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JOURNAL OF ADVANCES IN MATHEMATICS

If the propagator of QED were reversed, the mathematics of Nature would be much simpler

Jeffrey H. Boyd

Published May 22, 2020• 8 citations
Publisher

Abstract

In Quantum ElectroDynamics (QED) the propagator is a function that describes the probability amplitude of a particle going from point A to B. It summarizes the many paths of Feynman’s path integral approach. We propose a reverse propagator (R-propagator) that, prior to the particle’s emission, summarizes every possible path from B to A. Wave function collapse occurs at point A when the particle randomly chooses one and only one of many incident paths to follow backwards with a probability of one, so it inevitably strikes detector B. The propagator and R-propagator both calculate the same probability amplitude. The R-propagator has an advantage over the propagator because it solves a contradiction inside QED, namely QED says a particle must take EVERY path from A to B. With our model the particle only takes one path. The R-propagator had already taken every path into account. We propose that this tiny, infinitesimal change from propagator to R-propagator would vastly simplify the mathematics of Nature. Many experiments that currently describe the quantum world as weird, change their meaning and no longer say that. The quantum world looks and acts like the classical world of everyday experience.

DOI
10.24297/jam.v18i.8746

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The method of Feynman in evaluationg the particle propagator is reviewed. According to Feynman's ideas, apart from classical path, there are many possible paths of a partlcle to go from polnt a to point b in a given time interval. The propagator is the summation of the probability amplitude of all possible paths. By replacing the summation with integration the calculation can be done. Furthermore, lhe obrained propagator also leads ro lhe wave functions and energy of the system.

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In Quantum ElectroDynamics (QED) the propagator is a function that describes the probability amplitude of a particle going from point A to B. It summarizes the many paths of Feynman’s path integral approach. We propose a reverse propagator (R-propagator) that, prior to the particle’s emission, summarizes every possible path from B to A. Wave function collapse occurs at point A when the particle randomly chooses one and only one of many incident paths to follow backwards with a probability of one, so it inevitably strikes detector B. The propagator and R-propagator both calculate the same probability amplitude. The R-propagator has an advantage over the propagator because it solves a contradiction inside QED, namely QED says a particle must take EVERY path from A to B. With our model the particle only takes one path. The R-propagator had already taken every path into account. We propose that this tiny, infinitesimal change from propagator to R-propagator would vastly simplify the mathematics of Nature. Many experiments that currently describe the quantum world as weird, change their meaning and no longer say that. The quantum world looks and acts like the classical world of everyday experience.
This article proposes that an unexpected approach to the mathematics of a Schro ̋dinger wave packet and Quantum Electro-Dynamics (QED), could vastly simplify how we perceive the world around us. It could get rid of most if not all quantum weirdness. Schro ̋dinger’s cat would be gone. Even things that we thought were unquestionably true about the quantum world would change. For example, the double slit experiment would no longer support wave particle duality. Experiments that appeared to say that entangled particles can communicate instantaneously over great distances, would no longer say that. Although the tiny mathematical change is counterintuitive, Occam’s razor dictates that we consider it because it simplifies how we view Nature in such a pervasive way. The change in question is to view a Schro ̋dinger wave packet as part of a larger Elementary Wave traveling in the opposite direction. It is known in quantum mechanics that the same wave can travel in two countervailing directions simultaneously. Equivalent changes would be made to QED and Quantum Field Theory. It is known in QM that there are zero energy waves: for example, the Schro ̋dinger wave carries amplitudes but not energy.
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 is one of a series of articles building a map of elementary waves, based on experimental data and quantum mathematics. Previous articles showed that elementary waves carry no energy. Particles follow them backwards. Why? Elementary rays consist of probability amplitudes, which influence particles because that is what probability amplitudes do. Elementary waves are that part of nature corresponding to quantum mathematics. Since these waves are the physical analogs of quantum equations, those equations provide a roadmap to the world of elementary waves: a map written in hieroglyphs. Quantum math is our Rosetta stone. The quantum world is far, far more similar to the world of everyday experience than quantum experts think. Waves are in a superposition. Particles are not. Wave function collapse does not occur when we measure something. It had occurred much earlier, when the object came into existence. This resolves insoluble problems that stumped John von Neumann. The smooth functioning of a Schrödinger equation abruptly collapses into one specific eigenstate when a gun is fired, not when the bullet hits the target. The bullet that caused World War I is an example. That bullet caused an abrupt collapse of the smooth probabilities of commerce and diplomacy.
The quantum world is allegedly strange. But is it? What if there’s a simple mathematical explanation, and a simple solution? The success of quantum mechanics (QM) arises from the accuracy of its probability predictions, which are obtained by squaring amplitudes (the Born rule). Suppose for a moment that nature uses the negative of QM’s equations. When squared they would yield the same probabilities, confirmed by the same experiments and technological triumphs. If that were true, if nature uses the negative of QM’s equations, then the quantum world would become transparent, easy to understand. No more Schrödinger’s-cat. No quantum-eraser. No backwards-in-time cause-and-effect. No paradoxes nor enigmas. But, what’s a negative quantum equation? It could mean that particles follow zero-energy waves backwards, instead of forwards. That’s still an eccentric idea, a residual strangeness. Overall, it’s a bargain. We could swap one odd idea for another, because wave-particle duality is odd. We are accustomed to wave-particle duality. But we’ll show that experiments support the other arrangement: quantum particles follow zero-energy waves backwards. How could that possibly be true? We present substantial experimental evidence, new mathematics, and six dozen colorful illustrations. This is the Theory of Elementary Waves (TEW).
A path , in general, is defined by a determinate trajectory in time, from an initial to a final point. The classical trajectory is only one of the possible trajectories, and in quantum mechanics all the possible paths between the initial and final point come into play. Recall that the probability amplitude is a complex number that is assigned to each determinate path. Indeterminate paths are defined as a collection of determinate paths that are experimentally indistinguishable . In the Dirac–Feynman approach, the inherent indeterminacy of the quantum entity is realized by the degree of freedom – in undergoing time evolution – “taking” indeterminate paths [Baaquie (2013e)]. For a quantum degree of freedom evolving from an observed initial state to the observed final state – and with no other observations made – the Feynman path integral is a mathematical construction that computes the probability amplitudes by summing over all the allowed determinate paths of the degree of freedom – discussed in Feynman and Hibbs (1965), Zinn-Justin (1993), Zinn-Justin (2005) and Baaquie (2013e). Probability amplitude and time evolution Recall that the description of a quantum system, at a particular instant,isgiven by its state vector, namely |ψ>. To avoid confusion with the concept of a state vector, the term probability amplitude is used for describing a quantum entity undergoing transitions in time.