The kerfuffle is not dead yet. First, here’s a piece from The Guardian, specifically Jon Butterworth’s Life and Physics column: On Pauli and the interconnectedness of all things

Now, declaration of interest, Brian and Jeff are both old friends of mine, and I even starred briefly in “Night of the Stars” as “elbow behind Jonathan Ross’s head”. I have never met Sean, though I have read some of his work (and used his links) and I have a lot of respect for him. Anyway, this is about physics, not about taking sides in a celebrity scientist face-off.

My celebrity non-status must be why my contribution(s) are only hinted at (“some previous blogs” and “**it”; I guess you can call me et. al) but the main objections, or more precisely, my main objections (which I delineated) were the claim that a response to change in one electron’s energy would be instantaneous, and that the cause would be the Pauli Exclusion Principle. It seems to me that Jon admits that Brian Cox was incorrect on both of these points, though there’s some hedging on the instantaneous part — he gives an example of the electron in a potential well, i.e. an electromagnetic interaction, but then cites the phenomenon as being nonlocal, which I don’t understand. (Yet somehow he manages to conclude this was a “high-score draw”, which brings the Black Knight’s “We’ll call it a draw!” to mind)

So in principle one has to treat the potential of the whole universe, all the atoms, as a single system (a single Hamiltonian). All agree on this, as far as I can tell.

This already means that saying “it’s in a different place” is not sufficient reason to say of an electron “it’s in a different quantum state”.

This is something I don’t accept as given. I still point to my example of composite Fermions. Nature thinks that individual atoms are identical, because Fermionic atoms obey Fermi-Dirac statistics. If the electron energy levels were different, they would no longer be identical and would not do this. Nature seems to be saying that this assumption is incorrect.

Another issue has been pointed out by Dr. Skyskull in Pauli, “armchair physicists”, and “not even wrong”, in which he walks you through some of the background before discussing the problem, which is useful. (Part of the post concerns some of the remarks that have been made, and I’m happy to skip over that and focus on the physics, as I have already noted).

The additional argument comes near the end, regarding a claim that while the splitting is there, it’s so small that we can’t measure it, which garners a “physics fail” epithet.

Here Cox explicitly acknowledges that his “universal Pauli principle” consequences are something that not only cannot be measured today, but in principle can never be measured, by anyone

There a notion in science that can be summarized as: pics (i.e. experimental results) or it didn’t happen. You simply can’t make a claim in science without some kind experimental evidence to back it up — without that support it’s merely hypothesis or conjecture. You come to expect this from the fringe folks, but not from actual scientists. It’s hard to fathom that argument being brought up.

If you want to ruminate on the implications of treating the universe as a single system, fine — there’s a lot to discuss, such as “what does ‘identical’ really mean in this context?” Much of it will be interesting and some of it quite subtle. But presenting it as accepted science, to a lay audience? No.