2019/05/07 by I. Schmelzer, Ilja Schmelzer, Schmelzer, Ilja · 1 citation
Arts and Humanities · Physics and Astronomy · Psychology · #FOS: Physical sciences #Philosophy and History of Science #Philosophy and Theoretical Science #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1905.03075
arxiv created 2019/05/07 · openalex publication_date 2019/05/07 · arxiv updated 2019/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Wallstrom has argued that quantum interpretations which construct the wave function starting from Madelung variables ψ(q)=ρ(q)exp((i)/(ℏ)S(q)), in particular, many variants of Nelsonian stochastics, are not equivalent to quantum theory. Accepting this, we explicitly add the physical restriction (∀ q∈ Q)|ψ(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.