# The Naked Scientists Forum

### Author Topic: What's absolute maximum?  (Read 4183 times)

#### Geezer

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##### What's absolute maximum?
« on: 21/04/2011 06:45:03 »
We seem to have a pretty good handle on the limit of minimum temperature. What's the limit of maximum temperature?

#### CPT ArkAngel

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##### What's absolute maximum?
« Reply #1 on: 21/04/2011 07:49:08 »
According to established theories, there is no maximum.

#### Geezer

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##### What's absolute maximum?
« Reply #2 on: 21/04/2011 07:54:50 »
According to established theories, there is no maximum.

Jolly good. And why is that?

#### CPT ArkAngel

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##### What's absolute maximum?
« Reply #3 on: 21/04/2011 08:05:27 »
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...
« Last Edit: 21/04/2011 08:13:21 by CPT ArkAngel »

#### Geezer

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##### What's absolute maximum?
« Reply #4 on: 21/04/2011 08:17:11 »
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

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##### What's absolute maximum?
« Reply #5 on: 21/04/2011 08:25:20 »
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.

« Last Edit: 21/04/2011 08:44:05 by CPT ArkAngel »

#### JP

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##### What's absolute maximum?
« Reply #6 on: 21/04/2011 13:35:43 »
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

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##### What's absolute maximum?
« Reply #7 on: 21/04/2011 14:35:44 »
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

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##### What's absolute maximum?
« Reply #8 on: 21/04/2011 15:39:32 »
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

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##### What's absolute maximum?
« Reply #9 on: 21/04/2011 15:48:35 »
Further to above

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

Quote
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

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##### What's absolute maximum?
« Reply #10 on: 21/04/2011 21:02:25 »
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

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##### What's absolute maximum?
« Reply #11 on: 21/04/2011 23:06:54 »
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

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##### What's absolute maximum?
« Reply #12 on: 21/04/2011 23:35:20 »
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

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##### What's absolute maximum?
« Reply #13 on: 22/04/2011 04:05:05 »
Would the highest possible temperatures have existed during, or shortly after, the beginning of the Universe?
« Last Edit: 22/04/2011 07:58:09 by Geezer »

#### CPT ArkAngel

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##### What's absolute maximum?
« Reply #14 on: 22/04/2011 07:57:07 »
This is exactly what i mean by singularity... [^]

#### yor_on

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##### What's absolute maximum?
« Reply #15 on: 22/04/2011 20:51:19 »
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.

#### The Naked Scientists Forum

##### What's absolute maximum?
« Reply #15 on: 22/04/2011 20:51:19 »