real situations only approximately.

Therefore, unlike Schroedinger’s equation, cannot be considered a ‘basic statement’ and must be banned from the foundations. It should rather be a consequence of more elementary, exact features of the theory.

Indeed, Wigner ‘derives’ from first principles. The argument, given on pp.286-287, is identical to Feynman’s, assuming (without comment) the Markov property that provides the independence that allows to multiply probabilities:

[*If the first observation \[...\] This probability is $|(a_\kappa,b_\lambda)|^2$. The probability that the next measurement \[...\] is then $|(b_\lambda,c_\mu)|^2$ and the probability of both outcomes \[...\] is $|(a_\kappa,b_\lambda)(b_\lambda,c_\mu)|^2$ \[...\].* ]{}

Thus the formula, based on invalid reasoning, is suspect.

This suspicion is confirmed by realizing that the operator whose expectation is taken is generally not a projector, hence does not correspond to a ‘proposition’ in the traditional quantum logic calculus. But what sense should it make to talk about the probability of a statement that is not even logically well-formed?

It seems to me that the only formula for probabilities verified (abundantly) by experiments is the formula (see, e.g., equation (1.8) in Chapter 3 of [Davies]{} [@Dav]) P(B E|)=B(E) for the probability that, in a mixed state with the density matrix $\rho$, the generalized observable 