Everything is Connected

By Sean Carroll | February 23, 2012 10:09 am

They do things differently over in Britain. For one thing, their idea of a fun and entertaining night out includes going to listen to a lecture/demonstration on quantum mechanics and the laws of physics. Of course, it helps when the lecture is given by someone as charismatic as Brian Cox, and the front row seats are filled with celebrities. (And yes I know, there are people here in the US who would find that entertaining as well — I’m one of them.) In particular, this snippet about harmonics and QM has gotten a lot of well-deserved play on the intertubes.

More recently, though, another excerpt from this lecture has been passed around, this one about ramifications of the Pauli Exclusion Principle. (Headline at io9: “Brian Cox explains the interconnectedness of the universe, explodes your brain.”)

The problem is that, in this video, the proffered mind-bending consequences of quantum mechanics aren’t actually correct. Some people pointed this out, including Tom Swanson in a somewhat intemperately-worded blog post, to which I pointed in a tweet. Which led to some tiresome sniping on Twitter, which you can dig up if you’re really fascinated. Much more interesting to me is getting the physics right.

One thing should be clear: getting the physics right isn’t easy. For one thing, going from simple quantum problems of a single particle in a textbook to the messy real world is often a complicated and confusing process. For another, the measurement process in quantum mechanics is famously confusing and not completely settled, even among professional physicists.

And finally, when one translates from the relative clarity of the equations to a natural-language description in order to reach a broad audience, it’s always possible to quibble about the best way to translate. It’s completely unfair in these situations to declare a certain popular exposition “wrong” just because it isn’t the way you would have done it, or even because it assumes certain technical details that the presenter did not fully footnote. It’s a popular lecture, not a scholarly tome. In this kind of format, there are two relevant questions: (1) is there an interpretation of what’s being said that matches the informal description onto a correct formal statement within the mathematical formulation of the theory?; and (2) has the formalism been translated in such a way that a non-expert listener will come away with an understanding that is reasonably close to reality? We should be charitable interpreters, in other words.

In the video, Cox displays a piece of diamond, in order to illustrate the Pauli Exclusion Principle. The exclusion principle says that no two fermions — “matter” particles in quantum mechanics, as contrasted with the boson “force” particles — can exist in exactly the same quantum state. This principle is why chemistry is interesting, because electrons have to have increasingly baroque-looking orbitals in order to be bound to the same atom. It’s also why matter (like diamond) is solid, because atoms can’t all be squeezed into the same place. So far, so good.

But then he tries to draw a more profound conclusion: that interacting with the diamond right here instantaneously affects every electron in the universe. Here’s the quote:

So here’s the amazing thing: the exclusion principle still applies, so none of the electrons in the universe can sit in precisely the same energy level. But that must mean something very odd. See, let me take this diamond, and let me just heat it up a bit between my hands. 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. But this shift of the electron configuration inside the diamond has consequences, because the sum total of all the electrons in the universe must respect Pauli. Therefore, every electron around every atom in the universe must be shifted 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.

(Minor quibble: I don’t think that rubbing the diamond causes any “jumping” of electrons; the heating comes from exciting vibrational modes of the atoms in the crystal. But maybe I’m wrong about that? And in any event it’s irrelevant to this particular discussion.)

At face value, there’s no question that what he says here lies somewhere between misleading and wrong. It seems quite plain (that’s the problem with being a clear speaker) that he’s saying that the energy levels of electrons throughout the universe must change because we’ve changed the energy levels of some electrons here in the diamond, and the Pauli exclusion principle says that two electrons can’t be in the same energy level. But the exclusion principle doesn’t say that; it says that no two identical particles can be in the same quantum state. The energy is part of a quantum state, but doesn’t define it completely; we need to include other things like the position, or the spin. (The ground state of a helium atom, for example, has two electrons with precisely the same energy, just different spins.)

Consider a box with non-interacting fermions, all in distinct quantum states (as they must be). Take just one of them and zap it to move it into a different quantum state, one unoccupied by any other particle. What happens to the other particles in the box? Precisely nothing. Of course if you zap it into a quantum state that is already occupied by another particle, that particle gets bumped somewhere else — but in the real universe there are vastly more unoccupied states than occupied ones, so that can’t be what’s going on. Taken literally as a consequence of the exclusion principle, the statement is wrong.

But it’s possible that there is a more carefully-worded version of the statement that relies on other physics and is correct. And we might learn some physics by thinking about it, so it’s worth a bit of effort. I think it’s possible to come up with interpretations of the statement that make it correct, but in doing so the implications become so completely different from what the audience actually heard that I don’t think we can give it a pass.

The two possibilities for additional physics (over and above the exclusion principle) that could be taken into account to make the statement true are (1) electromagnetic interactions of the electrons, and (2) quantum entanglement and collapse of the wave function. Let’s look at each in turn.

The first possibility, and the one I actually think is lurking behind Cox’s explanation, is that electrons aren’t simply non-interacting fermions; they have an electric field, which means they can interact with other electrons, not to mention protons and other charged particles. If we change the ambient electric field — e.g., by moving the diamond around — it changes the wave function of the electrons, because the energy changes. Physicists would say the we changed the Hamiltonian, the expression for the energy of the system.

There is an interesting and important point to be made here: in quantum mechanics, the wave function for a particle will generically be spread out all over the universe, not confined to a small region. In practice, the overwhelming majority of the wave function might be localized to one particular place, but in principle there’s a very tiny bit of it at almost every point in space. (At some points it might be precisely zero, but those will be relatively rare.) Consequently, when I change the electric field anywhere in the universe, in principle the wave function of every electron changes just a little bit. I suspect that is the physical effect that Cox is relying on in his explanation.

But there are serious problems in accepting this as an interpretation of what he actually said. For one thing, it has nothing to do with the exclusion principle; bosons (who can happily pile on top of each other in the same quantum state) would be affected just as much as fermions. More importantly, it fails as a job of translation, by giving people a completely incorrect idea of what is going on.

The point of this last statement is that when you say “When I heat this diamond up all the electrons across the universe instantly but imperceptibly change their energy levels,” people are naturally going to believe that something has changed about electrons very far away. But that’s not true, in the most accurate meaning we can attach to those words. In particular, imagine there is some physicist located in the Andromeda galaxy, doing experiments on the energy levels of electrons. This is a really good experimenter, with lots of electrons available and the ability to measure energies to arbitrarily good precision. When we rub the diamond here on Earth, is there any change at all in what that experimenter would measure?

Of course the answer is “none whatsoever.” Not just in practice, but in principle. The Hamiltonian of the universe will change when we heat up the diamond, which changes the instantaneous time-independent solutions to the Schoedinger equation throughout space, so in principle the energy levels of all the electrons in the universe do change. But that change is completely invisible to the far-off experimenter; there will be a change, but it won’t happen until the change in the electromagnetic field itself has had time to propagate out to Andromeda, which is at the speed of light. Another way of saying it is that “energy levels” are static, unchanging states, and what really happens is that we poke the electron into a non-static state that gradually evolves. (If it were any other way, we could send signals faster than light using this technique.)

Verdict: if this is what’s going on, there is an interpretation under which Cox’s statement is correct, except that it has nothing to do with the exclusion principle, and more importantly it gives a quite false impression to anyone who might be listening.

The other possibly relevant bit of physics is quantum entanglement and wave function collapse. This is usually the topic where people start talking about instantaneous changes throughout space, and we get mired in interpretive messes. Again, these concepts weren’t mentioned in this part of the lecture, and aren’t directly tied to the exclusion principle, but it’s worth discussing them.

There is something amazing and magical about quantum mechanics that is worth emphasizing over and over again. To wit: unlike in classical mechanics, there are not separate states for every particle in the universe. There is only one state, describing all the particles; modest people call it the “many-particle wave function,” while visionaries call it the “wave function of the universe.” But the point is that you can’t necessarily describe (or measure) what one particle is doing without also having implications for what other particles are doing — even “instantaneously” throughout space (although in ways that have to be carefully parsed).

Imagine we have a situation with two electrons, each in a separate atom, with different energy levels in each atom. Quantum mechanics tells us that it’s possible for the system to be in the following kind of state: each electron is either in energy level 1 or energy level 2, and we don’t know which one (more carefully, they are in a superposition), but we do know that they are in different energy levels. So if we measure the first electron and find it in level 1, we know for sure that the other electron is in level 2, and vice-versa. This is true even if the two electrons are a jillion miles away from each other.

As far as I can tell, this isn’t at all what Brian Cox was talking about; he discusses heating up the electrons in a diamond by rubbing on it, not measuring their energies by observing them and then drawing conclusions about entangled electrons very far away. (In a real-world context it’s very unlikely that distant electrons are entangled in any noticeable way, although strictly speaking you could argue that everything is slightly entangled with everything else.) But there is some underlying moral similarity — this is, as mentioned, the context in which people traditionally talk about instantaneous changed in quantum mechanics.

