137 – The Fine Structure Constant

/ It is not 42, it’s 137 /


“When I die my first question to the Devil will be: What is the meaning of the fine structure constant?” – Wolfgang Pauli joked.

The brilliant physicist Richard Feynman famously thought that there is a number that all theoretical physicists of worth should “worry about“. He called it “one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man“. That magic number, called the FSC or – fine structure constant, a fundamental constant with a value which nearly equals 1/137.03599913, to be precise and it is denoted by the Greek letter alpha and it’s regarded as the best example of a pure number, one that doesn’t need units.

Physicist Laurence Eaves, a professor at the University of Nottingham, thinks this number would be the one you’d signal to the aliens to indicate that we have some measure of mastery over our planet and understand quantum mechanics. The aliens would know the number as well, especially if they developed advanced sciences.

It combines three of nature’s fundamental constants:

c the speed of light

q the electric charge carried by one electron

h the Planck’s constant

Hence appearing at the intersection of such key areas of physics as relativity, electromagnetism and quantum mechanics is what gives it’s allure:


Wolfgang Pauli referred to the fine structure constant during his Nobel lecture on December 13th, 1946 in Stockholm, saying a theory was necessary that would determine the constant’s value and “thus explain the atomistic structure of electricity, which is such an essential quality of all atomic sources of electric fields actually occurring in nature.” At the end of his remarkable journey this pioneer of quantum physics died in a hospital room numbered 137.

One use of this curious number is to measure the interaction of charged particles like electrons with electromagnetic fields. Alpha determines how fast an excited atom can emit a photon. It also affects the details of the light emitted by atoms. Scientists have been able to observe a pattern of shifts of light coming from atoms called “fine structure” (giving the constant it’s name). This fine structure has been seen in sunlight and the light coming from other stars. But why does nature insist on this number? It has appeared in various calculations in physics since the 1880s, spurring numerous attempts to come up with a Grand Unified Theory that would incorporate the constant since. So far no single explanation took hold. Recent research also introduced the possibility that the constant has actually increased over the last six billion years, even though slightly.

To know the math behind this fine structure constant more specifically, the way you arrive at alpha is by putting the 3 constants h, c, and e together in the equation:

As the units c, e, and h cancel each other out,
thepure number of 137.03599913 is left behind.

For historical reasons the inverse of the equation is used:

2πe2/hc = 1/137.03599913

If wondering what is the precise value of that fraction – it’s 0.007297351.

This dimensionless physical constant Arthur Eddington conjectured back in in 1929 that its reciprocal was in fact precisely the integer 137, which he claimed could be “obtained by pure deduction“. This conjecture was not widely adopted, and by the 1940s, the experimental values for the constant were clearly inconsistent with it.

Physicist Leon M. Lederman numbered his home near Fermilab 137 based on the significance of the number to those in his profession. Lederman expounded on the significance of the number in his book ”The God Particle: If the Universe Is the Answer, What Is the Question?”, noting that not only was it the inverse of the fine-structure constant, but was also related to the probability that an electron will emit or absorb a photon—i.e., Feynman’s conjecture. He added that it also contains the crux of electromagnetism (the electron), relativity (the velocity of light), and quantum theory (Planck’s constant). It would be less unsettling if the relationship between all these important concepts turned out to be one or three or maybe a multiple of pi. But the number 137, according to Lederman, “shows up naked all over the place“, meaning that scientists on any planet in the universe using whatever units they have for charge or speed, and whatever their version of Planck’s constant may be, will all come up with 137, because it is a pure number. Lederman recalled that Richard Feynman had even suggested that all physicists put a sign in their offices with the number 137 to remind them of just how much they do not know.

String theory, one well-backed bet for a next-generation theory of physics, proposes the existence of tiny, curled-up dimensions we can’t see. That has effects on things like alpha. “The status of the quantities we call constants is somewhat downgraded if you believe there are extra dimensions,” says cosmologist John Barrow at the University of Cambridge.

If there are really nine or 10 dimensions of space, with only three large, then the true unchanging constants of nature live in the total number of dimensions and the three-dimensional shadows that we observe are not true constants.

The Hebrew word קבלה (Kabbalah) has a Gematria value of 137. In Modern Hebrew, the root of Kabbalah ק-ב-ל can mean either “receiving” or “parallel“. Kabbalah is generally taken to mean “the received tradition“, which conveys the continuity of a tradition that has been passed down from generation to generation. Nevertheless, the earlier nuance of meaning is seen in the first appearances of its root in the ”Torah” (תורה) – Exodus (שמות) parts 26:5 and 36:12, where it means “parallel” or “corresponding” rather than “receiving“. In there it is used to describe the “corresponding loops“, which, when clasped together, enjoined the two sections of the Tabernacle’s (משכן) ceiling. These loops were suspended directly over the veil that divided the Holy Place and the Holy of Holies (קדש הקדשים).

Symbolically, this is the threshold between the physical dimension and the utterly spiritual dimension…

In other words: at the boundary line of the physical world, the number 137 emerges.

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. 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!

Richard Feynman


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