137 - Arthur I. Miller [25]
Sommerfeld’s primary contribution to atomic physics was his work on the fine structure problem. His brainwave was to apply relativity theory to Bohr’s theory, changing the mass of the electron following Einstein’s famous equation E = mc2. The result was astounding: an extra term appeared in Bohr’s equation for a single spectral line. This extra term made it possible to predict that certain lines would actually split and reveal their fine structure.
Sommerfeld called the quantity that set the distance between the split spectral lines in this extra term the “fine structure constant” and designated it with the Greek letter (alpha). His equation was:
The fine structure constant is made of three fundamental constants: the charge of the electron e (1.60 × 10-19 coulombs—a coulomb is the unit of electric charge); the speed of light c (3 × 108 meters/second), which defines relativity theory; Planck’s constant h (6.63 × 10-34 Joule-seconds), which defines quantum theory and determines the size of the grains into which the microscopic world is partitioned, be it grains of energy, mass, or even of space itself. (pi) is the ratio of the circumference of a circle to its diameter (3.141529). The constants e, c, and h had already been measured. Thus the discovery of the fine structure constant was a step toward the great goal of finding a theory that would unite the domains of relativity and quantum theory, the large and the small, the macrocosm and the microcosm.
There was one extraordinary feature of the fine structure constant. The three fundamental constants that make it up have dimensions—such as space and time—and therefore depend on the units in which they are measured, whether metric, imperial, or some other. So although they would certainly play an essential part in a relativity or quantum theory formulated by physicists on a planet in another galaxy, they might not have precisely the same values as they have on earth.
But when they come together to form the fine structure constant, something extraordinary happens. All of their units cancel out and as a result the fine structure constant is a pure number without any dimensions. No matter what the number system this will always be true. Sommerfeld calculated it as 0.00729—a rather unexciting way of expressing such a momentous result.
Sommerfeld’s extension of relativity into atomic physics was “a revelation,” wrote Einstein. Bohr wrote to Sommerfeld, “I do not believe ever to have read anything with more joy than your beautiful work.”
A dimensionless number of such fundamental importance had never before appeared in physics. Of course dimensionless numbers had always been present in equations, but never one that was deduced from fundamental constants of nature. Scientists later realized that if the numerical value of the fine structure constant were to differ by a mere 4 percent, almost all carbon and oxygen would be destroyed in every star in the universe and life on our planet would not exist or would be dramatically different. The fine structure constant was one of the primal numbers that bound all existence together.
One of the many puzzles that arose was the question of why spectral lines of atoms split when they were placed in a magnetic field, between the pole faces of a magnet. Back in the mid-nineteenth century the British scientist Michael Faraday had identified the phenomenon but his equipment was not yet precise enough to enable him to pursue it.
In 1896 Pieter Zeeman, a young Dutch researcher at the University of Leiden, was looking for a research problem. Going through physics journals from decades earlier, Zeeman came upon Faraday’s ruminations over the behavior of atoms in magnetic fields. With the more precise equipment at his disposal, he succeeded in discovering the additional split spectral lines caused by a magnetic field. This was dubbed the Zeeman effect.
Two years later all was not well again. When Zeeman tried using a weaker magnetic field, he found that the spectral lines