Editing Einstein–Podolsky–Rosen paradox (section)

== The "Paradox" paper ==
The term "Einstein–Podolsky–Rosen paradox" or "EPR" arose from a paper written in 1934 after Einstein joined the [[Institute for Advanced Study]], having [[Albert Einstein#1933: Emigration to the US|fled the rise of Nazi Germany]].<ref>{{Cite journal|last=Robinson|first=Andrew|date=2018-04-30|title=Did Einstein really say that?|url=https://www.nature.com/articles/d41586-018-05004-4|journal=Nature|language=en|volume=557|issue=7703|pages=30|doi=10.1038/d41586-018-05004-4|bibcode=2018Natur.557...30R|s2cid=14013938}}</ref><ref>{{cite web |last1=Levenson |first1=Thomas |title=The Scientist and the Fascist |url=https://www.theatlantic.com/science/archive/2017/06/einstein-germany-and-the-bomb/528534/ |website=The Atlantic |access-date=28 June 2021 |date=9 June 1917}}</ref>
The original paper<ref>{{cite journal|last1=Einstein|first1=Albert|last2=Podolsky|first2=Boris|last3=Rosen|first3=Nathan|date=May 15, 1935|title=Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?|journal=Physical Review|location=Princeton, New Jersey|publisher=Institute for Advanced Study|volume=47|issue=10|pages=777–780|doi=10.1103/PhysRev.47.777|bibcode=1935PhRv...47..777E|doi-access=free}}</ref> purports to describe what must happen to "two systems I and II, which we permit to interact", and after some time "we suppose that there is no longer any interaction between the two parts." The EPR description involves "two particles, A and B, [which] interact briefly and then move off in opposite directions."<ref name=Kumar2011>{{cite book|last=Kumar|first=Manjit|title=Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality|publisher=W. W. Norton & Company|edition=Reprint|year=2011|pages=[https://archive.org/details/quantumeinsteinb00manj/page/305 305–306]|isbn=978-0393339888|url-access=registration|url=https://archive.org/details/quantumeinsteinb00manj/page/305|accessdate=September 12, 2021|via=Internet Archive}}</ref> According to [[Heisenberg's uncertainty principle]], it is impossible to measure both the momentum and the position of particle B exactly; however, it is possible to measure the exact position of particle A. By calculation, therefore, with the exact position of particle A known, the exact position of particle B can be known. Alternatively, the exact momentum of particle A can be measured, so the exact momentum of particle B can be worked out. As [[Manjit Kumar]] writes, "EPR argued that they had proved that ... [particle] B can have simultaneously exact values of position and momentum. ... Particle B has a position that is real and a momentum that is real. EPR appeared to have contrived a means to establish the exact values of ''either'' the momentum ''or'' the position of B due to measurements made on particle A, without the slightest possibility of particle B being physically disturbed."<ref name=Kumar2011/>

EPR tried to set up a paradox to question the range of true application of quantum mechanics: quantum theory predicts that both values cannot be known for a particle, and yet the EPR thought experiment purports to show that they must both have determinate values. The EPR paper says: "We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete."<ref name=Kumar2011/> The EPR paper ends by saying: "While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible." The 1935 EPR paper condensed the philosophical discussion into a physical argument. The authors claim that given a specific experiment, in which the outcome of a measurement is known before the measurement takes place, there must exist something in the real world, an "element of reality", that determines the measurement outcome. They postulate that these elements of reality are, in modern terminology, [[principle of locality|local]], in the sense that each belongs to a certain point in [[spacetime]]. Each element may, again in modern terminology, only be influenced by events that are located in the backward [[light cone]] of its point in spacetime (i.e. in the past). These claims are thus founded on assumptions about nature that constitute what is now known as '''local realism'''<!--boldface per WP:R#PLA-->.<ref name=Jaeger2014>{{cite book|last=Jaeger|first=Gregg|title=Quantum Objects|publisher=Springer Verlag|pages=9–15|doi=10.1007/978-3-642-37629-0|year=2014 |isbn=978-3-642-37628-3 }}</ref>

[[File:NYT May 4, 1935.jpg|thumb|250px|Article headline regarding the EPR paradox paper in the May 4, 1935, issue of ''[[The New York Times]]'']]
Though the EPR paper has often been taken as an exact expression of Einstein's views, it was primarily authored by Podolsky, based on discussions at the [[Institute for Advanced Study]] with Einstein and Rosen. Einstein later expressed to [[Erwin Schrödinger]] that, "it did not come out as well as I had originally wanted; rather, the essential thing was, so to speak, smothered by the formalism."<ref>
{{cite journal|last=Kaiser|first=David|year=1994|title=Bringing the human actors back on stage: the personal context of the Einstein-Bohr debate|journal=British Journal for the History of Science|volume=27|issue=2|pages=129–152|doi=10.1017/S0007087400031861|jstor=4027432|s2cid=145143635 }}</ref> Einstein would later go on to present an individual account of his local realist ideas.<ref>{{cite journal |last1=Einstein |first1=Albert |year=1936 |title=Physik und Realität |journal=Journal of the Franklin Institute |volume=221 |issue=3 |pages=313–347 |doi=10.1016/S0016-0032(36)91045-1 }} English translation by Jean Piccard, pp 349–382 in the same issue, {{doi|10.1016/S0016-0032(36)91047-5}}).</ref> Shortly before the EPR paper appeared in the ''[[Physical Review]],'' ''[[The New York Times]]'' ran a news story about it, under the headline "Einstein Attacks Quantum Theory".<ref>{{cite news |title=Einstein Attacks Quantum Theory |url=https://www.nytimes.com/1935/05/04/archives/einstein-attacks-quantum-theory-scientist-and-two-colleagues-find.html |access-date=10 January 2021 |work=[[The New York Times]] |date=4 May 1935 |page=11}}</ref> The story, which quoted Podolsky, irritated Einstein, who wrote to the ''Times,'' "Any information upon which the article 'Einstein Attacks Quantum Theory' in your issue of May 4 is based was given to you without authority. It is my invariable practice to discuss scientific matters only in the appropriate forum and I deprecate advance publication of any announcement in regard to such matters in the secular press."<ref name="jammer1974">{{cite book|first=Max |last=Jammer |author-link=Max Jammer |year=1974 |title=The Philosophy of Quantum Mechanics: The Interpretations of QM in Historical Perspective |publisher=John Wiley and Sons |isbn=0-471-43958-4}}</ref>{{rp|189}}

