Hidden Variable Theory - EPR Paradox

EPR Paradox

Main article: EPR paradox

The debates between Bohr and Einstein essentially concluded in 1935, when Einstein finally expressed what is widely considered his best argument against the completeness of quantum mechanics. Einstein, Podolsky, and Rosen had proposed their definition of a "complete" description as one which uniquely determines the values of all its measurable properties. Einstein later summarized their argument as follows:

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 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.

Bohr answered Einstein's challenge by pointing out that, in accordance with the principle of complementarity, one of Einstein's assumptions, regarding the act of measurement, is not true in quantum mechanics: a quantum mechanical measurement not only states, but also prepares the physics of a system:

Einstein, Podolsky and Rosen contains an ambiguity as regards the meaning of the expression "without in any way disturbing a system." ... ven at this stage, 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."

Quantum mechanics is also not "local", essentially because the state of a system is described by the Hilbert vector, which includes the value at every site, . So in this instance Einstein was simply wrong, although he did sharply identify implications of the formalism of quantum mechanics that had been previously overlooked.