If one were to extrude the space-time continuum along a fifth dimension, and define existence as the limit at infinity along this dimension, then any time travel would be unstable and would never persist until infinity. Whatever effect a future event had on the past would alter time to prevent the future even from ever taking place (this is along the extruded dimension so that is "possible" to alter time).

Even if the effect is only to displace a few electrons, it will change circumstances ever so slightly. As you proceed along the extruded dimension till infinity, circumstantial changes accumulate until at some point the effect of those changes changes future circumstances enough that the time travel doesn't occur. At that point the discontinuity in space-time collapses.

This thought experiment demonstrates how there could be instabilities in existence. Even if you discount the fifth dimension, the fact remains that the time travel would have to have exactly the effect on the past that produces the circumstances that led to the time travel taking place. If even a small circumstance differs from that that time travel cannot exist. It would be like balancing a perfect ball on the tip of a perfectly sharp needle in a perfect gravitational field, and having it still be there at the end of time. If the ball is 1/googol off center, it'll eventually topple.

So it is possible, though exceedingly unlikely, that time travel could occur. The possibility of a free will in the time loop is almost certain to be enough of a disturbance to prevent the time loop from ever happening.

While I'm on the subject, let me share a pet peeve about portrayal of time travel in movies. For the most part I can't stand time travel in movies. With time travel there's an inherent lack of drama (if at first you don't succeed, you can just go back in time to prevent your own failure). Also, the logical effects of time travel don't lend themselves to escalation or payoff. Moviemakers deal with these difficulties with artificial time travel rules. This allows dramatic tension and explains the effects of time travel, but such rules invariably cause logical inconsistencies.

Logical inconsistencies are not a deal breaker in and of themselves; there's something called suspension of disbelief that moviemakers can expect to a degree from the audience. But when the movie tries to explain these articifial rules, it only creates more and more inconsistencies. The more it tries to exlpain the rules, the more inconsistent it gets, until the story is nothing but a confusing mess, and that pisses me off.

Therefore, here are my rules for creating a time travel movie that doesn't suck:

1. Keep dramatic devices to a minimum.
2. Whenever a plot device is used to create dramatic tension, just use it. Don't explain it; don't talk about; and don't address its logial flaws. Just state the rule and be done with it.
3. Don't explain, talk about, or even acknowledge any issues with time travel that aren't necessary to create drama.

Here are some movies that handled time travel well.

• Back to the Future

  Back to the Future's plot device was that Marty changed history, and if he didn't change it back he'd disappear within the week. Lots of logical loose ends here. Why didn't Marty disappear the instant he bumped into his dad? Why does it take week? Why does Marty go back to the "new" future? What happened to the Marty from the new future? Does Marty have memories of things that happened to the new Marty? If he doesn't, maybe he slowly acquires them over a week? Does he also lose memories of the old future over the week? Etc. Etc. Etc.

  The movie handles all these questions and logical loose ends perfectly: by ignoring them.

• The Terminator

  Another delightfully straightforward plot. The movie created dramatic tension by ignoring the fact that Kyle's presense meant that Sarah Connor must have survived (otherwise who would have given him the picture so that he would volunteer to go back?). It also ignored the issue of what the robots expected to happen if the Terminator should succeed. Does history instantly change the moment they send it back, and if it doesn't change it must have meant they failed?

  These questions simply weren't addressed, and it was the better for it.

• Bill and Ted's Excellent Adventure

  There was a pretty bad plot device ("the clock in San Dimas is always running": Bill and Ted weren't able for some reason to travel back in time to do their history report). That was actually too much tension; later in the movie they got around this rule by planning to go back in time after their report to hide things they'd need.

  But that's it: it was kept to a minimum. Bill and Ted never wondered why they had to deliver their report at a certain time according to their own watches (assuming Ted had managed to remember to wind it), or anything else like that.

  Furthermore, no attention was paid to the effect on history. Drama over whether Napoleon got back to France wasn't necessary; there was already enough of a story with their history report. So the movie wisely disregarded it altogether.

And now for some movies that didn't do it well.

• Back to the Future 2 and 3

  These movies addressed (at some point) all those artificial rules the first movie ignored. And the result was, well, Back to the Future 2 and 3.

• Terminator 2 and 3

  These movies addressed (at some point) all those artificial rules the first movie ignored.

  T2 was all right since it was a well done movie in many other ways. It must still be given credit for not raising the issue of where the technology came from. But things got out of hand enough to annoy me.

  T3 it got way out of hand, and it was a big reason why it sucked so bad, but I suspect it would have sucked even without all that time travel loonieness.