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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Local realism versus quantum theory: Violation of the generalized spin- s Bell inequalities for a set of three distinct axes

M. Ardehali

Published Jun 15, 1990• 1 citation
Publisher

Abstract

Some simple inequalities which demonstrate the incompatibility of local realism with quantum theory are derived. They establish, for the first time, necessary conditions for violation of the generalized spin-$s$ Bell inequalities for a set of three distinct noncoplanar axes. For $s=\frac{1}{2}$, however, these inequalities are equivalent to Wigner's results, thus giving necessary and sufficient conditions.

DOI
10.1103/physrevd.41.3837

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Some simple inequalities which demonstrate the incompatibility of local realism with quantum theory are derived. They establish, for the first time, necessary conditions for violation of the generalized spin-sss Bell inequalities for a set of three distinct noncoplanar axes. For s=12s=\frac{1}{2}s=21​, however, these inequalities are equivalent to Wigner's results, thus giving necessary and sufficient conditions.
Some new, powerful, and very simple Bell inequalities are derived. They establish that for two spin-sss particles in the singlet state, the quantum-theoretic Einstein-Podolsky-Rosen correlations for spin measurements along all pairs of directions from a set of NNN axes are incompatible with local realism for any set of distinct coplanar axes when N=3N=3N=3, and for any set of distinct axes whatever when N=4N=4N=4, with the possible exception of sets restricted by one of the constraints $\stackrel{^}{a}\ifmmode\pm\else\textpm\fi{}\stackrel{^}{b}\ifmmode\pm\else\textpm\fi{}\stackrel{^}{c}\ifmmode\pm\else\textpm\fi{}\stackrel{^}{d}=0$. These results hold for any value of the spin.
With Bell's inequalities one has a formal expression to show how essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a simple experimental arrangement. For the case of entangled pairs of spin-1/2 particles we propose an alternative measurement setup which is consistent to the necessary assumptions corresponding to the derivation of the Bell inequalities. We find that the Bell inequalities are never violated with respect to our suggested measurement process.
Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics.
For almost three decades in the twentieth century, the physics community believed that John von Neumann had proved the impossibility of completing quantum mechanics by a local realist, hidden-variables theory. Although Grete Hermann had raised strong objections to von Neumann's proof, she was largely ignored. This situation lasted, until John Bell rediscovered that von Neumann's proof was flawed: a \emph{sufficient} condition for local realism had been taken as a \emph{necessary} one. Bell subsequently established various constraints on hidden-variables theories, in the form of inequalities that can be submitted to experimental test. All performed tests to date have opened some loopholes. The quest to close them motivated great technical achievements and ongoing efforts to improve what has already been reached. There is, however, a rather ironic twist concerning Bell inequalities. On deriving them, Bell also took a sufficient condition for local-realism, as if it were a necessary one. As a consequence, even completely loophole-free Bell inequality violations would not disprove local realism. We argue that Bell inequalities cannot follow from local-realism alone. The proof is given by constructing three local-realist models that entail Bell inequality violations.
Two aspects of the Clauser-Horne conditions for the compatibility with local realism of measured spin-\textonehalf{} Einstein-Podolsky-Rosen correlations are investigated in the spin-sss case. (1) A new set of necessary conditions is given for compatibility with local realism. These conditions are violated for a large range of geometries. The range does not diminish with increasing sss, if the observed correlations are sufficiently near to the quantum-theoretic predictions. (2) A simple counterexample is given to the spin-1 generalization of a recent conjecture that the conditions tested by the Clauser-Horne spin-\textonehalf{} inequalities are sufficient as well as necessary for compatibility of the data with local realism.