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

By V. Allori, Sheldon Goldstein, Roderich Tumulka, Nino Zanghí. British Journal for the Philosophy of Science, 2006

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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. 1. Introduction2. Bohmian Mechanics3. Ghirardi, Rimini, and Weber3.1. GRWm3.2. GRWf3.3. Empirical equivalence between GRWm and GRWf4. Primitive Ontology4.1. Primitive ontology and physical equivalence4.2. Primitive ontology and symmetry4.3. Without primitive ontology4.4. Primitive ontology and quantum state5. Differences between BM and GRW5.1. Primitive ontology and quadratic functionals5.2. Primitive ontology and equivariance6. A Plethora of Theories6.1. Particles, fields, and flashes6.2. Schrödinger wave functions and many-worlds7. The Flexible Wave Function7.1. GRWf without collapse7.2. Bohmian mechanics with collapse7.3. Empirical equivalence and equivariance8. What is a Quantum Theory without Observers? Introduction Bohmian Mechanics Ghirardi, Rimini, and Weber3.1. GRWm3.2. GRWf3.3. Empirical equivalence between GRWm and GRWf GRWm GRWf Empirical equivalence between GRWm and GRWf Primitive Ontology4.1. Primitive ontology and physical equivalence4.2. Primitive ontology and symmetry4.3. Without primitive ontology4.4. Primitive ontology and quantum state Primitive ontology and physical equivalence Primitive ontology and symmetry Without primitive ontology Primitive ontology and quantum state Differences between BM and GRW5.1. Primitive ontology and quadratic functionals5.2. Primitive ontology and equivariance Primitive ontology and quadratic functionals Primitive ontology and equivariance A Plethora of Theories6.1. Particles, fields, and flashes6.2. Schrödinger wave functions and many-worlds Particles, fields, and flashes Schrödinger wave functions and many-worlds The Flexible Wave Function7.1. GRWf without collapse7.2. Bohmian mechanics with collapse7.3. Empirical equivalence and equivariance GRWf without collapse Bohmian mechanics with collapse Empirical equivalence and equivariance What is a Quantum Theory without Observers?

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

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