Once upon a time, I was involved in an abortive attempt to measure the variation of the fundamental constants. Thanks to that experience, I’ve always had an interest in these measurements, so a new paper describing an alternative way to detect changes in fundamental constants caught my eye.

The fundamental constants—the speed of light, Planck’s constant, the charge of the electron, etc.—are taken to be fixed in value. But there is no theory to explain the fundamental constants, nor is there a reason for them to be constant. They could have been different in the past, and they may be different in the future. Spectroscopic measurements of stars and galaxies at ever-increasing distances tell us that if the fundamental constants were different, it wasn’t by much. We now know that the limit for the relative variation of alpha is 10-17 per year.

Which constants should we measure?

When it comes to these measurements, physicists and astronomers generally focus on alpha and mu. Alpha, otherwise known as the fine structure constant, is a combination of the electric charge, the speed of light, and Plank’s constant. It describes the strength in binding energy between negatively charged electrons and the positively charged nucleus of an atom. Hence, it can be directly measured in the light emitted by hydrogen in distant stars.

However, alpha measurements like this have two potential problems. If excited, a lone hydrogen atom will emit a reasonably broad range of light—or at least "broad" compared to the size of the change we're trying to measure. In addition, the pressure and temperature of hydrogen in a star broadens that range further.

Mu is the ratio of the mass of the electron and the mass of the proton. This changes the binding energy of electrons to the nucleus, but it also has an effect on how atoms in a molecule vibrate (alpha also changes this). In space, where molecules don’t collide very often and are quite cold, the color of the light they absorb to set them vibrating is very precisely defined. Potentially smaller changes can therefore be measured. Unfortunately, our measurements of the absorption are simply not precise enough to detect any changes.

A new approach to mu and alpha

A group of theorists has noted that a confluence of technological developments may allow a new approach to measuring mu and alpha. They propose measuring the lengths of a block of material. The idea is that alpha and mu both change the length of the bonds between atoms. If alpha and mu are changing, so are bond lengths. Since the bond length is changing, so is the volume of material in a block (as long as the number of atoms does not change).

The question, then, is how much do bond lengths change? To get an estimate, the researchers used a combination of techniques to calculate the bond lengths of di-atoms of several materials (a Copper-Copper molecule, for instance). These were compared to experimental data to ensure that the calculations were reasonably accurate. The researchers found that for di-atoms, their calculations were accurate at about the 1 percent level. Further calculations found that mu and alpha changed the bond length by between one part in ten and one part in a million. Taking into account current experimental uncertainties, the researchers think these relative changes are accurate to within about 5 percent.

When scaling that to solids, the accuracy falls to about 20 percent (because bond lengths in bulk crystals are less accurately known for many materials). The relative size of the changes in bond length due to the change in alpha and mu, however, remain about the same, or even slightly larger.

So it seems pretty certain that if the fundamental constants change, the changes will turn up in bond length measurements.

How do we measure that?

On the other hand, the development of high-precision interferometers enables us to measure relative changes in length to a precision of 10-18. Using light, interferometers measure a relative change in the distance between two mirrors. This is the basis of gravitational wave observatories, which have a relative sensitivity of 10-22. If alpha was changing at the maximum possible rate, we should be able to see that very quickly in an interferometer with the same sensitivity as a gravitational wave observatory. Even using a high-precision interferometer, the measurements should detect changes in alpha within a reasonably short time (call it a year).

Initially, I was quite skeptical of this idea. I think the biggest problem will be preventing erosion or oxidation of the block during the measurement. Other problems like temperature or contamination from residual gases in a vacuum system have all been dealt with in other measurement systems, so that should be solvable. However, the stability of the chosen material will be critical, and that is not a simple problem to solve.

Still, I hope the researchers can make it work and create a magnificent interferometer to do the measurements.

Physical Review Letters, 2019, DOI: 10.1103/PhysRevLett.122.160801 (About DOIs)