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{{Quantum mechanics|cTopic=Interpretations}}
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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. There exist a number of contending schools of thought, differing over whether quantum mechanics can be understood to be [[determinism|deterministic]], which elements of quantum mechanics can be considered "real", and other matters.


This question is of special interest to [[Philosophy of physics|philosophers of physics]], as physicists continue to show a strong interest in the subject. They usually consider an interpretation of quantum mechanics as an interpretation of the [[Mathematical formulation of quantum mechanics|mathematical formalism]] of quantum mechanics, specifying the physical meaning of the mathematical entities of the theory.
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== History of interpretations ==
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|caption1=[[Erwin Schrödinger|Schrödinger]]
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|caption2=[[Max Born|Born]]
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|caption3=[[Hugh Everett|Everett]]
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The definition of quantum theorists' terms, such as ''[[wavefunction]]s'' and ''[[matrix mechanics]]'', progressed through many stages. For instance, [[Erwin Schrödinger]] originally viewed the electron's wavefunction as its charge density smeared across the [[field (physics)#Waves as fields|field]], whereas [[Max Born]] reinterpreted it as the electron's [[probability density]]{{dn|date=October 2013}} [[probability distribution|distributed]] across the field.<br>
 
Although the [[Copenhagen interpretation]] was originally most popular, [[quantum decoherence]] has gained popularity.  Thus the [[many-worlds interpretation]] has been gaining acceptance.<ref>Vaidman, L. (2002, March 24). Many-Worlds Interpretation of Quantum Mechanics. Retrieved March 19, 2010, from Stanford Encyclopedia of Philosophy: http://plato.stanford.edu/entries/qm-manyworlds/#Teg98</ref><ref>A controversial poll mentioned in ''The Physics of Immortality'' (1994) found that of 72 "leading cosmologists and other quantum field theorists", 58% including [[Stephen Hawking]], [[Murray Gell-Mann]], and Richard Feynman supported a many-worlds interpretation ["[http://www.hedweb.com/everett/everett.htm#believes Who believes in many-worlds?]", ''Hedweb.com'', Accessed online: 24 Jan 2011].</ref> Moreover, the strictly formalist position, shunning interpretation, has been challenged by proposals for falsifiable experiments that might one day distinguish among interpretations, as by measuring an [[AI]] consciousness<ref>''Quantum theory as a universal physical theory'', by David Deutsch, International Journal of Theoretical Physics, Vol 24 #1 (1985)</ref> or via [[Quantum computer|quantum computing]].<ref>''Three connections between Everett's interpretation and experiment Quantum Concepts of Space and Time'', by David Deutsch, Oxford University Press (1986)</ref>
 
== Nature of interpretation ==
More or less, all interpretations of quantum mechanics share two qualities:
# They interpret a ''[[scientific formalism|formalism]]''—a set of equations and principles to generate predictions via input of initial conditions
# They interpret a ''[[phenomenology (science)|phenomenology]]''—a set of observations, including those obtained by empirical research and those obtained informally, such as humans' experience of an unequivocal world
Two qualities vary among interpretations:
# [[Ontology]]—claims about what things, such as categories and entities, ''exist'' in the world
# [[Epistemology]]—claims about the possibility, scope, and means toward relevant ''knowledge'' of the world
 
In [[philosophy of science]], the distinction of knowledge versus reality is termed ''[[epistemic]]'' versus ''[[ontic]]''.  A general law is a ''regularity'' of outcomes (epistemic), whereas a causal mechanism may ''regulate'' the outcomes (ontic). A [[phenomenon]] can receive interpretation either ontic or epistemic.  For instance, [[indeterminism]] may be attributed to limitations of human observation and perception (epistemic), or may be explained as a real existing ''maybe'' encoded in the universe (ontic). Confusing the epistemic with the ontic, like if one were to presume that a general law actually "governs" outcomes—and that the statement of a regularity has the role of a causal mechanism—is a [[category mistake]].
 
In a broad sense, scientific theory can be viewed as offering [[scientific realism]]—approximately true description or explanation of the natural world—or might be perceived with antirealism. A realist stance seeks the epistemic and the ontic, whereas an antirealist stance seeks epistemic but not the ontic.  In the 20th century's first half, antirealism was mainly [[logical positivism]], which sought to exclude unobservable aspects of reality from scientific theory.
 
Since the 1950s, antirealism is more modest, usually [[instrumentalism]], permitting talk of unobservable aspects, but ultimately discarding the very question of realism and posing scientific theory as a tool to help humans make predictions, not to attain [[metaphysical]] understanding of the world.  The instrumentalist view is carried by the famous quote of [[David Mermin]], "Shut up and calculate", often misattributed to [[Richard Feynman]].<ref>For a discussion of the provenance of the phrase "shut up and calculate", see [http://scitation.aip.org/journals/doc/PHTOAD-ft/vol_57/iss_5/10_1.shtml]</ref>
 
Other approaches to resolve conceptual problems introduce new mathematical formalism, and so propose alternative theories with their interpretations.  An example is [[Bohmian mechanics]], whose empirical equivalence with the three standard formalisms—[[Erwin Schrödinger|Schrödinger]]'s [[Schrödinger equation|wave mechanics]], [[Werner Heisenberg|Heisenberg]]'s [[matrix mechanics]], and [[Richard Feynman|Feynman]]'s [[path integral formalism]], all empirically equivalent—is doubtful.
 
== Challenges to interpretation ==
Difficulties reflect a number of points about quantum mechanics:
# Abstract, mathematical nature of [[quantum field theories]]
# Existence of apparently [[quantum indeterminacy|indeterministic]] and yet irreversible processes
# Role of the [[observer (quantum physics)|observer]] in determining outcomes
# [[Quantum entanglement|Classically unexpected correlations]] between remote objects
# Complementarity of proffered descriptions
# Rapidly rising intricacy, far exceeding humans' present calculational capacity, as a system's size increases
 
The [[mathematical formulation of quantum mechanics|mathematical structure of quantum mechanics]] is based on rather abstract mathematics, like [[Hilbert space]].  In [[classical field theory]], a physical property at a given location in the field is readily derived.  In Heisenberg's formalism, on the other hand, to derive physical information about a location in the field, one must apply a [[quantum operation]] to a [[quantum state]], an elaborate mathematical process.<ref name=Kuhlmann>Meinard Kuhlmann, [http://www.scientificamerican.com/article.cfm?id=physicists-debate-whether-world-made-of-particles-fields-or-something-else "Physicists debate whether the world is made of particles or fields—or something else entirely"], ''Scientific American'', 24 Jul 2013.</ref>
 
[[Schrödinger equation|Schrödinger's formalism]] describes a [[waveform]] governing [[probability]] of outcomes across a field.  Yet how do we find in a specific location a particle whose [[wavefunction]] of mere [[probability density|probability distribution]]{{dn|date=October 2013}} of existence spans a vast region of space?
 
