Editing Wave function collapse (section)

==Physical approaches to collapse==
Quantum theory offers no dynamical description of the "collapse" of the wave function. Viewed as a statistical theory, no description is expected. As Fuchs and Peres put it, "collapse is something that happens in our description of the system, not to the system itself".<ref name=FuchsPeresNo>{{Cite journal |last=Fuchs |first=Christopher A. |last2=Peres |first2=Asher |date=2000-03-01 |title=Quantum Theory Needs No ‘Interpretation’ |url=https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=7596444653d614458ee7aea0422dabfc95ace3e6 |journal=Physics Today |language=en |volume=53 |issue=3 |pages=70–71 |doi=10.1063/1.883004 |issn=0031-9228}}</ref>

Various [[interpretations of quantum mechanics]] attempt to provide a physical model for collapse.<ref name=Stamatescu>{{Cite book |last=Stamatescu |first=Ion-Olimpiu |url=https://link.springer.com/10.1007/978-3-540-70626-7_230 |title=Wave Function Collapse |date=2009 |publisher=Springer Berlin Heidelberg |isbn=978-3-540-70622-9 |editor-last=Greenberger |editor-first=Daniel |location=Berlin, Heidelberg |pages=813–822 |language=en |doi=10.1007/978-3-540-70626-7_230 |editor-last2=Hentschel |editor-first2=Klaus |editor-last3=Weinert |editor-first3=Friedel}}</ref>{{rp|816}} Three treatments of collapse can be found among the common interpretations. The first group includes hidden-variable theories like [[de Broglie–Bohm theory]]; here random outcomes only result from unknown values of hidden variables. Results from [[Bell test|tests]] of [[Bell's theorem]] shows that these variables would need to be non-local. The second group models measurement as quantum entanglement between the quantum state and the measurement apparatus. This results in a simulation of classical statistics called quantum decoherence. This group includes the [[many-worlds interpretation]] and [[consistent histories]] models. The third group postulates additional, but as yet undetected, physical basis for the randomness; this group includes for example the [[objective-collapse interpretation]]s. While models in all groups have contributed to better understanding of quantum theory, no alternative explanation for individual events has emerged as more useful than collapse followed by statistical prediction with the Born rule.<ref name=Stamatescu/>{{rp|819}}

The significance ascribed to the wave function varies from interpretation to interpretation and even within an interpretation (such as the [[Copenhagen interpretation]]). If the wave function merely encodes an observer's knowledge of the universe, then the wave function collapse corresponds to the receipt of new information. This is somewhat analogous to the situation in classical physics, except that the classical "wave function" does not necessarily obey a wave equation. If the wave function is physically real, in some sense and to some extent, then the collapse of the wave function is also seen as a real process, to the same extent.{{citation needed| reason=the ontological wave function literature should be represented, the paragraph based on Stamatescu is too compact now.|date=March 2024}}

===Quantum decoherence===
{{Main|Quantum decoherence}}

Quantum decoherence explains why a system interacting with an environment transitions from being a [[Quantum state#Pure states as rays in a complex Hilbert space|pure state]], exhibiting superpositions, to a [[Quantum state#Mixed states|mixed state]], an incoherent combination of classical alternatives.<ref name="Stanford1" /> This transition is fundamentally reversible, as the combined state of system and environment is still pure, but for all practical purposes irreversible in the same sense as in the [[second law of thermodynamics]]: the environment is a very large and complex quantum system, and it is not feasible to reverse their interaction. Decoherence is thus very important for explaining the [[classical limit]] of quantum mechanics, but cannot explain wave function collapse, as all classical alternatives are still present in the mixed state, and wave function collapse selects only one of them.<ref name=Schlosshauer/><ref>{{cite journal |author1=Wojciech H. Zurek |title=Decoherence, einselection, and the quantum origins of the classical |journal=Reviews of Modern Physics |date=2003 |volume=75 |issue=3 |page=715 |doi=10.1103/RevModPhys.75.715 |arxiv=quant-ph/0105127 |bibcode=2003RvMP...75..715Z |s2cid=14759237 }}</ref><ref name="Stanford1" />

The form of decoherence known as [[einselection|environment-induced superselection]] proposes that when a quantum system interacts with the environment, the superpositions ''apparently'' reduce to mixtures of classical alternatives. The combined wave function of the system and environment continue to obey the Schrödinger equation throughout this ''apparent'' collapse.<ref name=Zurek>{{cite journal |last=Zurek |first=Wojciech Hubert |title=Quantum Darwinism |journal=Nature Physics |year=2009 |volume=5 |issue=3 |pages=181–188 |doi=10.1038/nphys1202 |arxiv = 0903.5082 |bibcode = 2009NatPh...5..181Z |s2cid=119205282}}</ref> More importantly, this is not enough to explain ''actual'' wave function collapse, as decoherence does not reduce it to a single eigenstate.<ref name=Schlosshauer>{{cite journal |last=Schlosshauer |first=Maximilian |title=Decoherence, the measurement problem, and interpretations of quantum mechanics |journal=Rev. Mod. Phys. |year=2005 |volume=76 |issue=4 |pages=1267–1305 |doi=10.1103/RevModPhys.76.1267 |arxiv = quant-ph/0312059 |bibcode = 2004RvMP...76.1267S |s2cid=7295619}}</ref><ref name="Stanford1">{{cite encyclopedia
  | last = Fine
  | first = Arthur
  | title = The Role of Decoherence in Quantum Mechanics
  | encyclopedia = Stanford Encyclopedia of Philosophy
  | publisher = Center for the Study of Language and Information, Stanford University website
  | date = 2020
  | url = https://plato.stanford.edu/entries/qm-decoherence/
  | format =
  | doi =
  | access-date = 11 April 2021}}</ref>