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

Decrypting the Central Mystery of Quantum Mathematics:

Jeffrey H. Boyd

Published Nov 9, 2019• 11 citations
Publisher

Abstract

The fact that loophole-free Bell test experiments have proved Einstein’s local realism wrong, does not prove that the quantum mechanical (QM) model is correct, because the Theory of Elementary Waves (TEW) Axioms can also explain the Bell test experiments. Bi-Rays are a pair of coaxial elementary rays traveling at the speed of light in countervailing directions. In a Bell test experiment a Bi-Ray stretches from Alice’s equipment, through the fiberoptic cable, across the 2-photon source, through more fiberoptic cable, to Bob’s equipment. A pair of entangled photons is born into that Bi-Ray. Each photon follows the same Bi-Ray in opposite directions. This model produces the same Bell test results found by QM. According to QM this would be classified as a “non-local” model, so it is no surprise that it can explain the Bell test results. But it is a different model than QM. TEW supports a more realistic view of Nature, based on better Axioms. Although QM can explain quantum experiments, it requires that you believe the quantum world is weird. TEW Axioms explain the quantum world in a way that is more intuitively similar to the world of everyday experience.

DOI
10.24297/jam.v17i0.8490

Related papers

Decrypting the Central Mystery of Quantum Mathematics:

Jeffrey H. Boyd

The Theory of Elementary Waves (TEW) is based on three new Axioms that lead to a different understanding of quantum mathematics. There is a massive amount of research data that supports TEW. This article will take six well established experiments from mainstream scientific journals and re-interpret their axioms from a TEW point of view. Although it is usually asserted that QM explains all existing quantum experiments, that is only true if you can convince yourself that the quantum world is weird. If you adopt TEW axioms, suddenly the quantum world transforms itself into looking ordinary, like everyday Nature. If, for example, time only goes forwards, never backwards; if there is no such thing as a quantum eraser; if nothing is transmitted faster than the speed of light, then TEW axioms allow you to make sense of a quantum world which QM can only explain if you allow for weirdness throughout Nature. TEW consists of axioms that allow us to understand the quantum world in a way that makes sense from the viewpoint of our everyday experience.

JOURNAL OF ADVANCES IN MATHEMATICS•Nov 9, 2019•11 citations

A new variety of local realism explains a Bell test experiment: the Theory of Elementary Waves (TEW) with no hidden variables

Jeffrey H. Boyd

In a recent article on the Theory of Elementary Waves (TEW) (see TEW eliminates Wave Particle Duality in JAP, February 2015), the most controversial aspect was the claim that TEW provides a local realistic explanation of the Alain Aspect 1982 experiment. That claim was not proved. This article fills in that gap by providing a local realistic explanation of a Bell test experiment published in 1998 by Weihs, Jennewein, Simon, et al. Advanced TEW uses no hidden variables, and therefore does not fall under the jurisdiction of Bells theorem. It rejects wave particle duality. It violates the Bell inequalities, yet is local and realistic. Particles follow a bi-ray, which is composed of two elementary rays, traveling at the speed of light in opposite directions, coaxially, conveying no energy. As was the case with the previous article, the main obstacle to credibility is that these assumptions sound incredible. It is wise sometimes to tolerate ridiculous ideas, lest we fail to recognize a paradigm shift when one comes along. Another obstacle to credibility is the multitude of unanswered questions. A truly fruitful theory raises more questions than it answers, by a ratio of 100 to 1. TEW fulfills that definition of fruitfulness.

JOURNAL OF ADVANCES IN PHYSICS•Mar 9, 2015•22 citations

A paradigm shift in mathematical physics, Part 4: Quantum computers and the local realism of all 4 Bell states

Jeffrey H. Boyd

Can quantum information systems be understood using local realism? The consensus is No. Quantum information is based on qubits and Bell states. According to conventional wisdom these cannot be understood using local realism. Invariably local realism is assumed, incorrectly, to refer only to the Einstein, Podolsky and Rosen (EPR) model. Today a radically different model of local realism has arisen. The Theory of Elementary Waves (TEW) is incompatible with Einsteins picture of reality but nevertheless is local and realistic. We show that the Bell test experiments that invalidate EPR, validate TEW! This article uses TEW to reproduce all four Bell states. From TEW we derive the Bell states. We also show that TEW can explain an experiment using remote entangled photons that have no shared history, which are entangled because ofentanglement swapping. The implications of our study for quantum information theory are unclear, except that the term nonlocal should be replaced with a more precise and fruitful term. Nonlocal is vague and misleading. Elementary ray is a verifiable and precisely defined term that can replace it. This paradigm shift could inspire a new generation of quantum information experiments.

JOURNAL OF ADVANCES IN MATHEMATICS•Nov 20, 2015•15 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 Theory of Elementary Waves (TEW) eliminates Wave Particle Duality

Jeffrey H. Boyd

Wave particle duality is a mistake. Another option was neither conceived nor debated, which is a better foundation for quantum mechanics. The Theory of Elementary Waves (TEW) is based on the idea that particles follow zero energy waves backwards. A particle cannot be identical with its wave if they travel in opposite directions. TEW is the only form of local realism that is consistent with the results of the experiment by Aspect, Dalibard and Roger (1982). Here we show that 1. although QM teaches that complementarity in a double slit experiment cannot be logically explained, TEW explains it logically, without wave function collapse, and 2. gives an unconventional explanation of the Davisson Germer experiment. 3. There is empirical evidence for countervailing waves and particles and 4. zero energy waves. 5. TEW clarifies our understanding of probability amplitudes and supports quantum math. 6. There is an untested experiment for which TEW and wave particle duality predict different outcomes. If TEW is valid, then wave particle duality is not necessary for quantum math, which is the most accurate and productive science ever. With a more solid foundation, new vistas of science open, such as the study of elementary waves.

