Are the (Dimensionless) Constants Constant?

In the previous post, I said that the fine structure constant alpha provides us with a way to measure whether the fundamental constants making it up (the electron charge, Planck’s constant, and the speed of light) have changed in the last few billion years. How, exactly, does that work?

The easiest way to see how the fine structure constant leaves a signature that can be detected millions or billions of years later is to think about its effect on atomic states. In the picture where you think of it as describing the ratio of the speed of an orbiting electron to the speed of light, it’s easy to see that alpha is the number that will describe the corrections due to relativistic effects. The major weird effects that show up in relativity, like time dilation and length contraction, have an effect that’s proportional to (roughly speaking) the square of the ratio of the speed of a moving object to the speed of light. For an electron in a simple atom, those effects will be very small– the ratio in question is 1/137, and the square of that is a very small number– but they will be present, and will lead to very small changes in the energy levels of those atoms.

It’s those energy shifts that are the key to making a measurement of alpha, as we have well over a hundred years’ experience in measuring the separation between energy levels in atoms– that’s the science of spectroscopy. If we look at the light emitted by atoms, the frequency of the light is proportional to the energy difference between the initial and final states, and changes in those energy levels lead directly to changes in the frequency of the light emitted. The changes can be pretty small, but we can make astonishingly precise measurements of the frequencies of light emitted by atoms, which allows us to make very precise measurements of alpha.

Spectroscopy also gives us a way to measure the change in the fine structure constant, by looking at the light emitted by atoms a long time ago, a long distance away. By comparing the spectrum of light emitted by, say, hydrogen atoms in a lab on Earth to the light emitted by hydrogen atoms in a distant galaxy, we can compare the value of the fine structure constant today to the value it had when that light left the other galaxy millions or billions of years ago.

Of course, there are lots of other things that can change the measured frequencies of spectral lines, including relative motion of the source and observer, and sorting all that stuff out is an incredibly difficult problem. They try to do this by measuring lots of different spectral lines from lots of different atoms, some of which are very sensitive to changes in alpha, and some of which aren’t. The lines that are insensitive to small changes are used to determine if there’s an overall shift relative to measurements made in the lab, and provide a correction for the lines that are more sensitive to changes in alpha. This should allow you to correct for any Doppler shifts caused by motion of the distant sources being studied, but as Rob notes, it’s a tricky business. At least two different groups have attempted to carry out this analysis, and they get different results (one finds a (barely) signficant change in alpha, while another group saw nothing).

Another cool spectroscopic possibility has been discussed by a number of people is to compare two different types of atomic clocks. Atomic clocks are based on measuring the frequency of light needed to drive a transition between two particular states of a particular atom, and there are lots of different atoms you can do this with. If you take two different clocks, based on two different atoms, you can arrange it so that one of the clocks is more sensitive to changes in alpha than the other. If you compare the frequencies of the two clocks over a few years, you could detect a change in the difference between their operating frequencies, and use that to measure the change in the fine structure constant.

The changes you’d be talking about are ridiculously small, but the science of clocks is amazingly precise– the best atomic clocks in operation are good to a few parts in 10¹⁵, and with a bit of work, you can hope to get the difference measurement into a range that’s competitive with the astrophysical measurements (the group that claimed to see a change put the magnitude at a few parts in 10⁵ over 12 billion years, which is several parts in 10¹⁶ per year). In order to improve the sensitivity and reduce other perturbations, it’s been proposed that the comparison should be done in space, which is probably just about the best science proposal anybody’s made for the International Space Station.

For all the great potential of spectroscopy to measure changes in alpha, the current state of the art comes not from atomic physics, but from geophysics. The fine structure constant turns out to be a crucial factor in determining the radioactive decay of certain elements, and the remains of a natural nuclear reactor (basically, deposits of uranium in a region where ground water acted as a moderator to allow a fission reaction to take place) at a place called Oklo in the African nation of Gabon contain traces that can be used to estimate the change in alpha in the two billion years or so since the reactor was active. Depending on how you analyze the results, these may show a change, but again, there’s no real consensus.

So, the jury is still out as to whether the fundamental constants are really constant, or are changing slightly over time. And, like most other big questions in physics, it’s not unreasonable to expect progress on this question in the next five years or so.

One final note on this– I originally cast the question in terms of looking at changes in the speed of light, but the thing that gets measured is a combination of three different constants– the electron charge, Planck’s constant, and the speed of light. So, which one of those is “really” changing? It’s a question that gets asked of every researcher in the field, and between hearing several talks on his and reading a number of articles on the subject, I’ve heard the complete set of answers– for each of the constants making up alpha, you can construct a reason why it’s the one that would “really” be changing, while the other two would remain constant.

Ultimately, it’s a meaningless question. In a very fundamental way, the fine structure constant is the thing that matters, and it doesn’t make any sense to talk about the individual constants changing. Which means that individual researchers are more or less free to attribute the change to whichever constant they like, when answering questions for pop-science articles…