The act of [[measurement in quantum mechanics|measurement]] can interact with the system state in peculiar ways, as found in [[double-slit experiment]]s.  The [[Copenhagen interpretation]] holds that the myriad probabilities across a quantum field are unreal, yet that the act of observation/measurement collapses the [[wavefunction]] and sets a single possibility to become real.  Yet [[quantum decoherence]] grants that all the possibilities can be real, and that the act of observation/measurement sets up new subsystems.<ref>Guido Bacciagaluppi, "[http://plato.stanford.edu/archives/win2012/entries/qm-decoherence The role of decoherence in quantum mechanics]", ''The Stanford Encyclopedia of Philosophy'' (Winter 2012), Edward N Zalta, ed.</ref>
 
[[Quantum entanglement]], as illustrated in the [[EPR paradox]], seemingly [[action at a distance (physics)|violates]] [[Principle of locality|principles of local causality]].<ref>''La nouvelle cuisine'', by John S Bell, last article of Speakable and Unspeakable in Quantum Mechanics, second edition.</ref>
 
[[complementarity (physics)|Complementarity]] holds that no set of classical physical concepts can simultaneously refer to all properties of a quantum system.  For instance, wave description ''A'' and particulate description ''B'' can each describe quantum system ''S'', but not simultaneously.  Still, complementarity does not usually imply that classical logic is at fault (although [[Hilary Putnam]] took such view in "[[Is logic empirical?]]"); rather, the composition of physical properties of ''S'' does not obey the rules of classical [[propositional calculus|propositional logic]] when using propositional connectives (see "[[Quantum logic]]").  As now well known, the "origin of complementarity lies in the [[non-commutativity]] of operators" that describe quantum objects (Omnès 1999).
 
Since the intricacy of a quantum system is exponential, it is difficult to derive classical approximations.
 
== Instrumentalist interpretation ==
{{main|Instrumentalist interpretation}}
 
Any modern scientific theory requires at the very least an instrumentalist description that relates the mathematical formalism to experimental practice and prediction. In the case of quantum mechanics, the most common instrumentalist description is an assertion of statistical regularity between state preparation processes and measurement processes. That is, if a measurement of a [[real number|real]]-value quantity is performed many times, each time starting with the same initial conditions, the outcome is a well-defined [[probability distribution]] agreeing with the real numbers; moreover, quantum mechanics provides a computational instrument to determine statistical properties of this distribution, such as its [[expected value|expectation value]].
 
Calculations for measurements performed on a system '''S''' postulate a [[Hilbert space]] ''H'' over the [[complex numbers]]. When the system '''S''' is prepared in a [[pure state]], it is associated with a [[vector (geometry)|vector]] in ''H''. Measurable quantities are associated with [[Hermitian operator]]s acting on ''H'': these are referred to as [[observable]]s.
 
Repeated measurement of an observable ''A'' where '''S''' is prepared in state ψ yields a distribution of values. The expectation value of this distribution is given by the expression
 
:<math> \langle \psi \vert A \vert \psi \rangle. </math>
 
This mathematical machinery gives a simple, direct way to compute a statistical property of the outcome of an experiment, once it is understood how to associate the initial state with a Hilbert space vector, and the measured quantity with an observable (that is, a specific Hermitian operator).
 
As an example of such a computation, the probability of finding the system in a given state <math>\vert\phi\rangle</math> is given by computing the expectation value of a (rank-1) [[projection operator]]
 
:<math>\Pi = \vert\phi\rangle \langle \phi \vert.</math>
 
The probability is then the non-negative real number given by
 
:<math>P = \langle \psi \vert \Pi \vert \psi \rangle = \vert \langle \phi \vert \psi \rangle \vert ^2. </math>
 
By abuse of language, a bare instrumentalist description could be referred to as an interpretation, although this usage is somewhat misleading since instrumentalism explicitly avoids any explanatory role; that is, it does not attempt to answer the question ''why''.
 
== Summary of common interpretations of quantum mechanics ==
 
=== Classification adopted by Einstein ===
An interpretation (i.e. a [[semantics|semantic explanation]] of the formal mathematics of quantum mechanics) can be characterized by its treatment of certain matters addressed by Einstein, such as:
 
* Realism
* Completeness
* [[Principle of locality#Local realism|Local realism]]
* [[Determinism]]
 
To explain these properties, we need to be more explicit about the kind of picture an interpretation provides. To that end we will regard an interpretation as a correspondence between the elements of the mathematical formalism '''M''' and the elements of an interpreting structure '''I''', where:
* The ''mathematical formalism'' '''M''' consists of the Hilbert space machinery of [[Bra-ket notation|ket-vectors]], [[self-adjoint operator]]s acting on the space of ket-vectors, unitary time dependence of the ket-vectors, and measurement operations. In this context a measurement operation is a transformation which turns a ket-vector into a probability distribution (for a formalization of this concept see [[quantum operation]]s).
* The ''interpreting structure'' '''I''' includes states, transitions between states, measurement operations, and possibly information about spatial extension of these elements. A measurement operation refers to an operation which returns a value and might result in a system state change. Spatial information would be exhibited by states represented as functions on configuration space. The transitions may be [[Quantum indeterminacy|non-deterministic]] or probabilistic or there may be infinitely many states.
 
The crucial aspect of an interpretation is whether the elements of '''I''' are regarded as physically real. Hence the bare instrumentalist view of quantum mechanics outlined in the previous section is not an interpretation at all, for it makes no claims about elements of physical reality.
 
The current usage of realism and completeness originated in the 1935 paper in which Einstein and others proposed the [[EPR paradox]].<ref>A. Einstein, B. Podolsky and N. Rosen, 1935, "[[EPR paradox|Can quantum-mechanical description of physical reality be considered complete?]]" ''Phys. Rev''. 47: 777.</ref>  In that paper the authors proposed the concepts ''element of reality'' and the ''completeness of a physical theory''. They characterised element of reality as a quantity whose value can be predicted with certainty before measuring or otherwise disturbing it, and defined a complete physical theory as one in which every element of physical reality is accounted for by the theory. In a semantic view of interpretation, an interpretation is complete if every element of the interpreting structure is present in the mathematics. Realism is also a property of each of the elements of the maths; an element is real if it corresponds to something in the interpreting structure. For example, in some interpretations of quantum mechanics (such as the many-worlds interpretation) the ket vector associated to the system state is said to correspond to an element of physical reality, while in other interpretations it is not.
 
Determinism is a property characterizing state changes due to the passage of time, namely that the state at a future instant is a [[Function (mathematics)|function]] of the state in the present (see [[time evolution]]). It may not always be clear whether a particular interpretation is deterministic or not, as there may not be a clear choice of a time parameter. Moreover, a given theory may have two interpretations, one of which is deterministic and the other not.
 
Local realism has two aspects:
 
* The value returned by a measurement corresponds to the value of some function in the state space. In other words, that value is an element of reality;
* The effects of measurement have a propagation speed not exceeding some universal limit (e.g. the speed of light). In order for this to make sense, measurement operations in the interpreting structure must be localized.
 
A precise formulation of local realism in terms of a [[local hidden variable theory]] was proposed by [[John Stewart Bell|John Bell]].
 
[[Bell's theorem]], combined with experimental testing, restricts the kinds of properties a quantum theory can have, the primary implication being that quantum mechanics cannot satisfy both the [[locality principle|principle of locality]] and [[counterfactual definiteness]].
 
=== The Copenhagen interpretation ===
{{main|Copenhagen interpretation}}
 
The [[Copenhagen interpretation]] is the "standard" interpretation of quantum mechanics formulated by [[Niels Bohr]] and [[Werner Heisenberg]] while collaborating in Copenhagen around 1927. Bohr and Heisenberg extended the probabilistic interpretation of the wavefunction proposed originally by Max Born. The Copenhagen interpretation rejects questions like "where was the particle before I measured its position?" as meaningless. The measurement process randomly picks out exactly one of the many possibilities allowed for by the state's wave function in a manner consistent with the well-defined probabilities that are assigned to each possible state. According to the interpretation, the interaction of an observer or apparatus that is external to the quantum system is the cause of wave function collapse, thus according to [[Paul Davies]], "reality is in the observations, not in the electron".<ref>http://www.naturalthinker.net/trl/texts/Heisenberg,Werner/Heisenberg,%20Werner%20-%20Physics%20and%20philosophy.pdf</ref> What collapses in this interpretation is the knowledge of the observer and not an "objective" wavefunction.
 
