The Ultraviolet Catastrophe

Guest Written by Benedict Goh

Hi readers! I want to credit this post to Benedict Goh, a physics student I’ve been working with. He’s authored most of this article about blackbody radiation and the ultraviolet catastrophe. Enjoy!

The Set-Up

Imagine a closed box with completely sealed walls. Let these sealed walls be perfectly reflective on the inside, like intense mirrors. Have you imagined it? Good. Now, poke a hole through one side of the box, and let energy come in. Now, let the energy flow in and wait. Eventually, the system settles in a state of ‘thermal equilibrium’. This means that energy throughout this box is evenly distributed. In this construction, the box will do two things. First, it will absorb light from the whole electromagnetic spectrum. Secondly, it will also emit light at varying frequencies as well. This construction is called a blackbody.

Inside a blackbody, there are electromagnetic waves being reflected against the walls. In the classical picture, these electromagnetic waves are governed by Maxwell’s equations. Since the box acts as a boundary in the x, y, and z directions, Maxwell’s equations dictate that these waves need to obey a set of boundary conditions at the wall, which puts a constraint on their frequencies. A detailed description of these boundary conditions is…