So let’s go back to our observer in Andromeda. Imagine that we have such a situation with two electrons in two atoms, in a mutually entangled state. We measure our electron to be in energy level 1. Is it true that we instantly know that our far-away friend will measure their electron to be in energy level 2? Yes, absolutely true.

But consider the same experiment from the point of view of our far-away friend. They know what the state of the electrons is, so they know that when they observe their electron it will be either in level 1 or level 2, and ours will be in the other one. And let’s say they even know that we are going to make a measurement at some particular moment in time. What changes about any measurement they could make on their electron, before and after we measure ours?

Absolutely nothing. Before we made our measurement, they didn’t know the energy level of their electron, and would give 50/50 chances for finding it in level 1 or 2. After we made our measurement, it’s in some particular state, but they don’t know what that state is. So again they would give a 50/50 chance for getting either result. From their point of view, nothing has changed.

It has to work out this way, of course. Otherwise we could indeed use quantum entanglement to send signals faster than light (which we can’t). Indeed, note that we had to refer to “time” in some particular reference frame, stretching across millions of light-years. In some other frame, relativity teaches us that the order of measurements could be completely different. So it can’t actually matter. It’s possible to say that the wave function of the universe changes instantaneously throughout space when we make a measurement; but that statement has no consequences. It’s just one of an infinite number of legitimate descriptions of the situation, corresponding to different choices of how we define “time.”

Verdict: I don’t think this is what Cox was talking about. He doesn’t mention entanglement, or collapse of the wave function, or anything like that. But even if he had, I would personally judge it extremely misleading to tell people that the energy of very far-away electrons suddenly changed because I was rubbing a diamond here in this room.

Just to complicate things a bit more, Brian in a tweet refers to this discussion of the double-well potential as some quantitative justification for what he’s getting at in the lecture. These notes are a bit confusing, but I’ve had a go at them.

The reason they are confusing is because they start off talking about the exclusion principle and indistinguishable particles, but when it comes time to look at equations they only consider single-particle quantum mechanics. They have a situation with two “potential wells” — think of two atoms, perhaps quite far away, in which an electron might find itself. They then consider the wave function for a single electron, ψ(x). And they show, perfectly correctly, that the lowest energy states of this system have nearly identical energies, and have the feature that the electron has an equal probability of being in either of the two atoms.

Which, as far as it goes, is completely fine. It illustrates an interesting example where the lowest-energy state of the electron can be really spread out in space, rather than being localized on a single atom. In particular, the very existence of the other atom far away has a tiny but (in principle) perceptible effect on the shape of the wave function in the vicinity of the nearby atom.

But this says very little about what we purportedly care about, which is the Pauli exclusion principle, something that only makes sense when we have more than one electron. (It says that no two electrons can be in the same state; it has nothing interesting to say about what one electron can do.) It’s almost as if the notes cut off before they could be finished. If we wanted to think about the exclusion principle, we would need to think about two electrons, with positions let’s say x1 and x2, and a joint quantum wave function ψ(x1, x2). Then we would note that fermions have the property that such a wave function must be “odd” in its arguments: ψ(x1, x2) = -ψ(x2, x1). Physically, we’re saying that the wave function goes to minus itself when we exchange the two particles. But if the two particles were in exactly the same state, the wave function would necessarily be unchanged when we exchanged the particles. And a function that is both equal to another function and equal to minus that function is necessarily zero. So that’s the exclusion principle: given that minus sign under exchange, two particles can never be in precisely the same quantum state.

The notes don’t say any of that, however; they just talk about the two lowest energy levels in a double-well potential for a single electron. They don’t demonstrate anything interesting about the exclusion principle. The analysis does imply, correctly, that changing the Hamiltonian of a particle somewhere far away (e.g. by altering the shape of one of the wells) changes, even if by just a little bit, the energy of the wave function defined over all space. That’s connected to the first possible interpretation of Cox’s lecture above, that heating up the diamond changes the Hamiltonian of the universe and therefore affects the wave function of every electron. Which also has nothing to do with the exclusion principle, so at least it’s consistent.

In terms of explaining the mysteries of quantum mechanics to a wide audience, which is the point here, I think the bottom line is this: rubbing a diamond here in this room does not have any instantaneous effect whatsoever on experiments being done on electrons very far away. There are two very interesting and conceptually central points worth making: that the Pauli exclusion principle helps explain the stability of matter, and that quantum mechanics says there is a single state for the whole universe rather than separate states for each individual particle. But in this case these became mixed up a bit, and I suspect that this part of the lecture wasn’t the most edifying for the audience. (The rest of the lecture still remains pretty awesome.)

Update: I added this as a comment, but I’m promoting it to the body of the post because hopefully it makes things clearer for people who like a bit more technical precision in their quantum mechanics. [Note the mid-update extra update.]

Consider the double-well potential talked about in the notes I linked to near the end of the post. Think of this as representing two hydrogen nuclei, very far away. And imagine two electrons in this background, close to their ground states.

To start, think of the electrons as free particles, not interacting with each other. (That’s a very bad approximation in this case, contrary to what is said in the notes, but we can fix it later.) As the notes correctly state, for any single electron there will be two low-lying states, one that is even E(x) and one that is odd O(x). When we now add the other electron in, they can’t both be in the same lowest-lying state (the even one), because that would violate Pauli. So you are tempted to put one in E(x1) and the other in O(x2).

But that’s not right, because they’re indistinguishable fermions. The two-particle wave function needs to obey ψ(x1, x2) = -ψ(x2, x1). So the correct state is the antisymmetric product: ψ(x1, x2) = E(x1) O(x2) – O(x1) E(x2).

That means that neither electron is really in an energy level; they are both part of an entangled superposition. If you zap one of them into a completely different energy, nothing whatsoever happens to the other one. It would now be possible for the other one to decay to be purely in the ground state, rather than a superposition of E and O, but that would require some interaction to allow the decay. (All this is ignoring spins. If we allow for spin, they could both be in the ground-state energy level, just with opposite spins. When we zapped one, what happens to the other is again precisely nothing. That’s what you get for considering non-interacting particles.)

[Second update: the below two italicized paragraphs are wrong, my bad. It’s actually quite a good approximation (although still an approximation) to ignore the electromagnetic interactions of the electrons, because after antisymmetrization you will almost always find precisely one electron in each well. If electrons were bosons, you’d get a similar quantum state because the interactions would be important, but for fermions the exclusion principle does the job. Final paragraph is still okay.]

But of course it’s a very bad approximation to ignore the interaction between the two electrons, precisely because of the above analysis; it’s not true that one is here and one is far away, they both are equally distributed between being here and being far away, and can interact noticeably.

Since electrons repel, the true ground state is one in which the wave function for one is strongly concentrated one one hydrogen atom, and the wave function for the other is strongly concentrated on the other. Of course it’s the antisymmetrized product of those two possibilities, because they are identical fermions. The energies of both are identical.

Now when you zap one electron to change its energy, you do change the energy of the other one, in principle. But it has nothing to do with the exclusion principle; it’s just because you’ve changed the amount of electrostatic repulsion by changing the spatial wave function of one of the electrons.

Furthermore, while you instantaneously change “the energy levels” available to the far-away electron by jiggling the one nearby, you don’t actually change the position-space wave function in the far-away region at all. As I said in the post, you’ve poked the other electron into a superposition rather than being in an energy eigenstate. Its wave function (to the extent that we can talk about it, e.g. by integrating out the other particles) is now a function of time. And the place where it’s actually evolving is completely inside your light cone, not infinitely far away. So there is literally nothing someone could do, in principle as well as practice, to detect any change as a far-away observer.

  • Jeremy

    I humbly submit that you’ve all got yourselves tied up in conceptual knots by not being clear enough about the distinction between language and reality — i.e. mathematical formalisms etc. (which consist of symbols) and the physical things they purport to describe (which consist of what the symbols refer to).

    I have yet to come across the physicist who was clear in his own mind about whether the wave function was one or the other.

  • Pingback: Brian Cox up the Exclusion Principle « In the Dark()

  • Mark Weitzman

    Clearly I agree with Sean’s analysis – but I am still confused when I study Quantum Field theory and they mention the cluster decomposition principle (see Weinberg’s QFT text vol. 1) stating that distant experiments are uncorrelated in contradiction with QM discussions of EPR experiments.

  • James

    Actually, I’m pretty sure he isn’t considering the electromagnetic interactions of the electrons, given that he has pointed to this page:

    http://www.hep.manchester.ac.uk/u/forshaw/BoseFermi/Double%20Well.html

    several times in defence of his statement, and in the second paragraph he says “Let us simplify the situation a little bit by neglecting the interaction between the two electrons”.

