# Is there an absolute maximum temperature?

25 March 2012

## Question

Dear Chris,

I have a question about absolute zero. If we can have a lower limit on temperature -absolute zero -i.e. so cold that nothing happens, why do we not have an upper limit - i.e. a temperature that is so hot that atoms and particles are so hot that they are ripped into the most elementary units and become so excited that theycannot react with anything around them. It has always seemed to me that there is a certain asymmetry about this temperature scale.

Thanks for taking questions from interested members of the public.

Regards
Bronwyn Higgs

We posed this question to Sam Gregson, High Energy Particle Physicist at the University of Cambridge...

Sam - The temperature of a system is simply related to the amount of energy in that system. Because the system can't have a negative energy, there is only so much heat you can remove from it and so a limit to how cold you can get. This is called absolute zero. We've got very close to it. Scientists in Finland have cooled rhodium atoms to a 10th of a billionth of a degree above absolute zero.

On the other hand, an absolute maximum temperature would require there to be a limit to the amount of energy you can give to a particle. As far as we know, there is no such limit. Although the speed of light is the universal speed limit, the reason you can't get there is that this would require an infinite amount of energy. So this speed limit does not limit the amount of energy and therefore, the temperature of an individual particle.

The most energetic particle ever observed was a cosmic ray over Utah, travelling at 99.999999999985% of the speed of light. It was probably a single proton with about 50 joules of energy. This is equivalent to about 5 trillion trillion degrees Celsius, and there is no evidence that this is the hottest you could get to.

As far as we know, you are just limited by the amounts of energy you can give to a particle. So you could say that the absolute maximum temperature is a temperature equivalent to all the energy in the universe, concentrated onto one particle. But that limits more accounting than basic physics.

Hannah - Thanks to Sam Gregson from Cambridge University and CERN. So temperature is related to thermal energy, and Einstein's theory of relativity means that although a particle has a universal speed limit, it doesn't have an energy limit. If you took all of the energy in the Universe and put it into one particle, you'd essentially run out of energy before you run out of capacity for energy, which is why we have no absolute maximum temperature...

## Related Content

### Maximum temperature

The printed answer doesnt address the question properly. The maximum temprature has to be the shortest wavelength. Below the Plank Length the fabric of the universe ceases to exist, and the concepts of time and distance become meaningless. The big bang, when it erupted, created the 4D universe by unfolding 4 of the 11 dimensions oif a string contained within one Plank length. Ergo, below that distance, the universe doesnt meaningfully exist, and thus it has to be the upper limit - thus the max temperature must be 1.4 x 10^32K. Above this, such radiation may disrupt the fabric of spacetime in such ways it ceases to exist locally, since it would disrupt the underlying Calibi-Yau Manifold. You may get a black hole, a wormhole or something entirely different we havent thought of yet.

### Speed limit

Wouldn't a particle supposedly *not* have a speed limit, since there is supposedly no energy limit? I mean, if you add more energy, the particle will go faster, eventually exceeding the speed of light.
Conversely, if there *is* a speed limit on a particle, wouldn't there also have to be an energy limit?

### Bronwyn

Would'nt the big bang be that one atom

### Planck Temperature

It's not false to say we have no reason to suppose there is an absolute temperature, but it's not entirely true either. The more precise case is we don't know if there is or is not an absolute maximum temperature, which is something the article could say a bit more directly for full disclosure. It's analogous to saying 'there is no such reason to say there is life on other planets'. That's true insofar as we haven't seen any, but we also haven't looked everywhere, so it's not entirely honest.

As for temperature, quantum mechanics gives us a very tiny distance known as the Planck Length below which the idea of distance doesn't seem to make sense. At high temperatures, objects emit radiation with a wavelength related to their energy (AKA Blackbody Radiation -- like when your toaster glows red hot). The Planck temperature (1.4 x 10^32 Kelvin) is the point where the radiation emitted from said object would be equal in wavelength to the Planck Length. There isn't much reason to suppose you couldn't *try* to add more heat to make the thing hotter, but we just literally don't know what would happen. We would need a theory of quantum gravity, which we don't have, because with that much energy in one place, general relativity comes into play and without quantum gravity we have no way of knowing what would happen. So while we indeed don't have a reason to think there is a maximum temperature, it would be more honest to say we don't know one way or the other.

### Absolute cold

Absolute cold at approx. -460 F where atoms do not function what happens when the temperature exceeds this negative threshold. What does a hydrogen atom revert too? The universe had to start with nothing and hydrogen was the the beginning of matter, light, energy.