Those who enjoy strolling through the Mega Curioso must have heard of the golden ratio, an irrational real algebraic constant (you can see here how to calculate it). It is everywhere, in nature and architecture, in women’s faces and in vegetables. Above the horizon, however, another number reigns: the constant of fine structure, the pure number that shapes the Universe and that, now, has become more accurate thanks to the work of a team of obstinate physicists.

Defined by the Greek letter alpha, it is the fundamental physical constant that quantifies the strength of the electromagnetic interaction between charged elementary particles. As a dimensionless quantity, the fine structure constant has no unity and is defined by the ratio 1/137.

The small number implies weak electromagnetism; therefore, charged particles form atoms whose electrons can change orbits and form chemical bonds. If the constant were smaller or larger, the stars would not be able to create carbon, and life based on it would not exist.

The fine-structure constant was introduced in 1916 by physicist Arnold Sommerfeld to quantify the tiny gap between two lines in the color spectrum emitted by certain atoms (they can be seen above, in the image of an interferometer).Source: CPI / Reproduction

“In our everyday world, everything is gravity or electromagnetism. That’s why alpha is so important, ”University of California physicist Holger Müller told *Quanta Magazine*.

## Continuous overcoming

It was his best result so far, nine years ago, and now surpassed by a team from the Parisian Kastler Brossel Laboratory, which arrived at the most accurate measurement of the fine structure constant, up to the 11th decimal place: a = 1 / 137.03599920611, with a merror range of 81 parts per trillion.

Saïda Guellati-Khélifa reached this result after 22 years of measuring the fine-structure constant through the force with which rubidium atoms jump out of their orbits when absorbing a photon. It was a measurement of her, in fact, that Müller overcame in 2011.

Physicist Saïda Guellati-Khélifa works in her laboratory in Paris.Source: Quanta Magazine / ean-François Dars and Anne Papillaut

The precision achieved will allow researchers to test the theory of the interrelationships between elementary particles, the so-called Standard Model of particle physics, a quantum field theory that describes the strong, weak and electromagnetic fundamental forces.

## Work continues

Between the values found by Guellati-Khélifa and Müller there is a difference in the seventh digit (which is greater than the margin of error observed in the two measurements). One or both are wrong – as the number found by Guellati-Khélifa is more accurate, it is being considered the correct one.

Both teams, however, will continue to seek more precision, improving the configurations of the experiments. In Paris, the used vacuum chamber will be replaced, while the California team won a new laser with a wider beam.

Holger Müller in his laboratory at Bekeley.Source: Berkeley Lab / Damon English / Disclosure

In any case, the two numbers found are close enough to the alpha value observed in measurements of Landé’s g factor (a multiplicative term that appears in the expression of an atom’s energy levels in a weak magnetic field). If the values were different, the answer would be that a new particle had been discovered.

But the numbers for the two groups of physicists agree with the best g-factor measurements, confirming the Standard Model. “It is the most precise agreement between theory and experiment,” said Guellati-Khélifa.