Spin Precession Equation (Larmor/Bloch Equation)

$$\frac{dS}{dt} = -\frac{g\mu_B}{\hbar}\, S \times B$$

Status: Proven.

This is the standard equation of motion for a magnetic moment (here, an electron’s spin $S$) in a magnetic field $B$ — the torque exerted by the field causes the spin to precess around the field direction rather than align with it directly, at a rate set by the gyromagnetic ratio ($g\mu_B/\hbar$). It’s a direct consequence of the relationship between angular momentum and torque applied to a magnetic dipole, and underlies phenomena from compass-needle-like classical precession up through quantum spin dynamics.

Real, independent confirmation: this exact equation (in its classical form, the Larmor equation; in its quantum/relaxation-inclusive form, the Bloch equation) is the working basis of electron spin resonance (ESR) spectroscopy, nuclear magnetic resonance (NMR) and MRI imaging, and atomic clock technology — all real, continuously operating technologies built directly on this formula being correct.

Used in: Paper 5 and Paper 6, applied without modification to model spin precession — PBT proposes a different mechanical origin for why $g\approx2$ (see the QED anomalous magnetic moment page for that separate, distinct claim), but this precession equation itself is standard, unmodified physics.