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Physics Essays

Special relativity and wave-particle duality

Enrique Cantera del Río

Published Dec 5, 2017• 0 citations
Publisher

Abstract

A SYMMETRY OF LORENTZ TRANSFORMATION IS PROPOSED FOR THE VISUALIZATION OF THE MOST BASIC PHYSICAL LANDSCAPE DERIVED FROM SPECIAL RELATIVITY. ALTHOUGH BASIC ARGUMENTS ,THE SYMMETRY SHOWS A CLOSE RELATIONSHIP WITH WAVE-PARTICLE DUALITY AND THE EXISTENCE OF TWO POSSIBLE STATES FOR THIS PHYSICAL RELATION. THE SPIN AND THE ABRAHAM-MINKOWSKI CONTROVERSY ARE ANALYZED REGARDING THIS IDEAS AND A NEW HYPOTHESIS ON WAVE-PARTICLE DUALITY IS PRESENTED.

DOI
10.4006/0836-1398-30.4.377

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A SYMMETRY OF LORENTZ TRANSFORMATION IS PROPOSED FOR THE VISUALIZATION OF THE MOST BASIC PHYSICAL LANDSCAPE DERIVED FROM SPECIAL RELATIVITY. ALTHOUGH BASIC ARGUMENTS ,THE SYMMETRY SHOWS A CLOSE RELATIONSHIP WITH WAVE-PARTICLE DUALITY AND THE EXISTENCE OF TWO POSSIBLE STATES FOR THIS PHYSICAL RELATION. THE SPIN AND THE ABRAHAM-MINKOWSKI CONTROVERSY ARE ANALYZED REGARDING THIS IDEAS AND A NEW HYPOTHESIS ON WAVE-PARTICLE DUALITY IS PRESENTED.
Abstract: In this paper a one to one correspondence is established between spacetime metrics of general relativity and the wave equations of quantum mechanics. This is done by first taking the square root of the metric associated with a space and from there, passing directly to a corresponding expression in the dual space. It is shown that in the case of a massless particle, Maxwell’s equation for a photon follows while in the case of a particle with mass, Dirac’s equation results as a first approximation. Moreover, this one to one correspondence suggests a natural explanation of wave-particle duality. As a consequence, the distinction between quantum mechanics and classical relativistic mechanics is more clearly understood and the key role of initial conditions is emphasized. PACS NUMBERS: 03.65, 04.60 I
Quantum mechanics is one of basics theories of modern physics, and it is also a theory established with some debates of assumptions. However, in the teaching process, if the assumption of wave-particle duality is directly given, it will be particularly difficult for students to understand. Therefore, based on the teaching practice and previous research, we assume that light corresponds to a kind of real particle starting from the classical electromagnetic theory, according to the description methods of wave optics and geometric optics, and the form of functional equations. Subsequently, employing Planck's quantum conditions, we discuss the connection between the wave nature and particle nature of light. And then the Planck-Einstein relation and the de Broglie relationship are derived, which reflect the wave-particle duality of light and real particle.
How can interfering light waves transport particle characteristics? Up to now it was supposed that wave-particle duality was a quantum mechanical phenomenon which was not accessible to any classical explanation. The present article is disproving this assumption, by showing o n e single case which is entirely subject to a classical explanation: Photons in vacuum. The suggested classical explanation of wave-particle duality is simple, and it is deriving directly from special relativity: The particle characteristics are transported directly from A to B, without any intermediate of spacetime, because the interval is zero. The observed wave is a sort of placeholder in our spacetime.
In Hawking’s view physics has been broken up into many partial theories, while the ultimate goal of physicists is to unify them. The two basic theories of 20th-century physics, relativity theory and quantum theory, are based on completely different logical prerequisites and exactly separate: matter is described as particles in relativity theory and as waves in quantum mechanics. Here, based on the identical logical prerequisites, we unify Einstein’s special relativity (SR) and de Broglie’s matter-wave theory (MWT) into the theory of dualistic relativity (DR), taking a significant step toward the unification of relativity and quantum mechanics. From the definition of time, we derive the Lorentz transformation in differential form and establish the theory of DR, which generalizes the wave-particle duality of matter motion, and uniformly derives Einstein’s formula E=mc2, Planck’s equation E=hf, and de Broglie’s relation λ=h/p. From the logical prerequisite completely different from Einstein’s hypothesis of the invariance of light speed and along the logical path completely different from Einstein’s SR, we have deduced the whole theoretical system of Einstein’s SR and de Broglie’s MWT. In the theory of DR, the two great formulae originally separated, Einstein’s formula E=mc2 and Planck’s equation E=hf, become a pair of twin formulae unified in an identical theoretical system.
Wave-particle duality, the revolutionary concept that particles can exhibit both wave-like and particle-like properties, was first proposed by Louis de Broglie. His equations connecting a particle's energy and momentum to the properties of its corresponding wave laid the groundwork for quantum mechanics. This fundamental principle explains the surprising results of the double-slit experiment and underlies many of quantum mechanics' unique behaviors. In this work, relying solely on Einstein's two postulates of special relativity, and the idea that time is single valued, we will demonstrate that a complete theory of relativity predicts a wave-like quantizable behavior for particle trajectories. We will prove that the theory of relativity predicts a first-order, spin-independent transport equation as an equation of motion for particles, in addition to the classical relativistic Hamiltonian. As key results, we will demonstrate that our theory provides an integrable solution for a free scalar particle, offering insights into the wave-particle duality observed in nature. For spinor particles, we will show that our theory generalizes Weyl theory to accommodate massive particles, while also allowing for modified Dirac-like particles.