Journal Article

On the Common Structure of Bohmian Mechanics and the Ghirardi–Rimini–Weber Theory

Valia Allori, Sheldon Goldstein, Roderich Tumulka and Nino Zanghì

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 59, issue 3, pages 353-389
Published in print September 2008 | ISSN: 0007-0882
Published online July 2008 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axn012
On the Common Structure of Bohmian Mechanics and the Ghirardi–Rimini–Weber Theory

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Bohmian mechanics and the Ghirardi–Rimini–Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about ‘matter’ moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of space-time points. The role of the wave function then is to govern the motion of the matter.

Introduction

Bohmian Mechanics

Ghirardi, Rimini, and Weber 3.1

GRWm

3.2

GRWf

3.3

Empirical equivalence between GRWm and GRWf

Primitive Ontology 4.1

Primitive ontology and physical equivalence

4.2

Primitive ontology and symmetry

4.3

Without primitive ontology

4.4

Primitive ontology and quantum state

Differences between BM and GRW 5.1

Primitive ontology and quadratic functionals

5.2

Primitive ontology and equivariance

A Plethora of Theories 6.1

Particles, fields, and flashes

6.2

Schrödinger wave functions and many-worlds

The Flexible Wave Function 7.1

GRWf without collapse

7.2

Bohmian mechanics with collapse

7.3

Empirical equivalence and equivariance

What is a Quantum Theory without Observers?

Journal Article.  14793 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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