Fine-structure constant: Is it really a constant?

It is often claimed that the fine-structure "constant" α is shown to be strictly constant in time by a variety of astronomical and geophysical results. These constrain its fractional rate of change ̇ \.αα to at least some orders of magnitude below the Hubble rate H₀. We argue that the conclusion is not as straightforward as claimed since there are good physical reasons to expect ̇ \.ααH₀. We propose to decide the issue by constructing a framework for α variability based on very general assumptions: covariance, gauge invariance, causality, and time-reversal invariance of electromagnetism, as well as the idea that the Planck-Wheeler length (10^-33 cm) is the shortest scale allowable in any theory. The framework endows α with well-defined dynamics, and entails a modification of Maxwell electrodynamics. It proves very difficult to rule it out with purely electromagnetic experiments. In a cosmological setting, the framework predicts an ̇ \.αα which can be compatible with the astronomical constraints; hence, these are too insensitive to rule out α variability. There is marginal conflict with the geophysical constraints; however, no firm decision is possible because of uncertainty about various cosmological parameters. By contrast the framework's predictions for spatial gradients of α are in fatal conflict with the results of the E\"otv\"os-Dicke-Braginsky experiments. Hence these tests of the equivalence principle rule out with confidence spacetime variability of α at any level.