Are the constants of nature constant?

About two billion years ago, uranium in a deposit in Gabon was rich enough for a natural chain reaction to start. It ran, intermittently, for hundreds of thousands of years.

The isotope ratios left behind depend sensitively on the position of a nuclear resonance, which depends on the strength of electromagnetism relative to the nuclear force. Measuring them limits any change in the strength of electromagnetism since then to about one part in ten million in the standard analysis, and one part in a hundred million in a 2015 reanalysis. Both lean on nuclear models, and some readings of the data allow a second solution in which the resonance did move.

It is among the tightest limits on any changing constant, and it comes from a rock rather than an instrument.

The other end of the timescale is measured directly. Two atomic clocks built on different transitions respond differently to a change in the fine-structure constant, so comparing their ratio over months bounds any present-day drift.

A 2008 comparison of aluminium and mercury ion clocks reached the seventeenth decimal place and found the ratio stable, which constrains the drift to a few parts in ten to the seventeenth per year.

Comparisons of two transitions in a single ytterbium ion, repeated over six years, have since brought the bound to a few parts in ten to the nineteenth per year.

Two methods separated by two billion years, and neither has seen anything move.

Only dimensionless combinations are meaningful. Asking whether the speed of light has changed is not a well-posed question, because the answer depends on the units, and the units are defined in terms of it.

The quantities that can be tested are ratios such as the fine-structure constant and the proton-to-electron mass ratio, which is why results are stated in terms of them.

One team has reported a slightly smaller fine-structure constant in light from distant quasars, and then a dipole across the sky. Another, analysing spectra from a different telescope, found nothing, and a 2022 measurement calibrated with a laser frequency comb finds no change at the level of about a part per million.

The disagreements turn on instrument calibration and on the statistics of combining many absorption systems. A 2015 study found distortions in both telescopes' wavelength scales that could account for one telescope's results and part of the other's; in 2020 a new analysis still found a spatial variation marginally preferred. That is the pattern of a measurement at the edge of what the instrument can do.

Theories that unify the forces, and theories with extra dimensions, typically contain fields whose values set the effective constants. If such a field rolls slowly, the constants drift.

So a detection would be evidence for a whole class of theories, and the absence of one constrains them. That is why the limits keep being pushed rather than being regarded as settled.

Nothing explains the numbers themselves. Some are measured to great precision, and none is derived.

Whether they are derivable at all, or whether they are accidents of how this region of the universe settled, is the question the fine-tuning argument tries to get at and does not answer.