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arXiv:2501.04380 · Chinese Physics B

Electric-type Stern–Gerlach effect

Jun Zhou, Zitao Fu, C. H. Oh, Jing‐Ling Chen

Published Oct 9, 2025• 0 citations
arXivHTMLPDF

Abstract

Abstract The Stern–Gerlach (SG) experiment is a fundamental experiment for revealing the existence of “spin”. In this experiment, beams of silver atoms are sent through inhomogeneous magnetic fields to observe their deflection. Thus, the conventional SG experiment can be viewed as a magnetic-type spin effect. In this work, we successfully generalize the SG effect from magnetic-type to electric-type by solving Dirac’s equation with a potential barrier, revealing an extraordinary spin effect. Beams of Dirac particles can be regarded as matter waves. Based on Dirac’s equation, we obtain the explicit forms of the incident, reflected, and transmitted waves. The electric-type SG effect shows that the reflected and transmitted waves can exhibit notable spatial shifts, which depend on the spin direction and the incident angle of the wave. The electric-type SG effect has potential applications for separating Dirac particles with different spin directions and for estimating the spin direction of Dirac particles. Some discussions related to the interaction between spin and the electric field are also presented.

DOI
10.1088/1674-1056/ae111e

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Abstract The Stern–Gerlach (SG) experiment is a fundamental experiment for revealing the existence of “spin”. In this experiment, beams of silver atoms are sent through inhomogeneous magnetic fields to observe their deflection. Thus, the conventional SG experiment can be viewed as a magnetic-type spin effect. In this work, we successfully generalize the SG effect from magnetic-type to electric-type by solving Dirac’s equation with a potential barrier, revealing an extraordinary spin effect. Beams of Dirac particles can be regarded as matter waves. Based on Dirac’s equation, we obtain the explicit forms of the incident, reflected, and transmitted waves. The electric-type SG effect shows that the reflected and transmitted waves can exhibit notable spatial shifts, which depend on the spin direction and the incident angle of the wave. The electric-type SG effect has potential applications for separating Dirac particles with different spin directions and for estimating the spin direction of Dirac particles. Some discussions related to the interaction between spin and the electric field are also presented.
We have studied a relativistically covariant Stern-Gerlach (SG) experiment for a relativistic spin and a Dirac spin. We have obtained the relativistic spin in an arbitrary frame by using the classical spin dipole tensor, which gives the covariant spin dipole interactions, and the relation between a spin and a spin magnetic dipole moment. The relativistic spin is shown to have problems to become a proper spin operator for a massive relativistic particle because of two reasons. First, the relativistic spin three-vector operators cannot satisfy the spin algebra. Second, the SG experiment for the relativistic particle provides a paradox between two observers in the particle rest frame and the laboratory frame, in which the particle is moving. We have shown that the paradox in the SG experiment is resolved by the Dirac spin, which is covariantly defined by a Lorentz transformation in the Dirac spinor representation. The Dirac spin three-vector operators satisfy the spin algebra. It is shown that the SG experiment for the Dirac spin in the inertial frame, where there is only magnetic field, can determine the spin without the information of the momentum of the particle. This shows that the reduced spin density matrix for the Dirac particle can be well-defined by integrating out the momentum degrees of freedom.
A thorough motion investigation and analysis was conducted again for the original Stern-Gerlach Experiment(SGE). The analysis is still based on the assumption that the atom passing the SG apparatus is a micromagnet due to the spin of its electron, the atoms in the source beam are with an orientation distribution of its angular momentum vectors, while the spin micromagnet is in the precession induced by an inhomogeneous magnetic field. It is the precession that keeps the silver beam with narrower orientation distribution of its angular momentum vectors after passing through the inhomogeneous magnetic field. The motion relativity was introduced in the SGE between the SG apparatus and the silver source beam, which interpreted all the detection phenomena in the multi-stage SGE. The research provided a new and convincing interpretation to the SGE with full satisfaction based on the classical physics without any mysterious or counter intuitive concepts introduced compared to quantum physics.
Abstract The Stern–Gerlach (SG) effect provided the first direct experimental evidence of the quantization of electron spin. Although some analog SG effects have been proposed in optical systems, finding a perfect optical analog for the SG effect remains a challenge. Here, a novel optical SG effect is demonstrated in periodically poled electro‐optical crystals. Induced by an applied electric field, the principal axes of crystal rock periodically along the propagation direction of light. When the quasi‐phase‐matching condition is satisfied, the electro‐optical coupling process within the periodically poled crystal can be accurately described by the Schrödinger–Pauli equation for spin‐1/2 particles. The output photons can be deflected toward opposite directions according to their intrinsic spin angular momentum (circular polarizations), since the transversely varying duty cycle of crystal arises an effective magnetic‐field gradient. Moreover, the output photons can be separated according to two arbitrary orthogonal polarization states, allowing us to construct high‐speed electro‐optically tunable polarization beam splitters for arbitrary orthogonal polarization states. Therefore, the optical SG effect provides not only a perfect optical analog for the quantum SG effect but also a useful optical element for optics and quantum physics.
Since its completion in 1922, the Stern-Gerlach experiment has long been regarded in mainstream quantum mechanics as a key experimental evidence for the 1/2 intrinsic spin of electrons, and a foundational observation for spatial quantization and quantum state collapse theory. Based on the basic standpoint of the light-origin theory, this paper adheres to the core criterion that magnetism is a secondary effect derived from the directional motion of electric charges, and re-examines the phenomenon that silver atomic beams split into two streams in a non-uniform magnetic field. This paper points out that the "intrinsic spin magnetic moment" defined by mainstream quantum theory cannot correspond to closed charge circulation inside the electron (the classical rotation model leads to the contradiction of superluminal speed), and violates the unified origin principle of "electricity generating magnetism" in electromagnetism. Essentially, it is a mathematical degree of freedom artificially introduced to fit experimental results. This paper proposes that the bifurcation effect of silver atomic beams can be fully explained by the orientation coupling between magnetic dipoles formed by ordered charge circulation of electrons inside atoms and an external non-uniform magnetic field. The magnetic dipoles of incident silver atoms are randomly distributed in orientation statistically, yet only two orientations, parallel and antiparallel to the external magnetic field, can remain stable in the gradient magnetic field, while intermediate orientations are unstable and excluded. Eventually the atomic beam separates into two discrete streams, with no need to introduce the hypothesis of intrinsic spin without physical carriers. This paper further designs a discriminative experimental scheme: in a single-electron trapping system with ultra-low temperature and strong magnetic shielding, after thermal jitter is sufficiently suppressed, if no stable self-sustained static magnetic dipole signal of the electron can be detected, it will constitute a direct test for the hypothesis of intrinsic spin magnetic moment.
Abstract We analyze idealized sequential Stern–Gerlach (SG) experiments with higher spin particles. This analysis serves at least two purposes: the widely discussed spin-1/2 case leads to some misunderstandings since the probabilities are always evenly distributed for the sequential orthogonal magnets, which does not generalize to higher spins. A detailed discussion of the higher spin case, as is done here, is highly useful. Secondly, the Wigner rotation matrices for generic spins become conceptually more transparent with this physical example. We also give compact formulas for the probabilities in terms of the angle between the sequential SG apparatus for generic spins. We work out the spin-1/2, spin-1 cases explicitly. Since there are some confusing issues regarding the actual experiment, we also compile a ‘facts and fiction’ section on the SG experiments.