An electron inside a molecule behaves like a tiny magnet, and its 'strength' can be measured with enormous precision. Physicists took the molecular ion HD⁺ — a nucleus made of a proton and a deuteron (heavy hydrogen), with a single electron circling around it — and placed it in a strong magnetic field of 4 teslas (roughly 80,000 times stronger than Earth's field).
Using high-precision spectroscopy, they measured how the electron responds to this field. The result: g = −2.00227854096, with an uncertainty of just 2×10⁻¹⁰ — that's like weighing an elephant and being off by a fraction of a milligram. This precision was made possible by new theoretical calculations that account for subtle quantum effects (the electron's interaction with its own radiation) and reduce the theoretical uncertainty by a factor of a thousand.
In addition, they measured the interaction between the spins (intrinsic 'rotations') of the electron and the nuclei. One coefficient matched theory, but the second one deviated slightly. This is not a crisis but rather a hint: perhaps the calculations are missing some very subtle effect that now needs to be found.
Such precision matters not for its own sake. The molecular ion HD⁺ is an ideal 'laboratory' for testing fundamental laws of physics: if measured values agree with first-principles calculations, our understanding of the quantum world is correct. If not, we stand on the brink of a new discovery.
The 4-tesla magnetic field used in the experiment is only slightly weaker than the field inside an MRI scanner, but 80,000 times stronger than Earth's field.