Considerations about the measurement of the magnetic moment and electric dipole moment of the electron

TL;DR

This work scrutinizes the standard interpretation of electron magnetic moment and EDM measurements through a classical Dirac-particle model with distinct center-of-charge and center-of-mass dynamics. It shows that observed spin precession and dipole-like signals arise from time-averaged internal motions (zitterbewegung) rather than intrinsic static moments, predicting a CM precession rate $ω_s=-ω_c/2$ in a uniform magnetic field. The analysis challenges the common relation $ω_s/gω_c=1/2$ used to extract the gyromagnetic ratio and demonstrates that EDM bounds depend on CM velocity and orientation, not solely on a fundamental dipole. Through natural-unit reformulations and numerical simulations aligned with Penning-trap setups, the paper argues for reinterpretation of precision $g$-factor results and EDM limits, and proposes experimental tests to probe the electron’s internal clock.

Abstract

The goal of the measurement of the magnetic moment of the electron $μ$, is to experimentaly determine the gyromagnetic ratio. The factor $g/2$ is computed by the accurate measurement of two frequencies, the spin precession frequency $ν_s$, and the cyclotron frequency $ν_c$, and is defined as $ν_s/ν_c=g/2$. These experiments are performed with a single electron confined inside a Penning trap. The existence of the electric dipole moment ${\bf d}_e$, involves the idea of an asymmetric charge distribution along the spin direction such that ${\bf d}_e=d_e{\bf S}/(\hbar/2)$. The energy shift $ΔU=2{d}_eE_{eff}$ of the interaction of the electric dipole of electrons with a huge effective electric field ${\bf E}_{eff}$, close to the nucleus of heavy neutral atoms or molecules, is calculated by a spin precession measurement and the value $d_e$ is determined. By using a classical model of a spinning electron, which satisfies Dirac's equation when quantized, we determine classically the time average value of the electric and magnetic dipole moments of this electron model when moving in a uniform magnetic field and in a Penning trap, with the same fields as in the real experiments, and obtain an estimated value of these dipoles. We compare these results with the experimental data and make some interpretation of the measured dipoles. The conclusion is that experiments do not measure what they purport to measure.

Figures (10)

• Figure 1: Model of a Penning trap where an electrostatic field between the positively charged lateral wall, and the two negatively charged caps, is established. Superimposed there is also a uniform axial magnetic field. Red lines correspond to the field lines of the electrostatic field.
• Figure 2: Motion of the spinless point particle (blue), with initial position in $(x_0,y_0,z_0)=(6,0,8)$, initial velocity $(\dot{x}_0,\dot{y}_0,\dot{z}_0)=(0,0.1,0)$, and where the parameter $a=0.001$. It is also depicted the projection of the motion (red) on the $XOY$ plane.
• Figure 3: Evolution of the ThO molecules inside the cavity. In the region $A$ where some molecules are excited (green to red) the corresponding excited electrons reverse the orientation of their electric dipole, absorbing some photons from the optical pumping. Later, the molecule makes a spontaneous emission in region $D$, where the detectors are located, and the energy of the emitted photons is measured.
• Figure 4: This model represents the circular motion, at the speed of light, of the center of charge of the electron in the center of mass frame. The center of mass is always a different point that the center of charge. The radius of this motion is $R_0=\hbar/2mc$, in this frame. The angular velocity is $\omega_0=2mc^2/\hbar$. This frequency, decreases when the center of mass moves. The local clock slows down when moving. The spin has two contributions: one ${\bi Z}$ from the orbital motion of the CC around the CM (Zitterbewegung) and another ${\bi W}$ in the opposite direction, related to the rotation with angular velocity $\bomega$ of a comoving Cartesian frame attached to the CC. The magnetic moment is related to the motion of the CC, and therefore to the zitterbewegung contribution to the spin, ${\bi Z}$, with a normal relation ${\bmu}=e{\bi Z}/2m$. It is when we expressed the magnetic moment in terms of the total spin ${\bi S}$, is when we the concept of gyromagnetic ratio $g=2$Rivasg=2 is obtained.
• Figure 5: Dirac particle in the center of mass reference frame, with the spin along the OZ axis. The initial position and velocity of the CC on the $XOY$ plane is determined by the phase $\psi$. The radius of this motion is $R_0=1/2$, in natural units.