Objective collapse theory
Encyclopedia
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.
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.
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.
Interpretation of quantum mechanics
An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...
. They are realistic, indeterministic and reject hidden variables
Hidden variables
Hidden variables may refer to:* Hidden variable theories, in physics a class of theories trying to explain away the statistical nature of quantum mechanics* Latent variables, in statistics, variables that are inferred from other observed variables...
. The approach is similar to the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...
, 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 collapseWavefunction collapse
In quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...
curtails the branching of the wavefunction and removes unobserved behaviour. Objective collapse theories differ from the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...
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.- 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 theoryGhirardi-Rimini-Weber theoryThe Ghirardi–Rimini–Weber theory, or GRW, is a collapse theory in quantum mechanics. GRW differs from other collapse theories by proposing that wave function collapse happens spontaneously. GRW is an attempt to avoid the measurement problem in quantum mechanics...
(GRW). - 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 interpretationPenrose interpretationThe Penrose interpretation is a prediction of Sir Roger Penrose about the relationship between quantum mechanics and general relativity. Penrose proposes that a quantum state remains in superposition until the difference of space-time curvature attains a significant level...
, which links collapse to gravitational stress in general relativisticGeneral relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
spacetimeSpacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
, with the threshold value being one gravitonGravitonIn physics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 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
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
, 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.
See also
- Interpretation of quantum mechanicsInterpretation of quantum mechanicsAn interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...
- Many-worlds interpretationMany-worlds interpretationThe many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an...
- Philosophy of informationPhilosophy of informationThe philosophy of information is the area of research that studies conceptual issues arising at the intersection of computer science, information technology, and philosophy.It includes:...
- Philosophy of physicsPhilosophy of physicsIn philosophy, the philosophy of physics studies the fundamental philosophical questions underlying modern physics, the study of matter and energy and how they interact. The philosophy of physics begins by reflecting on the basic metaphysical and epistemological questions posed by physics:...
- Quantum informationQuantum informationIn quantum mechanics, quantum information is physical information that is held in the "state" of a quantum system. The most popular unit of quantum information is the qubit, a two-level quantum system...
- Quantum entanglementQuantum entanglementQuantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...
- Coherence (physics)Coherence (physics)In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....
- Quantum decoherenceQuantum decoherenceIn quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...
- EPR paradoxEPR paradoxThe EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...
- Quantum Zeno effectQuantum Zeno effectThe quantum Zeno effect is a name coined by George Sudarshan and Baidyanath Misra of the University of Texas in 1977 in their analysis of the situation in which an unstable particle, if observed continuously, will never decay. One can nearly "freeze" the evolution of the system by measuring it...
- Measurement problemMeasurement problemThe measurement problem in quantum mechanics is the unresolved problem of how wavefunction collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer...
- Measurement in quantum mechanicsMeasurement in quantum mechanicsThe framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus....
- Ghirardi-Rimini-Weber theoryGhirardi-Rimini-Weber theoryThe Ghirardi–Rimini–Weber theory, or GRW, is a collapse theory in quantum mechanics. GRW differs from other collapse theories by proposing that wave function collapse happens spontaneously. GRW is an attempt to avoid the measurement problem in quantum mechanics...
- Wave function collapse
- Quantum gravityQuantum gravityQuantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
- Pondicherry interpretationPondicherry interpretationBorn and raised in Germany, Ulrich Mohrhoff joined the Sri Aurobindo International Centre of Education , Pondicherry , a department of the Sri Aurobindo Ashram as an undergraduate student in 1972. From 1974 to 1978 he studied physics at the University of Göttingen, Germany, and at the Indian...
- Penrose interpretationPenrose interpretationThe Penrose interpretation is a prediction of Sir Roger Penrose about the relationship between quantum mechanics and general relativity. Penrose proposes that a quantum state remains in superposition until the difference of space-time curvature attains a significant level...