does the temperature of a body depend upon the frame of reference from which it is observed?
I believe it does... Remember the red (or blue-) shift...
I think not at all. From Earth, you can see the Sun and the Moon at appr. 0.5 degree in visual angle, but they are very different in size. The red/blue shift is just the same.
But that's a special case of two very close objects. In the general, universal, case, the shift has to be taken into account.
Astronomers have measured temperature of lots of stars far away no matter they move away or towards us. So the idea: temperature is changing because of moving frame has no meaning.
That's a very interesting perspective. How exactly did you think they are the same?
I said appr. the same. The sources are every where. You can even check yourself. What is you idea behind that?
Yes they are, because the relative motion of the sun and moon is quite small relativistically. You're the one who brought up a bad example, so don't try to discredit the reasoning of others based on your poor judgement.
In the general case, given an object at an indeterminate distance of the observer, there is absolutely no way for the observer to ascertain the temperature of the object. He may measure a given radiation distribution, but -in the absence of a way to determine its relative velocity- he can't know the temperature.
Ohh, it's a misunderstanding. I did not mean the red/blue shift of the sun or the moon, but the apparent sizes of them are the same while they are very much different. The redshift is just some thing related to apparentness.
I don't know the answer to the OP's question, but if you are talking about observing the temperature of relativistically moving objects it would seem that you are probably talking about the question of how does the spectrum of a relativistically moving blackbody look. Clearly you have doppler redshift or blueshift on top of a time-dilation redshift, but is a blackbody spectrum at one temperature the same as a redshifted or blueshifted spectrum at another temperature?
I would say no, by definition. Temperature is a measure of the average KE of the molecules in a frame in which the momentum is zero. Otherwise, temperature would be frame dependent.
But the apparent frequency of any emitted radiation would of course be frame dependent.
Astronomers first identify the fingerprint spectral lines, which tell how much the star is redshifted. They can then artificially "undo" the redshift and fit a black body curve to the modified spectrum (deducing the rest frame temperature).
If they fitted the black body curve without accounting for redshift, they would get a different temperature. It's wrong to say this different temperature has no physical meaning, since, for example, basically it would be the temperature of a local system instantaneously in thermal equilibrium to the receding heat bath.
Look, I agree with your conclusion (much like Doc Al has now written, the classical concept of temperature as the variance in velocity and as a state variable suggests observer independence), just don't follow your reasoning.
I'm firmly with DocAl on this. The temperature is an internal measurement based upon molecular motion. To an outside observer (different frame), the only clue as to that temperature might be blue/red/neutral shifted according to the relative motion of the frames. If one knows the relative motion of those frames, then the temperature of one might be calculated from the other.
so the conclusion is that temp is independent of frame of reference?
There is an article in J Fluid Mech(1983), 136, pp 423-433 discussing the frame independence of temperature. This is the stuff that made poor Ludwig tie the knot.
Separate names with a comma.