About empty waves, their effect, and the quantum theory

TL;DR

This paper investigates whether empty waves in quantum mechanics can have observable effects, proposing an experiment to test this and analyzing its implications for the validity of the full/empty wave hypothesis within quantum theory.

Contribution

It introduces a more feasible experiment to detect empty wave effects and analyzes its implications, challenging the full/empty wave hypothesis within quantum formalism.

Findings

The experiment suggests empty waves influence observable phenomena.

Quantum theory does not support the full/empty wave hypothesis.

The proposed experiment is more intuitive and practically feasible.

Abstract

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.