The problem of contextuality and the impossibility of experimental metaphysics thereof

Recently a new impulse has been given to the experimental investigation of contextuality. In this paper we show that for a widely used definition of contextuality there can be no decisive experiment on the existence of contextuality. To this end, we give a clear presentation of the hidden variable models due to Meyer, Kent and Clifton (MKC), which would supposedly nullify the Kochen–Specker theorem. Although we disagree with this last statement, the models do play a significant role in the discussion on the meaning of contextuality. In fact, we introduce a specific MKC-model of which we show that it is non-contextual and completely in agreement with quantum mechanical predictions. We also investigate the possibility of other definitions of non-contextuality—with an emphasis on operational definitions—and argue that any useful definition relies on the specification of a theoretical framework. It is therefore concluded that no experimental test can yield any conclusions about contextuality on a metaphysical level.

► A non-contextual MKC-model is constructed that is empirically equivalent with QM.
► We discuss experimental tests for contextuality and their relation to this model.
► The model is also viewed in the light of operational definitions of contextuality.
► We argue that no metaphysical notion of contextuality is empirically accessible.