The ''Times'' story also sought out comment from physicist [[Edward Condon]], who said, "Of course, a great deal of the argument hinges on just what meaning is to be attached to the word 'reality' in physics."<ref name="jammer1974"/>{{rp|189}} The physicist and historian [[Max Jammer]] later noted, "[I]t remains a historical fact that the earliest criticism of the EPR paper – moreover, a criticism that correctly saw in Einstein's conception of physical reality the key problem of the whole issue – appeared in a daily newspaper prior to the publication of the criticized paper itself."<ref name="jammer1974"/>{{rp|190}}

=== Bohr's reply ===
The publication of the paper prompted a response by [[Niels Bohr]], which he published in the same journal (''[[Physical Review]]''), in the same year, using the same title.<ref name='Bohr1935'>{{cite journal |title=Can Quantum-Mechanical Description of Physical Reality be Considered Complete? |date=1935-10-13 |first=N. |last=Bohr |journal=[[Physical Review]] |volume=48 |issue=8 |pages=696–702 |doi=10.1103/PhysRev.48.696|bibcode=1935PhRv...48..696B |url=https://cds.cern.ch/record/1060284/files/PhysRev.48.696.pdf |doi-access=free }}</ref> (This exchange was only one chapter in [[Bohr–Einstein debates|a prolonged debate between Bohr and Einstein]] about the nature of quantum reality.)
He argued that EPR had reasoned fallaciously. Bohr said measurements of position and of momentum are [[Complementarity (physics)|complementary]], meaning the choice to measure one excludes the possibility of measuring the other. Consequently, a fact deduced regarding one arrangement of laboratory apparatus could not be combined with a fact deduced by means of the other, and so, the inference of predetermined position and momentum values for the second particle was not valid. Bohr concluded that EPR's "arguments do not justify their conclusion that the quantum description turns out to be essentially incomplete."

=== Einstein's own argument ===
In his own publications and correspondence, Einstein indicated that he was not satisfied with the EPR paper and that Podolsky had authored most of it. He later used a different argument to insist that quantum mechanics is an incomplete theory.<ref name=":0">{{cite journal|first1=Nicholas |last1=Harrigan |first2=Robert W.|author2-link=Robert Spekkens|last2=Spekkens |title=Einstein, incompleteness, and the epistemic view of quantum states |journal=[[Foundations of Physics]] |volume=40 |issue=2 |pages=125 |year=2010 |doi=10.1007/s10701-009-9347-0 |arxiv=0706.2661|bibcode=2010FoPh...40..125H |s2cid=32755624 }}</ref><ref name="howard">{{cite journal |last1=Howard |first1=D. |title=Einstein on locality and separability |journal=Studies in History and Philosophy of Science Part A |date=1985 |volume=16 |issue=3 |pages=171–201 |doi=10.1016/0039-3681(85)90001-9|bibcode=1985SHPSA..16..171H }}</ref><ref>{{Cite journal|last=Sauer|first=Tilman|date=2007-12-01|title=An Einstein manuscript on the EPR paradox for spin observables|url=http://philsci-archive.pitt.edu/3222/|journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics|language=en|volume=38|issue=4|pages=879–887|doi=10.1016/j.shpsb.2007.03.002|issn=1355-2198|bibcode=2007SHPMP..38..879S|citeseerx=10.1.1.571.6089}}</ref><ref>{{cite encyclopedia |last=Einstein |first=Albert |title=Autobiographical Notes |encyclopedia=Albert Einstein: Philosopher-Scientist |year=1949 |publisher=Open Court Publishing Company |editor-last=Schilpp |editor-first=Paul Arthur}}</ref>{{rp|83ff}} He explicitly de-emphasized EPR's attribution of "elements of reality" to the position and momentum of particle B, saying that "I couldn't care less" whether the resulting states of particle B allowed one to predict the position and momentum with certainty.{{efn|"Ob die <math>\psi_B</math> und <math>\psi_\underline{B}</math> als Eigenfunktionen von Observabeln <math>B,\underline{B}</math> aufgefasst werden können ist mir ''wurst''>." Emphasis from the original. "Ist mir wurst" is a German expression that literally translates to "It is a sausage to me", but means "I couldn't care less". Letter from Einstein to Schrödinger, dated 19th June 1935.<ref name="howard"/>}}

For Einstein, the crucial part of the argument was the demonstration of [[Quantum nonlocality|nonlocality]], that the choice of measurement done in particle A, either position or momentum, would lead to ''two different'' quantum states of particle B. He argued that, because of locality, the real state of particle B could not depend on which kind of measurement was done in A and that the quantum states therefore cannot be in one-to-one correspondence with the real states.<ref name=":0"/> Einstein struggled unsuccessfully for the rest of his life to find a theory that could better comply with his idea of locality.