Temperature of fast objects decreases?

[Crazy Tosser]

"If there is an object moving at a relativistic speed relative to us, we perceive time on it as running slower" - That statement is poorly worded because you cannot ever ever measure how fast the object is moving in time!

There is a mathematical axiom that I hope you people won't dispute: Motion in a dimension can only be measured as a ratio to it's motion in another dimension. In this case, motion in time can only be measured as it's ratio to motion in space. We see clocks on the object as running slower, because the actual hands of the clock have smaller speeds. That leads to observing the molecules of the object - as we see them, they also start moving slower, which leads to the conclusion that the overall temperature of the object decreases. That means that as an object's relativistic speed would be approaching that of light, it's temperature (relative to us) would be approaching absolute zero...

 

[atyy]

I think it has more to do with acceleration than relativistic speed. The Rindler observer who is constantly accelerated has a horizon. Padmanabhan has a really nice essay about "what happens if you mix cold and hot tea and pour it down a horizon, erasing all traces of “crime” in increasing the entropy of the world?

Gravity: the inside story
T. Padmanabhan
http://www.springer.com/physics/journal/10714
http://www.springerlink.com/content/l403540q87606463/

 

[Jonathan Scott]

"If there is an object moving at a relativistic speed relative to us, we perceive time on it as running slower" - That statement is poorly worded because you cannot ever ever measure how fast the object is moving in time!

There is a mathematical axiom that I hope you people won't dispute: Motion in a dimension can only be measured as a ratio to it's motion in another dimension. In this case, motion in time can only be measured as it's ratio to motion in space. We see clocks on the object as running slower, because the actual hands of the clock have smaller speeds. That leads to observing the molecules of the object - as we see them, they also start moving slower, which leads to the conclusion that the overall temperature of the object decreases. That means that as an object's relativistic speed would be approaching that of light, it's temperature (relative to us) would be approaching absolute zero...

But we DON'T see the molecules moving slower; we see them moving slower relative to the moving object, but much faster relative to us (when you include the overall motion) so the molecules have much higher kinetic energy relative to us, not lower.

 

[Dale]

But we DON'T see the molecules moving slower; we see them moving slower relative to the moving object, but much faster relative to us (when you include the overall motion) so the molecules have much higher kinetic energy relative to us, not lower.

After accounting for the bulk motion we also see them radiate a red-shifted spectrum. I don't know the answer, but is a red-shifted black body spectrum also a black-body spectrum?

 

[Dale]

Hi Crazy Tosser,

Formulating thermodynamics in a Lorentz-invariant fashion is definitely not easy. I think it is there have been several different attempts, but I don't believe that any have gained universal acceptance. In any case, it requires a solid understanding of the issues and a very careful definition of all terms. For instance:

That leads to observing the molecules of the object - as we see them, they also start moving slower, which leads to the conclusion that the overall temperature of the object decreases.

Here you neglect that the temperature of an ideal gas is related to the average kinetic energy of the molecules, not their velocity. As speed increases the same differential change in speed leads to a greater change in KE, so it doesn't follow immediately that the "random" KE is any different.

I encourage you to continue thinking along these lines, but be careful in defining the terms and issues.

 

[Naty1]

Crazy: great question!

I sure do not have any brilliant insights.

But I'd guess if your hypothesis were correct and well understood it would be standard fare for discussion in relativity...so I doubt the situation is as simple as you posit.

I do accept that kinetic energy is frame dependent and hence each observer measures a different value due to varying observed velocities. Whether this effects temperature? It's also difficult to intuitively see that as space shrinks due to length contraction what the effect is, if any, on temperature...usually compression causes pressure and heat...this is indirectly discussed in another thread where it appeared to me that no energy is expended to cause such lorentz contraction...so I'd guess there is no effect on temperature...

 

[Naty1]

Wikipedia may offer hints to those more well versed than I in thermodynamics:
Under
http://en.wikipedia.org/wiki/Equipartition_theorem,
two subtitles,

Extreme Relativistic Ideal Gases and Stellar Physics may offer some insights...

How does relativity treat density?? (as that helps determines the temperature of a star)

 

[Dale]

The problem with density is that it uses mass which is invariant and volume which is frame-variant due to simultaneity. That problem defining volume is one of the fundamental issues with a Lorentz-invariant formulation of thermodynamics.

 

[Naty1]

( None of this detracts from your posted question which is great; nor do I think these have any direct relevance to your question)

"If there is an object moving at a relativistic speed relative to us, we perceive time on it as running slower" - That statement is poorly worded because you cannot ever ever measure how fast the object is moving in time!

Doesn't seem so "poorly worded" to me...how about relativistic particles whose life is extended due to extended half life decay. We can and have "measured" that...or I can say "an object at rest moves thru time at speed c" and "an object in spatial motion has some of it's velocity diverted from motion time" (which can be calculated).

But it does, I guess, depend on what you mean by "measure".

There is a mathematical axiom that I hope you people won't dispute: Motion in a dimension can only be measured as a ratio to it's motion in another dimension. In this case, motion in time can only be measured as it's ratio to motion in space.

Never heard of such an axiom nor do I believe it yet; so I'll be happy to "dispute" it.

Wiki says:

In mathematics, the dimension of a space is roughly defined as the minimum number of coordinates needed to specify every point within it

Motion in the x dimension (x,t) is independent of motion in the y (y,t) dimension. and in your first statement you seem contradict this one because you say motion in time can't be measured, hence how do you devlop a "ratio" with one term missing?

 

[Crazy Tosser]

I thought that average temperature of a system depended on, roughly, velocities of the molecules relative to each other [oops]. But if it's kinetic energies, that means that if you throw an ice block at a high speed, relative to you it's hotter just because it has a higher kinetic energy?

Naty1, I was just typing the whole thing straight from my head... so now you have a unique opportunity to see what kind of a bloody mess goes in it :P

And in time, you really can't measure how fast it goes without some clues, like looking how fast things move in it. Time on another object could "stop" for a million years and then start again and you would never know.

Right now I am reading thermodynamics (better late than never). Thanks for the wonderful link, Naty1 :)