# On the Stern Gerlach experiment

The start of the discussion can be taken from the very nice Wikipedia article, [Stern Gerlach][https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment] The basic thing to note is the quote,

" If the particle is treated as a classical spinning magnetic dipole, it will precess in a magnetic field because of the torque that the magnetic field exerts on the dipole (see torque-induced precession). If it moves through a homogeneous magnetic field, the forces exerted on opposite ends of the dipole cancel each other out and the trajectory of the particle is unaffected. However, if the magnetic field is in-homogeneous then the force on one end of the dipole will be slightly greater than the opposing force on the other end, so that there is a net force which deflects the particle's trajectory. If the particles were classical spinning objects, one would expect the distribution of their spin angular momentum vectors to be random and continuous. Each particle would be deflected by an amount proportional to the dot product of its magnetic moment with the external field gradient, producing some density distribution on the detector screen. Instead, the particles passing through the Sternâ€“Gerlach apparatus are deflected either up or down by a specific amount. This was a measurement of the quantum observable now known as spin angular momentum, which demonstrated possible outcomes of a measurement where the observable has a discrete set of values or point spectrum. "

So the basic idea is that for a specific magnetic field you would introduce a depending ion if it is spin up and spin down. It also mention that no torque would be inserted because the assumption is that of a spinning rigid object like. This is a very good analysis indeed and an example of good scientific reproduction as we know what the conditions are.

So when you put it in one machine you can deflect all the spin up particles and collect them and you would not have changed their spin (classically). We call this apparatus Z because we pick out all with spin in the positive Z direction. Now let it go through another machine, call it X e.g. we will pick out all objects that has a spin in the X direction. This would pick out objects with spin (+Z,+X) now what about a third one that pick out spin's of direction $$-Z$$ according to deterministic logic we should have filtered away those and see no signal at all. Turns out that this is not the case. There are multiple possibility and you can see the result of the different filtering processes in the sequential experiments section in the Wikipedia article.

Now we are ready to find a loop hole. The conclusion of the result of all the experiments should be that the underlying model is different than assumed and that we do get a torque that turns the object's spin in the direction Z+ for the Z+ device unless if it's opposite. In order to do that we must have a extended body with forces that turns it. Now what about Mills Orbit sphere. It consists of spinning rings with different directions. Of cause if the orbitsphers main direction was in the Z+ direction and we picked that one out symmetry would imply that we do not introduce any torque. But let's tilt it 60 degrees. This still means there will be a balance and no torque as can be seen by the net currents essentially simulate that of a rotating solid body. But let's introduce precession. This means in Mills GUTCP model that as it wobbles (precess), the angular momentum will sometimes point i Z+ direction and sometimes pint in the Z- direction as the precession is quite big. This means that the forces want to increase or change the size of the precession as it is clearly not uniform and in essence this means that the movement of the angular momentum as changes and this can only be due to induced torques as demonstrated with this thought experiment. The effect is also there for cases where the angular momentum is always in the Z+ direction as the forces is dependent on the angle towards the gradient field (refer to the dot product). So the only case when you have precession and no modifying forces are in a stable position are when the total angular momentum is parallel to the gradient of the field and therefore we motivated why Mills GUTCP model could satisfy the Stern Gerlach experiment. The measurement simply could modify the angular momentum and the only obvious attractors of this dynamical system are in the +/- Z directions. As Mills model suggests that there is only one possible angle the object can precess at due to some argument that was not clearly described in GUTCP we could envision that the object aligns (quickly) and then follow the same deflective path meaning essentially that you get a quantization.