A night with the stars (Brian Cox on telly)

[dgwsoft]

http://www.bbc.co.uk/programmes/b018nn7l

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

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

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

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

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

I now know there is a deeper explanation of the exclusion principle, namely that the multi-particle wave-function of a half-integral spin particle is antisymmetric, and that means the probability of finding two of them in the same place is zero. So OK, Pauli and entanglement are connected. But I always like a simple explanation if one is available. What does the panel think? Did what Cox said amount to a good explanation for a general audience, or does it risk perpetuating a misunderstanding?

 

[Randomguy]

Just wrote a long reply...only for these damned forums to sign me out...so I lost it. Arrgh, let me rattle up something similar...

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

I now know there is a deeper explanation of the exclusion principle, namely that the multi-particle wave-function of a half-integral spin particle is antisymmetric, and that means the probability of finding two of them in the same place is zero. So OK, Pauli and entanglement are connected. But I always like a simple explanation if one is available. What does the panel think? Did what Cox said amount to a good explanation for a general audience, or does it risk perpetuating a misunderstanding?

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

This stuff can be used to explain the how shells fill up but it is fairly complex. As I understand it (and I may well be wrong), there are two electrons in the ground state because it is spatially symmetric and has L = 0 (zero angular momentum) and so the only possible state is the anti-symmetric singlet state. For the next shell up you have L = 1, so ml = -1, 0, 1 and so the possibilities are the singlet state + the 3 possible triplet states, making 8 in total. I think that's right, anyway.

 

[doodyone]

Cox is still wrong. Pauli concerns 'states' in a (quantum) system not absolute energy levels throughout the universe.

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

Unless he was being 'ironic'?

 

[bm0p700f]

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

Maybe I have my reasoning backwards. Also I think he tried to do much in 1 hour. My wife stopped listening and started blowing rasburries (litterally) and I am sure most of auidence did not understand most of what he was on about.

 

[macmerry]

Like the other correspondants I also thought - No, that can't be right - when he claimed to be changing the state of all electrons by warming up the diamond. I that were the case there would have been no need for the increasingly elegant entanglement experiments which have been repoted over the last few years. I'm sure I was taught that Pauli applies to the individual atoms which is why we get characteristic phenomena like spectral lines for the individual elements.

I'd be interested to see if there's any response from the BBC to growing comment in various forums.

 

[Randomguy]

Cox is still wrong. Pauli concerns 'states' in a (quantum) system not absolute energy levels throughout the universe.

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

Unless he was being 'ironic'?

But on a level appropriate for his audience, he was correct. Yes, technically Pauli's principle determines the states of a quantum system, but since the expectation of the energy is simply the expectation of the Hamiltonian and is the bra-ket combination <wavefunction|hamiltonian|wavefunction>, it's obvious that by changing the wavefunction you are changing the energy.

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

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

Maybe I have my reasoning backwards. Also I think he tried to do much in 1 hour. My wife stopped listening and started blowing rasburries (litterally) and I am sure most of auidence did not understand most of what he was on about.

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

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

Perhaps that's something akin to Brian Cox's argument. I would love to hear him state the rigorous version of his pop sci comments.

 

[jmk9]

I am also concerned about the specifics of this statement. However, it appears to me that some microscopic property of a particle must be measured in order for the same property in other particles to be known. However, heating the diamond between his hands hardly constitutes a measurement of any microscopic property. The only thing that is measured is the average temperature on the surface of the diamond.

Furthermore it seems to me that if it is the wavefunction of a large polyatomic system that is under question, then the situation is clearly different from that of modeling some part of the original system by considering it in isolation. The assumptions in these two cases are different.

 

[BrotherHod]

I am a little annoyed that Brian Cox has introduced the "woo woo" factor into science on national television. The "woo woo" factor I am referring to is something that has been highlighted several times in this thread and that is that rubbing the surface of a diamond will change the quantum states of a white dwarf 600 light years from here; essentially he is saying that everything is connected and invokes the Pauli Exclusion Principle to legitimise this claim. This is false.
Even if he didn't want to confuse his audience with wavefunctions and bra-ket notations there is still conceptually a major difference between saying no two electrons can occupy the same energy state WITHIN ONE ATOM and no two electrons can occupy the state WITHIN ONE UNIVERSE. The former is the Pauli Principle and the later is plain metaphysics (perhaps even Buddhism!). The nearest we can get to applying the Pauli Principle to multiple atoms is when these atoms are Quantum Entangled which does mean instantaneous action at a distance but here the atoms need to be entangled in the first place. Thus rubbing a rough cut diamond will have no effect on the rest of the universe other than heating up the surface and making your finger sore.
It would be nice for Brian Cox to add a more clear explanation as to why he thinks the whole universe is connected in the manner he has suggested and clear up the confusion he has caused.

