveled back in time you would arrive in such a parallel dimension.
The science itself is weak. There may be other explanations for the behavior of the photons, and the theory as proposed is difficult to prove. Such a theory should predict other results which could be discovered experimentally, but thus far no such results have been suggested. The best that can be said is that we don't know why photons behave the way they do in these circumstances, but it is possible that there might be interference from another dimension. That's a far cry from proving those other dimensions exist, and it is as likely that we will find another theory which explains this, and those allegedly proven dimensions will vanish like the ether through which light waves once, by all scientific accounts, traveled.
But even if it is so that other dimensions exist, that fact alone does not prove that they are in any way connected to time travel, or indeed that there is any way to reach them at all. One could as easily argue that having proved that there are other planets in the solar system, we have proved that people live on them. All such proof of other dimensions gives us is the possibility that we might be able to travel to such dimensions, and the related possibility that we might be able to travel to the past or future of such dimensions--none of which is clearly indicated by the present theory.
In fact, the Parallel Dimension theory would seem to fly in the face of the Einsteinian Relativity which supports our basic time travel theory. If you will recall, our thesis is that the two ends of our wormhole travel at different velocities through the galaxy, such that time is different for them. We've already demonstrated that a jet plane circling the earth at high velocity will experience slight time dilation (as measured on atomic clocks), yet the plane still lands at Kennedy airport on the same earth, as far as we can tell. With the wormholes, we're trying to increase the degree of time dilation by increasing the velocity and distance traveled by one side relative to the other. At what point does either end of this wormhole pass out of our dimension into another? If it isn't happening to our friends and family on the Concorde, why should it happen to the ends of the wormhole? And if both ends of the wormhole are still in our dimension, so are those who travel through it, even if they are temporally displaced in the process.
This would seem fatal to the Parallel Dimension theory at large. If the best chance for time travel involves this time dilation wormhole model, clearly a time travel theory must be developed to deal with travelers who move into their own past. The Parallel Dimension theory does not answer that at all, and while it may be very interesting in terms of imagined science fiction approaches to time travel, it is not adequate for the current wormhole theory.
On the pages of this site I have outlined and illustrated a theory originally expressed in an appendix to Multiverser:  The Game. Despite this somewhat inauspicious beginning, I've come to realize that it is a unique approach to time travel problems which solves many of the issues raised by science fiction writers over the past century. It is not without problems itself, as the correspondence on the site suggests. But it maintains causality within a single universe, permits free will, and provides consequences for changes in the past caused by events in the future. I invite you to read more. The site has been cleaned up recently, and you'll find a wealth of information about how this theory works in solving the problems of time travel covered in many science fiction films.