Many physicists have been both enchanted and perplexed by the number 137, one of the fundamental constants in physics. Nobel laureate Richard Feynman was no exception, for he once said:
“It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man.”
So what is this number that still remains a mystery? That takes a little explaining.
When an electron “jumps” to a lower shell in an atom, a quantum of electromagnetic radiation is emitted. This radiation, when analyzed by a spectrograph, shows up as a series of spectral lines. By such analysis, it was discovered that each of the various atoms, or elements, that populate the periodic table, has a unique pattern of spectral lines. These lines have been likened to DNA or fingerprints that uniquely identify each element, and they reflect the structure of the atom.
With an improvement in technology, it was later found that some of what had appeared as single lines were, upon closer inspection, actually split into two lines, and sometimes three—very close together. And the splitting of the lines reveal what is called the fine structure of the atom.
Arnold Sommerfeld, building on the work of Niels Bohr, developed the equation that gives the fine structure:
En,k = Z2/n2{1 + (2πe2/hc)2[n/k − 3/4]}(2.7 × 10-11 ergs)
Forget, for a moment, about how complicated this equation may look and notice only that the portion in bold font represents what Sommerfeld added to Bohr’s original equation, and that the key term is :
(2πe2/hc)2
When the known values (of π, e, h, and c) are plugged into this expression, it turns out to be a simple fraction:
1/137
This is the fine structure constant that defines the distance between the split spectral lines. For convenience, the fraction is sometimes referred to as 137. Sommerfeld called it alpha and the equation reads:
α = 2πe2/hc
where π is the ratio of the circumference of a circle to its diameter, e is the charge of the electron, h is Planck’s constant, and c is the velocity of light.
The discovery of the fine structure constant was empirical, not theoretical. No one has a clue as to why the value is 1/137. It is one of the abiding mysteries of physics.
To give a fuller version of the Feynman quote:
“There is a most profound and beautiful question associated with . . . 137. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.
“Immediately you would like to know where this number comes from: is it related to pi, or perhaps to the base of natural logarithms? Nobody knows. It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the ‘hand of God’ wrote that number, and ‘we don’t know how He pushed His pencil.’
“We know what kind of a dance to do experimentally to measure this number very accurately, but we don’t know what kind of a dance to do on a computer to make this number come out—without putting it in secretly!”
Wolfgang Pauli, another Nobel laureate in physics, once said that, if he ever had the opportunity, the first question he would ask God is, “Why 1/137?”
A curiosity, and a beauty, about the fine structure constant is that it is a pure number. The dimensions of the three other constants (e, h, and c) cancel out, so that alpha is a pristine, primal, and dimensionless number.
After a memorable dream about the fine structure of spectral lines, Pauli began to see a link between these lines and dark and light, the alternating stripes on tigers and wasps, black and white piano keys, the hexagrams of the I Ching, the game of chess, wave and particle and other complementary pairs. And all these are, as Arthur I. Miller observes, “symbolized by the splitting of spectral lines . . . This reinforced his belief that 137 was an archetypal number.”
In his book Deciphering the Cosmic Number, Miller points out something that I found very intriguing.
Planck’s constant (h) and the speed of light (c) are key elements, respectively, in quantum mechanics and relativity theory. As a very small number, Planck’s constant is a signature of the microcosm, just as speed of light, being very large, is a signature of the macrocosm.
In the fraction for the fine structure constant —
2πe2/hc
note how h and c are together, side by side, in the denominator, thus linking micro- and macro-cosm and showing, if the equation be true, that h can never be zero nor can c be infinite. Also, for alpha to be an enduring constant, if there were ever to be any change in h, there would have to be a corresponding, and proportional, change in c.
And so, for final reflection —
If there is a primal number that holds the key to the secrets of the universe, 137, or the fine structure constant, may be a good candidate.
Alpha, as a fundamental factor in the organizing principles that shape atomic structure, plays a key role in how atoms so beautifully constellate in the various dynamic forms that physics has revealed.
Miller again: “The fine structure constant is one of those numbers at the very root of the universe and of all matter. If it were different, nothing would be as it is. As Max Born put it, alpha ‘has the most fundamental consequences for the structure of matter in general.’”
I will end by asking you to remember a theme song from a Michael Caine movie:
What’s it all about . . . Alpha?
HyC