A night with the stars (Brian Cox on telly)


by dgwsoft
Tags: brian cox, quantum mechanics
Randomguy
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#19
Dec20-11, 12:48 PM
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Quote Quote by becox View Post
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/fo...le%20Well.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
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#20
Dec20-11, 12:56 PM
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Quote Quote by becox View Post
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/fo...le%20Well.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/que...nd-light-speed

http://sciencefocus.com/forum/pauli-...ars-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
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#21
Dec20-11, 01:05 PM
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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
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#22
Dec20-11, 08:54 PM
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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
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#23
Dec21-11, 12:01 AM
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Brian Cox comes on here?! I've learnt something new today.
StevieTNZ
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Dec21-11, 12:07 AM
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Quote Quote by BrotherHod View Post
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.

Quote Quote by guillefix View Post
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
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#25
Dec21-11, 02:30 AM
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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
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#26
Dec21-11, 03:36 AM
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Quote Quote by Randomguy View Post
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
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#27
Dec21-11, 06:58 AM
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Quote Quote by becox View Post
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/fo...le%20Well.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
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#28
Dec21-11, 07:32 AM
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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
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Dec21-11, 07:54 AM
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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
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#30
Dec21-11, 09:00 AM
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Quote Quote by Fredrik View Post
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
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#31
Dec21-11, 09:12 AM
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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
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Dec21-11, 09:42 AM
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Quote Quote by D H View Post
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
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#33
Dec21-11, 10:37 AM
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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
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#34
Dec21-11, 11:02 AM
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Quote Quote by jewbinson View Post
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.

Quote Quote by Friedrik
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 realised I meant 'breaking the degeneracy'. Can't edit that typo out now.
guillefix
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#35
Dec21-11, 01:37 PM
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Quote Quote by D H View Post
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.
sheaf
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#36
Dec22-11, 03:07 AM
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Quote Quote by sheaf View Post
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).
Of course this isn't right - after the perturbation, the system would continue in a superposition of energy eigenstates until a measurement occured wouldn't it ?


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