[chris (OP)]

Gerald has written to ask:

The highest achievable speed in the universe is c - the speed of light. If we forget for a moment that particles with a mass cannot achieve c, then the highest achievable speed for atoms is c and hence there is an absolute maximum of temperature too, as well as the minimum 0K.

Does such a theoretical maximum of temperature exist? If yes, how many Kelvin is it and does it exist anywhere in the universe?

What does everyone think?

[geordief]

Gerald has written to ask:

The highest achievable speed in the universe is c - the speed of light. If we forget for a moment that particles with a mass cannot achieve c, then the highest achievable speed for atoms is c and hence there is an absolute maximum of temperature too, as well as the minimum 0K.

Does such a theoretical maximum of temperature exist? If yes, how many Kelvin is it and does it exist anywhere in the universe?

What does everyone think?

I thought relative velocity was built into one of the definitions of temperature and so c  would rear its ugly head.

Density  could increase but there must be a limit to how relatively close interactions could be....

[jeffreyH]

Temperature is a local phenomena. In a remote frame of reference and depending upon the velocity of that frame time dilation comes into play. So that only vibrations and collisions local to the solid, liquid or gas can be considered important. Since all inertial frames have to be considered stationary. This then limits the speed of those vibrations etc. You also have to take into account particle collisions and how they operate in the transmission of heat.

[evan_au]

the highest achievable speed for atoms is c and hence there is an absolute maximum of temperature

Temperature is a measure of the average energy of the particles in a substance...

From a parallel thread on "Do all the atoms in a material have the same speed at a given temperature?":

The average energy of a group of atoms increases proportionally with temperature. Kinetic energy E=1/2mv2 = kT.
- where:
- E is Energy in Joules
- m is the mass in kilograms
- v is the velocity in meters/second
-  temperature T is measured in degrees Kelvin
- k is the Boltzman constant

It is true that velocity v cannot exceed the speed of light c.
However, as velocity approaches c, the relativistic mass increases towards infinity.
So there is no upper limit to the energy of the particles, or their temperature (except the energy of the whole universe).

Molecules as we are familiar with them cease to exist above a few thousand degrees, the material becoming a plasma, with very light (and high velocity) electrons and the much heavier (and lower velocity) atomic nuclei.

At the higher temperatures and pressures found in a neutron star, the atomic nuclei and electrons even lose their individual identity.

At the even higher temperatures and pressures thought to have existed in the Big Bang, exotic particles that can only be created in today's most powerful particle accelerators would have been common - and perhaps even heavier particles that we can't produce in the largest particle accelerators!

[Kryptid]

To the best of my knowledge, the temperature at which our current physics knowledge breaks down is the Planck temperature (2.55 x 10^32 degrees Fahrenheit).