 

[doodyone]

... It would be nice for Brian Cox to add a more clear explanation as to why he thinks the whole universe is connected in the manner he has suggested and clear up the confusion he has caused.

And the "confusion he has caused" is criminal.

 

[doodyone]

...it's obvious that by changing the wavefunction you are changing the energy.

Not wishing to be argumentative but why be overly technical, since the diamond is being heated (or cooled for that matter) the only thing that is obvious that the energy of the system is being changed.

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

 

[Fredrik]

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

Cox has said weird things before. He began a terrible documentary about the LHC with the words "In the beginning, there was nothing. Absolutely nothing. And then, there was an explosion". Before that, I had only heard the big bang described like that by creationists. (The quote is from memory. I believe it's correct, but it's certainly possible that I don't remember it exactly right).

 

[doodyone]

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

Reference the transmitted program 18th Dec: 35mins in
iPlayer may be different.

 

[sheaf]

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

Cox has said weird things before. He began a terrible documentary about the LHC with the words "In the beginning, there was nothing. Absolutely nothing. And then, there was an explosion". Before that, I had only heard the big bang described like that by creationists. (The quote is from memory. I believe it's correct, but it's certainly possible that I don't remember it exactly right).

Not sure if this is the right segment (I haven't got sound at the moment).

From the comments above, it sounds to me like maybe he's talking about a non relativistic quantum mechanics treatment - a multiparticle wavefunction given by an antisymmetrized product of non interacting single particle wavefunctions. If any of the single particle ones have the same energy then the antisymmetrized product vanishes.

 

[doodyone]

Not sure if this is the right segment (I haven't got sound at the moment).

For this clip: from 6:00 he talks about Pauli

 

[becox]

Seems to be some confusion here about the Pauli Principle. Jeff Forshaw and myself write about it in detail in our book The Quantum Universe, chapter 8. The essential point is that two widely separated hydrogen atoms should not be treated as isolated systems. If you'd like to see how we teach this to undergraduates in Manchester, have a read of this:

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

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

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

Brian

 

[sheaf]

Seems to be some confusion here about the Pauli Principle. Jeff Forshaw and myself write about it in detail in our book The Quantum Universe, chapter 8. The essential point is that two widely separated hydrogen atoms should not be treated as isolated systems. If you'd like to see how we teach this to undergraduates in Manchester, have a read of this:

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

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

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

Brian

Can you say anything about the relativistic case (assuming the word "instantaneous" was used in the clip - which I'll have to listen to when I get home !). You don't have an instantaneous shift in energy across spacelike separations presumably, otherwise you could signal ?

 

[bm0p700f]

That link becox is very illuminating. As the wavefunction of two electrons "overlaps" no how far they are they cannot be thought as localised or discrete anymore. So what happens to one effects the other. So Cox is right in a sense, is that right? If i understand that page properly then my understanding of the exclusion principle has certainly evolved.

 

[guillefix]

Ye we were watching this in class and the first thing I said when he said that a particle here affected all the others in the world was: "but not instantly" I mean don't mess with relativity again, enough with the neutrinos thing . The thing that I find closer to all the particles being "connected" is the fact that they interact by forces, this means that if you do somthing to a particle here, the force that all the other particles in the world will "feel" will be different and their energy will therefore be different. However, this doesn't happen instantly at all, as the particles by which the forces interact travel at a finite speed. When the two particles interact, they become then entangled, and therefore most particles in the universe are entangled (at least those that have existed for long enough so that a force-carrier might have been exhanged between them. However, I don't see why is the Pauli exclusion princpile necessary. Of course, no two particles can be in the same state because then they will be the same particle, but that doesn't imply that two particles cannot be in the same energy level, because their position is already different.
I wonder however that if we consider that the energy of an electron doesn't only depend on his position with respect to the nucleus but (in a muuuch lesser degree) in the position of all the rest of particles in the world, then in fact changing a certain particle around here will change the energy in that particle, but not instantly and with very little effect as long as it is not very close or something, which is the case in superconductors. I agree that everything is connected, but if things are far apart they are connected with their pasts (relativity). I think this should have been noted when saying this "woo woo" fact on telly. BTW if something I said is wrong tell me, because my background on quantum mechanics is far from solid

 

[Randomguy]

Seems to be some confusion here about the Pauli Principle. Jeff Forshaw and myself write about it in detail in our book The Quantum Universe, chapter 8. The essential point is that two widely separated hydrogen atoms should not be treated as isolated systems. If you'd like to see how we teach this to undergraduates in Manchester, have a read of this:

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

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

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

Brian

That is genius. Thanks for the link, it makes a lot of sense to me (or at least I think it does!).

