Physicists measure the fine structure constant directly for the first time

Angle of rotation: A light source (left) sends a beam of light through a topological insulator with an intrinsic magnetic field (centre), changing the direction of polarization by an angle that is given by the fine structure constant. (Courtesy: Tatiana Lysenko / TU Wien)

The value of the fine structure constant – perhaps the most important constant in nature as it dictates the strength of electromagnetism – has been measured directly by researchers in Austria and the US. The technique they used involves measuring how much the polarization of light rotates as it passes through a magnetic topological insulator, and while it is not as accurate as other methods, the researchers believe its directness could lead to cleaner tests of whether this supposed constant varies over time.

The fine structure constant, denoted α, is a dimensionless number with a physical interpretation that has evolved alongside physicists’ understanding of electromagnetism. When Arnold Sommerfeld introduced it in 1916, it was the velocity of an electron in the first circular orbit of the Bohr model of the atom, divided by the speed of light in vacuum. In quantum electrodynamics, it is the coupling constant that determines the strength of interactions between electrons and photons. What remains undisputed, however, is its centrality to physics, and the fact that it cannot be calculated theoretically – it is a free parameter that must be inserted into the Standard Model of particle physics. Its value is around 1/137, and if it were even slightly different – perhaps just 1/138 – it would rewrite the rules of chemistry and change stellar nuclear fusion so much that life could not exist.

Looking for α

Physicists are therefore keen to nail down α as precisely as possible and, crucially, to establish whether it has in fact remained constant over cosmological history. The most accurate measurement to date – of 1/137.03599920611, with an uncertainty of 81 parts per trillion – was made by using the recoil of rubidium atoms when struck by photons to measure the atoms’ mass. Other researchers have measured it using the electron’s magnetic moment, or the torque experienced by an electron in a magnetic field, but all measurements to date have been indirect: “You measure a few different numbers and then divide them or multiply them and then finally you get the fine structure constant,” explains Andrei Pimenov of the Vienna University of Technology (TU Wien), who led the new measurement.

The need for multiple measurements complicates efforts to achieve higher accuracies and would make it hard to interpret unexpected deviations. “Imagine you measure the fine structure constant and you see that something has changed,” Pimenov says. “If your experiment was a combination of several different experiments, you don’t know which specific experiment and which specific number was the reason for this change.”

Quantized polarization shifts

In the latest research, which is published in Applied Physics Letters, Pimenov and colleagues at TU Wien and the University of California, Los Angeles in the US passed polarized terahertz radiation through a topological insulator with the chemical formula (Cr0.12Bi0.26Sb0.62)2Te3 and observed how its polarization changed. Thanks to interactions of photons with electromagnetic fields, applying a magnetic field can cause the polarization of light to rotate. At high fields and low temperatures, these polarization shifts are quantized – a phenomenon known as the quantum Hall effect.

The size of these quantized shifts is proportional to the fine structure constant, so in principle, any material that displays the quantum Hall effect can be used to measure it. But there’s a catch: “In normal cases you need to apply huge magnetic fields,” Pimenov explains. The strength of this applied field then appears in the equations, making calibration difficult.

The material Pimenov and colleagues used, however, contains chromium ions. These give the material an intrinsic magnetic field, meaning that the polarization of incident electromagnetic radiation rotates even without an applied field (the quantum anomalous Hall effect). Better still, as the material is a topological insulator, this magnetic field is a topological invariant. Hence, when plane-polarized light passes through the material, its polarization rotates by a precise integer multiple of the fine structure constant. “In order to prove this, you have to write some complicated topological equations, but you cannot have 0.5α or 0.6α,” Pimenov says. “It’s either -1 or +1.”

“Just the first experiment”

The value Pimenov and his colleagues obtained for the fine structure constant was, as expected, approximately 1/137. However, he acknowledges that “our accuracy is not so good” because “this is just the first experiment”.

Asked about the research, Li Ge of the City University of New York, US, says he finds it “interesting”, although he adds that “it appears that the researchers had already obtained the bulk of their findings in a previous publication”. Ge therefore suggests that the only new result in the latest work is that the right-hand side of one equation is proportional to the fine structure constant. Pimenov, however, claims that the work represents a significant advance: “The main result of this work is the ability to obtain a fundamental physical constant in a direct experiment that does not rely on any other measurements or calibrations,” he says. “On the contrary, in the previous work no fundamental constants have been measured.”