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arXiv:2505.13704

Nonlinear Nonlocal: Comparing A. O. Barut's Theory to Mine with special emphasis on That Dot on the Screen

W. David Wick

Published May 19, 2025• 0 citations
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Abstract

In the 1980's and 90's, A. O Barut and colleagues developed a nonperturbative approach to electrodynamics eschewing so-called ``second-quantization". Based on incorporation of self-energy terms, the resulting nonlinear and nonlocal theory explained many well-known phenomena of atomic and radiation physics. In 2017, this author introduced a nonlinear, nonlocal theory with the intent of resolving the Measurement Problem. Barut also suggested that his theory resolved such paradoxes. Here I compare the two theories with special attention to That Dot on the Screen.

DOI
10.48550/arxiv.2505.13704

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In the 1980's and 90's, A. O Barut and colleagues developed a nonperturbative approach to electrodynamics eschewing so-called ``second-quantization". Based on incorporation of self-energy terms, the resulting nonlinear and nonlocal theory explained many well-known phenomena of atomic and radiation physics. In 2017, this author introduced a nonlinear, nonlocal theory with the intent of resolving the Measurement Problem. Barut also suggested that his theory resolved such paradoxes. Here I compare the two theories with special attention to That Dot on the Screen.
In 2017, this author proposed, as a resolution of the Measurement Problem, that terms be added to Schrodinger's wavefunction equation, rendering it nonlinear. Said equation derived from a trick employed by S. Weinberg in 1989 which may be unfamiliar to most physicists, as well as uninterpretable in terms of local ("particle") interactions. Motivated by A. O. Barut's work on electrodynamics, here I analyze which kinds of nonlinear theories can be derived from Lagrangian field-theory by integrating out some fields. The issues of "What is a local interaction?" and "Might there be Micro- and Macro-fields?" arise. In the end, I will argue that my 2017 theory cannot be given a "particle" interpretation, nor be derived from a splitting into the two categories of fields.
IntroductionPhysics has always had several different domains of application in on-going development, and physicists have always striven for unification among its different domains.Unification is usually achieved through development of so-called 'covering theories'.In the nineteenth century, the stunning example was Maxwell's Electrodynamics (MED), which unified electricity and magnetism as one domain of theory.Another major domain of theory then present was Newton's Mechanics (NM), which in the eighteenth century had really launched modern physics as a mathematical discipline.At the turn of the twentieth century, NM and MED were well in place, and were fulfilling many technologically important requirements.But there seemed to be an incompatibility between them.The problem concerned their invariance with respect to choice of reference frame: NM exhibited invariance if the allowed reference frames were all connected through Galilean transformations, whereas MED exhibited invariance if the allowed reference frames were all connected through Lorentz transformations.It looked as though one of these two theories must be more nearly correct than the other, but it was not clear which one was the better one.That problem seemed resolved with the advent of Einstein's Special Relativity Theory (SRT).SRT was believed to capture the true meaning of MED concerning the behavior of light signals, and SRT was certainly an endorsement of Lorentz transformation, so SRT was believed to offer the one possible revision of NM that could make mechanics fully consistent with MED.But meanwhile, new phenomena were being discovered at the micro scale of physics, and they often seemed inexplicable with any known theory, whether NM, SRT, or MED.These were phenomena suggesting quantization of light, quantized atomic states, atomic, molecular and crystal structures, radioactivity, etc.So at almost the same time as one problem seemed to be resolved, other problems were emerging.Since the earlier situation between NM and MED had demanded that Physics allow two seemingly discordant theories to co-exist until some good argument could replace one of them, the situation then presented by the new phenomena being discovered naturally invited the development of another potentially discordant theory: Quantum Mechanics (QM).The discovery of the photoelectric effect, and the introduction of the idea of the photon, initiated QM.Almost immediately, QM was developed to handle the Hydrogen atom, and the ground state thereof, the stability of which was thought to be impossible with MED.www.intechopen.
We use a self-field approach to quantum electrodynamics (QED) to show how one may obtain spontaneous emission and the Lamb shift in a two-level atom without second quantization of the radiation field. In addition, we compare the self-field formalism to that of the neoclassical theory of electrodynamics advanced by Crisp and Jaynes [Phys. Rev. 179, 1253 (1969)]. We show that the neoclassical model can be obtained from the self-field approach used here, but that the two are not equivalent. In particular, the self-field approach appears to give a more complete description of radiative processes. Finally, we show that the neoclassical theory's prediction of a nonexponential ``chirruped'' decay is most likely a mathematical artifact of the improper application of the superposition principle in a nonlinear model where such a principle does not hold. A correct treatment with self-field QED yields the usual exponential decay dynamics.