EPR Paradox

EPR is an acronym from the names of three physicists: Albert Einstein, Boris Podolsky and Nathan Rosen.  The ERP ‘gang’ designed a thought experiment intended to expose what they believed to be inadequacies of quantum mechanics.

According to quantum mechanics, a single system has its own mathematical wave function, its own unitary quantum-theoretical description. If such a single system can be transformed into two individual systems, doing so does not create two wave functions. Instead, theory indicates that each system shares the single wave function. The question then becomes, "What happens to this wave function when one and/or the other of the pair of individual systems is measured?"

Working through the equations, the EPR paper shows that measuring one feature of a system (ie, the momentum of one of the pair of particles), will reveal the same feature of the other particle. Measuring one characteristic of the first system will, according to quantum mechanics, make any related characteristic, in this case position, indeterminate. The EPR experiment suggested the possibility that not only would the momentum of the second be made known without the need of further experimental measurement, but also that the position of the second particle would be predicted in an indeterminate form according to the rules of the Heisenberg Uncertainty Principle.

EPR insisted, however, that since the two systems were physically separated, action on one particle could not affect the other particle, and it was therefore impossible that any indeterminacy could be induced in the system that was not directly measured. They then concluded that quantum mechanics was incomplete since it depicted a pair of systems such that after one measurement each had one determinate characteristic and one indeterminate characteristic. In reality, they concluded, one could measure the first system to get a real value for position of the second, and one could also have measured the first system to get a real value for the momentum of the second, the result being that the second system must have both a real position and a real momentum. They would both be determinate values, not just one of them as indicated by quantum mechanics.

If quantum mechanics is not incomplete, if quantum mechanics gives all of the information that is really available in nature, then, researchers conclude, changing some characteristic of one member of such a pair (now usually called an entangled pair) will not only make determinate the same characteristic of the other member of the pair, but it will also make indeterminate the second characteristic of the other member of the pair. The switch from a condition wherein both particles share the same wave function to a condition wherein one feature of one particle is made specific and its complex conjugate is made quantum mechanically indeterminate, and the same feature of the other particle is made correspondingly determinate while its complex conjugate is made quantum mechanically indeterminate, is something that occurs as the result of measuring the first feature in one of the paired particles, and that is reflected instantaneously in the other member of the pair. However, special relativity does not support any notion of instantaneous causal effect at a distance.