# Does maximum temperature exist?

1. Aug 27, 2004

### Human

I have been wondering about the temperature rules for some time.
Since the temperature has a zero point, (0 degrees Kelvin), I often wonder if the temperature has a maximum limit, i.e. "the Hagedorn temperature".

What do you think about it? Do you think the temperature has a maximum limit?
If so, how many degrees Kelvin do you think the limit is?

2. Aug 27, 2004

### The Binary Monster

The zero point is when a particle has absolutely no energy... is that correct?

So in theory, a maximum would be when a particle had the most possible energy it could have.

I don't see why there shouldn't be a maximum - perhaps with enough energy a particle would cease to be a particle and become pure energy... which would then dissapate? Would that then mean that there would be a maximum, because the temperature would simply begin to dissapate immediately at that temperature and any energy gained with instantaeously be lost through dissapation?

:: Ben ::

(I know I have some crazy ideas, and most of them will probably never even make a shred of sense. But bare with me, I want to stay creative... even if much of my creativity is in the form of bad ideas! :P )

Last edited: Aug 27, 2004
3. Aug 27, 2004

### MiGUi

Actually after infinite temperature there are the negative ones.

4. Aug 27, 2004

### Gza

My take on it would be that since temperature is a measure of average kinetic energy(KE = 1/2mv^2); and since increasing the temperature obviously increases the velocity of the particles you are heating, there will be a limit for the velocity at the speed of light, thereby showing there will be a limit for the temperature.

5. Aug 27, 2004

### The Binary Monster

Good point...

To reach the speed of light, a particle of any mass needs infinite energy. Saying that a particle may not reach the speed of light therefore places an upper limit on the maximum kinectic energy a particle could have and thus an upper limit on the temperature a particle may be be at. Effectively you are saying that a particle may not have infinite energy... which establishes that there must be a maximum temperature.

Is my logic correct?

:: Ben ::

6. Aug 27, 2004

### Ivan Seeking

Staff Emeritus
The trouble is that the mass can increase infinitely as the velocity of any particle approaches C. This would allow for an infinite increase in energy.

7. Aug 27, 2004

### The Binary Monster

I see what you mean, but surely even if the mass increases infinitely, infinite energy will mean that the particle will travel at the speed of light, whatever the mass... and as this isn't possible, there must be a limit?

:: Ben ::

8. Aug 27, 2004

### Chronos

The shortest wavelength possible is governed by the planck length. Try plugging that into the temperature equivalent formula and see what you get [it's pretty hot].

9. Aug 27, 2004

### The Binary Monster

...so do you think that the temperature equivalent of the energy of those waves also acts as the maximum temperature for particles? Are you thinking that wave/particle duality means that all matter has a temperature maximum equal to that of a wave? Or do particles have a different maximum to that of waves? What do you think?

:: Ben ::

10. Aug 27, 2004

### Chronos

Yes. Heat is a form of electromagnetic radiation.

11. Aug 27, 2004

### The Binary Monster

But isn't it also a form of kinetic energy? Or have I completely misunderstood that, somewhere?

:: Ben ::

12. Aug 27, 2004

### Gonzolo

The maximum temperature I can concieve is whatever temperature the Universe was at at age Plank time : about 10E-43 seconds old. It has cooled ever since. To reach that again, you would need a Big Crunch.

13. Aug 27, 2004

### Chronos

Kinetic energy is what excites the atoms causing them to emit radiation [i.e., heat].

14. Aug 27, 2004

### kjones000

My intuition leads me to the following:

At a certain point the kinetic energy of a collection of particles ceases to be something that can be thought of as temperature and transitions to simply being the kinetic energy of the particles. Just as it would be improper to think of the motion of galaxies moving away from us as increasing the temperature of the universe, it is improper to think of a plasma expanding in all directions as having a temperature based on the relative velocity of the particles.

IF the above is true, then the limiting factor is not how much energy you can pack into a small mass of plasma, but rather, how are you going to keep that plasma from spreading in all directions?

15. Aug 27, 2004

### Ivan Seeking

Staff Emeritus
This demand is still completely theoretical, isn't it?

16. Aug 27, 2004

### Nereid

Staff Emeritus
Yes.

