# Maximum speed of anything, temperature

## Main Question or Discussion Point

If temperature or heat, is particles vibrating, and nothing moves faster then light. Doesn't this create a fundamental limit to the temperature that can be reached?

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jtbell
Mentor
Temperature depends on the kinetic energy of the vibrating atoms, not their speed. Speed has an upper limit of c, but kinetic energy has no upper limit (at least in SR):

$$K = \frac {m_0 c^2} { \sqrt {1 - v^2 / c^2}} - m_0 c^2$$

If temperature or heat, is particles vibrating, and nothing moves faster then light. Doesn't this create a fundamental limit to the temperature that can be reached?
Classically temperature is proportional to the thermal kinetic energy. The formula for relativistic kinetic energy goes to infinity as the particle velocity aproaches the speed of light. This limits the maximum temperature of a system to the temperature achieved if an infinite amount of energy is added, which effectively puts the temperature limit at infinity too.

On a more practical level, atoms can not remain atoms above certain temperatures as they are smashed by highly energetic collisions. Some say the highest know temperature was the temperature of the universe one Planck interval after the big bang and that is equivalent to the Planck temperature ( about $$10^{32}$$ kelvin ). Some other opinions can be found here : http://www.pbs.org/wgbh/nova/zero/hot.html

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Isn't the Planck temperature around 10^32?

Isn't the Planck temperature around 10^32?
Yes. Sorry. Corrected the typo ;)