# Temperature: Absolute infinity

## Main Question or Discussion Point

I heard somewhere that it is a matter of debate whether or not there is an absolutely highest temperature, analogous to absolute zero. This puzzled me because I thought that this is a direct consequence of Einstein's relativity:

Temperature is average kinetic energy of a substance. But since the particles in the substance are limited by the highest speed, the speed of light, doesnt it make sense that your substance has to have a theoretical limit defined by this constraint?

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What you have to ask Mephisto is "what is the highest velocity given these constriants"

It's the "given these constraints" bit that usually tie people up. If you constrain the construct to travelling at less than or equal to light speed, then perhaps. But ask yourself this. If such a construct falls into a White Hole and pops out on the far side of the Universe, what was it's speed? Was it the relative speed of the item, or the Lorentzian equivalent of the time it would take for the object to arrive there?

(Personal note: I'm not sure that should you fall into such a wormhole and traverse 100 million light years in an instant that you and your ship would not arrive thier instantaneously, but 100 million years old. Bad for the passengers, awesome find for the archeologists....)

Staff Emeritus
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The thing that matters is not speed, but energy. While SR does put an upper limit on an object's speed, it places no such limit on its energy.

The thing that matters is not speed, but energy. While SR does put an upper limit on an object's speed, it places no such limit on its energy.
Other than it can't have more than all the energy in the universe.
So it can't have unlimited energy.

right?

So, would the maximum possible temperature be the kinetic energy of a particle when all other particles in the universe are at absolute zero?

Just spitballing.

QuantumPion
Gold Member
What's the binding energy of a proton? If the kinetic energy of your hydrogen gas was so large that all the protons smashed each other into bits, leaving only radiation, that could be the maximum temperature :)

While SR does put an upper limit on an object's speed, it places no such limit on its energy.
But GR does place a limit on energy density, since if this is too large a blackhole will be formed. I believe there is an upper limit like 10^60 horsepower :)