  The probability `measure' for measurements at two consecutive moments of time
is non-additive. These probabilities, on the other hand, may be determined by
the limit of relative frequency of measured events, which are by nature
additive. We demonstrate that there are only two ways to resolve this problem.
The first solution places emphasis on the precise use of the concept of
conditional probability for successive measurements. The physically correct
conditional probabilities define additive probabilities for two-time
measurements. These probabilities depend explicitly on the resolution of the
physical device and do not, therefore, correspond to a function of the
associated projection operators. It follows that quantum theory distinguishes
between physical events and propositions about events, the latter are not
represented by projection operators and that the outcomes of two-time
experiments cannot be described by quantum logic.
  The alternative explanation is rather radical: it is conceivable that the
relative frequencies for two-time measurements do not converge, unless a
particular consistency condition is satisfied. If this is true, a strong
revision of the quantum mechanical formalism may prove necessary. We stress
that it is possible to perform experiments that will distinguish the two
alternatives.
