The EPR Paradox is a thought experiment published in a paper in May 1935 by Albert Einstein and two of his postdoctoral research associates Boris Podolsky and Nathan Rosen that was meant to prove that Quantum Mechanics showed internal contradictions in it’s formulation. The authors claimed that if the description of physical reality given by the wave function is complete, then two quantities described by non-commuting operators could have simultaneous real values. We could for instance measure the position and the momentum of two entangled particles with more accuracy than that allowed by Heisenberg’s Uncertainty Principle. Therefore concluding that quantum-mechanical’s wave function description of reality is incomplete.
This thought experiment is considered to be one of the first papers to put the spotlight on quantum entanglement.
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This apparent paradox was finally solved by an experiment proposed by physicist J. S. Bell (see Bell’s Inequalities).
 “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?“, A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
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