Progress in the accuracy of the fundamental physical constants: 2010 CODATA recommended values

Every four years, the CODATA Task Group on Fundamental Constants presents tables of recommended values of the fundamental physical constants. Recently, 2010 CODATA recommended values (Mohr P J, Taylor B N, and Newell D B “CODATA recommended values of the fundamental physical constants: 2010” Rev. Mod. Phys. 84 1527 (2012)), based on global data up to 31 December 2010, were published. In the present review, we briefly analyze the new recommended values, as well as new original data, on which the determination is based. To facilitate the consideration, the data are subdivided into several groups. New original theoretical and experimental results are discussed for each group separately. Special attention is paid to experimental and theoretical progress in the determination of the Rydberg constant $R_{\infty}$, the electron–proton mass ratio $m_{\mathrm e}/m_{\mathrm p}$, the fine-structure constant $\alpha$, the Planck constant $h$, the Boltzmann constant $k$, the Newtonian constant of gravitation $G$, and the anomalous magnetic moment of the muon $\alpha_{\mu}$. In conclusion, the prospects of redefining units of the International System (SI) in terms of fundamental physical constants, which is currently under active discussion by the metrological community, are considered. The very possibility and efficiency of a practical realization of such a scenario with the redefinition directly depends on the status of the determination of the fundamental constants.