Imprints of the underlying structure of physical theories

Abstract

In the context of scientific realism, this paper intends to provide a formal and accurate description of the structural-based ontology posited by classical mechanics, quantum mechanics and special relativity, which is preserved across the empirical domains of these theories and explain their successful predictions. Along the lines of ontic structural realism, such a description is undertaken by a particular ontological commitment: the belief in the existence of a freestanding actual structure, approximately represented by a subgroup of the Inhomogeneous Symplectic Group (up to group homomorphisms), and their corresponding state-space representations. Accordingly, the hierarchy and the complexity of this group-theoretical structure is represented by appropriate philosophical tools, namely, by the language of partial structures. Upon this approach, the lack of knowledge of some relations that hold at the boundary between mathematics and physics, and the presence of surplus structure within the structural edifice are explored and represented. The conclusive issue appeals to an interesting example of a surplus but fruitful structure, where superposition of states with different mass are suggested to be actual relativistic remnants within non-relativistic quantum mechanics, as opposed to the standard interpretation in which they are empirically meaningless.