Thursday, December 22, 2005

MIT talk: a theory of nothing

Today, John McGreevy gave an entertaining MIT seminar mainly about the theory of nothing, a concept we will try to define later. The talk described both the work about the topology change induced by closed string tachyon condensation as well as the more recently investigated role that the tachyons may play for a better understanding of the Big Bang singularity. Because we have discussed both of these related projects on this blog, let's try to look at everything from a slightly complementary perspective.

Defining nothing

First of all, what is nothing? John's Nothing is a new regime of quantum gravity where the metric tensor - or its vev - equals zero. This turns out to be a well-defined configuration in three-dimensional gravity described as Chern-Simons theory. It is also the ultimate "paradise" studied in canonical gravity and loop quantum gravity.

Does "nothing" exist and is there anything to study about it? I remain somewhat sceptical. If the metric is equal to zero in a box, it just means that the proper lengths inside the box are zero, too. In other words, they are subPlanckian. The research of "nothing" therefore seems to me as nothing else from the research of the subPlanckian distances. This form of "nothing" is included in every piece of space you can think of, as long as you study it at extremely short distances. And we should not forget that the subPlanckian distances, in some operational sense, do not exist. I guess that John would disagree and he would argue that nothing is an "independent element" of existence; a phase in a phase diagram. I have some problems with this picture.

Tachyons create nothing




The next step in the system of ideas that John nicely promoted is the paradigm that the tachyons are very important for a correct understanding of "nothing". We know that the open string tachyons get a vev that describes a complete destruction of the original D-brane (or a D-brane pair) - the best state of "open string nothing" you can imagine. The twisted closed string tachyons of Adams, Polchinski, Silverstein describe the destruction of the orbifold singularity.

Allan, John, Eva, and their collaborators have extended this reasoning into localized winding closed string tachyons whose condensation is able to change the spacetime topology. For example, if you compactify two dimensions (out of ten) on a genus "g" Riemann surface, the condensation of the winding tachyons is able to cut a handle and reduce the genus. This perturbative instability is continuously connected with Witten's bubble nucleation.

This event also changes the Witten index - if it exists in this nonsupersymmetric background at all - and John argued that there are some "dust states" left behind in the region of nothing where the handle disappeared. I was not the only one who did not understand whether they feel lonely there - and more generally, what is exactly the physical relation between them and the rest of the space where the observations can actually be done. Do they have any observable consequences?

I also remain a bit cautious about the identification of the nothing we defined at the beginning (g_{mn}=0) and this new nothing (T=T_{0}) described as a tachyon condensate. These are - at least a priori - two different conditions. Also, as a person who has spent one half of his life behind the iron curtain, I find it difficult to believe that there is "nothing" behind the iron curtain. Nevertheless, one of the statements is that there is "nothing" behind the Liouville wall which sounds somewhat analogous to the iron curtain. A counterpart of the Liouville wall that is localized in time is used by John and Eva to screen the undesirable features of the Big Bang singularity.

I also remain unconvinced that there exists any CFT of the type they conjecture that is conformal even at the point "t=0", a CFT in which the dilaton gradient may be neglected (although the gradient seems necessary to generate the central charge from the missing spacetime coordinates inside "nothing"), and where the condensation of the tachyon remains localized to the vicinity of the Big Bang.

This discussion may become too philosophical very quickly but I strongly feel that the basic questions here have an almost philosophical character and many of them must be answered before one tries to study details. And many questions were asked during the talk; some of them may have been treated by John as jokes, but I personally found them as serious as the rest of the discussed topics. Hopefully John will tollerate my opinion that some questions must simply be treated as serious questions once these possible mechanisms are studied seriously.

Splitting the Universe

For example, the winding tachyon condensation can in principle be able not only to reduce the genus but also to split the Universe (i.e. split the compact manifold that exists at each point of the large dimensions) into two independent pieces. I like this possibility because it could lead to a vacuum selection mechanism that makes most vacua unstable except for e.g. the heterotic Standard Model vacua with the minimal values of the Hodge numbers; every other Universe could find a way to split into "simpler" vacua with smaller Hodge numbers. This is based on my belief that simple vacua in string theory - and in science in general - are preferred not only by our approach based on Occam's razor (those who prefer the Rube Goldberg machines will surely forgive me that I hijacked the word "our") but they are also preferred by Nature. We've seen this principle in action many times.

Attracting other Universes and wormholes

This is a nice possibility but there is another one which is even more drastic. Revert the process we just described. Prepare the radiation exactly in such a way that it will "reconnect" our Universe with another Universe that is still "waiting to join us" in some virtual reality - reality that was geometrically disconnected from our world at the beginning. Can such a thing happen? I think that any sane person would say that in practice, it will be impossible at least in this century. ;-) It is as impossible in practice as the creation of an "S-brane"; John agrees.

On the other hand, John mentioned this science-fiction topic, which is why it would be a good idea to have at least some approximate answers to some obvious questions like What is the probability that our experiments will be able to reconnect us with a different Universe? (Yes, of course, this question has been asked, too.) If someone proposes that such a process is in principle possible, then the questions like this one are legitimate ones and they should not be treated as jokes. Needless to say, there exists a certain set of possible answers that may show that the picture is inconsistent with the very basic properties of our Universe. I personally find it very likely that pure thought is enough to identify these possible mechanisms as inconsistent. These existential questions affecting similar scenarios should be studied simultaneously with some more detailed questions, if not before them - because we don't want to study something that is inconsistent.

Open questions

At any rate, there are many very provocative and intriguing questions raised by this work that is very stimulating but also unlikely to be accepted as the "final answer", for example
  • Does it make sense to study the very early, "t=0" behavior of our Universe at all? My answer is Yes.
  • Does it make sense to study physics of the beginning while keeping the initial conditions completely arbitrary? My answer is No.
  • Can the topology of space be changed? The answer is Yes.
  • Can the number of components of the Universe - the "spatial manifold" - change? The answer is We don't know for sure.
  • Can time start and end, and should we allow for a violation of unitarity in the finite neighborhood of the singularities?
  • If the answer to the question about splitting the Universe to pieces is Yes, we should ask How quickly the two components of the Universe get decoupled? We don't know.
  • Can this splitting of Universes play a role in destabilization of the majority of the landscape? We don't know; so far there is no clear indication that the answer is Yes.
  • Can the process of splitting be reverted so that we force another Universe to join us? Probably not in practice - but in principle, we don't know.
  • If we are able to change the topology of space, are we also able to create macroscopic wormholes and/or time machines? My answer is Probably no in practice, but we still don't know the answer in principle.
  • Are such possibilities consistent with unitarity, or do they force us to modify something essential about the structure of physics?
  • Can we reformulate everything in physics of perturbative string theory as a refined analysis of tachyon dynamics?
  • Is the tachyon really so naturally useful for all these new proposed applications, or do we propose such links because tachyons have been fashionable for 7 years, after the decades in which they were discriminated against as "ugly inconsistencies"? ;-)

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