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: μ =
The number in parentheses is the measurement uncertainty on the last two digits, corresponding to a relative standard uncertainty of
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.
Analysis of the molecular spectra from distant stars for a vareity of molecules that the variation in the ratio of the masses is smaller than one part in 107 over cosmological time. Measurements have been made with several molecules, including , methanol, ammonia, and carbon monoxide. The results are consistent across these measurements but they have different systematic errors.
A mathematical coincidence In a famously brief two-sentence paper published in Physical Review in 1951, Friedrich Lenz observed that the best experimental value for the mass ratio at the time (1836.12 ± 0.05) coincided almost perfectly with the mathematical expression 6. This is now believed to be a mathematical coincidence, since modern measurements with higher precision show the values are remarkably close but not identical: while .
See also Koide formula
References
Further reading