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 "corresponds" to reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments (not one prediction from quantum mechanics has been found to be contradicted by 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, which elements of quantum mechanics can be considered real, and what the nature of measurement is, among other matters.
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.
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. 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.
Moreover, the strictly formalist position, shunning interpretation, has been challenged by proposals for experiments that might one day distinguish among interpretations, as by measuring an AI consciousness or via quantum computing.[non-primary source needed]
The physicist N. David Mermin once quipped, "New interpretations appear every year. None ever disappear." As a rough guide to development of the mainstream view during the 1990s and 2000s, a "snapshot" of opinions was collected in a poll by Schlosshauer et al. at the "Quantum Physics and the Nature of Reality" conference of July 2011. The authors reference a similarly informal poll carried out by Max Tegmark at the "Fundamental Problems in Quantum Theory" conference in August 1997. The main conclusion of the authors is that "the Copenhagen interpretation still reigns supreme", receiving the most votes in their poll (42%), besides the rise to mainstream notability of the many-worlds interpretations: "The Copenhagen interpretation still reigns supreme here, especially if we lump it together with intellectual offsprings such as information-based interpretations and the Quantum Bayesian 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."
More or less, all interpretations of quantum mechanics share two qualities:
- They interpret a formalism—a set of equations and principles to generate predictions via input of initial conditions
- 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:
- 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, if for example 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.
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—Schrödinger's wave mechanics, Heisenberg's matrix mechanics, and Feynman's path integral formalism—has been demonstrated.
- Abstract, mathematical nature of quantum field theories: the mathematical structure of quantum mechanics is abstract without clear interpretation of its quantities.
- 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.
- Role of the observer in determining outcomes: the Copenhagen Interpretation implies 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 cause an effective branching process.
- Classically unexpected correlations between remote objects: entangled quantum systems, as illustrated in the EPR paradox, obey statistics that seem to violate principles of local causality.
- Complementarity of proffered descriptions: 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. This implies the composition of physical properties of S does not obey the rules of classical propositional logic when using propositional connectives (see "Quantum logic"). Like contextuality, the "origin of complementarity lies in the non-commutativity of operators" that describe quantum objects (Omnès 1999).
- 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.
- 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, signalling that most classical intuitions may be incorrect about the quantum world.
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 of numerous proposed interpretations of 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. There is no definitive historical statement of what is the Copenhagen interpretation. There are some fundamental agreements and disagreements between the views of Bohr and Heisenberg.
Hans Primas describes nine theses of the Copenhagen interpretation: quantum physics applies to individual objects, not only ensembles of objects; their description is probabilistic; their description is the result of experiments described in terms of classical (non-quantum) physics; the "frontier" that separates the classical from the quantum can be chosen arbitrarily; the act of "observation" or "measurement" is irreversible; the act of "observation" or "measurement" involves an action upon the object measured and reduces the wave packet; complementary properties cannot be observed simultaneously; no truth can be attributed to an object except according to the results of its measurement; and that quantum descriptions are objective, in that they are independent of physicists' mental arbitrariness.
Heisenberg emphasized a sharp "cut" between the observer (or the instrument) and the system being observed, while Bohr offered an interpretation that is independent of a subjective observer, or measurement, or collapse: there is an "irreversible" or effectively irreversible process causing the decay of quantum coherence or the wave packet which imparts the classical behavior of "observation" or "measurement".
Quantum information theories
- Information ontologies, such as J. A. Wheeler's "it from bit". These approaches have been described as a revival of immaterialism.
- 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. 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.
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" 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 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.
QBism, which originally stood for "quantum Bayesianism", is an interpretation of quantum mechanics that takes an agent's actions and experiences as the central concerns of the theory. This interpretation is distinguished by its use of a subjective Bayesian account of probabilities to understand the quantum mechanical Born rule as a normative addition to good decision-making. QBism draws from the fields of quantum information and Bayesian probability 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 wavefunction superposition, quantum measurement, and entanglement. According to QBism, many, but not all, aspects of the quantum formalism are subjective in nature. For example, in this interpretation, a quantum state is not an element of reality—instead it represents the degrees of belief an agent has about the possible outcomes of measurements. For this reason, some philosophers of science have deemed QBism a form of anti-realism. The originators of the interpretation disagree with this characterization, proposing instead that the theory more properly aligns with a kind of realism they call "participatory realism", wherein reality consists of more than can be captured by any putative third-person account of it.
