Editing Hidden-variable theory (section)

=== EPR paradox ===
{{Main|EPR paradox}}

Einstein argued that quantum mechanics could not be a complete theory of physical reality. He wrote,
{{blockquote|Consider a mechanical system consisting of two partial systems ''A'' and ''B'' which interact with each other only during a limited time. Let the ''ψ'' function [i.e., [[wavefunction]]] before their interaction be given. Then the Schrödinger equation will furnish the ''ψ'' function after the interaction has taken place. Let us now determine the physical state of the partial system ''A'' as completely as possible by measurements. Then quantum mechanics allows us to determine the ''ψ'' function of the partial system ''B'' from the measurements made, and from the ''ψ'' function of the total system. This determination, however, gives a result which depends upon which of the physical quantities (observables) of ''A'' have been measured (for instance, coordinates or momenta). Since there can be only one physical state of ''B'' after the interaction which cannot reasonably be considered to depend on the particular measurement we perform on the system ''A'' separated from ''B'' it may be concluded that the ''ψ'' function is not unambiguously coordinated to the physical state. This coordination of several ''ψ'' functions to the same physical state of system ''B'' shows again that the ''ψ'' function cannot be interpreted as a (complete) description of a physical state of a single system.<ref>{{Cite journal |author=Einstein A |year=1936 |title=Physics and Reality |journal=Journal of the Franklin Institute |volume=221|issue=3 |page=349 |doi=10.1016/S0016-0032(36)91047-5 |bibcode=1936FrInJ.221..349E }}</ref>}}

Together with [[Boris Podolsky]] and [[Nathan Rosen]], Einstein published a paper that gave a related but distinct argument against the completeness of quantum mechanics.<ref>{{Cite journal |first1=A. |last1=Einstein |first2=B. |last2=Podolsky |first3=N. |last3=Rosen |year=1935 |title=Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? |journal=Physical Review |volume=47 |issue= 10|pages=777–780 |doi=10.1103/physrev.47.777 |bibcode=1935PhRv...47..777E |doi-access=free }}</ref> They proposed a [[thought experiment]] involving a pair of particles prepared in what would later become known as an [[Quantum entanglement|entangled]] [[quantum state|state]]. Einstein, Podolsky, and Rosen pointed out that, in this state, if the position of the first particle were measured, the result of measuring the position of the second particle could be predicted. If instead the momentum of the first particle were measured, then the result of measuring the momentum of the second particle could be predicted. They argued that no action taken on the first particle could instantaneously affect the other, since this would involve information being transmitted faster than light, which is impossible according to the [[theory of relativity]]. They invoked a principle, later known as the "EPR criterion of reality", positing that: "If, without in any way disturbing a system, we can predict with certainty (i.e., with [[probability]] equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity." From this, they inferred that the second particle must have a definite value of both position and of momentum prior to either quantity being measured. But quantum mechanics considers these two observables [[Observable#Incompatibility of observables in quantum mechanics|incompatible]] and thus does not associate simultaneous values for both to any system. Einstein, Podolsky, and Rosen therefore concluded that quantum theory does not provide a complete description of reality.<ref>{{cite book |last=Peres |first=Asher |author-link=Asher Peres |title=Quantum Theory: Concepts and Methods |title-link=Quantum Theory: Concepts and Methods |pages=149 |publisher=Kluwer |year=2002}}</ref>

Bohr answered the Einstein–Podolsky–Rosen challenge as follows:
{{blockquote|[The argument of] Einstein, Podolsky and Rosen contains an ambiguity as regards the meaning of the expression "without in any way disturbing a system." ... [E]ven at this stage [i.e., the measurement of, for example, a particle that is part of an entangled pair], there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system. Since these conditions constitute an inherent element of the description of any phenomenon to which the term "physical reality" can be properly attached, we see that the argumentation of the mentioned authors does not justify their conclusion that quantum-mechanical description is essentially incomplete."<ref>{{Cite journal |author=Bohr N |year=1935 |title=Can Quantum-Mechanical Description of Physical Reality be Considered Complete? |journal=Physical Review |volume=48 |issue=8 |pages=700 |doi=10.1103/physrev.48.696|bibcode = 1935PhRv...48..696B |doi-access=free }}</ref>}}
Bohr is here choosing to define a "physical reality" as limited to a phenomenon that is immediately observable by an arbitrarily chosen and explicitly specified technique, using his own special definition of the term 'phenomenon'. He wrote in 1948:
{{blockquote|As a more appropriate way of expression, one may strongly advocate limitation of the use of the word ''phenomenon'' to refer exclusively to observations obtained under specified circumstances, including an account of the whole experiment.<ref>{{cite journal | author = Bohr N. | author-link = Niels Bohr | year = 1948 | title = On the notions of causality and complementarity | journal = Dialectica | volume = 2 | issue = 3–4| pages = 312–319 [317] | doi=10.1111/j.1746-8361.1948.tb00703.x}}</ref><ref>[[Léon Rosenfeld|Rosenfeld, L.]] (). 'Niels Bohr's contribution to epistemology', pp.&nbsp;522–535 in ''Selected Papers of Léon Rosenfeld'', Cohen, R.S., Stachel, J.J. (editors), D. Riedel, Dordrecht, {{ISBN|978-90-277-0652-2}}, p.&nbsp;531: "Moreover, the complete definition of the phenomenon must essentially contain the indication of some permanent mark left upon a recording device which is part of the apparatus; only by thus envisaging the phenomenon as a closed event, terminated by a permanent record, can we do justice to the typical wholeness of the quantal processes."</ref>}}

This was, of course, in conflict with the EPR criterion of reality.