“On the existence of empty waves in quantum theory”: a comment

Lucién Hardy

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.

Ladislav Kocis

X. Y. Zou, T. Grayson, L. J. Wang +1 more

The de Broglie pilot wave theory is a hybrid of quantum and classical concepts that was introduced in order to avoid the conceptual difficulties of the Copenhagen interpretation. According to some versions of this theory, there exist both photons and electromagnetic waves, and the waves are supposed not only to yield probabilities for the photons, but also to have a physical reality. Even an ″empty″ wave, which cannot give rise to photoelectric detection, is supposed to be capable of inducing observable effects. We have tested this theory in an experiment with two cascaded parametric down-converter crystals, in which the idler beam from the first crystal has been shown to induce coherence between the signal beams from the two crystals without inducing any emission. When the photon is removed from the first idler with the help of a beam splitter, the remaining empty wave is found not to induce coherence.

Pavel Bóna

Daniel M. Greenberger, Michael Horne, Herbert Joseph Bernstein +1 more

We recently proved a theorem extending the Greenberger-Horne-Zeilinger (GHZ) Theorem from multi-particle systems to two-particle systems. This proof depended upon an auxiliary assumption, the EPNT assumption (Emptiness of Paths Not Taken). According to this assumption, if there exists an Einstein-Rosen-Podolsky (EPR) element of reality that determines that a path is empty, then there can be no entity associated with the wave that travels this path (pilot-waves, empty waves, etc.) and reports information to the amplitude, when the paths recombine. We produce some further evidence in support of this assumption, which is certainly true in quantum theory. The alternative is that such a pilot-wave theory would have to violate EPR locality.