Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [157]
According to the uncertainty principle, a measurement that yields an exact value for the momentum of a microphysical object or system excludes even the possibility of simultaneously measuring its position. The question that Einstein wanted to answer was: Does the inability to measure its exact position directly mean that the electron does not have a definite position? The Copenhagen interpretation answered that in the absence of a measurement to determine its position, the electron has no position. EPR set out to demonstrate that there are elements of physical reality, such as an electron having a definite position, that quantum mechanics cannot accommodate – and therefore, it is incomplete.
EPR attempted to clinch their argument with a thought experiment. Two particles, A and B, interact briefly and then move off in opposite directions. The uncertainty principle forbids the exact measurement, at any given instant, of both the position and the momentum of either particle. However, it does allow an exact and simultaneous measurement of the total momentum of the two particles, A and B, and the relative distance between them.
The key to the EPR thought experiment is to leave particle B undisturbed by avoiding any direct observation of it. Even if A and B are light years apart, nothing within the mathematical structure of quantum mechanics prohibits a measurement of the momentum of A yielding information about the exact momentum of B without B being disturbed in the process. When the momentum of particle A is measured exactly, it indirectly but simultaneously allows, via the law of conservation of momentum, an exact determination of the momentum of B. Therefore, according to the EPR criterion of reality, the momentum of B must be an element of physical reality. Similarly, by measuring the exact position of A, it is possible, because the physical distance separating A and B is known, to deduce the position of B without directly measuring it. Hence, EPR argue, it too must be an element of physical reality. EPR appeared to have contrived a means to establish with certainty the exact values of either the momentum or the position of B due to measurements performed on particle A, without the slightest possibility of particle B being physically disturbed.
Given their reality criterion, EPR argued that they had thus proved that both the momentum and position of particle B are 'elements of reality', that B can have simultaneously exact values of position and momentum. Since quantum mechanics via the uncertainty principle rules out any possibility of a particle simultaneously possessing both these properties, these 'elements of reality' have no counterparts in the theory.15 Therefore the quantum mechanical description of physical reality, EPR conclude, is incomplete.
Einstein's thought experiment was not designed to simultaneously measure the position and momentum of particle B. He accepted that it was impossible to measure either of these properties of a particle directly without causing an irreducible physical disturbance. Instead, the two-particle thought experiment was constructed to show that such properties could have a definite simultaneous existence, that both the position and the momentum of a particle are 'elements of reality'. If these properties of particle B can be determined without B being observed (measured), then these properties of B must exist as elements of physical reality independently of being observed (measured). Particle B has a position