Condensed matter systems break Lorentz boosts for the simple reason of existing and being at rest in some frame, but maintain some type of homogeneity and isotropy. In particular, since, to the best of our knowledge, fundamental theories are Lorentz invariant, boosts are always broken spontaneously. Taking these basic features as the defining properties of condensed matter allows a systematic classification of 8 possible symmetry breaking patterns. Such a classification contains, among others, solids, fluids and superfluids. Some known physical systems evade such a classification. Others belong to it but are not realised in nature. In particular, nature seems to systematically avoid all those–in principle, conceivable–systems that contain the Goldstone bosons of the broken Lorentz boosts.

Centre de Physique Theorique de Marseille (CPT)