7 - Do Symmetries ‘Explain’ Conservation Laws? The Modern Converse Noether Theorem vs Pragmatism

Summary

Noether’s first theorem, in its modern form, does not establish a one-way explanatory arrow from symmetries to conservation laws, but such an arrow is widely assumed in discussions of the theorem in the physics and philosophy literature. It is argued here that there are pragmatic reasons for privileging symmetries, even if they do not strictly justify explanatory priority. To this end, some practical factors are adduced as to why Noether’s direct theorem seems to be more well-known and exploited than its converse, with special attention being given to the sometimes overlooked nature of Noether’s converse result and to its strengthened version due to Luis Martínez Alonso in 1979 and independently Peter Olver in 1986.