...So people know, this is nothing "new". Warp theory has been around for quite a while, I think this came back up because the movie is about to be released.
Basically, the concept is that according to general relativity space time is curved, allowing an object to move faster than light in curved space time. The argument for this is that the curvature could take the form of a wave in which a spaceship might be carried in a "bubble". In this “bubble”, space would be collapsing at one end and expanding at the other. The motion of the wave would carry the spaceship from one point in space to another in less time it would take light to go through unwarped space. However, the spaceship within the bubble would not have traveled faster than light.
And then there are wormholes:
Wormholes are distortions in space-time that could connect two points in the universe across an Einstein-Rosen Bridge. Although there are solutions to the Einstein equation of general relativity which allow for wormholes, they involve some assumption such as the existence of negative mass. Some however argue that such wormholes might have been created in the early universe.
So, the possibility of Warp more or less depends on the existence of negative mass, or ability to create it. We already know that space is warped, and that euclidean geometry is not how the universe is actually shaped. Gravity in fact I
think is the concentration of space around a mass, or certainly has something to do with it. Warp also does not mean you would go faster than light, just that it becomes possible to surpass the speed of light in the unwarped space around you.
Quote: "But what are we expanding into? What's at the edge of the universe (aside from a restaurant?)? What's beyond that edge?"
...Well, I'm not familiar with the theories for what we're expanding into, but there is no edge as you see it. Say you were to draw a perfectly strait line instantly all across the universe, you would end up with the other end of that line pointed at earth, right were it started. You see, the space itself is expanding. Try and imagine that all of the universe is flattened out and then wrapped around a sphere, and it's the sphere that is expanding. I think this has something to do with vector space.
If any of the stuff here confuses you, wiki Interstellar travel or warp or wormholes or geometry or something. Then you can point out any mistakes I've made.