Does the inertia of a body depend on its heat content?

Abstract

Einstein's assertion that, based on the relativity principle, inertial mass is to be associated with all forms of energy, was contested by Planck, who showed that a transfer of heat is to be associated with a transfer of inertial mass. The equivalence between mass and energy is interpreted in terms of the equivalence of the rate of heating of a body and the rate of increase of its inertial mass. In an adiabatic process, where the proper mass remains constant, it is the heat content, and not the energy, which is conserved because the pressure, and not the volume, is Lorentz-invariant. There are two categories of relativistic quantities: inertial and thermodynamic, which are transformed into one another by the work necessary to keep the body in motion at a constant velocity. In a non-adiabatic process, the rate of heating is Lorentz-invariant, and it must always be greater than the power that it generates. Therefore, the amount of heat developed in the rest frame has a corresponding inertial mass.