137: THE NUMBER THAT PUZZLED THE GREATEST MINDS
MORE THAN THREE DIGITS
Some numbers become familiar because we use them every day. Others attract attention because they reveal something unexpected about the world. For physicists, 137 belongs to the second group. Behind these three digits lies a connection between light, matter and one of the fundamental interactions of nature. That connection has inspired generations of physicists to ask why it has this particular numerical value.
WHERE THE STORY BEGAN
The story begins with the study of light emitted by atoms. When this light is separated into a spectrum, it produces distinct lines, each associated with a transition between atomic energy levels. Closer examination revealed that some lines were split into finer components, details that early atomic models could not fully explain.
In 1916, the German physicist Arnold Sommerfeld extended Niels Bohr’s model of the atom and introduced a quantity that helped describe this splitting. It became known as the fine structure constant. What began as a way of explaining small details in atomic spectra would acquire a much broader significance in quantum physics.
WHAT 137 ACTUALLY MEANS
The fine structure constant, represented by the Greek letter alpha, describes the strength of the electromagnetic interaction. This is the interaction through which electrically charged particles respond to one another and to light. Its value is approximately 0.00729735, or roughly 1 divided by 137.
More precisely, its inverse is approximately 137.035999177. The distinction matters. The number 137 is a memorable approximation, not an exact integer hidden in the laws of nature. Its scientific importance comes from the physical quantity it represents, rather than from the three digits alone.
A NUMBER WITHOUT UNITS
Most physical quantities depend on how we choose to measure them. A distance has a different numerical value in metres and feet, even though the distance itself remains unchanged.
Alpha is different. It is dimensionless, meaning it has no unit attached to it. Its definition brings together the elementary electric charge, Planck’s constant, the speed of light and the electric constant in a combination whose units cancel. Changing our measuring system does not change the result.
For physicists searching for a deeper explanation of nature, this makes its value particularly compelling. It cannot be explained simply as a consequence of our choice of units.
THE SEARCH FOR AN EXPLANATION
During the early twentieth century, the British astronomer Arthur Eddington became convinced that the constant’s value could be derived through mathematical reasoning rather than established through measurement. He eventually argued that its inverse should be exactly 137.
It was an ambitious attempt to connect the properties of matter with the structure of the universe, but increasingly precise measurements showed that the value was not an integer. His explanation did not survive. The episode illustrates both the appeal of the problem and its difficulty. Finding an elegant numerical pattern is not the same as establishing a physical explanation.
A QUESTION THAT CAPTURED GREAT MINDS
Eddington was not alone in his fascination. Wolfgang Pauli and Werner Heisenberg also wrestled with the significance of the constant. Later, Richard Feynman described it as “one of the greatest damn mysteries of physics”.
The frustration was not that physicists were unable to measure it or use it. The difficulty was explaining why it had the value that experiments revealed. Quantum electrodynamics, the theory describing the interaction of light and matter, could produce extraordinarily precise predictions. Yet the strength of that interaction still had to be established through measurement rather than derived from an accepted underlying theory.
A CONSTANT WITH A QUALIFICATION
There is another detail behind the familiar number. The value associated with 137 describes the strength of the electromagnetic interaction at very low energies. At higher energies, quantum effects change its effective strength, a phenomenon physicists call the running of the coupling.
This does not mean that the number changes unpredictably or that measurements contradict one another. It means that the effective strength depends on the energy scale at which the interaction is examined. The simple number that first attracts our attention belongs to a theory more subtle than its name might suggest.
PRECISION WITHOUT A FINAL ANSWER
Today, the fine structure constant is known with remarkable accuracy. NIST lists its inverse as approximately 137.035999177, with uncertainty appearing only in the final quoted digits.
Yet measuring a number more precisely and explaining its origin are different achievements. Physicists can test its value, compare independent measurements and use it in calculations, but no accepted theory derives that value from first principles. The enduring mystery is therefore specific. It is not what alpha does, but why nature gives it this particular strength.
THE FINAL CHAPTER OF OUR NUMBER TRILOGY
For Möels&Co, 137 will complete the Number Trilogy that began with the 528 and continued with the 369. Each number brings a different story to the collection.
What draws us to 137 is the meeting of precision and curiosity. It represents something that can be measured with extraordinary accuracy, yet still leaves a fundamental question unanswered. It gives the final chapter of our trilogy a story rooted in scientific discovery and the desire to understand more.
SOURCES:
https://arthurimiller.com/journalism/looking-back-the-odd-couple/
https://www.technologyreview.com/2009/10/20/29538/the-shadow-realm/
https://physicsworld.com/a/dreams-of-a-quantum-pioneer
https://arxiv.org/pdf/1812.08336
https://chemistryworld.com/opinion/untriseptium/3005076.article
https://www.informationphilosopher.com/presentations/Milan/papers/Atmanspacher-Pauli-Jung.pdf