Objective collapse theory

Quantum mechanics
$\Delta x\, \Delta p \ge \frac{\hbar}{2}$ Uncertainty principle
Introduction Mathematical formulations
Background Classical mechanics Old quantum theory Interference Bra-ket notation Hamiltonian
Fundamental concepts Quantum state · Wave function Superposition · Entanglement Complementarity · Duality Uncertainty · Measurement Exclusion · Decoherence Ehrenfest theorem Tunnelling · Nonlocality
Experiments Double-slit · Davisson–Germer Stern–Gerlach · Bell's inequality Popper · Schrödinger's cat Elitzur–Vaidman bomb tester Quantum eraser Delayed choice quantum eraser Wheeler's delayed choice
Formulations Schrödinger · Heisenberg Interaction · Matrix mechanics Sum over histories
Equations Schrödinger · Pauli · Klein–Gordon Dirac · Rydberg
Interpretations de Broglie–Bohm Consciousness-caused Consistent histories · Copenhagen Ensemble · Hidden variables Many-worlds · Objective collapse Pondicherry · Quantum logic Relational · Stochastic Transactional
Advanced topics Quantum information science Scattering theory Quantum field theory Quantum chaos
Scientists Bell · Bohm · Bohr · Born · Bose de Broglie · Dirac · Ehrenfest Everett · Feynman · Heisenberg Jordan · Kramers · von Neumann Pauli · Planck · Schrödinger Sommerfeld · Wien · Wigner
v · d · e

Objective collapse theories 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.

Compared to other approaches

Collapse theories stand in opposition to many-world 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.^[2]

Objections

The fact that these theories seek to extend the formalism is considered as violation of the principle of parsimony by some.

The fact that the collapse process, treated realistically is apparently superluminal and non-local is also considered a problem.

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.

Additionally, Peter Lewis argues that due to GRW's relaxing of the requirement that mutually exclusive states of affairs must be represented by orthogonal vectors (the standard orthonormal rule, or SOR) arithmetic will fail to apply to ordinary macroscopic objects.

Notes

1. ^ Frigg, Roman GRW theory in F. Weinert, D. Greenberger, B. Falkenburg, K. Hentschel (2008) A Compendium of Quantum Physics, Springer-Verlag
2. ^ Scaruffi, Pierro (1999) Review of Roger Penrose's Shadows of the Mind, Annotated bibliography of mind-related topics

See also

Interpretation of quantum mechanics Many-worlds interpretation Philosophy of information Philosophy of physics Quantum information Quantum entanglement Coherence (physics) Quantum decoherence EPR paradox

Quantum Zeno effect Measurement problem Measurement in quantum mechanics Ghirardi-Rimini-Weber theory Wave function collapse Quantum gravity Pondicherry interpretation Penrose interpretation

External links

Stanford Encyclopedia of Philosophy on Collapse Theories