Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Phenomenological Theory of the Stern-Gerlach Experiment

Version 1 : Received: 27 October 2022 / Approved: 31 October 2022 / Online: 31 October 2022 (10:02:16 CET)

How to cite: Rashkovskiy, S. Phenomenological Theory of the Stern-Gerlach Experiment. Preprints 2022, 2022100478. https://doi.org/10.20944/preprints202210.0478.v1 Rashkovskiy, S. Phenomenological Theory of the Stern-Gerlach Experiment. Preprints 2022, 2022100478. https://doi.org/10.20944/preprints202210.0478.v1

Abstract

We propose a phenomenological theory of spin behavior in a magnetic field, which explains from the point of view of classical physics the two-valued result of the Stern-Gerlach experiment. The behavior of the spin and intrinsic magnetic moment of an electron wave of an atom in an external magnetic field is considered. We show that in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector. Within the framework of classical electrodynamics, the calculation of the motion of an atomic beam in an inhomogeneous magnetic field is carried out, which reproduces the results of the Stern-Gerlach experiment.

Keywords

Stern-Gerlach experiment; phenomenological theory of spin behavior in a magnetic field; classical field theory; self-consistent Maxwell-Pauli theory

Subject

Physical Sciences, Particle and Field Physics

Comments (2)

Comment 1
Received: 28 January 2023
Commenter:
The commenter has declared there is no conflict of interests.
Comment: This theoretical article contains very interesting and detailed calculations suggesting that classical magnetic dipole, in strong enough external magnetic field, should align in parallel or anti-parallel way as in Stern-Gerlach experiment, I strongly recommend it.
It brings many questions, hopefully addressed in future articles, for example:
- comparison with experimental data, maybe dedicated experiments - e.g. of predicted minimal required magnetic field and its dependence, of time/distance required for alignment,
- the article suggests that up/down choice is made from simple condition of being above or below some calculated critical angle. Trying to see spin measurement this way, it is hard to imagine to be able to get violation of Bell-like inequalities (?) If so, what "quantum correction/addition" could allow for such violation?
- magnetic dipole in external magnetic field gets torque leading to precession, and rotating dipole becomes antenna radiating energy - what suggests alignment tendency without threshold for magnetic field (in contrast to this article). So why below this magnetic field threshold there would be no EM radiation of rotating dipole?
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Response 1 to Comment 1
Received: 2 February 2023
Commenter:
The commenter has declared there is no conflict of interests.
Comment: Thank you for your comments.
I would like to note the following:
1. In this article, for the first time, a theory is proposed that accurately describes in detail the Stern-Gerlach experiment and predicts two possible orientations of the magnetic moment relative to the magnetic field without any additional hypothesis and postulates.
The standard "explanation" that exists in quantum mechanics and which is inspired from the student's bench that the spin can have only two orientations in space, I do not consider an explanation, because it is a postulate that does not follow from any physical laws and cannot be deduced from any first principles. In fact, this is simply a statement of the fact that Stern and Gerlach observed.
2. The proposed theory predicts a new effect: the existence of a critical magnetic field, below which the Stern-Gerlach effect should not be observed. It would be very interesting to test this prediction of the theory experimentally.
3. A magnetic moment rotating in a magnetic field will indeed radiate electromagnetic waves in full accordance with classical electrodynamics. This is the so-called magnetic-dipole radiation (see, for example, Landau and Lifshitz, The Classical Theory of Fields). As a result of this effect, the magnetic dipole loses energy (in the form of electromagnetic radiation) and turns in a direction parallel to the magnetic field (i.e., it comes to a state with a minimum potential energy in a magnetic field). But this magnetic-dipole radiation cannot explain why in the Stern-Gerlach experiment some of the electrons are oriented parallel to the magnetic field, while the others are anti-parallel. It is easy to estimate the time of reversal of the magnetic moment relative to the magnetic field as a result of magnetic-dipole radiation: it is tens of hours. Thus, the magnetic-dipole radiation, although it exists, has nothing to do with the Stern-Gerlach effect.
As for my article, it cannot be considered in isolation from my other articles on this topic.
In particular, it makes no sense to consider it from the point of view of the Copenhagen interpretation of quantum mechanics, when it is assumed that everything in an atom is quantized, electrons make jumps from one level to another, zitterbewegung is responsible for everything, etc.
Below are also links to preprints with my recent results, which have not yet been published in journals:
https://arxiv.org/abs/2203.09466 https://www.preprints.org/manuscript/202204.0168/v1
https://www.preprints.org/manuscript/202210.0227/v1

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