The many-worlds interpretation is an interpretation of quantum mechanics in which a universal wavefunction obeys the same deterministic, reversible laws at all times; in particular there is no (indeterministic and irreversible) wavefunction collapse associated with measurement. The phenomena associated with measurement are claimed to be explained by decoherence, which occurs when states interact with the environment producing entanglement, repeatedly "splitting" the universe into mutually unobservable alternate histories—effectively distinct universes within a greater multiverse.
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).
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 de Broglie–Bohm theory of quantum mechanics (also known as the pilot wave theory) 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 spacetime, is 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. Collapse is explained as phenomenological.
Quantum Darwinism is a theory meant to explain the emergence of the classical world from the quantum world as due to a process of Darwinian natural selection induced by the environment interacting with the quantum system; where the many possible quantum states are selected against in favor of a stable pointer state. It was proposed in 2003 by Wojciech Zurek and a group of collaborators including Ollivier, Poulin, Paz and Blume-Kohout. The development of the theory is due to the integration of a number of Zurek's research topics pursued over the course of twenty-five years including: pointer states, einselection and decoherence.
The transactional interpretation of quantum mechanics (TIQM) by John G. Cramer is an interpretation of quantum mechanics inspired by the Wheeler–Feynman absorber theory. 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.
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; QM would need to be extended if objective collapse is correct. The requirement for an extension to QM means that objective collapse is more of a theory than an interpretation. Examples include
- the Ghirardi–Rimini–Weber theory
- the continuous spontaneous localization model
- the Penrose interpretation
Consciousness causes collapse (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. 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.
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." 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:
- The Copenhagen variant
- Kochen–Dieks–Healey interpretations
- Motivating early modal interpretations, based on the work of R. Clifton, M. Dickson and J. Bub.
Several theories have been proposed which modify the equations of quantum mechanics to be symmetric with respect to time reversal. (See Wheeler–Feynman time-symmetric theory.) 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.
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, Lev Vaidman, states that the two-state vector formalism dovetails well with Hugh Everett's many-worlds interpretation.
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.
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.
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.
|Interpretation||Year published||Author(s)||Deterministic?||Ontic wavefunction?||Unique
|Ensemble interpretation||1926||Max Born||Agnostic||No||Yes||Agnostic||No||No||No||No||No|
|Copenhagen interpretation||1927–||Niels Bohr, Werner Heisenberg||No||Some||Yes||No||Some||No||Yes||No||No|
|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|
|Many-worlds interpretation||1957||Hugh Everett||Yes||Yes||No||No||No||No||Yes||Ill-posed||Yes|
|Consciousness causes collapse||1961–
|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||Yes||No||Yes|
|Transactional interpretation||1986||John G. Cramer||No||Yes||Yes||No||Yes[g]||No||No[h]||Yes||No|
|Objective collapse theories||1986–
|Relational interpretation||1994||Carlo Rovelli||No||No||Agnostic[i]||No||Yes[j]||Intrinsic[k]||Possibly[l]||No||No|
|QBism||2010||Christopher Fuchs, Rüdiger Schack||No||No[m]||Agnostic[n]||No||Yes[o]||Intrinsic[p]||Yes||No||No|
- Both particle AND guiding wavefunction are real.
- Unique particle history, but multiple wave histories.
- But quantum logic is more limited in applicability than Coherent Histories.
- Quantum mechanics is regarded as a way of predicting observations, or a theory of measurement.
- Observers separate the universal wavefunction into orthogonal sets of experiences.
- In the consistent histories interpretation the collapse is a legitimate calculational procedure when describing the preparation of a quantum system, but it amounts to nothing more than a convenient way of calculating conditional probabilities.
- In the TI the collapse of the state vector is interpreted as the completion of the transaction between emitter and absorber.
