The radius of the proton is a fundamental constant, but have we got it right? The standard measurement is based on electron–proton scattering and the spectroscopy of atomic hydrogen. But a 2010 laser-spectroscopy study of muonic hydrogen — in which the electron is replaced by a muon — came up with a considerably different value. The discrepancy has since been confirmed in improved measurements, reported in 2013. Among the several theories proposed to explain this proton-radius anomaly, Roberto Onofrio points to gravity as the chief suspect.
Onofrio has previously suggested that quantum gravity might be manifest in weak interactions at the Fermi scale, if the gravitational and weak forces have equal strength at that scale through the unification of the two forces. From this assumption he has calculated the Lamb shift for muonic hydrogen, from which the experimental proton radius can be derived. The heavier muon has a smaller Bohr radius than the electron, and thus the difference in the measurements of proton radius would be a consequence of the different electron–proton and muon–proton interactions — breaking the expected universality of gravity.