Interpretations of quantum mechanics

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An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments, there exist a number of contending schools of thought over their interpretation. These views on interpretation differ on such fundamental questions as whether quantum mechanics is deterministic or stochastic, local or non-local, which elements of quantum mechanics can be considered real, and what the nature of measurement is, among other matters.

While some variation of the Copenhagen interpretation is commonly presented in textbooks, many thought provoking interpretations have been developed. Despite nearly a century of debate and experiment, no consensus has been reached among physicists and philosophers of physics concerning which interpretation best "represents" reality.^[1][2]

History

The definition of quantum theorists' terms, such as wave function and matrix mechanics, progressed through many stages. For instance, Erwin Schrödinger originally viewed the electron's wave function as its charge density smeared across space, but Max Born reinterpreted the absolute square value of the wave function as the electron's probability density distributed across space;^{[3]: 24–33} the Born rule, as it is now called, matched experiment, whereas Schrödinger's charge density view did not.

The views of several early pioneers of quantum mechanics, such as Niels Bohr and Werner Heisenberg, are often grouped together as the "Copenhagen interpretation", though physicists and historians of physics have argued that this terminology obscures differences between the views so designated.^[3][4] Copenhagen-type ideas were never universally embraced, and challenges to a perceived Copenhagen orthodoxy gained increasing attention in the 1950s with the pilot-wave interpretation of David Bohm and the many-worlds interpretation of Hugh Everett III.^[3][5][6]

The physicist

interpretation. In Tegmark's poll, the Everett interpretation received 17% of the vote, which is similar to the number of votes (18%) in our poll."

Some concepts originating from studies of interpretations have found more practical application in quantum information science.^[9][10]

Nature

More or less, all interpretations of quantum mechanics share two qualities:

1. They interpret a formalism—a set of equations and principles to generate predictions via input of initial conditions
2. They interpret a 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:

1. Epistemology—claims about the possibility, scope, and means toward relevant knowledge of the world
2. Ontology—claims about what things, such as categories and entities, exist in the world

In

.

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

Other approaches to resolve conceptual problems introduce new mathematical formalism, and so propose alternative theories with their interpretations. An example is

path integral formalism

—has been demonstrated.

Interpretive challenges

1. Abstract, mathematical nature of
   quantum field theories: the mathematical structure of quantum mechanics
   is abstract without clear interpretation of its quantities.
2. Existence of apparently indeterministic and irreversible processes: in classical field theory, a physical property at a given location in the field is readily derived. In most mathematical formulations of quantum mechanics, measurement is given a special role in the theory, as it is the sole process that can cause a nonunitary, irreversible evolution of the state.
3. Role of the observer in determining outcomes: the Copenhagen-type interpretations imply that the wavefunction is a calculational tool, and represents reality only immediately after a measurement, perhaps performed by an observer; Everettian interpretations grant that all the possibilities can be real, and that the process of measurement-type interactions causes an effective branching process.^[12]
4. violate principles of local causality.^[13]
5. Complementarity of proffered descriptions:
   non-commutativity
   of operators" that describe quantum objects (Omnès 1999).
6. Rapidly rising intricacy, far exceeding humans' present calculational capacity, as a system's size increases: since the state space of a quantum system is exponential in the number of subsystems, it is difficult to derive classical approximations.
7. Contextual behaviour of systems locally: Quantum contextuality demonstrates that classical intuitions, in which properties of a system hold definite values independent of the manner of their measurement, fail even for local systems. Also, physical principles such as Leibniz's Principle of the identity of indiscernibles no longer apply in the quantum domain, signaling that most classical intuitions may be incorrect about the quantum world.

