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Heisenberg's principle was an attempt to provide a classical explanation of a quantum effect sometimes called non-locality. According to EPR there were two possible explanations. Either there was some interaction between the particles, even though they were separated, or the information about the outcome of all possible measurements was already present in both particles.
The EPR authors preferred the second explanation according to which that information was encoded in some 'hidden parameters'. The first explanation, that an effect propagated instantly, across a distance, is in conflict with the theory of relativity.
They then concluded that quantum mechanics was incomplete since, in its formalism, there was no space for such hidden parameters.
Violations of the conclusions of Bell's theorem are generally understood to have demonstrated that hypotheses of Bell's theorem, also assumed by Einstein Poldolsky and Rosen, do not apply in our world. Most physicists who have examined the matter concur that experiments, such as those of Alain Aspect and his group, have confirmed that physical probabilities, as predicted by quantum theory, do show the phenomena of Bell-inequality violations that are considered to invalidate EPR's preferred "local hidden-variables" type of explanation for the correlations to which EPR first drew attention.[1][2]