Bell’s theorem

While this above state of affairs is decidedly counterintuitive, it has the virtue of simply and easily - at least in principle - accounting for one of the deep mysteries of quantum mechanics namely, an apparent noidocality as expressed by the Einstein-Podolsky-Rosen gcdarikcn experiment [ein35] and Bell s theorem [bell64] (see discussion box). Finite nature implies that any system that is allowed to evolve from some distant initial state possesses causality in all space-time directions. This implies, in particular, that no part of space can be considered to be causally separated from another, and that therefore the DM universe will always harbor effects that cannot be attenuated by distance. 

Bell s Theorem In a celebrated 1935 paper, Einstein, Podolsky and Rosen (EPR) [ein35] argued that quantum mechanics provides an essentially incomplete description of reality unless hidden variables exist. 

All of Bell s papers on the conceptual and philosophical problems of quantum mechanics, including his landmark PIPR paper in which he derives his famous inequality, are collected in [bell87. An excellent collection of papers exploring the philosophical consequences of Bell s theorem appears in a volume edited by Crushing and McMullin [cush89. ... 

Phenomena in the submicroscopic quantum world inevitably create apparent paradoxes from the viewpoint of classical macroscopic experience. We will focus in this chapter on two of the most counterintuitive aspects of quantum theory superposition (SchrOdinger s Cat) and entanglement (EPR and Bell s theorem). 

Bell s inequality provides a clear-cut test of local reality vs. quantum mechanics. The unambiguous answer, from a variety of experiments which we describe in the next section, is that quantum mechanics wins Thus, we can conclude that we live in a Universe which does not respect local reality. Quantum entanglement—a term introduced by Schrddinger—really happens In drawing this conclusion we are actually glossing over a number of still-unresolved hair-splitting metaphysical arguments. This remarkable result is often summarized as Bell s theorem ... 

Bell s theorem is by now a well-established experimental fact. The most accurate experiments have been based on analogs of the EPR-Bohm experiment measuring photon polarizations rather than spins of massive particles. Instead of spin-up and spin-down states, photons can have right and left circular polarizations. In certain processes, two photons with correlated polarizations—one left, one right— can be emitted in opposite directions. Wheeler had proposed in 1946 that the pair of photons emitted in the annihilation of positronium (see Fig. 7.12) were entangled with opposite polarizations. This was experimentally confirmed by Wu and Shaknov in 1949. 

Greenberger D. M., Horne M. A. and Zeilinger A., Bell s Theorem, Quantum Theory, and Conceptions of the Universe, (Kluwer, Dordrecht, 1989). 

Aspect experiment An experiment conducted by the French physicist Alain Aspect (1947- ) and his colleagues in the early 1980s to test Bell s inequality see Bell s theorem). The experiment involves producing... 

Leggett s theorem A result in quantum mechanics that is a generalization of Bell s theorem. This theorem, which was put forward in 2003 by the British physicist Anthony Leggett (1938- ), states that nonlocal hidden-variables theories make predictions that contradict the predictions of quantum mechanics. It was subsequently found that experiments agree with the predictions of quantum mechanics rather than of nonlocal hidden-variables theories. 

An alternative to the wave mechanical treatment of quantum mechanics is an equivalent formalism called matrix mechanics, which is based on mathematical operators. See also hidden-variables theory Bell s THEOREM. 

Bennett, C.H., Brassard, G., Mermin, D.N. Quantum cryptography without Bell s theorem. Physical Review Letters 68(5), 557-559 (1992)... 

The motivations for considering supplementary parameters will be found in the analysis of the famous Einstein-Podolsky-Rosen Gedankenexperiment. Introducing a reasonable Locality Condition, one can derive Bell s theorem, which states... 

As an abstract of this discussion, we can say that Bell s theorem states a conflict between Local Supplementary Parameters Theories and certain Quantum Mechanical predictions. It yields a quantitative criterion for this conflict, that will allow us to design sensitive experiments. 

Quantum Mechanics has been so much upheld in a great variety of experiments that Bell s Theorem might appear as an impossibility proof of supplementary parameters. However, situations in which this conflict arises (sensitive situations) are rare in 1965 none had been realized. 

A. Aspect, P. Grangier and G. Roger, Experimental Tests of Realistic Local Theories via Bell s Theorem, Phys. Rev. Lett. 

A total of 28 invited talks were delivered at the conference. These talks, which are presented in this volume, covered a wide range of topics in atomic physics in a broad sense. They extend from very basic problems (e.g., the interpretation of quantum mechanics in light of Bell s theorem and the feasibility of relativistic many-body calculations) to applied problems (e.g., laser detection of trace elements and spectroscopy of chemisorbed molecules). 

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