I'm also very confused....even theoretically...about what would happen if one ran into oneself after physically going back in time. It would seem impossible that there could be two of yourself occupying the same time period. Again, any thoughts on this?
It depends, I suppose, on what you mean by "what would happen?" Psychologically there might be some issues but as far as the strictly physical processes go nothing unusual should occur.
Think about it this way:
Instead of looking at some time traveler who meets himself from afar where you can see two whole human beings, get much closer to the action. Get so close that all you can see are electrons buzzing in their shells around their atomic nuclei. One electron pretty much looks like every other electron as do protons and neutrons. You see an ocean of this stuff floating around. What is it? Its the atoms that make up both bodies and its really no different that an ocean of atoms that make up two other folks' bodies. There's no violation of any physical laws here even though we might define the time traveler and his doppleganger twin as "the same person". You might say hey wait...we just violated conservation of mass/energy laws by transporting a mass from one time to another where it already exists. No problem. We didn't create any new mass/energy and we didn't in effect transport it in time any more than two masses traveling at different velocities move through time at different rates according to Special Relativity.
In any case the twins aren't going to shake hands and mutually annihilate as if one was matter and the other anti-matter.
Furthermore, aside from what we define as self-awareness the two aren't "the same". They existed, originally, at different times. For the most part, because they are living tissue, they probably no longer share much in the way of common atoms. Living tissue grows, dies, sluffs off cells, and grows new cells over time. In short it grows a new body many times over the course of a lifetime because it consumes food and water and turns that matter into new cells every day.
Time travel to the future isn't just a theoretical physics conjecture it's a fact that has been documented in experiment every day for the past century. Within the limits of its domain the Special Theory of Relativity is absolutely correct. If you go very fast relative to something else your clock will run more slowly than the "at rest" object. By "clock" we mean every physical process. Every physical process attached to the fast moving object runs more slowly than the same processes in the at rest frame. We witness this process in particle accelerators every day. For example we know the half-life of partices when they are at rest with the laboratory frame. We know how long they will "live" before underging radioactive decay. If we accelerate those same particles to near the speed of light, as does happen in a particle accelerator, they live longer. How much longer? They live longer precisely as predicted by Special Relativity. You need a boatload of fuel (and a really huge boat at that) but if you build a proper spaceship and accelerate it constantly, even at 1g, for a few years and you'll be going at 90% the speed of light. At that velocity for every year you are away people back home will age 2.3 years. Stay away for ten years and you've traveled 23 years into the future. Not very practicle and the engineering problems are monumental but in theory it is very doable.
Traveling to the past is another cat altogether. There are theories that involve, for the most part, hugely powerful gravitational fields that propose possible methods of time travel to the past. But each of them assume criteria such as totally empty space devoid of any matter or fields except gravitation or exotic matter that either can't exist or are not known to exist. Obviously its a bit difficult to have gravitation but no matter - gravity arises from matter. And to be a time traveler who is going to use that empty space is a bit problematic. The fact that the time traveler and whatever conveyance s/he uses to time travel in are there violates the premise of totally empty space.
We're a long, long way off from solving these issues, even theoretically.
