Editing Copenhagen interpretation (section)

==Principles==
There is no uniquely definitive statement of the Copenhagen interpretation.<ref name="camilleri2015"/><ref name="Cramer 649">{{cite journal |last=Cramer |first=John G. |author-link=John G. Cramer |title=The Transactional Interpretation of Quantum Mechanics |journal=[[Reviews of Modern Physics]] |date=1986 |volume=58 |issue=3 |page=649 |url=http://www.npl.washington.edu/npl/int_rep/tiqm/TI_20.html#2.0 |doi=10.1103/revmodphys.58.647 |bibcode=1986RvMP...58..647C |url-status=dead |archive-url=https://web.archive.org/web/20121108072338/http://www.npl.washington.edu/npl/int_rep/tiqm/TI_20.html#2.0 |archive-date=2012-11-08 |url-access=subscription }}</ref><ref>{{Cite journal|last1=Maleeh|first1=Reza|last2=Amani|first2=Parisa|date=December 2013|title=Pragmatism, Bohr, and the Copenhagen Interpretation of Quantum Mechanics|url=http://www.tandfonline.com/doi/abs/10.1080/02698595.2013.868182|journal=International Studies in the Philosophy of Science|language=en|volume=27|issue=4|pages=353–367|doi=10.1080/02698595.2013.868182|s2cid=170415674|issn=0269-8595|url-access=subscription}}</ref><ref>{{Cite book|last=Boge|first=Florian J.|url=https://www.worldcat.org/oclc/1086564338|title=Quantum Mechanics Between Ontology and Epistemology|date=2018|publisher=Springer|isbn=978-3-319-95765-4|location=Cham|pages=2|oclc=1086564338}}</ref> The term encompasses the views developed by a number of scientists and philosophers during the second quarter of the 20th century.<ref>{{cite book|first=Erhard |last=Scheibe |author-link=Erhard Scheibe |title=The Logical Analysis of Quantum Mechanics |publisher=Pergamon Press |year=1973 |isbn=9780080171586 |oclc=799397091 |quote=[T]here is no point in looking for ''the'' Copenhagen interpretation as a unified and consistent logical structure. Terms such as "Copenhagen interpretation" or "Copenhagen school" are based on the history of the development of quantum mechanics; they form a simplified and often convenient way of referring to the ideas of a number of physicists who played an important role in the establishment of quantum mechanics, and who were collaborators of Bohr's at his Institute or took part in the discussions during the crucial years. On closer inspection, one sees quite easily that these ideas are divergent in detail and that in particular the views of Bohr, the spiritual leader of the school, form a separate entity which can now be understood only by a thorough study of as many as possible of the relevant publications by Bohr himself.}}</ref> This lack of a single, authoritative source that establishes the Copenhagen interpretation is one difficulty with discussing it; another complication is that the philosophical background familiar to Einstein, Bohr, Heisenberg, and contemporaries is much less so to physicists and even philosophers of physics in more recent times.<ref name="chevalley1999"/> Bohr and Heisenberg never totally agreed on how to understand the mathematical formalism of quantum mechanics,<ref>{{Cite journal|last=Camilleri|first=Kristian|date=September 2007|title=Bohr, Heisenberg and the divergent views of complementarity|url=https://linkinghub.elsevier.com/retrieve/pii/S135521980600092X|journal=[[Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics]] |language=en|volume=38|issue=3|pages=514–528|doi=10.1016/j.shpsb.2006.10.002|bibcode=2007SHPMP..38..514C|url-access=subscription}}</ref> and Bohr distanced himself from what he considered Heisenberg's more subjective interpretation.<ref name="Faye-Stanford"/> Bohr offered an interpretation that is independent of a subjective observer, or measurement, or collapse; instead, an "irreversible" or effectively irreversible process causes the decay of quantum coherence which imparts the classical behavior of "observation" or "measurement".<ref name="Bell-Against-Measurement" /><ref>{{cite book |author-link=Niels Bohr |first=Niels |last=Bohr |orig-date=May 16, 1947 |date=1985 |title=Niels Bohr: Collected Works |volume=6: Foundations of Quantum Physics I (1926-1932) |editor-first=Jørgen |editor-last=Kalckar |pages=451–454 |url=https://www.nbarchive.dk/publications/bcw/ }}</ref><ref name="Stenholm">{{cite book |chapter=To fathom space and time |pages=121 |first=Stig |last=Stenholm | title=Quantum Optics, Experimental Gravitation, and Measurement Theory |editor-first=Pierre|editor1-link=Pierre Meystre |editor-last=Meystre |publisher=Plenum Press |year=1983 |quote=The role of irreversibility in the theory of measurement has been emphasized by many. Only this way can a permanent record be obtained. The fact that separate pointer positions must be of the asymptotic nature usually associated with irreversibility has been utilized in the measurement theory of Daneri, Loinger and Prosperi (1962). It has been accepted as a formal representation of Bohr's ideas by Rosenfeld (1966).}}</ref><ref>{{cite journal |title=Classical motion of meter variables in the quantum theory of measurement |first=Fritz |last=Haake |date= April 1, 1993 |journal=[[Physical Review A]] |doi=10.1103/PhysRevA.47.2506 |volume=47 |issue=4 |pages=2506–2517 |pmid=9909217 |bibcode=1993PhRvA..47.2506H }}</ref>

