Local barriers control relaxation near the glass transition up to millisecond time scales

Which phenomenon slows down the dynamics in super-cooled liquids and turns them into glasses is a long-standing question of condensed-matter. Most popular theories posit that the dynamics becomes cooperative as the temperature decreases: many events must occur in a coordinated fashion on a growing length scale for relaxation to occur. Instead, other approaches consider that local barriers associated with the elementary rearrangement of a few particles or `excitations' govern the dynamics. Here, we introduce a new algorithm, SEER, to resolve this conundrum. SEER can systematically extract hundreds of excitations and their energy from any given configuration. Remarkably, we find that the excitation density of states is essentially shifted to higher energy under cooling. This observation directly predicts how local barriers slow down the dynamics. We compare this prediction with the observed dynamics in liquids that can be equilibrated by swap algorithms up to millisecond time scales. The agreement is quantitative, revealing that cooperative effects are not controlling the fragility of the liquid, and suggesting new perspectives on the glass transition.