The Little Constant that Couldn't? More About the Fine Structure Constant
The fine structure constant, alpha (α), describes how electromagnetic radiation affects charged particles. It has the numerical value 0.007297351, with an uncertainty of 6 in the last decimal place, and as such is one of the best-measured numbers in physics.
This picture of Enrico Fermi, appearing on a recently issued stamp, contains, in the upper left corner, an incorrect formula for alpha. Proving that even Nobel Laureates make mistakes… (Credit: University of Chicago, courtesy AIP Emilio Segre Visual Archives.)
Note that α is quite a small number, very nearly 1/137. This makes theoretical physicists happy, because it is much easier to calculate things when the forces are not very strong. The theory of radiation and charged particles, called Quantum Electrodynamics (or QED for short), is probably the best understood and the most successful theory in all of physics. Some of its predictions have been verified experimentally to twelve decimal places.
Another important property of α is that it is dimensionless. It is formed as a ratio of three of the fundamental constants of Nature: the electric charge of the electron, e; the speed of light, c; and Planck's constant, which is usually written as h(bar), and which is necessary to describe quantum phenomena. Each of these 3 constants has dimensions, that is, it changes when you change your system of units. For example, the speed of light is very close to 3x108 meters per second, but if we want to know it in miles an hour, the answer is a different number, 6.7x108. However, when we form alpha by taking the ratio α=e2/h(bar)c, all the dimensions cancel out. The result is a dimensionless number, whose value is 0.007297351 no matter what system of units we use.
The fact that α is dimensionless has led some physicists to speculate that its value has some fundamental significance. It describes a fundamental property of the universe, and the question is whether its value is just an accident of how the universe happened to be put together, or whether its value is determined by some deep principle that we have yet to discover.
| A note on calculating alpha If you look up these constants in a textbook, and form the indicated ratio, you may or may not get the advertised number. This is because in some systems of units, one must additionally divide by 4p and in others by a constant denoted by 4pe0. This does not mean that a depends on the system of units. Rather, it means that in different systems of units one must define the same physical constant, α, in different ways. Here is a rule that will give you α using the constants in a randomly chosen physics text: find the expression for Coulomb's law, and use this to give you the magnitude F of the force between 2 electrons separated by a distance R. The expression will have the form F = ke2/R2 What k is will depend on the system of units the book is using. But whatever it is, the way to extract the fine structure constant from the numbers in the book is to calculate α= ke2/h(bar)c Another tricky point to note is that many books define something they call Planck's constant and denote it by h rather than h(bar). The relation between these two is that h(bar) = h/2p. |