Editing Bell's theorem (section)

===Free will theorem===
{{main|Free will theorem}}
The Kochen–Specker type of argument, using configurations of interlocking bases, can be combined with the idea of measuring entangled pairs that underlies Bell-type inequalities. This was noted beginning in the 1970s by Kochen,<ref>{{Cite journal |last1=Redhead |first1=Michael |author-link1=Michael Redhead |last2=Brown |first2=Harvey |author-link2=Harvey R. Brown |date=1991-07-01 |title=Nonlocality in Quantum Mechanics |journal=[[Aristotelian Society|Proceedings of the Aristotelian Society, Supplementary Volumes]] |language=en |volume=65 |issue=1 |pages=119–160 |doi=10.1093/aristoteliansupp/65.1.119 |issn=0309-7013 |jstor=4106773 |quote=A similar approach was arrived at independently by Simon Kochen, although never published (private communication).}}</ref> Heywood and Redhead,<ref>{{Cite journal|last1=Heywood|first1=Peter|last2=Redhead|first2=Michael L. G. |author-link2=Michael Redhead |date=May 1983|title=Nonlocality and the Kochen–Specker paradox |journal=[[Foundations of Physics]] |language=en|volume=13|issue=5|pages=481–499|doi=10.1007/BF00729511|bibcode=1983FoPh...13..481H |s2cid=120340929|issn=0015-9018}}</ref> Stairs,<ref>{{Cite journal|last=Stairs|first=Allen|date=December 1983|title=Quantum Logic, Realism, and Value Definiteness|journal=[[Philosophy of Science (journal)|Philosophy of Science]] |language=en|volume=50|issue=4|pages=578–602|doi=10.1086/289140|s2cid=122885859|issn=0031-8248}}</ref> and Brown and Svetlichny.<ref>{{Cite journal|last1=Brown |first1=H. R. |author-link1=Harvey Brown (philosopher) |last2=Svetlichny|first2=G.|date=November 1990|title=Nonlocality and Gleason's lemma. Part I. Deterministic theories|journal=[[Foundations of Physics]] |language=en|volume=20|issue=11|pages=1379–1387|doi=10.1007/BF01883492|bibcode=1990FoPh...20.1379B |s2cid=122868901 |issn=0015-9018}}</ref> As EPR pointed out, obtaining a measurement outcome on one half of an entangled pair implies certainty about the outcome of a corresponding measurement on the other half. The "EPR criterion of reality" posits that because the second half of the pair was not disturbed, that certainty must be due to a physical property belonging to it.<ref>{{Cite journal|last1=Glick|first1=David|last2=Boge|first2=Florian J.|date=2019-10-22|title=Is the Reality Criterion Analytic?|journal=[[Erkenntnis]]|language=en|volume=86|issue=6|pages=1445–1451|arxiv=1909.11893|bibcode=2019arXiv190911893G|doi=10.1007/s10670-019-00163-w|s2cid=202889160|issn=0165-0106}}</ref> In other words, by this criterion, a hidden variable <math>\lambda</math> must exist within the second, as-yet unmeasured half of the pair. No contradiction arises if only one measurement on the first half is considered. However, if the observer has a choice of multiple possible measurements, and the vectors defining those measurements form a Kochen–Specker configuration, then some outcome on the second half will be simultaneously impossible and guaranteed.

This type of argument gained attention when an instance of it was advanced by [[John Horton Conway|John Conway]] and [[Simon B. Kochen|Simon Kochen]] under the name of the [[free will theorem]].<ref>{{cite journal | last1 = Conway | first1 = John |first2=Simon |last2=Kochen | author-link1=John Horton Conway | author-link2=Simon B. Kochen |year = 2006 | title = The Free Will Theorem | journal = [[Foundations of Physics]] | volume = 36 | issue = 10 | pages = 1441 | doi = 10.1007/s10701-006-9068-6 |arxiv = quant-ph/0604079 |bibcode = 2006FoPh...36.1441C | s2cid = 12999337 }}</ref><ref>{{Cite web |last=Rehmeyer |first=Julie |date=2008-08-15 |title=Do subatomic particles have free will? |url=https://www.sciencenews.org/article/do-subatomic-particles-have-free-will |access-date=2022-04-23 |website=[[Science News]] |language=en-US}}</ref><ref>{{Cite web |last=Thomas |first=Rachel |date=2011-12-27 |title=John Conway – discovering free will (part I) |url=https://plus.maths.org/content/john-conway-discovering-free-will-part-i |access-date=2022-04-23 |website=[[Plus Magazine]] |language=en}}</ref> The Conway–Kochen theorem uses a pair of entangled [[qutrit]]s and a Kochen–Specker configuration discovered by [[Asher Peres]].<ref>{{cite journal |last1=Conway |first1=John H. |first2=Simon |last2=Kochen | author-link1=John Horton Conway | author-link2=Simon B. Kochen |title=The strong free will theorem |journal= [[Notices of the AMS]] |volume=56 |issue=2 |year=2009 |pages=226–232 |url=http://www.ams.org/notices/200902/rtx090200226p.pdf}}</ref>