A night with the stars (Brian Cox on telly)

[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.

 

[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).

Of course this isn't right - after the perturbation, the system would continue in a superposition of energy eigenstates until a measurement occurred wouldn't it ?

 

[becox]

Dear all,

Let me add a bit more by way of clarification, because I think it's interesting. I've already posted a detailed analysis of the behaviour of a two proton - two electron system, and shown how the exclusion principle leads to a covalent bond in a Hydrogen molecule. Let me paste a couple of pages from my book The Quantum Universe - to save you having to buy it - and annotate it in a couple of places.

In the book, we do the double well as I posted previously.

This is how we describe the situation:

"It seems that we must conclude that the pair of identical electrons in two distant hydrogen atoms cannot have the same energy but we have also said that we expect the electrons to be in the lowest energy level corresponding to an idealised, perfectly isolated hydrogen atom. Both those things cannot be true and a little thought indicates that the way out of the problem is for there to be not one but two energy levels for each level in an idealised, isolated hydrogen atom. That way we can accommodate the two electrons without violating the Exclusion Principle. The difference in the two energies must be very small indeed for atoms that are far apart, so that we can pretend the atoms are oblivious to each other. But really, they are not oblivious because of the tendril-like reaches of the Pauli principle: if one of the two electrons is in one energy state then the other must be in the second, different energy state and this intimate link between the two atoms persists regardless of how far apart they are.
This logic extends to more than two atoms – if there are 24 hydrogen atoms scattered far apart across the Universe, then for every energy state in a single-atom universe there are now 24 energy states, all taking on almost but not quite the same values. When an electron in one of the atoms settles into a particular state it does so in full “knowledge” of the states of each of the other 23 electrons, regardless of their distance away. And so, every electron in the Universe knows about the state of every other electron. We need not stop there – protons and neutrons are fermions too, and so every proton knows about every other proton and every neutron knows about every other neutron. There is an intimacy between the particles that make up our Universe that extends across the entire Universe. It is ephemeral in the sense that for particles that are far apart the different energies are so close to each other as to make no discernable difference to our daily lives.

This is one of the weirdest-sounding conclusions we’ve been led to so far in the book. Saying that every atom in the Universe is connected to every other atom might seem like an orifice through which all sorts of holistic drivel can seep. But there is nothing here that we haven’t met before. Think about the square well potential we thought about in Chapter 6. The width of the well determines the allowed spectrum of energy levels, and as the size of the well is changed, the energy level spectrum changes. The same is true here in that the shape of the well inside which our electrons are sitting, and therefore the energy levels they are allowed to occupy, is determined by the positions of the protons. If there are two protons, the energy spectrum is determined by the position of both of them. And if there are 1080 protons forming a universe, then the position of every one of them affects the shape of the well within which 1080 electrons are sitting. There is only ever one set of energy levels and when anything changes (e.g. an electron changes from one energy level to another) then everything else must instantaneously adjust itself such that no two fermions are ever in the same energy level.

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

This decadent multiplicity of energy levels is not just an esoteric device to evade the constraints of the Exclusion Principle. In fact, it is anything but esoteric because this is the physics behind chemical bonding. It is also the key idea in explaining why some materials conduct electricity whilst others do not and, without it, we would not understand how a transistor works."

We then go on to 3 wells, and then to 10^23 or so - which is the situation in small lump of silicon - and show that this multiplication of very closely-spaced energy levels, (correction added - the occupation of which is governed by) the Pauli principle, is the origin of the conduction and valance bands - i.e. the key to understanding how transistors work (which we also describe).

I'll admit that we just state that causality is preserved without proof in the book. The notion of causality in quantum field theory is actually a tricky one - there is a large literature on it if you do a search on Spires. But the description of the Universe as a single potential well, with an associated energy level spectrum, is surely valid unless one introduces new physics, which is not mandated by experiment - and I remind you that this rather counter-intuative picture is necessary at a macroscopic level (admittedly transistor-sized and not universe-sized) in order to understand the conduction and valence bands in semiconductors.

