Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

JOURNAL OF ADVANCES IN MATHEMATICS

A paradigm shift in mathematical physics, Part 3: A mirror image of Feynmans quantum electrodynamics (QED)

Jeffrey H. Boyd

Published Aug 4, 2015• 18 citations
Publisher

Abstract

Richard Feynmans book QED, written for a lay audience, is a trusted source of information about Quantum Electro-Dynamics by a Nobel laureate. It is a mirror image of the Theory of Elementary Waves (TEW), discovered by Lewis E. Little. Recent work on TEW, published in this journal, shows that an elementary ray has the shape of a cylindrical helix traveling in Euclidean space, with a complex amplitude. This is an analog in physical nature of Feynmans mathematical concept of an amplitude, which is the core of QED. The only substantial difference is that an amplitude is assumed by Feynman to travel in the same direction as the particle, but in TEW they travel in opposite directions. There is almost no empirical data to resolve that disagreement. Such evidence as exists favors the idea they travel in opposite directions. If we modify Feynmans QED in this way we end up with a theory symmetrical to QED. We nickname it QÆD, using the letter Æ to symbolize an ælementary ray. QÆD is a fountain of information about the nature of elementary rays, and resolves some of the problems that Feynman said he found in QED.

DOI
10.24297/jam.v11i2.1283

Related papers

A paradigm shift in mathematical physics, Part 1: The Theory of Elementary Waves (TEW)

Jeffrey H. Boyd

Why is quantum mathematics (QM) the only science based on probability amplitudes rather than probabilities? A paradigm shift called the Theory of Elementary Waves (TEW) posits zero energy waves traveling in the opposite direction as particles, which a particle follows backwards: like a probabilistic guidance system emanating from detectors. Probability amplitudes are the mathematical analog of these elementary rays. Although this proposal might sound like gibberish, that is the hallmark of a paradigm shift. Thomas Kuhn warns that previous paradigm shifts were rejected because they sounded like gibberish. TEW is internally coherent, explains a mountain of empirical data, and resolves insoluble problems of QM. For example, it dispenses with the need for wavefunction collapse because probability decisions are made at the particle source, not the detector. It is the only local realistic theory consistent with the Bell test experiments. That which QM calls “nonlocality,” TEW calls “elementary rays.” One term is vague, the other involves elegant mathematics. This article introduces that mathematical notation, explains complementarity in double slit experiments, and reinterprets Feynman diagrams. QM and TEW are partners that need each other. One is a science of observables; the other a science of how nature works independent of the observer.

JOURNAL OF ADVANCES IN MATHEMATICS•Jun 30, 2015•20 citations

A paradigm shift in mathematical physics, Part 2: A new local realism explains Bell test & other experiments

Jeffrey H. Boyd

An earlier article in this journal introduced a renegade theory called the Theory of Elementary Waves (TEW). Whereas quantum mathematics (QM) is a science of observables, TEW is a science of physical nature independent of the observer. They are symmetrical: complement and support each other. That article left three dangling threads that this article addresses: 1. Our claim that TEW is the only local realistic theory that can explain Bell test experiments, 2. Focusing on the medium in which elementary waves move, and 3. Demonstrating that there is zero experimental support wave particle duality. TEW is neither the hidden variable theory of Einstein, Podolsky and Rosen (EPR), nor the absorber theory of Wheeler and Feynman, nor an offshoot nor variant of quantum theory. It is a new paradigm, discovered by a dissident, Lewis E. Little who, after his PhD in physics, worked alone for decades outside the ivory tower of academic physics searching for and eventually finding a theory that explains quantum experiments based on local realism. The fate of new paradigms, unfortunately, is to be rejected as gibberish by leaders of the old paradigm. Plate tectonics was dismissed as absurd during the twentieth century.

JOURNAL OF ADVANCES IN MATHEMATICS•Jul 17, 2015•15 citations

The Boyd Conjecture

Jeffrey H. Boyd

The Boyd Conjecture is that the amplitude of an elementary ray from the Theory of Elementary Waves (TEW) is the physical analog of a probability amplitude from Quantum Mechanics (QM). Boyd learned TEW from his cousin Lewis E. Little, who had said that quantum math is the roadmap to the world of elementary waves, but we did not know how to read the map. He suggested that Boyd, with a degree in mathematics, should work on deciphering the map. In 2014 Boyd began thinking that amplitudes are the core of QM, and elementary rays the core of TEW: perhaps they were equivalent. Both decisively influence particle behavior without conveying any energy. This essay discusses the history, strengths, weakness and implications of this conjecture.

