How Does Relativity Affect Energy Distribution in a Moving Rod?

[pmb]

Something just occurred 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

 

[AndyW]

, that is a very interesting observation. You are correct in your thinking that the energy distribution of the rod will not be uniform in frame S'. This is due to the fact that as the rod moves in the x-direction, it experiences a Lorentz contraction, which causes the density of the rod to increase. This means that the energy per unit length will also increase, resulting in a non-uniform energy distribution.

In addition, as you mentioned, the Lorentz transformations do not preserve simultaneity, which means that the energy content of the rod will not be the same at different points in time in frame S'. This is due to the fact that events that are simultaneous in one frame may not be simultaneous in another frame.

However, as you also noted, there will always be a well-defined rest energy E_o of the rod in frame S. This is because in the rest frame of the rod, there is no relative motion and therefore no Lorentz contraction or time dilation effects.

Overall, your observation highlights the importance of considering the effects of relativity in different frames of reference when studying physical phenomena. Thank you for sharing your thoughts on this topic.