Hidden-Variables Models of Quantum Mechanics (Noncontextual and Contextual)

In the following discussion of hidden variables models of quantum mechanics the ► Hilbert space formulation of quantum mechanics and the standard interpretation of its notation and concepts will be taken to be initially understood, even though challenges to the standard interpretation are implicit in the proposals of ► hidden variables.

Very soon after the formulation of the new quantum mechanics by Werner Heisenberg (1901–76) and Erwin Schrodinger (1887–1961) its advocates, notably Niels Bohr (1885–1962) [1], made strong claims that the new theory provided a complete framework for physics. Nevertheless, conjectures that quantum mechanics does not provide a complete description of physical reality materialized in each of the two competing (but equivalent, as was eventually recognized) formulations of the theory by Heisenberg and Schrödinger. The ► Heisenberg Uncertainty Principle — asserting a limitation on the precision of simultaneous determinations of position and linear momentum — suggested to Albert Einstein (1879–1955) [2] that the uncertainty was due to limitations of customary experimentation, and that two quantum mechanically incompatible quantities could in principle be shown to have simultaneous precise values by more sophisticated measuring procedures.