JOURNAL OF ADVANCES IN PHYSICS•Apr 21, 2017•16 citations

There are two solutions to the equations of Feynman’s Quantum Electrodynamics (QED): the newly discovered solution is free of quantum weirdness

Jeffrey H. Boyd

No one previously noticed there is a second solution to the equations of Richard Feynman’s Quantum Electrodynamics (QED). It makes identical predictions in the lab. The new solution (Reverse-QED) is closer to nature: it is free of quantum weirdness. For example, it eliminates Schrödinger’s cat. This article is the first time the equations of R-QED have been published. The R-QED amplitude is the negative of Feynman’s amplitude. Because of the Born rule, both amplitude and negative amplitude, when squared, produce the same probability to be tested against empirical data. If you were to measure the distance from Los Angeles to New York City with R-QED’s accuracy, it would be exact to the breadth of a human hair. If reality corresponds to the newly discovered R-QED equations, but scientists use the old QED equations, the result would be predictions for the lab that are precisely accurate, but scientists would be unable to construct a coherent picture of the quantum world. R-QED is based on a different picture of how the quantum world is organized. Experiments, including a neutron interferometer experiment we review, show that particles follow waves backward. R-QED integrates in the same direction that the waves travel.

JOURNAL OF ADVANCES IN PHYSICS•Aug 17, 2020•7 citations

A proposed physical analog of a quantum amplitude: Corkscrew model from the Theory of Elementary Waves (TEW)

Jeffrey H. Boyd

This article proposes solutions to two riddles of quantum mechanics (QM): (1) What is the physical analog of aquantum amplitude?, (2) Why do electrons in a double slit experiment act differently if we look at them? The Theory of Elementary Waves (TEW) is an unconventional view of how nature is organized. Elementary ray amplitudes precede and travel in the opposite direction as particles, which then follow these amplitudes backwards. The amplitude A = |A| ei? is a vector in Hilbert space, but it moves through Euclidean space. This makes explicit something implicit in Feynman’s thinking, although Feynman had the amplitudes traveling in the wrong direction. In double slit experiments, the amplitude of elementary rays going though the two slits interfere before they reach the electron gun. Any experiment that detects which slit the electron uses, destroys the coherence of those two rays, destroying the interference. Because there is no interference, the target screen displays no interference fringe pattern. TEW represents a paradigm shift of seismic proportions, in both classical and quantum physics. Thomas Kuhn warns that paradigm shifts of this magnitude are usually rejected as preposterous. That is exactly what happened to Alfred Wegener’s idea of “continental drift.”

JOURNAL OF ADVANCES IN PHYSICS•Sep 1, 2015•15 citations

Paul Diracs view of the Theory of Elementary Waves

Jeffrey H. Boyd

Is science open to a new idea? Thomas Kuhn says paradigm shifts sound like gibberish to scientific leaders, and are rejected for that reason. The Theory of Elementary Waves (TEW) is such an idea: quantum particles follow waves moving in the opposite direction. Time always goes forwards. We focus on Paul Diracs 1930 book The Principles of Quantum Mechanics, applied to TEW. We keep Dirac notation and quantum math but replace the picture of how nature is organized. Wave interference and probabilistic effects occur prior to particle emission. Wave function collapse occurs at emission & there is no further interference. We have launched a successful program of teaching this form of physics in the format of YouTube music videos of five minutes duration. Some of our videos have been watched 40,000 times: within YouTube search for Jeffrey H Boyd to watch these amusing videos including one in which Yoda (from Star Wars) solves what Richard Feynman called the Fundamental Mystery of Quantum Mechanics.

