Tuesday, May 31, 2011

Horizon Complementarity

Sean Carroll had an interesting post at the Cosmic Variance blog. The post discusses the idea, outlined in a couple of recent papers, of finding a concordance between the multiverses which exist according to some speculative cosmological models and the many-worlds interpretation of quantum mechanics. Carroll provides a sketch of his own thoughts about how this might work. (The referenced papers are by Nomura and Bousso & Susskind).

I have some thoughts about this broad question, but for now I want to highlight one key notion utilized in the discussion, which is that of “horizon complementarity”.

I was familiar with the holographic principle, which says roughly that the information about what is inside a region of space-time can be encoded on the surface boundary of the region. This idea developed from the study of black holes, where it was earlier theorized that black hole entropy was proportional to the area of its event horizon. Horizon complementarity is likewise an extension of another idea which was developed in the study of black hole entropy/information paradox. Here’s a lengthy excerpt from Carroll (who is skilled in explaining difficult topics to a general audience - see the original for embedded links):

The idea of horizon complementarity is a generalization of the idea of black hole complementarity, which in turn is a play on the idea of quantum complementarity. (Confused yet?) Complementarity was introduced by Niels Bohr, as a way of basically saying “you can think of an electron as a particle, or as a wave, but not as both at the same time.” That is, there are different but equally valid ways of describing something, but ways that you can’t invoke simultaneously. 
For black holes, complementarity was taken to roughly mean “you can talk about what’s going on inside the black hole, or outside, but not both at the same time.” It is a way of escaping the paradox of information loss as black holes evaporate. You throw a book into a black hole, and if information is not lost you should (in principle!) be able to reconstruct what was in the book by collection all of the Hawking radiation into which the black hole evaporates. That sounds plausible even if you don’t know exactly the mechanism by which happens. The problem is, you can draw a “slice” through spacetime that contains both the infalling book and the outgoing radiation! So where is the information really? (It’s not in both places at once — that’s forbidden by the no-cloning theorem.)
Susskind and Gerard ‘t Hooft suggested complementarity as the solution: you can either talk about the book falling into the singularity inside the black hole, or you can talk about the Hawking radiation outside, but you can’t talk about both at once. It seems like a bit of wishful thinking to save physics from the unpalatable prospect of information being lost as black holes evaporate, but as theorists thought more and more about how black holes work, evidence accumulated that something like complementarity is really true. (See for example.)
According to black hole complementarity, someone outside the black hole shouldn’t think about what’s inside; more specifically, everything that is happening inside can be “encoded” as information on the event horizon itself. This idea works very well with holography, and the fact that the entropy of the black hole is proportional to the area of the horizon rather than the volume of what’s inside. Basically you are replacing “inside the black hole” with “information living on the horizon.” (Or really the “stretched horizon,” just outside the real horizon. This connects with the membrane paradigm for black hole physics, but this blog post is already way too long as it is.)
Event horizons aren’t the only kind of horizons in general relativity; there are also horizons in cosmology. The difference is that we can stand outside the black hole, while we are inside the universe. So the cosmological horizon is a sphere that surrounds us; it’s the point past which things are so far away that light signals from them don’t have time to reach us.
So then we have horizon complementarity: you can talk about what’s inside your cosmological horizon, but not what’s outside. Rather, everything that you think might be going on outside can be encoded in the form of information on the horizon itself, just like for black holes!
I’ve always thought that there is something problematic about referring to putative space-time regions beyond our ability to probe. If you take seriously that even local reality isn’t actualized until measured (as in QM), then it’s consistent to treat the “actual” universe as simply that patch which is in principle subject to a causal connection to the observer: the rest of reality consists of possible events or worlds.

Horizon complementarity seems to comport with this idea. As for the question of whether the possibilities encoded in QM somehow match a given cosmological model of the multiverse, I don’t have much claim to have an opinion, although I’m skeptical of the eternal inflation/supersymmetry picture favored by the authors of the papers referenced above.  Carroll's own idea would invoke vacuum fluctations within the actual universe as the multiverse of possibilia - I like this better, but the idea is at most provisional to the extent it relies on quantum field theory rather than a quantum gravity theory.

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