What is a Particle?

This is a short reflection on the notion of a ‘particle’ in particular and on the methodology of physics in general.

Abstract

According to the (Oxford English Dictionary) a particle is: “A minute fragment or quantity of matter; the smallest perceptible or discernible part of an aggregation or mass.”. This agrees with the commonsense definition of particles as ‘small things, out of which the bigger things are made of’.
Clearly, such a concept of particle is deeply rooted in the atomistic vision of the physical world, which — in turn — is supported by the development of physics in the past two centuries.
In philosophy of physics the ‘particle’ is often treated as a primitive notion (cf. (Eckstein and Heller 2022)), that is a concept which is “immediately understandable” and “employed without explaining its meaning” (Tarski 1994). The simplest example of such a primitive notion is that of a point in geometry.
Within an axiomatic approach, the primitive notions are utilised to spell out the axioms. Consequently, they are taken for granted, though they might be connected or restricted by the axioms. For instance, in geometry the axiom: “For every two points there exists a line that contains them both.” links the primitive notions of a point and a line.
In this spirit, particles as primitive concepts appear, in parallel to “light rays” in the celebrated Ehlers–Pirani–Schild (EPS) axiomatisation of relativistic spacetime (Elhers, Pirani, and Schild 1972). More precisely, the authors take ‘particle’ to mean a “worldline of a freely falling particle”. In either case, on the notions of particles and light rays a quasi-operational axiomatic system of a Lorentzian spacetime is established. As the authors admit, the particles are understood in the classical sense as “bodies whose extension and structure can, under suitable circumstances, be neglected”. In fact, assuming that the particles are quantum or, more generally, non-classical, may lead to very different structures and axiomatics (Adlam, Linnemann, and Read 2022; Eckstein and Heller 2022).