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I know you're thinking I'm going to bring up the parallel time-line issue, if I went back in time that in order for time to compensate for my tampering ways that there would need to be a new time-line created at the point of my entry, leaving us with 2 time-lines, one in which I never traveled back and one in which I did. You're wrong! You may be jumping to the next logical issue, if I traveled forward in time is there another parallel time-line issue? Wrong again! You may even be saying that quantum physics accounts for all these issues or that the recent discovery shows that we can change the past, to which I say no and no, but if you'd shut up and let me speak we may get on with today's order of business.
My real issue with time travel is that when generally thought about we consider moving forward and backwards in time, instantaneously via such methods as "Back to the Future", but perhaps I missed it, but I don't recall anyone addressing that you're not only challenged by traveling through space-time, but also space-space, because the Earth moves, so if you stood somewhere and traveled back a day you'd likely end up in the middle of space or inside the Earth. So time travel is a beyotch not only because (well, because it's impossible) you're moving back into the past but also because you need to be able to teleport to the exact location, syncing that up is on some kind of "Rain Man" multiplied by Will Hunting type insane. We'll definitely have our flying jet-packs first.
I will say that I haven't read H.G. Wells' "Time Machine", but I did see the (awful) movie and he may have circumvented this issue because his machine was not a vanishing thing, but rather a stable thing that stayed still while advancing (or retreating) through time, observing all things happening around it, thereby allowing it to stay in the sphere of the Earth and its gravity, acting as more of a "fast forward"/"rewind" rather than "skip to next chapter". I guess you could say he was ahead of his-- (bad pun truncated by smarter future-me).