- The transactional interpretation is explicitly non-local.
- Comparing histories between systems in this interpretation has no well-defined meaning.
- Any physical interaction is treated as a collapse event relative to the systems involved, not just macroscopic or conscious observers.
- The state of the system is observer-dependent, i.e., the state is specific to the reference frame of the observer.
- The interpretation was originally presented as local, but whether locality is well-posed in RQM has been disputed.
- A wavefunction merely encodes an agent’s expectations for future experiences. It is no more real than a probability distribution is in subjective Bayesianism.
- Quantum theory is a tool any agent may use to help manage their expectations. The past comes into play only insofar as an agent’s individual experiences and temperament influence their priors.
- Although QBism would eschew this terminology. A change in the wavefunction that an agent ascribes to a system as a result of having an experience represents a change in his or her beliefs about further experiences they may have. See Doxastic logic.
- Observers, or more properly, participants, are as essential to the formalism as the systems they interact with.
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." This position is not uncommon among practitioners of quantum mechanics. Others, like Nico van Kampen and Willis Lamb, have openly criticized non-orthodox interpretations of quantum mechanics.
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- von Neumann, John. (1932/1955). Mathematical Foundations of Quantum Mechanics. Princeton: Princeton University Press. Translated by Robert T. Beyer.
- [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.]
- Zvi Schreiber (1995). "The Nine Lives of Schrödinger's Cat". arXiv:quant-ph/9501014.
- Lombardi, Olimpia; Dieks, Dennis (2002-11-12). "Modal Interpretations of Quantum Mechanics". Stanford Encyclopedia of Philosophy. Science.uva.nl. Retrieved 2011-01-24.
- Watanabe, Satosi (1955). "Symmetry of physical laws. Part III. Prediction and retrodiction". Reviews of Modern Physics. 27 (2): 179–186. Bibcode:1955RvMP...27..179W. doi:10.1103/revmodphys.27.179. hdl:10945/47584.
- Aharonov, Y.; et al. (1964). "Time Symmetry in the Quantum Process of Measurement". Phys. Rev. 134 (6B): B1410–1416. Bibcode:1964PhRv..134.1410A. doi:10.1103/physrev.134.b1410.
- Aharonov, Y. and Vaidman, L. "On the Two-State Vector Reformulation of Quantum Mechanics." Physica Scripta, Volume T76, pp. 85-92 (1998).
- Wharton, K. B. (2007). "Time-Symmetric Quantum Mechanics". Foundations of Physics. 37 (1): 159–168. Bibcode:2007FoPh...37..159W. doi:10.1007/s10701-006-9089-1. S2CID 123086913.
- Wharton, K. B. (2010). "A Novel Interpretation of the Klein–Gordon Equation". Foundations of Physics. 40 (3): 313–332. arXiv:0706.4075. Bibcode:2010FoPh...40..313W. doi:10.1007/s10701-009-9398-2. S2CID 121170138.
- Heaney, M. B. (2013). "A Symmetrical Interpretation of the Klein–Gordon Equation". Foundations of Physics. 43 (6): 733–746. arXiv:1211.4645. Bibcode:2013FoPh...43..733H. doi:10.1007/s10701-013-9713-9. S2CID 118770571.
