A disputable assumption behind the empirical equivalence between pilot-wave theory and standard quantum mechanics

TL;DR

This paper critically examines the assumptions underpinning the claimed empirical equivalence between pilot-wave theory and standard quantum mechanics, questioning the validity of key derivations related to uncertainty and measurement outcomes.

Contribution

It identifies and analyzes a questionable assumption in the derivations of absolute uncertainty and POVMs, challenging the claimed foundational equivalence.

Findings

The assumption that 'information is always configurationally grounded' is problematic.

Questioning this assumption affects the derivations of absolute uncertainty and POVMs.

Implications for the foundational claims of pilot-wave theory are significant.

Abstract

The de Broglie-Bohm pilot-wave theory asserts that a complete characterization of an $N$-particle system is given by its wave function together with the (at-all-times-defined) positions of the particles, with the wave function always satisfying the Schr\"odinger equation and the positions evolving according to the deterministic "guiding equation". A complete agreement with the predictive apparatus of standard quantum mechanics, including the uncertainty principle and the probabilistic Born rule, is then said to emerge from these equations, without having to confer any special status to measurements or observers. Two key elements behind the proof of this complete agreement are absolute uncertainty and the POVM theorem. The former involves an alleged "naturally emerging, irreducible limitation on the possibility of obtaining knowledge within pilot-wave theory" and the latter establishes that the outcome distributions of all measurements are described by POVMs. Here, we argue that the derivations of absolute uncertainty and the POVM theorem depend upon the questionable assumption that "information is always configurationally grounded". We explain in detail why the offered rationale behind such an assumption is deficient and explore the consequences of having to let go of it.