Editing Wave function collapse (section)

==History==
The concept of wavefunction collapse was introduced by [[Werner Heisenberg]] in his 1927 paper on the [[uncertainty principle]], "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik", and incorporated into the [[mathematical formulation of quantum mechanics]] by [[John von Neumann]], in his 1932 treatise ''Mathematische Grundlagen der Quantenmechanik''.<ref name="C. Kiefer-2002">{{Cite book |last=Kiefer |first=Claus |url=http://link.springer.com/10.1007/978-3-662-10557-3_19 |title=Time, Quantum and Information. |date=2003 |publisher=Springer Berlin Heidelberg |isbn=978-3-642-07892-7 |editor-last=Castell |editor-first=Lutz |location=Berlin, Heidelberg |pages=291–299 |language=en |chapter=On the Interpretation of Quantum Theory — from Copenhagen to the Present Day |doi=10.1007/978-3-662-10557-3_19 |editor-last2=Ischebeck |editor-first2=Otfried}}</ref> Heisenberg did not try to specify exactly what the collapse of the wavefunction meant. However, he emphasized that it should not be understood as a physical process.<ref>{{cite journal |author=G. Jaeger |year=2017 |title="Wave-Packet Reduction" and the Quantum Character of the Actualization of Potentia |journal=Entropy |volume=19 |issue=10 |pages=13
|doi=10.3390/e19100513|bibcode=2017Entrp..19..513J |doi-access=free |hdl=2144/41814 |hdl-access=free }}</ref> Niels Bohr never mentions wave function collapse in his published work, but he repeatedly cautioned that we must give up a "pictorial representation". Despite the differences between Bohr and Heisenberg, their views are often grouped together as the "Copenhagen interpretation", of which wave function collapse is regarded as a key feature.<ref>{{cite journal|title=Niels Bohr on the wave function and the classical/quantum divide |author=Henrik Zinkernagel |year=2016 |doi=10.1016/j.shpsb.2015.11.001 |journal=Studies in History and Philosophy of Modern Physics |volume=53 |pages=9–19 |arxiv = 1603.00353|bibcode=2016SHPMP..53....9Z |s2cid=18890207 |quote=Among Bohr scholars it is common to assert that Bohr never mentions the wave function collapse (see e.g. Howard, 2004 and Faye, 2008). It is true that in Bohr’s published writings, he does not discuss the status or existence of this standard component in the popular image of the Copenhagen interpretation. }}</ref>

[[John von Neumann]]'s influential 1932 work ''[[Mathematical Foundations of Quantum Mechanics]]'' took a more formal approach, developing an "ideal" measurement scheme<ref name=HartleQMCosmology>Hartle, James B. [https://arxiv.org/pdf/1805.12246.pdf "The quantum mechanics of cosmology."] Notes from the lectures by the author at the 7th Jerusalem Winter School 1990 on Quantum Cosmology and Baby Universes. arXiv:1805.12246 (2018).</ref><ref name=SchlosshauerReview>{{Cite journal |last=Schlosshauer |first=Maximilian |url=https://link.aps.org/doi/10.1103/RevModPhys.76.1267 |title=Decoherence, the measurement problem, and interpretations of quantum mechanics |journal=Reviews of Modern Physics |date=2005-02-23 |volume=76 |pages=1267–1305 |language=en |doi=10.1103/RevModPhys.76.1267 |issn=0034-6861|arxiv=quant-ph/0312059 }}</ref>{{rp|1270|q=Note that von Neumann’s scheme is in sharp contrast to the Copenhagen interpretation, where measurement is not treated as a system-apparatus interaction described by the usual quantum-mechanical formalism, but instead as an independent component of the theory, to be represented entirely in fundamentally classical terms.}} that postulated that there were two processes of wave function change:

# The [[probability|probabilistic]], non-[[unitary transformation|unitary]], [[local realism|non-local]], discontinuous change brought about by observation and [[quantum measurement|measurement]] (state reduction or collapse).
# The [[deterministic]], unitary, continuous [[time evolution]] of an isolated system that obeys the [[Schrödinger equation]].

