Some consequences of the strengthened interpretative rules of quantum mechanics

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Abstract
In this paper some consequences of the strengthened interpretative rules of quantum mechanics, which were proposed in an earlier paper, are obtained. It is also seen that, in general, the usual interpretative rules are too weak to obtain these results. For example, it is proved from the strengthened rules that if f:R → R is a Borel function which is also τ‐definable, then for each observable A the procedure ``measure A and compute f(A outcome)'' is an f(A) measurement procedure. It is also shown that there exist Borel f and observables A such that the above procedure is not an f(A) measurement procedure. Two methods of measuring the sum A + B of two observables are then considered: The measurement of A and B on different systems followed by addition of the results and (if A and B commute) the simultaneous measurement of A and B on the same system followed by addition. It is proved from the strengthened rules that the first method is not a valid measurement procedure and the second is valid. Besides these, other processes such as procedures for preparing mixtures of different states, and the empirical generation of probability measures from outcome sequences are considered.

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