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Sheldon and Leonard co-author a paper on superfluid vacuum theory

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. ;-)

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snail feedback (18) :

reader br said...

For those intrigued for further information, Susskind starts to mention the vacuum as a condensate here from around 19 mins. As always, very clearly presented.

reader PlatoHagel said...

I think the idea about this superfluity nature existence has a strong correlation with what we understand in relation too, quark Gluon plasma? What happens in nuclear reaction on the sun?

Any research mentioned in relation to the superfluids, would it not have something to be have said in relation to quantum chromodynamics as well?

reader PlatoHagel said...

Researchers have proposed many ways to increase the robustness of superconductors, and atomic superfluids offer experimental means to test these ideas, Chin said.

“Superconductors can transfer energy without dissipation, that is, without energy loss, so a robust superconducting material can find widespread applications everywhere,” he said. At the moment, power companies still use copper wire for energy transmission, which carries
with it energy losses ranging from 30 to 40 percent from power plant to home or office. - See more at:

reader Luboš Motl said...

Dear Plato, superfluids and quark-gluon plasma may be viewed as "extreme fluids" so they're easy to confuse, perhaps. But by most measures, they're the opposite substances.

Superfluids have viscosity equal to zero. Quark gluon plasma has viscosity/entropydensity equal to 1/4*pi or so (perhaps times a finite factor of order one), very finite and pretty large, as also calculated from the AdS/CFT.

After all, the entropy density is also nonzero for QGP - the entropy of the vacuum has to be zero.

reader PlatoHagel said...

Yes opposite substances for sure, but in terms of superfluidity there are characteristics that shed light on the early universe, and as you mention. with regard to AdS/CFT.

So for me this is exciting, although, I dd not watch the episode, the idea here is far from any idea about aether in my view. Linked article in reply about research of roton, reveals an interesting correlation in my view about information transference capability in the early universe so this would seem quite natural for me as we push back our perspectives on the events of that early universe.

The theoretician and the experimentalism comes together, as we have seen in another blogger's expression of interest.

reader Shannon said...

LOL!... the horns... I had forgotten how funny Sheldon is.
Sorry I didn't see this one before.... :-D

reader Luboš Motl said...

Horn... You forgot how horny Sheldon is, right? :-))

reader Shannon said...

Haha I did... Easy to forget that Sheldon belongs to the family of horned animals :-)

reader Mikael said...

Hi Lubos,
great, I always wanted to know what this vacuum as a superconductor thing means. I think one thing to point out would be that the Higgs field actually aquires a non zero expectation value. So in this sense there is really something there in the vacuum.

reader John McVirgo said...

Haha, yeah Lubos sprung to mind when I heard 0:50:

"... I wish this blog would devote itself to real science, instead of wasting our time with crackpot wannabe theoreticians in a rush to publish"

Strangely, a Google search on this phrase only turns up the BBT Troll episode though.

reader Luboš Motl said...

Mikael, Yes or No. If we say that the vacuum expectation value of the Higgs is nonzero, E(H)=v, then it depends on the parameterization of the configuration space of the Higgs fields H. If we just subtract "v" from the relevant component of the Higgs,

h = H - v,

then the expectation value of the field "h" will be zero and the vacuum will therefore be "empty" according to your definition.

In general, one parameterization of the configuration space cannot be said to be "qualitatively better than another". The expectation value where H=v in the real vacuum is one that makes the electroweak symmetry more manifest. But there are other possible symmetries in the full theory that may be broken and whose unbroken points occur at "nonzero" expectation values if one uses some parameterization rooted in another symmetry-preserving point.

So whether some vev implies that the vacuum is non-empty depends on the conventions, on the reference configuration we are using to compare others with.

reader Luboš Motl said...

Right, sadly, there are not too many people in the world who sometimes say similar things. A TBBT character, your humble correspondent, and who is the third? Maybe Sheldon would say it to others, too. ;-)

reader Leo Vuyk said...

Lubos, You
wrote: “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

IMHO, there is a way out of the mass in motion problem, if:

The FORM and MICROSTRUCTURE of elementary particles, is supposed to be the origin of
FUNCTIONAL differences between Higgs- Graviton- Photon/Gluon-field and spinning propeller shaped Fermion particles.
If the vacuum is supposed to have resistance for these spinning propeller shaped
Fermions then this should be compensated by the energetic vacuum itself in
combination with a Fermionic propeller axis polarization and a so called Multiverse
based entanglement for each Fermion polarisation.
Cooper pairs are in that case, dual polarised connected non spinning-Fermion
propellers pushed from behind by the oscillating Higgs field.
Mass in motion in Quantum FFF Theory

reader W.A. Zajc said...

The viscosity to entropy density ratio for QGP is indeed finite, and about 1.5-2 times 1/4*pi at RHIC and 2-3 times 1/4*pi at the LHC. While the QGP’s viscosity is enormous (about 10^14 times that of water, and 100 times that of glass at the annealing point), so is its entropy density. The dimensionless ratio of viscosity to entropy density is smaller for QGP than for any other known substance - hence the “perfect liquid” appellation, since it’s this ratio that appears in the hydrodynamic equations of motion. The Ads/CFT calculation of precisely 1/4*pi was made in this famous paper by Kovtun, Son and Starinets. To appreciate how small 1/4*pi is, see Figure 2 in that paper, which compares the viscosity to entropy density ratio of liquid helium and water to this value.

reader Gordon said...

Well, Leonard should know all about fluids and condensates---after all, he started out as a plumber :)

reader Luboš Motl said...

Dear Bill, thanks for this addition! 1/4*pi may be very small from the viewpoint of someone like you who really has working practical experience with viscosities.

But for a full theories, it is a number of order one and a viscosity like that would be devastatingly high for a material's ability to pretend that it is vacuum. ;-) But so would any nonzero entropy density - there can't be any volume entropy density in the vacuum.

reader PlatoHagel said...

"In the quantum version of the theory, the state of higher energy density becomes unstable through barrier penetration; it is a false vacuum."

Well it is nice pushing back perspective on when the universe began......there has to to be some correlation with that thinking being experimentally pushed into questions regarding how the vacuum energy density had become the where is the false vacuum?

reader D Michael Mosher said...

I love it when those seeking a purely scientific answer to the UFT forget if your theory proves you don't exist, you aren't correct. There is something in our vacuum, else we wouldn't be here to postulate about it. Also, you are forgetting about entropy and homeostasis. There has to be something there for the vacuum to exist. The truth that every one seems to forget is the area of space is limitless and thus infinite, anything even the largest number imaginable is 0 when devided by infinity, so yes, whe taken against the back drop of infinity, the overall energy, the number of particles and population of the Galaxy is zero. But if it was truely zero, who of what would be discussing it right now. Science doesn't exist in a vacuum, and to think of space in the infinite is a huge mistake.

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