Author Cristinel Stoica replied on Feb. 21, 2018 @ 08:34 GMT
Dear Edwin,
There are some important parts where I agree with you. I wanted to state this from the beginning of my comment, in order to facilitate reading without feeling that I opposed you too much. There is something where we disagree too, but you will see there is some important part where I tend to agree with you.
But first let me clarify something. When I say that spin is 3D, I refer to the Block sphere representation (plus the phase), not that spin is a mere 3D rotation. To me the spin is perfectly described by a spinor. I agree with the Pauli spinor as the nonrelativistic limit of the Dirac spinor. If you want to describe the Pauli spin of the electron in a basis, ignoring the position and other degrees of freedom, the basis has two vectors. There are not only two states, there are infinitely many, it seems to be two states because the measurement is done in a particular basis, and by the projection postulate yields two possible outcomes. This description of the spin works perfectly and it is very simple and natural. By "simple" I don't mean is simple to our classical intuition, I mean that it arises naturally when combining special relativity with the requirement of unitarity, see Wigner's theorem. The "3D spin" I mention is the Bloch sphere representation, and the state vector, represented up to a phase factor by a 3D vector, is completely determined by the expectation values of the spin operators along the three axes (which give the components of that vector along the three axes).
Now here is a bridge over the gap between our views. While I take the spinor seriously, it is not directly observable. The observables are build out of the Dirac spinor by taking various products of Dirac matrices and evaluating the result on the spinor field. You know these are scalar, vector (the electromagnetic four-current), bivector (where the angular momentum is), trivector (or pseudovector), and a pseudoscalar (a tetravector). These quantities are observable, and for a single spin 1/2 particle they behave in many situations quite classically. Now by "classically" I mean a classical spinor field, not a quantized field (as in the so-called second quantization), but the point is that these quantities are differential forms. And in the nonrelativistic limit we can treat an external field as a classical field too, in particular the magnetic field of the Stern-Gerlach device. So I am pretty sure that a quasiclassical analysis of the electron in the magnetic field is useful and relevant. You can even approximate the particle with a ball following a classical trajectory, as long as it is not too localized so that Heisenberg's principle makes the trajectory too fuzzy. This bridge I try to present here to you is something I always found reasonable to be true, and thought that it is important to have such an analysis. My brief glance to your paper gave me the impression that you are doing this in a careful and serious way. I always pictured for myself the electron as interacting continuously with the Stern-Gerlach device and exchanging momentum, energy, and angular momentum with it. I didn't do a careful reading of your paper, but I think you do this, and if I am wrong please let me know.
As a general approach to quantum mechanics and quantum field theory, I think it is important to understand what happens. I don't belive in magical projectors, and I think measurements are not sharp, they are just interactions. But I don't think there is a description consistent with both L and SI. I will come back to this later. For now, I want to say that I see nothing wrong with the particle passing through a Stern-Gerlach device and landing either in the up region or in the down region, without a collapse or projection. Even though I see this in terms of spinor fields, I think we see this picture similarly. So probably if I will check all your math and physics I expect I will agree with your figure at page 20. If you did this analysis without adding new physics, with the right math, and got that picture at page 20, I think it is an important result.
Now, I have the feeling that you are not satisfied with this analysis, and want more, namely to disprove Bell. If you are interested in my 0.02$, here is what I would advise you. Take that paper, clean it for claims that Pauli and Bell were wrong (I will explain later why), and try to publish it. If I am right, you can make it be some "mainstream" analysis of the Stern-Gerlach experiment. And I think you can get it published in a journal with ISI IF.
Now, I promised you I will come back to Bell's theorem. It is completely irrelevant if he labels the two outcomes with +1 and -1, or +1/2 and -1/2, or |up> and |down>, or just "up" and "down". If you think it is relevant, let's consider then another version of Bell's theorem, one which I say is the same, and you may say is a weakened version. Let us refer only to spin being up or down along an axis, not to Pauli matrices, not to two-level systems. By up and down I call the two places where the particle arrives after going through the S-G device, those two regions you reproduce in your picture at page 20. This is also in agreement with my views, because there are no sharp measurements. So we just think in terms of yes/no measurements, answering to questions like "did the particle land on this "lip" of the iconic postcard, when oriented along this particular axis?"
If you want to prove that Bell was wrong, then your task (for a second paper I would recommend) is to provide an explanation of the EPR experiment based on your theory, in terms of these up and down along diferent axes. So we stick only with what we can see in the experiment, not with the projections you said Pauli made. Maybe you think you already have this proof, but I still suggest you to put it in a second paper, separate from the one-particle paper.
If I am right, then you are wasting a great opportunity by mixing your one-particle analysis with the idea that this disproves Bell. I think your reasoning is the following sillogism: "(1) I explained the S-G experiment without Pauli matrices and spin operators, (2) Bell assumes Pauli spin, therefore (3) I disproved Bell". I don't think this works, because I don't think you can get the same correlation as QM with your model, unless you add something that breaks either L or SI. If I am right, you can publish the one-particle paper. If you are right, you can publish the one-particle paper, and then make it easier for the reader to accept your model and to read your second paper, where you will explain EPR. So no matter who is right, I think your analysis may result in a paper, which I think will be useful for physics (but I repeat, this is based on a brief glance of your paper, maybe I project my own views on it).
Best regards,
Cristi
