APOD: Pauli Exclusion Principle: Why You... (2010 Feb 28)

[APOD Robot]

Pauli Exclusion Principle: Why You Don't Implode

Explanation: Why doesn't matter just bunch up? The same principle that keeps neutron stars and white dwarf stars from imploding also keeps people from imploding and makes normal matter mostly empty space. The observed reason is known as the Pauli Exclusion Principle. The principle states that identical fermions -- one type of fundamental matter -- cannot be in the same place at the same time and with the same orientation. The other type of matter, bosons, do not have this property, as demonstrated clearly by recently created Bose-Einstein condensates. Earlier this decade, the Pauli Exclusion Principle was demonstrated graphically in the above picture of clouds of two isotopes of lithium -- the left cloud composed of bosons while the right cloud is composed of fermions. As temperature drops, the bosons bunch together, while the fermions better keep their distance. The reason why the Pauli Exclusion Principle is true and the physical limits of the principle are still unknown.

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[JohnD]

This caption confuses me, and the original online article http://www.aip.org/mgr/png/2001/118.htm does too.

"Lithium has two stable isotopes, one of which is a boson (lithium-7), the other of which is a fermion (lithium-6). "

How is the ion of an atom become a fermion or a boson? I thought that both of these were classifications of sub-atomic particles, electrons, quarks etc.

JOhn

[henrystar]

I look at APOD every day, and this is the first time I've registered and commented.

First, let me respond to John's excellent question: whether an object is a fermion or a boson depends solely on the sum of the spins of the particles that make up the body. The two isotopes of Lithium have a different number of neutrons, each of which has spin 1/2. So, one isotope is a boson, the other is a fermion. That's all there is to it.

But now for the reason I registered: The last sentence of the caption is incorrect. The Pauli Exclusion Principle is justly called that because Pauli postulated it originally. But since the discovery of quantum mechanics, it has been fully understood - if the world is quantum mechanical, then the Pauli Exclusion Principle necessarily holds. As for the physical limits of the principle, it is not conceivable that the Pauli Exclusion Principle would be found in some limit not to hold, without quantum mechanics itself breaking down. Will quantum mechanics itself ever break down? In my opinion, no, for the fundamental reason that it is so simple and basic there is really no place for it to break! Took me six years of teaching quantum mechanics to understand that, and I published it in the American Journal of Physics, November 1990, link here: http://henry.pha.jhu.edu/henry.QM.reTeX.pdf

Cheers,

Dick Henry (Professor of Physics and Astronomy, The Johns Hopkins University)

[JohnD]

Thank you, Dick!
I hesitate to ask a Q that reveals my ignorance, but what about the other particles?
I find that protons and electrons also have spin of 1/2, and as they normally go in pairs, an atom will have integer spin, from that source.
But aren't these lithium ions? With an electron missing? So the spin due to protons and elctrons is not integer.
Let me work this out:
Lithium-6 atoms, with three protons, electrons and neutrons, will have non-integer spin, 9x1/2=4.5, but as an ion it will have integer spin.
Lithium-7 atoms, with three protons and electrons and four neutrons, will have integer spin, 10x1/2=5, but without an electron it won't.
OK.
But, we are told that Pauli prevents the collapse of ordinary matter, if it is composed of fermions.
What about atoms that have integer spin, like lithium-7, or any other atom that as such has integer spin and is therefore a boson?

Professor, I'm not challenging you, I'm asking for clarity!

John

[RJN]

First, thanks to Professor Henry for his insight and his reply to JohnD's interesting question. This is not my subfield, but in this reply-post I give a general reason for including that last line in the above referenced APOD. In the past, I have encountered this sentiment in several things I had read. I have searched the web anew for some of them and have a few tidbits. One tidbit is a quote from Wolfgang Pauli himself in the speech he gave as he accepted the Nobel Prize in Physics:

“Already in my original paper I stressed the circumstance that I was unable to give a logical reason for the exclusion principle or to deduce it from more general assumption. I had the feeling and I still have it today, that this is a deficiency. The impression that the shadow of some incompleteness fell here on the bright light of success of the new quantum mechanics seems to me unavoidable”.

Next, there appears to be several research papers that have searched, experimentally, for experimental limits of the Pauli Exclusion Principle in the past few years. One such paper is here: http://arxiv.org/abs/0803.0870 . In the introduction of the paper it says:

"The Pauli exclusion principle(PEP), which plays a fundamental role in our understanding of many physical and chemical phenomena, from the periodic table of elements, to the electric conductivity in metals, to the degeneracy pressure (which makes white dwarfs and neutron stars stable), is a consequence of the spin-statistics connection[1]. Although the principle has been spectacularly confirmed by the number and accuracy of its predictions, its foundation lies deep in the structure of quantum field theory and has defied all attempts to produce a simple proof,as nicely stressed by Feynman[2].