The more "presentational" question posed by some on the forum - namely that one shouldn't say that everything is connected to everything else for fear of misinterpretation - is interesting. In my view, the interpretation of quantum theory presented above is not only valid, but correct in the absence of new physics - and therefore everything IS connected to everything else. I was very careful to point out in the lecture that this does not allow any woo woo garbagee into the pantheon of the possible, as I think I phrased it.

My general position is that when communicating with the public we shouldn't spend our time triangulating off nutters. I'm having to deal with this in spades in my current series, Wonders of Life, where it is tempting to try to give creationists no ammunition at all by avoiding areas of doubt when describing the origin of life and the evolution of complex life on Earth. My strategy is to ignore such concerns, because these people shouldn't occupy any of our time! If we tried to take account of every nob head on the planet, we wouldn't have time to make the programs or write the books.

Brian

 

[becox]

By the way Fredrik - your criticism of Brian Greene stating that "everything has a speed c through spacetime" is utterly misplaced. This is in lecture number one of every good undergraduate course on special relativity - completely correct and not in the least misleading. Look at the metric and work it out for yourself!

 

[Dadface]

I think discussions of the type going on here may be avoided if science popularisers put even greater emphasis on the fact that theories are not necessarily absolute immutable truths.Perhaps a lesser emphasis on statements that can be interpreted as "this is how it is" and greater emphasis on statement that can be interpreted as "this is the way current theories show how it could be".
As a general observation it was a great programme,both fun and educational.The AS and A level physics students I know found a lot of the content to be useful and relevant to their studies and even more importantly it whetted their appetites for the subject even more.

 

[unusualname]

Hi Brian (becox)

Your argument is true in a finite universe with finite and conserved energy, but it might be problematic to apply it to an infinite expanding universe.

And not everyone believes in a global wavefunction of the universe.

But I do :-)

(btw I wish you'd used Gene Wilder's original version of 'Pure Imagination' at the end of your (cool) 'Wonders of the Universe' series)

 

[Fredrik]

By the way Fredrik - your criticism of Brian Greene stating that "everything has a speed c through spacetime" is utterly misplaced. This is in lecture number one of every good undergraduate course on special relativity - completely correct and not in the least misleading. Look at the metric and work it out for yourself!

A lot of my criticism of him was utterly misplaced, because in one of these threads, someone quoted Wikipedia, and I thought it was a Brian Greene quote. I stand by my comments about the quote, but I regret that I didn't make sure I knew where the quote was from.

What Greene means when he says that everything has speed c through spacetime is that the "magnitude" of the four-velocity vector is c. I'm certainly not denying that four-velocity is a useful concept, or that the magnitude of every four-velocity vector is c, but I reject the idea that the value of its magnitude can be used to explain things. The four-velocity vector is defined as the vector with magnitude c in the direction of the tangent of the world line, so the observation that its magnitude is c is hardly a profound insight.

It's not misleading to mention that the magnitude of the four-velocity is c, but it's misleading to suggest that this is the reason why there's such a thing as time dilation.

 

[qsa]

Dear all,

Let me add a bit more by way of clarification, because I think it's interesting...

Brian

I agree. see post #28



https://www.physicsforums.com/showthread.php?t=371254&highlight=susskind&page=2

 

[qsa]

Hi Brian (becox)

Your argument is true in a finite universe with finite and conserved energy, but it might be problematic to apply it to an infinite expanding universe.

And not everyone believes in a global wavefunction of the universe.

But I do :-)

(btw I wish you'd used Gene Wilder's original version of 'Pure Imagination' at the end of your (cool) 'Wonders of the Universe' series)

nice to see you back. please check your PM.

 

[akhmeteli]

This is how we describe the situation:
"… And so, every electron in the Universe knows about the state of every other electron. ..
… There is only ever one set of energy levels and when anything changes (e.g. an electron changes from one energy level to another) then everything else must instantaneously adjust itself such that no two fermions are ever in the same energy level…."
Brian

Interesting… However, you are talking about extremely small energy variations, so I wonder about that “instantaneously”… Indeed, as far as I understand, one cannot measure energy instantaneously with good accuracy. “Energy measurement time” times “energy measurement accuracy” should be at least of the order of the Plank constant. So I am not sure talking about an accurate value of energy within a limited time frame (let alone in terms of “instantaneously”) makes much sense, and my take is somewhat different: an electron at a distant star does not have to know anything about an electron on Earth instantaneously. True, in a million years it will have to “adjust itself”, but not before. The situation is similar to that with the Coulomb law: an electron at a distant star can indeed “feel” an electron on Earth, but not instantaneously.

