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A night with the stars (Brian Cox on telly)

  1. Dec 19, 2011 #1

    I did enjoy Brian Cox's program on quantum mechanics last night, but one bit left me thinking "no, that's not right!".

    The gist of it was that all the electrons in the universe have to be in constant communication to ensure that no two of them are ever in the same state. If he changed the energies of electrons in a diamond, by heating it in his hand, all the other electrons in the world would have to adjust their energies too.

    I think this may have been an attempt to show that entanglement follows from the Pauli exclusion principle, but was it a simplification too far?

    The Pauli principle confused me when I first heard it at school: did it mean that no two hydrogen atoms in the universe could be in their ground states simultaneously? I have always understood, since then, that it doesn't mean that, because which proton the electron is bound to is part of its state. So "in the first energy level around this proton" is a different state from "in the first energy level around that proton".

    The exclusion principle states that no two electrons can be in the same *state* not, as Cox seemed to be implying, that they may not have numerically the same energies. That is not forbidden as far as I know. We would not see nice spectral lines from billions of hydrogen atoms all making the same state transition at the same time, if it was.

    I now know there is a deeper explanation of the exclusion principle, namely that the multi-particle wave-function of a half-integral spin particle is antisymmetric, and that means the probability of finding two of them in the same place is zero. So OK, Pauli and entanglement are connected. But I always like a simple explanation if one is available. What does the panel think? Did what Cox said amount to a good explanation for a general audience, or does it risk perpetuating a misunderstanding?
  2. jcsd
  3. Dec 19, 2011 #2
    Just wrote a long reply...only for these damned forums to sign me out...so I lost it. Arrgh, let me rattle up something similar...

    Basically, I too am confused by the application of Pauli's exclusion principle to the whole Universe. Do the states of the electrons really shift everywhere? And if so, how exactly do they shift - has this been measured? Nevertheless, it is freaking awesome.

    I thought his explanation was fair enough, given how ridiculously confused everyone would be if he started discussing particle states as well. Of course, in reality, overall wavefunction symmetry is a combination of both spatial and spin symmetry, and so for electrons, for example (which are overall antisymmetric fermions), if the spin symmetry is symmetric the spatial symmetry must be anti-symmetric.

    This stuff can be used to explain the how shells fill up but it is fairly complex. As I understand it (and I may well be wrong), there are two electrons in the ground state because it is spatially symmetric and has L = 0 (zero angular momentum) and so the only possible state is the anti-symmetric singlet state. For the next shell up you have L = 1, so ml = -1, 0, 1 and so the possibilities are the singlet state + the 3 possible triplet states, making 8 in total. I think that's right, anyway.
  4. Dec 19, 2011 #3
    Cox is still wrong. Pauli concerns 'states' in a (quantum) system not absolute energy levels throughout the universe.

    I can't believe it hasn't been more heavily reported/criticised.

    Unless he was being 'ironic'?
  5. Dec 19, 2011 #4
    I too was confused about this. Every fermion in the univerise is entangled with each other surely not. If what Cox siad is the true intrepretation then how is any calculation of the energy levels of an electron in an atom possible. As the potential energy in a shell is fixed so a change in energy state would result in emission or absorption of radiation. I don't quite see how this is possible.

    Maybe I have my reasoning backwards. Also I think he tried to do much in 1 hour. My wife stopped listening and started blowing rasburries (litterally) and I am sure most of auidence did not understand most of what he was on about.
  6. Dec 19, 2011 #5
    Like the other correspondants I also thought - No, that can't be right - when he claimed to be changing the state of all electrons by warming up the diamond. I that were the case there would have been no need for the increasingly elegant entanglement experiments which have been repoted over the last few years. I'm sure I was taught that Pauli applies to the individual atoms which is why we get characteristic phenomena like spectral lines for the individual elements.

    I'd be interested to see if there's any response from the BBC to growing comment in various forums.
  7. Dec 19, 2011 #6
    But on a level appropriate for his audience, he was correct. Yes, technically Pauli's principle determines the states of a quantum system, but since the expectation of the energy is simply the expectation of the Hamiltonian and is the bra-ket combination <wavefunction|hamiltonian|wavefunction>, it's obvious that by changing the wavefunction you are changing the energy.

    Since few in his audience know what a wavefunction is it would have been impractical to try and explain Pauli's exclusion principle in terms of that.

    It appears to me that he's making an argument based on the idea of indistinguishable/identical particles. Essentially, in quantum statistics, particles behave differently to how one would expect in classical physics because particles such as electrons are indistinguishable from each other. In other words, if you have two electrons and swap them it's equivalent to having done nothing to them, because no one can tell the difference between before and after.

