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Brian Cox and the Pauli Exclusion Principle

  1. Feb 7, 2014 #1
    Hi,

    I know this is old news at this stage, but I was watching his public lecture on quantum mechanics, and he says the energy levels of all the electrons in the universe shift to adjust when he adds energy to electrons in a diamond.

    I understand that he should have used the phrase quantum state rather than energy level, and I understand that the shift is tiny, and effectively imperceptible, but even this does not sit well with me. Entanglement in quantum mechanics has always been about correlation, rather than causation. I don't see how manipulating the quantum states of electrons here could have an instantaneous effect on the quantum states of distant electrons without violating relativity.
     
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  3. Feb 7, 2014 #2

    Bill_K

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    That's the same question that was just asked and answered in this thread.
     
  4. Feb 7, 2014 #3
    I am thinking that he meant that to some imperceptible degree they are all correlated. As for spooky action at a distance, that just about sums up Quantum Mechanics.
     
  5. Feb 7, 2014 #4

    bhobba

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  6. Feb 7, 2014 #5

    Ken G

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    The problem is that Cox's comment could only apply if he was trying to be so precise that even remotely tiny effects should be viewed as relevant, but if one is being that precise, then there is already no such thing as "an electron in a diamond", for the simple reason that all electrons are indistinguishable particles, so just don't have personal identities. So the disconnect in the sentence by Cox comes from a fight between two different pictures that are mutually exclusive-- the Pauli exclusion principle, and the idea that electrons are individuals. This all stems from an incorrect way to state the principle, that "two electrons cannot be in the same state." States are how we predict the outcomes of experiments that involve electrons, but electrons are not distinguishable, so we should not pretend it makes precise sense to say "electron A is in state X and electron B is in state Y, where X and Y cannot be the same." If that sentence made perfect sense, there could not be a Pauli exclusion principle, because the correct way to say that principle is that the joint wave function of two electrons must acquire a minus sign when you swap the electron coordinates, which in turn implies that the joint wave function cannot involve two identical single-particle states. But notice it is still a joint wave function we are talking about, or we get no PEP!

    Of course, Cox is speaking to non-physicists, so there is great latitude in how we try to communicate the special features of quantum mechanics, without going into the details of joint wave functions. Hence if we are really being precise, we should not hold Cox to a standard of precision in the first place! But I do agree with the OP that the main "sin" in Cox's remark is that it swaps in causation where it should really only cite sources of correlation. A joint wave function is a source of correlation, but attributing causation to it is a much stickier issue and really depends on arbitrary interpretations.
     
    Last edited: Feb 7, 2014
  7. Feb 8, 2014 #6
    I think your idea of indistinguishable is slightly wrong. If they are in a different place the are mostly distinguishable!

    That said, the spatial overlap of the wave function, no matter how small, has to to be taken into account. It may be a blatant over-dramatisation, but hey that's show biz and Brian is doing a fabulous job in the U.K getting the youngsters interested in science; he's on prime-time TV a lot. All the best to him.
     
  8. Feb 8, 2014 #7

    Ken G

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    They are distinguishable in practice, sure, but Brian Cox is talking about imperceptible formal differences. If we are being perfectly precise, then we can never say two electrons "are in different places", because there is always some (incredibly tiny) probability we have lost track of which electron we are talking about, due to their indistinguishability. This manifests in ways that are related to the idea that entangled systems can present (very tiny) correlations even over vast distances. Entanglements can dwindle rapidly, and get to a point where we can ignore them and treat the electrons as though they were distinguishable, but it is never formally correct to do that. So it's the usual distinction between what quantum mechanics says as a formal theory, and the ways we really use it in practice (which involve idealizing the formal theory).
    Exactly, the wave function is formally a global thing, ever since the Big Bang. So all electrons are entangled, in some formal sense, which also means that none of them are distinguishable or individual. I think that is what Brian Cox is referring to, though if he is taking that stance, he should avoid language that he is doing anything to a particular electron.

