[Geezer (OP)]

We seem to have a pretty good handle on the limit of minimum temperature. What's the limit of maximum temperature?

[CPT ArkAngel]

According to established theories, there is no maximum.

[Geezer (OP)]

According to established theories, there is no maximum.

Jolly good. And why is that?

[CPT ArkAngel]

No maximum to density... No maximum for density because of singularities... Don't ask me about singularities because it is a belief which you know i disbelieve...  []

[Geezer (OP)]

No maximum to density... No maximum for density because of singularities... Don't ask me about singularities because it is a belief which you know i disbelieve...  []

I did not know that. But, based on what we know, is it not reasonable to project some maximum value?

[CPT ArkAngel]

Any quantity of energy in a singularity produces infinity so we need a theory without singularities. For my theory, it is Planck mass divided by 4πLp^3 / 3, where Lp is the Planck length. For the temperature, i did not calculate it.

[JP]

Some might argue it's the Planck temperature.  I disagree, since as I understand it, it's the limit where our theories break down, but that doesn't mean you can't go higher--we just can't model it.

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

Since temperature is a measure of average kinetic energy, at some point you're going to run out of energy to add to the system. 

[burning]

But temperature isn't about absolute motion.  The temperature of a single particle is meaningless.  It's only when you have a system of particles that you can talk about the system's temperature.  If the velocity of the particles relative to each other is low, you have a low temperature system.  It doesn't matter how fast that system is moving relative to you.

[imatfaal]

But temperature isn't about absolute motion.  The temperature of a single particle is meaningless.  It's only when you have a system of particles that you can talk about the system's temperature.  If the velocity of the particles relative to each other is low, you have a low temperature system.  It doesn't matter how fast that system is moving relative to you.

Burning - good user name for this topic - who said anything about single particles.  temperature can be viewed as proportional to average kinetic energy, or at constant volume the change in energy for a change in entropy but both do, as you say, refer to a system.

Recent research in laser confinement came up with very small systems that got screwy on the change of entropy/energy which some reporters described as a temperature of less that abs zero - and others described as either plus or minus infinity.  I will be honest it was all over my head and I didnt read it carefully but I will dig it out and see if I can reconcile it with T = dE/dS  (do we have curly partial ds?)

[imatfaal]

Further to above

simple answer from Eric Weisstein at Wolfram
http://scienceworld.wolfram.com/physics/Temperature.html

While there is no maximum theoretically reachable temperature, there is a minimum temperature, known as absolute zero, at which all molecular motion stops.

more complicated answer expanding on the +ve / -ve infinity madness from Physicsfaq
http://www.phys.ncku.edu.tw/mirrors/physicsfaq/ParticleAndNuclear/neg_temperature.html

So we have created a system where, as we add more and more energy, temperature starts off positive, approaches positive infinity as maximum entropy is approached, with half of all spins up.  After that, the temperature becomes negative infinite, coming down in magnitude toward zero, but always negative, as the energy increases toward maximum.  When the system has negative temperature, it is hotter than when it is has positive temperature.  If you take two copies of the system, one with positive and one with negative temperature, and put them in thermal contact, heat will flow from the negative-temperature system into the positive-temperature system.

[Geezer (OP)]

So we have created a system where, as we add more and more energy, temperature starts off positive, approaches positive infinity as maximum entropy is approached, with half of all spins up.  After that, the temperature becomes negative infinite, coming down in magnitude toward zero, but always negative, as the energy increases toward maximum.  When the system has negative temperature, it is hotter than when it is has positive temperature.  If you take two copies of the system, one with positive and one with negative temperature, and put them in thermal contact, heat will flow from the negative-temperature system into the positive-temperature system.

Well, that really clears things up a lot  []

[Bill S]

If temperature is a measure of the energy of particles in a system, and this is related to the speed at which the particles jiggle relative to one another, would the whole thing not reach some sort of maximum as the relative speeds of the particles approached the speed of light?  []

[JP]

Good point, Bill, but as particles approach the speed of light, it takes more and more energy to increase their speed by less and less.  Getting to the speed of light would take infinite energy.  Since temperature is a measure of energy...

[Geezer (OP)]

Would the highest possible temperatures have existed during, or shortly after, the beginning of the Universe?

[CPT ArkAngel]

This is exactly what i mean by singularity... [^]

[yor_on]

I'm pretty sure _maybe_ that the highest temperature would be the one existing directly after we got our macroscopic arrow of time. That as all temperatures is a definition of 'somethings' motion inside that arrow (molecules, atoms etc). So if we just could agree on where/when that 'arrow' first appeared?

Then that will be our definition of a 'highest temperature', well in our SpaceTime at least?


(I think we at TNS should take the lead here, let's give those whitecoated slightly unfocused and wildly staring men & wimma a helping hand. "Yes, gentlemen, and ladies, bring out your stopwatches and let us start measuring."

But no, all jocularity aside, I do think it's a point? Truly I do.