Einstein-Podolsky-Rosen

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. 

The second axiom, which is reminiscent of Mach s principle, also contains the seeds of Leibniz s Monads [reschQl]. All is process. That is to say, there is no thing in the universe. Things, objects, entities, are abstractions of what is relatively constant from a process of movement and transformation. They are like the shapes that children like to see in the clouds. The Einstein-Podolsky-Rosen correlations (see section 12.7.1) remind us that what we empirically accept as fundamental particles - electrons, atoms, molecules, etc. - actually never exist in total isolation. Moreover, recalling von Neumann s uniqueness theorem for canonical commutation relations (which asserts that for locally compact phase spaces all Hilbert-space representations of the canonical commutation relations are physically equivalent), we note that for systems with non-locally-compact phase spaces, the uniqueness theorem fails, and therefore there must be infinitely many physically inequivalent and... 

This bizarre prediction, known as the Einstein-Podolsky-Rosen paradox, has been verified many times in the laboratory. The most famous version involves two electrons manipulated into a mixed state with combined spin of 0, The electrons are separated in space before the spin of one (and only one) electron is measured, say, in a Stern-Gerlach machine. If that electron is found to be spin up, then by conservation of spin angular momentum, the other electron must be spin down, and vice versa. This holds true even if the ratio of the distance between the measurements to the time between the measurements is greater than the speed of light. See the discussion in Townsend [To, Sections 5,4 and 5,5] and the references therein. 

In this section we have presented a mathematical foundation for entanglement of quantum systems. This foundation lies behind most modern discussions of quantum computing, as well as the Einstein-Podolsky-Rosen paradox. 

Exercise 11.4 Can you exploit the Einstein-Podolsky-Rosen paradox to send information faster than the speed of light ... 

A. Kyprianidis and J. P. Vigier, Action-at-a-distance The mystery of Einstein-Podolsky-Rosen correlations, in F. Selleri (Ed.), Quantum Mechanics versus Local Realism The Einstein-Podolsky—Rosen Paradox, ISBN 0-30-642739-7, Plenum, New York, 1988, p. 273. 

P. R. Holland and J. P. Vigier, The quantum potential and signaling in the Einstein-Podolsky-Rosen experiment, Found. Phys. 18(7), 741-750 (1988). 

N. Cufaro-Petroni, A. Garuccio, F. Selleri, and J. P. Vigier, On a contradiction between the classical (idealized) quantum theory of measurement and the conservation of the square of the total angular momentum in Einstein-Podolsky-Rosen paradox, C. R. Acad. Sci., Ser. B (Sciences Physiques), 290(6), 111-114 (1980). 

N. Cufaro-Petroni and J. P. Vigier, Causal superluminal interpretation of the Einstein-Podolsky-Rosen paradox, Lett. Nuovo Cimento 26(5) (Ser. 2), 149-154 (1979). 

This chapter is organized as follows In Section 2, quantum states are briefly described. Section 3 presents aspects of standard quantum measurement model. Section 4 includes double-slit, Einstein-Podolsky-Rosen, and Tonomura s experiments. Section 5 illustrates calculations of quantum states for quantum measurements. In Section 6, atom interferometer experiment of Scully et al. is analyzed. A detailed discussion is presented in Section 7, emphasizing a physical perception of quantum mechanics. 

Abstract We consider a possible realization of the position- and momentum-correlated atomic pairs that are confined to adjacent sites of two mutually shifted optical lattices and are entangled via laser-induced dipole-dipole interactions. The Einstein-Podolsky-Rosen (EPR) "paradox" [Einstein 1935] with translational variables is then modified by lattice-diffraction effects. We study a possible mechanism of creating such diatom entangled states by varying the effective mass of the atoms. 

The preceding formalism of SU(2) phase states can be used in a number of problems of quantum physics. As an illustrative example of great importance, consider the so-called Einstein-Podolsky-Rosen (EPR) paradox [73] (see also discussions in Refs. 14, 15, 74, and 75). The EPR paradox touches on the conceptual problems of reality and locality and existence of hidden variables in quantum physics as well as the more technological aspects of quantum cryptography [34]. 

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