Editing Copenhagen interpretation (section)

==Nature of the wave function==
A wave function is a mathematical entity that describes the shape of a wave form. In the Copenhagen interpretation this wave form provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the wave function together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. Generally, Copenhagen-type interpretations deny that the wave function provides a directly apprehensible image of an ordinary material body or a discernible component of some such,<ref>{{cite journal | doi = 10.1038/121580a0 | volume=121 | title=The Quantum Postulate and the Recent Development of Atomic Theory | year=1928 | journal=[[Nature (journal)|Nature]] | pages=580–590 | last1 = Bohr | first1 = N. | issue=3050 | bibcode=1928Natur.121..580B| doi-access=free }}, p. 586: "there can be no question of an immediate connexion with our ordinary conceptions".</ref><ref>[[Werner Heisenberg|Heisenberg, W.]] (1959/1971). 'Language and reality in modern physics', Chapter 10, pp. 145–160, in ''Physics and Philosophy: the Revolution in Modern Science'', George Allen & Unwin, London, {{ISBN|0-04-530016 X}}, p. 153: "our common concepts cannot be applied to the structure of the atoms."</ref> or anything more than a theoretical concept.

=== Probabilities via the Born rule ===
{{Main|Born rule}}
The [[Born rule]] is essential to the Copenhagen interpretation.<ref>{{cite journal|last1=Bohr|first1=N.|year=1928|title=The Quantum Postulate and the Recent Development of Atomic Theory|journal=[[Nature (journal)|Nature]] |volume=121|issue=3050|pages=580–590|bibcode=1928Natur.121..580B|doi=10.1038/121580a0|doi-access=free}}, p. 586: "In this connexion [Born] succeeded in obtaining a statistical interpretation of the wave functions, allowing a calculation of the probability of the individual transition processes required by the quantum postulate."</ref> Formulated by [[Max Born]] in 1926, it gives the [[probability]] that a [[measurement in quantum mechanics|measurement of a quantum system]] will yield a given result. In its simplest form, it states that the probability density of finding a particle at a given point, when measured, is proportional to the square of the magnitude of the particle's wave function at that point.{{refn|group=note|While Born himself described his contribution as the "statistical interpretation" of the wave function,<ref>{{cite journal|last1=Born|first1=M.|author-link=Max Born|year=1955|title=Statistical interpretation of quantum mechanics|journal=[[Science (journal)|Science]] |volume=122|issue=3172|pages=675–679|bibcode=1955Sci...122..675B|doi=10.1126/science.122.3172.675|pmid=17798674}}</ref><ref>{{cite journal|quote=... the statistical interpretation, which I have first suggested and which has been formulated in the most general way by von Neumann, ...|author-link=Max Born |last=Born |first=M. |year=1953 |title=The interpretation of quantum mechanics |journal=[[British Journal for the Philosophy of Science]] |volume=4 |number=14 |pages=95–106|doi=10.1093/bjps/IV.14.95 }}</ref> the term "statistical interpretation" has also been used as a synonym for the [[ensemble interpretation]].<ref>{{cite journal|last1=Ballentine|first1=L.E.|year=1970|title=The statistical interpretation of quantum mechanics|url=http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/65291|journal=[[Reviews of Modern Physics]] |volume=42|issue=4|pages=358–381|bibcode=1970RvMP...42..358B|doi=10.1103/revmodphys.42.358|s2cid=120024263 |url-access=subscription}}</ref><ref>{{cite book|author-link=Max Born |last=Born |first=M. |year=1949 |chapter=Einstein's statistical theories |title=Albert Einstein: Philosopher-Scientist |editor-first=P. A. |editor-last=Schilpp |editor-link=Paul Arthur Schilpp |publisher=Open Court |location=La Salle IL |volume=1 |pages=161–177}}</ref>}}

