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Nadav Drukker's Physics Page

Recently I wrote a paper with my two colleagues Tomeu Fiol and Joan Simon on Goedel's universe in string theory. I will try to briefly explain it here. You can find the original paper at the preprint archive, but it would be very hard to understand without a knowledge of string theory.

I will not try to explain here what string theory is. There are some web pages dedicated to that subject. In particular see
The Second Superstring Revolution by John Schwarz.
The Official Superstring Theory Web Site.
M-Theory From Cambridge.
Superstrings! String Theory Home Page by John Pierre.
Superstring Theory by Brian Greene.

The structure of the universe is explained by Einstein's theory of General relativity. It describes the usual gravity we feel on earth, the forces between all the planets, stars, galaxies and so on. Our entire universe, which is expanding from the big bang can also be expressed in the equations of general relativity.

As theorists we may contemplate other universes, different from ours, and in 1949 Kurt Goedel found a solution to Einstein's equations which describes a very simple universe with time machines. By a time machine I mean a path one can take, usually thought of as a trip in a space ship. At the end of the trip you come back to the starting point, but at an earlier time...

Since then it was an open question if time machines are allowed in physics. Most researches believe that the answer is no, but there is no definitive answer yet. The problem is that it is not clear how to formulate the other laws of physics (classical or quantum mechanics) in those universes. The inconsistencies of time machines are clear in any movie on the subject, where the hero can change history and prevent her own creation.

So if we had a time machine I could throw a ball into it, it would go through the machine and come back to hit me in the head before I threw it. If I throw it hard enough it could knock me to the floor and prevent me from throwing the ball, so how do we avoid those contradictions?

Recently some new spaces were constructed (on paper that is, it's all theoretical) that people thought are solutions of string theory. They are very similar to Goedel's original solution, and there were some proposals that maybe string theory could work in the presence of time machines.

The point is that in the above discussion one takes the time machine universe from general relativity and tries to formulate quantum mechanics on it. But one cannot take the full interplay between the quantum theory and general relativity, since those are two separate theories. String theory combines both of them into an elegant (but very complicated) framework. So string theory seems like the natural place to look for answers to the clashes between the existence of time machines in general relativity and the other laws of physics.

In the example we studied we found a mechanism in string theory that prevents the creation of those time machines. If one starts from the universe with time machines the same mechanism will destroy it. It is a specific object that exists in the theory (unfortunately string theory is complicated with many different exotic types of particles, strings and other stuff that can live in space, which requires some technical knowledge to describe). One way of describing what happens is that this special object pops up whenever it sees a time machine, goes into it, fills it and prevents it from being used. In the process it causes a dramatic change in the form of the universe, and eliminates the time machine from it.

This mechanism we explained does not work yet for all possible time machines in string theory. But it is an encouraging step in trying to prove that there are no time machines in string theory. If it would be possible to prove that, and assuming that string theory describes the real world, it would mean that there are no time machines in our universe. This is not at all unexpected, but is not known for sure.