"Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message
news:1103068209.829203.108540@c13g2000cwb.googlegroups.com...

Hi John, about spin, take a model airplane, point it north.
Yaw 360 degrees, and Roll 180, the plane is pointed north
but upside down. Yaw 360 again and roll 180, and the plane
is upright pointed north.
I think that describes "spin 1/2" what do you think?

I don't know what John thinks, but I think you spew crap.
Franz

"Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message
news:1103068209.829203.108540@c13g2000cwb.googlegroups.com...

Hi John, about spin, take a model airplane, point it north.
Yaw 360 degrees, and Roll 180, the plane is pointed north
but upside down. Yaw 360 again and roll 180, and the plane
is upright pointed north.
I think that describes "spin 1/2" what do you think?
Regards
Ken S. Tucker

Now pitch 90 degrees. Is it pointing North still? How about rolling
180. Is it pointing South?
This is actually a real problem that came up when the rotation matrix
of a simulated commercial airliner was exported to a military simulator,
supposedly bug free. Commercial airliners do not fly vertically.
Military
jets do.
Androcles.

Ken S. Tucker wrote:

Hi John, about spin, take a model airplane, point it north.
Yaw 360 degrees, and Roll 180, the plane is pointed north
but upside down. Yaw 360 again and roll 180, and the plane
is upright pointed north.
I think that describes "spin 1/2" what do you think?

You are incorrect.

A spin 1/2 state will behave differently under a 360
degree rotation to what an integer spin state will do.
Thus, in your example, a spin 1/2 state would require
four 360 degree yaw plus 180 degree rolls to return
to the original state.

This is the point, and you seem to be studiously
avoiding understanding it. Consider a state described
by the following function:

f(theta) = exp( i theta / 2)

If you change theta by adding 360 degrees to it, you wind
up changing f to - f. And you have to go through a full
720 degrees to return to f. Your aircraft example does
not demonstrate this. If you were to go through *only*
a 360 degree yaw, you would be back where you started.
But a spin 1/2 state would be inverted after only a
360 degree yaw.

In classical mechanics, there are no valid states with
this property. A state with the property would be one
where f(0 degrees) = - f(360 degrees). But we have to
have, in classical mechanics, that f(0) = f(360 degrees).
If you rotate a classical object around a single axis,
and go through 360 degrees, you have to get back to
the same state you started with. So we have f = -f,
meaning it has to be zero.

Only in QM can we have f and -f describing physically
equivalent systems, because in QM we have the phase
as a quantity that is not directly observable. And
that's where the f(theta) example I gave comes in.
An electron can have, under some conditions, as part
of its wave function just exactly the kind of f(theta)
where adding 360 degrees to theta gives - f. And the
result is Fermion statistics, the Pauli exclusion
principle, and lots of other good things. But *none*
of these things exist in classical mechanics, and were
in fact very surprising when they first started to be
observed round about a century ago.
Socks