A little more detail on why I think that the idea of every electron affecting every other electron around the universe doesn’t wash.
One thing about scientists that nonscientists sometimes don’t get is that predictions have wide-ranging implications. You may think that something is true because it holds for a specific example, but if that idea is to be generally true, it has to hold up all across physics. (As an aside, this is a common stumbling block for crackpot theories). Claiming that “everything is connected” can be tested and indeed has been tested, even though the experiments were not made for the targeted purpose of falsifying this specific claim.
I’ve already given the example of atomic clocks, though any precision spectroscopy experiment would probably suffice. Brian gives the example of bands in semiconductors, and the Pauli Exclusion Principle is the source of this structure — the electron energy levels cannot be the same, so they “pile up” into bands. But his video takes that one step further, to affecting distant semiconductors. So, I ask, where are these bands in individual atoms? Why don’t we see them? Gather together a reasonable fraction of Avogadro’s number of atoms in a lattice and you get a fairly wide band of energies for a transition, even after you reduce thermal motion. Do the same to a gas, and do Doppler-free spectroscopy, and the transitions can be quite narrow.
Another example, as I mentioned in the comments, has to do with the behavior of composite Fermions, such as atoms. The Pauli Exclusion Principle is based on the behavior of identical particles. If all these electrons are in slightly different states, which differentiates the electrons, then the atoms themselves are not identical anymore. Which means that if you were to collect a bunch of them into a cold gas in some confining potential, you should be able to get them all to drop to the ground state (which would be a band). But we don’t see this behavior: You can form what is known as a Fermionic condensate, which is the analogue of a Bose-Einstein Condensate. But since the Fermionic atoms are identical, they are subject to the Pauli Exclusion Principle and can’t occupy the same energy states in the system; this adds a level of difficulty in forming them (you don’t have the same avenues of exchanging energy in collisions during evaporative cooling, since you are limited to one atom per energy level). But the bottom line is that this kind of system exists, which tells us that the atoms are identical to each other, and falsifies a prediction based on Brian’s conjecture.