  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 Schr\"{o}dinger 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.
