Fundamentality, Effectiveness and Objectivity of Gauge Symmetries

Much recent philosophy of physics has investigated the process of symmetry breaking. Here, I critically assess the alleged symmetry restoration at the fundamental scale. I draw attention to the contingency that gauge symmetries exhibit, i.e. the fact that they have been chosen from among a countably infinite space of possibilities. I appeal to this feature of group theory to argue that any metaphysical account of fundamental laws that expects symmetry restoration up to the fundamental level is not fully satisfactory. This is a symmetry argument in line with Curie’s 1 st principle. Further, I argue that this same feature of group theory helps to explain the “unreasonable” effectiveness of (this subfield of) mathematics in (this subfield of) physics, and that it reduces the philosophical significance that has been attributed to the objectivity of gauge symmetries