It’s a common trope in sci-fi to allow spaceships to travel FTL via entering an alternate “dimension” or universe where the laws of physics are different, allowing them to go faster than the speed of light, and then exiting when reaching the destination.
My question is, what would happen, scientifically speaking (as much as possible for this fictional scenario), to the speed of those vessels when they exit back into real space, having been travelling at the speed of light until that instance? Do they just immediately decelerate? What happens to their momentum then, where does it go?
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Usually in stories with this sort of FTL momentum is conserved in normal space. So whatever your momentum was when you went into hyper space (or whatever they call it) it will be the same when you come out.
Whatever speed they were travelling within hyperspace is irrelevant.
Scientifically speaking you are basically asking if magical teleportation would preserve momentum.
Science has no answers here, science isn’t involved. There is no data to give even a hint of an answer.
It depends a great deal on the means of travel within the ‘otherspace’ to come up with one single answer. As you’ve stated, many forms of FTL leverage traveling through a different medium to avoid violating general relativity – Star Wars and SG1 has hyperspace, Farscape Leviathans use a type dimensional hopping, Mass Effect leverages the mass relay system, etc etc etc. In all those cases real inertial velocity of the craft is preserved in transit (and is sometime vital to successful travel) so that when you exit into the ‘real universe’ you’re still going the same speed you were when you entered ‘otherspace.’ While the Star Trek warp drive doesn’t apply (being an alcubierre drive that bends spacetime to reduce perceived distance traveled from the observers standpoint) their model of ‘quantum slipstream’ does – velocity of the craft generating the slipstream is important and can positively or negatively affect the journey. Same for wormhole travel in that universe – the speed you enter the wormhole is preserved during the journey and you are spit out on the far side at the same velocity.
Without going into a specific universe or type of drive I can’t provide a more specific answer but the fact is, it varies by universe substantially.
It depends on how the alternate “subspace” or “hyperspace” works. Is it a shortened travel time? Or is it nearly instantaneous? Does your ship still have to achieve a massive velocity, or are the physical rules of this hyperspace different?
If your hyperspace is like typically described hyperspace travel, then your ship is probably traveling slower than light, but somehow the distances in hyperspace are shortened. Your exit vector can be calculated and adjusted, and your exit speed will be similar to its entry — not too fast, and little to no relativistic effects to deal with.
If your transit time is nearly instantaneous, almost like teleportation, your exit velocity may still be exactly the same as before. This could give a further problem, depending on your setting’s rules
If you leave a star system while coasting in a specific speed and direction, your emergence in the new system might leave you still traveling in that same speed and direction — except the star or planet you’re now orbiting has a different velocity that you’ll need to adjust for.