To make a warp drive you have to arrange spacetime so that you never locally travel faster than light but still arrive at your destination…faster than light. And in 1994 Mexican physicist Miguel Alcubierre figured out how.
Instead of space expanding between two points, Alcubierre asked, what if you arranged it so that space was compressed between two points? What if I look at a distant star or distant galaxy, or wherever my destination is, and instead of imagining the space between us getting bigger and bigger and bigger like it is in an expanding universe, what if I imagine that space getting smaller and smaller and smaller?
Alcubierre was able to construct this kind of spacetime where the distances between you and your destination get shorter by creating a very special kind of wave that travels with the spaceship. So the idea is that you you’re in your spaceship, and you sit inside of a bubble.
In front of the bubble, there’s a wave. You can imagine a wake that’s being pushed in front of the bubble. It’s not actually what’s happening, but it’s a good analogy. And you can imagine the space in front of the ship getting compressed. It’s getting squeezed together.
So if you had a ruler just hanging out in space and then Alcubierre’s ship comes towards you, that ruler is going to get shorter. It’s not a meter anymore. It’s going to be three quarters of a meter or a tenth of a meter. It will literally be shorter because space itself is compressed. That compression of space in front of the bubble pulls the bubble forward.
And behind the bubble space is stretched out, just like it is in an expanding universe. You’re stretching out the space behind you, pushing you along.
But amazingly, inside the bubble it’s flat space. There’s no movement whatsoever. If you were inside that bubble, which we’re going to go ahead and call a warp drive, and you’re sitting in the command chair of your spaceship, you wouldn’t feel anything. You don’t feel acceleration. You don’t feel movement at all.
According to your local observations you’re not moving. But your destination would come closer to you.
The Alcubierre warp drive expands space behind your bubble and compresses space in front of your bubble. It rearranges the geometry of space itself between you and your destination so that you arrive at your destination without even moving. And since no movement means no time dilation, all clocks on board the ship agree with clocks belonging to stationary observers outside the bubble.
This means that this wave-compression-expansion bubble setup can be made as powerful as you like, which means the trip can be as short as you want. It could take a year. It could take a microsecond. It doesn’t matter. Everyone would agree that you could arrive at your destination (or more accurately, your destination arrives at you) faster than light. So if I were to send a radio transmission saying “welcome to your destination,” you would beat that message.
That brings up major questions about causality, but that’s not general relativity’s problem.