Revision of the relativistic dynamics with variable rest mass and application to relativistic thermodynamics

Abstract

For point bodies with variable rest mass it is shown that the definition of forcem0dUi/dτ=Fi is better than the usual d(m0Ui))/dτ=Fi and the explicit equation of motion is given bym0dUi/dτ=Fiext+(z−1UiB−Ui)dm0/dτ, where the external forceFiext has been separated from the reaction force due to the ejected mass,UiB is the four-velocity of the mass centre of the ejected mass andz=UsBU2c−2. For extended bodies it is shown that the von Laue mechanical-energy flux (in the usual «synchronous» formulation) is not plausible. Moreover a new formulation, called «asynchronous» is given. By this formulation many problems receive an immediate solution. The resultant «asynchronous» force density is always orthogonal to the four-velocity, and the equations of motion for continuous media turn out to be formally equal to the classical equations. Expanding the new equations to the first order when the pressure is a regular function of space and time, one obtains the usual «synchronous» equations. In the asynchronous formulation, all quantities relevant to extended bodies transform in a covariant way. In particular, momentum and energy turn out to have the expression proposed by Rohrlich. The above concepts are applied to relativistic thermodynamics. It is shown that, for point bodies, heat transforms as in the recent Ott formulation. For extended bodies, in the usual «synchronous» formulation, heat transforms as pointed out by von Laue. In the «asynchronous» formulation we always haveQ=γQ0. TemperatureT is considered invariant and the relation dQ=TdS valid in the rest system only.