I go back to last week with my brand new time machine and shoot myself in the head.

Since I'm dead, I obviously can't travel back in time a week after my death. But if I DON'T travel back in time, there's no way that I could shoot myself, so then I don't die, so I can go back in time and shoot myself...

If I were to pull a stunt like that, I could very easily destroy the universe, at least according to Doc Brown.

This type of time paradox is usually resolved through a method of branches in time.

This line of thinking holds that just as every possibility creates a branching in reality (slow down at the yellow light, or speed up?), so a time-travel caused breakage would also cause two different paths, though one might, in a subtle way, end/loop a bit further up the line.

Thus one branch where the person lives, but travels back in time, and the other branch, where the person died a week ago...

Traveling into the future is a one way trip.. once you're there, there's no way back. Everything travels into the future, but at the same speed relative to all other objects in the universe.

Once you accelerate the speed at which you travel into the future, you go forward in time (it takes you less time to get where other objects are in the future). To the outside observer you appear to move slower and slower multiplied by the acceleration you're experiencing.

You can slow down to the normal speed, and even slower which would cause you to travel slower into the future than all other objects in the universe. To the outside observer you appear to move slower too, the same as with traveling into the future.

The concept of a 4th dimension seems incorrect, since every dimension can travel in 2 ways, back an forth. (3D = up and down, left and right, forward and backwards) Time could be classed as the 3.5th dimension, since you cannot travel backwards in time.

This rules out any strange paradoxes which might destroy the entire universe (as described by Doc Brown in Back to the future (which is a flawed term in itself.. once the future has happened, one cannot go back).

A time machine is something which can manipulate the speed at which time is progressing. Maybe we can achieve effects like this by generating massive gravitational fields which are stronger than the normal gravitational fields found around black holes.

Morgon77: The many-worlds hypothesis doesn't actually resolve this issue. The world in which the time-traveler shoots himself is still the same world in which the time-traveler exists, and hence can't have shot himself.

The essential problem is actually that of the cause and effect model of reality. This model holds that: (a) no event is without a cause and (b) no effect can cause its own cause (which is really just another way of stating (a)). The time-travel paradox can be resolved by supposing that, at the moment time-travel is developed, the universe bifurcates into one set of universes where time travel exists, one set where it doesn't, and in the set with time travel, there can be effects without causes; for instance, a time traveler can go back in time, kill himself, but continue to exist. He comes into existence at the moment of his appearance, his future self no longer exists.

Of course, in a universe where time travel is possible, all sorts of other laws of physics would have to go, such as conservation of mass; by traveling forward and backward in time, mass (such as gold bars) can be multiplied.