    But I’m with you on the “everybody goofs” thing. Personally I think he (and you and every other physicist with large exposure) deserves a large amount of leeway for talking to the public about physics and taking the risk of saying something that makes you look silly in front of your peers.

  • http://www.scottaaronson.com Scott Aaronson

    Sean, quick physics question (admittedly a naive and not very well-defined one): to what extent does the stability of matter “really” rely on the exclusion principle, and to what extent does it simply rely on electromagnetic repulsion? I agree that the former keeps the electrons around a given atom from all falling into the same orbit, but isn’t the latter more responsible for different atoms not piling on top of each other?

    • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean Carroll

      Scott, it’s a really good question that doesn’t get talked about in physics courses nearly as carefully as it should. But I believe it does depend on the exclusion principle (although electromagnetism is also crucial, obviously). At the very least, the orbital structure of electrons in atoms depends on the exclusion principle, and therefore chemistry does, and therefore the stability of matter does. But we like to think that the EP implies that atoms are kind of like hard spheres. I think that’s true, although I’ve never seen a careful derivation. Certainly without the EP you could literally pile atoms on top of each other in the same place; the net electrostatic repulsion would be zero, as the nuclei cancels the electrons. But there might not be stable solutions of that form, since the nuclei themselves (packed into a tinier space than the atoms) would repel.

      Alternatively: what would the world look like if electrons were bosons? Chemistry and matter would certainly be different, but I’m not sure what the density of different materials would look like.

  • http://mattleifer.info Matt Leifer

    My interpretation of what Brian Cox was trying to say is slightly different, but not necessarily more likely. Since the Pauli exclusion principle comes from the requirement that the global wavefunction of a bunch of fermions has to be antisymmetric under exchange, you can argue that there is a sense in which all the electrons in the universe are entangled, e.g. in a universe of only 2 electrons with two possible positions “here” and “far away”, the wavefunction would have to be of the form:

    psi(1,here) psi(2,far) – psi(1,far)psi(2,here)

    This looks like it is entangled, but there is nothing you could do to prove it by local measurements, since you can’t do a measurement that distinguishes 1 from 2 in any way.

    Of course, anyone who has read Sakurai knows that, if we only have access to observables in the “here” region, then this state will be indistinguishable from a single particle state psi(here), which is manifestly local. If you are one of those people who think of wavefunctions as being physically real, then there is one description in which Brian is correct and one in which he is incorrect and since they are operationally equivalent it is impossible to adjudicate. Of course, if you insist on only regarding measurement outcomes as physically real, then you will never observe any nonlocality this way, and I don’t think anyone would argue with that.

    There is an important point in all of this though. There is no such thing as “the wavefunction” of a set of quantum systems. The appropriate quantum state to use depends on what observables we have access to and what operations we have the ability to perform on systems. These are determined by symmetries and whether or not we have access to a system that breaks the symmetry. This is not just a matter of pure states sometimes being indistinguishable from mixed states, as in decoherence. There are also cases where a pure state representation get replaced by a different one, as this example shows.

    I consider this yet another reason to view the quantum state as a bearer of information, rather than a representation of reality. I’d be interested to hear what a many-worlds advocate like Sean has to say about it.

  • http://thefloatinglantern.wordpress.com Tim Martin

    Can someone tell me, or tell me where I can read, why no two fermions can have the same quantum state?

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean Carroll

    Matt– I have to run, so a half-thought-out answer will have to suffice. I am willing to say “the wave function is real,” but I mean that in the same way I might say “the metric is real” or “the vector potential is real.” That is, they are real once some gauge/frame/coordinates have been chosen. The description might be (certainly is, actually) highly non-unique.

    But the important thing is that we do believe in things called “what we can observe,” which should be independent of those choices. In a popular talk when we’re trying to increase the accuracy of people’s inner picture of the world, it’s often a good idea to stick to observable things.

  • TimG

    Apparently it was Freeman Dyson and Andrew Lenard who proved that degeneracy pressure is crucial in providing the stability of solid matter. Here are some citations I found on Wikipedia; I haven’t read the papers in question:
    FJ Dyson and A Lenard: Stability of Matter, Parts I and II (J. Math. Phys., 8, 423-434 (1967); J. Math. Phys., 9, 698-711 (1968) ); FJ Dyson: Ground-State Energy of a Finite System of Charged Particles (J.Math.Phys. 8, 1538-1545 (1967) )

  • http://www.physicsofsuperheroes.com Jim Kakalios

    Sean, you wrote: “And finally, when one translates from the relative clarity of the equations to a natural-language description in order to reach a broad audience, it’s always possible to quibble about the best way to translate. It’s completely unfair in these situations to declare a certain popular exposition “wrong” just because it isn’t the way you would have done it, or even because it assumes certain technical details that the presenter did not fully footnote. ”

    I’m sorry, but what was in the viedo is wrong. The Pauli Principle does not say that no two electrons can ever be in exactly the same quantum state. I can have an electron in Brian Cox’s studio, and another in Minneapolis, and they can be in exactly the same quantum state, because under this circumstance they are distinguishable. It is only when they are allowed to come so close together that their single particle wavefunctions overlap, and that then we can not make a meanignful distinction betwen the electron on the left and the one on the right that we must invoke Pauli. If what Brian Cox said were correct, then classical statistical mechanics would never work. We would always have to use Fermi-Dirac or Bose-Einstein statistics. But we know that at either low densities (so that the particles are well separated) or at high temperatures (so that the deBroglie wavelengths are small) that one can correctly employ Maxwell Boltzmann statistics (with the Gibbs degeneracy factor).

    Now, there are all aorts of interesting things one can say about how electrons satisfy the Pauli Principle when their wavefunctions overlap in a solid. If they are able to be in the same spatial location, then they must be in distinct momentum states – and one has a metal. Alternatively, they can all have exactly the same momentum state, if I put each electron in a separate box, as in a covalent bond in diamond.

    But it is not true that all electrons are connected to all other electrons, and to phrase it in this manner, by a mainstream physicist and author of several popular science books, provides support to believers in Quantum Woo.

  • TimG

    And here’s a video of Dyson talking about it:
    http://www.webofstories.com/play/4414

  • http://mattleifer.info Matt Leifer

    Sean — I am not sure about this analogy. In the case of GR, we can define everything and write down the equations of the theory in a coordinate free manner. The analogy to that would be some surrogate for the wavefunction that does not depend on the choice of accessible observables. However, the latter are needed to even define the Hilbert space, so I don’t see what the surrogate could be, at least in any conventional formulation of quantum theory.

    A many-worlder would usually define what can be observed in terms of the unitary evolution of the wavefunction (see Zurek’s argument to this effect http://arxiv.org/abs/quant-ph/0703160), but if the observables are needed to determine the correct wavefunction then isn’t this reasoning circular?

  • OldBob

    “Consider a box with non-interacting fermions, all in distinct quantum states (as they must be). Take just one of them and zap it to move it into a different quantum state, one unoccupied by any other particle. What happens to the other particles in the box? Precisely nothing. Of course if you zap it into a quantum state that is already occupied by another particle, that particle gets bumped somewhere else — but in the real universe there are vastly more unoccupied states than occupied ones, so that can’t be what’s going on. Taken literally as a consequence of the exclusion principle, the statement is wrong.”

    But surely Cox’s point is that if one considers two vastly separated atoms then if they both had excited states of *exactly* the same energy, and if say the atom on the left’s excited state was occupied already by its electron, then ‘zapping’ the atom on the rights electron into its excited state would zapping it into an already occupied state (ignoring the possibility of different spins etc), and would thus violate Pauli. I guess the excitation of the right hand electron doesn’t have to bump the left hand one somewhere else though, it could just mean that the right hand atoms excited state is ever so slightly different than the left’s.

  • Jeremy

    “That is, they are real once some gauge/frame/coordinates have been chosen. ”

    Some things “exist” in the sense that we can utter truths about them, but but they aren’t qute “real” in the sense that they don’t cause anything. For example, it’s true that the center of gravity of my hat is right in the middle of my head, but it doesn’t cause any harm to my brain because it isn’t really “real” in the second sense. If I re-define “my hat” its center of gravity moves somewhere else.

    The words ‘affect’ and ‘effect’ get used a lot in physics, but they aren’t used with much care. You can see this when cause and effect straddle the language-reality barrier.

    As another example of this silly confusion, consider “we can define everything” — without apparently caring whether we are defining terms (some of which can be defined) and the things the terms refer to (none of which can be defined).

    Let’s “get real” shall we?

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean Carroll

    Matt– sorry, still rushing, but… I think we should start with unitary evolution of the wavefunction, and get everything from that. (I.e. not start with observables.) We have a point in some manifold CP^n that evolves on a sub-torus. Everything else is taking subspaces, and that’s where things get interesting.

