Foundations of Physics Group


     Reality and Contextuality in physics

The quantum formalism contains features which may be considered objectionable by some. The most important of these are its subjectivity and indeterminism. The aim of the development of a hidden variables theory is to give a formalism which, while being empirically equivalent to the quantum formalism, does not possess these features. In his analysis of the hidden variables problem, von Neumann proved a mathematical result now known as von Neumann’s theorem . According to this theorem, no hidden variables theory can provide empirical agreement with quantum mechanics. According to John Bell,  some of von Neumann's assumptions are unreasonable ,, and so he believes that “the proof of von Neumann is not merely false but foolish!”

Further mathematical results were developed by Gleason in 1957 and by Kochen and Specker in 1967, which were claimed by some to imply the impossibility of hidden variables. In the words of Kochen and Specker: “If a physicist X believes in hidden variables... ...the prediction of X contradicts the prediction of quantum mechanics”. The Gleason, and Kochen and Specker arguments are in fact, stronger than von Neumann’s in that they assume linearity only for commuting observables. Despite this, a close analysis reveals that the impossibility proofs of Gleason and of Kochen and Specker share with von Neumann’s proof the neglect a possibility for hidden variables feature called contextuality (dependence of measurement results on the detailed experimental arrangement being employed.)

What follows from Kochen and Specker’s theorem is only that a non-contextual hidden variables theory will be in conflict with quantum mechanics. Thus, the general possibility of hidden variables has not been disproved.


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