This March seminar was about the strange concept of “varying constants” or more specifically, how these constants can help us test the equivalence principle. Jean-Phillipe started by explaining what a fundamental constant is and how, in order to allow them to vary with time, you need to replace them with dynamical fields and re-derive all necessary equations (such as the Einstein field equations) and their effects on the equivalence principle. It is hard to see if the equivalence principle is violated directly, but this violation can be inferred by the detection of time-varying fundamental constants, and vice versa.
Some methods for determining fundamental constants include the use of atomic clocks, meteorite dating, the Oklo mine (a depleted uranium mine in Gabon which formed a natural nuclear reactor), QSO (quasi-stellar objects) and the CMB.
Measurements of the spectra of Lyman alpha forests can constrain α, the fine structure constant, because changes in α affect different atomic lines differently. The Webb et al. team using the Keck telescope found strong evidence for variation in α whereas a follow-up team using the VLT found no evidence for variation meaning that the current status of the subject is in stasis and awaiting future improved data.