Bryan Sanctuary

Yes of course: if the beam is prepared as polarized in one direction, we know how it will be deflected when the filter is in the same direction, but I meant that the source is random, so every photon or silver atom emerges randomly oriented. In that case there is no way to predict if one particle will deflect up or down. That is an example of quantum indeterminism. Only after a statistically large number have passed the filter does quantum mechanics predict the state. Could also take a polarized beam, say z, and put it through filter oriented in some other way. From that polarized beam, you cannot predict how it will deflect. So this is a situation where quantum mechanics fails.

What a lot of varied answers and ideas about spin. Here I will say what spin is and also add something entirely different about spin. Of course spin was discovered in 1922 by Stern and Gerlach. Dirac was able to formulate spin using relativistic quantum mechanics IIn all derivations of spin you will see they depend upon there being a magnetic probe present. That is spin can only be formulated within quantum mechanics when an interacting probe is present. (That is because quantum mechanics is s theory of measurement). This leads to the usual Lorentz invariant spin being depicted as intrinsic angular momentum, with magnitude of 1/2 h-bar, and considered to be a point particle with a single axis of quantization. It obeys su(2) algebra, and has group property of SU(2). If you measure spin, like Stern and Gerlach, then you seem two pure states and these can be viewed as antipodal points on a Bloch Sphere. All very nice and all seems to work. But does it. Quantum mechanics fails to predict if a single particle with spin, say a silver atom, will be deflected up or down. That is quantum mechanics is indeterministic. Only after a statistically large number of particles have passed the Stern Gerlach filter does quantum mechanics predict the results (quantum mechanics is statistical). Finally, is you take an entangled singlet state and do correlation experiments on them, the usual conclusion is that Nature is non-local. I am just submitting a paper to Phys Rev A that makes a small change to spin, with far reaching consequences. Assume a spin in ISOLATION, has two axes of quantization (that is structure) rather than one. In that case, it can be shown that not only is Nature local and real, but also deterministic. The 2D spin model reproduced the quantum correlation that leads to violation of Bell's Inequalities without entanglement, and agrees with the usual spin in the presence of a probe field. So my findings are that spin is different in the presence of a probe (when you measure) and in the absence of a probe (in free flight). There is more on my blog, and the research paper will soon be available there.