Proton-electron mass ratio

Because it is a ratio, this constant is independent of every unit system, which makes it one of the numbers a theory of everything would have to explain and nobody yet can. It is measured by comparing cyclotron frequencies of a single proton and a single electron in the same Penning trap, now to 1.7 × 10⁻¹¹.

Its size is why matter behaves the way it does. Nuclei are so heavy compared with electrons that they can be treated as stationary while the electrons find their ground state — the Born-Oppenheimer approximation that makes quantum chemistry tractable — and molecular vibrational energies come out roughly √(m_e/m_p) ≈ 1/43 of electronic ones, rotations smaller still by the same factor again. That neat separation of electronic, vibrational and rotational spectra is a direct consequence of 1836. Astronomers also hunt for changes in this ratio in the spectra of distant quasars, as a test of whether the constants of nature drift over cosmic time.