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American Journal of Physics

Running backwards the Mermin device: Causality in EPR correlations

O. Costa de Beauregard

Published Jun 1, 1983• 4 citations
Publisher

Abstract

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.

DOI
10.1119/1.13219

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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.
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.
A new interpretation of quantum mechanics, similar to the Copenhagen interpretation, is developed from time-symmetry arguments and commonly held principles concerning time and causality. These principles, which are grounded in ideas outside of quantum mechanics, suggest that the strange features and paradoxes of quantum mechanics come from backward causation, in which future events can change the past. Using these principles this paper gives a better understanding of (and reasons for) stationary states, tunneling, wave-particle duality, the measurement problem with the collapse of the state vector, Hardy's paradox, non-locality, and the EPR paradox. These are only a few of the interpretational successes, and the model will be contrasted to other popular and/or recent interpretations. Unfortunately, this model is metaphysical, without any predictive power.
It has been claimed that quantum mechanics is a non-local theory, i.e., that the predictions of quantum mechanics are at odds with a conception of the world where all the interactions are mediated by local mechanisms. The cited reason is the violation of the Bell inequality in cases where measurements are performed on quantum systems of particles that have interacted in the past. Quantum mechanics predicts that the state of the particles in such a system are correlated, a result obtained from considering a thought-experiment often known as EPR. In this thesis, I will argue that the violation of the Bell inequality in EPR forces us to either accept that causes sometimes act both backwards and forwards in time, or give up some widely-held assumptions about causal relations or the role of causal explanations. First, I will present three principles regarding causality that I take be widely accepted. I will then present the background for the claim the quantum mechanics is a non-local theory, and discuss the implications of non-local causal influences in light of the Special Theory of Relativity. One argument against a causal explanation of the EPR-correlations will be discussed, and different models for the causal structure of EPR will be assessed. I will argue that a retrocausal model – models that include instances of retrocausation, where the direction of causation is the opposite of the direction of time – is the only viable option if we want to uphold the three principles presented in chapter 1. I will discuss the plausibility of rejecting one of these principles, and argue that at least one of the can be restricted in a way that still accounts for our commitment to it. Finally, I will assess the non-local models against the retrocausal models, and argue that a retrocausal model offers interpretational advantages over the non-local alternatives.
A solution of nonlocal EPR correlation between counter-propagating pair of polarization entangled photons emitted from a common source at S and detected at points P and Q is sought outside the EPR’s reality criterion of local causality but within the framework of time-symmetric quantum electrodynamics allowing the bi-directional signal transmission P S Q on the double-light cone where the future and the past cones share common light paths connecting the photon source S and the detection points P and Q.
There is an incompatibility between the symmetries of causal structure in relativity theory and the signaling abilities of probabilistic devices with inputs and outputs: while time reversal in relativity will not introduce the ability to signal between spacelike separated regions, this is not the case for probabilistic devices with spacelike separated input-output pairs. We explicitly describe a nonsignaling device which becomes a perfect signaling device under time reversal, where time reversal can be conceptualized as playing backwards a videotape of an agent manipulating the device. This leads to an arrow of time that is identifiable when studying the correlations of events for spacelike separated regions. Somewhat surprisingly, although the time reversal of Popescu-Rohrlich boxes also allows agents to signal, it does not yield a perfect signaling device. Finally, we realize time reversal using postselection, which could to lead experimental implementation.
It follows from the standard quantum formalism that in the time between any two noncommuting measurements there are two quantum states of the same system representing two complementary, forward and backward histories, histories that may be observed in two complementary experiments. It follows from this in turn that all interpretations of quantum mechanics based on the idea of a single state between measurements should be rejected. The non-existence of a faster-than-light nonlocality and of paradoxes in EPR-type experiments1 can be proved in the frame of the standard formalism when the reality of backward histories is taken into account.