 

[BrotherHod]

An interesting review of "A night with the Stars" and does raise some interesting ideas around science presentation today.

http://fieldlines.org/2011/12/23/double-twit-experiment-what-brian-cox-gets-wrong/

 

[dgwsoft]

Dear all,

Let me add a bit more by way of clarification, because I think it's interesting. I've already posted a detailed analysis of the behaviour of a two proton - two electron system, and shown how the exclusion principle leads to a covalent bond in a Hydrogen molecule. Let me paste a couple of pages from my book The Quantum Universe - to save you having to buy it - and annotate it in a couple of places.

...

Brian

Thanks for posting that, Brian. Your book was in my Christmas stocking this morning so I will read it before commenting further. (I also have The Grand Design by Stephen Hawing, and Hubble: Window on the Universe, so its a scientific Christmas for me!)

 

[md2perpe]

One thing that I haven't seen anyone saying in this thread is that by just being bound to different atoms (especially if these are separated by a huge distance), the states of two electrons are almost perpendicular (a more exact word for being distinct).

 

[md2perpe]

The only thing I can see that Brian Cox has shown in the Double Well calculations is that there are two "ground states" with somewhat different energies. But this says nothing about what happens when energy is added to the system!

The other electrons will only have to adjust their energies if you can inject such an amount of energi that one electron will go to an occupied state. But is that really possible? Perhaps you can only add such an amount of energy that the electron will go to a non-occupied state; then the other electrons won't have to adjust.

 

[ColinW]

To me there seems a world of difference between electrons associated with a fixed crystal lattice, whose atoms are obviously interacting (in some way that as an engineer and not a physicist I don't claim to understand) and electrons in material separated by a billion light years.
I see this as a lead up to a possible experiment where Professor Cox says, "Right, you guys watch this detector while I take the million dollar diamond up the street to rub it." and he's never seen again!

 

[md2perpe]

There is no real difference between electrons associated with a fixed crystal lattice and electrons separated by a billion light years. They all have to be in different states. And the states are universal.

 

[ColinW]

There is no real difference between electrons associated with a fixed crystal lattice and electrons separated by a billion light years. They all have to be in different states. And the states are universal.

Can you explain that a bit more, obviously without using the words Pauli exclusion principle, use of which I believe would be called a tautology?
More specifically can you explain how Professor Cox rubbing his diamond in London can affect electrons where you are, let alone on the other side of the universe?

 

[md2perpe]

There is no real difference between electrons associated with a fixed crystal lattice and electrons separated by a billion light years.

The electrons don't know if they are bound or free; they (rather: their wave functions) merely adjust to potentials. The wave functions cover all of universe but their amplitudes are differently distributed. For electron bound to a lattice, the amplitude is high inside the lattice, but low almost directly outside of it.

They all have to be in different states. And the states are universal.

Can you explain that a bit more, obviously without using the words Pauli exclusion principle, use of which I believe would be called a tautology?

Since this is the Pauli exclusion principle and it's not valid for all types of particles, I cannot explain this without reference to the Pauli exclusion principle.

More specifically can you explain how Professor Cox rubbing his diamond in London can affect electrons where you are, let alone on the other side of the universe?

No, I can't. I don't agree with Prof. Cox. I do agree that states are universal, but not that adding energy would force all electrons to adjust.

 

[ColinW]

My apologies. When I said "difference" I meant difference between the situations, not difference between the electrons.
I am actually quite happy to accept the Pauli exclusion principle (although I can't really understand it) and I accept its implications with regard to things like semiconductor energy bands. There is enough evidence for me to see that something is clearly happening and PEP is as good an explanation as any.
It was Professor Cox's universal (and apparently instantaneous) electron shuffling that I can't accept.

 

[gibbson_e]

So, in summary.. it isn't instantaneous?

 

[md2perpe]

In my view no distant adjustments are even needed, so there's no question "is it instantaneous?"

 

[StevieTNZ]

So, in summary.. it isn't instantaneous?

