Correction to: Nature Physics https://doi.org/10.1038/s41567-020-01150-7, published online 18 February 2021

In the published article, we erroneously based parts of our analysis on a preliminary value of the theoretical spin-averaged frequency and its QED uncertainty, and not on the value given in eq. (7). As a consequence, two expressions must be corrected.

Equation (5) must read

$$\mu /{m}_{e}=\,1223.899228707{(7)}_{\exp }{(21)}_{{\rm{theor}},{\rm{QED}}}{(37)}_{{\rm{theor}},{\rm{spin}}}{(3)}_{{\rm{CODATA}}2018}$$

Which has been corrected from

$$\mu /{m}_{e}=\,1223.899228668{(7)}_{\exp }{(20)}_{{\rm{theor}},{\rm{QED}}}{(37)}_{{\rm{theor}},{\rm{spin}}}{(3)}_{{\rm{CODATA}}2018}$$

For the sensitivity of the theoretical spin-averaged transition frequency to \(\mu /{m}_{e}\) we used \(\partial \mathrm{ln}{f}_{{\rm{spin}}-{\rm{avg}}}^{\left({\rm{theor}}\right)}\left(\mu /{m}_{{\rm{e}}}\right)/\partial \mathrm{ln}\left(\mu /{m}_{{\rm{e}}}\right)=-0.48457\).

Equation (6) must read

$${m}_{{\rm{p}}}/{m}_{{\rm{e}}}=\,1836.152673451\,{(11)}_{\exp }{(32)}_{{\rm{theor}},{\rm{QED}}}{(55)}_{{\rm{theor}},{\rm{spin}}}{(12)}_{{\rm{CODATA}}2018.{\rm{Fink}}-{\rm{Rau}}}$$

Which has been corrected from

$${m}_{{\rm{p}}}/{m}_{{\rm{e}}}=\,1836.152673384{(11)}_{\exp }{(31)}_{{\rm{theor}},{\rm{QED}}}{(55)}_{{\rm{theor}},{\rm{spin}}}{(12)}_{{\rm{CODATA}}2018.{\rm{Fink}}-{\rm{Rau}}}$$

The subscript text "–Rau" was cut off in the PDF version of the published article.

The deviation of \({m}_{{\rm{p}}}/{m}_{{\rm{e}}}\) with respect to CODATA18 is within the root-mean-squared

combined uncertainty of CODATA18 value and the above value.

The blue horizontal band in Figure 4 has been modified accordingly; however, the modification is so small that it is almost indiscernible.

In the paragraph below equation (4), “being closely proportional to \({R}_{\infty }\sqrt{{m}_{{\rm{e}}}/\mu }\)” has been corrected from \({R}_{\infty }\sqrt{{\mu /m}_{{\rm{e}}}}\).

The conclusions of the paper remain unchanged.