Understanding the Pauli Exclusion Principle

[susskind99]

When a fermion x approaches another fermion y does x send out bosons to y which tell it to get out of the way? In short, how does y know to get out of the way of x?

 

[Simon Bridge]

It doesn't have to know - there is no other way to go.
In principle, no two fermions in the Universe have exactly the same total quantum state.
It's as if each car has it's own lane on the motorway - sometimes the motorway lanes are close together and sometimes they are far apart.

Usually the effect is too small to bother with so we don't.
The size of the effect is related to the combined fields though... in that sense you do have exchange particles letting everyone know they are fermions or bosons by measuring each others spin. I get a bit of a cringe at the picture of particles firing stuff at each other - how do they know where to aim? It's more that there is a probability, that a package of "quantum numbers" will be exchanged, that varies with distance.

 

[susskind99]

The size of the effect is related to the combined fields though... in that sense you do have exchange particles letting everyone know they are fermions or bosons by measuring each others spin.

Could you please expand a bit on that sentence. What is a combined field?

It's more that there is a probability, that a package of "quantum numbers" will be exchanged

So they exchange a package of quantum numbers by exchanging bosons right?

 

[Simon Bridge]

What is a combined field?

Where do the "potential wells" in introductory QM come from?

So they exchange a package of quantum numbers by exchanging bosons right?

two electrons - for eg. have an electromagnetic field associated with each.
They can interact electromagnetically - in the particle model - by exchanging photons.
This means they know each other's spin etc.
Mathematically, the result is a bunch of numbers representing their state gets moved around.
But don't think that some particles float around and at some time exchange a boson, and then suddenly realize they are fermions and thus, politely, shift to different quantum states. I suppose you could imagine that the boson exchange shoves them into different states? But I don't think that accounts for the statistics.

PEP is not something that you can understand well by intuition about other things.
You should do the math. It's best treated as a manifestation of a symmetry. i.e. fermions know to have separate states for much the same reason your reflection knows to invert left and right.

 

[Cthugha]

See:
http://drmyronevans.wordpress.com/2...xclusion-principle-from-the-fermion-equation/

Myron Evans is a well known fringe scientist (politely speaking) who among other things claims/supports that "The very foundations of the CERN theory have collapsed and this is an irrefutable fact. I have pointed this out to the British Prime Minister." (see note 223 on the blog you linked, 2012/07/05/, - I do not want to link to it again). Also his claim that his derivation "is a major advance over quantum field theory" is pretty absurd.

Is there a deeper necessity to link to his stuff?Regarding the initial question: What is the OP's level of physics knowledge? If it is deep, the easiest thing is to do the math. As an explanation on a more handwaving level, one should keep in mind that for fermions are excitations of their corresponding fields. So two identical fermions are not really completely independent entities. An excitation of two indistinguishable particles is therefore way more complicated than two single distinguishable particles. In a somewhat simplifying picture, the symmetry properties of these fields influence how the probability amplitudes for processes leading to several excitations ending up in the same indistinguishable state behave. For bosonic fields probability amplitudes leading to high excitations of single states interfere constructively (giving rise to faeatures like bosonic final state stimulation or stimulated emission), while these amplitudes interfere destructively for fermions, which gives rise to stuff like the exclusion principle.

 

[Simon Bridge]

Myron Evans is a well known fringe scientist (politely speaking) who among other things claims/supports that "The very foundations of the CERN theory have collapsed and this is an irrefutable fact. I have pointed this out to the British Prime Minister." (see note 223 on the blog you linked, 2012/07/05/, - I do not want to link to it again). Also his claim that his derivation "is a major advance over quantum field theory" is pretty absurd.

Is there a deeper necessity to link to his stuff?

Good grief - that's what you get for just reading the abstract. Need a better example.

Stuff like:
http://scienceblogs.com/builtonfacts/2009/05/22/why-the-exclusion-principle/
http://en.wikipedia.org/wiki/Pauli_exclusion_principle#Connection_to_quantum_state_symmetry
... but I was trying for a step-by-step without having to do it myself.

 

[Cthugha]

Good grief - that's what you get for just reading the abstract. Need a better example.

Oh yes, he is good with words...I immediately remembered that blog because I fell for his tricks once, too.

 

[Simon Bridge]

The advantage of making these mistakes here is that someone usually notices and I can correct them.
The disadvantage is that, well, somebody noticed :(