The controversy is about whether all the electrons in the universe really move energy levels imperceptibly when Brian heats the diamond, whether it's instantaneous, and whether it is anything to do with the Pauli exclusion principle. The Pauli exclusion principle says that no two fermions can be in the same quantum state. Lily wrote a bit about it here.You can read Jon Butterworth's take on this whole thing. However, reading this, I think it reinforced why I became an experimentalist! :) Oh, I know, many of these "theoretical curiosity" can lead to important things. You don't have to tell me that. But then, one can say the same thing about String Theory. At some point, when there isn't anything that can be verified by experiments, it becomes only an OPINION! One can argue that it is in the equations, or in QM in this case. Well, I can say the same thing about the Higgs. Yet, we spent billions on making sure it DOES exists and not just simply someone's opinion!
Brian's main response to criticism so far has been to point to these lecture notes by his co-author Jeff Forshaw.
And here's a response from Sean Carroll (which also links to some previous blogs). Sean also spoke about it on Dr Kiki's science hour.
BTW, is this the most technical physics piece that has ever been written for a newspaper? I mean, when was the last time you open your local papers and read something like this?
If you treat each electron as though it sits in a "potential well" (created by the electrostatic field of the atomic nucleus), a good place to start is by thinking of a universe full of atoms as though it were a bunch of potential wells.I love it! :)
Next you have to solve this multiple-potential-well problem. Jeff's notes solve the Schroedinger equation for two wells as an example, and show that whereas for an infinite potential you'd have two spatially-localised energy levels with identical energies, for a finite potential you have two non-localised energy levels with very slightly different energies.