=== Many worlds ===
{{main|Many-worlds interpretation}}
 
The [[many-worlds interpretation]] is an interpretation of quantum mechanics in which a [[universal wavefunction]] obeys the same deterministic, [[CPT symmetry|reversible]] laws at all times; in particular there is no (indeterministic and [[irreversibility|irreversible]]) [[wavefunction collapse]] associated with measurement. The phenomena associated with measurement are claimed to be explained by [[Quantum decoherence|decoherence]], which occurs when states interact with the environment producing [[Quantum entanglement|entanglement]], repeatedly splitting the universe into mutually unobservable [[alternate histories]]—distinct universes within a greater [[multiverse]]. In this interpretation the wavefunction has objective reality.
 
=== Consistent histories ===
{{main|Consistent histories}}
 
The [[consistent histories]] interpretation generalizes the conventional Copenhagen interpretation and attempts to provide a natural interpretation of [[quantum cosmology]]. The theory is based on a consistency criterion that allows the history of a system to be described so that the probabilities for each history obey the additive rules of classical probability. It is claimed to be [[consistent]] with the [[Schrödinger equation]].
 
According to this interpretation, the purpose of a quantum-mechanical theory is to predict the relative probabilities of various alternative histories (for example, of a particle).
 
=== Ensemble interpretation, or statistical interpretation ===
{{main|Ensemble interpretation}}
 
The [[ensemble interpretation]], also called the statistical interpretation, can be viewed as a minimalist interpretation. That is, it claims to make the fewest assumptions associated with the standard mathematics. It takes the statistical interpretation of Born to the fullest extent. The interpretation states that the wave function does not apply to an individual system{{spaced ndash}}for example, a single particle{{spaced ndash}}but is an abstract statistical quantity that only applies to an ensemble (a vast multitude) of similarly prepared systems or particles. Probably the most notable supporter of such an interpretation was Einstein:
 
{{Quote|The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which become immediately unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems.|Einstein in ''Albert Einstein: Philosopher-Scientist'', ed. P.A. Schilpp (Harper & Row, New York)}}
 
The most prominent current advocate of the ensemble interpretation is Leslie E. Ballentine, professor at [[Simon Fraser University]], author of the graduate level text book ''Quantum Mechanics, A Modern Development''. An experiment illustrating the ensemble interpretation is provided in Akira Tonomura's Video clip 1.<ref>{{cite web
|url=http://www.hitachi.com/rd/research/em/doubleslit.html
|title=An experiment illustrating the ensemble interpretation
|publisher=Hitachi.com
|date=
|accessdate=2011-01-24}}</ref> It is evident from this [[double-slit experiment]] with an ensemble of individual electrons that, since the quantum mechanical wave function (absolutely squared) describes the ''completed'' interference pattern, it must describe an ensemble
 
The Ensemble interpretation is not popular, and is regarded as having been decisively refuted by some
physicists. [[John Gribbin]] writes:-
<blockquote>
"There are many difficulties with the idea, but the killer blow was struck when individual quantum entities such as photons were observed behaving in experiments in line with the quantum wave function description. The Ensemble interpretation is now only of historical interest."<ref>{{cite book | author=John Gribbin |title=Q is for Quantum|isbn=978-0684863153}}</ref></blockquote>
 
=== de Broglie–Bohm theory ===
{{main|de Broglie–Bohm theory}}
 
The [[de Broglie–Bohm theory]] of quantum mechanics is a theory by [[Louis de Broglie]] and extended later by [[David Bohm]] to include measurements.  Particles, which always have positions, are guided by the wavefunction.  The wavefunction evolves according to the [[Schrödinger wave equation]], and the wavefunction never collapses. The theory takes place in a single space-time, is [[Action at a distance (physics)|non-local]], and is deterministic. The simultaneous determination of a particle's position and velocity is subject to the usual [[uncertainty principle]] constraint. The theory is considered to be a [[hidden variable theory]], and by embracing non-locality it satisfies Bell's inequality. The [[measurement problem]] is resolved, since the particles have definite positions at all times.<ref>''Why Bohm's Theory Solves the Measurement Problem'' by T. Maudlin, Philosophy of Science 62, pp. 479-483 (September, 1995).</ref> Collapse is explained as [[Phenomenology (particle physics)|phenomenological]].<ref>''Bohmian Mechanics as the Foundation of Quantum Mechanics'' by D. Durr, N. Zanghi, and S. Goldstein in '''Bohmian Mechanics and Quantum Theory: An Appraisal''', edited by [[James T. Cushing|J.T. Cushing]], A. Fine, and S. Goldstein, Boston Studies in the Philosophy of Science 184, 21-44 (Kluwer, 1996) 1997 {{arxiv|quant-ph/9511016}}</ref>
 
=== Relational quantum mechanics ===
{{main|Relational quantum mechanics}}
The essential idea behind [[relational quantum mechanics]], following the precedent of [[special relativity]], is that different observers may give different accounts of the same series of events: for example, to one observer at a given point in time, a system may be in a single, "collapsed" [[Eigenvalues and eigenvectors|eigenstate]], while to another observer at the same time, it may be in a superposition of two or more states.  Consequently, if quantum mechanics is to be a complete theory, relational quantum mechanics argues that the notion of "state" describes not the observed system itself, but the relationship, or correlation, between the system and its observer(s).  The [[Quantum state vector|state vector]] of conventional quantum mechanics becomes a description of the correlation of some ''degrees of freedom'' in the observer, with respect to the observed system.  However, it is held by relational quantum mechanics that this applies to all physical objects, whether or not they are conscious or macroscopic. Any "measurement event" is seen simply as an ordinary physical interaction, an establishment of the sort of correlation discussed above.  Thus the physical content of the theory has to do not with objects themselves, but the relations between them.<ref>{{cite web
|url=http://plato.stanford.edu/entries/qm-relational/
|title=Relational Quantum Mechanics (Stanford Encyclopedia of Philosophy)
|publisher=Plato.stanford.edu
|date=
|accessdate=2011-01-24}}</ref><ref>For more information, see {{cite journal |doi=10.1007/BF02302261 |author=Carlo Rovelli |year=1996 |title=Relational Quantum Mechanics |journal=[[International Journal of Theoretical Physics]] |volume=35 |issue=8 |pages=1637 |arxiv=quant-ph/9609002|bibcode = 1996IJTP...35.1637R |authorlink= Carlo Rovelli }}</ref>
 
An independent [[Relational approach to quantum physics|relational approach to quantum mechanics]] was developed in analogy with David Bohm's elucidation of special relativity,<ref>David Bohm, ''The Special Theory of Relativity'', Benjamin, New York, 1965</ref> in which a detection event is regarded as establishing a relationship between the quantized field and the detector. The inherent ambiguity associated with applying Heisenberg's uncertainty principle is subsequently avoided.<ref>[http://www.quantum-relativity.org/Quantum-Relativity.pdf]. For a full account [http://www.quantum-relativity.org/Quantum_Optics_as_a_Relativistic_Theory_of_Light.pdf], see Q. Zheng and T. Kobayashi, 1996, "Quantum Optics as a Relativistic Theory of Light," ''Physics Essays'' 9: 447. Annual Report, Department of Physics, School of Science, University of Tokyo (1992) 240.</ref>
 
