16 July 2026

Photo: UHH/ Banerjee

Professor Robi Banerjee has long been fascinated by the numerical value of the fine-structure constant: How did we end up with such an odd number—approximately 1/137?

1/137 — this simple yet significant number has both fascinated and frustrated generations of physicists. Robi Banerjee, Professor at the Observatory and the Cluster of Excellence “Quantum Universe” at the University of Hamburg, is investigating the origin of the fine-structure constant.

The fine-structure constant—usually abbreviated in formulas with the Greek letter α (alpha)—is a dimensionless number with a value of approximately 1/137. It describes the strength of the interaction between electrons and photons. As a result, it appears wherever light interacts with matter: in the calculation of spectral lines, in the structure of atoms, and in the fundamentals of quantum mechanics. If its value were even slightly different, atoms could not exist stably, and life as we know it would be impossible.

Since its introduction by Arnold Sommerfeld in 1916, the peculiar value of the fine-structure constant has puzzled the greatest minds in physics. Paul Dirac called it the “most elementary, unsolved problem in physics.” Richard Feynman described the constant as “one of the greatest cursed mysteries of physics—a magic number that we encounter without explanation.” The question of why this number has exactly this value remains unanswered to this day.

A New Approach to an Old Puzzle

Robi Banerjee now presents a new approach that redefines the number. This approach is elegant in its simplicity: physics needs only three fundamental dimensions to describe the world: length, time, and mass. At the same time, there are four fundamental physical constants: the speed of light, the elementary charge of electrons, Planck’s constant for describing the energy and frequency of a photon—and the gravitational constant for the strength of gravity between two masses.

If one attempts to reduce these four constants to three, a single dimensionless combination emerges as a mathematical necessity—and that is precisely the fine-structure constant. Its form thus follows from the fundamental structure of physics itself.

“Even though I was unable to break down the numerical value of the fine-structure constant, the origin of its form has now become clearer,” says Banerjee. “I’m fascinated by how many areas there are where gravity doesn’t fit into quantum mechanical calculations. Once we understand how gravity fits together with the other forces at the smallest scale, we might also gain new insights into the fine-structure constant. I hope that my reflections will inspire other researchers to get to the bottom of this mystery.”

Gravity—the Great Link

Banerjee’s analysis makes one thing clear: Using this method, the gravitational constant cannot be converted into a dimensionless number; after the mathematical transformations, it stands alone. This is no coincidence, but rather reflects a deep, as yet unsolved problem: How gravity and quantum mechanics fit together at a fundamental level remains unclear to this day. It is precisely this tension between the fundamental forces of the universe that serves as the central theme in Banerjee’s own research. He investigates how stars form and what role gravity plays in the highest-energy processes in the universe. The fine-structure constant and gravity may be different mysteries, but perhaps the path to their solution leads through the same door.