Symmetry, crystals, and "time crystals"

"Spontaneous symmetry breaking" is a profound idea from condensed matter physics that has been adopted with a vengeance by the high energy physics community. Let me give an example. The laws of physics are, as far as we know, "translationally invariant" - they don't depend on our location in space, and if we move a little bit nothing happens to those laws. That's translational symmetry (and it turns out it's deeply connected to conservation of momentum, but that's another story). However, if we consider atoms moving about in space and worry about what configurations they like to adopt, the atoms tend spontaneously to adopt a lower symmetry state. For example, atoms will often arrange themselves into a regular spatial periodicity that we call a crystal structure. Now instead of space being continuously translationally invariant, the arrangement of atoms has a discrete translational symmetry - the arrangement of atoms reproduces itself if translated by integer multiples of a particular lattice parameter.

This week, two papers (here and here) appeared, from (the polymath) Frank Wilczek's group at MIT. Wilczek is one of the rare theorists who moves seamlessly between condensed matter and high energy theory. In these papers, the idea of "time crystals" is discussed. As science fiction-y as this sounds, it's real, but it is an application of this idea of spontaneous symmetry breaking, not some exotic Doctor Who concept. In analog with the above discussion, as far as we know, the laws of physics are also invariant under translations in time. The idea in these papers is that dynamical systems may spontaneously break that continuous translational invariance, and exhibit discrete time translation invariance instead. That means that dynamical systems may spontaneously take on periodicity in time! I need to read the second paper in detail soon - the quantum versions of these ideas seems very deep....