Assuming wormholes exist and you put some matter into one, how long would it take to reach the other end versus how far apart the two ends are? Basically, by how much does a wormhole stretch spacetime?
There's a recent popularization of wormhole physics that nicely lists the properties of the four wormhole examples that Morris and Thorne considered in Appendix A of their 1988 paper ("Wormholes in Spacetime and their use for interstellar travel: A tool for teaching general relativity"). These properties include traversal times. Here's a summary
Infinite-Exotic-Region Wormhole (exotic matter distributed throughout space) ~ 1 hour
Large-Exotic-Region Wormhole (exotic matter confined to large finite radius) $\geq$ 7 days
Medium-Exotic-Region Wormhole (exotic matter loosely restricted to throat) ~ 200 days
Small-Exotic-Region Wormhole (exotic matter closely restricted to throat and must have negative mass) $\geq$ 0.7 seconds
Morris and Thorne referred to the last example as "absurdly benign". It is not dissimilar to the thin-shell wormholes considered by Visser. In fact, some of Visser's thin-shell wormholes are a special case of the Morris-Thorne Type 4 "absurdly benign" class!
These times are completely independent of the distances between the mouths of each wormhole in normal space.
"The Physics of Stargates: Parallel Universes, Time Travel, and the Enigma of Wormhole Physics" by Enrico Rodrigo (2010), Chapter 5.
Standard reference for wormholes:
Excellent Wikipedia page:
From Wikipedia page:
“Wormholes which could actually be crossed, known as traversable wormholes, would only be possible if exotic matter with negative energy density could be used to stabilize them. (Many physicists such as Stephen Hawking, Kip Thorne, and others believe that the Casimir effect is evidence that negative energy densities are possible in nature.)”
The paper which started the whole “traversable wormhole research in the 80’s-90’s” is written in a very pedagogical style:
Morris, Michael S. and Thorne, Kip S. (1988). "Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity". American Journal of Physics 56 (5): 395–412.
Given the above background info, the answer to your question is: A traversable wormhole is basically a “hollow handle” which you can use to reach two different parts of the universe. It is like a tunnel, BUT there is no definite relation between the “length” of this tunnel (or the time you/light rays need to travel thru it) and the “distance” between its mouths (entry/exit points) as measured in the space-time outside the wormhole.
Put it in another way: we can find a solution to the Einstein’s eqs with a wormhole connecting two areas in space-time a few light years apart or many 1000’s light years apart. Basically: given the desired G tensor, we can find the appropriate T tensor (that is the appropriate energy-matter distribution) so that the wormhole can be comfortably traversed by a human (or a light ray) in a short time (hours, for ex.).
Kip Thorne, Matt Visser and others have modeled traversable wormholes requiring exotic matter. Dark energy is a form of exotic matter if it could be harnessed and amplified. What that would do to the information loss issue and the validity of unitarity in S-Matrix theory is, of course, a valid issue as pointed out above.
See Matt Visser's book "Lorentzian Wormholes"
Wormholes linking distant spacetime points are forbidden in string theory (as far as we know) and in modern gravity, because you would be able to make information loss in a local region by dumping one of two entangled pairs into the wormhole, and letting it come out elsewhere.
But a black hole attached to a white-hole (the classical wormhole) is possibly the correct view of all spinning and charged black holes in string theory. In this case, travesing the wormhole from your point of view will take a small amount of time, crossing the outer event horizon and the inner Cauchy horizon, then turning around and crossing out the white hole. You should emerge to the future of when you entered (in a loose sense, it is not possible to be strictly to the future in an eternal black hole picture), but nobody knows how such an emergence might work, because the classical model does not identify the white hole and black hole horizons.
The quantum mechnical model does identify the two event horizon types, but since this identification becomes invalid classically, the time to emerge should be long on a classical time scale, going as 1/hbar or some power. This is not justified by any precise calculation--- it is also possible that once you cross the black hole, you are just irreversibly trapped. I don't believe this possibility, because the irreversibility would then be independent of temperature, which is different from other cases where irreversibility is observed.