=== Elementary cycles ===
The idea at the base of this interpretation is the empirical fact that, as noted by [[Louis de Broglie]] with the [[wave-particle duality]], elementary particles have recurrences in time and space determined by their energy and momentum  through the [[Planck constant]].  This implies that every system in nature can be described in terms of elementary space-time cycles. These recurrences are imposed as semiclassical quantization conditions, similarly to the quantization of a [[particle in a box]].  The resulting cyclic mechanics are formally equivalent to both the canonical formulation and Feynman formulation of quantum mechanics,<ref>Dolce, D "Compact Time and Determinism for Bosons: foundations",  Foundations of Physics, 41, pp. 178-203 (2011) {{cite journal|author1=Donatello Dolce|title=Compact Time and Determinism for Bosons: Foundations|doi=10.1007/s10701-010-9485-4|year=2010|journal=Foundations of Physics|volume=41|issue=2|pages=178–203|arxiv=0903.3680|bibcode = 2010FoPh..tmp...86D }}</ref> for a review see.<ref>Dolce, D "On the intrinsically cyclic nature of space-time in elementary particles",  J. Phys.: Conf. Ser. 343 (2012) 012031 {{cite journal|author1=Donatello Dolce|title=On the intrinsically cyclic nature of space-time in elementary particles|doi=10.1088/1742-6596/343/1/012031|year=2012|journal=J.Phys.Conf.Ser.|volume=343|pages=012031|arxiv=1206.1140|bibcode = 2012JPhCS.343a2031D }}</ref>  It is an evolution of the [[Bohr-Sommerfeld quantization]] or the [[zitterbewegung]] and suggests that quantum mechanics emerges as statistical description of extremely fast periodic dynamics, as proposed by [[Gerard 't Hooft#Fundamental aspects of quantum mechanics|'t Hooft Determinism]].<ref>'t Hooft, G "The mathematical basis for deterministic quantum mechanics",  DOI:10.1088/1742-6596/67/1/012015, arxiv=quant-ph/0604008</ref>
The idea has originated applications in modern physics, such as a geometrical description of [[Gauge theory|gauge invariance]] <ref>Dolce, D "Gauge Interaction as Periodicity Modulation",  Annals of Physics, Volume 327, Issue 6, June 2012, pp. 1562-1592 {{cite journal|author1=Donatello Dolce|title=Gauge Interaction as Periodicity Modulation|doi=10.1016/j.aop.2012.02.007|year=2012|journal=Annals of Physics|volume=327|issue=6|pages=1562–1592|arxiv=1110.0315|bibcode = 2012AnPhy.327.1562D }}</ref> and an interpretation of the [[Maldacena duality]].<ref>Dolce, D "Classical geometry to quantum behavior correspondence in a Virtual Extra Dimension",  Annals #of Physics, Volume 327, Issue 9, September 2012, pp 2354-2387 {{cite journal|author1=Donatello Dolce|title=Classical geometry to quantum behavior correspondence in a Virtual Extra  Dimension|doi=10.1016/j.aop.2012.06.001|year=2012|journal=Annals of Physics|volume=327|issue=9|pages=2354|arxiv=1110.0316|bibcode = 2012AnPhy.327.2354D }}</ref>
 
=== Transactional interpretation ===
{{main|Transactional interpretation}}
The [[transactional interpretation]] of quantum mechanics (TIQM) by [[John G. Cramer]] is an interpretation of quantum mechanics inspired by the [[Wheeler–Feynman absorber theory]].<ref>{{cite web
|url=http://www.npl.washington.edu/npl/int_rep/qm_nl.html
|title=Quantum Nocality - Cramer |publisher=Npl.washington.edu
|date=
|accessdate=2011-01-24}}</ref> It describes a quantum interaction in terms of a standing wave formed by the sum of a retarded (forward-in-time) and an advanced (backward-in-time) wave. The author argues that it avoids the philosophical problems with the Copenhagen interpretation and the role of the observer, and resolves various quantum paradoxes.
 
=== Stochastic mechanics ===
{{main|Stochastic interpretation}}
An entirely classical derivation and interpretation of Schrödinger's wave equation by analogy with [[Brownian motion]] was suggested by [[Princeton University]] professor [[Edward Nelson]] in 1966.<ref>Nelson,E. (1966) Derivation of the Schrödinger Equation from Newtonian Mechanics, ''Phys. Rev.'' '''150''', 1079-1085</ref> Similar considerations had previously been published, for example by R. Fürth (1933), I. Fényes (1952), and [[Walter Weizel]] (1953), and are referenced in Nelson's paper. More recent work on the stochastic interpretation has been done by M. Pavon.<ref>M. Pavon, “Stochastic mechanics and the Feynman integral”, ''J. Math. Phys.'' '''41''', 6060-6078 (2000)</ref> An alternative stochastic interpretation was developed by Roumen Tsekov.<ref>{{cite journal|author1=Roumen Tsekov|title=Bohmian Mechanics versus Madelung Quantum Hydrodynamics|year=2012|pages=112–119|journal=Ann. Univ. Sofia, Fac. Phys. |arxiv=0904.0723|bibcode=2009arXiv0904.0723T|volume=SE}}</ref>
 
=== Objective collapse theories ===
{{Main|Objective collapse theory}}
Objective collapse theories differ from the [[Copenhagen interpretation]] in regarding both the wavefunction and the process of collapse as ontologically objective.  In objective theories, collapse occurs randomly ("spontaneous localization"), or when some physical threshold is reached, with observers having no special role.  Thus, they are realistic, indeterministic, no-hidden-variables theories.  The mechanism of collapse is not specified by standard quantum mechanics, which needs to be extended if this approach is correct, meaning that Objective Collapse is more of a theory than an interpretation.  Examples include the [[Ghirardi-Rimini-Weber theory]]<ref>{{cite web
|url=http://www.romanfrigg.org/writings/GRW%20Theory.pdf
|title=Frigg, R. GRW theory
|format=PDF
|date=
|accessdate=2011-01-24}}</ref> and the  [[Penrose interpretation]].<ref>{{cite web
|url=http://www.thymos.com/mind/penrose.html
|title=Review of Penrose's Shadows of the Mind
|publisher=Thymos.com
|date=
|accessdate=2011-01-24}}</ref>
 
=== von Neumann/Wigner interpretation: consciousness causes the collapse ===
{{Main|Von Neumann–Wigner interpretation}}
In his treatise ''The Mathematical Foundations of Quantum Mechanics'', [[John von Neumann]] deeply analyzed the so-called [[measurement problem]]. He concluded that the entire physical universe could be made subject to the Schrödinger equation (the universal wave function). He also described how measurement could cause a collapse of the wave function.<ref>von Neumann, John. (1932/1955). '''Mathematical Foundations of Quantum Mechanics'''. Princeton: Princeton University Press. Translated by Robert T. Beyer.</ref> This point of view was prominently expanded on by [[Eugene Wigner]], who argued that human experimenter consciousness (or maybe even dog consciousness) was critical for the collapse, but he later abandoned this interpretation.<ref>[Michael Esfeld, (1999), Essay Review: Wigner’s View of Physical Reality, published in Studies in History and Philosophy of Modern Physics, 30B, pp. 145–154, Elsevier Science Ltd.]</ref><ref name=Schreiber>{{cite arxiv|eprint=quant-ph/9501014|author1=Zvi Schreiber|title=The Nine Lives of Schrödinger's Cat|class=quant-ph|year=1995}}</ref>
 
