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

2008/07/12 by Valia Allori, Sheldon Goldstein, Roderich Tumulka +1 · 14 citations
Physics and Astronomy · #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #Noncommutative and Quantum Gravity Theories

paper · doi:10.1093/bjps/axn012

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. 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?

Citations

• A Philosopher Looks at Quantum Mechanics (Again)

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