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Physical Review Letters

Experimental Test of Local Hidden-Variable Theories

S. J. Freedman, John F. Clauser

Published Apr 3, 1972• 1,999 citations
Publisher

Abstract

We have measured the linear polarization correlation of the photons emitted in an atomic cascade of calcium. It has been shown by a generalization of Bell's inequality that the existence of local hidden variables imposes restrictions on this correlation in conflict with the predictions of quantum mechanics. Our data, in agreement with quantum mechanics, violate these restrictions to high statistical accuracy, thus providing strong evidence against local hidden-variable theories.

DOI
10.1103/physrevlett.28.938

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Physical Review A•Oct 1, 1992•138 citations
We have measured the linear polarization correlation of the photons emitted in an atomic cascade of calcium. It has been shown by a generalization of Bell's inequality that the existence of local hidden variables imposes restrictions on this correlation in conflict with the predictions of quantum mechanics. Our data, in agreement with quantum mechanics, violate these restrictions to high statistical accuracy, thus providing strong evidence against local hidden-variable theories.
We have measured the linear polarization correlation of the photons emitted in a radiative atomic cascade of calcium. A high-efficiency source provided an improved statistical accuracy and an ability to perform new tests. Our results, in excellent agreement with the quantum mechanical predictions, strongly violate the generalized Bell's inequalities, and rule out the whole class of realistic local theories. No significant change in results was observed with source-polarizer separations of up to 6.5 m.
We have measured the linear polarization correlation between the two photons from the $7^{3}S_{1}\ensuremath{\rightarrow}6^{3}P_{1}\ensuremath{\rightarrow}6^{1}S_{0}$ cascade of Hg200{\mathrm{Hg}}^{200}Hg200. The results were used to evaluate Freedman's version of the Bell inequality, $\ensuremath{\delta}<~0$. Our result is ${\ensuremath{\delta}}_{\mathrm{exp}}=+0.046\ifmmode\pm\else\textpm\fi{}0.014$, in clear violation of the inequality and in excellent agreement with the quantum mechanical prediction, ${\ensuremath{\delta}}_{\mathrm{QM}}=+0.044\ifmmode\pm\else\textpm\fi{}0.007$. An important feature of the experiment was the explicit measurement of the initial density matrix for the cascading atoms.
A family of theories called "deterministic local hidden variable theories" (DLHV) is characterized and their consequences are investigated for an experimentally realistic situation. An experiment on the polarization correlation of optical photon pairs emitted in certain atomic cascades is proposed as a test of the family of DLHV theories. The model-independent hidden variable predictions applicable to the realistic experimental arrangement are obtained by a generalization of a previous theorem of Bell. Quantum mechanical predictions for the same experimental situation are calculated for two cases: a J = 0 + J = 1 + J = 0 and a J = 1 + J = 1 + J = 0 electric dipole cascade. For both cascades, it is shown that the quantum mechanical and the DLHV predictions are in sufficient disagreement for an actual experimental test to be possible. Restrictions on detector solid angle and polarizer efficiency, necessary to obtain a decisive experiment, are explicitly given. The Einstein, Podolsky, and Rosen argument for the existence of a DLHV theory is reviewed.
The proposal is made of replacing the usual auxiliary assumptions needed for the derivation of testable Bell inequalities by an assumption resting only on symmetry considerations. It is shown that reliable atomic cascade tests of symmetric local hidden-variables theories should combine high statistics, cascades of type 0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0, and calcite polarizers. The three conditions have been achieved in experiments already performed, but never before simultaneously.
A local hidden-variable model is exhibited for the experiments by Aspect, Grangier, and Roger [Phys. Rev. Lett. 47, 460 (1981); 49, 91 (1982)] and Aspect, Dalibard, and Roger [Phys. Rev. Lett. 49, 1804 (1982)] measuring polarization correlation of optical-photon pairs. The model agrees with quantum-mechanical predictions for all measurable quantities even with ideal polarizers and detectors, and emphasizes the need of a high degree of directional correlation, besides the correlation of spin (or polarization or other quantities), in any test of locality. It is proved that homogeneous inequalities, involving only coincidence detection rates, cannot discriminate between quantum mechanics and local theories, which invalidates all previously used empirical tests. The role of supplementary assumptions, like the so-called no enhancement, for the derivation of Bell's inequalities is discussed. Finally it is conjectured that quantum mechanics might be compatible with local realism, if we assume that not all self-adjoint operators represent observables and not all density operators represent states.