Is there a theoretical highest possible temperature, or can temperatures range from 0 Kelvin to infinity?

An interesting subject in statistical thermodynamics. In ordinary systems there is no maximum but in certain systems it is possible to get hotter than infinite temperature on the Kelvin scale. In that case the entropy of the system is actually decreasing as the system becomes hotter. On the Kelvin scale the temperature is negative. In such a system, zero Kelvin approached from positive values is very cold while zero Kelvin approached from negative values is very hot.

It is covered here:

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

I did not read the entry closely so I cannot vouch for its accuracy in detail but the first paragraph or so looked ok.

There's a highest possible speed so there must be? Don't know what it is though. Then on page 1 of Google there's this (seems like you've hit upon a nerve):

http://www.wisegeek.com/what-is-the-...emperature.htm

How do you have a temperature higher than infinity K?

Well the first question to ask you back is the temperature of what? The temperature for all possible statistical physics systems one can imagine or do you have something particular in mind like the temperature of plasma or gas particles etc

As said, negative K.

An example: suppose you're looking at a group of atoms (say in a laser), and your measure of temperature is the orbital states of the electrons (and assume just two states for purposes of this discussion). At 0K, all electrons are in the ground state. As the temperature rises, the distribution of electrons changes, with some of the electrons going into the excited state. As the temperature increases, the difference in energy between the two states gets (relatively) reduced, compared to the energy in the system, so eventually at infinite temperature half the electrons are in the ground state, and half in the excited state. So the percent of electrons in the excited state is proportional to temperature, and with 50%, you're at infinite temperature.

But, as in a laser, the electrons are pumped into the excited state, and you can have more than 50% of the electrons in the excited state, which leads to a higher than infinite temperature. If you put a negative temperature in to the equations that predict the electron's distribution, you can describe the distribution of those electrons.

It depends on how quantum gravity works imo. As things get hotter and hotter, the laws of physics start to look different. At some point, atoms start to become unstable. Then nuclei start to break apart. Keep going and the weak and electromagnetic interactions become the same and the W and Z behave just like photons. Further, and gluons, W, Z and photons all behave the same. After that, the graviton is no longer separate and there is only 1 interaction (just estimating in my head, this happens at like 10^40 Kelvin). It is not really known what happens at his stage and "hotter". But everyday things like atoms, light and 1/r^2 gravity are long gone.

Planck temperature?

That's the highest possible temperature BEFORE quantum gravity takes over.

Are you sure ideas like temperature make sense after quantum gravity takes over?

We don't know

That's the point, we don't know if it can theoretically range from 0 to infinity.
(Obviously it can't be from 0 to infinity but still)

Yes, although this the highest temperature in which quantum gravity becomes important, it could happen sooner


Woops somebody already mentioned this exact point.

If heat is the movement, oscillation, of particles, wouldn't speed of light be an absolute ceiling?

Not really, since the particles themselves stop being stable at high enough temps.

There's no relativistic ceiling on kinetic energy though.

Infinity K + 1

+1. This issue with speed came to mind. Although I don't believe that the fastest possible speed is that of light. (yes I know thousands of physicists including the genius's) but physics all evidence is empirical so there is no definitive proof. So what am I saying....

According to accepted theory, yes there should be a highest possible temperature. (Everything turns into gas with the particles going at the speed of light) But I don't believe it personally.

Note that temperature is a function of average particle energy, not speed, and (were it not for the breakdown of forces discussed by a couple posters earlier in the thread), the energy of a particle is bounded only by the amount of energy available to accelerate it. If there is infinite energy in the universe (probably false, but unknown), then an infinite temperature could be achieved (again, but for the breakdown at the Planck temperature).

And I don't believe in gravity--all the evidence for it is just emperical.

Also, as said, it's the energy of the particles, not the speed that is related to temperature. Energy is unbounded...

If everything is energy, and it takes infinite energy to move energy at the speed of light - you have hit a pretty big dilemma.

There is just no way that any particle is going at the speed of light - and it certainly wouldn't be in the state gas.

The answer has been provided already, but

Great nickname. What makes you not believe it personally, and why do you not think that the speed of light is a fundamental limit? Since it was postulated more than a century ago it has been verified in probably tens of thousands of published journal articles, either explicitly or implicitly (because disregarding the finite speed of light would result in meaningless results for most experiments in most of physics)

But all the evidence is empirical! There's nothing definitive!

As long as you continue putting energy into a gas, you can raise it's temperature. The question is, how long can you keep doing this?

At some point in the process of giving them ever more energy, the constituent particles of the gas will become impossible to contain, at least due to tunneling if not the strength of the container. Also, too much energy in too confined a space could form a black hole, essentially erasing (almost) all of its temperature.

How does higher particle energy manifest itself, if not in terms of speed? I mean, what is a particle with higher energy doing that a particle with lower energy isn't?

It does manifest as speed, its just that kinetic energy is asymptotic to infinity as speed approaches c. So the speed of light ceiling on particle speed doesn't imply a similar ceiling on particle kinetic energy or gas temperature.