Variations of the von Neumann interpretation include:
 
: '''Subjective reduction research'''
::This principle, that consciousness causes the collapse, is the point of intersection between quantum mechanics and the mind/body problem; and researchers are working to detect conscious events correlated with physical events that, according to quantum theory, should involve a wave function collapse; but, thus far, results are inconclusive.<ref>Dick J. Bierman and Stephen Whitmarsh. (2006). ''Consciousness and Quantum Physics: Empirical Research on the Subjective Reduction of the State Vector''. in Jack A. Tuszynski (Ed). '''The Emerging Physics of Consciousness'''. p. 27-48.</ref><ref>C. M. H. Nunn et al. (1994). ''Collapse of a Quantum Field may Affect Brain Function''. '''Journal of Consciousness Studies'''. 1(1):127-139.</ref>
 
: '''Participatory anthropic principle (PAP)'''
:{{main|Anthropic principle}}
::[[John Archibald Wheeler]]'s participatory anthropic principle says that consciousness plays some role in bringing the universe into existence.<ref>{{cite web
|url=http://www.abc.net.au/rn/scienceshow/stories/2006/1572643.htm
|title=- The anthropic universe
|date=2006-02-18
|publisher=Abc.net.au
|accessdate=2011-01-24}}</ref>
 
Other physicists have elaborated their own variations of the von Neumann interpretation; including:
* [[Henry P. Stapp]] (''Mindful Universe: Quantum Mechanics and the Participating Observer'')
* Bruce Rosenblum and Fred Kuttner (''Quantum Enigma: Physics Encounters Consciousness'')
* Amit Goswami (''The Self-Aware Universe'')
 
=== Many minds ===
{{main|Many-minds interpretation}}
 
The many-minds interpretation of [[quantum mechanics]] extends the [[many-worlds interpretation]] by proposing that the distinction between worlds should be made at the level of the mind of an individual observer.
 
=== Quantum logic ===
{{main|Quantum logic}}
 
[[Quantum logic]] can be regarded as a kind of propositional logic suitable for understanding the apparent anomalies regarding quantum measurement, most notably those concerning composition of measurement operations of complementary variables. This research area and its name originated in the 1936 paper by [[Garrett Birkhoff]] and [[John von Neumann]], who attempted to reconcile some of the apparent inconsistencies of classical boolean logic with the facts related to measurement and observation in quantum mechanics.
 
=== Quantum information theories ===
[[Quantum information]]al approaches<ref>{{cite news
| url=http://www.quantum.at/fileadmin/links/newscientist/bit.html
| title=In the beginning was the bit
| work=New Scientist
| date=2001-02-17
| accessdate=2013-01-25 }}
</ref> have attracted growing support.<ref>{{cite news
| url=http://www.dailycamera.com/science-columnists/ci_22444536/kate-becker-quantum-physics-has-been-rankling-scientists
| title=Quantum physics has been rankling scientists for decades
| work=Boulder Daily Camera
| author=Kate Becker
| date=2013-01-25
| accessdate=2013-01-25 }}
</ref><ref>{{cite web
| url=http://arxiv.org/abs/1301.1069
| title=A Snapshot of Foundational Attitudes Toward Quantum Mechanics
| date=2013-01-06
| accessdate=2013-01-25 }}
</ref>  They subdivide into two kinds<ref>[http://users.ox.ac.uk/~bras2317/iii_2.pdf Information, Immaterialism, Instrumentalism: Old and New in Quantum Information. Christopher G. Timpson]</ref>
* Information ontologies, such as J. A. Wheeler's "[[it from bit]]". These approaches have been described as a revival of [[idealism|immaterialism]]<ref>Timpson,Op. Cit.: "Let us call the thought that information might be the basic category from which all else flows informational immaterialism."</ref>
* Interpretations where quantum mechanics is said to describe an observer's knowledge of the world, rather than the world itself. This approach has some similarity with Bohr's thinking.<ref>"Physics concerns what we can say about nature". (Niels Bohr, quoted in Petersen, A. (1963). The philosophy of Niels Bohr. Bulletin of the Atomic Scientists, 19(7):8–14.)</ref> Collapse (also known as reduction) is often interpreted as an observer acquiring information from a measurement, rather than as an objective event. These approaches have been appraised as similar to [[instrumentalism]].
<blockquote>
The state is not an objective property of an individual system but is that
information, obtained from a knowledge of how a system was prepared, which
can be used for making predictions about future measurements.
...A quantum mechanical state being a summary of the observer’s information
about an individual physical system changes both by dynamical laws, and
whenever the observer acquires new information about the system through
the process of measurement. The existence of two laws for the evolution
of the state vector...becomes problematical only if it is believed that the
state vector is an objective property of the system...The “reduction of the
wavepacket” does take place in the consciousness of the observer, not because
of any unique physical process which takes place there, but only because the
state is a construct of the observer and not an objective property of the
physical system<ref>Hartle, J. B. (1968). Quantum mechanics of individual systems. Am. J. Phys., 36(8):704–
712.
</ref>
</blockquote>
 
=== Modal interpretations of quantum theory ===
Modal interpretations of quantum mechanics were first conceived of in 1972 by B. van Fraassen, in his paper “A formal approach to the philosophy of science.”  However, this term now is used to describe a larger set of models that grew out of this approach. The [[Stanford Encyclopedia of Philosophy]] describes several versions:<ref>{{cite web
|url=http://www.science.uva.nl/~seop/entries/qm-modal/
|title=Modal Interpretations of Quantum Mechanics (Stanford Encyclopedia of Philosophy)
|publisher=Science.uva.nl
|date=
|accessdate=2011-01-24}}</ref>
 
* The Copenhagen variant
* Kochen-[[Dennis Dieks|Dieks]]-Healey Interpretations
* Motivating Early Modal Interpretations, based on the work of R. Clifton, M. Dickson and J. Bub.
 
=== Time-symmetric theories ===
Several theories have been proposed which modify the equations of quantum mechanics to be symmetric with respect to time reversal.<ref>Watanabe, Satosi. "Symmetry of physical laws. Part III. Prediction and retrodiction." Reviews of Modern Physics 27.2 (1955): 179.</ref> <ref>Aharonov, Y. et al., "Time Symmetry in the Quantum Process of Measurement." Phys. Rev. 134, B1410-1416 (1964).</ref><ref>Aharonov, Y. and Vaidman, L. "On the Two-State Vector Reformulation of Quantum Mechanics."  Physica Scripta, Volume T76, pp. 85-92 (1998).</ref><ref>Wharton, K. B. "Time-Symmetric Quantum Mechanics." Foundations of Physics, 37(1), pp. 159-168 (2007).</ref><ref>Wharton, K. B. "A Novel Interpretation of the Klein-Gordon Equation." Foundations of Physics, 40(3), pp. 313-332 (2010).</ref><ref>Heaney, M. B. "A Symmetrical Interpretation of the Klein-Gordon Equation." Foundations of Physics (2013): http://link.springer.com/article/10.1007%2Fs10701-013-9713-9.</ref>  This creates [[retrocausality]]: events in the future can affect ones in the past, exactly as events in the past can affect ones in the future.  In these theories, a single measurement cannot fully determine the state of a system (making them a type of [[hidden variables theory]]), but given two measurements performed at different times, it is possible to calculate the exact state of the system at all intermediate times.  The collapse of the wavefunction is therefore not a physical change to the system, just a change in our knowledge of it due to the second measurement.  Similarly, they explain entanglement as not being a true physical state but just an illusion created by ignoring retrocausality.  The point where two particles appear to "become entangled" is simply a point where each particle is being influenced by events that occur to the other particle in the future.
 
