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arXiv:quant-ph/0302026 · Physical Review A

Einstein-Podolsky-Rosen correlations and Galilean transformations

Paweł Caban, Jakub Rembieliński, Kordian A. Smoliński, Zbigniew Walczak

Published Jan 30, 2003• 11 citations
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Abstract

In this paper we calculate with full details Einstein-Podolsky-Rosen spin correlations in the framework of nonrelativistic quantum mechanics. We consider the following situation: two-particle state is prepared (we consider separately distinguishable and identical particles and take into account the space part of the wave function) and two observers in relative motion measure the spin component of the particle along given directions. The measurements are performed in bounded regions of space (detectors), not necessarily simultaneously. The resulting correlation function depends not only on the directions of spin measurements but also on the relative velocity of the observers.

DOI
10.1103/physreva.67.012109

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In this paper we calculate with full details Einstein-Podolsky-Rosen spin correlations in the framework of nonrelativistic quantum mechanics. We consider the following situation: two-particle state is prepared (we consider separately distinguishable and identical particles and take into account the space part of the wave function) and two observers in relative motion measure the spin component of the particle along given directions. The measurements are performed in bounded regions of space (detectors), not necessarily simultaneously. The resulting correlation function depends not only on the directions of spin measurements but also on the relative velocity of the observers.
The formula for the correlation function of spin measurements of two particles in two moving inertial frames is derived within Lorentz-covariant quantum mechanics formulated in the absolute synchronization framework. These results are the first exact Einstein-Podolsky-Rosen correlation functions obtained for Lorentz-covariant quantum-mechanical systems in moving frames under physically acceptable conditions, i.e., taking into account the localization of the particles during the detection and using the spin operator with proper transformation properties under the action of the Lorentz group. Some special cases and approximations of the calculated correlation function are given. The resulting correlation function can be used as a basis for a proposal of a decisive experiment for a possible existence of a quantum-mechanical preferred frame.
We calculate correlation functions for a relativistic Einstein-Podolsky-Rosen--type experiment with massive Dirac particles. We take into account the influence of the Newton-Wigner localization and perform the calculations for a couple of physically interesting states. In particular, we show that localization inside detectors does not significantly affect correlation functions in the case when localization regions are macroscopic or in the case when Einstein-Podolsky-Rosen particles are in a definite momentum state (irrespectively of the size of localization regions).
A local realistic model for quantum mechanics of two-particle Einstein-Podolsky-Rosen pairs is proposed. In this model, it is the strict obedience of conservation laws in each event at the quantum level that uphold the perfect correlation of two spatially-separated particles, instead of nonlocality in the orthodox formulation of quantum mechanics. Therefore, one can conclude that all components of the spin of two particles, and the position and momentum of a particle can be measured simultaneously. The proposed model yields the same statistical prediction on an ensemble of individual particles as the orthodox formulation does. This suggests that the wave function is not a complete description of individual particle as assumed in the orthodox formulation, but only a statistical description of an ensemble of particles.
We formulate the Einstein-Podolsky-Rosen (EPR) gedankenexperiment within the framework of relativistic quantum theory to analyze a situation in which measurements are performed by moving observers. We point out that under certain conditions the perfect anti-correlation of an EPR pair of spins in the same direction deteriorates in the moving observers' frame due to the Wigner rotation, and show that the degree of the violation of Bell's inequality prima facie decreases with increasing velocity of the observers if the directions of the measurement are fixed. However, this does not imply a breakdown of non-local correlation since the perfect anti-correlation is maintained in appropriately chosen different directions. When considering moving frames we must take account of this relativistic effect on the EPR correlation and on the violation of Bell's inequality for quantum communication.
Prediction of the correlation between the data does not cause any problems in an ideal Einstein–Podolsky–Rosen (EPR) experiment, but if both measurements are not really performed at the same time one should take into account that a particle is irreversibly absorbed by a detector during the measurement. We calculate with full details the destruction of quantum states during the spin measurement of a particle involving localization of a particle in a detector in a system of two distinguishable particles of spin-½ and consider an example of the destruction in the configuration typical for EPR experiments.