Everything is Connected

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.”)

Brian Cox - Everything is Connected to Everything

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.

109 Comments

109 thoughts on “Everything is Connected”

  1. ‘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.) 😀

    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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  3. 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.

  4. 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.”

  5. 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.

  6. @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”).

  7. @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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  9. 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’.

  10. 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!

  11. @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…

  12. @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)

  13. @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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  15. @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.

  16. @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…

  17. 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.

  18. ‘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.

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

  20. 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.

  21. “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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