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Ray

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- Thread starter rayveldkamp
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Ray

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"In quantum mechanics, the wave function psi(particle1, particle2) of

two fermions, such as electrons, must have the following property:

psi(particle1,particle2) = -psi(particle2,particle1)

So when the two particles are interchanged, the wave function changes

sign. If they are in the same quantum state, the wave function can't

change - so it must be zero. That is, there's zero probability that

the two particles can be in the same state. "

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Haelfix

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In my opinion, this is the single most compelling experimental reason to believe in all the weirdness of special relativity and quantum mechanics.

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Haelfix said:Actually it does have very deep roots. Its full derivation is a consequence of the mix of quantum mechanics and special relativity, quantum field theory. Without either one of those elements, you cannot logically have the so called spin-statistics theorem.

In its first (usually chemical useful) formulation,Pauli postulated the fact that 2 electrons could not be in the same quantum state.In the Dirac version of QM (the traditional formulation) is still kept as a postulate.Von Neumann used it to invent quantum statistical mechanics.And it was again Pauli who used indirectly (see below) to prove his theorem:the spin-statistics theorem (1940) is proven in the context of QED and a generalization to particle physics has been given by Lueders.

So my guess is it is the other way around.First postulate the symmetrization/antisymmetrization principle,then use it together with special relativity and quantization method to find out that there is a connection between spin ans statistics.

Allow me to quote from W.Pauli's famous article:"The Connection between spin and statistics."Phys.Rev.,58,p.716-722(1940) found in:"Wolfgang Pauli:<<Collected Scientific Papers>>",edited by R.Kronig and V.F.Weisskopf (1964,Interscience Pulblishers),Volume 2;p911-918:

Abstract:

"In the following paper we conclude for the relativistically invariant wave equation for free particles:From Postulate (I),according to which the energy must be positive,the necessity of Fermi-Dirac statistics for particles with arbitrary half-integer spin;from postulate (II),according to which observables on different space-time points with a space-like distance are commutable,the necessity of Einstein-Bose statistics for particles with arbitrary integer spin [...]"

Haelfix said:In my opinion, this is the single most compelling experimental reason to believe in all the weirdness of special relativity and quantum mechanics.

In the same article,Pauli says:

"In conclusion we wish to state,that according to our opinion the connection between spin and statisics is one of the most important apllications of the special relativity theory".

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"The Connection between spin and statistics"

Thanks

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rayveldkamp said:

"The Connection between spin and statistics"

Thanks

Note that dextercioby gave you the citation reference to the paper. However, if you meant where you could find it online without requiring a subscription access to Physical Review, then that's a different question.

I have given this link before (which, I think, made humanino weak in the knees after he discovered it), so here it is again. I probably should put it up in my Journal so that it can be easily found again for people who will be asking for something similar in about a month.

http://fangio.magnet.fsu.edu/~vlad/pr100/100yrs/html/chap14_toc.htm [Broken]

This link should contain almost all of the landmark QM papers. So BOOKMARK it! :)

Zz.

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Thanks for that.

Ray

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