Initially a thought in the thesis of young Louis de Broglie in 1923 for his doctorate from the Sorbonne. Attempting to reconcile special relativity with the quantum transformation relation (QTR), de Broglie assumed a hypothetical “phase wave” traveling faster than light that guides the physical displacement of an ► electron (see ► matter waves). In the thesis he derived its putative wavelength in the degenerate case of dipole oscillation, equal to ► Planck's constant divided by the momentum of the linearly oscillating particle; at the same time deriving the action-integral representation of the ► Bohr atom's orbital states by forcing every elliptical orbit to contain an integral number of phase wavelengths, as in Fig. 1.