The comparison of different atomic transition frequencies over time can be used to determine the present value of the temporal derivative of the fine structure constant $\alpha$ in a model-independent way without assumptions on constancy or variability of other parameters, allowing tests of the consequences of unification theories. We have measured an optical transition frequency at 688 THz in ${}^{171}\mathrm{Y}\mathrm{b}^{+}$ with a cesium atomic clock at 2 times separated by 2.8 yr and find a value for the fractional variation of the frequency ratio $f_{\mathrm{Y}\mathrm{b}}/f_{\mathrm{C}\mathrm{s}}$ of $(-1.2\pm 4.4)\times {10}^{-15}{\mathrm{y}\mathrm{r}}^{-1}$, consistent with zero. Combined with recently published values for the constancy of other transition frequencies this measurement sets an upper limit on the present variability of $\alpha$ at the level of $2.0\times {10}^{-15}{\mathrm{y}\mathrm{r}}^{-1}$ $(1\sigma )$, corresponding so far to the most stringent limit from laboratory experiments.

Sufficient progress towards redefining the International System of Units (SI) in terms of exact values of fundamental constants has been achieved. Exact values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant N A from the CODATA 2017 Special Adjustment of the Fundamental Constants are presented here. These values are recommended to the 26th General Conference on Weights and Measures to form the foundation of the revised SI.

A new independent value for the electron’s mass in units of the atomic mass unit is presented, $m_e=0.000\mathrm{}5485799092\left(4\right)\mathrm{u}$. The value is obtained from our recent measurement of the $g$ factor of the electron in ${}^{12}{\mathrm{C}}^{5+}$ in combination with the most recent quantum electrodynamical (QED) predictions. In the QED corrections, terms of order ${\alpha }^2$ were included by a perturbation expansion in $Z\alpha$. Our total precision is three times better than that of the accepted value for the electron’s mass.

Constraint on spin-dependent and spin-independent Yukawa potential at atomic scale is developed. That covers constraints on a coupling constant of an additional photon $\gamma${}* and a pseudovector boson. The mass range considered is from 1\,\,eV/c2 to 1\,\,MeV/c2. The strongest constraint on a coupling constant $\alpha${}$'${} is at the level of a few parts in 1013 (for $\gamma${}*) and below one part in 1016 (for a pseudovector) corresponding to mass below 1\,\,keV/c2. The constraints are derived from low-energy tests of quantum electrodynamics and are based on spectroscopic data on light hydrogenlike atoms and experiments with magnetic moments of leptons and light nuclei.