In physics, the proton-to-electron mass ratio (symbol μ or β) is the rest mass of the proton (a baryon found in atoms) divided by that of the electron (a lepton found in atoms), a dimensionless quantity, namely: The number in parentheses is the measurement uncertainty on the last two digits, corresponding to a relative standard uncertainty of

Discussion

μ is an important fundamental physical constant because:

Variation of μ over time

Astrophysicists have tried to find evidence that μ has changed over the history of the universe. (The same question has also been asked of the fine-structure constant.) One interesting cause of such change would be change over time in the strength of the strong force. Astronomical searches for time-varying μ have typically examined the Lyman series and Werner transitions of molecular hydrogen which, given a sufficiently large redshift, occur in the optical region and so can be observed with ground-based spectrographs. If μ were to change, then the change in the wavelength λi of each rest frame wavelength can be parameterised as: where Δμ/μ is the proportional change in μ and Ki is a constant which must be calculated within a theoretical (or semi-empirical) framework. Reinhold et al. (2006) reported a potential 4 standard deviation variation in μ by analysing the molecular hydrogen absorption spectra of quasars Q0405-443 and Q0347-373. They found that Δμ/μ = (2.4 ± 0.6). King et al. (2008) reanalysed the spectral data of Reinhold et al. and collected new data on another quasar, Q0528-250. They estimated that Δμ/μ = (2.6 ± 3.0), different from the estimates of Reinhold et al. (2006). Murphy et al. (2008) used the inversion transition of ammonia to conclude that < 1.8 at redshift z = 0.68. Kanekar (2011) used deeper observations of the inversion transitions of ammonia in the same system at z = 0.68 towards 0218+357 to obtain < 3. Bagdonaite et al. (2013) used methanol transitions in the spiral lensing galaxy PKS 1830-211 to find ∆μ/μ = (0.0 ± 1.0) × 10−7 at z = 0.89. Kanekar et al. (2015) used near-simultaneous observations of multiple methanol transitions in the same lens, to find ∆μ/μ < 1.1 × 10−7 at z = 0.89. Using three methanol lines with similar frequencies to reduce systematic effects, Kanekar et al. (2015) obtained ∆μ/μ < 4 × 10−7. Note that any comparison between values of Δμ/μ at substantially different redshifts will need a particular model to govern the evolution of Δμ/μ. That is, results consistent with zero change at lower redshifts do not rule out significant change at higher redshifts.

Footnotes