In the latest episode of The Big Bang Theory, Leonard Hofstadter had an interesting idea while he was talking to Penny: the spacetime is a surface of the superfluid. The surface tension could even explain the negative pressure of the positive cosmological constant which is a constant positive contribution to the vacuum energy density (they incorrectly talk about the negative energy). Sheldon completed the maths and wrote their joint paper quickly. It was a source of pride for much of the episode.
The Troll Manifestation: an excerpt
The sitcom referred to the Quantum Diaries blog – probably because the bloggers were drinking some wine with the filmmakers (Ken Bloom actually contributed the plot of the episode) – and Leonard quoted a flattering comment on that blog written by your humble correspondent.
The Cooper-Hofstadter paper is a variation of the superfluid vacuum theory that has been around for quite some time. While the "surface of superfluid" and "surface tension" could be interesting twists, it seems a bit hard to understand what it could mean quantitatively – probably because it means nothing. Much of these theories seem to be all about words that can't be elaborated upon. Wikipedia correctly introduces the superfluid vacuum theory as one that may be a "fringe theory".
The broader theory began almost a century ago as a revival of the luminiferous aether. Of course, the aether has been ruled out by Albert Einstein's discovery of the special theory of relativity. The spacetime can't be filled with any "stuff composed of any particles or anything that may be localized" because that would pick a preferred reference frame.
However, in quantum field theory, the vacuum isn't quite empty. It has all the violent quantum fluctuations. Doesn't it revive the concept of the aether? Well, yes and no. The quantum fluctuations are in no way composed of "individual particles". By definition, "particles according to quantum field theory" mean excitations by creation operators raising the vacuum. The vacuum itself doesn't have any!
On the other hand, there is "something" in the vacuum and this "something" may be said to be vaguely analogous to the "aether". If you want the analogy to be more specific, it's better to compare this "something" to a Bose-Einstein condensation – a superconductor or a superfluid – because these are the real-world types of materials that eliminate the friction and dissipation. If you move in other materials, you are slowed down by friction and electrical resistance and similar effects. Those may go away in superconductors and superfluids, so these super- substances are better models for the vacuum which, as we know, is friction-free and allows objects to keep their inertia.
In fact, in the electroweak theory, this analogy goes much further. The Higgs field is a kind of a "superconductor" and even the phases of the Higgs field may be interpreted as the phases we know from superconductors. In other words, superconductors in condensed matter physics may be described as a field theory with a spontaneously broken electromagnetic \(U(1)\) gauge group. It's broken by a condensate of composite charged \(Q=-2e\) particles, the Cooper pairs (of electrons).
(To be honest, these Cooper pairs are *not* named after Sheldon Cooper but rather after Leon Cooper. Similarly, the Nobel prize laureate Hofstadter who got it with Mössbauer for the electron-nuclear scattering wasn't Leonard Hofstadter but Leonard could have been named after Robert Hofstadter – who was born 100 years and 1 day ago.)
If you look at this analogy from the other direction, you may understand why some people refer to the spontaneous breaking of the electroweak \(SU(2)_W\times U(1)_Y\) gauge group as the "electroweak superconductivity". As far as I can say, this is just a matter of an "unusual diplomatic language", one that tries to mask that condensed matter physics is just squalid state physics, as Murray Gell-Mann discovered decades ago.
But more seriously, is there something else that condensed matter physics may teach us? I am a bit skeptical. While it's true that the Higgs field is a kind of a Bose-Einstein condensate or even a superconductor, many other analogies with the condensed matter counterparts simply fail. In condensed matter, the superconductors are ultimately composed of atoms – nuclei and electrons – but this seems impossible for the vacuum because that would almost certainly break the Lorentz symmetry and violate special relativity. The superfluids and superconductors may eliminate some anti-inertial effects such as friction or resistance – which is why they are better models of the vacuum than generic materials – but they cannot (naturally) eliminate all Lorentz-violating effects and terms.
So the "vacuum as a superconductor or superfluid" is just a matter of terminology. It's jargon that may be taken seriously up to some point but not quite literally.
Years ago, I talked to a crackpot named Friedwardt Winterberg, a guy who used to be a student of Werner Heisenberg, if you believe him. You shouldn't be surprised that I was the only guy at the Santa Barbara conference who would talk to him. However, as he learned quickly, it wasn't necessarily because I was more enthusiastic about his crazy theories. It's probably more accurate to say that I have always been more enthusiastic about debunking garbage. For years, I would be getting snail mail from him etc.
What Sheldon and Leonard want to add to this picture is to say that we live on the "surface of a superfluid". That's surely a new addition but what does it exactly mean, what explanatory power or evidence can it add to the picture, how can it be translated to mathematics, and is that better than the old models? I am not sure. The "surface of a superfluid" surely makes this model analogous to a braneworld scenario where the Standard Model lives at the end-of-the-world brane. So it may be either a variation of the Hořava-Witten (HW) heterotic M-theory; or the Randall-Sundrum (RS) models.
If that's so, it should be possible to formulate the "general properties" of this Cooper-Hofstadter model in terms o the usual HW or RS formalisms. How do the Cooper-Hofstadter models differ from the HW and RS models we know from literature? And is there anything good about this difference? It is not clear to me. So at the end, I probably tend to agree with the sentiments expressed by the anonymous trolls according to the sitcom (the most important anonymous troll turned out to be Stephen Hawking, he told us, who just wanted to have some fun: once you sit on the chair for 40 years, you may get a bit bored).
If there's some wisdom or evidence in the Cooper-Hofstadter paper or related research that I am overlooking, I surely hope that we will be clearly told what it is. ;-)