Realistic Spin Measurement
In the previous post, we have described a Spin Measurement process, performed with a Stern-Gerlach apparatus, in the framework of our Local-Realist theory of quantum mechanics. Despite not being based on complex-valued spinors and matrix operators, our model is able to retrieve the main QM results. In particular, the probability of distribution of spin (spin "up" or "down") at the exit of a SG apparatus, as a function of the initial preparation and of the direction of the magnetic field.
One of the most puzzling aspects of QM spin is that, when multiple SG are linked in sequence, they do not act as simple selectors, i.e., filtering out particles with one of the spin values (i.e., states pre-existing to the measurement) and blocking the others.
Give a look to the Wikipedia article on that, where three experiments are depicted (reproduced below). The first case discloses a quite unsurprising behavior: since only the z-up beam enters the 2nd SG, we expected to find only z-up particles at the exit of the 2nd SG. The second case can be still classically understood: it could reveal that the z-up beam from the 1st SG was composed of 50% particles with x-up spin and 50% particles with x-down spin.
However, the third case seemingly contradicts this interpretation. In fact, instead of finding only z-up particles at the exit of the 3rd SG, we still find 50% z-up particles and 50% z-down particles. The conclusion of such experiments is that we cannot determine both z-spin and x-spin simultaneously. The selection of x-up beam completely destroys any previous information about z-spin. A spin measurement is not simply a filter but instead they alter the state by observing it.
In the standard picture, these QM results are obtained using the mathematical machinery already discussed in the previous post. Instead, our model follows a different approach. For us, spin is not an operator but an intrinsic quantity attached to each particle of an ensemble of similarly prepared particles. A spin state is defined by our "polarization" numbers, as discussed in this post. Moreover, when an external force is experienced, the polarization instantaneously takes the value of the local field, multiplied by the current spin attached to the particle.
This "External Reset" mechanism is indeed responsible for the results of the sequential measurements described above. This process is discussed in my 2020 ArXiV paper, an excerpt of which is reproduced below. In particular, the final formula coincides with the prediction that QM obtains using matrices and spinors.
In fact, with QM you would expand the eigenstate of the first field orientation in terms of the eigenspinors of the 2nd field; the coefficients of the linear combination yield the probabilities when squared. The result is the same as in our model. So, if s(1) = 1 and cos(β(1),β(2)) = 0, the probabilities of x-spin up and down is 50% each. This is what happens at the exit of the 2nd and 3rd Stern-Gerlachs of the illustrations above.
Our model's mechanism is eventually quite simple. Although not in formal scientific publications, at least not to the best of my knowledge, sometimes similar approaches have emerged in public discussions. The main objection is that if the magnetic moment of the particle (replaced in our model by the "polarization") 'jumps', then magnetic energy would also jump and energy conservation would be violated.
Indeed, my recent paper includes a further mechanism that couples momentum with spin in an energy conservation framework and that will play a fundamental role in spin entanglement, as will be discussed in a future post.
One of the most puzzling aspects of QM spin is that, when multiple SG are linked in sequence, they do not act as simple selectors, i.e., filtering out particles with one of the spin values (i.e., states pre-existing to the measurement) and blocking the others.
Give a look to the Wikipedia article on that, where three experiments are depicted (reproduced below). The first case discloses a quite unsurprising behavior: since only the z-up beam enters the 2nd SG, we expected to find only z-up particles at the exit of the 2nd SG. The second case can be still classically understood: it could reveal that the z-up beam from the 1st SG was composed of 50% particles with x-up spin and 50% particles with x-down spin.
Source: Wikipedia, file Sg-seq.svg, by user Francesco Versaci
However, the third case seemingly contradicts this interpretation. In fact, instead of finding only z-up particles at the exit of the 3rd SG, we still find 50% z-up particles and 50% z-down particles. The conclusion of such experiments is that we cannot determine both z-spin and x-spin simultaneously. The selection of x-up beam completely destroys any previous information about z-spin. A spin measurement is not simply a filter but instead they alter the state by observing it.
In the standard picture, these QM results are obtained using the mathematical machinery already discussed in the previous post. Instead, our model follows a different approach. For us, spin is not an operator but an intrinsic quantity attached to each particle of an ensemble of similarly prepared particles. A spin state is defined by our "polarization" numbers, as discussed in this post. Moreover, when an external force is experienced, the polarization instantaneously takes the value of the local field, multiplied by the current spin attached to the particle.
This "External Reset" mechanism is indeed responsible for the results of the sequential measurements described above. This process is discussed in my 2020 ArXiV paper, an excerpt of which is reproduced below. In particular, the final formula coincides with the prediction that QM obtains using matrices and spinors.
Our model's mechanism is eventually quite simple. Although not in formal scientific publications, at least not to the best of my knowledge, sometimes similar approaches have emerged in public discussions. The main objection is that if the magnetic moment of the particle (replaced in our model by the "polarization") 'jumps', then magnetic energy would also jump and energy conservation would be violated.
Indeed, my recent paper includes a further mechanism that couples momentum with spin in an energy conservation framework and that will play a fundamental role in spin entanglement, as will be discussed in a future post.
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