Microscopic nature of the Johari-Goldstein secondary relaxation
In plain words
Below the glass point most molecules are frozen, yet glasses of even rigid molecules still show a faster, smaller relaxation, the Johari-Goldstein $\beta$ process. Which molecular motions produce it, and whether it is the precursor of the main relaxation, is disputed.
Precise statement
In molecular glass formers, including glasses of rigid molecules, dielectric and mechanical spectra show a secondary $\beta$ relaxation that persists below $T_g$ with Arrhenius $\tau_\beta(T)$ and an empirical activation energy of roughly $24\ k_B T_g$ per molecule (approximate). Determine whether it is carried by localized islands of mobility or by small-angle motion of all molecules, and whether it is the precursor of the alpha relaxation as assumed in coupling-type models. An answer identifies the motions in a model glass equilibrated near or below T_g and reproduces the measured $\beta$ peak and its link to $\tau_\alpha$.
What would settle it
Simulation of a swap-equilibrated model glass that resolves which particles and motions produce the $\beta$ peak and reproduces its activation energy and its relation to $\tau_{\alpha}$, consistent with NMR and dielectric data.