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

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

Spooky action at a distance indeed.

 

[dgwsoft]

Seems to be some confusion here about the Pauli Principle. Jeff Forshaw and myself write about it in detail in our book The Quantum Universe, chapter 8. The essential point is that two widely separated hydrogen atoms should not be treated as isolated systems. If you'd like to see how we teach this to undergraduates in Manchester, have a read of this:

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

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

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

Brian

Thanks for responding, Brian. Your book is already on my Christmas list

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

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

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

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

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

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

http://physics.stackexchange.com/questions/18527/pauli-exclusion-principle-and-light-speed

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

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

 

[Randomguy]

Surely it must be an entanglement effect?

The way I see his argument, he's essentially saying that everything is entangled. Presumably it's only in very controlled, carefully manipulated settings where these effects actually become large enough to be observable.

 

[nonequilibrium]

Can someone clear up my confusion: the Pauli principle never said that two electrons can't have the same energy (they can never be in the same state, but two states can have the same energy, think degeneracy), so why aren't they allowed to have the same energy?

For example I'm thinking of a box with two neutral, non-interacting particles (but possibly entangled and all that). There are degenerate energy levels, so the two particles can coexist in the same energy state.

What am I overlooking?

 

[StevieTNZ]

Brian Cox comes on here?! I've learned something new today.

 

[StevieTNZ]

I am a little annoyed that Brian Cox has introduced the "woo woo" factor into science on national television. The "woo woo" factor I am referring to is something that has been highlighted several times in this thread and that is that rubbing the surface of a diamond will change the quantum states of a white dwarf 600 light years from here; essentially he is saying that everything is connected and invokes the Pauli Exclusion Principle to legitimise this claim. This is false.

Bruce Rosenblum, in his book Quantum Enigma, says that everything is interconnected due to entanglement.

Ye we were watching this in class and the first thing I said when he said that a particle here affected all the others in the world was: "but not instantly" I mean don't mess with relativity again

It seems it is instant though. Whether anything travels to the other particle or not, well - that's where the trouble would lie in regards to special relativity.

 

[ajw1]

To be clear: the statement from Brian is not about settling energy levels/states like one has to adjust the ocean level when one take a drop out of it. He suggested that every electron somehow is aware of the state of all other electrons in the universe, and adjusts accordingly.

One should be able to come up with some evidence before making such a bold statement public.

 

[jewbinson]

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

For the hydrogen atom, you can model the overall wavefunction of the atom to be the wavefunction of the c.o.m. + the wavefunction of the internal motion of the system. So is Brian Cox' argument based on the idea that every particle has a wavefunction based on the c.o.m. of the universe (assuming there is a localised one)? Do we need to assume a localised c.o.m. of the universe for this idea to work, or can we approach the idea as if every point in the universe is the c.o.m. of the universe? I know this is handwavy, but still... and bear in mind that I don't know what the Pauli exclusion principle is...

 

[doodyone]

Seems to be some confusion here about the Pauli Principle. Jeff Forshaw and myself write about it in detail in our book The Quantum Universe, chapter 8. The essential point is that two widely separated hydrogen atoms should not be treated as isolated systems. If you'd like to see how we teach this to undergraduates in Manchester, have a read of this:

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

Who'd have thought it.

My undergraduate days at Manchester started just before you left primary school and Loebinger was freshly doctored. I'm well out of touch. Have ordered your book and one other.

Follow the argument, can't follow the maths. Although following the maths regardless of reference to any sense of reality is one way to proceed, I can't help but think that this is one extension of Pauli too far. But then, that has been the nature of this subject since it started. And what do I know?

It's such an astounding conclusion that I'm sure you'd expect more of a reaction than has been the case.

 

[DrDu]

The interesting point here is whether arbitrary large regions of the universe - or even the whole universe - can still be described by a unique wavefunction. While this view seems to be popular among cosmologists, it is interesting that most of the attempts to derive the Fermi-Bose alternative deny this, like the Dopplicher-Haag-Roberts theory, or at least show that only these two alternatives are compartible with the cluster decomposition principle, which says that the results of 2 experiments involving sufficiently localized observables should be independent if the experiments are sufficiently far separated.
Also in solid state physics, to refer to the diamond example, one mostly works with Greensfunctions and not with wavefunctions for the whole crystal.

