Fine-structure constant: Is it really a constant?

It is often claimed that the fine-structure "constant" $\alpha$ is shown to be strictly constant in time by a variety of astronomical and geophysical results. These constrain its fractional rate of change $\frac{\dot{\alpha }}{\alpha }$ to at least some orders of magnitude below the Hubble rate $H_0$. We argue that the conclusion is not as straightforward as claimed since there are good physical reasons to expect $\frac{\dot{\alpha }}{\alpha }\ll H_0$. We propose to decide the issue by constructing a framework for $\alpha$ 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 (${10}^{-33\mathrm{}}$ cm) is the shortest scale allowable in any theory. The framework endows $\alpha$ 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 $\frac{\dot{\alpha }}{\alpha }$ which can be compatible with the astronomical constraints; hence, these are too insensitive to rule out $\alpha$ 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 $\alpha$ are in fatal conflict with the results of the Eötvös-Dicke-Braginsky experiments. Hence these tests of the equivalence principle rule out with confidence spacetime variability of $\alpha$ at any level.