Influential interpretations

Copenhagen interpretation

The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics principally attributed to Niels Bohr and Werner Heisenberg. It is one of the oldest attitudes towards quantum mechanics, as features of it date to the development of quantum mechanics during 1925–1927, and it remains one of the most commonly taught.^[14][15] There is no definitive historical statement of what is the Copenhagen interpretation, and there were in particular fundamental disagreements between the views of Bohr and Heisenberg.^[16][17] For example, Heisenberg emphasized a sharp "cut" between the observer (or the instrument) and the system being observed,^[18]: 133 while Bohr offered an interpretation that is independent of a subjective observer or measurement or collapse, which relies on an "irreversible" or effectively irreversible process which imparts the classical behavior of "observation" or "measurement".^{[19][20][21][22]}

Features common to Copenhagen-type interpretations include the idea that quantum mechanics is intrinsically indeterministic, with probabilities calculated using the Born rule, and the principle of complementarity, which states certain pairs of complementary properties cannot all be observed or measured simultaneously. Moreover, properties only result from the act of "observing" or "measuring"; the theory avoids assuming definite values from unperformed experiments. Copenhagen-type interpretations hold that quantum descriptions are objective, in that they are independent of physicists' mental arbitrariness.^{[23]: 85–90} The statistical interpretation of wavefunctions due to Max Born differs sharply from Schrödinger's original intent, which was to have a theory with continuous time evolution and in which wavefunctions directly described physical reality.^{[3]: 24–33 [24]}

Many worlds

The

.

Quantum information theories

Quantum informational approaches^[25][26] have attracted growing support.^[27][8] They subdivide into two kinds.^[28]

• Information ontologies, such as J. A. Wheeler's "
  it from bit". These approaches have been described as a revival of immaterialism.^[28]
• 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.[29] 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. James Hartle writes,

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.^[30]

Relational quantum mechanics

The essential idea behind

QBism

and aims to eliminate the interpretational conundrums that have beset quantum theory.

QBism deals with common questions in the interpretation of quantum theory about the nature of

Consistent histories

The

.

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

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 – for example, a single particle – but is an abstract statistical quantity that only applies to an ensemble (a vast multitude) of similarly prepared systems or particles. In the words of Einstein:

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 text book Quantum Mechanics, A Modern Development.

De Broglie–Bohm theory

The

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.^[41] It describes the collapse of the wave function as resulting from a time-symmetric transaction between a possibility wave from the source to the receiver (the wave function) and a possibility wave from the receiver to source (the complex conjugate of the wave function). This interpretation of quantum mechanics is unique in that it not only views the wave function as a real entity, but the complex conjugate of the wave function, which appears in the Born rule for calculating the expected value for an observable, as also real.

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.^[42] 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.^[43][44]

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.

Modal interpretations of quantum theory

Modal interpretations of quantum mechanics were first conceived of in 1972 by Bas van Fraassen, in his paper "A formal approach to the philosophy of science". Van Fraassen introduced a distinction between a dynamical state, which describes what might be true about a system and which always evolves according to the Schrödinger equation, and a value state, which indicates what is actually true about a system at a given time. The term "modal interpretation" now is used to describe a larger set of models that grew out of this approach. The Stanford Encyclopedia of Philosophy describes several versions, including proposals by Kochen, Dieks, Clifton, Dickson, and Bub.^[45] According to Michel Bitbol, Schrödinger's views on how to interpret quantum mechanics progressed through as many as four stages, ending with a non-collapse view that in respects resembles the interpretations of Everett and van Fraassen. Because Schrödinger subscribed to a kind of post-Machian neutral monism, in which "matter" and "mind" are only different aspects or arrangements of the same common elements, treating the wavefunction as ontic and treating it as epistemic became interchangeable.^[46]

Time-symmetric theories

Time-symmetric interpretations of quantum mechanics were first suggested by

), 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.

Not all advocates of time-symmetric causality favour modifying the unitary dynamics of standard quantum mechanics. Thus a leading exponent of the two-state vector formalism,

Other interpretations

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.

Related concepts

Some ideas are discussed in the context of interpreting quantum mechanics but are not necessarily regarded as interpretations themselves.

Quantum Darwinism

Quantum Darwinism is a theory meant to explain the emergence of the

.

