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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