“Reverse Engineering” the de Broglie Wave

Volume 9, Issue 1, pages 44-63

Daniel Shanahan

By subjecting the de Broglie wave to an inverse Lorentz transformation, an attempt is made to return this mysterious wave to a form that is physically viable in the rest frame of the associated particle. The attempt is unsuccessful: it is found that in that frame, the wave becomes an oscillation that varies in time, but not in space, and cannot be identified with the spatially-extended sinusoidal wave that accompanies the moving particle. It is shown that this difficulty is a consequence of the restricted manner in which de Broglie reconciled the phases of particle and wave in his doctoral thesis of 1924. Although he assumed that the particle is surrounded in its rest frame by a spatially extended “periodic phenomenon”, he applied his “theorem of the harmony of phases”, not to that extended waveform, but to a single oscillating point within the waveform. As such a point moves, it does describe a sinusoidally varying phase, but this is the varying phase, not of a wave, but of a moving and oscillating point. Had de Broglie applied his harmonizing of phase to the full underlying waveform, a wave with the characteristics of the de Broglie wave would have emerged, in a physically reasonable manner, as the relativistically induced modulation (a dephasing) of the underlying wave structure. After showing that there is considerable support for this interpretation in de Broglie’s thesis, consideration is given to the implications of such an interpretation for relativity, quantum mechanics and particle structure.

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