What’s so significant about the number 137?

Consider this article from Dr James G. Gilson PhD: This number is the value of the fine-structure constant (the actual value is one over one-hundred and thirty seven), which is defined as the charge of the electron (q) squared over the product of Planck’s constant (h) times the speed of light (c). This number actually represents the probability that an electron will absorb a photon. However, this number has more significance in the fact that it relates three very important domains of physics: electromagnetism in the form of the charge of the electron, relativity in the form of the speed of light, and quantum mechanics in the form of Planck’s constant. Since the early 1900’s, physicists have thought that this number might be at the heart of a GUT, or Grand Unified Theory, which could relate the theories of electromagnetism, quantum mechanics, and most especially gravity. However, physicists have yet to find any link between the number 137 and any other physical law in the universe. It was expected that such an important equation would generate an important number, like one or pi, but this was not the case.

World renowned physicist Richard Feynman said of this number: “There is a most profound and beautiful question associated with the observed coupling constant, e, the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to -0.08542455. (My physicist friends won’t recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. 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 for a coupling comes from: is it related to p 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 dance to do on the computer to make this number come out, without putting it in secretly!”