So, what happens if you add energy to a small volume (with particles)? If the energy is EM, you get furious pair production, and the particles exit your small region tout de suite, and your small region cools down. Thus you will get an equilibrium temperature, and there will be a max (no matter how much more EM energy you pump into your test region, it won't get any hotter).

The only hotter temp you can get is, as Chronos said, the first Planck second of the universe.

17. Aug 27, 2004

### Metallicbeing

Very good Gonzolo. I knew someone would say it.

Edit: Sorry Chronos, They're right. You did say it first.

Last edited: Aug 28, 2004
18. Aug 28, 2004

### marcus

of about 1.4 x 1032 kelvin.

then gonzolo says:
"The maximum temperature I can concieve is whatever temperature the Universe was at at age Plank time : about 10E-43 seconds old. It has cooled ever since. To reach that again, you would need a Big Crunch."

yes that is the same temperature that Chronos is talking 'bout.

then Nereid confirmed Chronos reply and gave a physical argument for temp maxing out, concluding that:
"The only hotter temp you can get is, as Chronos said, the first Planck second of the universe."

finally Metallicbeing says Ah at last someone, gonzolo, has answered the question.

-----------------
if anything is missing it is a link to the National Institute website (NIST)
where they actually give this temperature, expressed in kelvin, and where they give a formula for it in terms of fundamental constants G, hbar, c, k
which agrees with what Chronos said (the temp corresp to planck wavelength light)

so let me get the link to NIST
http://physics.nist.gov/cgi-bin/cuu/Value?plktmp|search_for=universal_in!

if you click on the symbol TP for planck temp
you will get the formula
(thats how the NIST constants site generally works)
and otherwise they just give you the most accurately known value for it.

here's the main URL
http://physics.nist.gov/cuu/Constants/

Last edited: Aug 28, 2004
19. Aug 28, 2004

### sol2

Thanks all, I enjoyed the exchange as it affirms the things I have been saying all along.

20. Aug 28, 2004

### The Binary Monster

Surely all the ideas here based on the Planck length and/or Planck time are heavily theoretical?

And Chronos, thanks for correcting me and helping me understand. I know it may seem basic to you but I'm only just getting into this...

:: Ben ::

21. Aug 28, 2004

### marcus

I tried to think how to answer. Probably there's an easy obvious answer, like Yes, but that didnt seem quite right.

personally I dont think I would base the argument on planck time and planck length----the planck temperature is pretty basic

the planck speed is c, the speed of light
the other quantities can also be pretty basic in their own categories.
the planck speed c is a basic speed
the planck temperature TP is a basic temp

----------
I guess it is like this, Monster, when you first go to college you take a Freshman physics course and in that course you meet G, c, hbar, and k.

k is the Boltzmann constant, as in PV = nkT, or any of the other kT formulas.

and the professor's strategy will be to make you do problem after problem using these constants to get the answer. over and over.
use G, use c, use hbar, use k, use G, use c, use .......etc.

after a while it dawns on you, the Freshman, that these are fundamental proportions built into the fabric of nature. they are the keys that unlock the doors. they are the ratios in the laws of nature.

much much later, someone you meet casually on a skiing trip says hey
did you know that if you combine G, c, hbar, and k in the only way that you can which makes a temperature then you get a temperature called Planck temperature which is sort of the hottest things can get?

and you say, cool that reminds me of the speed of light which is sort of the fastest things can get.

you say this is "heavily" theoretical?
I dont know as I would say quite that, it is light and deep at the same time.
and tantalizingly ambiguous too. but the feel is not exactly heavy

22. Aug 28, 2004

### The Binary Monster

Thanks for the explanation/correction... As of yet I haven't even become a freshman yet - not till next year. So you see I wouldn't have reached that yet - only through a little of my own reading.

But still, I enjoyed the post. It's interesting, and I guess it's taught me a little more about Planck quantities. :)

23. Aug 30, 2004

### phenylalanine

Surely the theoretical maximum temp. is the speed of light - 0.1 reccuring?

24. Aug 30, 2004

### Nereid

Staff Emeritus
Why?

And (belated) Welcome to Physics Forums phenylalanine!

25. Sep 1, 2004

### phenylalanine

What I meant was that the maximum temp. that could be acheived is when the mean velocity of the particles is c - 0.1 as that is as fast as the particles could move without actually acheiving c.