    Likewise, my guess is that he's arguing that, in theory, it's possible for electrons far away from each other to be in identical environments relative to an identical nucleus. Thus, without knowledge of Pauli's Exclusion Principle one might expect them to have identical energy levels. Pauli, however, shows that is simply impossible.

    Perhaps that's something akin to Brian Cox's argument. I would love to hear him state the rigorous version of his pop sci comments.
  8. Dec 19, 2011 #7
    I am also concerned about the specifics of this statement. However, it appears to me that some microscopic property of a particle must be measured in order for the same property in other particles to be known. However, heating the diamond between his hands hardly constitutes a measurement of any microscopic property. The only thing that is measured is the average temperature on the surface of the diamond.

    Furthermore it seems to me that if it is the wavefunction of a large polyatomic system that is under question, then the situation is clearly different from that of modeling some part of the original system by considering it in isolation. The assumptions in these two cases are different.
  9. Dec 20, 2011 #8
    I am a little annoyed that Brian Cox has introduced the "woo woo" factor into science on national television. The "woo woo" factor I am referring to is something that has been highlighted several times in this thread and that is that rubbing the surface of a diamond will change the quantum states of a white dwarf 600 light years from here; essentially he is saying that everything is connected and invokes the Pauli Exclusion Principle to legitimise this claim. This is false.
    Even if he didn't want to confuse his audience with wavefunctions and bra-ket notations there is still conceptually a major difference between saying no two electrons can occupy the same energy state WITHIN ONE ATOM and no two electrons can occupy the state WITHIN ONE UNIVERSE. The former is the Pauli Principle and the later is plain metaphysics (perhaps even Buddhism!). The nearest we can get to applying the Pauli Principle to multiple atoms is when these atoms are Quantum Entangled which does mean instantaneous action at a distance but here the atoms need to be entangled in the first place. Thus rubbing a rough cut diamond will have no effect on the rest of the universe other than heating up the surface and making your finger sore.
    It would be nice for Brian Cox to add a more clear explanation as to why he thinks the whole universe is connected in the manner he has suggested and clear up the confusion he has caused.
  10. Dec 20, 2011 #9
    And the "confusion he has caused" is criminal.
  11. Dec 20, 2011 #10
    Not wishing to be argumentative but why be overly technical, since the diamond is being heated (or cooled for that matter) the only thing that is obvious that the energy of the system is being changed.

    Exactly when and how the 'energy level' of an electron changes isn't the issue, it's his assertion that all the electrons in the universe adjust their energy levels to ensure no two have the same; and that's just bollocks.
  12. Dec 20, 2011 #11


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    Does anyone have an exact quote or a link to a video? If it's a video that's more than a few minutes long, please include a statement about when the relevant statement begins.

    Cox has said weird things before. He began a terrible documentary about the LHC with the words "In the beginning, there was nothing. Absolutely nothing. And then, there was an explosion". Before that, I had only heard the big bang described like that by creationists. (The quote is from memory. I believe it's correct, but it's certainly possible that I don't remember it exactly right).
  13. Dec 20, 2011 #12
    Reference the transmitted program 18th Dec: 35mins in
    iPlayer may be different.
  14. Dec 20, 2011 #13
    Not sure if this is the right segment (I haven't got sound at the moment).

    From the comments above, it sounds to me like maybe he's talking about a non relativistic quantum mechanics treatment - a multiparticle wavefunction given by an antisymmetrized product of non interacting single particle wavefunctions. If any of the single particle ones have the same energy then the antisymmetrized product vanishes.
  15. Dec 20, 2011 #14
    For this clip: from 6:00 he talks about Pauli
  16. Dec 20, 2011 #15
    Seems to be some confusion here about the Pauli Principle. Jeff Forshaw and myself write about it in detail in our book The Quantum Universe, chapter 8. The essential point is that two widely separated hydrogen atoms should not be treated as isolated systems. If you'd like to see how we teach this to undergraduates in Manchester, have a read of this:

    http://www.hep.manchester.ac.uk/u/forshaw/BoseFermi/Double Well.html

    But I do also recommend our book, because the argument is extended to explain semiconductors.

    doodyone - in particular, I suggest you pay close attention, especially if you're an undergraduate. You might up your degree classification!