The reference is to Feynman's famous "The Feynman Lectures on Physics." Here Feynman has been quoted as saying:

“Why is it that particles with half-integral spin are Fermi particles whereas particles with integral spin are Bose particles? We apologize for the fact that we cannot give you an elementary explanation. This probably means that we do not have a complete understanding of the fundamental principle involved.”

- RJN

[ems57fcva]

RJN write/quoted -

The reference is to Feynman's famous "The Feynman Lectures on Physics." Here Feynman has been quoted as saying:

“Why is it that particles with half-integral spin are Fermi particles whereas particles with integral spin are Bose particles? We apologize for the fact that we cannot give you an elementary explanation. This probably means that we do not have a complete understanding of the fundamental principle involved.”

I don't see that this does much to defend the statement that

The reason why the Pauli Exclusion Principle is true and the physical limits of the principle are still unknown.

The reason lies in the math that you actually link to. The Feynmann quote is dealing with the issue of why it is the half-integral spin particles thast obey the Pauli Exclusion Principle instead of the ones with integral spins. Even if things were the other way around, the Pauli Exclusion Principle would still be present, even though it would apply to a different class of particles.

As for the issue of the physical limits of the principle: Like any other quantum mechanical principle, the potential of its having macroscopic effects actually exists. (Indeed, our not imploding can be considered to be a macroscopic effect.) So there are no practical physical limits. Instead as one comes to deal with more and more particles in more and space, their aggregate behavior comes more and more to be in accord with classical mechanics.

All the same, I do understand your concern. Quantum mechanics is just plain wierd and many physicists still struggle with the issues of its interpretation.

[biddie67]

The APOD submissions travel from outer space to near-Earth space and now to inner-inner space - I loved this collection of links.

I have been working my way through a DVD survey course on quantum mechanics that I ordered from an online website. Maybe I'm getting dotty in my old age by attempting this but I'm fascinated - it's like attempting to learn a bizzare language and a quite fuzzy math all at the same time.

One of my favorite programs to listen to is "Coast to Coast AM" and I have to declare that my ability to merrily and freely associate ideas, no matter their source, can come up with some crazy conjunctions .... with a slight mischievious grin here's my latest:
invisible ghosts are bosons; materialized ghosts are fermions!!!

(( laughing )) hope that statement doesn't get me blocked from this board

[bystander]

... I have to declare that my ability to merrily and freely associate ideas, no matter their source, can come up with some crazy conjunctions ...

With respect to free association, you have a way to go to compete with neufer.

[JohnD]

Interesting that Feynman ackowledged quantum physics might be incomplete.

I've just been reading "Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality" by Manjit Kumar
http://www.amazon.co.uk/Quantum-Einstei ... 292&sr=1-1

It's a history of the development of quantum physics, from Plank onwards, and as the title says, with the debate with Einstein, who too declared that quantum physics was incomplete and therefore not a tenable theory. The account left Feynman out completely - I wonder why, now.

JOhn

[DaveBone]

So you have a solid composed of lithium bosons and fermion. Does this mean that as you cool this solid, it will contract more than a solid composed of just fermions. If the bosons will "shrink" together, they should take up less physical space. I wonder if this has been tested and what the results are?

[JohnD]

Dave,
Revealing my ignorance further, I think that these are 'gases' or 'vapours' of LItium.
I presume they are produced in the same way as Bose-Einstein condensates (http://en.wikipedia.org/wiki/Bose%E2%80 ... condensate).
But that makes me ask another Q.
Descriptions of B-E condenstes are that they are made from a vapour of rubinium atoms, at a temperature similar to the above, very close to absolute zero..

I find that the boiling point of rubidium is about 976 K, and of lithium 1516K.
How can a vapour of such an element exist so close to absolute zero?
Clearly, a B-E 'condensate' is not dew drops of metal, but a cloud of atoms.

How come?
John

PS No one has answered my earlier Q. Professor Henry, please?

[RJN]

JohnD,

I believe that Prof. Henry did answer your previous question: an ion can be either a fermion or a boson. Here is an interesting discussion: http://www.physicsforums.com/archive/in ... 77752.html .

As to your present question, although it is not my subfield, I think it is quite difficult to make a Bose-Einstein condensate. One must have a bunch of identical bosons cooled below a critical temperature given here: http://en.wikipedia.org/wiki/Bose-Einstein_condensate .

- RJN

[neufer]

The same principle that keeps neutron stars and white dwarf stars from imploding also keeps people from imploding and makes normal matter mostly empty space. The observed reason is known as the Pauli Exclusion Principle. The principle states that identical fermions -- one type of fundamental matter -- cannot be in the same place at the same time and with the same orientation.

The other type of matter, bosons, do not have this property.

So then Tiger Woods & Jim Bunning are both Bozons