Locality and nonlocality in quantum mechanics: A two-proton EPR experiment

Abstract

Two ''thought experiments'' are central to most discussions of the famous EPR paradox: Experiment 1, in which two electrons with spins initially coupled Ž to total spin S are carried apart to a great distance e.g., in a molecular dissociation . process , and Experiment 2, which is similar but refers to two bare protons. The crucial question to be asked is whether the spin coupling will be conserved at all distances: if it Ž is, then the system exhibits ''nonlocality'' the two particles stay ''correlated'' in some . way, even at infinite distance and thus violates Einstein's principle of locality-which denies that possibility. A recent discussion of Experiment 1 shows that nonlocality is the rule only up to a point at which the singlet᎐triplet interval is small enough to be bridged by weak interaction with the ''heat bath'' in which the system is embedded: Beyond that point, the system is no longer described by a wave function but instead by a statistical Ž . ensemble. When ensemble averaging is admitted, the spin-correlation function Q r , r c 1 2 decreases to zero at all points in space and the coupling is broken; the particles are then independent and neither can be influenced by its previous interaction with the other. In the present work, the same approach is used to discuss the two-proton system Ž . Experiment 2 . The conclusions are similar: The protons are described by appropriate wave packets, with an initial overlap sufficient to give a substantial singlet᎐triplet Ž separation ⌬ E, and, again, the spin coupling is broken when the overlap and, . consequently, ⌬ E decreases to a sufficiently small value. ᮊ 1999 John Wiley & Sons, Inc.Int J Quant Chem 74: 573᎐584, 1999 Key words: EPR experiment; spin correlation; density matrix; decoherence U Dedicated to George Hall-a master-builder of mathematical models.

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