Contextuality of the probability current in quantum mechanics

TL;DR

This paper examines the properties of quantum probability currents, revealing discontinuities in flux lines under different experimental contexts and frames, challenging the notion of a consistent relativistic quantum fluid.

Contribution

It highlights the contextual and frame-dependent discontinuities of quantum probability currents, questioning the possibility of a relativistically consistent quantum fluid model.

Findings

Flux lines of quantum probability current show discontinuities with setup changes.

Discontinuities occur in both non-relativistic and relativistic frameworks.

A consistent relativistic quantum probability fluid cannot be defined.

Abstract

We revisit an argument proposed by Hardy \cite{Hardy-1} concerning local realistic theories, but in terms of the motion of the probability fluid and its current within standard quantum mechanic. We emphasize surprising properties of the flux lines of this current in configuration space, in particular (quasi) discontinuous variations when the context (the experimental setup) is changed. This occurs in both Galilean and Einsteinian relativity. In the latter case, discontinuous variations also appear without changing the setup, when the Lorentzian reference frame is changed. A relativistically consistent definition of the motion of a quantum probability fluid is therefore impossible.