Possible Strengthening of the Interpretative Rules of Quantum Mechanics

Abstract

The usual interpretative rules of quantum mechanics are presented and are shown to be too weak. The reason is that they do not include the intuitive requirement of randomness of the outcome sequence obtained from an infinite repetition of measuring an observable on a state. A strengthening of the rules is proposed which includes, in essence, a precise definition of randomness. The resultant rule is seen to be intuitively more satisfying than the usual rules and to include the expectation value rule and to include essentially all of the spectrum rule of the usual rules. It also suggests that the relationship between the foundations of mathematics and quantum mechanics may be quite deep and complex.