Experimental Test of the Bell Inequalities


The beginning of this century marked a revolution in Physics. In merely 30 years, starting with Planck's explanation of the black body radiation in 1900, the picture of physics was radically changed by the introduction of Quantum Mechanics. Quantum Mechanics is a very counterintuitive theory that continues to puzzle physicists throughout the world. Its interpretation is still debated, new ways of interpretation are introduced almost daily.

Ironically, Einstein was one of the main players in the introduction of Quantum Mechanics. Specifically, he explained the photo effect with Planck's energy quanta, which were later called photons and introduced the concepts of absorption and spontaneous and stimulated emission of radiation. Despite these tremendeous advances Einstein contributed to making Quantum Mechanics possible, Einstein always doubted the completeness of Quantum Mechanics. Specifically, the random nature of Quantum Mechanics and the spooky action-at-a-distance (non-locality) were things he deeply rejected. His famous quote "Subtle is the Lord, but he does not play dice!" illustrates his attitude towards Quantum Mechanics.

In 1935, together with Rosen and Podolsky, he published his famous article "Can Quantum Mechanical Description be considered complete?" (Einstein, 1935). In this paper, he introduces a gedankenexperiment (EPR-Experiment), illustrating the deficencies of Quantum Mechanics.

In the following I will briefly sketch the experiment. I will, however, use Bohm's version of the experiment introduced in the 1950's. Conceptually, it is easier to understand than Einstein's original gedankenexperiment. Suppose you have a system consisting of two particles, each with spin 1/2 in an entangled state, i.e

|?>=(|+>1|?>2 ? |?>1|+>2),

where the + and - indicate spin up and down, respectivley. The indices indicate the particle number. The system is therefore in a state with a total spin S=0, i.e. the singlet state. If particle one is found with spin up (+), particle two has to be in spin down (-) and vice versa. Please note, however, that the direction with respect to which the spins are oriented is not defined. Only the relative spin orientation of the particles is known. This is one of the things that Einstein disliked. He felt that the particles should have some kind of tag (hidden variables) associated with them, that would predetermine the orientation. The gedankenexperiment now involves the separation of the two particles and the independent measurement of their spin orientation. The entanglement between the two particles produces the non-local character or action-at-a-distance. In principle one could perform the measurement for one particle here on earth, while the second particle travels light years away. And yet quantum mechanics tells me that immediately when spin up for one particle is measured, the other one has to be down. This collapse of the wave function occurs instantaneously without the need of some signal transfer limited by the speed of light. Finally, Einstein came to the conclusion that there is a contradiction in the experiment with the quantum mechanical concept of commuting operators. The spin (up/down) can be measured on particle one. Consequently the spin direction of particle 2 is inferred from the result of this measurement. By contrast, a measurement of spin left/right can be performed on that very particle. Seemingly, you have information of spin up/down and left/right for one particle producing a contradiction of quantum mechanics.

For a long time no progress in this problem was made. Arguments were only philosophical in nature until 1964 when Bell proved that local hidden variable (LHV) theories that complete Quantum Mechanics in the Einsteinian sense could exist. Moreover, he showed that the statistical predictions of correlations in an EPR type experiment by any LHV theory obey an inequality whereas the corresponding predictions of Quantum Mechanics can violate this inequality. In other words, due to their local character correlations LHV theories show weaker than in Quantum mechanics. For the first time experiments that were able to decide between LHV theories and Quantum Mechanics were possible.

Experimental requirements for these tests are high: high detection efficiency, strong correlation, i.e. a very pure entangled state, very good analyzers and finally a high spatial correlation of the two particles. As a result, it took 8 years for the first tests to be performed. And still today the final answer has not been determined due to the existing loopholes in all previous experiments.

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Prof. Dr. Thomas Walther

Laser und Quantenoptik
Institut für Angewandte Physik
Fachbereich 05 - Physik
Technische Universität Darmstadt
Schlossgartenstr. 7
D-64289 Darmstadt

+49 6151 16-20831 (Sekretariat)

+49 6151 16-20834 (Fax)




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