Can Pauli's Exclusion Principle be Explained? A Decade Later

[esmeralda4]

Hi,

I have been reading Bill Bryson's A Short History of Nearly Everything and have got to the bit about Pauli's Exclusion Principle.

It states that 'certain pairs of subatomic particles, even when separated by the most considerable distances, can instantly 'know' what the other is doing.'

It later says '...the phenomenon was proved in 1997'.

and later still...

'No-one has ever explained how the particles achieve this feat. Scientists have dealt with this problem, according to Yakir Anaranov, by 'not thinking about it'.


BUT, this book was written in 2003 and it's now 2012. Have we made any progress on this? Can this now be explained?

Many thanks

 

[Ken G]

BUT, this book was written in 2003 and it's now 2012. Have we made any progress on this? Can this now be explained?

There's no fundamental new insights that I know of, but be aware that those popularizing writers are running pretty fast and loose with the actual physics here. What we still don't know are the reasons for the two key inputs:
1) why electrons are indistinguishable from each other
2) why electrons have half-integer spin, so if you exchange any two of them, the state you use to describe those two electrons must acquire a minus sign.
But we do know quite well what these two statements must imply for quantum mechanics. Never mind the mathematical details of that #2, it takes you very deeply into the machinery of both relativity and quantum mechanics! But the point is, combining #1 and #2 gives you the Pauli exclusion principle, because if you imagine that two electrons are in the exact same state, then if you exchange them, you cannot say the state you get is any different, because they were indistinguishable and in the same states, so how can you change the full state by interchanging the particles? So #1 tells you that the full state must stay the same if you interchange the particles, but #2 tells you the full state must acquire a minus sign if you do that. What state can both stay the same and acquire a minus sign? Only one-- the null state, which means it is a nonexistent state, which means the particles cannot be in this nonexistent state, which means they cannot both be in the same single-particle state, which is the Pauli exclusion principle.

As for one particle "instantly knowing" about the other particle, I would say that is a rather bad characterization of what is going on. It's totally against the spirit of #1-- if two particles are indistinguishable, you must avoid any language that suggests you can distinguish the particles. Talking about one particle knowing what the other particle is doing is pretending that you can distinguish the particles, which you cannot, so the language is meaningless, and that is the actual source of the conundrum.

 

[esmeralda4]

Thanks for the excellent reply.

Can you tell me more about these pairs of electrons? Where are they paired? In a atom? Or does every electron (even lepton) have a paired particle?

Many thanks again.

 

[Ken G]

Can you tell me more about these pairs of electrons? Where are they paired?

It's true for any pair, pairing them is just an analysis device. It's true for any number of electrons also, it's just easier to think about pairs. The main point is that since electrons are indistinguishable, they don't actually have their own personal state, there is just one state for all the electrons you are considering. However, we can analyze that full state in terms of single-particle states, and when we do that, we find that the full state of all the electrons we are considering cannot look like any two of those electrons are in the same single-particle state.

Now, we usually do imagine that electrons have their own personal state when the electrons are not interacting with each other, but it's just a simplifying device to avoid complexities that we know aren't going to matter. The writers you mention are talking about the general situation, not the simplified situation, but since physics is about making simplifications, I think they have themselves pointed in the wrong direction. That's the real reason "physicists don't think about it"-- physicists naturally avoid thinking about things unless they are going to matter.

 

[Naty1]

You can read about 'spooky action at a distance' [as I think Einstein called it]
or quantum entanglement.

I think the reason no progress has been made is that this is a cornerstone of one of the most profound and fundamental questions in physics.

The other description [besides not thinking out it] is 'shut up and calculate' which means
we know the mathematics of QM gives us answers which agree with observations, but what do the observations and mathematics mean?? How can we describe, how can we understand that.

 

[esmeralda4]

But... (and here's where my ignorance is going to come through!) is it not possible to isolate a single electron in say an electric field?

What about in the case of the Photoelectric effect when a single photon can cause the emission of a photo-electron? How would you know which other electron it is paired with?

Thanks again.

 

[DrewD]

But... (and here's where my ignorance is going to come through!) is it not possible to isolate a single electron in say an electric field?

This is actually a very difficult question to fully answer. It depends on what you mean by isolate. If it is in an electric or magnetic field, something must be creating that field, so it is not isolated. But for most purposes, you can indeed separate electrons in such a way that they are not entangled with other particles. But that has nothing to do with the discussion.

There is no inherent pairing of electrons. The Exclusion Principle means that no two indistinguishable fermions (such as electrons) can be in the same state. Like Ken said, it just makes it simpler for us if we think of two at a time. Its like saying that momentum is conserved in a collision and then only having one particle. Of course momentum is conserved, it never hits anything! Well, an electron can't possible violate the exclusion principle if there is only one of them. But if we consider 218 of them, it becomes too difficult for our soft brains to handle.

(NOTE: Spooky action at a distance refers to entanglement which is different from the Exclusion Principle. Only more recently was it noted that the Exclusion Principle also required extremely minor changes over large distances)

 

[Ken G]

I agree with everything DrewD said. If you have just a single electron you are interested in, and it's pretty clearly isolated from its surroundings (so even though it is indistinguishable from other electrons, this doesn't matter-- you can imagine it is distinguishable, and do fine), then these issues don't really crop up-- it's not that they aren't there, it's that they don't matter. We do this in physics all the time-- we focus on what matters, and pretend nothing else exists, and it works pretty well. But when you start to talk about really tiny effects, then things you didn't count as mattering suddenly do start to matter, and the whole concept of an "isolated electron" starts to break down. But that doesn't mean we can't still use the concept-- we can, and do, we just aren't worrying about those "tiny effects" because they might be truly astronomically small. When they matter, we need significantly more sophisticated treatments.

 

[esmeralda4]

Thanks for all the replies. Sounds like this is a fascinating area of Physics. I have many more questions but feel I ought to do some research rather than sound incredibly ignorant. Can anyone direct me to a web page that can offer an introduction to this? Not wikipedia, that got me scratching my head after first couple of paragraphs. Or is there an another area of Physics that I should tackle first which is fundamental to understanding this principle? Many thanks.