Possible experimental test of local commutativity

A direct experimental test for local commutativity (i.e., [A, B]=0 if A and B are associated with mutually spacelike regions) is proposed. It consists of a comparison of the distribution of outcomes of A measurements in the two cases where A alone is measured (no measurement apparatus for B present) and where both are measured on the same sample, in short, a test of the compatibility of the two observation procedures for A and B. The implication compatibility → commutativity (substantially proved by von Neumann, but questioned by Park and Margenau) is proved in a stronger form, with close attention paid to the distinction between different procedures corresponding to a given self-adjoint operator.