Trying to understand Spin Decomposition ?

[Widdekind]

There is always some "slop" in spin direction, even after QM Measurement, since [math] \mu_z^2 = \left( \frac{\hbar}{2} \right)^2 \hbar^2 \times m^2 < \mu^2 = \frac{3 \hbar^2}{4} = \hbar^2 \times m (m+1)[/math]. Thus, when an electron is "spin up", it is still in a super-position state, of many "wobbling off-kilter" spin states, more-or-less spinning "up", but also w/ components in other directions. Is the following figure an apt visualization, of this process, which would explain why, the "spin up" state, is still a super-position of "half spin left, half spin right" ??

 

fig.1 --

viewed "from the side", a "spin up" state contains components, which are spinning both clockwise,

and counter-clockwise, relative to that "sideways" direction

[swansont]

Spin up is not a superposition, it's the z component. A superposition implies you have good quantum numbers, and you don't. You can't collapse the superposition with a measurement.

[Widdekind]

If a state prepared as spin "up", is subsequently quantum-Measured, along an orthogonal direction (e.g., "left-right"), the probability is 1/2 that the state will be observed, in either of the two orthogonal, and mutually anti-parallel, states... yes? Thus, the spin "up" state, can be construed, as a SP, of "left" and "right". That's the impression I get, from Kenneth Ford's 101 Quantum Questions.

[swansont]

If it was in a superposition you should be able to see interference effects. What would they be?

[mississippichem]

Is this "sloppiness" observed in EPR hyperfine transitions?