Pauli Exclusion Principle and Relativity

[_heretic]

The Pauli Exclusion Principle says, roughly, that no two atoms are allowed to occupy the same energy states at the same time. The result of this is apparently that every atom must change its energy state in response to every other atom so as to obey this rule. The well known physicist Brian Cox likes to mention this, such as in his book The Quantum Universe: Everything that Can Happen Does Happen, to say that this implies that the energy states of atoms billions of light years away from one another must change their energy states simultaneously in obedience of this rule. In his book, he assures the reader that this does not violate the theories of relativity because information can not be communicated by making use of this and so temporal paradox situations are avoided.

 

However, surely this is not good enough because relativity tells us that there is no universal time, each particle has its own time. So if the Pauli Exclusion Principle really does say what Brian Cox says, should that not imply that the energy states of atoms must also retroactively be changed at all time points so that the rule applies at some arbitrarily chosen time? In addition to this, which frame of reference is supposed to be the preferred one which every atom alters its energy state with respect to?

Edited September 22, 2012 by _heretic

[md65536]

To quote someone famous, "Brian Cox is Full of **it"

Meanwhile, this Guardian article seems to concede there's some truth to the interconnectedness of all things. It explains that the effect is non-local, so effectively instantaneous across distance "(whatever than might mean)", so I guess relativity of simultaneity would not apply???

 

I wouldn't bother trying to resolve the apparent paradox of it, because as it's mentioned, it can't be used to transfer information and so there's no violation of SR. However I agree with the first link above. Brian Cox is either wrong or he's explaining it wrong, because his explanation (that distant electrons shift their state in response to his example actions) implies a causative effect, which requires information transfer. The electrons across the universe don't change as an effect of his rubbing of a crystal.

 

I don't know the answer to your question. I suspect it's based on BS from Cox. However if it's true that there's some mechanism that ensures all atoms in the universe are instantaneously each in unique states, I suppose it would apply to all possible instants. Because there's no information transfer, it would have to be an automatic property of the atoms, not a causal "response" to other atoms. They would not have to be "changed retroactively", because they would already have been satisfying all applicable physical laws.

Edited September 22, 2012 by md65536

[swansont]

I think Prof Cox is in error.

 

The paradox of his claim is that if the electrons are in distinct states as a result of the PEP, then the atoms they are in must also be in distinct states, which makes them distinguishable, and thus would not obey the PEP. But they do. Which implies that the premise is wrong. (He disagrees, but has not explained or rebutted this in any detail)

[_heretic]

I think Prof Cox is in error.

 

The paradox of his claim is that if the electrons are in distinct states as a result of the PEP, then the atoms they are in must also be in distinct states, which makes them distinguishable, and thus would not obey the PEP. But they do. Which implies that the premise is wrong. (He disagrees, but has not explained or rebutted this in any detail)

 

This is a shame to see that Prof Cox may well just be wrong here. Especially when he repeats the mistake in his book.

 

So, is the Pauli Exclusion Principle at odds with Relativity in anyway?

[swansont]

This is a shame to see that Prof Cox may well just be wrong here. Especially when he repeats the mistake in his book.

 

So, is the Pauli Exclusion Principle at odds with Relativity in anyway?

Not in any way I am aware of.

[_heretic]

Not in any way I am aware of.

 

Thanks.

 

[MigL]

I would also re-examine your definition of the Pauli Exclusion principle, It states that no more than one fermion, ie particles which obey Fermi-Dirac statistics, can occupy the same state. A subtle but sizeable difference.

[Cap'n Refsmmat]

My quantum mechanics professor requires us to submit a question after every class to prove that we were in attendance. I've submitted Cox's interpretation of the Pauli exclusion principle as mine. I'll let you know if I get an answer.

[Ronald Hyde]

I must say that this whole question of measurement, superposition of states, uncertainty principle, etc., is totally overlaid with a fog of confusion, and needs a thoroughgoing

workup that lifts that fog. I know that Karl Popper has written a book about the measurement process that is highly regarded but I haven't read it, and even if it were

relevant the language in it might need to be 'updated', words change meaning and are added in 'living languages'. I would trust almost nothing I read, as is. I would suggest

that you learn the rules of Quantum Mechanics till you know them like the back of your hand, there are only a few rules, and work out every problem with them. They have

NEVER proved to to be wrong in any situation.

 

Richard Feynman said "If you don't think Quantum Mechanics is crazy, you don't understand Quantum Mechanics". Completely true.

 

Murray Gell-Mann, who was across the hallway from Feynman, said "Well, Quantum Mechanics is non-intuitive". Completely true.

