Before answering your question, we need to define "time travel". Do you consider it "warping" out of your time and into another time, or in anyone getting to a time that would normally be beyond your lifespan? I can't say I have ever heard of method one, I doubt it has anything to do with relativity. Method two is only time travel depending on which definition you choose. If you consider time travel the second definition, then yes going to "sleep" would technically be considered this. Here's an exerpt from a previous post of mine explaining the theory of relativity's way of dealing with time travel:
According to Einstein's theory of Special Relativity, as you increase your speed relative to another observer, that observer will note time as passing more slowly for you than for them. There is an extremely good article at
http://science.howstuffworks.com/relativity.htm that explains why this happens and does so in very easy to understand, non mathematical terms, if you would like to know more about it. Once you accept time dilation as it's called (which actually refers to what the moving observer sees), then you can see how it can be used to "travel" to the future. If you were to blast off in a spaceship and accelerate to 0.9999999999999 the speed of light, for every 1 second that passes for you, about 2236068 seconds would pass for everyone back on Earth (to anyone who knows how to use the Lorentz equations, yes I did calculate this, I left the math out for simplicity's sake). If you maintained this speed for 24 hours, over 6,000 years would pass back on earth. You could then return to Earth having hardly aged but millenia after you left, effectively "travelling" to the future. Unfortunately, reaching such fantastic speeds is no easy task. Another relativistic effect is that as you increase your mass, more and more energy is required to accelerate. This number becomes infinite at the speed of light (the Universe imposes many contraints making accelerating to the speed of light impossible). Particles in atom smashers are accelerated to speeds comparative to the one I mentioned, but accelerated a spaceship to that speed would be quite a feat indeed. Still, it's possible. Time travel to the past is a different matter. It's not simply a matter of traveling faster than light (not only is this impossible, but plugging such a value into Einstein's equation yield's an imaginary number, as opposed to the negative number that would suggest time reversal). There are possibilities though. There are objects called cosmic strings, their existence is purely theoretical but if they do exist they are highly concentrated strings of energy, remnants of the Big Bang, that are thinner than a nucleus of an atom but several million kilometres long. Two of these strings circling each other would warp spacetime (now we're dealing with Einstein's Theory of General Relativity) so significantly, that spaceship flying around them could theoretically arrive back at it's starting point before it even left! Again, the existence of these strings is purely mathematical. Still, it is possible. Special relativity says that events that are simultaneous in one reference frame aren't necessarily simultaneous in another (see the article I mentioned). That means one observer could see an event happen and it's in their past, while it has yet to happen for another observer, it's in their future. This suggests that what we call the past and future are forever frozen in spacetime and the present is just our fleeting impression of the Universe as it is as we hurdle through time. If that's the case, the past and future are always there, always part of the Universe, and it's only accessing them that's the question. Perhaps the methods I suggested are the ways of going about this.
It's important to note that the purpose of relativity (special and general) is not time travel, the "ability" to do so only comes from basic fact that time is relative. "Time travel" to the future is insanely more easy than travel to the fast. In fact, relativistic future time travel happens all the time, as particles that are traveling at extremely high speeds, come to rest in our frame of reference, thereby "jumping" to the future.
Omin said:
And, if 2 is somewhat accurate, it seems to contradict high speeds creating time travel, because in this analogy, when I sleep I travel through time, because I've slowed down while everything went by me.
Another important thing to note is that you are ALWAYS traveling through time. Trees grow, particles decay, people die...in the sleep case, nothing related to relativity is happening, as relativity's method of time travel involves changing your velocity through time. In this example, your velocity through time doesn't change, you really only increase your lifespan. So, "time travel" is really a misnomer, since we're always time travelling.
The whole concept can be pretty complicated, but I hope that helps.
