Originally answered on Quora:
If you traveled in a spaceship at the speed of light and looked out a window, what would you see?
Oooh…. I love relativity! This'll be fun.
Okay, so we've got a magical spaceship that can go at the speed of light. Cool. We climb in, wave goodbye to the friends and family we will probably never see again, and take off. To be nice to Earth, we'll keep it fairly slow until we get a good distance away.
You're flying through space and you decide to kick it up to light speed. What happens?
Well, with relativity you have two basic effects: time contraction and length contraction.
Basically, as you go closer to light speed, your personal “clock” “ticks” slower than a “normal” clock. So if you synchronized watches with someone on Earth, flew around at .5 c (that's half of light speed) for a while, then came back, your watches would show different times. Or maybe they would show the same time but he has a beard and you still have only peach fuzz. Either way, much more time has passed for Earth than it has for you.
The other effect is one that causes distances to distort. As in literally distort, not an optical illusion. A board that is two feet long in my hand will be - not look, but be - one foot long to someone going .5 c (the exact length of the board might be off, but it will be shorter).
For most people, this is hard enough to take in, even without going into the other stuff that makes all of that possible. But let's get to the really fun part: you kick it up to 1 c. Exactly light speed.
Honestly, you're probably just energy at this point. Not a human, not a space ship. Just pure energy. Probably light in some form. Photons, maybe. Not sure about that. But some kind of energy.
Let's break physics even more, though, and say that you are still very much human and alive. What do you see?
Ignoring the problems that come with moving as fast as the light particle that's supposed to enter your eye… Everything is happening all at once. Imagine the history and future of the universe on VHS (if anyone remembers those…) and you hit fast forward. A lot. Infinitely, actually. You would experience the death of the universe instantly after hitting light speed. That's how fast time moves outside you.
To an outside observer who is not going relativistic speeds but can still somehow see you, you aren't moving. At all. Not moving, no aging. Not even breathing. Your time has slowed down so much from their point of view that you may as well be frozen… As you hurtle through space at light speed. Right.
That's just the time contraction portion. Add in the length contraction now too. From your perspective, the universe has gone two-dimensional. If we call the x-direction the one in which you are traveling, the x-width of the universe is…. Zero. The whole universe. Weird…
Go back to that outside perspective. Now you'd expect that your ship appears to be infinitely long, right? Wrong. See when two things are moving at relativistic speeds relative to each other, it does not matter which one is the one going really fast. To you in this scenario, Earth may as well be moving really fast away from you and you not moving at all.
So this length contraction goes both ways. The universe is the “other” from your perspective, so it shrinks to nothing. To Earth, you are the “other”, so you shrink. That is, you compress to a two-dimensional disc that was (and is) your space ship.
So what do you see? A whole lot of nothing. But it looks pretty dang cool.
This answer has been modified slightly for clarity and to fix grammatical errors