= Trapped-electron spin-jump readout
<Hans Georg Dehmelt> describes a $4\ \mathrm K$, $5\ \mathrm T$ <Penning trap>, with positive ring and negative endcaps $8\ \mathrm{mm}$ apart. Axial RF emission tracked an injected seven-<Electron> bunch losing particles; reducing the drive retained the last <Electron>. A weak magnetic bottle converted <spin> changes into axial-<frequency> changes. At successive probe <frequencies>, counted spin flips traced a resonance.<Experiments with an isolated subatomic particle at rest by Hans Georg Dehmelt>[Dehmelt, pp. 584–589, Figs. 1, 3, 6–7; Columbia scan]{ref}
The inference can be explained without inventing a detector calibration. Let a weak bottle have on-axis field $B_z\simeq B_0+bz^2$. The <magnetic dipole potential energy> adds $-\mu_zbz^2$ to the axial <harmonic oscillator> <potential energy>, so
$$
\omega_{z,\mu}^2\simeq\omega_z^2-\frac{2\mu_zb}{m}.
$$
A change in the <magnetic dipole moment> therefore shifts the monitored axial <angular frequency>. This is a simplified readout model, not a quantitative reconstruction of the historical bottle. It illustrates how a transition in one degree of freedom becomes a detectable change in another.
For the positive <electron spin g-factor> convention, uniform-field <spin> precession and free <cyclotron> motion give
$$
\omega_s=\frac{g_s}{2}\frac{eB}{m},\qquad
\omega_c=\frac{eB}{m},\qquad
a_e=\frac{g_s-2}{2}=\frac{\omega_s-\omega_c}{\omega_c},\qquad e>0.
$$
Thus an <anomalous magnetic moment> measurement compares <frequencies> rather than requiring an equally precise absolute <magnetic field> calibration. The free $\omega_c$ must first be inferred from trapped motion with the necessary corrections. A spin-flip count versus probe <frequency> supplies evidence for a transition resonance; it does not directly measure a spatial <Electron> radius. Nor is this radio readout an optical <fluorescence> record: different experiments require different preparations and detectors. In a precision comparison, repeat scans with changed drive strength and monitor <magnetic field> drift, motional excitation and detector back-action; these are experimental-design checks, not additional historical observations asserted here.
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