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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?

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This comes close to our prohibition on fictional physics in the FAQ. But I know that the possibility of real wormholes is studied in GR, and I'm not sure how much is known about them, so I'll refrain from closing this without getting some feedback from someone who knows about that area of research. – David Zaslavsky♦ Jan 20 '12 at 19:24
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That's why I wrote "Assuming wormholes exist". It's theoretical physics, but not any less credible than string theory. I'm just wondering what these objects would be like if we happened to discover that they do occur in nature. – John Jan 20 '12 at 20:54
The issue is not with credibility or with how well a theory corresponds to reality, but whether it's possible to create a mathematical model that answers the question based on mainstream physics research. If a question is based on such a model, it's fine, even if the model doesn't exactly correspond to reality. The prohibition on fictional physics is really about keeping ill-defined questions off the site. – David Zaslavsky♦ Jan 20 '12 at 21:27
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Also, for the benefit of other readers: if a question is not well defined because it relies on some idea for which there is no accepted model, then saying "assuming [idea] is true" doesn't make it any more appropriate. – David Zaslavsky♦ Jan 20 '12 at 21:29

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There's a recent popularization of wormhole physics that nicely lists the properties of the four wormhole examples that Morris and Thorne considered in their 1988 paper. These properties include traversal times. Here's a summary

  1. Infinite-Exotic-Region Wormhole (exotic matter distributed throughout space) ~ 1 hour

  2. Large-Exotic-Region Wormhole (exotic matter confined to large finite radius) >= 7 days

  3. Medium-Exotic-Region Wormhole (exotic matter loosely restricted to throat) ~ 200 days

  4. Small-Exotic-Region Wormhole (exotic matter closely restricted to throat) >= 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.

These times are completely independent of the distances between the mouths of each wormhole in normal space.

Source: The Physics of Stargates -- Parallel Universes, Time Travel, and the Enigma of Wormhole Physics, by Enrico Rodrigo (2010), Chapter 5

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Quick comment on whether wormholes are physical: We can NOT assume that physical = "does not violate the Weak Energy Condition". There are quantum states that are clearly physical that nonetheless violate all proposals for an energy condition that defines physicality (including the WEC). Moreover, it's possible to eliminate destructive feedback-loops and time-travel paradoxes associated with traversable wormholes by invoking the Many Worlds interpretation. So the goal of current research is to prove the nonexistence of wormholes, or deal with the outlandish consequences of their existence. – Belizean Jan 29 '12 at 0:43
do you have the distances for those wormholes??? Thanks for the times! – John Jan 29 '12 at 19:45
@Belizean: I think you are being glib regarding the WEC. The examples you are thinking about where quantum fields violate WEC are likely the cases where you have a shrinking black hole, so that the renormalized stress-energy tensor on the black hole surface must allow the surface area to shrink, and so violates WEC in this sense. But this process must be described in a string theory completion (or some other quantum gravity theory), and it is pretty clear just from no-information loss that you aren't going to get stuff to go anywhere far away. – Ron Maimon Feb 2 '12 at 12:15
As for resolving time-travel with many worlds, that's completely speculative--- you need to ensure that there is a well defined many-worlds on a CTC background, and I don't see why that should be so, considering that the path integral does not have initial and final surfaces to slice along. If you know how to resolve a path integral on a CTC background, please tell, but I think it is just as difficult as resolving the classical time travel issues. – Ron Maimon Feb 2 '12 at 12:16
@Ron Maimon: The examples I’m thinking of have nothing to do with black holes. It was recently noticed that you can always find a quantum state of a simple scalar field that violates the NEC (and therefore the WEC) to an arbitrary degree in a conformally flat spacetime. Regarding quantum mechanics and CTCs, a consistent formulation of quantum theory in the presence of CTCs was put forward over 20 years ago. It was necessary to base it on Many Worlds Interpretation in order to eliminate paradoxes. – Belizean Feb 5 '12 at 4:31
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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"

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Visser's book is the standard reference on wormholes. – magma Jan 24 '12 at 10:46
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Standard reference for wormholes:

Visser’s book

Excellent Wikipedia page:

Wormholes

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,[1] Kip Thorne,[2] and others[3][4][5] 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.).

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This is accurate in describing the idea, but it is no good as physics. Such a traversable wormhole can be boosted, and using two copies of such wormholes, you can make a time machine. Any geometry can give you a stress-energy tensor, but only if the matter satisfies at least the weak energy condition can you call it physical. The traversable wormholes are not physical in this regard, and the time-machine argument tells you that this is so for fundamental reasons. – Ron Maimon Jan 24 '12 at 21:57
@RonMaimon Absolutely, that's why I quoted the exotic matter paragraph. CTC (closed timelike curves) are another problem. But the OP was asking a very specific fact, assuming that wormholes exist. So the question appears to me more mathematical than physical – magma Jan 24 '12 at 22:09
We agree, but just to be clear-- the original wormhole idea of Einstein and Infeld(?) is that you have a black-hole white-hole linked together. This thing is possibly physical if both are at the same place, and possibly describes real astrophysical rotating black holes, although in the Einstein et al analysis, the two were distantly separated. This is the reason for my answer. I have no problem with your answer now that you explained. – Ron Maimon Jan 24 '12 at 22:43
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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.

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"This is not justified by any precise calculation" so you're saying that our math doesn't let us calculate just how much a wormhole shortens travel time? What about in General Relativity? – John Jan 23 '12 at 16:07
@John: The wormhole is not shortening any travel time--- you aren't going anywhere. It is the time between absorption and reemission in a black hole. I personally can't get the answer, and I know it is not in the literature, but we know how to calculate it in theory, and it is just my own failing that I don't know the answer today. I think about it from time to time. – Ron Maimon Jan 23 '12 at 17:08

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