=== Collapse ===
{{Main|Wave function collapse}}
The concept of wave function collapse postulates that the wave function of a system can change suddenly and discontinuously upon measurement. Prior to a measurement, a wave function involves the various probabilities for the different potential outcomes of that measurement. But when the apparatus registers one of those outcomes, no traces of the others linger. Since Bohr did not view the wavefunction as something physical, he never talks about "collapse". Nevertheless, many physicists and philosophers associate collapse with the Copenhagen interpretation.<ref name="Faye-Stanford" /><ref name="Howard 2004" />

Heisenberg spoke of the wave function as representing available knowledge of a system, and did not use the term "collapse", but instead termed it "reduction" of the wave function to a new state representing the change in available knowledge which occurs once a particular phenomenon is registered by the apparatus.<ref>W. Heisenberg "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik," ''Zeitschrift für Physik'', Volume 43, 172–198 (1927), as translated by John Wheeler and Wojciech Zurek, in ''Quantum Theory and Measurement'' (1983), p. 74.  ("[The] determination of the position selects a definite "''q''" from the totality of possibilities and limits the options for all subsequent measurements.  ... [T]he results of later measurements can only be calculated when one again ascribes to the electron a "smaller" wavepacket of extension λ (wavelength of the light used in the observation).  Thus, every position determination reduces the wavepacket back to its original extension λ.")</ref> 

===Role of the observer===
Because they assert that the existence of an observed value depends upon the intercession of the observer, Copenhagen-type interpretations are sometimes called "subjective".<ref>{{cite journal|last=Howard |first=Don |title=Entangled quantum histories |journal=[[Nature (journal)|Nature]] |volume=456 |pages=706–707 |year=2008 |issue=7223 |doi=10.1038/456706a|bibcode=2008Natur.456..706H }}</ref> All of the original Copenhagen protagonists considered the process of observation as mechanical and independent of the individuality of the observer.<ref name="Heisenberg, W 1971 pp. 114">"Of course the introduction of the observer must not be misunderstood to imply that some kind of subjective features are to be brought into the description of nature." [[Werner Heisenberg|Heisenberg, W.]] (1959/1971). Criticism and counterproposals to the Copenhagen interpretation of quantum theory, Chapter 8, pp. 114–128, in ''Physics and Philosophy: the Revolution in Modern Science'', third impression 1971, George Allen & Unwin, London, at p. 121.</ref> [[Wolfgang Pauli]], for example, insisted that measurement results could be obtained and recorded by "objective registering apparatus".<ref name="PauliEinstein"/>{{Rp|117–123}} As Heisenberg wrote,

{{Blockquote|Of course the introduction of the observer must not be misunderstood to imply that some kind of subjective features are to be brought into the description of nature. The observer has, rather, only the function of registering decisions, i.e., processes in space and time, and it does not matter whether the observer is an apparatus or a human being; but the registration, i.e., the transition from the "possible" to the "actual," is absolutely necessary here and cannot be omitted from the interpretation of quantum theory.<ref name="Heisenberg 1958"/>{{rp|137}}}}

In the 1970s and 1980s, the theory of [[Quantum decoherence|decoherence]] helped to explain the appearance of quasi-classical realities emerging from quantum theory,<ref>See, for example:
*{{cite journal|last=Zeh|first=H. Dieter|author-link=H. Dieter Zeh|year=1970|title=On the Interpretation of Measurement in Quantum Theory|journal=[[Foundations of Physics]]|volume=1|issue=1|pages=69–76|bibcode=1970FoPh....1...69Z|doi=10.1007/BF00708656|s2cid=963732}}
*{{cite journal|last=Zurek|first=Wojciech H.|author-link=Wojciech H. Zurek|year=1981|title=Pointer Basis of Quantum Apparatus: Into what Mixture does the Wave Packet Collapse?|journal=[[Physical Review D]]|volume=24|issue=6|pages=1516–1525|bibcode=1981PhRvD..24.1516Z|doi=10.1103/PhysRevD.24.1516}}
*{{cite journal|last=Zurek|first=Wojciech H.|author-link=Wojciech H. Zurek|year=1982|title=Environment-Induced Superselection Rules|journal=[[Physical Review D]]|volume=26|issue=8|pages=1862–1880|bibcode=1982PhRvD..26.1862Z|doi=10.1103/PhysRevD.26.1862}}</ref> but was insufficient to provide a technical explanation for the apparent wave function collapse.<ref name="schlosshauer2019">{{cite journal|last=Schlosshauer|first=M.|year=2019|title=Quantum Decoherence|journal=[[Physics Reports]]|volume=831|pages=1–57|arxiv=1911.06282|bibcode=2019PhR...831....1S|doi=10.1016/j.physrep.2019.10.001|s2cid=208006050}}</ref>

