On Aerts’ (overlooked) solution to the EPR paradox
One of the most fascinating gedankenexperiment (thought experiments) of physics was formulated by Einstein and two of his collaborators, Podolsky and Rosen (EPR), in the 1930s. A lot of ink followed, but basically most physicists today believe that the argument of EPR has been superseded by the early experiments of Aspect on pairs of entangled photons, and by other similar experiments that followed, which proved, through the violation of the famous Bell’s inequalities, that entanglement is a reality of the physical world with which we have to deal.
On the other hand, EPR, in their reasoning, though not consciously, had pointed their finger at something deeper about quantum physics, which had nothing to do with the experimental discovery of quantum entanglement. The question is very subtle, and this explains why it took almost fifty years from the article of EPR (which was published in 1935) to understand all the consequences of their reasoning, which in fact was a reasoning ex absurdum.
The understanding came thanks to the work of the Belgian physicist Diederik Aerts, who in his research doctorate (we are in the early eighties) tried to understand, at a fundamental level, which mathematical structure was possessed by a theory capable of describing composite systems, formed by multiple entities, such as bipartite systems consisting of two physical entities. In doing so, he obviously began to study the simplest situations, and the simplest of all was obviously that of a bipartite system whose parts were separated, in the sense that the measurement of physical quantities carried out on one of the two parts could not influence in whatsoever way the measurement of physical quantities carried out on the other part. This is obviously a common situation in our daily reality, composed of macroscopic bodies with spatial properties.
But Aerts’ big surprise was that he was able to prove that the quantum formalism was incapable of describing this simple situation of two separate entities, and more generally the situation of separate measurement processes, that is, measurements that do not influence each other. In other words, EPR, which in their reasoning had implicitly assumed that quantum theory was instead able to describe situations of separation, thus arriving at their paradox, had put their finger on a type of incompleteness that at that time, understandably, they did not at all hypothesized.
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