Temperature and special relativity

[Marthius]

I was wondering about the relation of relativity to temperature of a body. Temperature is the measure of the average velocity of the particles in a system, which is D/T. So here is my question, as one is to approach the speed of light relative to some given object, wouldn’t that object move tangentially towards absolute zero. The only reason I ask is because I have heard about some of the strange properties of matter that may arise at these temperatures, and I was wondering how the problem resolves itself.

 

[gendou2]

Let's start with a hot object, a star.
You are in a spaceship traveling past the star at near light speed.
The star light will be blue-shifted as you approach and red-shifted as you recede.
One way to measure heat coming off an object is by measuring the light it emits.
Since the starlight coming from a different reference frame has been doppler shifted, we measure the emitting body as having a different temperature then we would if it were in our reference frame.

Now, we measured the temperature, but we also know how fast we're moving, so we can calculate the correct temperature! So, the behavior of the star is not changing due to our fly by. Thank goodness.

 

[Crosson]

I don't remember the details, but I am pretty sure that Gravitation by Misner, Thorne, and Wheeler have a chapter on temperature in relativistic fluids, something like chapter 28.

Sorry if I am wrong about this reference, but I do remember thinking about relativistic temperature in a cosmology course and finding a reference that satisfied my questions.

 

[shadowpuppet]

I was wondering about the relation of relativity to temperature of a body. Temperature is the measure of the average velocity of the particles in a system, which is D/T. So here is my question, as one is to approach the speed of light relative to some given object, wouldn’t that object move tangentially towards absolute zero. The only reason I ask is because I have heard about some of the strange properties of matter that may arise at these temperatures, and I was wondering how the problem resolves itself.

The electromagnetic interaction would cease because light could not catch up to it, so it may act adiabatically with regard to the stationary universe, but according to the Unruh Effect the system would seem to you to actually be much hotter than it really is (due to interaction with the vacuum; to avoid reinventing the luminiferous æther, it is interesting to speculate that if the vacuum corresponds to space-time it can be dragged as occurs in the Lense-Thirring effect)...this assertion is founded in the quantum mechanics of relativistic observers in different frames of reference.

 

[Marthius]

Let's start with a hot object, a star.
You are in a spaceship traveling past the star at near light speed.
The star light will be blue-shifted as you approach and red-shifted as you recede.
One way to measure heat coming off an object is by measuring the light it emits.
Since the starlight coming from a different reference frame has been doppler shifted, we measure the emitting body as having a different temperature then we would if it were in our reference frame.

Now, we measured the temperature, but we also know how fast we're moving, so we can calculate the correct temperature! So, the behavior of the star is not changing due to our fly by. Thank goodness.

So then if i understand you correctly, even though the object will apear to be cooler, it will not exibit the properties of a cooler object because we can still calculate its proper temperature in its own refrence frame?

 

[maverick_starstrider]

The temperature is a function of the average kinetic energy (among other things). Within a system one will have equipartition of vector directions. So if the box is traveling in the x direction, not only will the y and z components be uneffected but at any given moment would not a given particle have an equal probability of going in either the + or - x direction and thus any relativistic shift would come out in the 'wash'?

 

[gendou2]

So then if i understand you correctly, even though the object will apear to be cooler, it will not exibit the properties of a cooler object because we can still calculate its proper temperature in its own refrence frame?

That sums up my understanding quite well.
Here's another way of thinking about it: There is no preferred reference frame.
The laws of nature are the same in all reference frames.
So, an object moving fast relative to you is actually sitting still, in it's own reference frame.
You might say it doesn't "know" that it's "moving fast".

Now, acceleration on the other hand, will certainly have thermal effects.
That would be a neat topic to learn about.