Extension of the Einstein-Podolsky-Rosen paradox and Bell's theorem

Abstract

In their original paper, Einstein, Podolsky, and Rosen (EPR) questioned the probabilistic nature of the quantum theory using an argument based on the quantum-mechanical correlations between two distant particles which had once interacted. Bell later proved that the quantum theory and any local theory differ significantly in their predictions for these experimentally measurable correlations. It is shown that the arguments of EPR can be extended to apply equally well to certain properties of a single particle or system and that, in analogy with Bell's theorem, the predictions of the quantum theory for certain single-particle experiments are in disagreement with the predictions of any local theory. For example, based on either the quantum theory or existing experimental observations, it is possible to arrange for a photon to have a negligible probability of not being absorbed by some system of finite dimensions, such as one of a large number of atoms, within a finite time interval. It is shown that any local theory which satisfies this requirement must also require that negligible interference effects occur in an optical interferometer at sufficiently low intensities from an incoherent source in combination with sufficiently large separation $L$ between the two optical paths. Time-reversal invariance is used to estimate the requirement $L\ensuremath{\gg}\frac{3{\ensuremath{\lambda}}^{2}}{4{\ensuremath{\pi}}^{2}{r}_{c}}$, where $\ensuremath{\lambda}$ is the wavelength of the light and ${r}_{c}$ is the classical radius of the electron; at optical wavelengths this distance is on the order of 10 m. The same separation should also be required between the photon detectors in any optical experiment based on Bell's theorem. A review of the literature indicates that no existing experimental data, either from optical interferometers or experiments based on Bell's theorem, can be used to distinguish between the local and quantum theories. An investigation of low-intensity optical interference at large path separations is proposed for this purpose.