Basic Information
The Chronology Protection Conjecture by Stephen Hawking pretty much says Time Travel can't happen. Or at least, it can't happen for anything larger than the sub-microscopic.
In his original paper, Hawking humorously compares the coincidence of mathematics that would seem to prevent Time Travel with an organization not unlike fictional Time Police:
It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the universe safe for historians.
Relativity allows for Closed Timelike Curves, but some models suggest that the infinite energy density of such a curve would destroy a time machine the instant it was created. The Chronology Protection Conjecture assaults some spacetime time machine models, such as the Tipler Cylinder.
This conjecture is at odds with other concepts in time travel physics, such as the Novikov Self-Consistency Principle, and Parallel Universe concepts. All three schools of thought, however, do agree that Temporal Paradox is extremely unlikely to ever occur. One possibility is that a wormhole or other spacetime distortion might function just fine until you attempt to use it in a way that would violate causality - then it would collapse before any paradox could happen.
Unless someone finds a working theory of Quantum Gravity, we can't even begin to test the CPC, that's why the CPC itself is a conjecture, not a theory.
One particularly good piece of evidence supporting the CPC is the lack of noticable Time Tourists. In this day and age when populations are closely accounted for, and big brother is everywhere, we see surprisingly little evidence that people are coming back in time to experience historic events as they happen. If one were to believe that time travel were to ever become popular or accessible, our history and current day would be over run with time travelers. Since we've had no such temporal mobbing or Collapse of Causality, we must assume that either time travel is impossible, or time travel is tightly controlled. Occam's Razor suggests time travel is impossible, as that's more likely than a complicated scenario involving infallible Time Police. However, its notable that at least one other option exists. It's possible that time machines will be built one day, but can only send you forward in time, or can only send you back in time no earlier than the date of the machine's creation. If either were the case, since no time machines have been built yet, we wouldn't have time tourists yet.
Sources
Game and Story Use
- The Scully will probably be quite aware of Hawking's CPC, and use it to shoot down any notions of a Time Machine or Portal To The Past. Doesn't mean the skeptics (or Hawking) have to be correct.
- In a game where the Time Police have a sense of humor, there might be an actual CPA, or Chronological Protection Agency, who took their name from Hawking's paper. Such an agency, rather than just fixing temporal paradox and solving time crimes, would actively strive to prevent anyone (other than themselves) from ever achieving Time Travel. They might even resort to sabotage.
- One way to keep the PC Mad Scientist from mucking up causality might be to have his time machine melt down the instant it's turned on. That's a little heavy-handed, though, and might not sit well with your players.