Re: Do free particles have spin?

From: Timo Nieminen (timo_at_physics.uq.edu.au)
Date: 09/28/04 

Date: Tue, 28 Sep 2004 12:57:25 +1000

On Mon, 27 Sep 2004, David Rutherford wrote:

> Gregory L. Hansen wrote:
> >
> > It's a vector sum of horizontal and vertical motion. The "direction" is
> > given by the axis of rotation, which is mutually perpendicular to the two
> > components.
> >
> > That's what I tried to express above. Circular polarization can be
> > expressed as a combination of two transverse polarization modes. The
> > field of a circularly polarized light wave doesn't point in the direction
> > of propagation, but a vector that describes how the field rotates
> > (clockwise or counterclockwise) points along the direction of propagation.
>
> But the polarization is always transverse to the direction of
> propagation, not in the direction of propagation like the spin
> orientation is, even for circularly polarized light.

The direction of the electric and magnetic field vectors is perpendicular
to the direction of propagation. These are not the circular polarisation
vector. The circular polarisation vector is parallel or antiparallel to
the direction of propagation.

Note that for an EM wave with no orbital angular momentum about the
direction of propagation, the angular momentum density is fully described
by the polarisation and intensity.

Note that this angular momentum density can be mathematically and
experimentally be shown to be spin density.

> If the spin is described by the same vector that describes the rotation
> of the field, then what about linearly polarized light? That vector
> would be the zero vector, since the field is not rotating. Does that
> mean that in the case of linear polarization the photon has no spin?

The average value of the photon spin is zero. The spin of the EM field is
zero.

Note what happens when the beam is incident on a circularly-polarising
beamsplitter (ie a 1/4 wave plate and polarising beamsplitter). 

-- 
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

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