- Yakir Aharonov, Lev Vaidman: The Two-State Vector Formalism of Quantum Mechanics: an Updated Review. In: Juan Gonzalo Muga, Rafael Sala Mayato, Íñigo Egusquiza (eds.): Time in Quantum Mechanics, Volume 1, Lecture Notes in Physics 734, pp. 399–447, 2nd ed., Springer, 2008, ISBN 978-3-540-73472-7, doi:10.1007/978-3-540-73473-4_13, arXiv:quant-ph/0105101, p. 443
- Olimpia, Lombardi; 1979-, Fortin, Sebastian; Federico, Holik; Cristian, López (2017). "Interpretations of Quantum Theory: A Map of Madness". What is quantum information?. pp. 138–144. arXiv:1509.04711. doi:10.1017/9781316494233.009. ISBN 9781107142114. OCLC 965759965. S2CID 118419619.CS1 maint: numeric names: authors list (link)
- John L. Heilbron (1988), "The Earliest Missionaries of the Copenhagen Spirit", in E. Ullmann-Margalit (ed.), Science in Reflection, pp. 201–233,
This resolution of EPR, which Rosen later characterized as a stipulation that "[physical] reality is whatever quantum mechanics is capable of describing," was applauded for its clarity by Bohr's close associates. Heisenberg, Klein, and Kramers particularly liked the reduction of the EPR thought experiment to the familiar problem of the diaphragm with holes. Perhaps the most interesting responses came from Bohr's old friend, the physicist C. W. Oseen, and from his new ally, the physicist-philosopher Philipp Frank. Oseen had understood at last what he now recognized that Bohr had been saying all along: before a measurement an atom's state with respect to the quantity measured is undefined. Frank saw that Bohr had indeed transfixed EPR on an essential ambiguity. What Frank liked most was the implication that physicists should avoid the term and concept of "physical reality". He understood Bohr to mean that complementarity characterized measuring procedures, not the things measured. Bohr acknowledged that that was indeed what he had had in mind.
- Henrik Zinkernagel (2016), "Niels Bohr on the wave function and the classical/quantum divide", Studies in History and Philosophy of Modern Physics, 53: 9–19, arXiv:1603.00353, Bibcode:2016SHPMP..53....9Z, doi:10.1016/j.shpsb.2015.11.001, S2CID 18890207,
For a start, discussions of the Copenhagen interpretation in the literature are ambiguous between two different views of the wave function, both of which of course accept the Born interpretation.5 Sometimes the Copenhagen (and Bohr’s) interpretation is associated with the epistemic view of the quantum state, according to which the quantum state is but a representation of our knowledge of the physical system, and thus not a real existing entity in itself. On this view the ‘collapse’ of the wave function is not a physical process, and it just reflects an update of our information about the system; see e.g. Zeilinger (1999). By contrast, the Copenhagen interpretation has also been associated with an ontological view of the quantum state, in which the wave function somehow describes a real wave, and the collapse is a real physical process – presumably induced by the observer. This ontological view is usually attributed to von Neumann in his 1932 textbook exposition of quantum mechanics; see e.g. Henderson (2010). [...] Thus, for Bohr, the wave function is a representation of a quantum system in a particular, classically described, experimental context. Three important points need to be made regarding this contextuality: 1) When a measurement is performed (that is, when an irreversible recording has been made; see below), then the context changes, and hence the wave function changes. This can formally be seen as a "collapse" of the wave function, with the square quotes indicating that we are not talking about a physical process in which a real wave collapses.
- W. Heisenberg (1955), "The Development of the Interpretation of the Quantum Theory", in W. Pauli (ed.), Essays dedicated to Niels Bohr on the occasion of his seventieth birthday, Pergamon Press,
Of course it is entirely justified to imagine this transition, from the possible to the actual, moved to an earlier point of time, for the observer himself does not produce the transition; but it cannot be moved back to a time when the compound system was still separate from the external world, because such an assumption would not be compatible with the validity of quantum mechanics for the closed system. We see from this that a system cut off from the external world is potential but not actual in character, or, as BOHR has often expressed it, that the system cannot be described in terms of the classical concepts. We may say that the state of the closed system represented by a Hilbert vector is indeed objective, but not real, and that the classical idea of "objectively real things" must here, to this extent, be abandoned.
- Niels Bohr (1958), "Quantum Physics and Philosophy—Causality and Complementarity", Essays 1958-1962 on Atomic Physics and Human Knowledge, p. 3,
The description of atomic phenomena has in these respects a perfectly objective character, in the sense that no explicit reference is made to any individual observer and that therefore, with proper regard to relativistic exigencies, no ambiguity is involved in the communication of information.
