Question

There has been some heated debate as to whether the laws of physics allow for traversable wormholes. Some physicists claim we require exotic matter to construct wormholes, but then others counter the Casimir effect with ordinary matter is sufficient. But these same physicists seldom come up with an explicit solution or state of ordinary matter keeping the throat of a wormhole open via the Casimir effect. Yet others claim with extra dimensions, a Gauss-Bonnet interaction is sufficient to keep the wormhole throat open, but opposing physicists claim such a term can't arise from string theory.

So, my question is, do traversable wormholes exist as solutions to string theory?

Answer 1

It is known that Lorentzian wormholes can exist only if they respond to matter sources that violate some energy conditions. This is a general phenomena: a lot of what makes gravity special is that it is universally attractive. If you violate energy conditions then gravity can become repulsive, and then it is less distinguished from other forces.

On the other hand, it is believed that negative energy matter does not exist, mostly because this will cause instability (producing more of it will lower the energy indefinitely, so no reason for such production to stop at any point). It has never been observed, which is another reason to doubt it exists.

There are some attempts to involve quantum mechanics in order to circumvent this classical result (for example the Casimir effect can result in negative energies). However, if quantum effects are to violate a classical result, there is no way they are small. Then, you have to understand the full quantum mechanics, you cannot reach any conclusion based on the first quantum corrections. Same comment applies to any other attempt to add effects that are normally small (like higher derivative terms). Either you understand the full picture or you cannot come to any reliable conclusion.

There is also an independent problem, which is that wormhole spacetimes are unstable - small fluctuations tend to be magnified in parts of the geometry and therefore change it drastically. So even if you can write down a metric, it is not clear it is a good approximation to a real physical situation.

Having explained some of the issues, it should be clear that you have to understand quite a bit of quantum gravity to address these questions. I don't think that string theory is currently well-understood enough to resolve the question, or even to change anybody's mind either way. For what it is worth, my feeling is that what we know so far indicates wormholes don't exist.