Editing Philosophy of physics (section)

==="Locality" and hidden variables===
{{main|EPR paradox|Bell's theorem}}
[[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. "Local" here 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 putative properties of quantum particles that are not included in the theory but nevertheless affect the outcome of experiments. In the words of physicist [[John Stewart Bell]], for whom this family of results is named, "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>

The term is broadly applied to a number of different derivations, the first of which was introduced by Bell in a 1964 paper titled "On the [[EPR paradox|Einstein Podolsky Rosen Paradox]]". Bell's paper was a response to a 1935 [[thought experiment]] that [[Albert Einstein]], [[Boris Podolsky]] and [[Nathan Rosen]] proposed, arguing that quantum physics is an "incomplete" theory.<ref name="EPR">{{cite journal | title = Can Quantum-Mechanical Description of Physical Reality be Considered Complete? | date = 1935-05-15 | first1 = A. | last1 = Einstein |first2=B. |last2 = Podolsky |first3=N. |last3 = Rosen | author-link1 = Albert Einstein | author-link2 = Boris Podolsky | author-link3 = Nathan Rosen | journal = [[Physical Review]] | volume = 47 | issue = 10 | pages = 777–780 | bibcode = 1935PhRv...47..777E |doi = 10.1103/PhysRev.47.777 | doi-access = free }}</ref><ref name=Bell1964>{{cite journal | last1 = Bell | first1 = J. S. | author-link = John Stewart Bell | year = 1964 | title = On the Einstein Podolsky Rosen Paradox | url = https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf | journal = [[Physics Physique Физика]] | volume = 1 | issue = 3| pages = 195–200 | doi = 10.1103/PhysicsPhysiqueFizika.1.195 }}</ref> By 1935, it was already recognized that the predictions of quantum physics are [[probability|probabilistic]]. Einstein, Podolsky and Rosen presented a scenario that involves preparing a pair of particles such that the quantum state of the pair is [[quantum entanglement|entangled]], and then separating the particles to an arbitrarily large distance. The experimenter has a choice of possible measurements that can be performed on one of the particles. When they choose a measurement and obtain a result, the quantum state of the other particle apparently [[Wave function collapse|collapses]] instantaneously into a new state depending upon that result, no matter how far away the other particle is.  This suggests that either the measurement of the first particle somehow also influenced the second particle faster than the speed of light, ''or'' that the entangled particles had some unmeasured property which pre-determined their final quantum states before they were separated.  Therefore, assuming locality, quantum mechanics must be incomplete, as it cannot give a complete description of the particle's true physical characteristics. In other words, quantum particles, like [[electron]]s and [[photon]]s, must carry some property or attributes not included in quantum theory, and the uncertainties in quantum theory's predictions would then be due to ignorance or unknowability of these properties, later termed "hidden variables".

Bell carried the analysis of quantum entanglement much further. He 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. This constraint would later be named the ''Bell inequality''. Bell then showed that quantum physics predicts correlations that violate this inequality. Consequently, the only way that hidden variables could explain the predictions of quantum physics is if they are "nonlocal", which is to say that somehow the two particles can carry non-classical correlations no matter how widely they ever become separated.<ref name="C.B. Parker 1994 542">{{cite book | first = Sybil B. | last = Parker | title = McGraw-Hill Encyclopaedia of Physics | edition = 2nd | page = [https://archive.org/details/mcgrawhillencycl1993park/page/542 542] | date = 1994 | publisher = McGraw-Hill | isbn = 978-0-07-051400-3 | url = https://archive.org/details/mcgrawhillencycl1993park| url-access = registration }}</ref><ref name = "ND Mermin 1993-07">{{cite journal | last = Mermin |first = N. David |author-link=N. David Mermin |title = Hidden Variables and the Two Theorems of John Bell | journal = [[Reviews of Modern Physics]] | volume = 65 |pages = 803–15 | number = 3| date = July 1993  | url = http://cqi.inf.usi.ch/qic/Mermin1993.pdf |arxiv=1802.10119|doi = 10.1103/RevModPhys.65.803 |bibcode = 1993RvMP...65..803M |s2cid = 119546199 }}</ref>

Multiple variations on Bell's theorem were put forward in the following years, introducing other closely related conditions generally known as 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. To date, 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 any local hidden variable theory.<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/physicists-are-closing-the-bell-test-loophole-20170207/|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 philosophers. While the significance of Bell's theorem is not in doubt, its full implications for the [[interpretation of quantum mechanics]] remain unresolved.