    Easy for me to say! Obviously carrying this program from start to finish isn’t something I’ve ever done, but maybe somebody has.

  • CEV

    ‘they are real once some gauge/frame/coordinates have been chosen.’

    there must exist at least one object which is measurable, but does not abide to a specific set of co-ordinates. Some Euclidean restrictions might hold true, but not all. Any static, smooth field configuration is topologically trivial. (as it goes to zero by a homotopy restriction). The image of the set of critical points of a smooth function f from one Euclidean space or manifold to another has Lebesgue measure. Can there exist finite-energy static critical points, in more than one spatial dimension?

  • Moshe

    “quantum mechanics says there is a single state for the whole universe rather than separate states for each individual particle”

    Isn’t this statement true already in classical physics? Different particles can interact and/or be correlated without being quantum (and gravity guarantees that “everything is connected” already on the classical level). In fact, seems to me that statement, when referring to the whole universe, is much more unproblematic in classical mechanics than it is in quantum mechanics.

  • Chris

    @7 Tim
    Good read “Pauli’s Exclusion Principle: The Origin and Validation of a Scientific Principle” also
    “The Story of Spin”

  • zwi swoo

    Let’s call a spade a spade here – the fundamental problem is that Brian Cox isn’t a particularly profound or interesting or productive physicist. He’s done nothing – besides being dishy – that should make him a de facto public spokesperson for the LHC or for ATLAS, and basically milks his good looks and B-list musician status for TV appearance after TV appearance, newspaper articles, and even a frickin TED talk. Especially when even the best can make mistakes in talking about quantum mechanics, it was never exactly unexpected that he would get it wrong. [FWIW, I hope I’m not understood to be arguing that dishiness is incompatible with academic intellect – Robert Nozick and Lisa Randall both count as hella dishy, and I trust no-one thinks of either as intellectually uninteresting. But Cox has been selected for on the appearance metric, not the accomplishment one]

  • Igor Khavkine

    @Scott#5, @Sean#8:

    Some classic results on the stability of matter are summarized in Lieb’s Rev.Mod.Phys. 48 553 article. Pauli exclusion does matter (Sec. IV). The Coulomb energy is the same for bosons and fermions, but the estimates for the kinetic energy are different. For fermions, one can show the existence a lower bound on the total energy per particle. Such a bound precludes the particle density from piling up in an arbitrarily small volume. For bosons, one can show that the energy per particle can be made arbitrarily large and negative, with a sufficiently large number of particles.

  • PL Hayes

    Those double well potential notes are confusing, and incomplete, but what if you do complete them (i.e. make localised states for a left electron and a right electron out of the sum and difference [resp.] of those even (E) and odd (O) energy eigenstates, then antisymmetrise the product to find you get something like -E⊗O + O⊗E)? Could that be what Brian Cox had in mind?

  • Rebeka Fox

    I am at a disadvantage in not being at an advanced stage of learning with respect to these principles. But, I would like to say that–all things aside–I like the abstraction created by the statement that in fact no two electrons can exist in the same state throughout the universe. Not only would such an abstraction represent a profound change in thinking, but has the potential to defend or rebuke a number of theories that explain observable phenomena. Regardless of whether or not Brian Cox has taken the correct approach on how this could be evaluated as an emergent property of the physical universe, this idea represents new thinking and that must be applauded. Who isn’t guilty of getting a little ahead of themselves?

    Maybe the idea just needs a little more time to be thought through in a deeper mathematical sense that more accurately reflects the standard current approach to QM. Brian Cox is adamant about his not introducing new physics but maybe the idea warrants a new approach, even if this wasn’t his intention. I have read a lot of opinions today and it has given me a lot to think about as I continue to develop my own opinions on the matter. My first immediate thought is to reduce this statement to there is a symmetry such that no two charges maintain identical wavefunctions with respect to their local frames. In whatever respect, the idea will plague me to my end I’m sure!

  • CEV

    correction on: 17. CEV Says:
    February 23rd, 2012 at 1:35 pm

    Lebesgue measure zero** (null)

    Dr. Carroll, I would be very thankful if you would blog about the Higgs field and Higgs mechanism. To be more precise, it has been stated in the literature of the standard model, that a field ‘phi’ is a multiplet coupled with complex scalar fields that transform a representation of a non-abelian lie-group G coupled with a one-form gauge potential. What would be the effects of introducing gauge potentials of higher forms? I understand that adding a quadratic term with respect to the gauge potential would break gauge symmetry, but does the idea of the higgs field being a constant as it approaches infinity hold? How can we preserve the ground-state when working with finite energy lagrangian densities?

  • Jerry Schwarz

    There is an aspect of the discussion that has nothing to do with physics. There are practitioners of “alternative medicine” who justified their nonsense by saying everything is connected to everything else. And that quantum mechanics support this. They seem to be talking mostly about entanglement, although whether they understand the physics is doubtful. To give than more quotes to use in their propaganda, such as Brian Cox seems to have done is a bad idea.

  • Thomas

    Here’s the full episode, 58 minutes: http://youtu.be/4f9wcSLs8ZQ

  • http://www.darkbuzz.com Roger

    Yes, Cox is talking about Pauli exclusion. And yes, there is theory for what he says. The catch is that he is talking about an “imperceptibly change”. That is the flaw in many popular explanations of quantum mechanics. They attribute a reality to theoretical constructs that could never be measured.

  • http://www.ph.utexas.edu/~siva/ Siva

    @SeanCarroll and @ScottAaronson:
    For a long time, I was under the impression that it’s (primarily) electromagnetism. The following article gives strong indications that it’s the Pauli exclusion principle. I’m still not fully convinced (haven’t digested the article enough to accept what it says), but heading that way. This is a good treatment of the topic, and the only reference I’ve seen.

    The Stability of Matter by Elliott Lieb
    http://rmp.aps.org/abstract/RMP/v48/i4/p553_1

  • Jesse M.

    Jim Kakalios wrote:
    “The Pauli Principle does not say that no two electrons can ever be in exactly the same quantum state. I can have an electron in Brian Cox’s studio, and another in Minneapolis, and they can be in exactly the same quantum state, because under this circumstance they are distinguishable.”

    How can they be in the “same quantum state” if one is known to be in Brian Cox’s studio and another is known to be in Minneapolis? Doesn’t the quantum state includes the complete set of probability amplitudes on position eigenstates, so that only if both have the same probability to be found in any specific volume of space can they be said to be in the exact same quantum state? As I understand it the exclusion principle would also say that there is an ever-decreasing likelihood that they will be in two different states that are very close to one another (with a lot of overlap of the single particle wave functions, as you said), but the probability only goes to zero for states that are identical in every way (including the position distribution), and that’s what I believe is meant by “same quantum state”.

  • http://lablemminglounge.blogspot.com Lab Lemming

    Expanding on the quibble, the band gap in diamond is about 5.5 eV, so Cox’s hands would have to be glowing in the UV at 50,000 degrees to actually move the electrons out of their sp3 bonds.

    Apologies for sullying this theoretical site with base solid state physics.

  • PL Hayes

    @Jesse M.

    I think perhaps a bit more precision in language and description would be helpful here. QM seems to demand it but often doesn’t get it…

    Particles are ‘identical’ if they have the same fixed non-dynamical properties, e.g. mass, charge, spin dimension. (Position is a dynamical property).

    Two ‘states’ – the mathematical objects which /describe/ quantum physical systems – are ‘indistinguishable’, and describe observationally indistinguishable systems, if they differ only by a permutation of ‘identical’ particles.

    The Pauli exclusion principle says that in a ‘state’ describing a system of ‘identical’ fermions, no two of them can occupy the ‘state’ with the same single-particle ‘quantum numbers’. http://en.wikipedia.org/wiki/Quantum_number

  • Daniel Macdonald

    A simple thought experiment
    Imagine we have to electrons one electron is in the Andromeda galaxy the first electron is in our lab on the earth. At present we do not know the energy levels of either electron. If we measure the first electron in our lab and find it in level 1, we know for sure that the other electron in the Andromeda galaxy is in level 2. Now imagine that we have learned to travel to the Andromeda galaxy and we repeat the exact same experiment with the exact same electrons at the same time. The experimenter in the Andromeda galaxy measures their first electron and finds it to be in level I and knows for sure the other electron in the earth lab is at energy level 2. How is this possible or is it.

  • Prof Alan Woodward

    Sean -I think what I’m reading in your notes above is the Pauli exclusion principle does not lead to the fact that separated electrons will have differing energies. You refer instead to other effects such as the Coulomb effect which of course does indeed lead to the splitting of energy levels.

    However, you do appear to accept that a wavefunction is spread universally, albeit that it decays exponentially and hence at large distances there is little operlap between the wavefunctions of two fermions.

