The Double-Slit Paradox
Keywords: Maxwell equations, electron, velocity, oscillations, wave particle, double-slit paradox
Summary: It is shown directly from the Maxwell equations that the velocity of an electron with average v will oscillate about that value, giving rise to a non-radiating electromagnetic wave in the neighborhood of the electron. The oscillations are characterized by the de Broglie relation, which is normally simply postulated. Applying the result, the wave-particle paradox of electron diffraction by a double slit is resolved: the electron goes through only one aperture, but the wave surrounding it is diffracted by both of them. In the neighborhood of the electron the group velocity of the diffracted field is slowed to that of the electron, giving rise to the observed diffraction pattern.