 

Paul Dirac said "Shut up and calculate". Completely true.

 

All three are telling you the very same thing, what it says when you do the QM calculation is what is true,

not what some would be philosopher says.

[imatfaal]

Ronald - are you sure about any of those quotes? Shut up and calculate wasn't Dirac, and the others seem like paraphrases

[Ronald Hyde]

Ronald - are you sure about any of those quotes? Shut up and calculate wasn't Dirac, and the others seem like paraphrases

Feynman is a direct quote, Gell-Mann may be paraphrased but he said something very much like it, and the third one has been attributed to several people, but Dirac was the earliest

one I saw it attributed to. I would very much like to hear who else might have said it, I would like to know who originated it.

[imatfaal]

Direct quote from where? Paraphrased from what quote?

 

Many physicists have subscribed to the instrumentalist interpretation of quantum mechanics, a position often equated with eschewing all interpretation. It is summarized by the sentence "Shut up and calculate!". While this slogan is sometimes attributed to Paul Dirac^[29] or Richard Feynman, it is in fact due to David Mermin.

 

I would not normally bother challenging quotes like this - but appending 'Completely true' does raise a red flag and really mean that they should be sourced and direct quotes

[ajb]

Not in any way I am aware of.

 

I think I would say that special relativity and the exclusion principle are deeply linked. The positive energy unitary irreducible representations of the Poincare group are labelled by mass & spin and correspond to elementary particles.

 

Spin has a relativistic origin and so I would find it difficult to really separate the two. Recall that in non-relativistic quantum mechanics, spin is simply bolted on to the theory based on phenomenology. Spin is very mysterious without relativity.

[_heretic]

My quantum mechanics professor requires us to submit a question after every class to prove that we were in attendance. I've submitted Cox's interpretation of the Pauli exclusion principle as mine. I'll let you know if I get an answer.

 

Excellent, thanks a lot for that

 

All three are telling you the very same thing, what it says when you do the QM calculation is what is true,

not what some would be philosopher says.

 

Fair enough, but the thing is, do we understand what the QM calculations are telling us?

[Ronald Hyde]

Direct quote from where? Paraphrased from what quote?

I would not normally bother challenging quotes like this - but appending 'Completely true' does raise a red flag and really mean that they should be sourced and direct quotes

Thank you for that David Mermin, I will look into that. I always look into things, that's just me. The 'completely true, refers to the validity of the meaning of statement, not the

valididity of the exact wording. I'm revising the Gell-Mann phrase, he used counter-intuitive, doesn't that sound more like him? The Feynman statement is exact, verbatim and it

might even be in his lectures, but I have more important things to do than looking for it, it's not indexed for that kind of searching.

 

BTW, for anyone reading this, all these 'greats' have tons of quotable phrases, not just funny but full of meaning for anyone who want to do Physics, or just likes it. So I collect

them.

 

More on the saga of "Dick and Murray". They both came from New York, from 'modest circumstances', were recognized early, were top notch at mathematics ( wish I was ) but

they rose up quickly because they had what I call 'native talent'. They needed little instruction to learn anything and could figure it out themselves, and solve problems on

their own, unaided. Fascinating studies in Humanity. Because Feynman's story is well documented I'll say something about Murray.

 

Caltech was an engineering school and wanted to gain prestige in the Physics area, they only taught 'engineering level' Physics and wanted to have an accelerator and some

particle physics to attract more students, etc.. So they chose to hire these two and gave them about double the going salary, and put them across the hall from each other.

They pretty much kept to themselves, Feynman didn't really do much teaching or take on any students until they practically forced him to do the famous lectures ( thank you

Leighton and Sands for saving them for us ) but Murray was more participative. He taught, even took his students on field trips, he was an Auduboner ( birder ), now understand

that both these guys, and me too for that matter, I love Nature and the outdoors, I think real physicists are 'country boys' at heart.

 

Understand that I've never met these two but I'm a huge collector of anything and everything to do with Physics and Math. And if anyone tells you that 'Physics is personality

neutral' do not believe them. Maybe on the teaching end but on the doing it very much depends on personality. That being said, here are some of the things said by and about

Murray. He's still with us BTW.

 

Murray will forgive ignorance but not stupidity.

 

My colleagues are afraid to use their intuition.

 

That which is not strictly forbidden is compulsory. This quote alone is worth a page of digression. I found it linked to T.H.White but I thought it came from George Orwell.

 

One thing you need to know about Murray is that he is a short peppery guy ( locally compact ) from New York where words might have been a form of self defense,

and he is very sharp of tongue.

 

I'm sure that I have more quotes of him but I just found the wikiquotes ( never used it before ) and there are tons of them.

