1. Order of Kilopi
Join Date
May 2004
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6,971

## Absolute... Highest tempreture

I've thought of this before but today my friend asked me if there was an absolute highest tempreture, it got me thinking...

As a material heats up it's particles start moving faster.
As it cools down they move slower- once they stop the temprature is called absolute zero- about 273degree's.
What happens when you heat somthing up so that the particles are wizzing around at the speed of light? That must be the highest temprature right?
Would there be any realtivistic effects on the material at that temprature...? What would that temprature be..?

2. Working backwards from what supposedly happened after the big bang...

Wouldn't protons/neutrons split into quarks and whatever else they're made of first? At so many trillions and trillions of degrees?

with regards

3. Originally Posted by mickal555
What happens when you heat somthing up so that the particles are wizzing around at the speed of light? That must be the highest temprature right?
The temperature is related directly to the mean kinetic energy of the particles. We then generally use the nonrelativistic formula relating velocity to kinetic energy to relate temperature to velocity indirectly. If the particles were moving fast enough, we'd have to use the relativistic equation for kinetic energy, and since the energy of the particles increases without bound as they approach ever closer to the speed of light, the temperature would also increase without bound.

Conveniently, I ran some numbers recently on this sort of idea for dirkbontes in this thread; he was thinking that intergalactic gas could be moving relativistically and that the resulting mass increase could account for dark matter. You can see the temperatures that would result from hydrogen gas with particles moving very close to the speed of light.

4. There should be some sort of maximum temperature in practice; if all the matter except one particle (a proton, for instance) in the observable universe were annihilated, and all that energy were imparted to that one single particle;

then that particle would attain the highest possible temperature in our universe.
Of course there would be no way to measure that temperature- as all the thermometers would have been converted into energy; but it should be calculable.

5. Originally Posted by eburacum45
There should be some sort of maximum temperature in practice; if all the matter except one particle (a proton, for instance) in the observable universe were annihilated, and all that energy were imparted to that one single particle;

then that particle would attain the highest possible temperature in our universe.
Of course there would be no way to measure that temperature- as all the thermometers would have been converted into energy; but it should be calculable.
There is a bound well before that which is reached in heating material (i.e. sidestepping the borderline philsophical debate as to whether the early Universe could have gone thorugh a hotter phase) - the Hagedorn temperature, where energy loss through production of particle/antiparticle pairs throttles further heating. I seem to recall it's of order 10^10 K.

Hmm. According to this article, one can think of this as a melting point for hadrons into quark matter, and rapid enough heating can cause the quark motions to increase, so it's not as absolute as it once looked.

6. Established Member
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Sep 2003
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2,405
The standard hot big bang model proponents posit that the hot big bang was initiated by a quantum fluctuation. If we assume that the current physical (much larger than the observable) universe is contained within a Euclidian 3-space sphere of a diameter of 75 billion light years and were able to compute the total energy of all the particles and photons when the rest mass of the particles is multiplied by c^2, we could arrive at an enormous number of joules. Using E = Planck's constant multiplied by the primal frequency as a defining equation and solving for frequency by plugging in the value for total energy computed in the second sentence above, we will have wrapped up the total energy of the universe in the equivalent of a single photon of exceedingly high frequency very near the moment of initiation (before it's shattered by the Quantum Fluctuation) of the hot big bang. If we convert this hypothetical (I don't really believe there was one) frequency to temperature, what would that temperature be?

E = ? = (planck's constant)*(speed of light)/(wave length of primal photon) = (primal energy in eV).
(Wave length of primal photon) = (speed of light)/(frequency of primal photon).
One degree kelvin = 8.62 * 10^-5 eV.

Once we guess at the value of E computed as suggested in the second sentence, we have a good start on computing the highest temperature that may have been actually reached equivalent to that of the primal photon.

7. Originally Posted by ngc3314
There is a bound well before that which is reached in heating material (i.e. sidestepping the borderline philsophical debate as to whether the early Universe could have gone thorugh a hotter phase) - the Hagedorn temperature, where energy loss through production of particle/antiparticle pairs throttles further heating. I seem to recall it's of order 10^10 K.

Hmm. According to this article, one can think of this as a melting point for hadrons into quark matter, and rapid enough heating can cause the quark motions to increase, so it's not as absolute as it once looked.
If mass of any object increases high enough due to relativity, the object will collapse into a black hole. Perhaps the temperature at which individual quarks become black holes is the highest attainable temperature.

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