- Elitzur, Avshalom C.; Cohen, Eliahu; Okamoto, Ryo; Takeuchi, Shigeki (2018). "Nonlocal Position Changes of a Photon Revealed by Quantum Routers". Scientific Reports. 8 (1): 7730. arXiv:1707.09483. Bibcode:2018NatSR...8.7730E. doi:10.1038/s41598-018-26018-y. PMC 5955892. PMID 29769645.
- Martin-Dussaud, P.; Rovelli, C.; Zalamea, F. (2019). "The Notion of Locality in Relational Quantum Mechanics". Foundations of Physics. 49 (2): 96–106. arXiv:1806.08150. Bibcode:2019FoPh...49...96M. doi:10.1007/s10701-019-00234-6. S2CID 50796079.
- Smerlak, Matteo; Rovelli, Carlo (2007-03-01). "Relational EPR". Foundations of Physics. 37 (3): 427–445. arXiv:quant-ph/0604064. Bibcode:2007FoPh...37..427S. doi:10.1007/s10701-007-9105-0. ISSN 0015-9018. S2CID 11816650.
- Pienaar, Jacques (2019). "Comment on "The Notion of Locality in Relational Quantum Mechanics"". Foundations of Physics. 49: 1404–1414. arXiv:1807.06457. Bibcode:2019FoPh...49.1404P. doi:10.1007/s10701-019-00303-w.
- P. A. M. Dirac, The inadequacies of quantum field theory, in Paul Adrien Maurice Dirac, B. N. Kursunoglu and E. P. Wigner, Eds. (Cambridge University, Cambridge, 1987) p. 194
- F. J. Duarte (2014). Quantum Optics for Engineers. New York: CRC. ISBN 978-1439888537.
- van Kampen, N. G. (2008). "The scandal of quantum mechanics". Am. J. Phys. 76: 989.
- Lamb, W. E. (2001). "Super classical quantum mechanics: the best interpretation of nonrelativistic quantum mechanics." Am. J. Phys. 69: 413-421.
- 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.
- 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.
- Jackiw, Roman; Kleppner, D. (2000). "One Hundred Years of Quantum Physics". Science. 289 (5481): 893–898. arXiv:quant-ph/0008092. Bibcode:2000quant.ph..8092K. doi:10.1126/science.289.5481.893. PMID 17839156. S2CID 6604344.
- 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.
- 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.
- Tegmark, Max; Wheeler, J. A. (2001). "100 Years of Quantum Mysteries". Scientific American. 284 (2): 68–75. Bibcode:2001SciAm.284b..68T. doi:10.1038/scientificamerican0201-68. S2CID 119375538.
- 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.
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.
- Adan Cabello (15 November 2004). "Bibliographic guide to the foundations of quantum mechanics and quantum information". arXiv: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.
- F. J. Duarte (2014). Quantum Optics for Engineers. New York: CRC. ISBN 978-1439888537. Provides a pragmatic perspective on interpretations. For general readers.
- Bernard d'Espagnat, 1976. Conceptual Foundation of Quantum Mechanics, 2nd ed. Addison Wesley. ISBN 0-8133-4087-X.
- Bernard d'Espagnat, 1983. In Search of Reality. Springer. 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. 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) Entanglement, Information, and the Interpretation of Quantum Mechanics. Springer. ISBN 978-3-540-92127-1.
- N. David Mermin (1990) Boojums all the way through. Cambridge Univ. Press. ISBN 0-521-38880-5.
- Roland Omnès, 1994. The Interpretation of Quantum Mechanics. Princeton Univ. Press. ISBN 0-691-03669-1.
- Roland Omnès, 1999. Understanding Quantum Mechanics. Princeton Univ. Press.
- Roland Omnès, 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.
- Roger Penrose, 1994. Shadows of the Mind. Oxford Univ. Press. 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.
- Styer, Daniel F.; Balkin, Miranda S.; Becker, Kathryn M.; Burns, Matthew R.; Dudley, Christopher E.; Forth, Scott T.; Gaumer, Jeremy S.; Kramer, Mark A.; et al. (March 2002). "Nine formulations of quantum mechanics" (PDF). American Journal of Physics. 70 (3): 288–297. Bibcode:2002AmJPh..70..288S. doi:10.1119/1.1445404.
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