Time for Speculation
Time travel is a favorite trope of science fiction going back to at least A Connecticut Yankee in King Arthur's Court and The Time Machine. It took until the mid-40s for someone to come up with the grandfather paradox, which has been pretty well beaten to death in the years since. (How many times has Star Trek alone used it?)
So I started thinking about time and time travel, primarily to see if I could find a theory that would result in new ideas for a time-travel story. While story ideas were not forthcoming, I did come up with a reasonably interesting idea.
Since Einstein and Minkowski, we've become used to thinking of time as the fourth dimension. In normal life, we think about locations basically in terms of three numbers: x, y, z, latitude, longitude, and elevation, Fifth and Broadway on the 14th floor, whatever. But if we want to meet someone at Fifth and broadway on the 14th floor, we have to also tell them what time we're going to meet, say 1:00 PM. Einstein's general relativity showed that we have to think about time in general as a fourth dimension for everything, not just dates with the brunette you met on the subway, so we always need x,y,z,t.
Now, imagine we could step back from the universe and look at the whole thing, all at once. Then what we think of as our history becomes a path through the whole four-dimensional universe: Fourth and Broadway on the street at 12:54 PM, Fifth and Broadway on the street at 12:56, in the elevator at 12:58, at the new friends office at 1:00 PM. Physicists call this a world line.
Now, you can also imagine that small changes lead to slightly different world lines: the elevator makes a few extra stops and you're a minute late, or you took a taxi and you're a few minutes early but you took a different path. Since we've stepped back, with Godlike omniscience we see not only everything that is actually on your world line, but every possible world line -- so both of those along with all possible other choices are part of the whole picture, along with every other possible arrangement of the pieces: you took the subway, you walked, a taxi brought you down Broadway from uptown (to the sound of honking and shouting, I think Broadway is one way the other direction). In fact, our omniscient view even includes arrangements that aren't possible, like the one where you simply levitated, or just disappeared one instant and re-appeared the next, teleporting where you wanted to go.