=== Branching space-time theories ===
BST theories resemble the many worlds interpretation; however, "the main difference is that the BST interpretation takes the branching of history to be a feature of the topology of the set of events with their causal relationships... rather than a consequence of the separate evolution of different components of a state vector."<ref name="Sharlow"/> In MWI, it is the wave functions that branches, whereas in BST, the space-time topology itself branches.
BST  has applications to Bells theorem, quantum computation and quantum gravity. It also has some resemblance to hidden variable theories and the ensemble interpretation.: particles in BST have multiple well defined trajectories at the microscopic level. These can only be treated stochastically at a coarse grained level, in line
with the ensemble interpretation.<ref name="Sharlow">[http://philsci-archive.pitt.edu/3781/1/what_branching_spacetime_might_do.pdf Sharlow, Mark; "What Branching Spacetime might do for Phyiscs"] p.2</ref>
 
=== Other interpretations ===
{{main|Minority interpretations of quantum mechanics}}
As well as the mainstream interpretations discussed above, a number of other interpretations have been proposed which have not made a significant scientific impact for whatever reason. These range from proposals by mainstream physicists to the more [[occult]] ideas of [[quantum mysticism]].
 
== Comparison of interpretations ==
The most common interpretations are summarized in the table below. The values shown in the cells of the table are not without controversy, for the precise meanings of some of the concepts involved are unclear and, in fact, are themselves at the center of the controversy surrounding the given interpretation.
 
No experimental evidence exists that distinguishes among these interpretations. To that extent, the physical theory stands, and is consistent with itself and with reality; difficulties arise only when one attempts to "interpret" the theory.  Nevertheless, designing experiments which would test the various interpretations is the subject of active research.
 
Most of these interpretations have variants. For example, it is difficult to get a precise definition of the Copenhagen interpretation as it was developed and argued about by many people.
 
{| class=wikitable
|-  style="text-align:center; background:lightgrey;"
!Interpretation
!Author(s)
![[Determinism|Deterministic?]]
![[Wave function#Ontology|Wavefunction<br>real?]]
!Unique<br>history?
![[Hidden variable theory|Hidden<br>variables]]?
![[Wavefunction collapse|Collapsing<br>wavefunctions?]]
!Observer<br>role?
![[Locality principle|Local]]?
![[Counterfactual definiteness|Counterfactual<br>definiteness]]?
![[Universal wavefunction|Universal<br>wavefunction]]<br>exists?
|- align=center
| style="background:lightgrey;"|[[Ensemble Interpretation|Ensemble interpretation]]
| style="background:lightgrey;"|[[Max Born]], 1926
| style="background:lightyellow;"|Agnostic
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
| style="background:lightyellow;"|Agnostic
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
|- align=center
| style="background:lightgrey;"|[[Copenhagen interpretation of quantum mechanics|Copenhagen interpretation]]
| style="background:lightgrey;"|[[Niels Bohr]], [[Werner Heisenberg]], 1927
|bgcolor=pink|No
|bgcolor=pink|No{{ref|note1|1}}
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
| style="background:lightgreen;"|Yes{{ref|note1|2}}
| style="background:lightgreen;"|Causal
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
|- align=center
| style="background:lightgrey;"|[[de Broglie–Bohm theory]]
| style="background:lightgrey;"|[[Louis de Broglie]], 1927, [[David Bohm]], 1952
| style="background:lightgreen;"|Yes
| style="background:lightgreen;"|Yes{{ref|note3|3}}
| style="background:lightgreen;"|Yes{{ref|note4|4}}
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
| style="background:lightgreen;"|Yes
|- align=center
| style="background:lightgrey;"|[[Interpretation of quantum mechanics#von Neumann/Wigner interpretation: consciousness causes the collapse|von Neumann interpretation]]
| style="background:lightgrey;"|[[John von Neumann]], 1932, [[John Archibald Wheeler]], [[Eugene Wigner]]
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
| style="background:lightgreen;"|Causal
|bgcolor=pink|No
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
|- align=center
| style="background:lightgrey;"|[[Quantum logic]]
| style="background:lightgrey;"|[[Garrett Birkhoff]], 1936
| style="background:lightyellow;"|Agnostic
| style="background:lightyellow;"|Agnostic
| style="background:lightgreen;"|Yes{{ref|note5|5}}
|bgcolor=pink|No
|bgcolor=pink|No
| style="background:lightyellow;"|Interpretational{{ref|note6|6}}
| style="background:lightyellow;"|Agnostic
|bgcolor=pink|No
|bgcolor=pink|No
|- align=center
| style="background:lightgrey;"|[[Many-worlds interpretation]]
| style="background:lightgrey;"|[[Hugh Everett]], 1957
| style="background:lightgreen;"|Yes
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
|- align=center
| style="background:lightgrey;"|[[Popper's experiment|Popper's interpretation]]<ref>Marie-Christine Combourieu: Karl R. Popper, 1992: About the EPR controversy. ''Foundations of Physics'' '''22''':10, 1303-1323</ref>
| style="background:lightgrey;"|[[Karl Popper]], 1957<ref>Karl Popper: The Propensity Interpretation of the Calculus of Probability and of the Quantum Theory. ''Observation and Interpretation''. Buttersworth Scientific Publications, Korner & Price (eds.) 1957. pp 65–70.</ref>
| style="background:pink;"|No
| style="background:lightgreen;"|Yes
|bgcolor=lightgreen|Yes
|bgcolor=lightgreen|Yes
|bgcolor=pink|No
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
| style="background:lightgreen;"|Yes{{ref|note13|13}}
|bgcolor=pink|No
|- align=center
| style="background:lightgrey;"|Time-symmetric theories
| style="background:lightgrey;"|[[Satosi Watanabe]], 1955
| style="background:lightgreen;"|Yes
| style="background:lightgreen;"|Yes
| style="background:lightgreen;"|Yes
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
|- align=center
| style="background:lightgrey;"|[[Stochastic interpretation]]
| style="background:lightgrey;"|[[Edward Nelson]], 1966
|bgcolor=pink|No
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
|- align=center
| style="background:lightgrey;"|[[Many-minds interpretation]]
| style="background:lightgrey;"|[[H. Dieter Zeh]], 1970
| style="background:lightgreen;"|Yes
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
| style="background:lightyellow;"|Interpretational{{ref|note7|7}}
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
|- align=center
| style="background:lightgrey;"|[[Consistent histories]]
| style="background:lightgrey;"|[[Robert B. Griffiths]], 1984
| style="background:lightyellow;"|Agnostic{{ref|note8|8}}
| style="background:lightyellow;"|Agnostic{{ref|note8|8}}
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
| style="background:lightyellow;"|Interpretational{{ref|note6|6}}
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
|bgcolor=pink|No
|- align=center
| style="background:lightgrey;"|[[Objective collapse theory|Objective collapse theories]]
| style="background:lightgrey;"|[[Ghirardi–Rimini–Weber theory|Ghirardi–Rimini–Weber]], 1986,<br>[[Penrose interpretation]], 1989
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
|bgcolor=pink|No
|- align=center
| style="background:lightgrey;"|[[Transactional interpretation]]
| style="background:lightgrey;"|[[John G. Cramer]], 1986
|bgcolor=pink|No
| style="background:lightgreen;"|Yes
| style="background:lightgreen;"|Yes
|bgcolor=pink|No
| style="background:lightgreen;"|Yes{{ref|note9|9}}
|bgcolor=pink|No
|bgcolor=pink|No{{ref|note14|14}}
|bgcolor=lightgreen|Yes
|bgcolor=pink|No
|- align=center
| style="background:lightgrey;"|[[Relational quantum mechanics|Relational interpretation]]
| style="background:lightgrey;"|[[Carlo Rovelli]], 1994
| style="background:lightyellow;"|Agnostic
|bgcolor=pink|No
| style="background:lightyellow;"|Agnostic{{ref|note10|10}}
|bgcolor=pink|No
| style="background:lightgreen;"|Yes{{ref|note11|11}}
| style="background:lightgreen;"|Intrinsic{{ref|note12|12}}
| style="background:lightgreen;"|Yes
| style="background:pink;"|No
|bgcolor=pink|No
|}
 
