Monday, April 29, 2013

Spin in Flatland!

What is Spin?

When you find something new and unexpected, it is natural to associate that with some other phenomenon that you are more familiar with. This is the case according to the invention of Spin, which was the interpretation of the Stern-Gerlach experiment's results.

The Stern–Gerlach experiment consists of sending a beam of particles through an inhomogeneous magnetic field and observing their deflection. The results show that particles possess an "intrinsic angular momentum" this is most closely analogous to the angular momentum of a classically spinning object, "but that takes only certain quantized values" (see http://en.wikipedia.org/wiki/Stern-Gerlach_experiment).

For example, tiny current loops will have an associated magnetic moment. Thus, they could be thought of as tiny magnets. If you send these tiny magnets through an inhomogeneous magnetic field, they will land into a detector screen according to its initial orientation. Thus, each tiny current loop would be deflected by a different amount, producing some density distribution on the detector screen. This is not what is observed in the Stern-Gerlach experiment, which means that the "Spin" phenomenon detected has nothing to do with current loops, magnets and/or spinning objects. It is something else.....

Lets say that these particles are as shown in the post "Matter Wave". The particle is a toroid made with a current. Always, this  toroid intersects at present time in a symmetrical way. Half of the toroid is in the past and the other half in the future. This current produces an internal magnetic field. If the toroid flips 180º, its internal magnetic field is inverted. As a consequence, the particle can switch between these two structures. This would be the origin of the 50:50 percent probability for either structure to show up, see Figure 1.




Figure 1 Present time flat particle intersection and its 180º flip structure. Notice that, after this transformation, the internal magnetic field gets inverted. This is the origin of the 50:50 percent probability to get either structure.

I took disk magnets and arranged them as suggested in Figure 1. I pass them through an external magnetic field. The result of the experiment is shown in Figure 2. Please do this experiment, it is very easy!



Figure 2 Flatland version of the Stern-Gerlach experiment.

I think this is the flatland equivalent of the space-land Stern-Gerlach experiment. Given that the particle can switch between these two structures, there is a 50:50 percent probability to have either configuration.

Thus, the 50:50 percent probability and the "superimposition of states" are needed to account for the two different outcomes of this experiment. This is fully consistent with the predictions of Quantum Mechanics.

This may indicate a way to understand the Stern-Gerlach experiment without a classic analogy.