Abstract
Nelson's stochastic interpretation of quantum mechanics is extended from the case of pure states to that of mixed states. It is shown that a pure probabilistic formalism, which applies the Newton-Nelson law to the initial position and velocity distributions, does not reproduce the time evolution predicted by quantum mechanics. In order to recover the latter, a new notion must be introduced, that of pure quantum states, over which the mixture has to be decomposed, and which then satisfy the Newton-Nelson law independently.
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