Bell's theorem is based on the assumption that any possible realistic model must represent the measurement results of a polarization measurement on entangled photons in the form A(a, l) and B(b, l), where a and b are the settings of the polarizers and l is a hidden statistical parameter in any form. See J.S. Bell, On The Einstein Podolsky Rosen Paradox. Physics (Long Island City N.Y.), 1964, 1, 195. From this he derives Bell's inequality, which is violated by QM. However, it is well known that the singlet state, like all Bell states, is not separable. This means that without further intervention the state of each of the two particles is not only not known, but that a separate state of each of the two photons does not even exist. The reason for this is the indistinguishability of the photons that form the entangled state. A valid model has thus to take into account the indistinguishability of the photons from the entangled state.
See “On a contextual model refuting Bell’s theorem”, EPL 2021 134 (10004).
If there is no defined state of a single photon from the entangled state, then there is also no definable measurement result A(a, l) or B(b, l). If there were measurement results A(a, l) or B(b, l) for a permissible value of l, then these could only result from the states of the individual systems, which, however, do not exist because of the non-separability. Thus we have the case that non-existent states produce defined measurement results, which is a contradiction. A correlation of effects of non-existent states can therefore only be based on spooky action at a distance. Establishing this does not require Bell's inequality and its violation.
