Please define what you precisely mean that the SG magnet "does not change the spin". Clearly it changes the spin state, if the particle wasn't prepared in an ##s_z## eigenstate. That's crucial for the SGE being the measurement of the spin-##z## component (with the position or momentum of the particle behind the magnet as the "pointer observable").PeterDonis said:Yes, with the full experiment--i.e., including the filtering out of one output beam, so it is now a preparation procedure. But the SG device by itself has no filtering. That is done by an additional device. And the OP of this thread is not talking about the filtering, just about the SG device itself (and the calcite crystal itself). I stand by my statement that the SG device itself does not change the spin; only the full filtering process, which requires an additional device, does.
Indeed, and the polarization state of photons letting them go through a birefringent crystal is pretty analogous to the SGE. Both can be said to be "polarizing beam splitters".PeterDonis said:And note that, while, as I noted before, technical difficulties have precluded doing other kinds of experiments with SG devices, such as making the equivalent of a Mach-Zehnder interferometer, analogous experiments with photons have of course been done. So restricting attention to just the simple filtering process ignores all the other things that can in principle be done with an SG device or a calcite crystal.
I've already done that multiple times in this thread.vanhees71 said:Please define what you precisely mean that the SG magnet "does not change the spin".
No, it doesn't. It entangles the spin degree of freedom with the linear momentum degree of freedom. It doesn't change the amplitudes of the spin components at all. I've already said this multiple times in this thread.vanhees71 said:Clearly it changes the spin state, if the particle wasn't prepared in an ##s_z## eigenstate.
Yes, and that is what the OP of the thread was asking about.Haborix said:It is true that after leaving the magnetic field the spin and momentum are entangled and the modulus of the coefficients in front of each of the spin components is the same.
Yes, and this is not what the OP of the thread was asking about. That's why I have emphasized the difference between the two cases.Haborix said:if you throw a half wall in after the magnetic field, the spin state of the beam making it past the wall is different than the spin state that left the source and the that the left the magnetic field.
If the state involves from an unentangled to an entangled state, the state is changing. How else would you be able to use the SG magnet as a preparation apparatus for spin-##z## eigenstates? Of course, if you trace out the spatial/momentum information you are right (for the usual idealized approximation). But that's not what makes the SGE inteteresting!PeterDonis said:I've already done that multiple times in this thread.No, it doesn't. It entangles the spin degree of freedom with the linear momentum degree of freedom. It doesn't change the amplitudes of the spin components at all. I've already said this multiple times in this thread.
The overall state changes. The amplitudes of the spin components do not change. The latter is what I have been saying. Please read carefully; I am getting a little tired of people "refuting" claims in this thread that I have not made.vanhees71 said:If the state involves from an unentangled to an entangled state, the state is changing.
I don't know how to say that the amplitudes of the spin components don't change, which is what I said in multiple posts in this thread, any clearer. If you misunderstood that, I have no idea how to fix that.vanhees71 said:Sometimes it's not only the fault of the reader, if one's misunderstood!
Yes, we've already agreed on that earlier in the thread.vanhees71 said:You are right (with pretty high accuracy).
Yes, if you have a detector after the SG device or you filter one of the beams out. But that involves something else in addition to the SG device, and the measurement/preparation requires that something else. Without that something else, with just the SG device, which is what the OP of the thread was originally asking about, these "state changes" do not occur. We've already discussed that earlier in the thread too.vanhees71 said:What I meant is that the state changes if it's not a spin-##z## eigenstate such that you can measure and/or prepare spin-##z## eigenstates.
We discussed this earlier in the thread too. Yes, these complications are present and a complete, rigorous analysis would include them. I think that's beyond the scope of what the OP was originally asking about, but the effects you describe are real, yes.vanhees71 said:The spin as a whole moves, i.e., it precesses around the direction of the magnetic field, which is the key for understanding the SGE in terms of QT, which is surprisingly never discussed in the textbook literature, where it is discussed qualitatively in a semiclassical way. I'll write a short note on it over the weekend.
I didn't say the complications were wrong. I said they are not part of what the OP of the thread was originally asking about. You don't need to do a complete, rigorous analysis of the entire effect in order to address the OP's question: just knowing that the SG device entangles the spin and linear momentum degrees of freedom is enough.vanhees71 said:Yes, and I don't understand, why you claim it's wrong!
This is fine. In fact it might make a good Insights article.vanhees71 said:As I said, I'll prepare a short writeup as soon as possible.