Abstract

The study of the ontology of theoretical symmetries in physics has long being the question of choice between the usual Newtonian and Leibnizian interpretations. These were saying respectively that a theoretical symmetry corresponds to unobservable changes or is a mere mathematical surplus. But recently the notions of direct empirical status and indirect empirical status were introduced in addition. DES is usually defined as a status that a theoretical symmetry has when it is matched with an empirical symmetry in the world. IES is usually described as an empirical status opposed to DES and exemplified by the fact for theoretical symmetries to entail conservation laws via Noether's theorems. In this contribution I provide a framework for thinking of the ontology of theoretical symmetries in terms of their components, describe with its help the usual Newtonian and Leibnizian interpretations of theoretical symmetries, compare with them the ontological significance bestowed on theoretical symmetries by DES and IES, and generalise these empirical statuses further. I also pay a particular attention to whether global/local distinctions matter to any of the ontological interpretations and statuses considered, and the conclusion is that they do not.