 

Anyone is welcome to question my veracity at any time, but please do it like imatfaal, politely and with a well defined question. Undue rudeness will get me to use the 'report'

button, I've been instructed that that is the way to handle things, and enough reports will be handled by the staff. Likewise if I question someone's veracity I will always give

a supported line of reasoning, as I have in the past. That is just they way I do things, nothing without a reason.

 

I think I would say that special relativity and the exclusion principle are deeply linked. The positive energy unitary irreducible representations of the Poincare group are labelled by mass & spin and correspond to elementary particles.

 

Spin has a relativistic origin and so I would find it difficult to really separate the two. Recall that in non-relativistic quantum mechanics, spin is simply bolted on to the theory based on phenomenology. Spin is very mysterious without relativity.

 

The way that I understand this, and I could be very well wrong, but the logical chain is this. I'll give the Wigner interpretation, the 'little group' SO(3) of rotations, is a subgroup of

the Poincare group, the big group, which includes rotations and boosts. However you can't have boosts alone as a group, the way you can rotations, because successive boosts

generate rotations. When you introduce spin into the picture, from the outside as it were, only the values spin 1/2 and 1 are consistent with the Poincare group.

 

Along the same lines, years ago I found that you could derive the exclusion principle from spin and rotations alone at non-relativistic speeds. And I found out that this guy Feynman

had done the same thing and was quite proud of himself, but I have never seen his derivation. I would love to find it. And this is kind of funny, but I ran across a web page that had

a link to another page that purported to debunk about a dozen common fallacies. Never wanting to carry around any false reasonings in my little bag of tricks, I went there to look and one of then was that you had to use relativity to derive the exclusion principle.

 

Fair enough, but the thing is, do we understand what the QM calculations are telling us?

It's going to return an amplitude, the square of which is the probability of that happening. The usual stuff.

How that is interpreted may be context related, context is always important. Right now I can't say much

more than that, I'm getting tired and hot and my little brain stops working then. I'll come back to this

latter.

[Obelix]

The Pauli Exclusion Principle says, roughly, that no two atoms are allowed to occupy the same energy states at the same time.

 

NO MORE THAN two - 2 - atoms.

[Cap'n Refsmmat]

My professor's response was essentially "I don't know what Brian Cox is talking about", incidentally.

[md65536]

I've been thinking about this some more and want to repeat what I said except hopefully more clearly.

 

Cox explains his point by saying that when he rubs a diamond, heating up the atoms, all the other atoms in the universe shift in order to allow the diamond's atoms to change states. But this is misleading, because there's no causal relationship.

 

I could instead claim that some atoms in the universe want to be in the state currently occupied by some of the atoms in the diamond, and so the atoms in the diamond are forced to change energy state, and they do that by having Cox rub it. Of course, this is an absurd explanation, as is the implication that the desire of some atoms somewhere are the cause of Cox's rubbing. And rightly so... there is no causal relationship between the different atoms changing energy state. That doesn't mean that Pauli's exclusion principle doesn't hold, it's just not causation.

 

And that's a problem with the way Cox explains it. My causal example is absurd, but Cox's is equally wrong, yet it is plausible enough to imply a classical "common sense" connection (ie. causation) between his actions and all the atoms in the universe.

[Ronald Hyde]

If you're intuition is that something isn't right here, I would say that you're intuition is entirely correct. The mere fact that someone might apply

'classical common sense' to questions involving QM and modern Physics is dangerous. Water doesn't run uphill, but liquid Hellium-3 can. Einstein

'quit' QM because he thought it conflicted with his idea that 'God doesn't play dice', that the inner workings of the World were deterministic. I can

find no reason to believe that QM conflicts with the notion that the world might be deterministic, none. And I've gone over this with a fine toothed

comb. So my take on all these questions may be very different from the usual views, some might say highly speculative, but to me they are just

thoroughly thought out. However, that doesn't answer your question, it only shows that I think it's more involved than Mr. Cox or maybe you think.

 

Suppose that you're sitting in front of a little black box with a knob on it, the knob has three positions, the center on is 'do nothing' the others are

'change something over here' and 'change something over there'. The changes all involve putting energy and a change of entropy into a system.

The two 'change' positions may start long casual chains that make many changes in the world. You can see that the ordinary notion of causality

involves entropy and energy, trying to use the notion of causality where those are not involved can be very tricky indeed.

 

It really goes back to my earlier statement that these questions need a thorough workup.

[_heretic]

My professor's response was essentially "I don't know what Brian Cox is talking about", incidentally.

 

So Prof Cox is in error it seems. Did your Professor explain the correct understanding of the principle?