Do quantum-mechanical systems always possess definite properties dictated by their states?

In the article the possibility of breaking the eigenvalue-eigenstate link in quantum mechanics is considered. An argument is presented to the effect that there are some non-maximal observables for which the implication from eigenstates to eigenvalues is not valid, i.e. such that although the probability of revealing certain value upon measurement is one, they don't possess this value before the measurement. It is shown that the existence of such observables leads to contextuality, i.e. the thesis that one Hermitean operator can represent more than one physical observable. Finally, contextuality brought about by these considerations is compared with contextuality suggested by the Kochen-Specker paradox.
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