\Such experiments are challenging. The first problem is that the laboratory apparatus itself may be sensitive to changes in the constants. The size of all atoms could be increasing, but if the ruler you are using to measure them is getting longer, too, you would never be able to tell. Experimenters routinely assume that their reference standards—rulers, masses, clocks—are fixed, but they cannot do so when testing the constants. They must focus on constants that have no units—they are pure numbers—so their values are the same irrespective of the units system. An example is the ratio of two masses, such as the proton mass to the electron mass.
One ratio of particular interest combines the velocity of light, c, the electric charge on a single electron, e, Planck’s constant, h, and the so-called vacuum permittivity, ε0. This famous quantity, alpha (α) = e2/2ε0hc, called the fine-structure constant, was first introduced in 1916 by Arnold Sommerfeld, a pioneer in applying the theory of quantum mechanics to electromagnetism. It quantifies the relativistic (c) and quantum (h) qualities of electromagnetic (e) interactions involving charged particles in empty space (ε0). Measured to be equal to 1/137.03599976, or approximately 1/137, α has endowed the number 137 with a legendary status among physicists (it usually opens the combination locks on their briefcases).
If α had a different value, all sorts of vital features of the world around us would change. If the value were lower, the density of solid atomic matter would fall (in proportion to α3), molecular bonds would break at lower temperatures (α2), and the number of stable elements in the periodic table could increase (1/α). If α were too big, small atomic nuclei could not exist, because the electrical repulsion of their protons would overwhelm the strong nuclear force binding them together. A value as big as 0.1 would blow carbon apart.
The nuclear reactions in stars are especially sensitive to α. For fusion to occur, a star’s gravity must produce temperatures high enough to force nuclei together despite their tendency to repel one another. If α exceeded 0.1, fusion would be impossible (unless other parameters, such as the electron-to-proton mass ratio, were adjusted to compensate). A shift of just 4 percent in α would alter the energy levels in the nucleus of carbon to such an extent that the production of this element by stars would shut down.
The second experimental problem, less easily solved, is that measuring changes in the constants requires high-precision equipment that remains stable long enough to register any changes. Even atomic clocks can detect drifts in the fine-structure constant only over days or, at most, years. If α changed by more than four parts in 1015 over a three-year period, the best clocks would see it. None have. That may sound like an impressive confirmation of constancy, but three years is a cosmic eyeblink. Slow but substantial changes during the long history of the universe would have gone unnoticed.
Fortunately, physicists have found other tests. During the 1970s scientists at the French atomic energy commission noticed something peculiar about the isotopic composition of ore from a uranium mine in Oklo, Gabon: it looked like the waste products of a nuclear reactor. About two billion years ago Oklo must have been the site of a natural reactor.
In 1976 the late Alexander Shlyakhter of the Petersburg Nuclear Physics Institute in Russia and of Harvard University noticed that the ability of a natural reactor to function depends crucially on the precise energy of a particular state of the samarium nucleus that facilitates the capture of neutrons. And that energy depends sensitively on the value of α. So if the fine-structure constant had been slightly different, no chain reaction could have occurred. One did occur, however, which implies that the constant has not changed by more than one part in 108 over the past two billion years. (Physicists continue to debate the exact quantitative results because of the inevitable uncertainties about the conditions inside the natural reactor.)