Some thoughts that have nothing to do with actual time travel (whatever that is) and everything to do with what players actually want to see with time travel. We're emphasizing gaming here, not the actual consequences of the fact that fundamental equations don't have a time component.
In part, this is sparked by a Mutants & Masterminds session I ran where the players just expected to end up in the past. I wasn't actually planning a time travel session, but clearly that's what they expected from the setup. So we went through time, with me vamping and trying to make sure that they caused the things they suspected they would cause. (They helped, because they suspected they would cause it.)
One of the characters, immersed in the whole superhero-supervillain subculture since birth said, effectively, "You have to go back to WWII. It's on your superhero bucket list. You won't feel like you really made it until you do."
So when you're devising your time travel scenario:
- You can change the past. Maybe not a huge amount, but you can do it.
- You can't change the big things. You still want a recognizable future to go back to.
- You want consequences. Maybe you can't kill Hitler or stop 9/11, but you can erase yourself or the person you love.
- You want to interact with yourself. If you were alive in the time period (because some characters are immortal or long-lived), you want to be there.
- You want to interact with the people you've heard about. Going into the past and being Joe Schmoe isn't nearly as interesting as discovering that you have to convince the first Golden Warrior to give up his Ring of Ares so that the third Golden Warrior can take it from a Soviet spy in 1956, and the person who's going to help you is your great grandmother, who thinks you're kind of hot.
From your point of view, you want time travel to have limitations or your life will be awful:
- You can't blip fifteen seconds into the past to change the outcome of the fight you just had.
- Time travel is not so easy that they can readjust their arrival time every time they fail.
- They can't stay in the past (unless you want someone to replace his grandfather).