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Proceedings of the National Academy of Sciences

A Critical Experiment on the Statistical Interpretation of Quantum Mechanics

Arthur E. Ruark

Published Apr 1, 1928• 1 citation
Publisher

Abstract

Consider a dynamical system with a single coordinate q, and energy E, and let [ represent the Schrodinger wave function of this system.It is commonly stated that the function
DOI
10.1073/pnas.14.4.328

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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.
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Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen-Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a "probability amplitude." A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper, we present a new perspective on such determinism. The ideas are based on the equations of motion or "Quantal Newtonian" Laws obeyed by each electron. These Laws, derived from the temporal and stationary-state Schrödinger equation, are interpreted in terms of "classical" fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. According to the Second Law, each electron experiences an external field-the quantal Coulomb-Lorentz law. It also experiences an internal field representative of properties of the system: correlations due to Coulomb repulsion and Pauli principle; the density; kinetic effects; and an internal magnetic field component. There is a response field. The First Law states that the sum of the external and internal fields experienced by each electron vanishes. These fields are akin to those of classical physics: They pervade all space; their structure is descriptive of the quantum system; the energy of the system is stored in these fields. It is in the classical behavior of these fields, which arise from quantal sources that one may then speak of determinism in quantum mechanics.