JOURNAL OF ADVANCES IN PHYSICS•Mar 29, 2017•17 citations
Richard Feynmans book QED, written for a lay audience, is a trusted source of information about Quantum Electro-Dynamics by a Nobel laureate. It is a mirror image of the Theory of Elementary Waves (TEW), discovered by Lewis E. Little. Recent work on TEW, published in this journal, shows that an elementary ray has the shape of a cylindrical helix traveling in Euclidean space, with a complex amplitude. This is an analog in physical nature of Feynmans mathematical concept of an amplitude, which is the core of QED. The only substantial difference is that an amplitude is assumed by Feynman to travel in the same direction as the particle, but in TEW they travel in opposite directions. There is almost no empirical data to resolve that disagreement. Such evidence as exists favors the idea they travel in opposite directions. If we modify Feynmans QED in this way we end up with a theory symmetrical to QED. We nickname it QÆD, using the letter Æ to symbolize an ælementary ray. QÆD is a fountain of information about the nature of elementary rays, and resolves some of the problems that Feynman said he found in QED.
Why is quantum mathematics (QM) the only science based on probability amplitudes rather than probabilities? A paradigm shift called the Theory of Elementary Waves (TEW) posits zero energy waves traveling in the opposite direction as particles, which a particle follows backwards: like a probabilistic guidance system emanating from detectors. Probability amplitudes are the mathematical analog of these elementary rays. Although this proposal might sound like gibberish, that is the hallmark of a paradigm shift. Thomas Kuhn warns that previous paradigm shifts were rejected because they sounded like gibberish. TEW is internally coherent, explains a mountain of empirical data, and resolves insoluble problems of QM. For example, it dispenses with the need for wavefunction collapse because probability decisions are made at the particle source, not the detector. It is the only local realistic theory consistent with the Bell test experiments. That which QM calls “nonlocality,” TEW calls “elementary rays.” One term is vague, the other involves elegant mathematics. This article introduces that mathematical notation, explains complementarity in double slit experiments, and reinterprets Feynman diagrams. QM and TEW are partners that need each other. One is a science of observables; the other a science of how nature works independent of the observer.
An earlier article in this journal introduced a renegade theory called the Theory of Elementary Waves (TEW). Whereas quantum mathematics (QM) is a science of observables, TEW is a science of physical nature independent of the observer. They are symmetrical: complement and support each other. That article left three dangling threads that this article addresses: 1. Our claim that TEW is the only local realistic theory that can explain Bell test experiments, 2. Focusing on the medium in which elementary waves move, and 3. Demonstrating that there is zero experimental support wave particle duality. TEW is neither the hidden variable theory of Einstein, Podolsky and Rosen (EPR), nor the absorber theory of Wheeler and Feynman, nor an offshoot nor variant of quantum theory. It is a new paradigm, discovered by a dissident, Lewis E. Little who, after his PhD in physics, worked alone for decades outside the ivory tower of academic physics searching for and eventually finding a theory that explains quantum experiments based on local realism. The fate of new paradigms, unfortunately, is to be rejected as gibberish by leaders of the old paradigm. Plate tectonics was dismissed as absurd during the twentieth century.
The Boyd Conjecture is that the amplitude of an elementary ray from the Theory of Elementary Waves (TEW) is the physical analog of a probability amplitude from Quantum Mechanics (QM). Boyd learned TEW from his cousin Lewis E. Little, who had said that quantum math is the roadmap to the world of elementary waves, but we did not know how to read the map. He suggested that Boyd, with a degree in mathematics, should work on deciphering the map. In 2014 Boyd began thinking that amplitudes are the core of QM, and elementary rays the core of TEW: perhaps they were equivalent. Both decisively influence particle behavior without conveying any energy. This essay discusses the history, strengths, weakness and implications of this conjecture.
No one previously noticed there is a second solution to the equations of Richard Feynman’s Quantum Electrodynamics (QED). It makes identical predictions in the lab. The new solution (Reverse-QED) is closer to nature: it is free of quantum weirdness. For example, it eliminates Schrödinger’s cat. This article is the first time the equations of R-QED have been published. The R-QED amplitude is the negative of Feynman’s amplitude. Because of the Born rule, both amplitude and negative amplitude, when squared, produce the same probability to be tested against empirical data. If you were to measure the distance from Los Angeles to New York City with R-QED’s accuracy, it would be exact to the breadth of a human hair. If reality corresponds to the newly discovered R-QED equations, but scientists use the old QED equations, the result would be predictions for the lab that are precisely accurate, but scientists would be unable to construct a coherent picture of the quantum world. R-QED is based on a different picture of how the quantum world is organized. Experiments, including a neutron interferometer experiment we review, show that particles follow waves backward. R-QED integrates in the same direction that the waves travel.
This article proposes solutions to two riddles of quantum mechanics (QM): (1) What is the physical analog of aquantum amplitude?, (2) Why do electrons in a double slit experiment act differently if we look at them? The Theory of Elementary Waves (TEW) is an unconventional view of how nature is organized. Elementary ray amplitudes precede and travel in the opposite direction as particles, which then follow these amplitudes backwards. The amplitude A = |A| ei? is a vector in Hilbert space, but it moves through Euclidean space. This makes explicit something implicit in Feynman’s thinking, although Feynman had the amplitudes traveling in the wrong direction. In double slit experiments, the amplitude of elementary rays going though the two slits interfere before they reach the electron gun. Any experiment that detects which slit the electron uses, destroys the coherence of those two rays, destroying the interference. Because there is no interference, the target screen displays no interference fringe pattern. TEW represents a paradigm shift of seismic proportions, in both classical and quantum physics. Thomas Kuhn warns that paradigm shifts of this magnitude are usually rejected as preposterous. That is exactly what happened to Alfred Wegener’s idea of “continental drift.”
Is science open to a new idea? Thomas Kuhn says paradigm shifts sound like gibberish to scientific leaders, and are rejected for that reason. The Theory of Elementary Waves (TEW) is such an idea: quantum particles follow waves moving in the opposite direction. Time always goes forwards. We focus on Paul Diracs 1930 book The Principles of Quantum Mechanics, applied to TEW. We keep Dirac notation and quantum math but replace the picture of how nature is organized. Wave interference and probabilistic effects occur prior to particle emission. Wave function collapse occurs at emission & there is no further interference. We have launched a successful program of teaching this form of physics in the format of YouTube music videos of five minutes duration. Some of our videos have been watched 40,000 times: within YouTube search for Jeffrey H Boyd to watch these amusing videos including one in which Yoda (from Star Wars) solves what Richard Feynman called the Fundamental Mystery of Quantum Mechanics.