 

[Fredrik]

My first reaction was that it must be a major misunderstanding on his part. But after reading his comment here and the web page he referenced, I think it's clear that it's not. He's using a very simple model* of the electrons' environment, and what he said on TV is roughly what that model says.

*) He's using the quantum theory of a single particle in Galilean spacetime that is influenced only by a classical potential to calculate the energy levels accessible to the particle, and he's simplifying the problem by making the idealizing assumption that the potential is piecewise constant. Since the theory doesn't say that the Pauli principle holds, but experiments and a better theory (QED) does, he's adding it to this theory as an extra assumption.

I think his exact choice of words is misleading in a few places. For example, at 7:17 he says (roughly) that the energy levels in different atoms have to be slightly different. A model that treats each atom individually would say that this is false. If what he had in mind is that the electrons live in an environment that can be modeled by a potential with multiple "wells" (one for each atom), then he's not even talking about the energy levels defined by each atom (the energy levels "in" each atom). He's talking about the energy levels in the environment defined by all the atoms.

The statement at 8:23 is also weird, because it suggests that every electron in the universe must change its energy in response to what's going on in that diamond. But what he had in mind is just that when one electron is bumped up to a higher energy level, that level is now accessible to all the other electrons.

At 8:34 he even says that the electrons respond "instantly". I'm not sure what to think about this. I think "instantly" may actually be the appropriate word to use because we're talking about what this specific naive theory says. We seem to be talking about a theory in which nothing changes. We just have N electrons sitting in N different energy states, and that's it. So when he's heating the diamond, he's going outside of what that theory can handle, and he's just replacing the list of which states are occupied with another one. The change is "instantaneous" because there's no change at all in the theory, so we're simply replacing the never-changing N-particle state with another that is now more appropriate, because of something that the theory can't actually handle.

I think that in a more accurate model, one in which an electron can emit a photon and transition to a lower energy level, the word "eventually" should replace "instantly". When one of the lower levels is made accessible, then in each time interval, each electron has a non-zero probability to make a transition to that energy state.

We could argue that some other model would be more accurate (in particular a relativistic theory where electromagnetic interactions cause transitions), or that his exact choice of words was misleading, but I don't think what he said (or meant to say) is completely wrong. There is at least a quantum theory that agrees with him.

 

[D H]

We could argue that some other model would be more accurate (in particular a relativistic theory where electromagnetic interactions cause transitions), or that his exact choice of words was misleading, but I don't think what he said (or meant to say) is completely wrong. There is at least a quantum theory that agrees with him.

That is a charitable way to put it. One could also argue that his choice of words was highly misleading, that what he said was not even wrong, and that he took one particular interpretation of quantum mechanics way out of context.

To me, Greene is doing a disservice to science. He should be making science more understanding to the general public. That is not what he is doing. He is instead mystifying science. Every episode of one of those shows featuring Greene or one his standard cohort (Kaku, Carroll) sends people to this site asking us to explain what they meant.

It's also good to keep in mind that the very network that produces the bulk of these pop-sci shows also produce boatloads of shows on Nostradamus, the Illuminati, and "ancient astronauts."

 

[bm0p700f]

That is the problem with popularising this level of Physics as the concepts are quite advanced and it leaves me with a fair degree of Physics/Science education somewhat perplexed although I do grasp the ideas he was trying to convey and provided by becox in that link.

Any energy transition though must involve energy. Where is all this energy coming from to change the energy states of every electron in universe when he heats the diamond. Given the energy changes in other electrons cannot be measured why did he bother going inot this depth. He could have spent the entire hour ust doing the lecture of the solidity. I bet most people left that lecture theatre uterly confused.

 

[Fredrik]

That is a charitable way to put it. One could also argue that his choice of words was highly misleading, that what he said was not even wrong, and that he took one particular interpretation of quantum mechanics way out of context.

To me, Greene is doing a disservice to science. He should be making science more understanding to the general public. That is not what he is doing. He is instead mystifying science. Every episode of one of those shows featuring Greene or one his standard cohort (Kaku, Carroll) sends people to this site asking us to explain what they meant.

Yes, less charitable interpretations are certainly possible. I'm really just saying that there is a charitable interpretation.

