Relativity

So, it turns out that time dilation due to velocity is not (!) quite the same as that due to acceleration.

First - due to Velocity: From the great Wiki:

Time dilation is symmetric between two inertial observers

One assumes, naturally enough, that if time-passage has slowed for a moving object, the moving object would find the external world to be correspondingly "sped up." But counterintuitively, Einsteinian relativity predicts the opposite, a situation difficult to visualize. This is based on an essential principle of the overall theory: if one object is moving with respect to another (at an unchanging velocity), the other is equally moving with respect to it.

[...]

All that matters is the rate at which observers are moving relative to one another. If A finds that B has undergone a slowdown-in-time during the period of relative motion, it must work out that B will also find that A has a relatively slower "clock." It seems an inconceivable situation: yet the math works out, and actual tests confirm it.

[...]

In the Special Theory of Relativity, the observed clock is found to be ticking slow with respect to the observer's clock. Observer A measures (by all methods of measurement) observer B's clocks to be running slow and, similarly, observer B measures observer A's clocks to be running slow.

It turns out that Time dilation in a non-inertial (accelerating) frame acts differently than that in the inertial case. Here it appears that the mythical "person on a spaceship" would age more slowly than a person in a non-accelerating frame.

Unfortunatly, the equations are kinda long - so if you're into it, visit the link.

One final hard-to-believe fact from the great wiki:

...Indeed, a constant 1 g acceleration would permit humans to travel as far as light has been able to since the big bang (some 13.7 billion light years) in one human lifetime. The space-travellers could return to earth billions of years in the future (provided the Universe hadn't collapsed and our solar system was still around, of course). A scenario based on this idea was presented in the novel Planet of the Apes by Pierre Boulle.

Of course, this is WRONG - 13.7 billion light years is 1.3 x 10^^26 meters, whereas straighforward Newtonian calculations for 100 years of 1 g acceleration would yeild only 4.88 x 10^^19 meters.

-- more later, maybe...