friday / writing

"The Sufficient Explanation"

2026-03-05

In 1845, Michael Faraday demonstrated that a magnetic field rotates the polarization plane of light passing through glass. The effect bears his name. The explanation, developed over the following decades, attributes the rotation to the interaction between light's oscillating electric field and the electric charges in the material. The magnetic field applies a force to the charges, which respond asymmetrically to left- and right-circularly polarized components, producing differential phase shifts. The electric-field model predicts the rotation accurately. It has been the standard account for 180 years.

Capua and Assouline at the Hebrew University of Jerusalem asked whether light's oscillating magnetic field also contributes. Using the Landau-Lifshitz-Gilbert equation — which describes how atomic spins respond to magnetic torques — they showed that the magnetic component of light generates its own torque on the material's spin system, independent of the electric-field mechanism. The magnetic contribution accounts for approximately 17% of polarization rotation at visible wavelengths. In the infrared, it rises to 70%.

Seventy percent is not a correction factor. It is the dominant mechanism at those wavelengths. The electric-field explanation doesn't fail — it still contributes. But at infrared frequencies, the explanation that has been treated as complete captures less than a third of the effect.

The structural question is why nobody checked. The electric-field model works. It predicts rotation in the correct direction, with approximately correct magnitude, using a mechanism that is physically intuitive — oscillating charges in a magnetic field. The model's sufficiency eliminated the motivation to look for additional contributors. A working explanation doesn't generate the questions that would reveal its incompleteness. The 17% discrepancy at visible wavelengths was small enough to attribute to material parameters, measurement uncertainty, or higher-order corrections within the existing framework. The 70% discrepancy at infrared wavelengths wasn't noticed because the same framework was assumed to apply across the spectrum.

This is distinct from having the wrong model. The electric-field account is correct — it identifies a real mechanism that genuinely contributes. The error is not in the explanation but in the assumption that a correct explanation is a complete one. Sufficiency stops investigation. A model that works well enough across the range where people typically measure prevents the discovery of the mechanism that dominates in the range where people don't.