One of the most dissatisfying aspects of modern physics is the fundamental constants. It's not that they are constant that bothers anyone, it is their very existence that is offensive to right-thinking people. Fundamental constants are needed to get working versions of the mathematical models we use to explain our observations. But their values are entirely derived from experimental measurements. There is no theory that predicts the value of fundamental constants like the speed of light or Planck's constant.

To make matters worse, we cannot even be sure that the fundamental constants are constant. A recent paper in Physical Review Letters presents an analysis of astronomical data indicating that either the fundamental constants do change—but not in some simple, easily measured fashion—or there is something very wrong with their analysis.

Why constants may not be constant

Before we get to the data, let's take a very brief detour into why we might think that the fundamental constants might change. The speed of light as, perhaps, the ultimate constant, comes to us through considering how light propagates through the vacuum. This turns out to be determined by the electrical and magnetic properties of the vacuum—basically, light propagates by wiggling charges that pop in and out of existence in the vacuum.

But if the properties of the vacuum are found to change, then so too will the speed of light. Our model for the vacuum doesn't preclude this, but our observations tell us that, if it has, it didn't change drastically. Now, since the vacuum has been expanding away like crazy since time began, it isn't unreasonable to assume that vacuum properties might have changed. Hence, in the distant past, the speed of light might have been different.

Similar arguments can be made for the other fundamental constants. We know so little about this that we can't even say if they apply to any, all, or none of the constants. With that lack of knowledge, it makes sense to measure as many of them as possible at once, so researchers tend to concentrate on what's called the fine structure constant.

The fine structure constant contains the speed of light, Plank's constant, the charge of an electron, and the permittivity of vacuum in one bundle. Its job is to determine how strongly electrically charged particles couple to each other. This constant helps to determine what colors of light different atoms and molecules will absorb and emit. This is very convenient, because we are good at spectroscopy: we can measure absorption and emission very accurately and use that data to determine the value for the fine structure constant.

One measurement, many constants

This is exactly what people have been doing: buying a boat load of telescope time, observing the spectra from distant quasars, calculating the value of the fine structure constant, and determining if it is different from that measured here on Earth. Since the quasars are located at vast distances from us, the light we observe now was emitted much earlier in the history of the Universe. So if the fine structure constant was different, the light will have a different color from that emitted by the same elements on Earth.

The results turned out to be a bit of a mess. Some experiments failed to find any change, others observed that the fine structure constant was smaller in the past, and yet others found that it was larger in the past. When looking at all these results, the only conclusion that doesn't result in a migraine is that the fine structure constant is constant.

Luckily, there are physicists made of sterner stuff than me. What they noted is that the experiments are getting more and more precise. Those results that suggest that the fine structure changes are far less likely to be the result of statistical flukes than they were in earlier work. Maybe there is a variation that is more complicated than initially thought.

Now, there is a precedent here. The cosmic microwave background was initially thought to be isotropic—it's the same where ever you look. However, accurate measurements show that there is a slight difference and the Universe seems to have some sort of global orientation. This might also imply that the fundamental constants could be different depending on which direction we look.

Checking with quasars

To test this, a group of Australian researchers observed quasars with the Keck telescope and the Very Large Telescope. Because of their different locations, they look at different sections of the night sky with a small overlap. The combination had common quasars to use to eliminate measurement uncertainties, but could still look different directions to see if there were different fundamental constants.

To make sense of the data, they assumed that, like the cosmic microwave background, there was a preferential direction to the Universe, and depending on the direction and distance of the quasar, they would see a different fine structure constant. What followed was a whole lot of statistics related to trying to determine if the results of the analysis were themselves just an accident of chance.

Unlike the cosmic microwave background measurements, we don't have a firm theory on which to ground any measurements, so the statistical analysis becomes much more important. In the end, the researchers could conclude the following: their findings are not dominated by a few outlier measurements; their data follows a form that may (with some imagination) be consistent with the anisotropy observed in the cosmic microwave background; and, finally, the results are statistically significant to just over four standard deviations, meaning there is a 99.99 percent certainty that their data does indicate a consistent change to the fine structure constant.

99.99 sounds pretty good, yet the paper's conclusions are very tentative. Perhaps, the authors say, the results are due to some measurement artifact in the instrument or data processing. I would imagine that they are awaiting the magic five-sigma confidence. In particle physics, if the results are such that you can claim that the signal has a significance of five-sigma, then people will accept that it is real. Otherwise, it might be a fluke.

Even now, though, these results are likely to have theorists going back over their models and classifying them into "those that fit the data" and "those that don't." So, even if the results don't hold up exactly as the researchers would like them to, they are still good enough to rule out many different models and act as inspiration for new directions in fundamental physics.

Physical Review Letters, 2011, DOI: 10.1103/PhysRevLett.107.191101