You'd think it is instantaneous. If the particles in question followed the exclusion principle, one particle jumps into a new state currently occupied by another particle, then the other particle would need to jump to another state to satisfy the principle. At no point should the two particles share the same state.

 

[akhmeteli]

You'd think it is instantaneous. If the particles in question followed the exclusion principle, one particle jumps into a new state currently occupied by another particle, then the other particle would need to jump to another state to satisfy the principle. At no point should the two particles share the same state.

I respectfully disagree for reasons given in post 44 in this thread - I am not sure energy can be well defined at some point in time. So if the energy is not quite definite, you cannot say with certainty that the two particles are in the same state.

 

[DrDu]

Dear all,

There is an intimacy between the particles that make up our Universe that extends across the entire Universe. It is ephemeral in the sense that for particles that are far apart the different energies are so close to each other as to make no discernable difference to our daily lives.

Brian

But the fact that these differences become effectively unmeasurable for systems being considerably far appart is formalized under the name "cluster decomposition principle" and occupies quite a fundamental position in quantum field theory. Explicitly it is used to rule out quantum field theories with other statistics like multidimensional or projective representations of the permutation symmetry group (see e.g. "quantum field theory" by S. Weinberg).
From that point of view the Fermi and Bose statistics are the only statistics which lead to the notion of independent systems at large distances due to the exponential fall off of energy level splittings below not only any practical level of precision relevant for our daily lives but below any imaginable level however small we may choose it.

 

[Q-reeus]

#58 provides a resolution in terms of exponential fall off with distance of energy level splittings. This still seems to imply there is iaaad (instantaneous action at a distance) but it gets too feeble to matter. Consider the following as a possible counterexample to iaaad. Suppose we have a normally conducting two-wire TL (transmission line), shorted at both ends A and B. End A is magnetically linked to a small coil energized with a near instantaneous voltage pulse. By transformer action we expect an induced emf that travels the length of the TL at near light speed as a voltage-current pulse. We do not expect the far end B to know anything about the event at A until the pulse arrives. What though if the TL is wholly superconducting - all superconducting Cooper paired electrons share the single ground state wavefunction. So if there is any spooky aaad going on, B should somehow be instantly effected by event at A, right? But that would break the taboo of instantaneous communication. So what kind of iaaad can be going on in this situation that physically means anything at all?

 

[Ken G]

I think one possible path out of the morass of worrying about whether all the electrons in the universe are "instantaneously" connected is to simply notice that there is really no requirement for us to imagine that there is any such thing as "all the electrons in the universe", as independent real entities. If we imagine they are independently real but indistinguishable, we have to wonder how they can be somehow connected to each other. But it seems to me, the whole point of indistinguishability is that the particles are not actually separate objects in the first place. So, they are connected by virtue of not being different, rather than by virtue of being different but indistinguishable.

Let's see this by turning the question around-- instead of thinking about a bunch of electrons, and ask what states they are in, let's start by thinking about a bunch of states, and asking whether or not they are occupied by an electron. In other words, let's treat the states, and their presence or absence of occupation, as what is real, rather than the electrons (all we need to know about the electrons is how many there are, a separate constraint on the reality of the states). Since the electrons are indistinguishable, when we ask "is this state occupied by an electron", we never need to ask "which electron", only yes or no is it occupied.

Now if we asked, is the occupation of one state "connected to" the occupation of the other states, we would have to say yes-- there are only so many electrons to go around, so every state that is occupied reduces the access of every other state to electrons. Hence if I measure a particular energy state as being occupied by an electron in some star, let's say, and if all the states have nondegenerate energies, then this measurement will affect the expected occupation number of every other state in that star because that information has changed the environment of all those electrons in some very small way. Without getting into the possible distinctions between what is actually real and what we can know about what is actually real, we have to allow that when our description of the reality changes instantaneously, then for all scientific purposes, the reality itself has changed instantaneously. Certainly no other observer will get a contradictory result to that, because our conception of the full reality must include all the experiences of the observers everywhere. So when one person rubs a diamond, the reality is instantaneously different, and it is instantaneously different everywhere because it is all one thing, but this cannot be used to send signals or propagate "effects" faster than c.