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arXiv:quant-ph/0603018 · Physics Essays

Causal Loops and Collapse in the Transactional Interpretation of Quantum Mechanics.

‎Louis Marchildon

Published Sep 1, 2006• 18 citations
arXivHTMLPDF

Abstract

Cramer's transactional interpretation of quantum mechanics is reviewed, and a number of issues related to advanced interactions and state vector collapse are analyzed. Where some have suggested that Cramer's predictions may not be correct or definite, I argue that they are, but I point out that the classical-quantum distinction problem in the Copenhagen interpretation has its parallel in the transactional interpretation.

DOI
10.4006/1.3025811

Related papers

The transactional interpretation of quantum mechanics

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The interpretational problems of quantum mechanics are considered. The way in which the standard Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the transactional interpretation, is presented. The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet is relativistically invariant and fully causal. A detailed comparison of the transactional and Copenhagen interpretations is made in the context of well-known quantum-mechanical Gedankenexperimente and "paradoxes." The transactional interpretation permits quantum-mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the Copenhagen interpretation. The transactional interpretation is shown to provide insight into the complex character of the quantum-mechanical state vector and the mechanism associated with its "collapse." It also leads in a natural way to justification of the Heisenberg uncertainty principle and the Born probability law ($P=\ensuremath{\psi}{\ensuremath{\psi}}^{*}$), basic elements of the Copenhagen interpretation.

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The interpretation of quantum mechanics (or, for that matter, of any physical theory) consists in answering the question: How can the world be for the theory to be true? That question is especially pressing in the case of the long-distance correlations predicted by Einstein, Podolsky and Rosen, and rather convincingly established during the past decades in various laboratories. I will review four different approaches to the understanding of long-distance quantum correlations: (i) the Copenhagen interpretation and some of its modern variants; (ii) Bohmian mechanics of spin-carrying particles; (iii) Cramer's transactional interpretation; and (iv) the Hess-Philipp analysis of extended parameter spaces.

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Cramer's transactional interpretation of quantum mechanics is reviewed, and a number of issues related to advanced interactions and state vector collapse are analyzed. Where some have suggested that Cramer's predictions may not be correct or definite, I argue that they are, but I point out that the classical-quantum distinction problem in the Copenhagen interpretation has its parallel in the transactional interpretation.
The interpretational problems of quantum mechanics are considered. The way in which the standard Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the transactional interpretation, is presented. The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet is relativistically invariant and fully causal. A detailed comparison of the transactional and Copenhagen interpretations is made in the context of well-known quantum-mechanical Gedankenexperimente and "paradoxes." The transactional interpretation permits quantum-mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the Copenhagen interpretation. The transactional interpretation is shown to provide insight into the complex character of the quantum-mechanical state vector and the mechanism associated with its "collapse." It also leads in a natural way to justification of the Heisenberg uncertainty principle and the Born probability law ($P=\ensuremath{\psi}{\ensuremath{\psi}}^{*}$), basic elements of the Copenhagen interpretation.
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 transactional interpretation of quantum mechanics [1] was originally published in 1986 and is now about 14 years old. It is an explicitly nonlocal and Lorentz invariant alternative to the Copenhagen interpretation. It interprets the formalism for a quantum interaction as describing a “handshake” between retarded waves (ψ) and advanced waves (ψ*) for each quantum event or “transaction” in which energy, momentum, angular momentum, and other conserved quantities are transferred. The transactional interpretation offers the advantages that (1) it is actually “visible” in the formalism of quantum mechanics, (2) it is economical, involving fewer independent assumptions than its rivals, (3) it is paradox-free, resolving all of the paradoxes of standard quantum theory including nonlocality and wave function collapse, (4) it does not give a privileged role to observers or measurements, and (5) it permits the visualization of quantum events. We will review the transactional interpretation and some of its applications to “quantum paradoxes.”
Abstract—Since the beginning, quantum mechanics has raised major foundational and interpretative problems. Foundational research has been an important factor in the development of quantum cryptography, quantum information theory and, per-haps one day, practical quantum computers. Many believe that, in turn, quantum information theory has bearing on foundational research. This is largely related to the so-called epistemic view of quantum states, which maintains that the state vector represents information on a system and which has led to the suggestion that quantum theory needs no interpretation. I will argue that this and related approaches fail to take into consideration two different explanatory functions of quantum mechanics, that of accounting for classically unexplainable correlations between classical phenomena and that of explaining the microscopic structure of classical objects. The epistemic view provides no answer to what constitutes the main question of interpretation: How can the world be for quantum mechanics to be true? I will then review three different approaches to understanding quan-tum mechanics, namely, Bohmian mechanics, Everett’s relative states, and Cramer’s transactional interpretation. I will show that these approaches answer the above question, as well as other foundational ones. This paper is written from the perspective that different logically consistent interpretations, far from leading to confusion, in fact contribute to increased understanding of the theory. I.
The interpretation of quantum mechanics (or, for that matter, of any physical theory) consists in answering the question: How can the world be for the theory to be true? That question is especially pressing in the case of the long-distance correlations predicted by Einstein, Podolsky and Rosen, and rather convincingly established during the past decades in various laboratories. I will review four different approaches to the understanding of long-distance quantum correlations: (i) the Copenhagen interpretation and some of its modern variants; (ii) Bohmian mechanics of spin-carrying particles; (iii) Cramer's transactional interpretation; and (iv) the Hess-Philipp analysis of extended parameter spaces.