involving the observables $p^2+a^2q^2$ where $a$ is a parameter. Commenting on it, Schr[ö]{}dinger writes on p. 165:

[*Should one now think that because we are so ignorant about the relations among the variable-values held ready in one system, that none exists, that far-ranging arbitrary combination can occur? That would mean that such a system of “one degree of freedom” would need not merely two numbers for adequately describing it, as in classical mechanics, but rather many more, perhaps infinitely many.* ]{}

Schr[ö]{}dinger dismisses this as not viable, but as I’ll show now, there is a serious possibility that precisely this is the case, thus invalidating Schr[ö]{}dinger’s conclusion that it is not possible to ascribe to the momentarily unknown or not exactly known variables determinate values. His conclusion is only valid if one ascribes to each observable vector $K$ a determinate value that is to be used in the calculations for [*all*]{} $u\cdot K$.

However, as was observed already by [von Neumann]{} [@vNeu IV.1.E], one cannot, in general, combine the measuring recipes for two noncommuting observables to one for their sum, so that the sum of two observables is only implicitly characterized through the axioms. This should forbid the naive use 