Cramer's (1986) transactional interpretation of quantum mechanics posits retrocausal influences in quantum processes in an attempt to alleviate some of the interpretational difficulties of the Copenhagen interpretation. In response to Cramer's theory, Maudlin (2002) has levelled a significant objection against any retrocausal model of quantum mechanics. I present here an examination of the transactional interpretation of quantum mechanics and an analysis of Maudlin's critique. I claim that, although Maudlin correctly isolates the weaknesses of Cramer's theory, his justification for this weakness is off the mark. The cardinal vice of the transactional interpretation is its failure to provide a sufficient causal structure to constrain uniquely the behaviour of quantum systems and I contend that this is due to a lack of causal symmetry in the theory. In contrast, Maudlin attributes this shortcoming to retrocausality itself and emphasises an apparently fundamental incongruence between retrocausality and his own metaphysical picture of reality. I conclude by arguing that the problematic aspect of this incongruence is Maudlin's assumptions about what is appropriate for such a metaphysical picture.
The merit of positing retrocausal influences in quantum mechanics is relatively well known: explicit violation of the assumption of independence in the derivation of Bell's Inequality resurrects the local hidden variables program of quantum interpretations. Positing retrocausality in nature, however, is a somewhat unpopular proposal. One of the most significant obstacles for retrocausal approaches to quantum mechanics is the objection levelled at Cramer's (1986) transactional interpretation of quantum mechanics by Maudlin (2002), who claims that his objection poses a problem for "any theory in which both backwards and forwards influences conspire to shape events". This paper is an examination of Maudlin's objection to retrocausality.
The examination proceeds as follows. I begin in §2 with an introduction to Wheeler and Feynman’s (1945) attempted time symmetric formulation of classical electrodynamics, from which the transactional interpretation of quantum mechanics originates. I then introduce in §3 Cramer’s extension of the Wheeler-Feynman formalism to a retrocausal transaction mechanism for modelling quantum processes. §4 sets out the details of the transactional interpretation and I briefly mention there some of the advantages Cramer’s theory has over the Copenhagen interpretation of quantum mechanics: most notably that the retrocausal structure allows a ‘zigzag’ causal explanation of the nonlocality associated with Bell-type quantum systems. In §5 I set out the details of Maudlin’s inventive thought experiment that constitutes his objection to Cramer’s theory. I examine in §6 some replies that have been made in response to Maudlin’s objection defending the transactional interpretation.
In §7 I offer my own analysis of Maudlin’s experiment according to the transactional interpretation with a view to showing that, despite the putative defences considered, there is still a problem to be overcome. What is lacking in Cramer’s theory is a causal structure that can constrain uniquely the behaviour of a quantum system and this is exactly the problem that Maudlin’s experiment emphasises. I diverge from Maudlin, however, in the justification for why the transactional interpretation suffers this shortcoming. I claim in §8 that it is the failure of the transactional interpretation to ensure causal symmetry that is impeding such unique determination of behaviour. In contrast, Maudlin attributes this shortcoming to retrocausality itself and emphasises an apparently fundamental incongruence between retrocausality and his own “metaphysical picture of the past generating the future”. I present an argument that it is Maudlin’s assumption about the appropriateness of this metaphysical picture that is problematic here, and not retrocausality.
2 The Wheeler-Feynman absorber theory of radiation Our narrative begins with a problem of classical electrodynamics: an accelerating electron emits electromagnetic radiation, and through this process the acceleration of the electron is damped. Various attempts were initially made to account for this phenomenon in terms of the classical theory of electrodynamics but largely these lacked either empirical adequacy or a coherent physical interpretation. Wheeler and Feynman (1945) set out to remedy this situation by reinterpreting Dirac’s (1938) theory of radiating electrons. I will make no attempt here to give an analysis of this problem, nor of its ensuing evolution.
What is important for our purposes is the nature of the interpretation that Wheeler and Feynman proffer as a resolution, for it is this interpretation that is the motivation for the transactional interpretation of quantum mechanics.
The core of Wheeler and Feynman’s absorber theory of radiation is a suggestion that the process of electromagnetic radiation should be thought of as an interaction between a source and an absorber rather than as an independent elementary process. 1 Wheeler and Feynman imagine an accelerated point charge located within an absorbing system and consider the nature of the electromagnetic field associated with the acceleration. An electromagnetic disturbance initially travels outwards from the source and perturbs each particle of the absorber. The particles of the absorber then generate together a subsequent field. According to the Wheeler-Feynman view, this new field is comprised of half the sum of the retarded (forwards-in-time) and advanced (backwards-in-time) solutions to Maxwell’s equations. The sum of the advanced effects of all the particles of the absorber then yields an advanced incoming field that is present at the source simultaneous with the moment of emission. The claim is that this advanced field exerts a finite force on the source which has exactly the required magnitude and direction to account for the observed energy transferred from source to absorber; this is Dirac’s radiative damping field. In addition, when this advanced field is combined with the equivalent half-retarded, ha
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