Editing Second (section)

=== Rydberg constant ===
A definition based on the [[Rydberg constant]] would involve fixing the value to a certain value: <math>R_{\infty}=\frac{m_\text{e} e^4}{8 \varepsilon_0^2 h^3 c}=\frac{m_\text{e} c \alpha^2}{2h}</math>. The Rydberg constant describes the energy levels in a hydrogen atom with the nonrelativistic approximation <math>E_n \approx -\frac{R_{\infty} c h}{n^2}</math>.

The only viable way to fix the Rydberg constant involves trapping and cooling hydrogen. This is difficult because it is very light and the atoms move very fast, causing Doppler shifts. The radiation needed to cool the hydrogen – {{val|121.5|u=nm}} – is also difficult. Another hurdle involves improving the uncertainty in QED calculations, specifically the [[Lamb shift]] in the 1s-2s transition of the hydrogen atom.<ref name=":10">{{Cite journal |last=Gill |first=Patrick |date=2011-10-28 |title=When should we change the definition of the second? |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |volume=369 |issue=1953 |pages=4109–4130 |bibcode=2011RSPTA.369.4109G |doi=10.1098/rsta.2011.0237 |pmid=21930568 |s2cid=6896025|doi-access=free }}</ref>