* {{note label|note1|1}} According to Bohr, the concept of a physical state independent of the conditions of its experimental observation does not have a well-defined meaning. According to Heisenberg the wavefunction represents a probability, but not an objective reality itself in space and time.
* {{note label|note2|2}} According to the Copenhagen interpretation, the wavefunction collapses when a measurement is performed.
* {{note label|note3|3}} Both particle <small>AND</small> guiding wavefunction are real.
* {{note label|note4|4}} Unique particle history, but multiple wave histories.
* {{note label|note5|5}} But quantum logic is more limited in applicability than Coherent Histories.
* {{note label|note6|6}} Quantum mechanics is regarded as a way of predicting observations, or a theory of measurement.
*  {{note label|note7|7}} Observers separate the universal wavefunction into orthogonal sets of experiences.
* {{note label|note8|8}} If wavefunction is real then this becomes the many-worlds interpretation.  If wavefunction is less than real, but more than just information, then Zurek calls this the "existential interpretation".
* {{note label|note9|9}} In the TI the collapse of the state vector is interpreted as the completion of the transaction between emitter and absorber.
* {{note label|note10|10}} Comparing histories between systems in this interpretation has no well-defined meaning.
* {{note label|note11|11}} Any physical interaction is treated as a collapse event relative to the systems involved, not just macroscopic or conscious observers.
* {{note label|note12|12}} The state of the system is observer-dependent, i.e., the state is specific to the reference frame of the observer.
* {{note label|note13|13}} Caused by the fact that Popper holds both CFD and locality to be true, it is under dispute whether Popper's interpretation can really be considered an interpretation of Quantum Mechanics (which is what Popper claimed) or whether it must be considered a modification of Quantum Mechanics (which is what many Physicists claim), and, in case of the latter, if this modification has been empirically refuted or not. Popper exchanged many long letters with Einstein, Bell etc. about the issue.
* {{note label|note14|14}} The transactional interpretation is explicitly non-local.
* {{note label|note15|15}} The assumption of intrinsic periodicity is an element of non-locality consistent  with relativity as the periodicity varies in a causal way.
 
== See also ==
{{Col-begin}}
{{Col-break}}
* [[Afshar experiment]]
* [[Bohr–Einstein debates]]
* [[Glossary of quantum philosophy]]
* [[Macroscopic quantum phenomena]]
* [[Penrose interpretation]]
{{Col-break}}
* [[Path integral formulation]]
* [[Philosophical interpretation of classical physics]]
* [[Quantum gravity]]
* [[Quantum Zeno effect]]
{{Col-end}}
 
== Sources ==
* Bub, J. and Clifton, R. 1996. “A uniqueness theorem for interpretations of quantum mechanics,” ''Studies in History and Philosophy of Modern Physics'' 27B: 181-219
* [[Rudolf Carnap]], 1939, "The interpretation of physics," in ''Foundations of Logic and Mathematics'' of the ''[[International Encyclopedia of Unified Science]]''. University of Chicago Press.
* Dickson, M., 1994, "Wavefunction tails in the modal interpretation" in Hull, D., Forbes, M., and Burian, R., eds., ''Proceedings of the PSA''  1" 366–76. East Lansing, Michigan: Philosophy of Science Association.
* --------, and Clifton, R., 1998, "Lorentz-invariance in modal interpretations" in Dieks, D. and Vermaas, P., eds., ''The Modal Interpretation of Quantum Mechanics''. Dordrecht: Kluwer Academic Publishers: 9–48.
* Fuchs, Christopher, 2002, "Quantum Mechanics as Quantum Information (and only a little more)." {{arxiv|quant-ph/0205039}}
* -------- and A. Peres, 2000, "Quantum theory needs no ‘interpretation’," ''Physics Today''.
* Herbert, N., 1985. ''Quantum Reality: Beyond the New Physics''. New York: Doubleday. ISBN 0-385-23569-0.
* Hey, Anthony, and Walters, P., 2003. ''The New Quantum Universe'', 2nd ed. Cambridge Univ. Press. ISBN 0-521-56457-3.
* [[Roman Jackiw]] and D. Kleppner, 2000, "One Hundred Years of Quantum Physics," ''[[Science]]'' 289(5481): 893.
* [[Max Jammer]], 1966. ''The Conceptual Development of Quantum Mechanics''. McGraw-Hill.
* --------, 1974. ''The Philosophy of Quantum Mechanics''. Wiley & Sons.
* Al-Khalili, 2003. ''Quantum: A Guide for the Perplexed''. London: Weidenfeld & Nicholson.
* de Muynck, W. M., 2002. ''Foundations of quantum mechanics, an empiricist approach''. Dordrecht: Kluwer Academic Publishers. ISBN 1-4020-0932-1.<ref>{{cite book
|url=http://books.google.com/?id=k3rUe8XVjJUC&printsec=frontcover&dq=an+empiricist+approach#v=onepage&q=&f=false |title=Foundations of quantum mechanics: an empiricist approach
|last=de Muynck
|first=Willem M
|publisher=Klower Academic Publishers
|year=2002
|isbn=1-4020-0932-1
|accessdate=2011-01-24}}</ref>
* [[Roland Omnès]], 1999. ''Understanding Quantum Mechanics''. Princeton Univ. Press.
* [[Karl Popper]], 1963. ''Conjectures and Refutations''. London: Routledge and Kegan Paul. The chapter "Three views Concerning Human Knowledge" addresses, among other things, instrumentalism in the physical sciences.
* [[Hans Reichenbach]], 1944. ''Philosophic Foundations of Quantum Mechanics''. Univ. of California Press.
* [[Max Tegmark]] and J. A. Wheeler, 2001, "100 Years of Quantum Mysteries," ''[[Scientific American]]'' 284: 68.
* [[Bas van Fraassen]], 1972, "A formal approach to the philosophy of science," in R. Colodny, ed., ''Paradigms and Paradoxes: The Philosophical Challenge of the Quantum Domain''. Univ. of Pittsburgh Press: 303-66.
* [[John A. Wheeler]] and [[Wojciech Hubert Zurek]]  (eds), ''Quantum Theory and Measurement'', Princeton: Princeton University Press, ISBN 0-691-08316-9, LoC QC174.125.Q38 1983.
 
== References ==
{{reflist|2}}
 
== Further reading ==
Almost all authors below are professional physicists.
 
