Relativity of Steady Energy Flow

If a continuous medium has a internal stress, either compressive or tensile, it has an internal density of mass/energy larger than that of the same medium when unstressed. If this medium is in motion, the moving density of stress-induced mass/energy constitutes an apparent flow of energy that is consistent with the F·v power associated with the internal forces whose points of application are moving. In systems involving steady motion, this flow of energy is only apparent to observers for which a stressed part of the system is in motion. In a system with stressed parts that have motion relative to each other, observers identify a flow of energy only in those parts that are in motion relative to the observer. Hence, different observers can have different views as to the path of the steady flow of energy in the system. This contrasts with the case of pulsed energy flow, in which all observers could identify the position of a localized disturbance, and would associate energy transport with that pulse. The relativity of steady energy flow is a theme of prob. 65 of [1], in which one part of the system is a moving elastic belt. The technical complexity of belt drives, in which necessary slippage at the drive pulleys [2, 3] tends to excite stress waves [4, 5], perhaps obscures the relativity of energy flow in this example [6]. For a possibly simpler example in which the relativity of steady energy flow can be discussed from both macroscopic and microscopic points of view, consider a 1-dimensional ideal gas consists of n point molecules of mass m that are confined within a region of length L. The temperature T can be modeled by supposing that all molecules have the same speed v = kT/m, where k is Boltzmann’s constant. If the confining walls/pistons are fixed, the gas exerts a pressure ( = force F for the 1-dimensional case) given by F = nk