Inertia from radiation. A semiclassical approach

Starting from a thought experiment based on an accelerated reflecting cavity that contains a radiation bath, is evaluated the cavity-radiation dynamical interaction. The radiation is considered as a monochromatic flux of photons that bouncing onward and backward in the direction of acceleration. For this case, in each reflection, the delay originated by the time of flight of photons causes a difference of velocity between the receiving and emitting reflecting faces in the opposite ends of cavity, and consequently, a Doppler shift. Despite to the ends of the cavity are at rest relative to each other, this phenomenon generates a difference of radiation pressure between these, that behave as the inertia of the radiation bath and verifies the Newton’s 2nd Law for non-relativistic conditions. This result has interesting implications on the current theoretical pictures of dynamical properties of photons.