* [[David Z Albert]], 1992. ''Quantum Mechanics and Experience''. Harvard Univ. Press. ISBN 0-674-74112-9.
*[[John S. Bell]], 1987. ''Speakable and Unspeakable in Quantum Mechanics''. Cambridge Univ. Press, ISBN 0-521-36869-3. The 2004 edition (ISBN 0-521-52338-9) includes two additional papers and an introduction by [[Alain Aspect]].
* Dmitrii Ivanovich Blokhintsev, 1968. ''The Philosophy of Quantum Mechanics''. D. Reidel Publishing Company. ISBN 90-277-0105-9.
* [[David Bohm]], 1980. ''Wholeness and the Implicate Order''. London: Routledge. ISBN 0-7100-0971-2.
* {{cite arxiv |author=Adan Cabello |date=15 November 2004 |title=Bibliographic guide to the foundations of quantum mechanics and quantum  information |class=quant-ph |eprint=quant-ph/0012089}}
* [[David Deutsch]], 1997. ''[[The Fabric of Reality]]''. London: Allen Lane. ISBN 0-14-027541-X; ISBN 0-7139-9061-9. Argues forcefully ''against'' instrumentalism. For general readers.
* [[Bernard d'Espagnat]], 1976. ''Conceptual Foundation of Quantum Mechanics'', 2nd ed. Addison Wesley. ISBN 0-8133-4087-X.
* --------, 1983. ''In Search of Reality''. Springer. ISBN 0-387-11399-1.
* --------, 2003. ''Veiled Reality: An Analysis of Quantum Mechanical Concepts''. Westview Press.
* --------, 2006. ''On Physics and Philosophy''. Princeton Univ. Press.
* [[Arthur Fine]], 1986. ''The Shaky Game: Einstein Realism and the Quantum Theory. Science and its Conceptual Foundations''. Univ. of Chicago Press. ISBN 0-226-24948-4.
* Ghirardi, Giancarlo, 2004. ''Sneaking a Look at God’s Cards''. Princeton Univ. Press.
* [[Gregg Jaeger]] (2009) [http://www.springer.com/physics/quantum+physics/book/978-3-540-92127-1 ''Entanglement, Information, and the Interpretation of Quantum Mechanics''.] Springer. ISBN 978-3-540-92127-1.
* [[N. David Mermin]] (1990) ''[http://www.cambridge.org/catalogue/catalogue.asp?isbn=0521388805 Boojums all the way through.]'' Cambridge Univ. Press. ISBN 0-521-38880-5.
* [[Roland Omnes]], 1994. ''The Interpretation of Quantum Mechanics''. Princeton Univ. Press. ISBN 0-691-03669-1.
* --------, 1999. ''Understanding Quantum Mechanics''. Princeton Univ. Press.
* --------, 1999. ''[[Quantum Philosophy]]: Understanding and Interpreting Contemporary Science''. Princeton Univ. Press.
* [[Roger Penrose]], 1989. ''[[The Emperor's New Mind]]''. Oxford Univ. Press. ISBN 0-19-851973-7. Especially chpt. 6.
* --------, 1994. ''[[Shadows of the Mind]]''. Oxford Univ. Press. ISBN 0-19-853978-9.
* --------, 2004. ''[[The Road to Reality]]''. New York: Alfred A. Knopf. Argues that quantum theory is incomplete.
*{{cite journal
|last=Styer |first=Daniel F.
|authorlink=Daniel F. Styer
|date=March 2002
|title=Nine formulations of quantum mechanics
|journal=[[American Journal of Physics]]
|volume=70 |issue= 3|pages=288–297
|arxiv=
|bibcode= 2002AmJPh..70..288S
|doi=10.1119/1.1445404
|last2=Balkin
|first2=Miranda S.
|last3=Becker
|first3=Kathryn M.
|last4=Burns
|first4=Matthew R.
|last5=Dudley
|first5=Christopher E.
|last6=Forth
|first6=Scott T.
|last7=Gaumer
|first7=Jeremy S.
|last8=Kramer
|first8=Mark A.
|last9=Oertel
|first9=David C.
}}
 
== External links ==
{{Wikiversity|Making sense of quantum mechanics}}
*[[Stanford Encyclopedia of Philosophy]]:
** "[http://plato.stanford.edu/entries/qm-bohm/ Bohmian mechanics]" by Sheldon Goldstein.
** "[http://plato.stanford.edu/entries/qm-collapse/ Collapse Theories.]" by Giancarlo Ghirardi.
** "[http://plato.stanford.edu/entries/qm-copenhagen/ Copenhagen Interpretation of Quantum Mechanics]" by Jan Faye.
** "[http://plato.stanford.edu/entries/qm-everett/ Everett's Relative State Formulation of Quantum Mechanics]" by Jeffrey Barrett.
** "[http://plato.stanford.edu/entries/qm-manyworlds/ Many-Worlds Interpretation of Quantum Mechanics]" by Lev Vaidman.
** "[http://plato.stanford.edu/entries/qm-modal/ Modal Interpretation of Quantum Mechanics]" by Michael Dickson and Dennis Dieks.
** "[http://plato.stanford.edu/entries/qt-entangle/ Quantum Entanglement and Information]" by [[Jeffrey Bub]].
** "[http://plato.stanford.edu/entries/qm/ Quantum mechanics]" by Jenann Ismael.
** "[http://plato.stanford.edu/entries/qm-relational/ Relational Quantum Mechanics]" by Federico Laudisa and [[Carlo Rovelli]].
** "[http://plato.stanford.edu/entries/qm-decoherence/ The Role of Decoherence in Quantum Mechanics]" by Guido Bacciagaluppi.
* Willem M. de Muynck, [http://www.phys.tue.nl/ktn/Wim/muynck.htm#quantum Broad overview] of the realist vs. empiricist interpretations, against oversimplified view of the measurement process.
* Schreiber, Z., "[http://arxiv.org/abs/quant-ph/9501014 The Nine Lives of Schrodinger's Cat.]" Overview of competing interpretations.
* [http://xstructure.inr.ac.ru/x-bin/subthemes3.py?level=2&index1=362483&skip=0 Interpretations of quantum mechanics on arxiv.org.]
* [http://www.johnsankey.ca/qm.html The many worlds of quantum mechanics.]
* [http://www.decoherence.de/ Erich Joos' Decoherence Website.]
* [http://home.sprynet.com/~owl1/qm.htm Quantum Mechanics for Philosophers.] Argues for the superiority of the Bohm interpretation.
* [http://www.miguel-montenegro.com/Hidden_cultural_variables.htm Hidden Variables in Quantum Theory: The Hidden Cultural Variables of their Rejection.]
* [http://frombob.to/many.html Numerous Many Worlds-related Topics and Articles.]
* [http://www.quantum-relativity.org/ Relational Approach to Quantum Physics.]
* [http://cc3d.free.fr/tim.pdf Theory of incomplete measurements.] Deriving quantum mechanics axioms from properties of acceptable measurements.
* [http://www.mat.univie.ac.at/~neum/physics-faq.txt Alfred Neumaier's FAQ.]
* [http://www.mtnmath.com/faq/meas-qm.html  Measurement in Quantum Mechanics FAQ.]
 
{{DEFAULTSORT:Interpretations Of Quantum Mechanics}}
[[Category:Quantum measurement| ]]
[[Category:Quantum mechanics]]
[[Category:Interpretation (philosophy)]]
 
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Latest revision as of 23:30, 24 February 2014

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