RE: Some notes about time travel
You do realize that if you traveled back in time about 10 seconds you'd be floating in the void of space, right? Everything is moving. How do you determine what spatial reference frame you're in? Are you stationary with respect to the center of the galaxy? The sun is moving. The earth is moving. You wind up in interstellar space. Fix yourself to the sun? The earth is moving, you wind up in interplanetary space. Fix yourself to the center of the earth? Do it right and you won't accidentally kill yourself when you wind up in the past, although if you weren't careful and you time traveled in a low-lying region you might teleport yourself into the center of a mountain, or underneath an ocean, which would mean instant death.
There's no guarantee that you could even fix your position with respect to the galaxy, or any other structure in the universe. If you try to time travel within the universe, assuming the universe has a center, you might wind up being fixed to that. If that's the case, anyone who has ever attempted to travel from the future to the past died slowly in the intergalactic voids. That's a much better explanation of why there's no time travelers.
Or perhaps to be perfectly clear, there are time travelers. You're one. I'm one. And we're both moving into the future at a speed of one second per second.
Yes, that is the first thing written in my notes that are pictured at the end of the post: "or perhaps going back in time requires remaining at the same point in space (so you'd probably end up in outer space)..."
However, that is a supposition that doesn't necessarily have mathematical or physical basis, I came to realize.
It's possible that time travel would transport you through only time and not space, yes. However, it seems to be more likely that it would transport you through spacetime. In a closed timelike curve, for example, you could go as far back as to when and where the time machine was created. I should've mentioned that in the post. Your travel would be restricted to the location of the time machine.
At least that would be the case with a CTC, which looks to be the most likely future form of time travel.
Excellent point, though!