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Published January 2022 | Supplemental Material + Published
Book Section - Chapter Open

Symmetry, Transactions, and the Mechanism of Wave Function Collapse


The Transactional Interpretation of quantum mechanics exploits the intrinsic time-symmetry of wave mechanics to interpret the ψ and ψ* wave functions present in all wave mechanics calculations as representing retarded and advanced waves moving in opposite time directions that form a quantum "handshake" or transaction. This handshake is a 4D standing-wave that builds up across space-time to transfer the conserved quantities of energy, momentum, and angular momentum in an interaction. Here, we derive a two-atom quantum formalism describing a transaction. We show that the bi-directional electromagnetic coupling between atoms can be factored into a matched pair of vector potential Green's functions: one retarded and one advanced, and that this combination uniquely enforces the conservation of energy in a transaction. Thus factored, the single-electron wave functions of electromagnetically-coupled atoms can be analyzed using Schrödinger's original wave mechanics. The technique generalizes to any number of electromagnetically coupled single-electron states—no higher-dimensional space is needed. Using this technique, we show a worked example of the transfer of energy from a hydrogen atom in an excited state to a nearby hydrogen atom in its ground state. It is seen that the initial exchange creates a dynamically unstable situation that avalanches to the completed transaction, demonstrating that wave function collapse, considered mysterious in the literature, can be implemented with solutions of Schrödinger's original wave mechanics, coupled by this unique combination of retarded/advanced vector potentials, without the introduction of any additional mechanism or formalism. We also analyze a simplified version of the photon-splitting and Freedman–Clauser three-electron experiments and show that their results can be predicted by this formalism.

Additional Information

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Received: 17 June 2020 / Revised: 3 August 2020 / Accepted: 14 August 2020 / Published: 18 August 2020. Supplementary Materials: The following are available online at http://www.mdpi.com/2073-8994/12/8/1373/s1. The authors are grateful to Jamil Tahir-Kheli for sharing his unmatched knowledge and understanding of physics history, and his deeply insightful critique of the approach developed here, during many thoughtful discussions down through the years. We thank Ruth Kastner and Gerald Miller for helpful comments and for rubbing our noses in the probabilistic approach to QM. We are particularly grateful to Nick Herbert for asking about transition time in our calculations, which led us to important new insights. David Feinstein, Glenn Keller, Ed Kelm, and Lloyd Watts caught many bugs and offered helpful suggestions. We thank Jordan Maclay for asking us to write this paper for a special issue of Symmetry and for making useful comments and suggestons. Finally, we thank our four anonymous reviewers, whose penetrating comments and questions led to major improvements in this paper. This research received no external funding. Author Contributions: Both authors contributed to this work in roughly equal amounts. It started as a short internal report written by JGC discussing Mathematica calculations based on CAM's book. Following this, CAM made major contributions in expansion to the present length and produced most of the discussion of equations and formalism. All authors have read and agreed to the published version of the manuscript. The authors declare that there are no conflicts of interest.

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Published - Cramer_2020p1373.pdf

Supplemental Material - symmetry-12-01373-s001.zip


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August 22, 2023
March 5, 2024