Editing Bell's theorem (section)

{{Short description|Theorem in physics}}

{{Redirect|Bell inequality|the related experiments|Bell test}}

'''Bell's theorem''' is a term encompassing a number of closely related results in [[physics]], all of which determine that [[quantum mechanics]] is incompatible with [[Local hidden-variable theory|local hidden-variable theories]], given some basic assumptions about the nature of measurement. The first such result was introduced by [[John Stewart Bell]] in 1964, building upon the [[Einstein–Podolsky–Rosen paradox]], which had called attention to the phenomenon of [[quantum entanglement]].

In the context of Bell's theorem, "local" refers to the [[principle of locality]], the idea that a [[particle]] can only be influenced by its immediate surroundings, and that interactions mediated by [[Field (physics)|physical fields]] cannot propagate faster than the [[speed of light]]. "[[Hidden-variable theory|Hidden variables]]" are supposed properties of quantum particles that are not included in quantum theory but nevertheless affect the outcome of experiments. In the words of Bell, "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."<ref>{{cite book | first = John S. | last = Bell | author-link = John Stewart Bell | title = Speakable and Unspeakable in Quantum Mechanics | publisher = Cambridge University Press | date = 1987 | page = 65 | isbn = 9780521368698 | oclc = 15053677}}</ref>

In his original paper,<ref name="Bell1964" /> Bell deduced that if measurements are performed independently on the two separated particles of an entangled pair, then the assumption that the outcomes depend upon hidden variables within each half implies a mathematical constraint on how the outcomes on the two measurements are correlated. Such a constraint would later be named a '''Bell inequality'''. Bell then showed that quantum physics predicts correlations that violate this [[Inequality (mathematics)|inequality]]. Multiple variations on Bell's theorem were put forward in the years following his original paper, using different assumptions and obtaining different Bell (or "Bell-type") inequalities.

The first rudimentary experiment designed to test Bell's theorem was performed in 1972 by [[John Clauser]] and [[Stuart Freedman]].<ref>{{cite press release |url=https://www.nobelprize.org/prizes/physics/2022/press-release/ |title=The Nobel Prize in Physics 2022 |date=October 4, 2022 |work=[[Nobel Prize]] |publisher=[[The Royal Swedish Academy of Sciences]] |access-date=6 October 2022}}</ref> More advanced experiments, known collectively as ''[[Bell test]]s'', have been performed many times since. Often, these experiments have had the goal of "closing loopholes", that is, ameliorating problems of experimental design or set-up that could in principle affect the validity of the findings of earlier Bell tests. Bell tests have consistently found that physical systems obey quantum mechanics and violate Bell inequalities; which is to say that the results of these experiments are incompatible with local hidden-variable theories.<ref name="NAT-20180509">{{cite journal |author=The BIG Bell Test Collaboration |title=Challenging local realism with human choices |date=9 May 2018 |journal=[[Nature (journal)|Nature]] |volume=557 |issue=7704 |pages=212–216 |doi=10.1038/s41586-018-0085-3 |pmid=29743691 |bibcode=2018Natur.557..212B |arxiv=1805.04431 |s2cid=13665914 }}</ref><ref>{{Cite web |url=https://www.quantamagazine.org/20170207-bell-test-quantum-loophole/ |title=Experiment Reaffirms Quantum Weirdness |last=Wolchover |first=Natalie |author-link=Natalie Wolchover |date=2017-02-07 |work=[[Quanta Magazine]] |language=en-US |access-date=2020-02-08}}</ref> 

The exact nature of the assumptions required to prove a Bell-type constraint on correlations has been debated by physicists and by [[philosophy of physics|philosophers]]. While the significance of Bell's theorem is not in doubt, different [[interpretations of quantum mechanics]] disagree about what exactly it implies.