The explanatory role of empty waves in quantum theory

In this chapter we are concerned with two classes of interpretations of quantum mechanics: the epistemological (the historically dominant view) and the ontological. The first views the wave function as just a repository of (statistical) information on a physical system. The other treats the wave function primarily as an element of physical reality, whilst generally retaining the statistical interpretation as a secondary property. There is as yet only theoretical justification for the program of modelling quantum matter in terms of an objective spacetime process; that some way of imagining how the quantum world works between measurements is surely better than none. Indeed, a benefit of such an approach can be that “measurements” lose their talismanic aspect and become just typical processes described by the theory.

In the quest to model quantum systems one notes that, whilst the formalism makes reference to “particle” properties such as mass, the linearly evolving wave function ψ(x) does not generally exhibit any feature that could be put into correspondence with a localized particle structure. To turn quantum mechanics into a theory of matter and motion, with real atoms and molecules consisting of particles structured by potentials and forces, it is necessary to bring in independent physical elements not represented in the basic formalism. The notion of an “empty wave” is peculiar to those representatives of this class of extended theories which postulate that the additional physical element is a corpuscle-like entity or point particle. For clarity, we shall develop the discussion in terms of a definite model of this kind whose properties are well understood and which it is established reproduces the empirical content of quantum mechanics: the de Broglie–Bohm theory, a prominent representative of the class of ontological interpretations (Holland, 1993).