Frank Wilczek gave an impressive physics colloquium at MIT last month, called “What is Space?” and it really gave me a new view of the physical world. I had read about spontaneous symmetry-breaking in quantum field theory texts, but I had not appreciated that the space around us can be viewed as a condensate. This was also the first time I’ve heard the word “superconductor” used in the sense he meant, but it seems like a somewhat natural generalization after some pondering.

He put up slides of his talk here (warning: this file did not agree with the Firefox on Linux in my office, but I was able to view it in Safari at home), but there were a couple differences between the slides and the lecture he gave. First, he only presented the first 2/3 of the slides, so it was interesting to read the slides that he rejected and tossed to the end. Second, in the talk, he really emphasized the point that truly empty space is a fundamentally explosive medium, because quark-antiquark pairs have negative energy. In particular, the space we see is quite full of such pairs, which mutually repel, so there is an equilibrium concentration. Also, these pairs are made of real particles, and are not virtual (although I don’t understand the significance of this statement). I had never seen this idea before, and I wonder if the negative energy claim is a result of some reasonably recent lattice QCD computations, or if I’ve simply failed to pay attention in the past.

At the end, there were a lot of questions from the audience about extra dimensions and strings, and he ducked all of them. I had been meaning to ask if he expected the nature of the condensates to change in or near the event horizon of a black hole, but unfortunately, I was unable to think of a good way to say it in English words at the time.

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Just some [not-so-tangential-as-they-might-appear-at-first] comments,

• the analogy between symmetry breaking (hep-th) and superconductivity (cond-mat) has to be taken with a fairly big grain of salt: after all, having Lorentz symmetry is a big game-changer: http://arxiv.org/abs/0907.3466 . Having said that, in the particular case that Wilczek applies this analogy [above], it’s “fair game” (you just have to keep the previous warning in the back of your head ;-) ).

• As for the “negative energy” of QCD, think in terms of QCD beta function, http://en.wikipedia.org/wiki/Asymptotic_freedom . This is really what he had in mind (for obvious reasons: it won him the Nobel ;-) ), and the fact that it’s sign is negative is quite a big deal.

PS: sorry for the mishap with the above comment — you can just delete it.

[Done. -S.C.]Thanks for pointing out the connection with asymptotic freedom and the beta function. I found a nice informal description of anti-screening in Wilczek’s Nobel prize lecture.

Actually, nothing special happens at the event horizon of a black hole. The name is more apt than you might think: An event horizon is just a kind of horizon. A horizon is a place where the view is cut off from a distance, but if you’re there, nothing much is happening locally. The phase state of the vacuum might well change near the singularity of a black hole, however.

There is one inessential caveat to that. The derivative of the gravity force (the tidal force) of a medium-sized black hole is quite large, even well outside of its event horizon. So macroscopic objects tend to get kneaded and ripped apart. But even then, nothing novel is happening on the subatomic scale, only events induced by particle collisions. If you fall into a very large black hole, then bad news awaits you as you approach the singularity, but you won’t notice the event horizon itself.

Greg, that is the standard GR story I have seen in textbooks, and I certainly find it appealing. However, when I read the literature on black hole thermodynamics and the information paradox, the unusual causal structure in the interior of the event horizon seems to prompt people to make theories involving exotic behavior, often including situations where curvature (if it is meaningful at all) doesn’t become huge. Examples include transitions to different phases of the metric condensate at the horizon, and macroscopic stringy superpositions (like the whole interior becomes a big “fuzzball” of string, or something). I’ve even heard that there are some condensed-matter physicists who don’t think black holes form at all, and claim that the spacetime near a collapsing star undergoes a phase transition before an event horizon can form, but I don’t know how well-accepted their views are. I was just hoping to hear Wilczek’s take on that.

Scott, I don’t really understand what you’re saying. Of course, one issue is that it isn’t possible to look inside of a black hole. So we can make an analogy to the far side of the moon, which we also couldn’t see until the 1950s. Absent a testable hypothesis, the question is what is the most parsimonious description, which in the case of the moon was that the far side look a lot like the near side.

GR is both a tested physical theory and a confirmed physical theory. In GR, a rapidly accelerating environment, such as an object hovering near an event horizon, can be very unusual. In a parsimonious combination of GR and quantum field theory, such an environment is subject to quantum corrections, and Hawking radiation exists for similar reasons. But a (small) object falling through an event horizon is not doing anything special in its own reference frame.

I don’t know whether these “macroscopic stringy superpositions” are meant as a new parsimonious model of quantum effects in a black hole, or just a new description of the same thing, or as some kind of alternative to standard GR. For the moment it sounds confusing.

Greg, I can’t say I really understand what I’m saying either. My vague recollection from what I’ve read is that the global geometry in the interior of the event horizon (as specified by GR) makes it difficult to define a meaningful notion of quantum field theory in that region, even at a physical level of rigor. For example, there is no reasonable notion of asymptotic future, so there are no S-matrices. I seem to recall that there are analogous global obstructions to making pure quantum gravity meaningful in a positive cosmological constant universe.

The hypothesis that an infalling observer in an inertial frame doesn’t do anything special when passing through the event horizon requires an assumption that the conditions inside the event horizon are similar to those outside. If I recall correctly, the Beckenstein-Hawking entropy calculation suggests that (parsimonious descriptions aside) from the standpoint of outside observers, all internal states consistent with the externally observed mass, charge, and angular momentum are equally likely. Naturally, you could ask me to define words like “likely” and “internal state”, and I would be completely stumped. At any rate, the exotic theories I brought up before seem to be a consequence of reasoning that rather than having a classical picture with small quantum corrections, except very close to the singularity, we really have a situation where the quantum corrections are dominant all over the place.