From what I've been taught in physics in school, temperature is average kinetic energy, particles can't move quicker than the speed of light and there is no max temperature (please correct me if I'm wrong). Surely that is a contradiction.
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5Particles approach $E \to \infty$ as $v \to c$. – Michael Seifert Nov 18 '22 at 19:34
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Does this answer your question? Is there any upper limit on a particles kinetic energy? – Chemomechanics Nov 18 '22 at 19:37
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Or Upper limit to the temperature of a body? – Chemomechanics Nov 18 '22 at 19:41
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this observation is a key part of the Chandrasekhar limit. $E/p = \beta$ gets saturated and it's bye bye white dwarf. – JEB Nov 19 '22 at 03:00
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You surely have Newton's formula for the kinetic energy in mind: $$E_\text{kin}=\frac{1}{2}mv^2 \tag{1}$$ But this formula is only an approximation valid for speeds $v$ much smaller than the speed of light $c$. More exactly you need to use the formula for the relativistic kinetic energy: $$E_\text{kin}=mc^2\left(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1\right) \tag{2}$$
For small speeds ($v\ll c$) you can approximate this formula (2) by the simpler Newtonian formula (1). But for larger speeds this approximation is not valid anymore. And especially for $v\to c$ you get $E_\text{kin}\to\infty$.
And because kinetic energy has no upper limit, also temperature has no upper limit as well.
Thomas Fritsch
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