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arXiv:1312.6398 · Physica Scripta

Entanglement swapping in the transactional interpretation of quantum mechanics

Louis Marchildon

Published Dec 1, 2014• 0 citations
arXivHTMLPDF

Abstract

The transactional interpretation of quantum mechanics, which uses retarded and advanced solutions of the Schrodinger equation and its complex conjugate, offers an original way to visualize and understand quantum processes. After a brief review, we show how it can be applied to different quantum situations, emphasizing the importance of specifying a complete configuration of absorbers. We consider in more detail the phenomenon of entanglement swapping, and see how the apparent retroactive enforcement of entanglement can be understood in the transactional interpretation.

DOI
10.1088/0031-8949/2014/t163/014022

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The transactional interpretation of quantum mechanics, which uses retarded and advanced solutions of the Schrodinger equation and its complex conjugate, offers an original way to visualize and understand quantum processes. After a brief review, we show how it can be applied to different quantum situations, emphasizing the importance of specifying a complete configuration of absorbers. We consider in more detail the phenomenon of entanglement swapping, and see how the apparent retroactive enforcement of entanglement can be understood in the transactional interpretation.
The transactional interpretation of quantum mechanics, which uses retarded and advanced solutions of the Schrödinger equation and its complex conjugate, offers an original way to visualize and understand quantum processes.After a brief review, we show how it can be applied to different quantum situations, emphasizing the importance of specifying a complete configuration of absorbers.We consider in more detail the phenomenon of entanglement swapping, and see how the apparent retroactive enforcement of entanglement can be understood in the transactional interpretation.
The transactional interpretation of quantum mechanics, following the time-symmetric formulation of electrodynamics, uses retarded and advanced solutions of the Schrodinger equation and its complex conjugate to understand quantum phenomena by means of transactions. A transaction occurs between an emitter and a specific absorber when the emitter has received advanced waves from all possible absorbers. Advanced causation always raises the specter of paradoxes, and it must be addressed carefully. In particular, different devices involving contingent absorbers or various types of interaction-free measurements have been proposed as threatening the original version of the transactional interpretation. These proposals will be analyzed by examining in each case the configuration of absorbers and, in the special case of the so-called quantum liar experiment, by carefully following the development of retarded and advanced waves through the Mach-Zehnder interferometer. We will show that there is no need to resort to the hierarchy of transactions that some have proposed, and will argue that the transactional interpretation is consistent with the block-universe picture of time.
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.”
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.
Quantum nonlocality is discussed as an aspect of the quantum formalism that is seriously in need of interpretation. The Transactional Interpretation of quantum mechanics, which describes quantum processes as transactional "handshakes" between retarded ψψψ waves and advanced ψ∗ψ*ψ∗ waves, is discussed. Examples of the use of the Transactional Interpretation in resolving quantum paradoxes and in understanding the counter-intuitive aspects of the formalism, particularly quantum nonlocality, are provided.
Quantum nonlocality is discussed as an aspect of the quantum formalism that is seriously in need of interpretation.The Transactional Interpretation of quantum mechanics, which describes quantum processes as transactional "handshakes" between retarded ψ waves and advanced ψ * waves, is discussed.Examples of the use of the Transactional Interpretation in resolving quantum paradoxes and in understanding the counter-intuitive aspects of the formalism, particularly quantum nonlocality, are provided. What is an Interpretation of Quantum Mechanics?Interpretations of quantum mechanics provide accounts of the meaning of the quantum formalism, guidance as to how to use the formalism to connect with nature and to make predictions on the outcome of experiments, and understanding of the counterintuitive aspects of the formalism.The first interpretation of quantum mechanics was the Copenhagen Interpretation, developed by Werner Heisenberg and Niels Bohr in the late 1920s.(See reference [1] for a complete description of and references for the Copenhagen Interpretation.)It quickly became the orthodox view of the meaning of the quantum formalism, and it is currently used in most quantum mechanics textbooks.However, its ambiguities have generated a large number of interpretational paradoxes associated with relativity conflicts, wave-particle duality, observer-dependent behavior, wave function collapse, and quantum nonlocality.These problems generated by the Copenhagen Interpretation have led to a plethora of alternative "interpretations", many of which are outlined in this book.The reader is cautioned, however, to examine each of these interpretations carefully to determine if it really qualifies for the status of a full interpretation, in that it deals with