=== Completion by hidden variables? ===
{{main|Hidden-variable theory}}
In metaphysical terms, the Copenhagen interpretation views [[quantum mechanics]] as providing knowledge of phenomena, but not as pointing to 'really existing objects', which it regards as residues of ordinary intuition. This makes it an [[epistemic]] theory. This may be contrasted with Einstein's view, that physics should look for 'really existing objects', making itself an [[ontic]] theory.<ref>[[Max Jammer|Jammer, M.]] (1982). 'Einstein and quantum physics', pp. 59–76 in ''Albert Einstein: Historical and Cultural Perspectives; the Centennial Symposium in Jerusalem'', edited by G. Holton, Y. Elkana, Princeton University Press, Princeton NJ, {{ISBN|0-691-08299-5}}. On pp. 73–74, Jammer quotes a 1952 letter from Einstein to Besso: "The present quantum theory is unable to provide the description of a real state of physical facts, but only of an (incomplete) knowledge of such. Moreover, the very concept of a real factual state is debarred by the orthodox theoreticians. The situation arrived at corresponds almost exactly to that of the good old Bishop Berkeley."</ref>

The metaphysical question is sometimes asked: "Could quantum mechanics be extended by adding so-called "hidden variables" to the mathematical formalism, to convert it from an epistemic to an ontic theory?" The Copenhagen interpretation answers this with a strong 'No'.<ref>[[Werner Heisenberg|Heisenberg, W.]] (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, ''Z. Phys.'' '''43''': 172–198. Translation as 'The actual content of quantum theoretical kinematics and mechanics' [https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19840008978.pdf here]: "Since the statistical nature of quantum theory is so closely [linked] to the uncertainty in all observations or perceptions, one could be tempted to conclude that behind the observed, statistical world a "real" world is hidden, in which the law of causality is applicable. We want to state explicitly that we believe such speculations to be both fruitless and pointless. The only task of physics is to describe the relation between observations."</ref> It is sometimes alleged, for example by [[John Stewart Bell|J.S. Bell]], that Einstein opposed the Copenhagen interpretation because he believed that the answer to that question of "hidden variables" was "yes". By contrast, [[Max Jammer]] writes "Einstein never proposed a hidden variable theory."<ref>[[Max Jammer|Jammer, M.]] (1982). 'Einstein and quantum physics', pp. 59–76 in ''Albert Einstein: Historical and Cultural Perspectives; the Centennial Symposium in Jerusalem'', edited by G. Holton, Y. Elkana, Princeton University Press, Princeton NJ, {{ISBN|0-691-08299-5}}, p. 72.</ref> Einstein explored the possibility of a hidden variable theory, and wrote a paper describing his exploration, but withdrew it from publication because he felt it was faulty.<ref>{{cite journal |last1=Belousek |first1=D.W. |year=1996 |title=Einstein's 1927 unpublished hidden-variable theory: its background, context and significance |journal=[[Studies in History and Philosophy of Modern Physics]] |volume=21 |issue=4 |pages=431–461 |bibcode=1996SHPMP..27..437B |doi=10.1016/S1355-2198(96)00015-9 }}</ref><ref>{{cite journal |last1=Holland |first1=P |year=2005 |title=What's wrong with Einstein's 1927 hidden-variable interpretation of quantum mechanics? |journal=[[Foundations of Physics]] |volume=35 |issue=2 |pages=177–196 |doi=10.1007/s10701-004-1940-7 |arxiv=quant-ph/0401017|bibcode=2005FoPh...35..177H |s2cid=119426936 }}</ref>