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Probabilities in deBroglie-Bohm Theory: Towards a Stochastic Alternative

Dürr, Patrick and Ehmann, Alexander (2017) Probabilities in deBroglie-Bohm Theory: Towards a Stochastic Alternative. [Preprint]

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Abstract

We critically examine the role and status probabilities, as they enter via the Quantum Equilibrium Hypothesis, play in the standard, deterministic interpretation of deBroglie’s and Bohm’s Pilot Wave Theory (dBBT), by considering interpretations of probabilities in terms of ignorance, typicality and Humean Best Systems, respectively. We argue that there is an inherent conflict between dBBT and probabilities, thus construed. The conflict originates in dBBT’s deterministic nature, rooted in the Guidance Equation. Inquiring into the latter’s role within dBBT, we find it explanatorily redundant (in particular for dBBT’s solution of the Measurement Problem, which only requires that the corpuscles possess definite positions), and subject to a number of difficulties. Following a suggestion from Bell, we propose to abandon the Guidance Equation, whilst retaining dBBT’s point particle-based Primitive Ontology, with positions as local beables. The resultant theory, which we identify as a stochastic, minimally deBroglie-Bohmian theory, describes a random walk through configuration space. Its probabilities, we propose, are best understood as dispositions of possible corpuscle configurations to manifest themselves. We subsequently evaluate the merits of sdBBT vis-à-vis dBBT, such as the justification of the Symmetrisation Postulate and the violation of the Action-Reaction Principle. Not only is sdBBT an attractive Bohmian theory that, whilst retaining dBBT's virtues, overcomes many of its shortcomings; it also sparks off a number of exciting follow-up questions, such as a comparison between sdBBT and other stochastic hidden-variable theories, e.g. Nelson Stochastics, or between sdBBT and the Everett interpretation.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Dürr, Patrickpatrick-duerr@gmx.de
Ehmann, AlexanderAlexanderEhmann@AlexanderEhmann.com
Keywords: Bohmian Mechanics, Probabilities, Primitive Ontology, Bell's Version of the Everett Interpretation, Dispositions, Temporal Solipsism
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Mr. Patrick M. Duerr
Date Deposited: 26 Feb 2017 15:04
Last Modified: 26 Feb 2017 15:04
Item ID: 12859
Subjects: Specific Sciences > Physics > Quantum Mechanics
Date: 20 January 2017
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/12859

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