What would happen when there is the warping of space occupied by matter? For example, if there is a ship propelled by the Alcubierre Drive, what would happen if it collided with something with mass? And how (if it does) would that differ from normal physics?
Baryonic matter by necessity occupies spacetime, but since the theoretical Alcubierre drive warps spacetime, there wouldn't actually be any travel through it and no additional interaction with baryonic matter would occur due to it. Miguel Alcubierre's proposal for warp drive does call for exotic matter to create a distortion in spacetime, when perceived as Euclidean space, but it's often misunderstood as faster-than-light (FTL) travel. Theoretical Alcubierre drive does not violate general relativity, but achieves perceived FTL via local expansion and contraction of spacetime, behind and in front of the spacecraft, respectively.
If we simplify it with an analogy, if we'd have to fold a sheet of paper to demonstrate theoretical travel through a wormhole, Alcubierre drive would analogously create a local ripple (pardon my choice of words, some call it a bubble) in this sheet of paper, our 2-dimensional representation of spacetime. This could look something like this:
Two-dimensional visualization of the Alcubierre drive, showing the opposing regions of expanding and contracting spacetime
that displace the central region (Source: Wikipedia on Alcubierre drive)
This 2-dimensional representation of spacetime shows that it would exclude interaction with any baryonic matter between outside and inside of the ripple while such drive would be able to warp spacetime around it, but at the same time does not prohibit normal interaction with matter inside it. This means that, unless you've created a ripple large enough to include in it an object already on collision course with your spaceship before you turned your Alcubierre drive on, or turned your drive off at an inconvenient place, you wouldn't have to fear collision. Well, that's to my understanding at least, it's not an easy idea to wrap one's head around.
Suggested additional reading:
Nice thing about the Alcu Drive is that it gives you a realistic example of the "energy shield" you see in a lot of science fiction. The warp bubble essentially protects you from all outside menaces.
On what can happen to those outside menaces, that's another matter and is impossible to know for sure, could be anything from not being touch at all (some people have compare the Alcu Drive to what we see in fiction with hyperspace, it essentially take you out of the universe and place you in another point of the universe without interacting in between) whether as something similar to a hyperspace "jump" or to be "out of phase". However it is also possible that the bubble does affects mass, not anything inside the bubble, but let's say a meteorite or another ship stationary could be bend as space, which probably would destroye them. Entering a planet could be from just making a very very large hole on one side of the surfice and coming out from the other side or causing massive damage tho that may depend on the ship's size (I mean if is like a small capsule won't be the same as if it is like the Enterprise). Stars and other objects like pulsars and even black holes are to large to be affected unless is something like the Death Star, to give you an example of proportion the Enterprise at the side of the sun would be like comparing a needle with a house, and the sun is one of the smallest stars we know.