  17. Dec 20, 2011 #16
    Can you say anything about the relativistic case (assuming the word "instantaneous" was used in the clip - which I'll have to listen to when I get home !). You don't have an instantaneous shift in energy across spacelike separations presumably, otherwise you could signal ?
  18. Dec 20, 2011 #17
    That link becox is very illuminating. As the wavefunction of two electrons "overlaps" no how far they are they cannot be thought as localised or discrete anymore. So what happens to one effects the other. So Cox is right in a sense, is that right? If i understand that page properly then my understanding of the exclusion principle has certainly evolved.
  19. Dec 20, 2011 #18
    Ye we were watching this in class and the first thing I said when he said that a particle here affected all the others in the world was: "but not instantly" I mean don't mess with relativity again, enough with the neutrinos thing :rofl:. The thing that I find closer to all the particles being "connected" is the fact that they interact by forces, this means that if you do somthing to a particle here, the force that all the other particles in the world will "feel" will be different and their energy will therefore be different. However, this doesn't happen instantly at all, as the particles by which the forces interact travel at a finite speed. When the two particles interact, they become then entangled, and therefore most particles in the universe are entangled (at least those that have existed for long enough so that a force-carrier might have been exhanged between them. However, I don't see why is the Pauli exclusion princpile necessary. Of course, no two particles can be in the same state because then they will be the same particle, but that doesn't imply that two particles cannot be in the same energy level, because their position is already different.
    I wonder however that if we consider that the energy of an electron doesnt only depend on his position with respect to the nucleus but (in a muuuch lesser degree) in the position of all the rest of particles in the world, then in fact changing a certain particle around here will change the energy in that particle, but not instantly and with very little effect as long as it is not very close or something, which is the case in superconductors. I agree that everything is connected, but if things are far apart they are connected with thier pasts (relativity). I think this should have been noted when saying this "woo woo" fact on telly. BTW if something I said is wrong tell me, because my background on quantum mechanics is far from solid
  20. Dec 20, 2011 #19
    That is genius. Thanks for the link, it makes a lot of sense to me (or at least I think it does!).

    To summarise the argument as I see it, it's essentially saying that since no potential barrier can really be infinite the wavefunction of each electron must overlap into other possible potential wells of other atoms. So if you simplify the model and have two electrons in their respective wells, separated by a large potential barrier in the middle, with infinite potential at either end, the wavefunctions of each electron will overlap into the others well. Thus you have to think of the overall wavefunction as a combination of all possible wavefunctions.

    Mathematically, it's shown that, when looking at the possible solutions for an individual electron, the wavefunction can have either odd or even parity. When this is combined with the large wavefunction of the electron in the other well, this splits the energies, creating a degeneracy. The degeneracy is only tiny though, so both electrons are seen at being almost exactly the same energy in their respective potential wells. If you were to change the energy level of one of the electrons though, we're forced to conclude that the overlap of the wavefunction into the other potential well would change and consequently the wavefunction of the system as a whole would change.

    Spooky action at a distance indeed.
    Last edited: Dec 20, 2011
  21. Dec 20, 2011 #20
    Thanks for responding, Brian. Your book is already on my Christmas list :smile:

    I think I follow your double-well example. It is effectively a model of the hydrogen molecule. So yes, there are in principle two energy levels however far apart the protons get, and for N protons, N energy levels. (And the time to oscillate from the vicinity of one atom to the other is proportional to the difference in the energy levels - a very long time if they are far apart)

    So if we take the view that an electron is free to roam the entire universe, then whenever we move a bit of matter we change the Hamiltonian and shift all those energy levels a bit. (And that is true for a single electron, without even considering a multi-particle wave functions and entanglement). I think the problem (as always) is how to put this into ordinary language.

    "Every electron around every atom in the universe must be shifting as I heat the diamond up to make sure that none of them end up in the same energy level. When I heat this diamond up all the electrons across the universe instantly but imperceptibly change their energy levels. So everything is connected to everything else".

    So, to be picky
    1) On the view of universe-wide wave-functions, we are really giving up the idea of atoms with localized electrons. And any electron that is known to be, say, in a white dwarf star, is not in a universe-wide energy eigenstate, so does not have a definite energy. If we allow ourselves to talk about "every electron around every atom in the universe", and think of those electrons as having definite energy levels, then we are making the approximation that the atoms can be treated independently.

    2) If we are talking about the effect of changing the Hamiltonian, and not an entanglement effect, then surely that influence can not travel faster then light, so the change will not be instantaneous?

    But as I said that is being picky. It is probably impossible to explain QM to a general audience without saying something that will upset the physics geeks. And this has upset a few:


    http://sciencefocus.com/forum/pauli-exclusion-principle-brian-cox-night-with-the-stars-t2393.html [Broken]

    Nevertheless, I think you are doing a great job of explaining science to the masses and I look forward to reading the book.
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