Thermal Radiation & Photon Gasses

One thing that has always puzzled me is thermal radiation. This is electromagnetic radiation from an object simply because it is warm. I never understood why a warm body emits light (NB: I use “light” and “electromagnetic radiation” interchangeably).

In quantum mechanics, we are taught that light is emitted with a sharply defined color—given by the energy difference between levels. I guess it could make sense that if, naively, hot bodies consisted of atoms in motion and that there were a continuum of motional states, then there could be a continuous energy spectrum.

But this means that the atoms would be losing energy to emit thermal radiation, thus cooling it. Hence it seems like all bodies would then be at zero temperature and all the energy in the universe would be in light.

Here’s the insight I recently found:
Remember that there is a vacuum electromagnetic field, containing an infinite number of modes. Each mode has a certain number of photons. Here’s the kicker: the vacuum field is in thermal contact with the hot body! That is, the electromagnetic field is in thermal equilibrium with the hot body! Therefore, since the body has a nonzero temperature, then there must be a nonzero photon distribution in all the modes. This distribution is exactly the distribution of thermal radiation.

Thermal Radiation & Photon Gasses

One thing that has always puzzled me is thermal radiation. This is electromagnetic radiation from an object simply because it is warm. I never understood why a warm body emits light (NB: I use “light” and “electromagnetic radiation” interchangeably).

In quantum mechanics, we are taught that light is emitted with a sharply defined color—given by the energy difference between levels. I guess it could make sense that if, naively, hot bodies consisted of atoms in motion and that there were a continuum of motional states, then there could be a continuous energy spectrum.

But this means that the atoms would be losing energy to emit thermal radiation, thus cooling it. Hence it seems like all bodies would then be at zero temperature and all the energy in the universe would be in light.

Here’s the insight I recently found:
Remember that there is a vacuum electromagnetic field, containing an infinite number of modes. Each mode has a certain number of photons. Here’s the kicker: the vacuum field is in thermal contact with the hot body! That is, the electromagnetic field is in thermal equilibrium with the hot body! Therefore, since the body has a nonzero temperature, then there must be a nonzero photon distribution in all the modes. This distribution is exactly the distribution of thermal radiation.

Oooh… WordPress…

Hm… I happened to check this out on Christmas! A gift to myself?

I’ll have to see if wordpress can be loaded onto my U of M account…

Oooh… WordPress…

Hm… I happened to check this out on Christmas! A gift to myself?

I’ll have to see if wordpress can be loaded onto my U of M account…

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