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JOURNAL OF ADVANCES IN MATHEMATICS

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

Jeffrey H. Boyd

Published Jun 30, 2015• 20 citations
Publisher

Abstract

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.

DOI
10.24297/jam.v10i9.1908

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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.
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.”
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.
This article proposes a solution to the double slit experiment of Quantum Mechanics. We attack the problem from a previously untried angle. Unsolved math problems must be attacked from unexpected angles because every conventional approach has already been tried and failed. Richard Feynman warned that the quantum world is such a strange place that humans can’t understand it. There is empirical evidence of particles following zero energy waves backwards, although that is counterintuitive. Schr˝odinger waves carry zero energy: they carry probability amplitudes instead. In our proposed model zero energy Schr˝odinger waves emanating from every point on the target screen pass backwards through the two slits, interfere at the particle gun, and a particle randomly chooses which wave to follow backwards. Once that decision is made the particle follows its wave with a probability of one, through only one slit (it doesn’t matter which slit) and inevitably strikes that point from which its wave emanates. This produces the same math and same pattern on the target screen. We propose three Axioms of the Theory of Elementary Waves (TEW) as a better platform for mathematics in this experiment than the Axioms of QM. This constitutes a paradigm shift.
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.
Every discussion of quantum computing starts with wave-particle duality, to explain how qubits differ from bits. But what if wave-particle duality were wrong? How would we explain quantum computing then? A little-known science called the Theory of Elementary Waves (TEW) says that quantum particles follow zero-energy waves backwards. Wave-particle duality cannot be true if waves and particles travel in opposite directions. This article proposes the first-ever TEW theory of quantum circuits. Elementary waves emanate from measuring devices and travel backwards through the circuits, whereas qubits move forwards through the wires and gates following those waves backwards. Quantum computers are known to be reversible. After we present that way-of-thinking, we will explain some of the evidence that TEW is valid. There is a mountain of empirical evidence from outside information technology. TEW is a maverick theory, out-of-step with the consensus about how quantum computers work. At first TEW sounds counterintuitive. Its advantage is Occam’s Razor: we present a simpler explanation of quantum circuits. We will present the quantum computer equivalent of saying that before the box is open Schrödinger’s cat is already dead or alive, but not both. Observing the cat simply tells us what was already true before we looked.