Intuition on equipartition of energy (EM waves)

[center o bass]

Hi!

I try to get some intuitive understanding on the equipartition theorem stating that in thermal equilibrium, energy is evenly distributed among all degrees of freedom of a physical system.

This is indeed intuitive for a system consisting of composite particles with translational and rotational motion: each degree of freedom is just a kind of velocity, and with the randomness of thermal equilibrium it is intuitive that the energy is distributed equally among the different velocities. By reference to the ideal gass law, this amount should be $1/2 k T$.

However, what about electromagnetic waves: it is intuitive that the energy should be distributed equally amongst the polarizations -- however, why is the energy, also here, $1/2 kT$?

Is it intuitive that the energy associated to a degree of freedom of a material particle is the same as the energy corresponding to degree of freedom of an electromagnetic wave? I.e. $1/2 k T$?

 

[Jano L.]

I would not call it intuitive, but it's hard to agree what does it mean. I would call it formal - Poynting energy can be written down formally in a way resembling the way harmonic oscillator's energy is written down. Physics is completely different (field vs. particle) but on a paper, the formulae look almost the same so people thought "let's try to apply the equipartition theorem to the field and see what happens".

 

[center o bass]

I would not call it intuitive, but it's hard to agree what does it mean. I would call it formal - Poynting energy can be written down formally in a way resembling the way harmonic oscillator's energy is written down. Physics is completely different (field vs. particle) but on a paper, the formulae look almost the same so people thought "let's try to apply the equipartition theorem to the field and see what happens".

Indeed -- if it were not the case that this had to agree with the experimental notion of temerature -- i would think it was more of a definition of electromagnetic temperature.