Mechanics is generally considered to be the mother of all physics. Louis de Broglie showed us an alternate path in his Nobel Prize Lecture, but few of us have been listening. De Broglie is known for the relationship between momentum and wavelength in elementary texts, but the reasoning which leads to this relationship is rarely discussed. This reasoning is based on an elegant and subtle application of the principle of relativity which is nevertheless accessible even to beginning physics students. The course begins with optics and waves where key ideas about diffraction, interference, dispersion relations, phase and group velocity, and geometrical optics are introduced.
Relativistic kinematics is covered next.
De Broglie's argument is then invoked to obtain the dispersion relation for the free relativistic matter wave. Elementary quantum mechanics follows. Asking how one can introduce interactions between particles leads to the idea of potential energy. From here it is a short jump to gauge theory, the elementary consequences of which are developed using analogs of Snell's law. Electromagnetism falls out of this discussion in a natural way, as does a qualitative but nontrivial discussion of the Standard Model.