# Relativity and Temperature

1. Aug 14, 2006

### blumfeld0

As I understand it, temperature is really a measure of the average motion of particles. In SR when an object is going at a speed appreciable to the speed of light it will be time dilated, length contracted etc.
But what if we were to measure its temperature; since it is going a lot faster won't its temperature be much larger (hotter) compared to its rest temperature?
Is there a formula for this?
is it just that T'= Trest*gamma where gamma is just (1-v^2/c^2)^(-1/2)?

thank you

2. Aug 14, 2006

### bernhard.rothenstein

3. Aug 14, 2006

### pervect

Staff Emeritus
You might try looking at http://arxiv.org/abs/physics/0505004

It presents a particular version of relativistic thermo called van-Kampen Israel theory, but it has some links to other papers.

It seems like one of the easier to understand treatments from what I've seen. However, thermodynamics really isn't one of my strong points.

The treatment in this paper winds up with a four-vector to represent "inverse temperature".

Instead of delta-S = Delta-Q / T, one has

delta-S = Energy-momentum-4-vector * inverse-temperature 4-vector

where the product is a "dot" product of two 4-vectors into a scalar.

I can't really comment too much on other versions of relativistic thermodynamics, or their merits and dismerits, or why there is a controversy, unfortunately.

Most textbook treatments I've seen just work the problem in the rest frame of the fluid anyway.

4. Feb 13, 2009

### dbaron13

Wouldn't temperature reflect the blue-shift/red-shift phenomenon? i.e. Appear hotter coming than going? Or shoujld that be vice-versa, hotter going than coming (as heat is an infrared wavelength)...

Last edited: Feb 13, 2009
5. Feb 13, 2009

### AEM

There's a book titled Relativity Thermodynamics and Cosmology by Richard C. Tolman that may be available as a Dover reprint from one of the many used book dealers that are online. It's going to be rather dated --it was originally published in 1934. However, it's got some good basic stuff in it if you're really interested in thermodynamics in both Special and General Relativity.

6. Feb 14, 2009

### Naty1

Blumfeld: good question!!!! I wish I could think of a good answer!!!

I suspect that's a key insight but like other posters my thermodynamics is too limited for me to have an opinion. The question of the link between information entropy and thermodynamic entropy is a hotly debated topic but a first guess is that fast objects are not hotter.

It's interesting to note that an acceleraing frame an observer measures surroundings as HOTTER than a non accelerating observer...this was discussed in another thread here not too long ago.

Wikipedia discusses relativistic heat conduction at :

http://en.wikipedia.org/wiki/Relativistic_heat_conduction

And it appears some refinements of that theory might be required.

Roger Penrose notes in THE ROAD TO REALITY that the refinement of thermodynamics is statistical mechanics so that might be an area for further study in answering the question. And in Chapter 27 he discusses even more fundamental "puzzling issues in thermodynamics".
But not explicitly the relationship to relativity.