Proton Measured with Record Precision, Confirming Standard Model to One Trillionth of a Percent

Scientists at the Max Planck Institute of Quantum Optics in Germany have measured the charge radius of the proton with unprecedented precision, resolving a years-long puzzle in particle physics and providing one of the most stringent tests ever conducted of the Standard Model — the theoretical framework that describes all known subatomic particles and their interactions. The new measurement, published in Nature in February 2026, confirms the proton's radius at 0.8406 femtometers with an uncertainty of just 0.0015 femtometers, and shows that quantum electrodynamics agrees with experiment to better than one trillionth of a percent.

Lead researcher Lothar Maisenbacher and colleagues made the measurement by examining a previously untested energy-level transition in hydrogen atoms — from the 2S excited state to the 6P state. They measured the transition frequency at 730,690,248,610.79 kilohertz, with an uncertainty of just 0.48 kilohertz. From that extraordinary measurement, they extracted the proton's charge radius with approximately 2.5 times greater precision than earlier hydrogen spectroscopy experiments had achieved. Science News described the result as confirming "the proton is tinier than once thought," settling a controversy that had prevented physicists from testing their key theories with the precision they required.

The so-called proton radius puzzle began more than a decade ago, when a 2010 measurement using muonic hydrogen — a form of hydrogen in which the electron is replaced by the much heavier muon particle — gave a proton radius significantly smaller than values obtained from conventional electron-based hydrogen spectroscopy. The discrepancy suggested either that the Standard Model was wrong, that there was some unknown systematic error in the measurements, or that the electron and muon interacted with the proton differently than theory predicted. Subsequent high-precision measurements gradually pushed the electron-based value smaller, narrowing the gap, and the new Munich result firmly places the electron-based measurement in agreement with both the muonic hydrogen value and Standard Model predictions.

Quantum electrodynamics, or QED, is the branch of the Standard Model that describes how electrically charged particles interact with light and with each other. It is already the most precisely tested theory in all of science, with previous experiments verifying its predictions to parts per billion. The new proton measurement pushes that verification further still, to 0.7 parts per trillion — roughly one-trillionth of a percent. Physicist Emily Conover of Science News noted the measurement "leaves even less room than before for rival theories," meaning any physics beyond the Standard Model must now operate within significantly narrower parameters.

The practical significance extends beyond confirming existing theory. The extreme precision of atomic hydrogen spectroscopy makes it a natural tool for searching for tiny deviations from known physics that might point toward new particles or forces. Any future discrepancy between a proton size measurement and QED predictions — even a fraction of a femtometer — could signal physics beyond the Standard Model. By establishing the proton's radius with this level of confidence, the Munich team has set a high-precision baseline against which future anomalies can be measured. The result also validates the atomic physics techniques required for next-generation atomic clocks, quantum computing benchmarks, and searches for dark matter that couples to ordinary matter through tiny shifts in atomic energy levels.