Objective-collapse theories

Objective-collapse theories differ from the Copenhagen interpretation by regarding both the wave function and the process of collapse as ontologically objective (meaning these exist and occur independent of the observer). In objective theories, collapse occurs either randomly ("spontaneous localization") or when some physical threshold is reached, with observers having no special role. Thus, objective-collapse theories are realistic, indeterministic, no-hidden-variables theories. Standard quantum mechanics does not specify any mechanism of collapse; quantum mechanics would need to be extended if objective collapse is correct. The requirement for an extension means that objective-collapse theories are alternatives to quantum mechanics rather than interpretations of it. Examples include

• the Ghirardi–Rimini–Weber theory^[56]
• the continuous spontaneous localization model
• the Penrose interpretation

Comparisons

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. For another table comparing interpretations of quantum theory, see reference.^[57]

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 by many people.

Interpre­tation	Year pub­lished	Author(s)	Determ­inistic?	Ontic wave­function?	Unique history?	Hidden variables?	Collapsing wave­functions ?	Observer role?	Local dyna­mics?	Counter­factually definite?	Extant universal wave­function?
Ensemble interpretation	1926	Max Born	Agnostic	No	Yes	Agnostic	No	No	No	No	No
Copenhagen interpretation	1927	Niels Bohr, Werner Heisenberg	No	Some[58]	Yes	No	Some[59]	No[60][61]	Yes	No	No
De Broglie–Bohm theory	1927– 1952	Louis de Broglie, David Bohm	Yes	Yes[a]	Yes[b]	Yes	Phenomen­ological	No	No	Yes	Yes
Quantum logic	1936	Garrett Birkhoff	Agnostic	Agnostic	Yes[c]	No	No	Interpre­tational[d]	Agnostic	No	No
Time- symmetric theories	1955	Satosi Watanabe	Yes	No	Yes	Yes	No	No	No[62]	No	Yes
Many-worlds interpretation	1957	Hugh Everett	Yes	Yes	No	No	No	No	Yes	Ill-posed	Yes
Consciousness causes collapse	1961– 1993	John von Neumann, Eugene Wigner, Henry Stapp	No	Yes	Yes	No	Yes	Causal	No	No	Yes
Many-minds interpretation	1970	H. Dieter Zeh	Yes	Yes	No	No	No	Interpre­tational[e]	Yes	Ill-posed	Yes
Consistent histories	1984	Robert B. Griffiths	No	No	No	No	No[f]	No[g]	Yes	No	Yes
Transactional interpretation	1986	John G. Cramer	No	Yes	Yes	No	Yes[h]	No	No[i]	Yes	No
Objective-collapse theories	1986– 1989	Giancarlo Ghirardi, Alberto Rimini, Tullio Weber, Roger Penrose	No	Yes	Yes	No	Yes	No	No	No	No
Relational interpretation	1994	Carlo Rovelli	No[63]	No	Agnostic[j]	No	Yes[k]	Intrinsic[l]	Possibly[m]	No	No
QBism	2010	Christopher Fuchs, Rüdiger Schack	No	No[n]	Agnostic[o]	No	Yes[p]	Intrinsic[q]	Yes	No	No

The silent approach

Although interpretational opinions are openly and widely discussed today, that was not always the case. A notable exponent of a tendency of silence was Paul Dirac who once wrote: "The interpretation of quantum mechanics has been dealt with by many authors, and I do not want to discuss it here. I want to deal with more fundamental things."^[66] This position is not uncommon among practitioners of quantum mechanics.^[67] Similarly Richard Feynman wrote many popularizations of quantum mechanics without ever publishing about interpretation issues like quantum measurement.^[68] Others, like Nico van Kampen and Willis Lamb, have openly criticized non-orthodox interpretations of quantum mechanics.^[69][70]