    So, thinking through the simplest N-Particle interaction: two hydrogen atoms in the ground state but separate by a vast distance. Do they both to be opposite spins? I think we all agree that to answer this requires a definition of the quantum state ie not jus spin and the fact that they are in the ground state but also the energy.

    That being so, if you imagine a box of width L, with each atom localised to either end quarter of the box then the possible values of the energy are given by:

    En=h2(pi)2n2/2ML2

    Do you diagree with this? Assuming you don’t then all other things being equal in the quantm state, it is the energies that must differ. This is not transmitted as such, hence there is no relativistic problem, but teh wave function does change instantly. Obviously if you tried to measur eit teh wavefunction would collapse into a particualr eigenstate and then you would have to communicate the measurement but that does not mean it does not exist.

    In any event from the defininition of the energy of our fermion the momentum is deduced as:

    p=h(pi)n/L

    As Delta p ~ nh/L from the uncertainty pricniple it means the energies can only be determined with an accuracy of:

    Delta E ~ h2(pi)2n2/ML2

    but this is much larger than En – En-1 so there is no chance of the macroscopic situation (such as that referred to in atomic clocks in teh Blog that started this) will conflict with classical intuition nor is it ever likely would would be able to measure the energy difference.

    Hence, the exclusion princple can lead to differing energies for distant fermions albeit you can measure it for a variety of reasons.

    Assuming everyone is agreed on that then I think the rest of what you say above is rather unfair bearing in mind that this was trying to explain a counterintutive subject within the confines of a prime time television show.

  • http://www.gregegan.net Greg Egan

    The web page on the double-well potential at:

    http://www.hep.manchester.ac.uk/u/forshaw/BoseFermi/Double%20Well.html

    ends with a nice animation. An electron is initially localised in the left-hand well. Because its wave function is constructed from two slightly different energy eigenstates of the full potential, over time the electron’s most probable location cycles between the two wells.

    However … there’s a big difference between the relevance of this to molecular orbitals and its relevance to macroscopically separated systems. Modelling the potential this way for two hydrogen nuclei a metre apart in which you initially localise an electron around one of them, the time scale on which the cycle takes place would be of the order of 10^(10^9) seconds. The age of the universe is about 4 x 10^17 seconds.

  • http://x-sections.blogspot.com Rhys

    OldBob wrote:
    “But surely Cox’s point is that if one considers two vastly separated atoms then if they both had excited states of *exactly* the same energy, and if say the atom on the left’s excited state was occupied already by its electron, then ‘zapping’ the atom on the rights electron into its excited state would zapping it into an already occupied state (ignoring the possibility of different spins etc), and would thus violate Pauli.”

    The problem is that it wouldn’t. The two atoms are in different places, and this distinguishes the electron states. But I think most people would infer exactly what you inferred from what Cox said. That’s what makes his little ramble so awful.

    Communicating science accurately to the broader public is difficult. I’m genuinely unsure whether it is better to do a bad job of it, as Cox did here, or to not do it all.

  • OldBob

    @Rhys #35 :”The two atoms are in different places, and this distinguishes the electron states”

    A lot of the points (mine included) made here and other places seem to hinge on this, is it really the case that position is a valid distinguisher for Pauli (just like spin and energy are)? If so then I would buy that Cox is indeed wrong in the sense that Sean means. I shamefully can’t quite remember if position counts or not, maybe someone could point me toward an elucidating reference or provide arguments.

  • http://www.physicsofsuperheroes.com Jim Kakalios

    Jesse M. (no. 29 above):

    I meant same quantum state aside from position. If they are well separated, meaning that their separation is much larger than their individual deBroglie wavelengths, then they are distinguishable.
    In this case Pauli does not enter into it.

    I’m an experimentalist (like Lab Lemming (3), a “base solid state” physicist), not a theorist. But if what Brian Cox were saying were true, then no two H atoms should ever have exactly the same emission line spectra. While it is true that an exponentially decaying wavefunction only has zero amplitude at a distance of infinity, I would expect that any shift in the energy levels to be less than the intrinsic line width of the energy levels arising from the Uncertainty Principle.

  • http://x-sections.blogspot.com Rhys

    @OldBob
    Basically, yes. The exclusion principle says that two electrons cannot occupy the same state (have the same wavefunction). “Being over here” and “being over there” are clearly two different states.

    This whole issue is of course fairly complicated, as Sean has explained; the problem is that what Brian Cox says in that clip is misleading, and therefore counter-productive to attempts to bring some understanding of quantum mechanics to the wider public.

  • OldBob

    @Rhys #38

    If position is a valid distinguishable for Pauli, why then in an atom do electrons simply not pile up in the ground energy state but with wavefunctions *slightly* displaced in position from being centralized on the center of mass? Surely this would be satisfy Pauli and also leave the atom in a lower energy state than each of the electrons having different spins/ang mom/excited energies…

  • Jesse M.

    @OldBob #39, I think it’s because the *energy* of electrons in an atom is typically known (and perhaps is also what is effectively “measured” by environmental decoherence even if an experimentalist hasn’t measured it), and two electrons in the lowest energy eigenstate (the ground energy) automatically have the same position distribution (not the same precise position because that can’t be known exactly simultaneously with position). For higher energy eigenstates in an atomic potential well, I think the same is true if both the energy and the angular momentum are known (or is it that angular momentum differences in the same orbital lead to slight differences in energy? I’ve forgotten).

  • http://www.physicsofsuperheroes.com Jim Kakalios

    @OLDBob #39: Position is important for determining when the indistinguishability of the electrons must be taken into account. When the two seperate one electron wavefunctions must be decsribed by a single wavefunction that describes both particles. the fact that electrons have spin 1/2 means that this wavefunction must be anti-symmetric under the exchange of positions of the two electrons. In that case, the wavefunction is exactly zero if the two electrons are at the same location, or at sifferent positions, with the same quantum numbers. As the probability of finding the electrons depends on the square of this wavefunction, one will never find the two electrons at the same location, or the same quantum state if they are in the same state. In an atom, if they have the same principle, orbital and azimuthal quantum numbers, the only remaining degree of freedom is spin. As there are only tow possible spin quantum numbers, one can have two electrons in the same state, one spin up and spin down, but then the third electron with either spin up or spin down, must reside in another quantum state.

    Position is not a quantum number, but it is important for determining when one has to worry about Pauli and when it is not relevant.

  • Gizelle Janine

    Not impressive. I’ve said things like this after drinking Guniness, and I’m not wearing a blazer on TV with jet black hair, I’m also not even semi-famous. Gay. :D

    I love the collapse of the wave function stuff, all very important stuff just to talk about, but yay, awesome post. (How many times have I f***ing said that one, eh?)

    By the way, you’re armchair now, huh? I had no idea. I respect you less now, just so you know. Losing one reader wont hurt you, I’m sure… :D

    That s**t with Andromeda is f****ing crazy, by the way. I got Redshift WAY TOO LATE, or early, I can’t tell.

    Also, who the f**k is Brian Cox?!?!?! GEEEZ. What a windmill.

    -__-

  • Gizelle Janine

    Also…not to call out Jennifer here, but you’re no snore. Just depends on who you apply it to…GEEEEEEZZZZ.

  • prianikoff

    #37 “if what Brian Cox were saying were true, then no two H atoms should ever have exactly the same emission line spectra.”

    Has anyone ever measured the emission line spectra of a single hydrogen atom?

    Another point; why do spin 1/2 fermions mostly seem to end up being electrons, rather than positrons?

    Finally, I’m not convinced that Pauli himself wouldn’t have agreed with Cox’s interpretation.

    Some might find it slightly arkward to recall that Pauli contributed towards Carl Jung’s ideas on Synchronicity. Even Brian Cox might regard this as an example of “Wu-Wu”.

  • Lorena

    I don’t know a thing about physics but what I think I understand from what brian cox said doesnt make sense to me. if his audience is regular people who know no more physics than what they’ve learned, and forgotten, at high school, like me, what he said is basically that by every little thing we do or touch arranges the electrons, and then all the electrons around it create some sort of “ripple” effect in which electrons all over the universe are changing :S :S that’s what I imagine from what he said, a ripple effect of electrons changing in all directions coming out of my house, the earth, the galaxy the local cluster of galaxies and the universe …..

  • http://thefloatinglantern.wordpress.com Tim Martin

    Question about Sean’s comment above (#8), in which he writes “Certainly without the [exclusion principle] you could literally pile atoms on top of each other in the same place.”

    I just want to confirm whether this literally means “in the same place.” As in, Atom 1 and Atom 2 are in the exact same location.

    It seems like an odd thing to ask, since “everybody knows” that two objects can’t occupy the same space at the same time. But this intuition is based on a world where EM and the exclusion principle keep atoms from ever actually touching each other, so it’s impossible to force objects together. My question is, if these barriers didn’t exist, would it be possible for two particles to occupy exact same space at the same time?

