Playing with Spin Filters

I will follow the instructions very similar to what you can see here:(http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SternGerlach/SternGerlach.html). For simplicity, I would not collimate the particle after it has been separated. Thus, the filtered electron will continue in a straight line down the filter. The flat electrons movement in a magnetic field just obeys the spin separation and do not move as negative particles in a magnetic field.

Figure 1 Spin-right flat electron filter

Figure 1 shows a Stern-Gerlach apparatus, in which a block of lead stops the "spin left" flat electrons. One-half of the incident beam, the "spin left" electrons will be stopped inside the filter, while all the "spin-right" flat electrons will emerge in the same direction before they entered the magnetic field. Thus, this is a "filter" that selects "spin-right" flat electrons.

Figure 2. A second "spin-right" electron filter will not affect the selected spin.

On Figure. 2, We now put a second filter after the first with the same orientation. The second filter has no effect. Half of the electrons from the electron gun emerge from the first box, and all of those electrons pass through the second filter. So, once "right" is defined by the first filter, it is the same as the "right" defined by the second.

Figure 3. A Spin right filter follow by a spin left filter will block all the electrons.

On Figure 3, Now we put the second filter after the first and a block to the right relative to the first. As always, half of the beam of electrons from the electron gun emerge from the first filter, and none of those electrons emerge from the second filter. So, evidently once the first filter defines "right" that definition is the second filter's definition of "left".

Fig. 4 Flatland version of the Space-Land Stern-Gerlach experiment.

Here is another orientation for the second filter, this time it is oriented at 90° relative to the first one. To repeat once again, half of the beam of electrons from the electron gun emerge from the first filter. It turns out that one-half of those electrons pass through the second filter. So if we have two definitions of "right" from two filters at right angles to each other, one half of the electrons will satisfy both definitions. This is because the intersection of the flat electron will change to the intersection of the donut through it equator (see Particle-wave duality post). This will occur with a 50:50 percent probability. Thus, from the 16 flat electrons that went into this second filter, 8 are retained and the other 8 passed through. These 8 flat electrons that passed through have  again 50:50 percent probability to produce the original orientations again. As a result a left filter that should have blocked all the remained electrons can block just half of them. 

This is in perfect agreement with Quantum Mechanic predictions.