The principle that (RT) symmetry transformations always relate solutions that are representationally equivalent has been widely endorsed in the philosophy of symmetries. In recent years, however, it has been argued that this principle is false. The most well-known argument in this respect is developed by Gordon Belot in “Symmetry and Equivalence,” where he presents several cases of symmetry transformations of differential equations that map solutions onto other solutions that do not seem to represent physically equivalent states of the system. For example, there are symmetries of the harmonic oscillator that map a state of the spring characterized by certain positive amplitude A onto a different state where the amplitude is zero. As Belot puts it, “an approach to understanding physical theories that leaves us unable to see these distinctions is not something we can live with.” In this talk, I show that the cases Belot presents do not succeed once we are explicit about how the mathematical equations in our model are being used to represent the concrete physical systems in question. More precisely, I show that once we are explicit about (a) the concrete system that we want to model, (b) the kind of model we want to use, and (c) the types of measurements that we want to consider, a natural interpretation of the symmetries in question arises that is compatible with (RT). I end the talk by connecting my proposal to David Wallace’s recent work on the philosophy of symmetries.
Philosophy of Physics Seminar Convenor for MT21: James Read | Philosophy of Physics Group Website