Deriving the Relativistic Compton Wavelength Once Again: Correcting the Moving-Electron Derivation and Defending Relativistic Mass

A previous paper argued that the Compton wavelength of a moving particle should be extended by using relativistic mass. We argue that the central result of that paper was correct, but that the derivation used to reach it contained an important error: the moving electron’s relativistic energy was included, while its initial relativistic momentum was omitted. This paper corrects the moving-electron Compton-scattering derivation and shows that the reduced relativistic Compton wavelength, \kambda_C,r= h/mcγ, appears naturally when the full relativistic energy-momentum structure is included. We further defend the use of relativistic mass as a valid and useful concept when applied consistently, and argue that resistance to this concept has likely delayed recognition of the relativistic Compton wavelength. Finally, we discuss the view that the Compton wavelength is the more fundamental matter wavelength, while the de Broglie wavelength is a derivative quantity. In Haug’s Planck-scale framework, the reduced relativistic Compton wavelength is bounded between the reduced rest-mass Compton wavelength and the Planck length, giving it a natural role in quantum-gravity considerations.