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The geometrical aspects of the bell inequalities

A.A. Tyapkin, Milan Vindushka

Foundations of PhysicsFeb 1, 19914 citations

A note on the geometric interpretation of Bell's inequalities

Paolo Dai Pra, Michele Pavon, Neeraja Sahasrabudhe

Using results of Pitowsky and Gupta, we show in a direct, elementary fashion that, in the case of three spins, Bell's inequalities indeed provide a representation of the tetrahedron of all spin correlation matrices as intersection of half-spaces.

arXiv:1301.4823Jan 21, 20130 citations

Bell's Inequality and Heisenberg Measurements on Relativistic Quantum Systems

Ulrich Faigle

Bell's inequality plays an important role with respect to the Einsteinian question about the physical reality of quantum theory. While Bell's inequality is usually viewed within the geometric framework of a Hilbert space quantum model, the present note extends the theory of Heisenberg measurements to quantum systems with representations in general orthogonal geometric spaces and, in particular, the Minkowski spaces of relativity theory. A Feynmanian numerical example exhibits two measurements that admit a joint probabilistic interpretation in Minkowski space while they are not jointly observable in Hilbert space. The analysis shows that probabilistic interpretations of quantum measurements may depend not only on the measuring instruments and the system states but also on the geometric space in which the measurements are conducted. In particular, an explicit numerical example is given of a Heisenberg measurement with a complete set of common observables that violates Bell's inequality in Minkowski space but, mutatatis mutandis, satisfies it in Hilbert space.Bell's inequality plays an important role with respect to the Einsteinian question about the physical reality of quantum theory. While Bell's inequality is usually viewed within the geometric framework of a Hilbert space quantum model, the present note extends the theory of Heisenberg measurements to quantum systems with representations in general orthogonal geometric spaces and, in particular, the Minkowski spaces of relativity theory. A Feynmanian numerical example exhibits two measurements that admit a joint probabilistic interpretation in Minkowski space while they are not jointly observable in Hilbert space. The analysis shows that probabilistic interpretations of quantum measurements may depend not only on the measuring instruments and the system states but also on the geometric space in which the measurements are conducted. In particular, an explicit numerical example is given of a Heisenberg measurement with a complete set of common observables that violates Bell's inequality in Minkowski space but, mutatatis mutandis, satisfies it in Hilbert space.

arXiv:2304.12873Apr 25, 20230 citations

A new interpretation of Bell's inequalities

E. C. G. Sudarshan, Tony Rothman

International Journal of Theoretical PhysicsJul 1, 199318 citations

A defense of local realism

Cristian Dumitrescu

Bell's inequalities (and the CHSH inequalities) were used in order to rule out certain hidden variable theories (or interpretations of quantum mechanics). In this short note, I will prove that Bell's results represent a strong argument in favor of a deeper, nonlinear underlying reality.

Jan 1, 20180 citations

On an alternative interpretation of the bell inequalities

Willem M. de Muynck, Omar Abu-Zeid

Physics Letters AFeb 1, 198424 citations

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