Incompatibility of standard completeness and quantum mechanics.
The completeness of quantum mechanics (QM) is generally interpreted to be or entail the following conditional statement (called standard completeness (SC)): If a QM system S is in a pure non-eigenstate of observable A, then S does not have value ak of A at t (where ak is any eigenvalue of A). QM itself can be assumed to contain two elements: (i) a formula generating probabilities; (ii) Hamiltonians that can be time-dependent due to a time-dependent external potential. It is shown that, given (i) and (ii), QM and SC are incompatible. Hence, SC is not the appropriate interpretation of the completeness of QM.
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