Beautiful Science: A Fine Number

There is a unique, non-dimensional atomic constant in physics known as “alpha” or the “Fine Structure Constant”. It is better known by its reciprocal number which is roughly 1/137. The formula for alpha depends on just three parameters: the square of the charge of an electron, ½ x Planck’s constant, and the speed of light denoted by c. As shown, alpha is the ratio of the strength of electromagnetism (one of the four fundamental forces of nature) to the strong nuclear force (another fundamental force of nature).

Who would care about a number as precise as 1/137.035999206? Physicists, that’s who. In physics, this number is known as the Fine-Structure Constant and is denoted by the Greek alphabet, alpha. Despite its ungainly appearance, alpha is one of the most important numbers in modern physics, and indeed, a crucial number that accounts for our very existence.

Consider the role of alpha in physics. The current gold standard theoretical model of the Universe is the Standard Model which unifies three of the four known fundamental forces (excluding gravity) and their carrier particles. In other words, the Standard Model answers in one grand equation, this question: what is everything made of, and how does it hold together? For this reason, and despite its incompleteness, this elegant model epitomizes the triumph of sheer human thinking in the goal towards understanding the Universe and our place in it. Fortunately, countless tests have proven that the Standard Model is correct. One of these tests has to do with alpha. To cut a long story short, the value of alpha can be inferred precisely by measuring a factor known as the electron g-factor, a constant related to an electron’s magnetic moment or torque. With a lot of math, you can link alpha with the electron g-factor. The two constants must match very closely, else the Standard Model falls apart. Fortunately, they do, a result that was demonstrated by Holger Mueller and his team at Berkeley in 2018.

Just days ago, four physicists, led by Saida Guiellati-Khelifa at the Kastler Brossel Laboratory in Paris has reported the most precise measurement yet of the Fine-Structure Constant, alpha. The team measured alpha to the 11th decimal place, reporting that α = 1/137.035999206. With a margin of error of just 81 parts per trillion, the new measurement is nearly three times more precise than the one obtained by the Mueller group in 2018.

Saïda Guellati-Khélifa in her laboratory in Paris. She and her team of scientists gauges the fine-structure constant by measuring how strongly rubidium atoms recoil when they absorb a photon. (the Müller group at Berkely does the same with cesium atoms)

A factor of three is a big deal in the world of theoretical physics. Mueller’s group has already shown that the Standard Model deserves the accolade of being the most accurate integrative model of the Universe. The new measurement pushes the agreement between theory and experiment even closer, bolstering our faith in the correctness of the Standard Model upon which many things in the known Universe hangs.

Not resting on their laurels, both Guiellati-Khelifa and Müller have set their sights in making further improvements. The Berkeley team has switched to a new laser with a broader beam that allows it to strike their cloud of cesium atoms more evenly, while the Paris team plans to replace their vacuum chamber, among other things.

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