Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

TL;DR

This paper demonstrates that non-Markovian collapse models in quantum mechanics can be exactly reformulated as Bohmian theories, revealing deep connections and foundational implications between these two approaches.

Contribution

It shows that non-Markovian collapse models are mathematically equivalent to Bohmian theories with a carefully constructed bath, unifying these interpretations.

Findings

Collapse models can be recast as Bohmian theories with an extended system.

The stochastic wave-function in collapse models is conditioned on Bohmian hidden variables.

The noise in collapse models is a linear functional of Bohmian variables.

Abstract

Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schr\"odinger equation, and extract definite measurement outcomes either from the wave function (e.g. mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schr\"odinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predictions of orthodox quantum mechanics, whilst Bohmian mechanics can be argued to reproduce them. However, it turns out that collapse models and their primitive ontology can be exactly recast as Bohmian theories. More precisely, considering (i) a system described by a non-Markovian collapse model, and (ii) an extended system where a carefully tailored bath is added and described by Bohmian mechanics, the stochastic wave-function of the collapse model is exactly the wave-function of the original system conditioned on the Bohmian hidden variables of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian variables. The randomness that seems progressively revealed in the collapse models lies entirely in the initial conditions in the Bohmian-like theory. Our construction of the appropriate bath is not trivial and exploits an old result from the theory of open quantum systems. This reformulation of collapse models as Bohmian theories brings to the fore the question of whether there exists `unromantic' realist interpretations of quantum theory that cannot ultimately be rewritten this way, with some guiding law. It also points to important foundational differences between `true' (Markovian) collapse models and non-Markovian models.