Online research in philosophy

Schrödinger’s first proposal for the interpretation of quantum mechanics was based on a postulate relating the wave function on configuration space to charge density in physical space. Schrödinger apparently later thought that his proposal was empirically wrong. We argue here that this is not the case, at least for a very similar proposal with charge density replaced by mass density. We argue that when analyzed carefully, this theory is seen to be an empirically adequate many-worlds theory and not an empirically (...) inadequate theory describing a single world. Moreover, this formulation—Schrödinger’s first quantum theory—can be regarded as a formulation of the many-worlds view of quantum mechanics that is ontologically clearer than Everett’s. (shrink)

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? CiteULike Connotea Del.icio.us What's this? (shrink)

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. (shrink)