Do(es the influence of) empty waves survive in configuration space?

TL;DR

This paper examines whether empty waves in the de Broglie-Bohm interpretation influence other particles in configuration space, finding that effective collapse can prevent such influence even when empty waves are present.

Contribution

It challenges the analogy between empty waves and radio-waves by showing that empty waves in configuration space may not influence other particles after a detection event.

Findings

Empty waves may not influence other particles post-detection.

Effective collapse occurs in configuration space.

Analogy with radio-waves is limited.

Abstract

The de Broglie-Bohm interpretation is a no-collapse interpretation, which implies that we are in principle surrounded by empty waves generated by all particles of the universe, empty waves that will never collapse. It is common to establish an analogy between these pilot-waves and 3D radio-waves, which are nearly devoided of energy but carry nevertheless information to which we may have access after an amplification process. Here we show that this analogy is limited: if we consider empty waves in configuration space, an effective collapse occurs when a detector clicks and the 3ND empty wave associated to a particle may not influence another particle (even if these two particles are identical, e.g. bosons as in the example considered here).