  The impossibility of theories with hidden variables as an alternative and
replacement for quantum mechanics was discussed by J. von Neumann in 1932. His
proof was criticized as being logically circular, by Grete Hermann soon after,
and as fundamentally flawed, by John Bell in 1964. Bell's severe criticism of
Neumann's proof and the explicit (counter) example of a hidden variable model
for the measurement of a quantum spin are considered by most researchers,
though not all, as the definitive demonstration that Neumann's proof is
inadequate. Despite being an argument of mathematical physics, an ambiguity of
decision remains to this day. I show that Neumann's assumption of the linear
additivity of the expectation values, even for incompatible (noncommuting)
observables, is a necessary constraint related to the nature of observable
physical variables and to the conservation laws. Therefore, any theory should
necessarily obey it to qualify as a physically valid theory. Then, obviously,
the hidden variable theories with dispersion-free ensembles that violate this
assumption are ruled out. I show that it is Bell's counter-example that is
fundamentally flawed, being inconsistent with the factual mechanics. Further,
it is shown that the local hidden variable theories, for which the Bell's
inequalities were derived, are grossly incompatible with the fundamental
conservation laws. I identify the intrinsic uncertainty in the action as the
reason for the irreducible dispersion, which implies that there are no
dispersion-free ensembles at any scale of mechanics. With the unconditional
validity of its central assumption shown, Neumann's proof is fully resurrected.