See also

References

Sources

• Bub, J.; Clifton, R. (1996). "A uniqueness theorem for interpretations of quantum mechanics". Studies in History and Philosophy of Modern Physics. 27B: 181–219.
  doi:10.1016/1355-2198(95)00019-4
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• Rudolf Carnap, 1939, "The interpretation of physics", in Foundations of Logic and Mathematics of the International Encyclopedia of Unified Science. Chicago, Illinois: 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" 366–376. 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
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• Hey, Anthony, and Walters, P., 2003. The New Quantum Universe, 2nd ed. Cambridge University Press.
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• S2CID 6604344
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• 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 & Nicolson.
• de Muynck, W. M., 2002. Foundations of quantum mechanics, an empiricist approach. Dordrecht: Kluwer Academic Publishers.
  ISBN 1-4020-0932-1
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• Roland Omnès, 1999. Understanding Quantum Mechanics. Princeton, New Jersey: Princeton University 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. University of California Press.
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• 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: 303–366.
• ISBN 0-691-08316-9
  , LoC QC174.125.Q38 1983.

Further reading

Almost all authors below are professional physicists.

• ISBN 0-674-74112-9
  .
• 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
  .
• ISBN 0-7100-0971-2
  .
• Adan Cabello (15 November 2004). "Bibliographic guide to the foundations of quantum mechanics and quantum information".
  arXiv:quant-ph/0012089
  .
• ISBN 0-7139-9061-9
  . Argues forcefully against instrumentalism. For general readers.
• ISBN 978-1439888537
  . Provides a pragmatic perspective on interpretations. For general readers.
• ISBN 0-8133-4087-X
  .
• ISBN 0-387-11399-1
  .
• Bernard d'Espagnat, 2003. Veiled Reality: An Analysis of Quantum Mechanical Concepts. Westview Press.
• Bernard d'Espagnat, 2006. On Physics and Philosophy. Princetone, New Jersey: Princeton University Press.
• ISBN 0-226-24948-4
  .
• Ghirardi, Giancarlo, 2004. Sneaking a Look at God's Cards. Princeton, New Jersey: Princeton University Press.
• ISBN 978-3-540-92127-1
  .
• ISBN 0-521-38880-5
  .
• ISBN 0-691-03669-1
  .
• Roland Omnès, 1999. Understanding Quantum Mechanics. Princeton, New Jersey: Princeton University Press.
• Roland Omnès, 1999. Quantum Philosophy: Understanding and Interpreting Contemporary Science. Princeton, New Jersey: Princeton University Press.
• ISBN 0-19-851973-7
  . Especially chapter 6.
• ISBN 0-19-853978-9
  .
• Roger Penrose, 2004. The Road to Reality. New York: Alfred A. Knopf. Argues that quantum theory is incomplete.
• Lee Phillips, 2017. A brief history of quantum alternatives. Ars Technica.
• doi:10.1119/1.1445404
  .

External links

Wikiquote has quotations related to Interpretations of quantum mechanics.

Wikiversity has learning resources about Making sense of quantum mechanics

• Stanford Encyclopedia of Philosophy:
  • "Bohmian mechanics" by Sheldon Goldstein.
  • "Collapse Theories." by Giancarlo Ghirardi.
  • "Copenhagen Interpretation of Quantum Mechanics" by Jan Faye.
  • "Everett's Relative State Formulation of Quantum Mechanics" by Jeffrey Barrett.
  • "Many-Worlds Interpretation of Quantum Mechanics" by Lev Vaidman.
  • "Modal Interpretation of Quantum Mechanics" by Michael Dickson and Dennis Dieks.
  • "Philosophical Issues in Quantum Theory" by Wayne Myrvold.
  • "Quantum-Bayesian and Pragmatist Views of Quantum Theory" by Richard Healey.
  • "Quantum Entanglement and Information" by Jeffrey Bub.
  • "Quantum mechanics" by Jenann Ismael.
  • "Quantum Logic and Probability Theory" by Alexander Wilce.
  • "Relational Quantum Mechanics" by Federico Laudisa and Carlo Rovelli.
  • "The Role of Decoherence in Quantum Mechanics" by Guido Bacciagaluppi.
• Internet Encyclopedia of Philosophy:
  • "Interpretations of Quantum Mechanics" by Peter J. Lewis.
  • "Everettian Interpretations of Quantum Mechanics" by Christina Conroy.