On the EPR paper “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?” | Quantum Science Philippines
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On the EPR paper “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?”

LUTCHIE DYAN S. MENDOZA

In the May 15, 1935 issue of Physical Review , Albert Einstein co-authored a paper with his two postdoctoral research associates at the Institute for Advanced Study, Boris Podolsky and Nathan Rosen. The paper, known as EPR, became a centerpiece in debates, challenging the validity of Quantum Theory.

The paper features a striking case where two quantum systems interact in such a way as to link both their spatial coordinates in a certain direction and also their linear momenta (in the same direction). As a result of this “entanglement”, determining either position or momentum for one system would fix (respectively) the position or the momentum of the other.  In quantum mechanics, in the case of two physical quantities described by non- commuting operators, the knowledge of one prevents the knowledge of the other (Heisenberg Uncertainty Principle). Thus, the paper asserts that, either (1) the quantum- mechanical description of reality given by the wave function is not complete or (2) when the operators corresponding to two physical quantities, like position and momentum, do not commute the two quantities can not have simultaneous reality. The authors affirm that one or another of these assertions must hold, giving rise to these two premises: (1) if quantum mechanics were complete (first option failed) then the second option would hold, that is, incompatible quantities cannot have real values simultaneously but (2) that if quantum mechanics were complete, then incompatible quantities (in particular position and momentum) could indeed have simultaneous, real values. They conclude that quantum mechanics is incomplete. The conclusion certainly follows since otherwise if the theory were complete one would have a contradiction. To establish the premises, the authors discuss the idea of a complete theory, offering only a necessary condition. In order for a theory to be complete, every element of the physical reality must have a counterpart in the physical theory, further requiring the criterion: 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. This is the famous EPR Criterion of Reality.

To realize their assertions further, the authors provided a thought experiment wherein the two quantum systems (one system is labeled Albert while the other system is named Neils) interact in such a way that  conservation of relative position and momentum hold following their interaction. The paper constructs an explicit wave function for the combined system that satisfies both conservation principles. The critical point in the paper centers on the two assumptions made by the authors, namely, separability and locality.  The first assumption states that at the time when measurements will be performed on Albert’s system there is some reality that pertains to Niels’ system alone. In effect, they assume that Niels’ system maintains its separate identity even though it is correlated with Albert’s. The second assumption supposes that no real change can take place in Niels’ system as a consequence of a measurement made on Albert’s system. Locality implies that the prediction of the position of Niels’ system does not involve any change in the reality of Niels’ system. Since the prediction does not disturb Neils’ system, all the pieces are in place to apply the Criterion of Reality. Hence, the authors concluded that Niels’ system can have real values or elements of reality for both position and momentum simultaneously. The negation of the first premise leads to the negation of the only alternative.

Following the result of the thought experiment, separability, locality as well as the application of the Criterion of Reality, EPR concludes that quantum- mechanical description of a physical reality given by the wave functions is not complete.

Reference:

A. EINSTEIN, N. ROSEN and B. PODOLSKY, Phys. Rev. 47, 777 (1935).

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