No, you are not wrong. But time dilation is a strange phenomenon. Einstein postulated that when two bodies move relatively to each other, both will observe that the other's clock slow down. If you travel to Alpha Centauri and back at the speed of light, while I stay on Earth, you might get back after my death while you yourself will only have aged a few years.
But remember that this is all theory...nothing material will ever reach the speed of light, because the energy needed to accelerate an object to that speed will crush the object and turn it into energy at an ever increasing rate. (This is an over-over-simplification). A starship will most likely never be able to reach a speed of 99% of the light speed.
I suggets you read the book "E=mc2, The Biography of an Equation", by David Bodanis. Or better yet, read "Relativity" by Albert Einstein. It's not that hard. Well, it is. But not. Get it?
This is also coverd in depth by Carl Sagan, Stephen Hawking, and many other cosmology writers. In "How to build a time machine" Paul Davies does a good job explaining the Time Dilation effect. It's full of paradoxes but it makes sense in some strange way.
Which I probably don't, sorry about that.
Tormod
