electron spin
JWMeritt
spinning electron (point source, ya know). Differentiate between "magnetic
fields" and Lorentz-contracted electric fields.
James W. Meritt, CISSP, CISA
Cl.Massé
20020128141718...@mb-fo.aol.com...
> Oh, let's have fun - what is the TANGENTIAL velocity on the "surface"
> of a spinning electron (point source, ya know).
Taken as a classical electron, it is greater than the light velocity.
But it is a quantum object, described by the Dirac equation.
--
~~~~ %20cl...@free.fr%20 LPF
Liberty, Equality, Profitability.
PSmith9626
Jim is reminding us of the classical lorentz theory.
As we know, dirac's spin is not rotation about anything in physical space.
best
penny
>Taken as a classical electron, it is greater than the light velocity.
>But it is a quantum object, described by the Dirac equation.
Lorentz wrote many papers on electrons as classically rotating objects of
finite size.
In fact, he first published E=mc^2 ( yes, before Einstein ) in this special
context.
Cl.Massé
20020131231742...@mb-fm.aol.com...
> As we know, dirac's spin is not rotation about anything in physical
> space.
Dear Penny,
The rotation of the energy flux at the boundary, i.e. where
grad (psi^bar psi) /= 0.
PSmith9626
Spin is an operator that takes its values in a spin bundle. Nothing in physical
space rotates. There is a factor of two difference from the physical space
case, because of the double covering of the orthogonal group by the spin group.
best
penny
>The rotation of the energy flux at the boundary, i.e. where
>grad (psi^bar psi) /= 0.
Not exactly.
Cl.Massé
> Spin is an operator that takes its values in a spin bundle. Nothing in
> physical space rotates. There is a factor of two difference from the
> physical space case, because of the double covering of the orthogonal
> group by the spin group.
Not exactly. The spin is the observable associated to the spin
operator, which is a rotation generator. For half integral spin, it is
the one of a Cartan representation. The spin is associated to the
transformation property of the wave function by a rotation, it is a
Noether invariant. It isn't a vector, but a rank 2 antisymmetric
tensor.
> >The rotation of the energy flux at the boundary, i.e. where
> >grad (psi^bar psi) /= 0.
> Not exactly.
The energy flux have a moment wrt the classical center of the electron,
that is, the expectation value of the position <psi| x |psi>.
If in a material the spins are flipped, it gets an angular momentum.
That's an experimental fact.
PSmith9626
No. The spin is the eigenvalue of the spin operator which takes its values in
an double covering of the orthogonal group. It is not a rotation in three
dimensional space.
In fact rotation of an object by 360 degrees is not an identity in quantum
mechanics. One needs to rotate 720 degrees because of the double covering
mentioned above.
More carefully, spin is the eigenvalue of a spinor thought of as an order
one element of the clifford algebra bundle assoicated to a spin bundle.
The "Dirac" ( actually Atiyah-Bott ) operator is a clifford twisted first
order operator on the associated Sobolev Bundle.
best
penny
CF: Spin Geometry by Michelson and Lawson.
>Not exactly. The spin is the observable associated to the spin
>operator, which is a rotation generator. For half integral spin, it is
>the one of a Cartan representation.
>The spin is associated to the
>transformation property of the wave function by a rotation, it is a
>Noether invariant. It isn't a vector, but a rank 2 antisymmetric
>tensor.
Quaint.
Out of date by seventy years. It isn't a vector but a section of a clifford
operator bundle. Yes, the equation has an infinitesimal noether symmetry etc.
But where and on what does this equation operate?
Not on physical space. In your language,but on an internal symmetry space. That
is on a bundle.
>The energy flux have a moment wrt the classical center of the electron,
>that is, the expectation value of the position <psi| x |psi>.
>If in a material the spins are flipped, it gets an angular momentum.
>That's an experimental fact.
It is your interpetation of a different mathematical fact.Think "internal
symmetry space".
And even more interesting is the Metaplectic group bundle because that gives
geometric quantization.
best
penny