JOURNAL OF ADVANCES IN PHYSICS•Feb 23, 2015•15 citations

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
The fact that loophole-free Bell test experiments have proved Einstein’s local realism wrong, does not prove that the quantum mechanical (QM) model is correct, because the Theory of Elementary Waves (TEW) Axioms can also explain the Bell test experiments. Bi-Rays are a pair of coaxial elementary rays traveling at the speed of light in countervailing directions. In a Bell test experiment a Bi-Ray stretches from Alice’s equipment, through the fiberoptic cable, across the 2-photon source, through more fiberoptic cable, to Bob’s equipment. A pair of entangled photons is born into that Bi-Ray. Each photon follows the same Bi-Ray in opposite directions. This model produces the same Bell test results found by QM. According to QM this would be classified as a “non-local” model, so it is no surprise that it can explain the Bell test results. But it is a different model than QM. TEW supports a more realistic view of Nature, based on better Axioms. Although QM can explain quantum experiments, it requires that you believe the quantum world is weird. TEW Axioms explain the quantum world in a way that is more intuitively similar to the world of everyday experience.
The Theory of Elementary Waves (TEW) is based on three new Axioms that lead to a different understanding of quantum mathematics. There is a massive amount of research data that supports TEW. This article will take six well established experiments from mainstream scientific journals and re-interpret their axioms from a TEW point of view. Although it is usually asserted that QM explains all existing quantum experiments, that is only true if you can convince yourself that the quantum world is weird. If you adopt TEW axioms, suddenly the quantum world transforms itself into looking ordinary, like everyday Nature. If, for example, time only goes forwards, never backwards; if there is no such thing as a quantum eraser; if nothing is transmitted faster than the speed of light, then TEW axioms allow you to make sense of a quantum world which QM can only explain if you allow for weirdness throughout Nature. TEW consists of axioms that allow us to understand the quantum world in a way that makes sense from the viewpoint of our everyday experience.
In a recent article on the Theory of Elementary Waves (TEW) (see TEW eliminates Wave Particle Duality in JAP, February 2015), the most controversial aspect was the claim that TEW provides a local realistic explanation of the Alain Aspect 1982 experiment. That claim was not proved. This article fills in that gap by providing a local realistic explanation of a Bell test experiment published in 1998 by Weihs, Jennewein, Simon, et al. Advanced TEW uses no hidden variables, and therefore does not fall under the jurisdiction of Bells theorem. It rejects wave particle duality. It violates the Bell inequalities, yet is local and realistic. Particles follow a bi-ray, which is composed of two elementary rays, traveling at the speed of light in opposite directions, coaxially, conveying no energy. As was the case with the previous article, the main obstacle to credibility is that these assumptions sound incredible. It is wise sometimes to tolerate ridiculous ideas, lest we fail to recognize a paradigm shift when one comes along. Another obstacle to credibility is the multitude of unanswered questions. A truly fruitful theory raises more questions than it answers, by a ratio of 100 to 1. TEW fulfills that definition of fruitfulness.
Can quantum information systems be understood using local realism? The consensus is No. Quantum information is based on qubits and Bell states. According to conventional wisdom these cannot be understood using local realism. Invariably local realism is assumed, incorrectly, to refer only to the Einstein, Podolsky and Rosen (EPR) model. Today a radically different model of local realism has arisen. The Theory of Elementary Waves (TEW) is incompatible with Einsteins picture of reality but nevertheless is local and realistic. We show that the Bell test experiments that invalidate EPR, validate TEW! This article uses TEW to reproduce all four Bell states. From TEW we derive the Bell states. We also show that TEW can explain an experiment using remote entangled photons that have no shared history, which are entangled because ofentanglement swapping. The implications of our study for quantum information theory are unclear, except that the term nonlocal should be replaced with a more precise and fruitful term. Nonlocal is vague and misleading. Elementary ray is a verifiable and precisely defined term that can replace it. This paradigm shift could inspire a new generation of quantum information experiments.
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.
Wave particle duality is a mistake. Another option was neither conceived nor debated, which is a better foundation for quantum mechanics. The Theory of Elementary Waves (TEW) is based on the idea that particles follow zero energy waves backwards. A particle cannot be identical with its wave if they travel in opposite directions. TEW is the only form of local realism that is consistent with the results of the experiment by Aspect, Dalibard and Roger (1982). Here we show that 1. although QM teaches that complementarity in a double slit experiment cannot be logically explained, TEW explains it logically, without wave function collapse, and 2. gives an unconventional explanation of the Davisson Germer experiment. 3. There is empirical evidence for countervailing waves and particles and 4. zero energy waves. 5. TEW clarifies our understanding of probability amplitudes and supports quantum math. 6. There is an untested experiment for which TEW and wave particle duality predict different outcomes. If TEW is valid, then wave particle duality is not necessary for quantum math, which is the most accurate and productive science ever. With a more solid foundation, new vistas of science open, such as the study of elementary waves.
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.