    PS: Chris #19, thanks for the recommendations.

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  • prianikoff

    #46 “.. if these barriers didn’t exist, would it be possible for two particles to occupy exact same space at the same time?”

    Try looking here:-
    http://en.wikipedia.org/wiki/Sagittarius_A*

  • http://Facebook Angela Garcia

    Rubbing a diamond should have little effect. It’ll get the electrons to spin, but then that’s what electrons do. They spin in opposite directions. Electrons generally are arranged in pairs, except for the outer most shell in certain families, i.e. Alkalai Metals. Heating them ,will get them to move faster( spin). But, they really don’t go anywhere. Because the diamond has such an incredibly high melting point( try a nuclear explosion), it won’t change states. ( Solid to liquid)

    As far as Uncertainty, what about Higgs Boson? These are particles, but they have no mass, and therefore do not follow the classic definition of matter. However, as they move, they acquire mass.

    Angela Garcia as NeonMosfet

  • http://Facebook Angela Garcia

    Rubbing a diamond should have little effect. It’ll get the electrons to spin, but then that’s what electrons do. They spin in opposite directions. Electrons generally are arranged in pairs, except for the outer most shell in certain families, i.e. Alkalai Metals. Heating them ,will get them to move faster( spin). But, they really don’t go anywhere. Because the diamond has such an incredibly high melting point( try a nuclear explosion), it won’t change states. ( Solid to liquid)

    As far as Uncertainty, what about Higgs Boson? These are particles, but they have no mass, and therefore do not follow the classic definition of matter. However, as they move, they acquire mass.

    Angela Garcia as NeonMosfet

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean Carroll

    I wrote a long comment here, but decided to move it up to the post itself, so check it out.

  • http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig

    @46: Bosons don’t follow the exclusion principle, and many bosons can occupy the same place.

  • Gizelle Janine

    This is relevent on so many levels…

    http://www.youtube.com/watch?v=LqeC3BPYTmE&feature=share

  • Count Iblis

    An interesting problem for students who have just learned about fermions, bosons, (anti) symmetrization of wavefunctions is the following. Bosons can be composite particles, consisting of a bound state of fermions, so how can two such bosons be in the same state if the particles they consist of can’t :) .

  • http://jbg.f2s.com/quantum2.txt James gallagher

    Composite bosons can’t break pauli exclusion for their constituents, otherwise you’d be able to create infinitley dense noble compounds for example.

  • http://jbg.f2s.com/quantum2.txt James gallagher

    Brian Cox should have told his wacky celeb audience that everything is probably connected but propagation of any deterministic effect is limited by Einstein’s speed of light bound.

    A more subtle point, not discussed anywhere, is whether rubbing a diamond (or your bottom for example) is consistent with unitary evolution of the global probability state.

    ie when exercising free-will are we still bound by unitary evolution?

  • PL Hayes

    “But of course it’s a very bad approximation to ignore the interaction between the two electrons, precisely because of the above analysis; it’s not true that one is here and one is far away, they both are equally distributed between being here and being far away, and can interact strongly.”

    “Since electrons repel, the true ground state is one in which the wave function for one is strongly concentrated one one hydrogen atom, and the wave function for the other is strongly concentrated on the other.”

    Well… that’s very different from my understanding of the appropriate quantum description of this system – as a product state constructed from a pair of localised (by attraction, not repulsion) states on the seemingly intuitively reasonable and necessary assumption of negligible interaction.

  • http://jbg.f2s.com/quantum2.txt James Gallagher

    #57 yes it’s a product state for all reasonable calculations
    (eg see http://books.google.co.uk/books?id=2zypV5EbKuIC&lpg=PP1&pg=PA273#v=onepage&q&f=false )

    but….. is it really a product state wrt nature’s gigantic state vector?

    This discussion is a bit silly, Cox was doing pop sci not a careful CERN presentation on super neutrinos, I mean the point he wanted to amaze his audience with was that the wave function spreads everywhere in the universe according to current understanding of QM – now that may change if/when QG is understood but it’s basically what we all believe right?

    (ok, maybe he gave the impression of the possibility of ftl information but I really doubt it will cause the harm predicted by some crazy people around the internets)

  • Massaro

    Thank you so much for explaining the double well notes. When I read it, I was completely satisfied with my (mis)understanding that you described as “So you are tempted to put one in E(x1) and the other in O(x2)”.

  • Henry

    “in the real universe there are vastly more unoccupied states than occupied ones” – why is this? Is there not a finite number of possible quantum states for a given fermion? And how does that number tally with the universal population of the given fermion?

  • Chris

    Talking of the Pauli exclusion principle, Pauli was also famous for using the expression that something was “not even wrong” which I think applies perfectly to Brian Cox’s statement
    “imperceptibly change”. I could say when I cough all the atoms in the Universe imperceptibly change!

  • PL Hayes

    @Chris #61. Quite right but I get the impression Cox is well aware of that “not even wrong”-ness aspect of his thought experiment. I did find it mildly amusing to see him in another clip from that TV prog. explaining, with Jim Al-Khalili’s assistance, why atoms are mostly empty space. Quite recently Jim Al-Khalili, in one of his excellent TV progs, explained why even atomless empty space isn’t really empty. ;-)

  • Raza

    Even without getting into the Exclusion Principle, all particles in the Universe are connected to each other by force F=G*M1*M2/R^2 and F will be non zero, however small.

  • Chris

    Raza,

    I think the main gripe with Cox’s statement is that the effect is instantaneous for all the electrons in the Universe which may be true in your Newtonian example but of course isn’t in general relativity or quantum field theory which enforces that no communication can be made faster than the speed of light.

  • Raza

    Chris,

    I always thought the Newtonian formula was also true within the speed of light so that different bodies will get attracted at different times depending on their distances.

    One thing that has always puzzled me and I have not come across a satisfactory answer, is how does matter or energy “know” about the laws of physics / nature and then behave accordingly. It is almost as if everything that existed has a DNA which embodies all the laws of nature and provides instructions on how to interact just as organic DNA does. Any thoughts, anyone?

  • prianikoff

    Lab Lemming #30
    “Cox’s hands would have to be glowing in the UV at 50,000 degrees to actually move the electrons”

    Diamonds exhibit a phenomenon loosely know as triboluminescence, whereby they can emit light when undergoing friction. It’s also regularly observed in other carbon compounds such as sugar crystals – for example when chewing a “Life Saver”.

    The phenomenon has not been fully explained, but in diamond crystals there are impurities in the crystal lattice which act in a similar way to the dopants used in electronic semi-conductors.

    When a diamond is being cut, or rubbed, a few electrons within the crystal will be triggered into changing their quantum level. Depending what originally caused them to be at a threshold energy state, they will either cascade down to their ground state, or ionise nitrogen molecules from the atmosphere. This results in the emission of photons and clearly affects the neighbouring electrons.

    See for example:-
    “Triboluminescence from diamond”
    J R Hird, A Chakravarty and A J Walton

    http://iopscience.iop.org/0022-3727/40/5/023

  • John R Ramsden

    @Raza (#65) How do they know? Analogous to higher-order entities, such as animals, they or their constituents can behave in all kinds of ways, in theory; but only certain modes are compatible with continued existence, as individuals or species. And physicists are lucky that everything at atomic scales and below happens so incredibly fast by everyday standards that only the most symmetric “laws” persist long enough to be detectable.

    Take unitarity for example. By instrumentalists this is simply assumed; but from a realist standpoint, one could suggest that given some underlying process of constant dissipation and regeneration, modelled by an evolving complex function for the purpose of this explanation, unitarity is what remains when values of modulus less than one shrink away to insignificance and those of modulus greater than one inflate away to an equally undiscernable state.

    If that idea has any merit then cosmic inflation during the Big Bang, and dark energy today, might turn out to be manifestations of deviations from unitarity, but evolutions that restore it in other ways.

    If it doesn’t contradict the above, I also think that inflation and dark energy might be nature’s way of dealing with Fermionic particles and fields that have somehow managed to become “close” enough in respects which would otherwise violate the Exclusion Principle. That would give a realist explanation of this, and perhaps the No Cloning law. But again it would require some form of regeneration to even begin to make sense.

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  • http://lablemming.blogspot.com/ Lab Lemming

    Re 66:
    This refers to breaking bonds- mechanically this time, which then leaves unbonded electrons that need homes. Not relevant to rubbing, unless Cox’s hands are covered in polishing grit.

  • prianikoff

    #69 Quantum effects mean that qualitative thresholds are reached due to various causes – straw, camel’s back…

  • http://gnomonicablog.com Fernando Curiel

    I wish my teachers could have explained so clearly this subject back when I was an undergraduate in physics. Great job Sean! Clear and to the point… I enjoyed Wonders, but being famous is one thing, being famous and wrong an insist on a position is famous goof.

