First, I consider the following as given: All the galaxies, solar systems and planets in the universe travel on a different route at a different velocity through space, mostly moving away from each other.
Now, imagine we would be able to create a wormhole from planet x in solar system y in galaxy z to planet a in solar system b in galaxy c. Since both planets are moving in different directions, I see 2 options how it could work.
1) The wormholes would travel with the planets, constantly changing the spacetime-wrapping.
2) The wormholes would stay at the position they were initially created, which means the planets would move away from them, after they were created. But the spacetime-wrapping would stay the same.
I know most people (me included) think that option 1 is the case. But the following question really made me think, and led me to the question I'm now asking:
If option 1 was the case, what would happen if someone entered the wormhole? Would he keep the velocity of the planet where he entered at the planet he came out, which means he would move away from the target planet? Or would he adopt the velocity of the target-planet? If the latter was the case, would this person notice the slow-down/speed-up/direction-change? Could the person even die?
I'm not a physicist, so I may assume totally wrong concepts. I'm sorry about that.
Answer
Wormholes don't just exist by themselves, they have to be created by a form of matter called exotic matter (which almost certainly doesn't exist, but let's gloss over this). To construct a wormhole you need to gather up some exotic matter and arrange it in a particular configuration.
So if the exotic matter is moving the wormhole will move along with it. However you may find that a considerable force is required to move the matter at the two ends of the wormhole because as they move energy will have to be put into the spacetime warping between them.
Re the second question: a wormhole is not like a Star Trek transporter that instantly moves you from one place in space to another. If you pass through a wormhole you would be floating freely$^1$ just like the astronauts in free fall in the International Space station. Falling through the spacetime in a wormhole is no different to falling through the spacetime around the Earth, except that the spacetime in a wormhole has a rather special shape.
Generally speaking, falling freely through spacetime does change your velocity (as measured by someone who is not falling freely). For example, when Felix Baumgartner jumped out of his capsule his speed relative to the ground changed from zero to Mach 1.25. In that case it was the spacetime curvature caused by the mass of the earth that accelerated him. In the case of the wormhole it would be the spacetime curvature caused by whatever exotic matter you used to construct the wormhole.
So when you emerge from the far end of the wormhole your speed will almost certainly be different to the speed you had when you jumped in. Exactly what your speed will be depends on the exact geometry. The speed will make absolutely no difference to you unless there is something in your way, so putting the far end in a closed room would be a bad (and very messy :-) mistake. In any of the more realistic science fiction stories that use wormholes (and remember, this is science fiction we're talking about) the ends of the wormholes are floating in space so anything emerging from them has lots of room to slow down.
$^1$ though there maybe tidal forces
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