I was reading up the other day on Einstein's theory of relativity (which, as you know, has been tested) - particularly time travel paradoxes. A little background on the original experiment:

Quote:

In 1975, Professor Carrol Alley tested Einstein's theory using two synchronised atomic clocks. Carol loaded one clock onto a plane, which was flown for several hours, while the other clock remained on the ground. At the end of its flight, the clock on the plane was slightly behind the one on the ground. Time had actually slowed down for the clock on the plane. It had travelled forward in time.



Picture this: A person is in a train without any walls. Another person is standing outside the train. There is a flashlight on the floor of the train facing the ceiling. The train drives by the person standing outside the train. Hypothetically speaking, the person not on the train sees the light move dialognally (assuming the train was going VERY fast), while the person inside the train, relative to the motion of the train, ONLY sees the light move straight up. Thus, the person on the ouside, sees the light moving a further distance in the same amount of time as the person on the inside of the train (picture a right triangle). Now, keep in mind, light CANNOT be accelerated, the speed of light is a constant. So, how is it possible that the light moves a greater velocity in the same amount of time? This is because time slows down for the person inside the train. Freaky concept?

From the Pythagorean Theorem, the equation can be derived:

T = t1 / sqrt( 1 - ( ( x * c^2) / c^2 ) )

Where T = time of the object at rest, t1 = time of the moving object, c = the speed of light, and x = a variable to gauge how close the velocity is to the speed of light. (Note that the c^2's cancel out).

Now, say the train is going 99% the speed of light, thus x is .99. Time for the person on the train, t1, is 1 year. Plug it in. You'll find that time itself on Earth has passed by 7 years. Weird, eh? Now, try .999 - 20 years. .9999 - 70 years.

Now, even creepier - say you are going the speed of light. Plug it into the equation: sqrt(1-1) = 0. 1 / 0 = undefined. Undefined = infinity. The universe has literally ended, an infinite amout of time has past - time becomes irrelevent to you.

Continuing, what would happen if you go beyond the speed of light? While this appears to a barrier in our universe, if you CAN go beyond it, the opposite would happen - time would slow down to a reverse.

Lastly: The paradox. Imagine I discover a way to go beyond the speed of light, and I travel back in time. The year is 1970. My father in a senior in high school. I walk up to him, pull out a shotgun, and shoot him dead. Poof - I disappear, as my father was never allive to meet my mother, and thus I cease to ever have existed. But wait: If I havn't existed - then who could have shot my dad? Which means he'd still be allive, which means I'd be born, which means I'd go back in time and shoot him, which means I'd never have existed! Freaky? I think so.

That's all I have. Correct me if I'm made any mistakes, and please share any other paradoxes

--Eric