The calculation of the electron’s magnetic moment has long stood as a testbed for classical and quantum theories. While early models treated the electron as a point particle or current loop with charge, e, such approaches failed to match experimental measurements, necessitating quantum electrodynamics (QED) corrections.

The Light Charge Hypothesis [1] [2] introduces a new framework in which the electron consists of two oppositely charged components, each with magnitude, $q_p=\sqrt{{\epsilon }_o\ast h\ast c}$, orbiting at the speed of light. This internal structure allows a revisitation of the current loop derivation of the magnetic moment, incorporating relativistic effects via length contraction. This work derives a corrected form of the magnetic moment and demonstrates consistency with observed values.

This paper begins by recalling the classical equation for the magnetic moment of a current loop:

$\mu =I\ast A$

where I is the current and A is the area enclosed by the loop. This framework is applicable here since the light charges orbiting at relativistic speeds effectively form a current loop.

Current is defined as:

$I=\frac{\Delta q}{\Delta t}$

where $\Delta q$ is the effective charge and $\Delta t$ is the period of rotation. For the Light Charge Hypothesis, $\Delta t$, is the time it takes one charge to complete an orbit. Assuming the light charge travels at speed, c, and accounting for relativistic length contraction, the contracted radius is

$r_v=r_o\ast \sqrt{1-\frac{v^2}{c^2}}$

where $r_o$ is the rest-frame radius of the electron. The period is then:

$\Delta t=\frac{2\ast \pi \ast r_v}{c}$

The area of the loop is

$A=\pi \ast r_v^2=\pi \ast r_o^2\ast \left(1-\frac{v^2}{c^2}\right)$

To find the effective charge, q_eff, we equate Energy under two frames. From the model in [3] , each orbiting charge has magnitude, and the energy of the system is $E=q\ast V$ where $V=k\ast q/r$.

$E=\frac{2\ast k\ast q_p^2}{r_o}$

Under length contraction, the Light Charge Hypothesis reinterprets this as a system with a modified effective charge, q_eff, and contracted radius r_v:

$E=\frac{k\ast q_{eff}^2}{r_o\ast \sqrt{1-\frac{v^2}{c^2}}}$

Remembering the relation for the fine structure constant:

$\alpha =\frac{e^2}{2\ast {\epsilon }_o\ast h\ast c}=\frac{e^2}{2\ast q_p^2}$

And equating the two yields:

$q_{eff}=\frac{e}{\sqrt{\alpha }}\ast {\left(1-\frac{v^2}{c^2}\right)}^{\frac{1}{4}}$

Substituting into $\mu =I\ast A$, we have:

$\mu =\frac{e}{\sqrt{\alpha }}\ast {\left(1-\frac{v^2}{c^2}\right)}^{\frac{3}{4}}\ast c\ast r_o\ast \frac{1}{2}$

Then from [1] ro can be substituted out.

$r_o=\frac{h}{2\ast \pi \ast m_{electron}\ast c}$

Yielding

$\mu =\frac{e\ast h_{bar}}{2\ast m_{electron}}\ast \frac{1}{\sqrt{\alpha }}\ast {\left(1-\frac{v^2}{c^2}\right)}^{\frac{3}{4}}$

Recognizing that the Bohr magneton is

$\mu =\frac{e\ast h_{bar}}{2\ast m_{electron}}$

This paper rewrites:

$\mu ={\mu }_B\ast \frac{1}{\sqrt{\alpha }}\ast {\left(1-\frac{v^2}{c^2}\right)}^{\frac{3}{4}}$

This matches the QED-style form:

$\mu ={\mu }_B\ast \frac{g}{2}$

Which implies

$\frac{g}{2}=\frac{1}{\sqrt{\alpha }}\ast {\left(1-\frac{v^2}{c^2}\right)}^{\frac{3}{4}}$

Substituting the experimental value g/2 = 1.00115965218073, the implied velocity becomes v = 0.980978935 * c.

An alternative derivation uses the relativistic cyclotron relation. Starting with:

$\frac{m\ast v^2}{r}\ast \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}=q_{effective}\ast \left(v\times B\right)$

Solving for B, we use:

$w=\frac{v}{r}=2\ast \pi \ast f_c\ast r$

Combining and solving yields an expression for the Lorentz factor.

$\sqrt{1-\frac{v^2}{c^2}}=2\ast \pi \ast f_c\ast m_{electron}\ast \frac{1}{q_{effective}}\ast \frac{1}{B}$

The magnetic moment of a current loop is also expressed as:

$\mu =\frac{q\ast v\ast r}{2}$

$\mu =\frac{q_{effective}\ast c\ast r_o\ast \sqrt{1-\frac{v^2}{c^2}}}{2}$

Substituting in the previous equation gives the following:

$\mu =\frac{q_{effective}\ast c\ast r_o}{2}\ast 2\ast \pi \ast f_c\ast m_{electron}\ast \frac{1}{q_{effective}}\ast \frac{1}{B}$

Which simplifies to

$\mu =\frac{q_{effective}\ast c}{2}\ast \frac{h}{2\ast \pi \ast m_{electron}\ast c}\ast 2\ast \pi \ast f_c\ast m_{electron}\ast \frac{1}{q_{effective}}\ast \frac{1}{B}$

$\mu =\frac{h}{2}\ast f_c\ast \frac{1}{B}$

Given the experimental values of f = 149 GHz and g/2 = 1.00115965218073, solving gives B = 5.316690762164 T, v = 0.980978935c.

Thus, with precise values for f and v, one can derive B and consequently, the magnetic moment using this compact expression.

By revisiting the electron’s magnetic moment using the Light Charge Hypothesis and incorporating relativistic contraction effects, we derive a closed-form expression that agrees with experimental data.

The result

$\mu ={\mu }_B\ast \frac{1}{\sqrt{\alpha }}\ast {\left(1-\frac{v^2}{c^2}\right)}^{\frac{3}{4}}$

naturally explains the observed deviation in g/2 without invoking perturbative QED. Furthermore, the identity

$\mu =\frac{h}{2}\ast f_c\ast \frac{1}{B}$

Provides a second, experimentally grounded derivation, confirming consistency with cyclotron frequency measurements. These results support the physical plausibility of the Light Charge Hypothesis and offer a promising direction for modeling other elementary particles.