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- From: jbaez@zermelo.mit.edu (John C. Baez)
- Subject: Re: the nature of exclusion
- Message-ID: <1992Aug14.210429.23650@galois.mit.edu>
- Sender: news@galois.mit.edu
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- Organization: MIT Department of Mathematics, Cambridge, MA
- References: <1992Aug14.020848.11073@math.ucla.edu>
- Date: Fri, 14 Aug 92 21:04:29 GMT
- Lines: 34
-
- In article <1992Aug14.020848.11073@math.ucla.edu> barry@arnold.math.ucla.edu (Barry Merriman) writes:
- >we all know that fermions satisfy the exclusion
- >priciple, which rules out their being in the same state.
- >
- >But what is the operational nature of this exclusion?
- >That is, if I take two fermions and try to put them in the
- >same state, what stops me?
-
- How are you going to try?
-
- >Presumably there would be some "resisting force", but on the
- >other hand, none of the four forces seem to come into play.
- >I've heard it called statistical repulsion, which is a nice way to
- >avoid discussing what is going on.
- >
- >I realize the exclusion is reflected in the symetries of the
- >wave function, but I feel like I could try and force the wave
- >function out of this particular type of symmetry, and I wonder what prevents
- >me from actually doing it.
-
- I don't think anyone can answer your question until you make a
- suggestion for how you might try to "force" the wavefunction out of this
- symmetry!
-
- E.g.: "Why is 2 + 2 = 4. What stops me if I try to add two and two and
- get 5?" "Well, how are you going to "try" to do that?"
-
- Certainly compressing a gas of fermions is harder than compressing a gas
- of bosons because of Pauli exclusion. You can say "I'll try hard to
- squeeze it down so they all get squished into the same state" -- but
- even as you squeeze down the position you let your fermions occupy,
- there's plenty of room in *phase* space -- they will just get squished
- over to regions of high momentum hence high energy -- so it takes a lot
- of energy to squish down a fermionic gas.
-