Is the Electron Orbital Gyromagnetic Factor Exactly Equal to 1?

High precision measurements and calculations of the hyperfine and fine structure of the hydrogen atom spectrum were crucial to the development of Quantum Field Theory (QED). High precision measurement of the magnetic moment of the electron have subsequently been important in the testing of QED, with much effort devoted to the accurate measurement of the anomaly (g_S – 2) in the spin gyromagnetic factor g_S. The g-factor for the electron’s spin magnetic moment g_S has been measured to a precision of 2.8 parts in 10¹³. The spin g-factor is the ratio of the magnetic moment to the spin angular momentum S, measured in units of the Bohr magneton m_B. Its agreement with the prediction of Quantum Field Theory provides the most precise confirmation of theory with experiment in all of physics. In contrast, the orbital g-factor g_L is known only to about 1 part in 10⁴. Experiments will be described to measure g_L to much higher precision and preliminary calculations of relativistic corrections to g_L will be presented. Finally, a conceptual analysis of relativistic quantum mechanics will be presented, with comments on the steps needed to calculate g_L.