The Wallstrom objection as a possibility to augment quantum theory

TL;DR

This paper explores how adding a physical restriction to quantum theories based on Madelung variables can help distinguish and potentially falsify certain interpretations, especially in relativistic scalar fields.

Contribution

It introduces a physical restriction to quantum theories with Madelung variables, analyzing its implications for falsifiability and interpretation choices in relativistic quantum fields.

Findings

Adding the restriction enhances empirical testability of these theories.

Particle ontology variants are more likely to be falsified than field ontology variants.

Switching to a field ontology may circumvent the Wallstrom objection.

Abstract

Wallstrom has argued that quantum interpretations which construct the wave function starting from Madelung variables $\psi(q)=\rho(q)\exp(\frac{i}{\hbar}S(q))$, in particular, many variants of Nelsonian stochastics, are not equivalent to quantum theory. Accepting this, we explicitly add the physical restriction $(\forall q\in Q)|\psi(q)|^2>0$ in the configuration space representation to quantum theory. The resulting theories depend on the choice of the configuration space $Q$. The restriction adds possibilities to falsify such theories, making them preferable following Popper's criterion of empirical content until they have been really falsified. Considering the case of a relativistic scalar field, we argue that it is reasonable to expect that the variant based on particle ontology can be (or even has been already) falsified, while to falsify the variant based on field ontology seems much harder, if not impossible. If correct, switching to a field ontology seems a reasonable choice for interpretations based on Madelung variables to circumvent the Wallstrom objection.