MadSci Network: Physics
Query:

Re: Why does and electron have 1/2 spin???

Date: Mon Jun 26 15:59:34 2000
Posted By: Ronald Fisch, Physics, Washington University
Area of science: Physics
ID: 960950224.Ph
Message:

I am not sure what you mean when you ask "WHY does an electron
have spin 1/2" (in angular momentum quantum units)?  It is an experimental
fact that the behavior of electrons is correctly predicted by a model in
which the electron has spin 1/2.  Therefore the model of spin 1/2 electrons
is a useful model for understanding our universe.  But I can't tell you WHY
the universe is made this way.

Spin 1/2 means much more than the fact that you have to rotate an electron
around twice to have it look the same.  Because an electron has spin 1/2,
if you put it in a magnetic field it can have two different "eigenstates".
Its spin can point either parallel (up) or antiparallel (down) relative to
the magnetic field.  All spin 1/2 particles are "fermions".  Fermions have
the symmetry property that if you have several of them, then the quantum
mechanical wave-function which describes these particles acquires a minus
sign under interchange of any two of them.  Because of this, if you try
to put two electrons into the same quantum state, the wave-function must
be zero.  This is the "Pauli Principle", and it means that such a state is
not allowed.  This property of electron wave-functions is the basis for
understanding the properties of atoms and molecules.

The reason why spin 1/2 particles must be fermions is explained by the
"Spin-Statistics Theorem", which is usually considered to be a
fundamental result of relativistic quantum theory.  The same theorem also
explains why spinless particles must be "bosons", which have the property
that the quantum mechanical wave-function is unchanged under the
interchange of two of them.  The reasons why the Spin-Statistics Theorem
is true are a subject of continuing interest.  See, for example, the
recent article by I. Duck and E. C. G. Sudarshan, American Journal of
Physics 66: 284-303 (1998).

There are many books which discuss this subject at an introductory level.
My favorite is Volume 3 of "The Feynman Lectures on Physics".



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