Reply to ‘Comment on “ ‘Relativistic’ particle dynamics without relativity” ’ [Am. J. Phys. 87, 144–145 (2019)] Available to Purchase

I respond here to a recent comment¹ by Di Matteo regarding my paper “‘Relativistic’ particle dynamics without relativity.”² In that paper, I begin by recounting a 1906 thought experiment by which Einstein³ demonstrated, completely independently of the relativity postulates, that the transport of energy E must be accompanied by an increment of mass δm = E/c². With that result, by means of the same thought experiment using a material particle instead of a pulse of light, I demonstrate that the momentum of a particle with mass m (measured at rest), velocity v, and kinetic energy K must be given by p = (m + K/c²) v. From there, it is easy to derive the usual high-speed (“relativistic”) expressions p = mγv and K = m(γ − 1)c², with γ being the familiar Lorentz factor (1 − v²/c²)...