# Energy of a moving rod

Something just occured to me. Suppose you have a warm metal rod in deep space. It will begin to cool off. Let the rod be of such a nature that the linear energy density (as well as the temperature) is uniform along the length (this is okay if the radius of the wire is small). Let the rod be at rest in S and lay on the x-axis. Move to frame S' moving relative to S in the x-direction. Then in S' the rod will not have a uniform energy distribution (and it won't have a uniform temperature as well).

What happens is that in S the energy of the rod is uniformly deccreaseing alonmg its length. At t = 0 the left end has the same energy content as the right end. But since Lorentz transformations do not preserve simulataneity the the ends of the rods won't have the same energy content in frame S'. The linear energy density will decrease linearly from one end of the rod to the other. While there is always a well defined rest energy E_o of the rod in S the energy of the rod in S' is not given by

E = gamma*E_o

Pete