No, 600 million years after the Big Bang, the (observable) universe was 600 million light years across, just like you'd expect.

What you have to realize is that after the Big Bang, space itself expanded, and continues to expand. Light travels through space at the speed of light, but the space between us and this object has been expanding at almost the speed of light. It's like trying to catch up to the leader in a race. If you're just a little faster than the leader, it can take a long time to catch him. In this case, 13 billion years.

The reason that light can't escape from a black hole is that the massive gravity of the black hole sucks in space faster than the speed of light. Light, traveling through space at only the speed of light, just gets sucked in slower. It's like trying to paddle a canoe up Niagara Falls.

In relativity, nothing can travel faster than light. But space, in this definition, is not a thing: it's nothing. It can expand or contract faster than light.

Well, now, except for that whole inflation thing. Which, as I understand it (as a toddler understands a turbine), was when the universe blew out all to hell in fractions of a second.

Regardless, it all makes my head as'plode

Bob - dammit. I came in to work all geared up (well, as geared up as one can get on a normal Friday after a weekend of traveling) to get things done and then I read your post. My head now hurts from attempting to contemplate what you've written.

I'll have my boss send you an invoice for the lost productivity.

Not entirely true. Matter and energy cannot travel faster than light, it's true, as it would take an infinite amount of energy to accelerate either to that point. But the edge of a wave propogation has been modeled (and experimentally confirmed) to be able to move faster than the speed of light, in certain space-time conditions.

It's kind of like the question of a frictionless tube stuffed with identical snooker balls, long enough to wrap around the world three or four times. You stick another snooker ball in one end, and a snooker ball pops out the other instantly... apparently faster than light itself can move. No, the snooker ball didn't actually move faster than the speed of light, but the wave propogation through the unique material (a frictionless tube full of identical snooker balls) did.

This way, information can in fact move faster than light, even though light itself cannot. They've actually done something similar with supercooled and photon-charged composites (replace "frictionless tube" with "superconductor," and "snooker balls" with "photons").