Bohmian Collapse

Wilhelm, Isaac

Antoine Tilloy, Howard M. Wiseman

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 Schrödinger 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 Schrödinger 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.

Marko Toroš, Sandro Donadi, Angelo Bassi

Abstract We discuss the emergence of classical trajectories in Bohmian mechanics, when a macroscopic object interacts with an external environment. We show that in such a case the conditional wave function of the system follows a dynamics which, under reasonable assumptions, corresponds to that of the Ghirardi–Rimini–Weber (GRW) collapse model. As a consequence, Bohmian trajectories evolve classically. Our analysis also shows how the GRW (istantaneous) collapse process can be derived by an underlying continuous interaction of a quantum system with an external agent, thus throwing a light on how collapses can emerge from a deeper level theory.

Mauricio Suárez

Roman Sverdlov

The purpose of this paper is to unite Pilot Wave model with GRW ideas through a proposal that Bohmian particle serves as a source of continuous collapse. The continuous trajectory of a particle allows the particle-centered collapse mechanism to be continuous as well. This allows us to remove the "stochastic" element from typical GRW proposals.

Detlev Dürr, Sheldon Goldstein, Roderich Tumulka +1 more