Empty waves: A genuine effect?

Constantine Pagonis

Lucién Hardy

S. Jeffers, J. Sloan

Robert B. Griffiths

Sofia Wechsler

When a quantum object -- a particle as we call it in a non-rigorous way -- is described by a multi-branched wave- function, with the corresponding wave-packets occupying separated regions of the time-space, a frequently asked question is whether the quantum object is actually contained in only one of these wave-packets. If the answer is positive, then the other wave-packets are called in literature empty waves. The wave-packet containing the object is called a full wave, and is the only one that would produce a recording in a detector. A question immediately arising is whether the empty waves may also have an observable effect. Different works were dedicated to the elucidation of this question. None of them proved that the hypothesis of full/empty waves is correct - it may be that the Nature is indeed non-deterministic and the quantum object is not confined to one region of the space-time. All the works that proved that the empty waves have an effect, in fact, proved that if there exist full and empty waves, then the latter may have an observable effect. This is also the purpose and the limitation of the present work. What is shown here is that if the hypothesis is true, the empty waves have an influence. An experiment is indicated which reveals this influence. The analysis of the experiment is according to the quantum formalism. This experiment has the advantage of being more intuitive and practically more feasible than a previous proposal also in agreement with the quantum formalism. However, the presently proposed experiment also shows that the quantum theory is not in favor of the above hypothesis.

Peter Holland

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.