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The British Journal for the Philosophy of Science Advance Access published online on July 11, 2008
The British Journal for the Philosophy of Science, doi:10.1093/bjps/axn012
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© The Author (2008). Published by Oxford University Press on behalf of British Society for the Philosophy of Science. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

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

Dedicated to GianCarlo Ghirardi on the occasion of his 70th birthday

Valia Allori, Sheldon Goldstein, Roderich Tumulka and Nino Zanghì

Department of Philosophy, Northern Illinois University, Zulauf Hall 920, DeKalb, IL 60115, USA vallori{at}niu.edu
Department of Mathematics, Physics and Philosophy, Rutgers, the State University of New Jersey, Hill Center, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA oldstein{at}math.rutgers.edu
Department of Mathematics, Rutgers, the State University of New Jersey, Hill Center, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA tumulka{at}math.rutgers.edu
Dipartimento di Fisica dell'Università di Genova, and INFN sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy zanghi{at}ge.infn.it


  Abstract

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.

  1. Introduction
  2. Bohmian Mechanics
  3. Ghirardi, Rimini, and Weber
    3.1 GRWm
    3.2 GRWf
    3.3 Empirical equivalence between GRWm and GRWf

  4. 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

  5. Differences between BM and GRW
    5.1 Primitive ontology and quadratic functionals
    5.2 Primitive ontology and equivariance

  6. A Plethora of Theories
    6.1 Particles, fields, and flashes
    6.2 Schrödinger wave functions and many-worlds

  7. The Flexible Wave Function
    7.1 GRWf without collapse
    7.2 Bohmian mechanics with collapse
    7.3 Empirical equivalence and equivariance

  8. What is a Quantum Theory without Observers?


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