Editing Bell test (section)

==Overview==
{{Main|Bell's theorem}}
The Bell test has its origins in the debate between Einstein and other pioneers of quantum physics, principally [[Niels Bohr]].  One feature of the theory of quantum mechanics under debate was the meaning of [[Heisenberg's uncertainty principle]].  This principle states that if some information is known about a given particle, there is some other information about it that is impossible to know.  An example of this is found in observations of the position and the momentum of a given particle.  According to the uncertainty principle, a particle's momentum and its position cannot simultaneously be determined with arbitrarily high precision.<ref>{{Cite web | title=What Is the Uncertainty Principle and Why Is It Important? | url=https://scienceexchange.caltech.edu/topics/quantum-science-explained/uncertainty-principle | access-date=2023-04-03}}</ref>

In 1935, Einstein, [[Boris Podolsky]], and [[Nathan Rosen]] published a claim that quantum mechanics predicts that more information about a pair of [[quantum entanglement|entangled particles]] could be observed than Heisenberg's principle allowed, which would only be possible if information were travelling instantly between the two particles. This produces a [[paradox]] which came to be known as the "[[EPR paradox]]" after the three authors. It arises if any effect felt in one location is not the result of a cause that occurred in its [[light cone|past light cone]], relative to its location. This [[action at a distance]] seems to violate [[causality (physics)|causality]], by allowing information between the two locations to travel faster than the speed of light.{{citation needed|date=July 2022}} However, it is a common misconception to think that any information can be shared between two observers faster than the speed of light using entangled particles; the hypothetical information transfer here is between the particles. See [[no-communication theorem]] for further explanation.

Based on this, the authors concluded that the quantum wave function does not provide a complete description of reality.  They suggested that there must be some local hidden variables at work in order to account for the behavior of entangled particles.  In a theory of hidden variables, as Einstein envisaged it, the randomness and indeterminacy seen in the behavior of quantum particles would only be apparent.  For example, if one knew the details of all the hidden variables associated with a particle, then one could predict both its position and momentum.  The uncertainty that had been quantified by Heisenberg's principle would simply be an artifact of not having complete information about the hidden variables.  Furthermore, Einstein argued that the hidden variables should obey the condition of locality:  Whatever the hidden variables actually are, the behavior of the hidden variables for one particle should not be able to instantly affect the behavior of those for another particle far away.  This idea, called the [[principle of locality]], is rooted in intuition from classical physics that physical interactions do not propagate instantly across space.  These ideas were the subject of ongoing debate between their proponents. In particular, Einstein himself did not approve of the way Podolsky had stated the problem in the famous EPR paper.<ref>{{Cite book |title=The Shaky Game: Einstein, Realism, and the Quantum Theory |last=Fine |first=Arthur |publisher=University of Chicago Press |year=1996 |edition=2nd |location=Chicago |author-link=Arthur Fine }}</ref><ref>{{Cite journal |last1=Harrigan |first1=Nicholas |author2-link=Robert Spekkens |last2=Spekkens |first2=Robert W. |date=2010-02-01 |title=Einstein, Incompleteness, and the Epistemic View of Quantum States |journal=Foundations of Physics |language=en |volume=40 |issue=2 |pages=125–157 |arxiv=0706.2661 |doi=10.1007/s10701-009-9347-0 |issn=0015-9018 |bibcode = 2010FoPh...40..125H |s2cid=32755624 }}</ref>

In 1964, [[John Stewart Bell]] proposed his famous theorem, which states that no physical theory of hidden local variables can ever reproduce all the predictions of quantum mechanics.  Implicit in the theorem is the proposition that the determinism of classical physics is fundamentally incapable of describing quantum mechanics.  Bell expanded on the theorem to provide what would become the conceptual foundation of the Bell test experiments.{{citation needed|date=July 2022}}

A typical experiment involves the observation of particles, often photons, in an apparatus designed to produce entangled pairs and allow for the measurement of some characteristic of each, such as their [[Spin (physics)|spin]]. The results of the experiment could then be compared to what was predicted by local realism and those predicted by quantum mechanics.{{citation needed|date=July 2022}}

In theory, the results could be "coincidentally" consistent with both. To address this problem, Bell proposed a mathematical description of local realism that placed a statistical limit on the likelihood of that eventuality.  If the results of an experiment violate Bell's inequality, local hidden variables can be ruled out as their cause.  Later researchers built on Bell's work by proposing new inequalities that serve the same purpose and refine the basic idea in one way or another.<ref name="Clauser-1969">{{Cite journal|last1=Clauser|first1=John F.|author-link=John Clauser|last2=Horne|first2=Michael A.|last3=Shimony|first3=Abner|author-link3=Abner Shimony|last4=Holt|first4=Richard A.|s2cid=18467053|date=1969-10-13|title=Proposed Experiment to Test Local Hidden-Variable Theories|journal=Physical Review Letters|volume=23|issue=15|pages=880–884|doi=10.1103/PhysRevLett.23.880|bibcode=1969PhRvL..23..880C|doi-access=free}}</ref><ref>{{Cite journal|last1=Braunstein|first1=Samuel L.|last2=Caves|first2=Carlton M.|author-link2=Carlton M. Caves|date=1988|title=Information-Theoretic Bell Inequalities|journal=Physical Review Letters|volume=61|issue=6|pages=662–665|doi=10.1103/physrevlett.61.662|pmid=10039398|bibcode = 1988PhRvL..61..662B }}</ref>  Consequently, the term "Bell inequality" can mean any one of a number of inequalities satisfied by local hidden-variables theories; in practice, many present-day experiments employ the [[CHSH inequality]]. All these inequalities, like the original devised by Bell, express the idea that assuming local realism places restrictions on the statistical results of experiments on sets of particles that have taken part in an interaction and then separated.{{citation needed|date=July 2022}}

To date, all Bell tests have supported the theory of quantum physics, and not the hypothesis of local hidden variables. These efforts to experimentally validate violations of the Bell inequalities resulted in [[John Clauser]], [[Alain Aspect]], and [[Anton Zeilinger]] being awarded the 2022 [[Nobel Prize in Physics]].<ref>{{Cite news |last1=Ahlander |first1=Johan |last2=Burger |first2=Ludwig |last3=Pollard |first3=Niklas |date=2022-10-04 |title=Nobel physics prize goes to sleuths of 'spooky' quantum science |language=en |work=Reuters |url=https://www.reuters.com/world/aspect-clauser-zeilinger-win-2022-nobel-prize-physics-2022-10-04/ |access-date=2022-10-04}}</ref>