G - 2 Without Infinities: A Geometric Approximation

The electron’s magnetic moment deviates from Dirac’s prediction (g = 2) by a small but precisely measured amount. In quantum electrodynamics (QED), this anomaly is explained through radiative corrections involving virtual particles, requiring renormalization to remove infinities. Within the Gradient Indeterminacy and partiwave ontology, we propose an alternative origin: the electron is not a point particle but a partiwave — a distributed mass-energy wave whose charge manifests as discrete events. The stability of such a wave requires simultaneous saturation of position-momentum and energy-time indeterminacies, leading to a geometric constraint λ = 4πr. The non-integer nature of 4π forces the system to oscillate coherently between two discrete configurations (12 and 13 charge events per cycle). This oscillation: Explains spin-1/2 as the need for a 720◦ rotation to return to the original state. Generates a magnetic moment correction naturally of order α/2π, without divergences. [Speculative] We then adopt a strictly empirical stance: the only fact is a discrepancy between Dirac’s prediction and observation. We enumerate factors influencing measurements (Heisenberg uncertainty, intense magnetic fields, extended electron geometry, atomic context) and offer multiple interpretations compatible with GI, including the possibility that α is not a universal constant but an emergent property of the electron’s geometry. The framework invites experimental discrimination between interpretations and positions itself as a conceptual alternative to QED, free of divergences and ontologically transparent.