  • Jim

    “simple quantum problems of a single particle in a textbook”.

    When I did this stuff we used to calculate energy levels of a particle in a box.
    Have things now moved on to the case of a particle in a text book? (Can a text book reasonably be modelled as a box?) :-)

  • twistor59

    @Sean : you said
    “As far as I can tell, this isn’t at all what Brian Cox was talking about; he discusses heating up the electrons in a diamond by rubbing on it, not measuring their energies by observing them and then drawing conclusions about entangled electrons very far away. (In a real-world context it’s very unlikely that distant electrons are entangled in any noticeable way, although strictly speaking you could argue that everything is slightly entangled with everything else.) But there is some underlying moral similarity — this is, as mentioned, the context in which people traditionally talk about instantaneous changed in quantum mechanics.”

    however, on checking chapter 8 of Cox and Forshaw’s book, to which he’s referred people in connection with this discussion, the authors state, referring to the universe:

    “There is only ever one set of energy levels and when anything changes (e.g. an electron changes from one energy level to another) then everything else must instantaneously adjust itself so that no two fermions are ever in the same energy level.

    The idea that electrons ‘know’ about each other instantaneously sounds like it has the potential to violate Einstein’s Theory of Relativity. Perhaps we can build some sort of signalling apparatus that exploits this instantaneous communication to transmit information at faster-than-light speeds. This apparently paradoxical feature of quantum theory was first appreciated in 1935 by Einstein in collaboration with Boris Podolsky and Nathan Rosen; Einstein called it ‘spooky action at a distance’ and did not like it. It took some time before people realized that, despite its spookiness, it is impossible to exploit these long range correlations to transfer information faster than light and that means the law of cause and effect can rest safe.”

    So his instantaneous effects are indeed referring to EPR-style correlations. Your other hypothesis about what he might mean, namely that we *do* consider the tiny electromagnetic interaction between the electrons definitely wasn’t part of his argument, because earlier in that same book chapter, talking about the double well model he says:

    “The way to think more clearly about the implications of the Exclusion Principle is to stop thinking in terms of two isolated atoms and think instead of the system as a whole: we have two protons and two electrons and our task is to understand how they organize themselves. Let us simplify the situation by neglecting the electromagnetic interaction between the two electrons – this won’t be a bad approximation if the protons are far apart, and it doesn’t affect our argument in any important way.”

    I await with interest the resolution of this issue. I expect there will need to be some changes or clarifications to chapter 8 of the book.

  • PL Hayes

    Hello twistor59.

    Despite what Sean has written here (which I have to say I find even more bizarre and confusing than Cox’s stuff (#57)) I can’t see how it could be such a bad approximation. What the book lacks is a clarity and precision of description appropriate/necessary to the subject. I suspect pernicious “particle is wave function is real”-ism has led Cox (and Forshaw) to believe it unnecessary to think in terms of preparations and measurements etc. You can see how silly those “diamond rubbing” remarks were just fine without leaving the context of the double potential well model.

  • twistor59

    Hello PL Hayes-from-badscience.net !

    I think there are many confused interpretations flying around, but Sean’s opening post did certainly clarify a few things for me. Brian Cox promised us, on Tom Swanson’s blog:

    “I’ll be preparing a full explanation of this for publication somewhere, and will post a link here when it’s up. Thanks for the interesting debate – it’s raised additional points that require clarification, and I’ll deal with them all.

    The explanation is essentially that in my book, The Quantum Universe, chapter 8, which you could read if so motivated! ”

    so I guess we’ll have to wait and see what he comes up with.

  • Gizelle Janine

    ‘ie when exercising free-will are we still bound by unitary evolution?”

    @James gallagher: I’d say the question of anything involving free will would automatically have to do with perecption, individual or otherwise. Of course unitary evolution by definition would have something to do with it, maybe they’re best friends? (That’s how I fall asleep at night, on a bed of perception, blanketed by unitary evolution.) :D

    Oh and Wiki: “In quantum mechanics, a quantum operation (also known as quantum dynamical map or quantum process) is a mathematical formalism used to describe a broad class of transformations that a quantum mechanical system can undergo. This was first discussed as a general stochastic transformation for a density matrix by George Sudarshan.[1] The quantum operation formalism describes not only unitary time evolution or symmetry transformations of isolated systems, but also the effects of measurement and transient interactions with an environment. In the context of quantum computation, a quantum operation is called a quantum channel”

    Don’t let me get into superposition. *starts crying loudly*

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  • Anon8

    Double post, sorry.

  • Anon8

    Sean, I must agree with Lorena’s comment #45 and it coincides with zwi woo’s comment #20. I can’t really fathom what you’re describing here–all I know is other respected physicists such as yourself are saying that Cox is somehow wrong and misleading. I’m sure most of the audience is just as clueless about physics. They’re going to walk away with the idea that Lorena pointed out: That everything is connected and what you do with rubbing a diamond here is causing the electrons to bounce around and have an effect everywhere.

    Someone on You Tube commented that: ” I love random YouTube commenters telling a world famous particle physicist that he’s wrong about particle physics.”

    If you or whomever are going to say he’s misleading then I think you ought to put it in equally simple terms that that audience would understand because they’re going to say to friends, “I learned so much, how fascinating, everything is connected just by rubbing a diamond in the studio!” Another “butterfly effect” idea. It’s one thing to debate with fellow scientists here to confirm your thoughts and all, but there’s a TV audience out there and that’s the crux of what needs to be addressed regarding this video…what this “world famous” person has said and what is now planted in their minds and will be repeated.

    I was referred here by 3QuarksDaily, btw.

  • darue

    I think this recent article may be relevant…

    The wavefunction is a real physical object after all, say researchers

    17 November 2011

    http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392

    “Robert Spekkens, a physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, who has favoured a statistical interpretation of the wavefunction, says that Pusey’s theorem is correct and a “fantastic” result, but that he disagrees about what conclusion should be drawn from it. He favours an interpretation in which all quantum states, including non-entangled ones, are related after all.”

  • OldBob

    Still no rebuttal from the Coxinanator? will be interesting to see where this goes….

    For what it’s worth I think it was probably erronenous for him to make his statements on the back of the Pauli principle, given that it is fine for spatially seperated wavefunctions to be in the same energy/spin state as they are distinguished by position.

    I don’t think he is really guilty of the most serious charge to do with instantaneous and faster than light propagation; it seems clear from ch8 of his book, that he was certainly aware of this (and gets around it by suggesting no information is transmitted despite signalling etc). So whether he casuaully said it or not, I think he was certainly aware and should be allowed some license for being a presenter for making that kind of goof.

    Anyway, whichever way this debate swings if he replies further I think we shouldn’t be too harsh on him; he may no be a signicant scientist in terms of monumental conributions (he is an experimentalist after all, they work in teams, how many individuals can you name?) but he has done a lot of good for Physics in the UK. This year with fees rising Physics is one of the only subjects where applications are actually up, the so called “Brain Cox” effect and all that.

    Anyway, I wish he would hurry up and reply.

  • joeblow

    Nerds!

  • PL Hayes

    @OldBob

    I think that’s still a bit unfair. There is only one wavefunction in any one approximate description of Cox’s pair of electrons. The very uninteresting position-distinguished one looks like ψ⊗φ for non-overlapping ψ and φ. But Cox didn’t choose that one – he chose an ostensibly more precise one which forces you to think about it a little bit before (probably) charging it with being ”not even erroneous” (rather than “erroneous”).

  • OldBob

    @PL Hayes “he chose an ostensibly more precise one”- Could you say some more? not sure I quite follow…

    “before (probably) charging it with being ”not even erroneous” (rather than “erroneous”).”

    Do you mean this as in ‘not even wrong’? i.e. not even well formulated enough to be even charged with wrong…or something else

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  • Stevie C

    Very interested to read this article. It reinforces a perception I have about Brian Cox that has been developing recently, in that I have serious doubts as to his academic ability. Most recently, a few weeks ago I heard him explain on BBC Radio Wales (in response to a question asking why the Moon is sometimes a circle and other times is banana shaped) that the phases of the Moon are caused by the shadow of the Earth on its surface..! I was amazed. I have the recording of the show if anyone would like to hear it. On the same day I checked his Twitter account to see if this error had been raised, but there was no sign – just the occasional smattering of his abusive tweets that feature the word ‘nobber’.

  • http://www.cthisspace.com Claire C Smith

    I have a deep interest in physics so thought I might comment about this.

    Brian Cox is great, but all this is a bit odd and quite frankly, I was a bit shocked when viewing this talk. I was going to say, on line, the same thing, much like Sean has said here, about how Mr Cox presented this idea of the Pauli E P – be it in a very odd way during this lecture, but I didn’t want to impose you see, although I was going to tweet it at some point just after the talk.

