In addition to time dilation, there's also compression of length. Two sides of the same coin, really. The length that a relativistic traveller measures in the direction of his motion is shortened by an amount depending on his speed. This is the Lorentz contraction.
Travelling at 90% of the speed of light (0.9c), the Lorentz contraction is a factor of about 2.3. The distance that we on Earth would measure as 20 light years would only be 20/2.3 = 8.7 light years to the astronaut. If he increases his velocity to 0.99c, the contraction factor is about 7 times, so the astronaut would measure it to be only 2.85 light years. As you go faster, the contraction factor approaches infinity as speed approaches the speed of light. Thus, IF a traveller could travel at the speed of light, the Lorentz contraction would be infinite and, in theory, he would simultaneously occupy all points in the universe.
Nope...ain't going to happen.
Any physicists are welcome to correct me.
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