Editing Bell's theorem (section)

== Interpretations ==
{{main|Interpretations of quantum mechanics}}
Reactions to Bell's theorem have been many and varied. Maximilian Schlosshauer, Johannes Kofler, and Zeilinger write that Bell inequalities provide "a wonderful example of how we can have a rigorous theoretical result tested by numerous experiments, and yet disagree about the implications."<ref>{{Cite journal| arxiv=1301.1069
 | title=A Snapshot of Foundational Attitudes Toward Quantum Mechanics
 | journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
 | volume=44
 | issue=3
 | pages=222–230
 | date=2013-01-06
 | last1=Schlosshauer
 | first1=Maximilian
 | last2=Kofler
 | first2=Johannes
 | last3=Zeilinger
 | first3=Anton
 | author-link3=Anton Zeilinger
 | doi=10.1016/j.shpsb.2013.04.004
 | bibcode=2013SHPMP..44..222S
 | s2cid=55537196
 }}</ref>

=== The Copenhagen interpretation ===
[[Copenhagen interpretation|Copenhagen-type interpretations]] generally take the violation of Bell inequalities as grounds to reject the assumption often called [[counterfactual definiteness]] or "realism", which is not necessarily the same as abandoning realism in a broader philosophical sense.<ref>{{Cite journal|last=Werner|first=Reinhard F. |author-link=Reinhard F. Werner |date=2014-10-24|title=Comment on 'What Bell did'|journal=[[Journal of Physics A: Mathematical and Theoretical]]|volume=47|issue=42|pages=424011|doi=10.1088/1751-8113/47/42/424011|issn=1751-8113 |bibcode=2014JPhA...47P4011W|s2cid=122180759 }}</ref><ref>{{cite book|last=Żukowski|first=Marek|title=Quantum &#91;Un&#93;Speakables II |chapter=Bell's Theorem Tells Us Not What Quantum Mechanics is, but What Quantum Mechanics is Not |date=2017|series=The Frontiers Collection|pages=175–185|editor-last=Bertlmann|editor-first=Reinhold|place=Cham|publisher=Springer International Publishing|doi=10.1007/978-3-319-38987-5_10|isbn=978-3-319-38985-1|editor2-last=Zeilinger|editor2-first=Anton |editor-link2=Anton Zeilinger |arxiv=1501.05640|s2cid=119214547}}</ref> For example, [[Roland Omnès]] argues for the rejection of hidden variables and concludes that "quantum mechanics is probably as realistic as any theory of its scope and maturity ever will be".<ref name="omnes">{{cite book|first=R. |last=Omnès |author-link=Roland Omnès |title=The Interpretation of Quantum Mechanics |publisher=Princeton University Press |year=1994 |isbn=978-0-691-03669-4 |oclc=439453957 }}</ref>{{Rp|531}} Likewise, [[Rudolf Peierls]] took the message of Bell's theorem to be that, because the premise of locality is physically reasonable, "hidden variables cannot be introduced without abandoning some of the results of quantum mechanics".<ref>{{cite book|last=Peierls |first=Rudolf |author-link=Rudolf Peierls |title=Surprises in Theoretical Physics |pages=26–29 |publisher=Princeton University Press |year=1979 |isbn=0-691-08241-3}}</ref><ref>{{cite journal|last=Mermin |first=N. D. |author-link=N. David Mermin |title=What Do These Correlations Know About Reality? Nonlocality and the Absurd |journal=[[Foundations of Physics]] |volume=29 |year=1999 |issue=4 |pages=571–587 |arxiv=quant-ph/9807055 |bibcode=1998quant.ph..7055M |doi=10.1023/A:1018864225930}}</ref>

