Objective collapse theory

Quantum mechanics
Uncertainty principle
Introduction Glossary History
Background Classical mechanics Old quantum theory Bra–ket notation Hamiltonian Interference
Fundamentals Complementarity Decoherence Entanglement Energy level Measurement Nonlocality Quantum number State Superposition Symmetry Tunnelling Uncertainty Wave function (collapse)
Experiments Afshar Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman Franck–Hertz Mach–Zehnder Popper Quantum eraser (delayed-choice) Schrödinger's cat Stern–Gerlach Wheeler's delayed-choice
Formulations Overview Heisenberg Interaction Matrix Phase-space Schrödinger Sum-over-histories (path integral)
Equations Dirac Klein–Gordon Pauli Rydberg Schrödinger
Interpretations Overview Bayesian Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective collapse Quantum logic Relational Stochastic Transactional
Advanced topics Quantum chaos Quantum computing Density matrix Quantum field theory Fractional quantum mechanics Quantum information science Relativistic quantum mechanics Scattering theory Quantum statistical mechanics
Scientists Aharonov Bell Blackett Bloch Bohm Bohr Born Bose de Broglie Candlin Compton Dirac Davisson Debye Ehrenfest Einstein Everett Fock Fermi Feynman Glauber Gutzwiller Heisenberg Hilbert Jordan Kramers Pauli Lamb Landau Laue Moseley Millikan Onnes Planck Rabi Raman Rydberg Schrödinger Sommerfeld von Neumann Weyl Wien Wigner Zeeman Zeilinger

Objective collapse theories, also known as quantum mechanical spontaneous localization models (QMSL), are an approach to the interpretational problems of quantum mechanics. They are realistic, indeterministic and reject hidden variables. The approach is similar to the Copenhagen interpretation, but more firmly objective.

The most well-known examples of such theories are:

• Ghirardi–Rimini–Weber theory
• Penrose interpretation

Compared to other approaches

Collapse theories stand in opposition to many-worlds interpretation theories, in that they hold that a process of wavefunction collapse curtails the branching of the wavefunction and removes unobserved behaviour. Objective collapse theories differ from the Copenhagen interpretation in regarding both the wavefunction and the process of collapse as ontologically objective. The Copenhagen interpretation includes collapse, but it is non-committal about the objective reality of the wave function, and because of that it is possible to regard Copenhagen-style collapse as a subjective or informational phenomenon. In objective theories, there is an ontologically real wave of some sort corresponding to the mathematical wave function, and collapse occurs randomly ("spontaneous localization"), or when some physical threshold is reached, with observers having no special role.

Variations

Objective collapse theories regard the present formalism of quantum mechanics as incomplete, in some sense. (For that reason it is more correct to call them theories than interpretations.) They divide into two subtypes, depending on how the hypothesised mechanism of collapse stands in relation to the unitary evolution of the wavefunction.

1. Collapse is found "within" the evolution of the wavefunction, often by modifying the equations to introduce small amounts of non-linearity. A well-known example is the Ghirardi–Rimini–Weber theory^[1] (GRW).
2. The evolution of the wavefunction remains unchanged, and an additional collapse process ("Objective reduction") is added, or at least hypothesised. A well-known example is the Penrose interpretation, which links collapse to gravitational stress in general relativistic spacetime, with the threshold value being one graviton.

Problems and drawbacks

GRW collapse theories have unique problems. In order to keep these theories from violating the principle of the conservation of energy, the mathematics requires that any collapse be incomplete. Almost all of the wave function is contained at the one measurable (and measured) value, but there are one or more small "tails" where the function should intuitively equal zero but mathematically does not. It is not clear how to interpret these "tails". They might mean that a small bit of matter has collapsed elsewhere than the measurement indicates, that with very low probability an object might "jump" from one collapsed state to another, or something else entirely. All of these options seem counterintuitive.

The original QMSL models had the drawback that they did not allow dealing with systems with several identical particles, as they did not respect the symmetries or antisymmetries involved. This problem was addessed by a revision of the original GRW proposal known as CSL (continuous spontaneous localization) developed by Ghirardi, Pearle Rimini in 1990.

Notes

• Giancarlo Ghirardi , Collapse Theories, Stanford Encyclopedia of Philosophy (First published Thu Mar 7, 2002; substantive revision Tue Nov 8, 2011)

See also