In 1957 [[Hugh Everett III]] proposed a model of quantum mechanics that dropped von Neumann's first postulate. Everett observed that the measurement apparatus was also a quantum system and its quantum interaction with the system under observation should determine the results. He proposed that the discontinuous change is instead a splitting of a wave function representing the universe.<ref name=SchlosshauerReview/>{{rp|1288}} While Everett's approach rekindled interest in foundational quantum mechanics, it left core issues unresolved. Two key issues relate to origin of the observed classical results: what causes quantum systems to appear classical and to resolve with the observed probabilities of the [[Born rule]].<ref name=SchlosshauerReview/>{{rp|1290}}<ref name=HartleQMCosmology/>{{rp|5}}

Beginning in 1970 [[H. Dieter Zeh]] sought a detailed quantum decoherence model for the discontinuous change without postulating collapse. Further work by [[Wojciech H. Zurek]] in 1980 lead eventually to a large number of papers on many aspects of the concept.<ref>{{Cite journal |last=Camilleri |first=Kristian |date=2009-12-01 |title=A history of entanglement: Decoherence and the interpretation problem |url=https://www.sciencedirect.com/science/article/pii/S1355219809000562 |journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics |series=On The History Of The Quantum |volume=40 |issue=4 |pages=290–302 |doi=10.1016/j.shpsb.2009.09.003 |issn=1355-2198}}</ref> Decoherence assumes that every quantum system interacts quantum mechanically with its environment and such interaction is not separable from the system, a concept called an "open system".<ref name=SchlosshauerReview/>{{rp|1273}} Decoherence has been shown to work very quickly and within a minimal environment, but as yet it has not succeeded in a providing a detailed model replacing the collapse postulate of orthodox quantum mechanics.<ref name=SchlosshauerReview/>{{rp|1302}}

By explicitly dealing with the interaction of object and measuring instrument, von Neumann<ref name="Grundlagen"/> described a quantum mechanical measurement scheme consistent with wave function collapse. However, he did not prove the ''necessity'' of such a collapse. Von Neumann's projection postulate was conceived based on experimental evidence available during the 1930s, in particular [[Compton scattering]]. Later work refined the notion of measurements into the more easily discussed ''first kind'', that will give the same value when immediately repeated, and the ''second kind'' that give different values when repeated.<ref>
{{cite book
 |author=W. Pauli
 |year=1958
 |chapter=Die allgemeinen Prinzipien der Wellenmechanik
 |editor=S. Flügge
 |title=Handbuch der Physik
 |volume=V |page=73
 |publisher=Springer-Verlag
 |location=Berlin
|language=de}}</ref><ref>
{{cite journal
 |author1=L. Landau |author2=R. Peierls
  |name-list-style=amp |year=1931
 |title=Erweiterung des Unbestimmtheitsprinzips für die relativistische Quantentheorie
 |journal=[[Zeitschrift für Physik]]
 |volume=69
 |issue=1–2 |pages=56–69
 |doi=10.1007/BF01391513
|bibcode = 1931ZPhy...69...56L |s2cid=123160388
 |language=de}})</ref><ref>Discussions of measurements of the second kind can be found in most treatments on the foundations of quantum mechanics, for instance, {{cite book
 |author=J. M. Jauch
 |year=1968
 |title=Foundations of Quantum Mechanics
 |url=https://archive.org/details/foundationsofqua0000jauc
 |url-access=registration
 |publisher=Addison-Wesley
 |page=[https://archive.org/details/foundationsofqua0000jauc/page/165 165]
}}; {{cite book
 |author=B. d'Espagnat
 |year=1976
 |title=Conceptual Foundations of Quantum Mechanics
 |publisher=W. A. Benjamin
 |pages=18, 159
}}; and {{cite book
 |author=W. M. de Muynck
 |year=2002
 |title=Foundations of Quantum Mechanics: An Empiricist Approach
 |page=section 3.2.4 |no-pp=yes
 |publisher=Kluwer Academic Publishers
}}</ref>