Different commentators and researchers have associated various ideas with the term.<ref name=":5" /> [[Asher Peres]] remarked that very different, sometimes opposite, views are presented as "the Copenhagen interpretation" by different authors.{{refn|group=note|"There seems to be at least as many different Copenhagen interpretations as people who use that term, probably there are more. For example, in two classic articles on the foundations of quantum mechanics, Ballentine (1970) and Stapp (1972) give diametrically opposite definitions of 'Copenhagen.'"<ref>{{cite journal  |first=Asher |last=Peres |author-link=Asher Peres |title=Popper's experiment and the Copenhagen interpretation |year=2002 |volume=33 |page=23 |journal=[[Studies in History and Philosophy of Modern Physics]] |arxiv=quant-ph/9910078|bibcode=1999quant.ph.10078P |doi=10.1016/S1355-2198(01)00034-X }}</ref>}} [[N. David Mermin]] coined the phrase "Shut up and calculate!" to summarize Copenhagen-type views, a saying often misattributed to [[Richard Feynman]] and which Mermin later found insufficiently nuanced.<ref>{{cite journal|journal=[[Physics Today]] |volume=42 |number=4 |year=1989 |page=9 |doi=10.1063/1.2810963 |first=N. David |last=Mermin |author-link=N. David Mermin |title=What's Wrong with this Pillow?|bibcode=1989PhT....42d...9D }}</ref><ref>{{cite journal|doi=10.1063/1.1768652|title=Could Feynman have said this?|journal=[[Physics Today]]|volume=57|issue=5|pages=10–11|year=2004|last1=Mermin|first1=N. David|author-link=N. David Mermin |bibcode=2004PhT....57e..10M|doi-access=free}}</ref> Mermin described the Copenhagen interpretation as coming in different "versions", "varieties", or "flavors".<ref name="Mermin 2017">{{Cite book|last=Mermin|first=N. David|title=Quantum &#91;Un&#93;Speakables II |chapter=Why QBism is Not the Copenhagen Interpretation and What John Bell Might Have Thought of It |date=2017-01-01|publisher=Springer International Publishing|isbn=9783319389851|editor-last=Bertlmann|editor-first=Reinhold|series=The Frontiers Collection|pages=83–93|language=en|arxiv=1409.2454|doi=10.1007/978-3-319-38987-5_4|s2cid=118458259|editor2-last=Zeilinger|editor2-first=Anton |editor-link2=Anton Zeilinger}}</ref>

Some basic principles generally accepted as part of the interpretation include the following:<ref name="Faye-Stanford"/>
# Quantum mechanics is intrinsically indeterministic.
# The [[correspondence principle]]: in the appropriate limit, quantum theory comes to resemble classical physics and reproduces the classical predictions.
# The [[Born rule]]: the [[wave function]] of a system yields probabilities for the outcomes of measurements upon that system.
# [[complementarity principle|Complementarity]]: certain properties cannot be jointly defined for the same system at the same time. In order to talk about a specific property of a system, that system must be considered within the context of a specific laboratory arrangement. Observable quantities corresponding to mutually exclusive laboratory arrangements cannot be predicted together, but the consideration of multiple such mutually exclusive experiments is necessary to characterize a system.