    So he should not have said "Just gently warming it up, and put a bit of energy into it, so I’m shifting the electrons around. Some of the electrons are jumping into different energy levels." That language is not consistent with the rest of the point he is making, because it acts as though we have particular electrons within the diamond that we are doing something to. But what we are actually doing, if you take the perspective of quantum mechanics, is watching the wave function of the universe evolve in time, and any change in the outcome of observations on the diamond that involve electron behavior is entangled with the rest of the universe. If you say it that way, it's just a restatement of "spooky action at a distance," which is not controversial. It only sounds even weirder than that, and incorrectly so, if you say that doing something to some particular set of electrons is having an effect on some other particular set of electrons. It is the joint wave function that is involved, not particular electrons, or else you don't have a PEP.
     
  9. Feb 8, 2014 #8

    vanhees71

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    I think, the following blog puts this nonsense right:

    http://blogs.scienceforums.net/swansont/archives/11081

    which is quoted by Carrol (see bhobba's posting) in his also very clear statement, but I think one should clearly say that something is wrong when it is wrong. To popularize science is a very difficult issue and thus to some extent I can excuse if something is not presented accurately, but I don't think that popularization serves the purpose of science if it mystifies issues. Science is the opposite of mystifying things, and the public who is paying for a lot of very expensive science projects like the LHC has the right to be informed correctly about what comes out of this endeavor and not being mystified. If they want to have esoterics they can get it everywhere, but if somebody watches a feature about science on TV, he or she expects to be informed about science and not esoterics. Such nonsense claims do more harm than good for science and it's funding with tax payer's money!

    I don't know Brian Cox (I'm located in Germany), but such esoterics is quite common in popularizing science for the public. Once I've seen a TV feature in the German TV about the LHC, which only addressed bogus stuff like the creation of black holes that destroy the earth etc. instead of explaining the really exciting science which is really going on there and in other labs to figure out the fundamental building blocks of our universe. Science popularization doesn't need esoterics to make an exciting narrative about the scientific endeavor. It's fascinating enough by itself to make an exciting story in TV, public lectures, popular science books, etc. There are really very good popular-science things out there, e.g., what I've seen when I was in the US in features like NOVA was excellent. There's also a German-French TV channel (ARTE) available here in Germany that produces very good science features, including very good documentaries about particle physics, cosmology, dark matter, dark energy, Bose-Einstein condensates, etc. So it is in fact possible to popularize these complicated issues without getting them totally wrong!
     
  10. Feb 8, 2014 #9
    This blog post says


    How do we know that 'separate' systems are not entangled at the quantum level(ever since the Big Bang). Or is he taking a semi-classical look in expressing his opinion suggesting electrons are little balls?

    I probably shouldn't be saying this, but in general, the quantum physicists are a rather confused lot(due to the nature of the quantum world) so it's expected that noise will be generated when popularizing stuff they themselves don't understand. I am more worried for the ones who believe they truly understand it all well enough(now i am going into hiding).
     
    Last edited: Feb 8, 2014
  11. Feb 8, 2014 #10
    Separate systems would have a weak but permanent entanglement. This entanglement is "assumed" in standard quantum mechanics but it can be derived from the algebra of quantum field theory.

    I think Ken G's post makes a lot of sense.
     
  12. Feb 8, 2014 #11
    Also, quantum fields separated by spacelike intervals evolve independently (they don't commute), so there's now way interacting with the fields on earth could affect the fields at the edge of the universe.
     
  13. Feb 8, 2014 #12
  14. Feb 8, 2014 #13

    bhobba

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    Mate this is complicated stuff - people can and do make 'errors' all the time - I certainly do.

    Regarding this issue I think you need to go right back to basics and look at the Pauli exclusion principle. In fact it doesn't say electrons can't be in the same state. It says when electrons are interchanged then the wavefunction changes sign. This means for composite systems if they are in the same state the wavefuiction cancels ie is zero - which is not possible:
    http://www.physics.ohio-state.edu/~eric/teaching_files/writing.course/sample3.shortdraft.pdf [Broken]

    This applies to any electrons anywhere.

    But now for some caveats. If they are bound in different atoms the particles they are bound with are also part of the composite systems state. Then we have other particles they are entangled with. This gives a lot more freedom for those electrons wavefunctions to not cancel on exchange of electrons.

    Thanks
    Bill
     
    Last edited by a moderator: May 6, 2017
  15. Feb 8, 2014 #14

    bhobba

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    Errrrr. Cant see how you arrive at that.

