Abstract
The empirical meaning of the simultaneity of measurement of several observables is carefully analyzed. General criteria sufficient to guarantee the internal consistency of a framework including simultaneous measurements of incompatible observables are put forward. The case is illustrated with the example of simultaneous measurements of position and momenta of particles in quantum mechanics. It is pointed out that, in general, the outcome of measurements of incompatible observables cannot be described statistically by means of the probability measures of mathematical statistics, which have primarily been introduced only with compatible observables in mind. The concept of complex probability measure is put forward. A generalization of the current interpretation of quantum mechanics is proposed that would also include the case of incompatible observables, by taking advantage of the concept of complex probability measure.
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