    So here it is: I was surprised that no one said anything until now.

    I had thought that, at the onset, as Mr Cox presented this with an actual diamond, that in this theory he was talking about, that it was much more to do with entanglement than the Pauli E P. So that 1st of all is a completely odd thing to do anyway, especially when he is the ambassador of physics and science. It also meant that people watching the talk, must have thought that that would be the truth, or at least if not, they would have thought it a bit muddled up, if they knew some physics anyway. As it is, Mr Cox also said the word chance in the talk at some point. So, what is it with the word ‘chance’ as an idea, combined with the theory that is the Pauli Exclusion Principle together in this talk?

    Strange really – only one person should know that!

  • PL Hayes

    @OldBob

    Although the size of the energy level splitting decreases to arbitrarily tiny levels when the separation between the wells grows arbitrarily large, the e⊗o-o⊗e description would appear to be, “in principle” at least, a correction to the ψ⊗φ description. OTOH, the model’s a gross approximation in the first place…

  • JG

    @Stevie C

    you have a “perception” about Brian Cox that you have been “developing recently”
    you have a recording of a radio wales show he recently appeared on
    you check his twitter account

    you are a bit of a nobber aren’t you?

    re the radio show question, I bet if the presenter had said ‘isn’t that lunar eclipses?” he would have instantly corrected the mistake, I’m sure most physicists occasionally give incorrect answers due to not concentrating fully – I mean it’s only radio wales, probably with about a dozen people listening (including you)

  • Stevie C

    @JG

    Oooh. I don’t know what you’re trying to achieve with your response, but I’ve clearly hit a nerve here that has pained you so much that you’ve resorted to insulting not only me but a nation of millions of people.

    I’ll thus address each of your comments with the same consideration that you gave me and everyone else. I’m not a fan of trading insults, but hey, if that what it takes to break through to BC fanbois/girlz, so be it…

    ‘Perception’ – yes. One ‘perceives’ the world. Maybe you don’t have this ability because you’re so blinded by celebrity. How is ‘Heat’ magazine these days? Still enjoying the pictures? I hear they even use capital letters on some pages.

    I have ‘the recording’. It was available for download after the interview, in the same way that the ‘Everything is Connected’ video that started off this thread was. Presumably the download (but not the video as implied by your lack of response to that) does not meet with your approval because it is evidence of a cock-up that for some reason you’re uncomfortable with, suggesting you’d rather bury it and let the people who listened to it believe something that isn’t true. You’re not religious (or BC himself) are you..?

    Twitter: You actually think there’s something wrong with looking at a Twitter account that has over 650,000 ‘followers’. Oh my word. Maybe you think all those ‘followers’ are ‘nobbers’ too? I tell you what, instead of just lurking around a blog here or there in the hope that one person posts something you can spew your condescending, grander-than-thou insults over before slithering away, why not ‘tweet’ them to the aforementioned masses instead to really show what a grown-up, sensible person you are?

    Radio show answer: If you think that question was sooo difficult that a professor of physics requires more than the level of concentration needed to breathe to answer it correctly, then I BET opening ‘Heat’ magazine with your opposable thumb is truly the pinnacle of your mighty existence.

    You’re either working for BC, or wish you were, but I have another ‘perception’ that you might even be him. You twunt.

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  • JG

    @StevieC

    lol

    Yes, I should apologise for the dig at radio wales, I’m sure it has more than a dozen listeners.

    It is hilarious that you think I might be BC, was it my initials that gave you this ‘perception’?

    I assure you that the wavefunction of Brian Cox and myself is almost an exact product state, but when I wiggle my bum I bet all his fermions jiggle around in an imperceptible and probabilistic fashion.

  • D of B

    @JG…

    A lunar eclipse looks *nothing like* the phases of the moon at all. Nothing like it. Sounds like Cox for some reason repeated a very common misunderstanding about it. Maybe because that’s what he believes and he didn’t have his science script writers handy to correct him. Just speculating, that’s all…

  • JG

    They are both a view of partial reflection from the moon aren’t they, so *nothing like* (x2) isn’t really accurate.

    Heisenberg couldn’t explain how a battery worked in his phd defense, does that mean he was a bad scientist? I bet if StevieC had a recording of his fumbling explanation he’d be posting with mischievous delight all over the internet too.

  • D of B

    ‘Looks nothing like’ – read the text. You like to add a bit of spin, don’t you…

    As for comparing Brian Cox with Heisenberg..!? Wow. You really must be besotted/deluded.

  • JG

    No, the Heisenberg anecdote was to illustrate what a feeble point StevieC is making, that obviously went over your insubstantial head.

  • dissembly

    Sean Carrol wrote: “Before we made our measurement, they didn’t know the energy level of their electron, and would give 50/50 chances for finding it in level 1 or 2. After we made our measurement, it’s in some particular state, but they don’t know what that state is. So again they would give a 50/50 chance for getting either result. From their point of view, nothing has changed.”

    Say what? Why don’t they just perform the same measurement that we performed in our galaxy? If we found the electron in state 1, they can find it in state 2.

    There is no magical genie reaching down to mess with the result, surely.

    I thought physicists were very explicit about the fact that this is a legitimate example of information appearing to travel faster than light. That’s the whole reason the thought experiment was conceived of in the first place, to say “Quantum mechanics can’t be true, because it theoretically allows information faster than light.” And yet, it’s true.

  • OldBob

    “Say what? Why don’t they just perform the same measurement that we performed in our galaxy? If we found the electron in state 1, they can find it in state 2. ”

    The point, I believe, is that even though we’ve measured ours in say, state 1, and know that they will get state 2 upon measurement, *they* do not know our result, and until they measurement they can only say 50/50 either way. We also can’t communicate our result to them faster than lightspeed.

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  • OldBob
  • Raedha
  • Oldbob

    I notice Cox Wiki says “Royal Society University Research Fellow”, this is different to FRS right? I’m not exactly sure what this means though if not FRS..(but he is not on the list of FRS & not eminent enough in scientic terms surely etc). Is this some kind of other accolade?

  • http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig

    A FRS is a Fellow of the Royal Society. This is quite an honour. Almost all members are professors, and only a minority of professors are members (at least in astrophysics). (Note: essentially anyone can become a FRAS, a Fellow of the Royal Astronomical Society. Similar term, huge difference. As such, putting “FRAS” after one’s name is a bit like lawyers in the US putting “Esq.” after their name: since anyone can do it, it really isn’t much of a distinction.

    A Royal Society University Research Fellow is a scientist who is funded by a grant from the Royal Society. Quite a prestigious fellowship compared to the typical postdoc, but much lower down than FRS.

    There used to be a gentlemen’s agreement that Royal Society Research Fellows would get university-funded professorships afterwards.

  • http://jbg.f2s.com/quantum2.txt James Gallagher

    Sean Carroll says (#16)

    “Matt– sorry, still rushing, but… I think we should start with unitary evolution of the wavefunction, and get everything from that. (I.e. not start with observables.) We have a point in some manifold CP^n that evolves on a sub-torus. Everything else is taking subspaces, and that’s where things get interesting.
    Easy for me to say! Obviously carrying this program from start to finish isn’t something I’ve ever done, but maybe somebody has.”

    it’s even simpler, just consider the state vector U(t) in C^n evolving according to

    U(t+tdelta) = exp(hL).U(t) -U(t)

    for some anti-hermitian “lagrangian” matrix L, then 3D “space” is dynamically emergent

    http://vixra.org/abs/1203.0039

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  • http://jbg.f2s.com/quantum2,txt James Gallagher

    The -U(t) “subtracting the Universe” bit explains renormalisation shenanigans – although now we know why you are allowed to subtract large numbers

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  • Lilian Weimer

    It’s all a bit high brow for most of us frankly. I enjoyed the lecture very much and my understanding of quantum physics is at best almost non existent but I have a basic curiosity about how our universe works in broad strokes. The way that we teach science of any kind in Britain is only good for putting kids into irreversible comas and anyone whose presentation is such that it engages people with only a casual interest in any of the sciences must be a good thing. Einstein once said that if you can’t explain it to a six year old you don’t understand it yourself- Cox was metaphorically doing that on this particular occasion so give him some slack and be glad that he generates some interest in his subject – unless ya’ll would rather be in an elite club and die with the knowledge in you ;)

  • Kazue

    There is zero correlation between being a charismatic speaker and having the correct ideas, right? Well, not if you have celebrities listening to you. A celebrity audience is a clear indication that you have moved up to the upper echelons of society and intelligence.

    Clearly Mr. Cox feels very powerful by rubbing a very large (yellow?) diamond between his well manicured hands. We should not pay so much attention to the validity of his statements but rather celebrate his boyish looks, well coiffed hair, and supernatural magnetism because it marks a new era of physicists who look and think more like the Backstreet Boys.

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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .

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