    It looks spot on to me eg:
    'Well, no. The issue isn’t the Pauli Exlusion Principle itself — that’s sound science. It’s what he’s done with it. The first, obvious problem is that relativity tells us that the communication can’t be instantaneous. The second is that the Pauli Exclusion Principle doesn’t work this way. It applies to a single system in which you have all these identical electrons, and they can’t be in the same exact state. This is because of their QM behavior if you were to exchange them — something has to be different about the two electrons. In a crystal, the energies are slightly different as a result, and you get a band of energies. But this does not extend beyond the system, be it crystal or even individual atoms — the electrons belong to different systems, which are not co-located. Exchanging electrons meaning exchanging systems as well. That’s what’s different.'

    That's exactly the point I made. You have to go right back to what the Pauli exclusion principle says. Its a statement about electron exchange in composite systems. For two electrons its easy to see the electrons cant be in the same state because its state, in order to obey the exclusion principle is UaUb - UbUa. If Ua and Ub are the same then the wavefunction cancels so they cant be in the same state. For electrons in different atoms those atoms and electrons form the composite systems and there is a lot more freedom in preventing wavefunction cancellation on exchange ie the system state is a lot more complicated than UaUb - UbUa.

    Thanks
    Bill
     
  16. Feb 8, 2014 #15

    Ken G

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    The problem there seems to come down to the fact that Cox appears to equate a "state of identically equal energy" with "the identically same state", and I'm not sure why he does that. Had he just said that all electrons are indistinguishable, so there's always a tiny chance that if I think I'm doing something to an electron in a diamond, I'm actually doing it to an electron halfway across the universe, he would have been on firmer footing. Like entanglement, electron exchange is not constrained by the rules of relativity. But like the original poster said, the way causation works always ends up still being constrained by relativity, even though the correlations mediated by a joint wave function, and its implied entanglements and exchanges, are not. So it just seems like Cox is not distinguishing the kinds of things that should be limited by the speed of light, with those that need not be. Still, he is hardly the first to do that-- people who popularize entanglement often make little effort to make those kinds of distinctions, so doing the same with the PEP is not that shocking. I don't really like failing to make that distinction in either the entanglement or PEP contexts, but we should at least be fair about how we hand out our passes!
     
  17. Feb 9, 2014 #16
    Two ways:
    The part about the constraint to the speed of light of communication seemed totally irrelevant to the subject matter and the fact that entanglement wasn't mentioned once.

    Yes there was real science there, but short on QM.
     
  18. Feb 9, 2014 #17

    bhobba

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    Its not irrelevant.

    Obviously relativity prevents, as Brian stated, far away electrons instantaneously changing. That situation requires QFT - not QM - which is a whole new ball game.

    And yes Brian did not mention entanglement, which a close analysis shows is actually very important to understanding what's going on.

    The behavior of two electrons not entangled with anything, bound (which is really a form of entanglement) etc is contained by the fact the wave-function changes sign under electron exchange - that's why they can't be the same state. But when entangled its not that simple - not by a long shot eg the state depends on what its entangled with - so what state can't it be the same as?

    Thanks
    Bill
     
    Last edited: Feb 9, 2014
  19. Feb 9, 2014 #18
    I think we might be talking about different things. I was referring to the blog in post #12 by swansont.

    With regard to the entanglement isn't every electron entangled with everything other one? If so wouldn't you expect a change in the Hamiltonian of the system to affect every one somewhat?
     
  20. Feb 9, 2014 #19

    bhobba

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    I suspect we are.

    Of course not.

    For example, even though for simplicity its not analysed that way, but rather as simply being in a potential well, electrons in an atom are entangled with the nucleus. Its easy to see this because, if you move the nucleus then the electrons go along with it ie the electrons state depends on the state of the nucleus which is the definition of entanglement. This means the electrons bound in one atom are distinguishable from the electrons in another atom. Only the electrons in that atom are affected by changes in that atoms nucleus. This breaks the fundamental indistinguishably for the exclusion principle to hold.

    Thanks
    Bill
     
  21. Feb 9, 2014 #20

    Bill_K

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    No. It's called the Cluster Decomposition Principle.

     
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