This is also the route taken by interpretations that descend from the Copenhagen tradition, such as [[consistent histories]] (often advertised as "Copenhagen done right"),<ref>{{Cite journal|last=Hohenberg|first=P. C.|author-link=Pierre Hohenberg|date=2010-10-05|title=Colloquium : An introduction to consistent quantum theory|journal=[[Reviews of Modern Physics]] |language=en |volume=82 |issue=4 |pages=2835–2844 |arxiv=0909.2359 |doi=10.1103/RevModPhys.82.2835 |issn=0034-6861 |bibcode=2010RvMP...82.2835H|s2cid=20551033}}</ref>{{rp|2839|q=CQT most definitely opts for retaining locality (EPR2) and rejecting classical realism (EPR1)}} as well as [[QBism]].<ref>{{Cite book|chapter-url=https://plato.stanford.edu/entries/quantum-bayesian/|title=[[Stanford Encyclopedia of Philosophy]] |last=Healey|first=Richard|publisher=Metaphysics Research Lab, Stanford University|year=2016|editor-last=Zalta|editor-first=Edward N.|chapter=Quantum-Bayesian and Pragmatist Views of Quantum Theory|access-date=2021-09-16|archive-date=2021-08-17|archive-url=https://web.archive.org/web/20210817204745/https://plato.stanford.edu/entries/quantum-bayesian/|url-status=live}}</ref>

=== Many-worlds interpretation of quantum mechanics ===

The [[Many-worlds interpretation]], also known as the [[Hugh Everett III|Everett]] interpretation, is dynamically local, meaning that it does not call for [[action at a distance]],<ref name=BrownTimpson/>{{rp|17}} and deterministic, because it consists of the unitary part of quantum mechanics without collapse. It can generate correlations that violate a Bell inequality because it violates an implicit assumption by Bell that measurements have a single outcome. In fact, Bell's theorem can be proven in the Many-Worlds framework from the assumption that a measurement has a single outcome. Therefore, a violation of a Bell inequality can be interpreted as a demonstration that measurements have multiple outcomes.<ref>{{cite journal |first1=David |last1=Deutsch |author-link1=David Deutsch |first2=Patrick |last2=Hayden |author-link2=Patrick Hayden (scientist) |title=Information flow in entangled quantum systems |journal=[[Proceedings of the Royal Society A]] |date=2000 |volume=456 |issue=1999 |pages=1759–1774 |doi=10.1098/rspa.2000.0585|arxiv=quant-ph/9906007|bibcode=2000RSPSA.456.1759D |s2cid=13998168 }}</ref>

The explanation it provides for the Bell correlations is that when Alice and Bob make their measurements, they split into local branches. From the point of view of each copy of Alice, there are multiple copies of Bob experiencing different results, so Bob cannot have a definite result, and the same is true from the point of view of each copy of Bob. They will obtain a mutually well-defined result only when their future light cones overlap. At this point we can say that the Bell correlation starts existing, but it was produced by a purely local mechanism. Therefore, the violation of a Bell inequality cannot be interpreted as a proof of non-locality.<ref name=BrownTimpson>{{Cite book|first1=Harvey R. |last1=Brown |author-link1=Harvey R. Brown |first2 = Christopher G. |last2=Timpson|chapter=Bell on Bell's Theorem: The Changing Face of Nonlocality|title=Quantum Nonlocality and Reality: 50 years of Bell's theorem |editor-first1=Mary |editor-last1=Bell |editor-first2=Shan |editor-last2=Gao |publisher=Cambridge University Press|year=2016|pages = 91–123|arxiv=1501.03521|doi=10.1017/CBO9781316219393.008|isbn = 9781316219393|s2cid = 118686956}}</ref>{{rp|28|q=In our discussion of locality in the Everett interpretation we have sought to provide a constructive example illustrating precisely how a theory can be dynamically local, whilst violating local causality}}

