# Relativistic thermodynamics problem

1. Jun 29, 2007

### bernhard.rothenstein

Authors (Tolmann, Arzelies) consider that proper temperature T(0) and non-proper one T are related in the I inertial reference frame by
T=T(0)/(1-uu/cc)^1/2 (1) whereas in I' they are related by T'=T(0)/(1-u'u'/cc)^1/2 (2). Expressing the right side of (1) as a function of u' via the addition law of relativistic velocities we obtain
T=T'(1+Vu'/cc)/(1-VxV/cc)^1/2. (3)
Do you see some physics behind (3). Has u'T'/cc a physical meaning eventually via the Boltzmann constant?
Thanks

2. Jun 29, 2007

### pervect

Staff Emeritus
The question of how to treat relativistic thermodynamics comes up from time to time, but usually doesn't get much of an answer. My thinking on the topic is based on the arguments presented in http://arxiv.org/abs/physics/0505004

which argues for inverse temperature as a 4-vector and which I personally find convincing. Unfortunately, I have *not* read all the relevant literature in this field (relativistic thermodynamics) thus it's quite possible that as a result of this I'm missing some of the fine or not-so-fine points.

Here are a couple of quotes from the above paper:

Apparently there has been some amount of controversy in the field, the authors state:

Thus the early papers such as those of Tollman may not be representative of the current thinking.

Unfortunately, it is not particularly clear to me how one could go about demonstrating whether or not the above paper is representative of current thinking either - all I can say is that I find the arguments presented in this paper convincing.

Last edited: Jun 29, 2007