Measurements of the electron magnetic moment (the “g-value”) probe the electron’s interaction with the fluctuating vacuum. With a quantum electrodynamics calculation, they provide the most accurate determination of the fine structure constant. Comparisons with independent determinations of the fine structure constant are the most precise tests of quantum electrodynamics and probe extensions to the Standard Model of particle physics. I will present two new measurements of the electron magnetic moment. The second, at a relative uncertainty of 0.28 parts-per-trillion, yields a value of the fine structure constant with a relative accuracy of 0.37 parts-per-billion, over 10-times smaller uncertainty than the next-best methods. The high precision arises from the combination of many useful techniques. A single-electron quantum cyclotron, so-called because a quantum nondemolition measurement resolves the lowest cyclotron and spin levels, is held in a cylindrical Penning trap, whose well-understood cavity-mode structure inhibits spontaneous emission and creates calculable frequency shifts due to electron–cavity coupling. A low temperature (100 mK) narrows the linewidths of the measured frequencies and inhibits stimulated absorption in the cyclotron motion, effectively locking it in the quantum ground state. The signal from the electron’s axial motion is fed back as a drive, forming a single-particle self-excited oscillator and increasing the signal-to-noise.