[[Hans Primas]] and [[Roland Omnès]] give a more detailed breakdown that, in addition to the above, includes the following:<ref name="omnes" />{{rp|85}}
# Quantum physics applies to individual objects. The probabilities computed by the Born rule do not require an ensemble or collection of "identically prepared" systems to understand.
# The results provided by measuring devices are essentially classical, and should be described in ordinary language.  This was particularly emphasized by Bohr, and was accepted by Heisenberg.{{refn|group=note|Bohr declared, "In the first place, we must recognize that a measurement can mean nothing else than the unambiguous comparison of some property of the object under investigation with a corresponding property of another system, serving as a measuring instrument, and for which this property is directly determinable according to its definition in everyday language or in the terminology of classical physics."<ref>{{cite book|first=N. |last=Bohr |chapter=The Causality Problem in Atomic Physics |title=New Theories in Physics |pages=11–30 |location=Paris |year=1939 |publisher=International Institute of Intellectual Co-operation |oclc=923465888}}</ref> Heisenberg wrote, "Every description of phenomena, of experiments and their results, rests upon language as the only means of communication. The words of this language represent the concepts of ordinary life, which in the scientific language of physics may be refined to the concepts of classical physics. These concepts are the only tools for an unambiguous communication about events, about the setting up of experiments and about their results."<ref name="heisenberg1959">{{cite book|first=Werner |last=Heisenberg |author-link=Werner Heisenberg|year=1971 |orig-year=1959 |chapter=Criticism and counterproposals to the Copenhagen interpretation of quantum theory |pages= 114–128 |title=Physics and Philosophy: the Revolution in Modern Science |publisher=George Allen & Unwin |location=London}}</ref>{{rp|127}} }}
# Per the above point, the device used to observe a system must be described in classical language, while the system under observation is treated in quantum terms. This is a particularly subtle issue for which Bohr and Heisenberg came to differing conclusions. According to Heisenberg, the boundary between classical and quantum can be shifted in either direction at the observer's discretion. That is, the observer has the freedom to move what would become known as the "[[Heisenberg cut]]" without changing any physically meaningful predictions.<ref name="omnes"/>{{rp|86}} On the other hand, Bohr argued both systems are quantum in principle, and the object-instrument distinction (the "cut") is dictated by the experimental arrangement. For Bohr, the "cut" was not a change in the dynamical laws that govern the systems in question, but a change in the language applied to them.<ref name="camilleri2015"/><ref name="peres1998" />
# During an [[Measurement in quantum mechanics|observation]], the system must interact with a laboratory device. When that device makes a measurement, the wave function of the system [[wave function collapse|collapses]], irreversibly reducing to an [[Introduction to eigenstates|eigenstate]] of the [[observable]] that is registered. The result of this process is a tangible record of the event, made by a potentiality becoming an actuality.{{refn|group=note|Heisenberg wrote, "It is well known that the 'reduction of the wave packets' always appears in the Copenhagen interpretation when the transition is completed from the possible to the actual. The probability function, which covered a wide range of possibilities, is suddenly reduced to a much narrower range by the fact that the experiment has led to a definite result, that actually a certain event has happened. In the formalism this reduction requires that the so-called interference of probabilities, which is the most characteristic phenomena [''sic''] of quantum theory, is destroyed by the partly undefinable and irreversible interactions of the system with the measuring apparatus and the rest of the world."<ref name="heisenberg1959"/>{{rp|125}} Bohr suggested that "irreversibility" was "characteristic of the very concept of observation", an idea that Weizsäcker would later elaborate upon, trying to formulate a rigorous mathematical notion of irreversibility using thermodynamics, and thus show that irreversibility results in the classical approximation of the world.<ref name="camilleri2015"/> See also Stenholm.<ref name="Stenholm" />}}
# Statements about measurements that are not actually made do not have meaning. For example, there is no meaning to the statement that a photon traversed the upper path of a [[Mach–Zehnder interferometer]] unless the interferometer were actually built in such a way that the path taken by the photon is detected and registered.<ref name="omnes"/>{{rp|88}}
# Wave functions are objective, in that they do not depend upon personal opinions of individual physicists or other such arbitrary influences.<ref name="omnes"/>{{rp|509–512}}

There are some fundamental agreements and disagreements between the views of Bohr and Heisenberg. For example, Heisenberg emphasized a sharp "cut" between the [[Observer (quantum physics)|observer]] (or the instrument) and the system being observed,<ref name="PauliEinstein">{{cite book|first=Wolfgang |last=Pauli |author-link=Wolfgang Pauli |chapter=Albert Einstein and the development of physics |title=Writings on Physics and Philosophy |editor-first1=C. P. |editor-last1=Enz |editor-link1=Charles Enz |editor-first2=K. |editor-last2=von Meyenn |publisher=Springer-Verlag |location=Berlin |orig-year=1958 |year=1994 |bibcode=1994wpp..book.....P }}</ref>{{Rp|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 could take place within the quantum system.<ref name="Bell-Against-Measurement">{{Cite journal|last=Bell|first=John|author-link=John Stewart Bell |date=1990|title=Against 'measurement'|journal=[[Physics World]] |language=en|volume=3|issue=8|pages=33–41|doi=10.1088/2058-7058/3/8/26|issn=2058-7058}}</ref>

Another issue of importance where Bohr and Heisenberg disagreed is [[wave–particle duality]]. Bohr maintained that the distinction between a wave view and a particle view was defined by a distinction between experimental setups, whereas Heisenberg held that it was defined by the possibility of viewing the mathematical formulas as referring to waves or particles. Bohr thought that a particular experimental setup would display either a wave picture or a particle picture, but not both. Heisenberg thought that every mathematical formulation was capable of both wave and particle interpretations.<ref>{{cite journal | last1 = Camilleri | first1 = K. | year = 2006 | title = Heisenberg and the wave–particle duality | journal = [[Studies in History and Philosophy of Modern Physics]] | volume = 37 | issue = 2| pages = 298–315 | bibcode = 2006SHPMP..37..298C | doi = 10.1016/j.shpsb.2005.08.002 }}</ref><ref>{{cite book|last=Camilleri |first=K. |year=2009 |title=Heisenberg and the Interpretation of Quantum Mechanics: the Physicist as Philosopher |publisher=Cambridge University Press |location=Cambridge UK |isbn=978-0-521-88484-6 |oclc=638813030}}</ref>