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Journal of Physics Conference Series

Quantum particle, light clock or heavy beat box?

Martin B. van der Mark

Published Jun 1, 2019• 2 citations
Publisher

Abstract

Abstract A standing wave of light inside a cavity, while observed from a moving frame, is seen to have a spatial beat of precisely the same nature as that of the de Broglie wave of a quantum particle. The structural forces that hold together the cavity against the internal radiation pressure are compared to the so-called Poincaré stresses inside an elementary particle, as are required for the particle’s stability. This seems to work best if the cavity is non-rigid and hence is itself oscillating, coupled to the radiation inside.

DOI
10.1088/1742-6596/1251/1/012049

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Abstract A standing wave of light inside a cavity, while observed from a moving frame, is seen to have a spatial beat of precisely the same nature as that of the de Broglie wave of a quantum particle. The structural forces that hold together the cavity against the internal radiation pressure are compared to the so-called Poincaré stresses inside an elementary particle, as are required for the particle’s stability. This seems to work best if the cavity is non-rigid and hence is itself oscillating, coupled to the radiation inside.
It is argued that the de Broglie wave is not the wave usually supposed, but the relativistically induced modulation of an underlying carrier wave that moves with the velocity of the particle. In the rest frame of the particle this underlying structure has the form of a standing wave. De Broglie also assumed the existence of this antecedent standing wave, but it would appear that he failed to notice its survival as a carrier wave in the Lorentz transformed wave structure. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, evidencing a more natural unity between matter and radiation than might otherwise be contemplated, and avoiding the necessity of recovering the particle velocity from a superposition of such waves. Because the Schrödinger and other wave equations for massive particles were conceived as equations for the de Broglie wave, this interpretation of the wave is also relevant to such issues in quantum mechanics as the meaning of the wave function, the nature of wave-particle duality, and the possibility of well-defined particle trajectories.
The electromagnetic component waves, comprising together with their generating oscillatory massless charge a material particle, will be Doppler shifted when the charge hence particle is in motion, with a velocity vvv, as a mere mechanical consequence of the source motion. We illustrate here that two such component waves generated in opposite directions and propagating at speed ccc between walls in a one-dimensional box, superpose into a traveling beat wave of wavelength ${\mitΛ}_d$$=(\frac{v}{c}){\mitΛ}$ and phase velocity c2/v+vc^2/v+vc2/v+v which resembles directly L. de Broglie's hypothetic phase wave. This phase wave in terms of transporting the particle mass at the speed vvv and angular frequency ${\mitΩ}_d=2πv /{\mitΛ}_d$, with ${\mitΛ}_d$ and ${\mitΩ}_d$ obeying the de Broglie relations, represents a de Broglie wave. The standing-wave function of the de Broglie (phase) wave and its variables for particle dynamics in small geometries are equivalent to the eigen-state solutions to Schrödinger equation of an identical system.
The analogy between Einstein’s “Aarau Question” of riding on a light-wave and— nevertheless—“seeing” the light-wave running away with velocity “c” and Mugur-Schachter’s proposal to associate with every particle having non-zero proper mass a progressive plane wave moving with invariant velocity “V” with respect to the particle, is shown not to solve any difficulties in fundamental physics. The spinning ring model of charged particles, however, provides an “internal clock” with a frequency independent of the relative motion of possible “observers”.
In his famous doctoral dissertation, de Broglie assumed that a massive particle is surrounded in its rest frame by a standing wave. He argued that as observed from another inertial frame this wave becomes the superluminal wave now known as the de Broglie wave. It is shown here that under a Lorentz transformation, such a standing wave becomes, not the de Broglie wave, but a modulated wave moving at the velocity of the particle. It is the modulation that has the superluminal velocity of the de Broglie wave and should be recognized as the true de Broglie wave. De Broglie's demonstrations relied, variously, on his "theorem of the harmony of phases", on a mechanical model, and on a spacetime diagram. It is shown that in each case the underlying wave was inadvertently suppressed. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, avoiding the awkward device of recovering the particle velocity from a superposition of such waves. The deeper wave structure implied by this de Broglie wave must also impinge on such issues in quantum mechanics as the meaning of the wave function and the nature of wave-particle duality.