The roads not taken: empty waves, wave function collapse and protective measurement in quantum theory

Abstract

Within the class of ontological interpretations of quantum theory where a physical system comprises a particle and a field (wavefunction) guiding it, an empty wave is a segment of the wavefunction not containing the particle. We examine the impact of this concept on the debate between the epistemological and ontological viewpoints. The theoretical merits of the empty wave in avoiding the wavefunction collapse hypothesis, and in supplying conceptual precision in the application of quantum mechanics, are emphasized. Particular reference is made to path detection in interferometry and it is shown how a consistent application of the particle and empty wave concepts dispels the suggestion that this is a theory. The problem of how the reality of an empty wave might be demonstrated by its effect on other systems is examined and general arguments advanced against this possibility. However, these arguments are not conclusive and we describe how the technique of protective measurement suggests a method to probe the empirical implications of empty waves and potentially distinguish between the epistemological and ontological perspectives.