Topological phase transitions for the whole universe...?

Question

Physicist Grigory Volovik has put forward some ideas about the universe undergoing a topological phase transition (especially in the early stages of the universe). He published a book called "The Universe in a Helium Droplet" where he explained his ideas. You can find a brief discussion about it here.

In one discussion I had with Mr. Volovik, he mentioned that depending on the type of topological phase transition that could have occurred in the universe, all the fundamental symmetries of the universe (spacetime symmetries, translation symmetries, CPT invariance, internal invariances...) could be all emergent from a more fundamental state without symmetries (like in Holger Nielsen's random dynamics proposal where all symmetries in the universe would be emergent)

I asked him if this was all speculation or if there was some truth behind and he replied that although we don't know if the universe actually took this "path", we know that this topological phase transition would be possible. But is this true? Would that be possible according to what we currently know about physics (although we don't know if this actually occurred at some point of the universe's history)? Or, on the contrary, we don't even know if these transitions are even possible to begin with?

Answer 1

There is a general misunderstanding regarding symmetry and order. People from time to time conflate symmetry with order. But they are two different notions.

Let's look at an example:

• A: a crowd of people walk in random directions.
• B: a crowd of people walk in the same direction.

B is obviously more ordered than A. However A enjoys higher symmetry, since A is rotationally symmetric, while B losses the rotational symmetry since B picks out a specific direction.

Folks like Volovik come from the condensed matter physics background. They are familiar with Landau's phase transition paradigm, where a certain order parameter gains non-zero expectation value upon a phase transition.

A quintessential example is the superconductivity phase transition, where the BCS order parameter breaks the $U(1)$ gauge symmetry. It should be highlighted that the superconductivity order breaks symmetry, rather than generating symmetry.

In our physical world, order might be emergent via phase transition , while symmetry is usually spontaneously broken in the process. Therefore, if someone talks about the fundamental symmetries of the universe being emergent through phase transition (topological or not), you should be very careful about what he/she really means by "symmetry".