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Calculation of the effective RPM of a spherical 5mm ferrite magnet Br=0.4 T to emulate the intrinsic spin gyromagnetic ratio of |γ/2π|~28 GHz/T(NIST) motion of an isolated electron

Emmanouil N. Markoulakis, Emmanuel Antonidakis

Published Feb 27, 2022• 0 citations
OpenAlex

Abstract

We calculate an effective mechanically induced spin rotation per minute (RPM) value of a sphere ferrite electrical insulator magnet with 5mm diameter, that will emulate classically the intrinsic spin gyromagnetic ratio of an isolated electron and that could be used in a Stern-Gerlach apparatus experiment to investigate if the known quantum behavior of the quantization of spin could be emulated macroscopically. This could be used to verify the "dressed" nature of the electron particle having a finite charge radius and also that the electron possesses actual classical spin.

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New Journal of Physics•Jun 28, 2011•24 citations
We calculate an effective mechanically induced spin rotation per minute (RPM) value of a sphere ferrite electrical insulator magnet with 5mm diameter, that will emulate classically the intrinsic spin gyromagnetic ratio of an isolated electron and that could be used in a Stern-Gerlach apparatus experiment to investigate if the known quantum behavior of the quantization of spin could be emulated macroscopically. This could be used to verify the "dressed" nature of the electron particle having a finite charge radius and also that the electron possesses actual classical spin.
Abstract The anomalous Zeeman effect made it clear that charged particles like the electron possess a magnetic dipole moment. Classically, this could be understood if the charged particle possesses an eigenrotation, that is, spin. Within Nelson's stochastic mechanics, it was shown that the model of a rotating charged ball is able to reproduce the well‐known spin expectation values. This classically motivated model of intrinsic rotation described in terms of a stochastic process is revisited here within the formalism of stochastic optimal control theory. Quantum Hamilton equations (QHE) for spinning particles are derived, which reduce to their classical counterpart in the zero quantum noise limit. These equations enable the calculation of the common spin expectation values without the use of the wave function. They also offer information on the orientation dynamics of the magnetic moment of charged particles beyond the behavior of the spin averages.
We have performed high-precision experimental measurements of spin precession using a dressed 3{}^{3}3He atomic beam. Spin dressing uses an oscillating magnetic field that is both detuned to high frequency and orthogonal to a static magnetic field to effectively change the gyromagnetic ratio of a spin. We verify the validity of the spin-dressing Hamiltonian in regions beyond the limiting solution in which the Larmor frequency is much smaller than the frequency of the dressing field. We also evaluate the effect of magnetic field misalignment, i.e. if the oscillating magnetic field is not orthogonal to the static magnetic field. Modulation of the dressing-field parameters is also discussed, with a focus on whether such a modulation can be approximated merely as a time-dependent, dressed gyromagnetic ratio. Furthermore, we discuss implications for a proposed search for the neutron electric dipole moment, which would employ spin dressing to make the effective 3{}^{3}3He and neutron magnetic moments equal.
The behavior of an atom in a nonuniform magnetic field is analyzed, as well as the motion of a classical magnetic dipole (a spinning charged ball) and a rotating charged ring. For the atom it is shown that, while the magnetic field does no work on the electron-orbital contribution to the magnetic moment (the source of translational kinetic energy being the internal energy of the atom), whether or not it does work on the electron-spin contribution to the magnetic moment depends on whether the electron has an intrinsic rotational kinetic energy associated with its spin. A rotational kinetic energy for the electron is shown to be consistent with the Dirac equation. If the electron does have a rotational kinetic energy, the acceleration of a silver atom in a Stern-Gerlach experiment or the emission of a photon from an electron spin flip can be explained without requiring the magnetic field to do work. For a constant magnetic field gradient along the z axis, it is found that the classical objects oscillate in simple harmonic motion along the z axis, the total kinetic energy -- translational plus rotational -- being a constant of the motion. For the charged ball, the change in rotational kinetic energy is associated only with a change in the precession frequency, the rotation rate about the figure axis remaining constant.
The classical Hamiltonian of a point charged particle with intrinsic spin, which is composed of the relativistic orbit Hamiltonian and the spin Hamiltonian. This spin Hamiltonian can be derived from the Thomas-Bargmann-Michel-Telegdi equation. In our thesis, we will prove that the classical Hamiltonian in which the gyromagnetic ratio equals 2 is in agreement with the low-energy limit of the Dirac equation, the relativistic quantum theory for a spin-1/2 charged particle. For this purpose, we apply the Foldy-Wouthuysen transformation to the Dirac Hamiltonian under the assumptions of the static and homogeneous electromagnetic fields. Furthermore, in order to maintain such a correspondence in arbitrary gyromagnetic ratio cases, we perform the F-W transformation to the Dirac-Pauli Hamiltonian, which is the Dirac Hamiltonian plus the anomalous magnetic dipole moment Hamiltonian. Up to the twelfth-order of F-W transformed Dirac and Dirac-Pauli Hamiltonian, the calculation results are in accord with the corresponding classical Hamiltonians.
In the Stern–Gerlach experiment, silver atoms were separated according to their spin state (Gerlach and Stern 1922 Z. Phys. 9 353–355). This experiment demonstrates the quantization of spin and relies on the classical description of motion. However, so far, no design has led to a functional Stern–Gerlach magnet for free electrons. Bohr and Pauli showed in the 1930 Solvay conference that Stern–Gerlach magnets for electrons cannot work, at least if the design is based on classical trajectories (Pauli W 1932 Proc. of the 6th Solvay Conf. 2 (1930) (Brussels: Gauthier-Villars) pp 183–86, 217–20, 275–80; Pauli W 1964 Collected Scientific Papers ed R Kronig and V F Weiskopf, vol 2 (New York: Wiley)). Here, we present ideas for the realization of a Stern–Gerlach magnet for electrons in which spin and motion are treated fully quantum mechanically . We show that a magnetic phase grating composed of a regular array of microscopic current loops can separate electron diffraction peaks according to their spin states. The experimental feasibility of a diffractive approach is compared to that of an interferometric approach. We show that an interferometric arrangement with magnetic phase control is the functional equivalent of an electron Stern–Gerlach magnet.