The set of orientations of a measuring device (e.g., a Stern-Gerlach magnet) produced by the action of a Lie group constitutes a honmogeneous space S (e.g., a sphere). A hidden-variable measure determines a metric D on S, the triangle inequality being Bell's inequality. But identification of S with Hilbert-space projectors induces a locally convex metric d on S. The Einstein-Podolsky-Rosen (EPR) hypotheses imply that D= ${\mathit{d}}^{2}$ , which is impossible because the square of a locally convex metric cannot be a metric. This proves the Bell-EPR theorem. Classical systems avoid the contradiction by allowing only values d=0,1. The ``watchdog'' effect is shown to result from the form of the quantum-mechanical metric.The set of orientations of a measuring device (e.g., a Stern-Gerlach magnet) produced by the action of a Lie group constitutes a honmogeneous space S (e.g., a sphere). A hidden-variable measure determines a metric D on S, the triangle inequality being Bell's inequality. But identification of S with Hilbert-space projectors induces a locally convex metric d on S. The Einstein-Podolsky-Rosen (EPR) hypotheses imply that D=${\mathit{d}}^{2}$, which is impossible because the square of a locally convex metric cannot be a metric. This proves the Bell-EPR theorem. Classical systems avoid the contradiction by allowing only values d=0,1. The ``watchdog'' effect is shown to result from the form of the quantum-mechanical metric.

Physical Review LettersJul 15, 199118 citations

On fuzzy hidden variables

Sylvia Pulmannová

Fuzzy Sets and SystemsJun 10, 20058 citations

Hidden Variables, Non Contextuality and Einstein-Locality in Quantum Mechanics

Virendra Singh

We discuss the problem of hidden variables and the motivation for introducting them in quantum mechanics. These include determinism, and the problem of meassurement and incompleteness. We first discuss Von-Neumann's imposisbility proof and then analyse it's weakness in terms of Bell's explicit hidden variable model of spin one-half particles. We next discuss Gleason's theorem and Kochen-Specker theorem and bring out the troublems with non contextual hidden variable theories. An important role is played by Einstein locality in the discussion of hidden variable theories as was first brought out by Einstein, Podolsky and Rosen. We elaborate it's various implications such as Bell's theorem in terms of Bell's inequalities as well as later work in which Bell's theorem follows without using inequalities.We discuss the problem of hidden variables and the motivation for introducting them in quantum mechanics. These include determinism, and the problem of meassurement and incompleteness. We first discuss Von-Neumann's imposisbility proof and then analyse it's weakness in terms of Bell's explicit hidden variable model of spin one-half particles. We next discuss Gleason's theorem and Kochen-Specker theorem and bring out the troublems with non contextual hidden variable theories. An important role is played by Einstein locality in the discussion of hidden variable theories as was first brought out by Einstein, Podolsky and Rosen. We elaborate it's various implications such as Bell's theorem in terms of Bell's inequalities as well as later work in which Bell's theorem follows without using inequalities.

arXiv:quant-ph/0507182Jul 19, 20051 citation

On the possibility of local hidden-variable theories

Emilio Santos

Physics Letters AJul 1, 19755 citations

{\mathit{d}}^{2}

, which is impossible because the square of a locally convex metric cannot be a metric. This proves the Bell-EPR theorem. Classical systems avoid the contradiction by allowing only values d=0,1. The ``watchdog'' effect is shown to result from the form of the quantum-mechanical metric.