This was Cox, not Greene, but we've had similar discussions about Greene in the past. The "everything has speed c through spacetime" comment from "The elegant universe" has indeed confused a lot of people and sent some of them here to ask about it. The discussion of that is actually one of the reasons I'm being so charitable here. I made some pretty harsh comments about what I thought was a Greene quote, and realized much later that the quote was from Wikipedia. It may have been inspired by Greene, but the nonsense comments weren't actually his. I didn't want to make a similar mistake here. In this case, there was of course no doubt that Cox had made those comments, but I still didn't want to say that he was wrong until I was sure, so I read his comment here and started thinking about whether he could be right.

I think his comments were misleading, but not completely wrong.

 

[sheaf]

Can I just check that my understanding of what Fredrik is proposing is correct:

What's happening is that when I perturb electron A, the energy eigenstates of the combined system of A and B change instantaneously, and the system begins evolving towards a new energy eigenstate, which it eventually settles down in. Whilst it's evolving, it's not in a stationary state.

So all that happens "instantaneously" is that the combined system now possesses a new energy eigenstate (stationary state).

 

[Randomguy]

For the hydrogen atom, you can model the overall wavefunction of the atom to be the wavefunction of the c.o.m. + the wavefunction of the internal motion of the system. So is Brian Cox' argument based on the idea that every particle has a wavefunction based on the c.o.m. of the universe (assuming there is a localised one)? Do we need to assume a localised c.o.m. of the universe for this idea to work, or can we approach the idea as if every point in the universe is the c.o.m. of the universe? I know this is handwavy, but still... and bear in mind that I don't know what the Pauli exclusion principle is...

I don't think that's what he's saying. Details about the internal degrees of freedom of the system are contained in the Hamiltonian, which I assume would be constant in its form (the sum of all the individual Hamiltonians each atom in the Universe). He's saying though that when looking at the wavefunction of an electron in any particular region you have to look at the contributions from the wavefunctions of all electrons everywhere, because the electrons are all identical. But these contributions from electrons far far away to the overall wavefunction when looking in that particular region will be tiny and hence negilible.

That said, the guys above have written arguments as to why they think Brian is wrong. I have a fair knowledge of quantum mechanics (almost finished my degree at Cambridge) but I certainly don't have an in depth understanding by any stretch of the imagination.

The statement at 8:23 is also weird, because it suggests that every electron in the universe must change its energy in response to what's going on in that diamond. But what he had in mind is just that when one electron is bumped up to a higher energy level, that level is now accessible to all the other electrons.

But if that energy level is now accessible the overall wavefunction of the Universe must shift by the tiniest amount to reflect this and so surely the energies in atoms across the Universe must shift by the tiniest amount too?

In reality of course it would be completely unmeasurable (and hence claiming it happens is dangerous) but does it not make sense theoretically?

(Interesting post btw)

EDIT: Bah, rereading my earlier post, post #19, just realized I meant 'breaking the degeneracy'. Can't edit that typo out now.

 

[guillefix]

That is a charitable way to put it. One could also argue that his choice of words was highly misleading, that what he said was not even wrong, and that he took one particular interpretation of quantum mechanics way out of context.

To me, Greene is doing a disservice to science. He should be making science more understanding to the general public. That is not what he is doing. He is instead mystifying science. Every episode of one of those shows featuring Greene or one his standard cohort (Kaku, Carroll) sends people to this site asking us to explain what they meant.

It's also good to keep in mind that the very network that produces the bulk of these pop-sci shows also produce boatloads of shows on Nostradamus, the Illuminati, and "ancient astronauts."

Couldn't agree more. It is true that we need to communicate science to the public, but if by doing so you only confirm their suspicions that it's too hard to understand, then you are obviously not doing a good job as a science communicator.

Relating to the work posted by Brian, I want to confirm if my view is right because I cannot yet follow the maths, but I think I understood the concept. What I understood is that because the position of the two particles is defiend by a wavefunction that has a non-zero possibility in every point in the universe (which can be "seen", as Brian said, as electrons jumping to Jupiter and to all the stars in the universe), then there is a possibility that these electron in the diamond goes to the place of another electorn in a distant star. Therefore, there is the possibility that that electron will have to shift its energy in order to not occupying the same state as its new unexpected partner. This means, I think, that the expected value of the energy is slightly different than that if the electron in the diamond didn't exist or had a different wavefunction. This is my intuitive view of the so-called universal wavefunction, which might be wrong, but agrees with what I currently understand.