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We test the consistency of several independent astrophysical measurements offundamental dimensionless constants. In particular, we compare directmeasurements of the fine-structure constant $\alpha$ and the proton-to-electronmass ratio $\mu=m_p/m_e$ (mostly in the optical/ultraviolet) with combinedmeasurements of $\alpha$, $\mu$ and the proton gyromagnetic ratio $g_p$ (mostlyin the radio band). We point out some apparent inconsistencies, which suggestthat hidden systematics may be affecting some of the measurements. Thesefindings demonstrate the importance of future more precise measurements withALMA, ESPRESSO and ELT-HIRES. We also highlight some of the implications of thecurrently available measurements for fundamental physics, specifically forunification scenarios.

Consistency tests of the stability of fundamental couplings and unification scenarios