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Physical Review Letters

Lorentz and CPT Invariances and the Einstein-Podolsky-Rosen Correlations

O. Costa de Beauregard

Published Mar 21, 1983• 31 citations
Publisher

Abstract

The $S$-matrix scheme allows a straightforward formalization of the Einstein-Podolsky-Rosen nonseparability either of distant measurements issuing from a common preparation, or of distant preparations converging into a common measurement. This implies Lorentz and $\mathrm{CPT}$ invariance of the causality concept at the elementary level, which is a quantal and relativistic extension of the 1876 Loschmidt reversibility statement.

DOI
10.1103/physrevlett.50.867

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The SSS-matrix scheme allows a straightforward formalization of the Einstein-Podolsky-Rosen nonseparability either of distant measurements issuing from a common preparation, or of distant preparations converging into a common measurement. This implies Lorentz and CPT\mathrm{CPT}CPT invariance of the causality concept at the elementary level, which is a quantal and relativistic extension of the 1876 Loschmidt reversibility statement.
Time reversal of Mermin’s reasoning is exemplified in the case of spin-0 photon pairs issuing from cascade transitions, or converging to produce an ‘‘anticascade’’ or ‘‘echelon absorption.’’ Nonseparability of the two distant measurements (respectively, preparations), as tied by propagation of the two particles, is thus relayed either in the common past preparation or future measurement, so that the causality concept turns out to be arrowless at the quantal level. When expressed in the relativistic S matrix formalism, it is CPT invariant.
We show that the Tomonaga-Schwinger formalism in quantum field theory provides a manifestly Lorentz covariant description of an Einstein-Podolsky-Rosen (EPR) correlated state defined on a curved-space-like surface. This avoids the notion of a universal time and clearly demarcates between the completion of the measuring process on a member of an EPR pair and its nonlocal effect on the state of its partner. Being reciprocal and restricted to a spacelike surface, the latter is deterministic but not causal and is consistent with Lorentz invariance.