Making My Case
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.
You have attracted the attention of Luboš Motl and he agrees with you. In truth Motl does not seem to agree with many people quite the opposite in fact.
http://motls.blogspot.com/2012/02/brian-cox-misunderstands-locality-pauli.html
Swansont:
Your statement about the natural line-widths in doppler free atomic spectroscopy really drives home the point. If the energy level of some electron in some similar groundstate in some nearby atom was actually a perturbation on some electron in the atom of interest, the natural linewidths in these types of spectroscopy would not correspond directly to the energy-time uncertainty principle.
The natural linewidths do in fact correspond closely to that predicted by the Energy-Time HUP.
If electrons behave in the way that Dr. Cox has implied, then should we also not observe splitting in the nuclear magnetic resonance spectra of any symmetric molecule with at least two identical atoms? For example, the two hydrogen atoms in water would not be in a degenerate condition, so their electron-nuclear shielding effects would be different. This should be observed as there are NMR experiments as well as ESR that can detect this said non-degeneracy out to many decimal places.
Perhaps there is some effect that Dr. Cox is aware of that I am not. If there is, the effect must be so small and so finesse that a general pop-sci audience shouldn’t be hearing about it anyway.
My conclusion from all this: physics is counterintuitive and hard.
Cox is talking about a purely theoretical model in which the energy shifts are tiny, much tinier than any current puny experiment can detect.
That’s pretty bleedin’ obvious isn’t it?
If you don’t agree with it then you don’t agree with the current formulation of QM.
So either you have suggestions for corrections to the postulates of QM or you should all STFU
JG, if the shifts are there it makes the atoms no longer identical, in which case composite Fermions would not obey Fermi-Dirac statistics, as I have pointed out. I don’t see any wiggle room here.
You can’t see the wiggles, nothing can detect them, maybe nothing ever will, but by standard QM they DO exist. The joint state for any two fermions in the universe is not exactly a product state, there is a miniscule overlap of the wave functions. But this will have no observable consequence for fermi-dirac stats or any other known phenomena
Also the effect is just a probabilistic one, not deterministic, the only deterministic law in nature is deterministic schrödinger evolution of a probabilistic state vector
I’m sure Cox will explain this is what he meant, even if he didn’t make it clear in the video.
If QM contains an effect that is even in principle never measurable, or always unmeasurably small, then why should we consider the statement that the effect exists to be a scientific or physical one?
I can claim that invisible pieces of tickertape connect every single electron to every other but the forces they transmit are too weak to ever be measured … well, that’s not going to be science. So how is Cox’s unmeasurably tiny degree of connectedness any more of a scientific statement?
To be a theory of physics rather than a mathematical or metaphysical speculation, QM needs to have measurable consequences. Any aspect of QM that will never be measurable is not one that belongs to physics, however nicely it meshes with the rest of the theory.