=== Non-local hidden variables ===

Most advocates of the hidden-variables idea believe that experiments have ruled out local hidden variables.{{refn|group=note|[[E. T. Jaynes]] was one exception,<ref name="E.T. Jaynes 1989">{{Cite book |year=1989 |last1=Jaynes |first1=E. T. |title=Maximum Entropy and Bayesian Methods |chapter=Clearing up Mysteries — the Original Goal |pages=1–27 |url=http://bayes.wustl.edu/etj/articles/cmystery.pdf |doi=10.1007/978-94-015-7860-8_1 |isbn=978-90-481-4044-2 |citeseerx=10.1.1.46.1264 |access-date=2011-10-18 |archive-date=2011-10-28 |archive-url=https://web.archive.org/web/20111028131916/http://bayes.wustl.edu/etj/articles/cmystery.pdf |url-status=live }}</ref> but Jaynes' arguments have not generally been found persuasive.<ref name="Gill2002">{{cite book|chapter=Time, Finite Statistics, and Bell's Fifth Position|first=Richard D.|last=Gill|pages=179–206|title=Proceedings of the Conference Foundations of Probability and Physics - 2 : Växjö (Soland), Sweden, June 2-7, 2002 |volume=5|publisher=Växjö University Press|date=2002|arxiv=quant-ph/0301059 }}</ref>}} They are ready to give up locality, explaining the violation of Bell's inequality by means of a non-local [[hidden variable theory]], in which the particles exchange information about their states. This is the basis of the [[Bohm interpretation]] of quantum mechanics, which requires that all particles in the universe be able to instantaneously exchange information with all others. One challenge for non-local hidden variable theories is to explain why this instantaneous communication can exist at the level of the hidden variables, but it cannot be used to send signals.<ref>{{Cite journal |last1=Wood |first1=Christopher J. |last2=Spekkens |first2=Robert W. |author-link2=Robert Spekkens |date=2015-03-03 |title=The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning |url=https://iopscience.iop.org/article/10.1088/1367-2630/17/3/033002 |journal=[[New Journal of Physics]] |volume=17 |issue=3 |pages=033002 |arxiv=1208.4119 |bibcode=2015NJPh...17c3002W |doi=10.1088/1367-2630/17/3/033002 |s2cid=118518558 |issn=1367-2630}}</ref> A 2007 experiment ruled out a large class of non-Bohmian non-local hidden variable theories, though not Bohmian mechanics itself.<ref>{{cite journal |doi=10.1038/nature05677 |title=An experimental test of non-local realism |year=2007 |last1=Gröblacher |first1=Simon |last2=Paterek |first2=Tomasz |last3=Kaltenbaek |first3=Rainer |last4=Brukner |first4=Časlav |author-link4=Časlav Brukner |last5=Żukowski |first5=Marek |last6=Aspelmeyer |first6=Markus |last7=Zeilinger |first7=Anton |author-link7=Anton Zeilinger |journal=[[Nature (journal)|Nature]] |volume=446 |issue=7138 |pages=871–5 |pmid=17443179|bibcode = 2007Natur.446..871G | arxiv= 0704.2529 |s2cid=4412358 }}</ref>

The [[transactional interpretation]], which postulates waves traveling both backwards and forwards in time, is likewise non-local.<ref>{{Cite journal|last=Kastner|first=Ruth E.|date=May 2010|title=The quantum liar experiment in Cramer's transactional interpretation|url=https://linkinghub.elsevier.com/retrieve/pii/S135521981000002X|journal=[[Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics]] |language=en|volume=41|issue=2|pages=86–92|arxiv=0906.1626|bibcode=2010SHPMP..41...86K|doi=10.1016/j.shpsb.2010.01.001|s2cid=16242184|access-date=2021-09-16|archive-date=2018-06-24|archive-url=https://web.archive.org/web/20180624053010/https://linkinghub.elsevier.com/retrieve/pii/S135521981000002X|url-status=live}}</ref>

===Superdeterminism===
{{Main|Superdeterminism}}
A necessary assumption to derive Bell's theorem is that the hidden variables are not correlated with the measurement settings. This assumption has been justified on the grounds that the experimenter has "[[free will]]" to choose the settings, and that it is necessary to do science in the first place. A (hypothetical) theory where the choice of measurement is necessarily correlated with the system being measured is known as ''superdeterministic''.<ref name=larsson14/>

A few advocates of deterministic models have not given up on local hidden variables. For example, [[Gerard 't Hooft]] has argued that superdeterminism cannot be dismissed.<ref>{{cite book |last='t Hooft |first=Gerard |author-link=Gerard 't Hooft |title=The Cellular Automaton Interpretation of Quantum Mechanics |volume=185 |publisher=Springer |year=2016 |doi=10.1007/978-3-319-41285-6 |isbn=978-3-319-41284-9 |oclc=951761277 |series=Fundamental Theories of Physics |s2cid=7779840 |url=http://www.oapen.org/search?identifier=1002003 |access-date=2020-08-27 |archive-date=2021-12-29 |archive-url=https://web.archive.org/web/20211229062338/https://library.oapen.org/handle/20.500.12657/27994 |url-status=live }}</ref>