The Superfluid Universe

Several advocates of an “emergence” approach to fundamental physics come from the world of condensed matter physics (an old blog post which briefly discussed Robert B. Laughlin’s views is here).

Grigory Volovik is a prominent (and award-winning) theorist who has been working on applying the knowledge gained in his research on superfluids to the case of explaining how gravity and the matter fields of current theory may themselves be emergent features of a deeper reality – a sort of “super” quantum vacuum. {UPDATED 2 February 2008 -- minor edits}

Until recently I had only read a little about superfluids or condensed matter physics. Superfluids have surprising collective behaviors (like zero viscosity) which can be topologically stable despite micro-physical imperfections. Although their characteristics are exhibited at a macroscopic scale, the tools of quantum field theory are needed to explain them. As he explains in this older article (from 1999), Volovik thinks one particular variety of superfluid even displays characteristics which make it a good model for the entire universe: this is the one created by supercooling the He-3 helium isotope. In reaching this conclusion, he explains that the condensed matter system used must be fermionic. We need both fermionic and bosonic fields and in the He-3 superfluid the atoms behave as fermions, and quantum bose fields appear as low-energy collective modes. (Interestingly, in He-4 superfluid, the atoms behave as bosons – who knew? – and I guess there is no analogous way to recover fermions as some collective mode). Now, a He-3 superfluid is not the only fermionic system (or Fermi system) known, and Volovik explains how the topologies differ between the alternatives (he looks at systems which feature a “Fermi surface” as opposed to the “Fermi point” of He-3). He concludes the He-3 superfluid’s topology has the symmetries which create analogous features with the quantum fields of particle physics and also of gravity. It is hard for me to follow the details, but it looks like an impressive match, although Volovik concedes in the article that he hasn’t shown that analogies exist for quite the whole particle zoo of the standard model.

Now, in this recent paper, “Emergent Physics: Fermi point scenario”, one can see that Volovik’s confidence that his work shows the right path to fundamental physics has grown. In the paper, he begins by discussing the cosmological constant problem and the particle mass hierarchy problem, as a prelude to explaining why they are more natural expectations of his model.

First he explains that in a Fermi point vacuum all of physical laws (except for quantum mechanics itself) can be seen as effective laws which naturally emerge at low energy. He discusses again how the symmetries of the Fermi point system give one the fields of particle physics and gravity. He then shows how vacuum energies get nullified in a way that leads to consistency with a low cosmological constant. When it comes to the hierarchy problem, the Fermi point system has elements which come from macroscopic (topologically robust) emergent features and ones which come from micro-structure. The observed masses (or zero masses) of various particles are shown to be consistent (in approximate order of magnitude) with the model. (Again, I have trouble following the specific arguments here, so please see the paper.)

In a concluding section, Volovik explains the contrast between his approach, which treats gravity as an effective emergent theory, and other approaches to quantum gravity which treat general relativity as something fundamental and then try (so far unsuccessfully) to unify it with the standard model.

(Note also that Volovik has a full-length book on this topic, which I have not read, called: The Universe in a Helium Droplet)

This is the first time I’ve grappled with Volovik’s approach and any thoughts I have are extremely tentative. I would say at this point that his model adds to a growing argument that emergent approaches to fundamental physics are promising. On the other hand, it still seems to be more of an analogy rather than a candidate for a fundamental theory. The reason I say this is that the toolkit for analyzing the Fermi point system (and other condensed matter systems) is quantum field theory. The approach, then, seems to have a circular aspect to it: one is trying to explain gravity (among other things) using a theory which has a formalism which embeds a background (flat, special relativistic) space-time. If there could be a way to get the same kind of outcome starting only with (a network of?) elementary quantum mechanical systems, that might be a better candidate for a fundamental theory.