I know that absolute zero is the lowest possible temperature, and I've heard that there is no maximum temperature (no upper limit on how hot something can get), but I don't know the explanation for that.

My understanding is that temperature is a measure of the average kinetic energy of a system of particles. If kinetic energy depends on the velocities of the particles and particle velocity is limited to be less than the speed of light, then wouldn't that mean that there is an upper limit on possible temperatures?

Question

I know that absolute zero is the lowest possible temperature, and I've heard that there is no maximum temperature (no upper limit on how hot something can get), but I don't know the explanation for that.

My understanding is that temperature is a measure of the average kinetic energy of a system of particles. If kinetic energy depends on the velocities of the particles and particle velocity is limited to be less than the speed of light, then wouldn't that mean that there is an upper limit on possible temperatures?

amistre64 · Answer

0 is the ideal of no kinetic energy; everything has stopped moving

in theory, if we continually pump energy into a system; then what is the maximum value that that system can take on?

at least thats my take on it

amistre64 · Answer

and another thought, what happens as something approaches the speed of light; do the particles act in the same way?  or is it more along the lines that the speed of light is an ideal as well, therefore in order to obtain it you would have to have infuse the system with an infinite amount of energy?

jfraser · Answer

from what i remember of relativistic physics, when you keep pumping energy into a system moving closer and closer to the speed of light, the added eneryg is transferred into the mass of the object, and not just its speed. So the objects will get heavier as they get more energy.

Since KE = 1/2 mv^2, even if v is capped by the speed of light, m can constantly increase to an infinite value. WHen we take the average KE to find a temperature, it still has no upper limit.

anonymous · Answer

Yeah, that was the only thing I could think of too: the relativistic increase in mass and its contribution to the KE. When I thought about it a little later I remembered that velocity has a limit, but momentum can increase without bound so why not KE.

Based on those principles, that makes sense, but there would still be a conservation of energy thing to deal with. It would take infinite energy to increase the momenta of a system to infinite levels and that energy would have to come from somewhere. 

Thanks, amistre and JFraser. That helps reconcile that, but now of course my mind is contemplating cosmic hugeness. Eventually, I always get a sense of vertigo when I do that.