$1$, as it should be. Moreover, $P_{u,-u}=0$, as it should be. The probabilities depend continuously on $u$ and $v$, in a very natural way.

One would get precisely the same probabilities if one had extremely fragile, classical spheres, painted white on one hemisphere and black on the other one, and each sphere would be destroyed after observing the color at a single point. One could still calculate probabilities for the colors of the other points, and any rotationally symmetric classical probability model produces precisely the same probabilities as we just calculated for the spin.

More details on such a classical model for electron spin can be found in [Kochen & Specker]{} [@KocS]. They show that, under natural assumptions, such a classical model is restricted to two-state systems. (In a companion paper [@Neu1], I’ll show how one can reinterpret quantum mechanics in such a way that the assumptions of Kochen and Specker become irrelevant, thus removing this very restictive conclusion.) In any case, one such model is enough to invalidate the cogency of Schr[ö]{}dinger’s conclusion.

To summarize, Schr[ö]{}dinger’s argument demonstrates that, in quantum mechanics, one cannot calculate the values for linear combinations of noncommuting observables from the values of the observables 