  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 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. To
resolve this conundrum, our central result is to introduce an algorithm, SEER,
which can systematically extract hundreds of excitations and their energy from
any given configuration. We also provide a novel measurement of the activation
energy, characterizing the liquid dynamics, based on fast quenching and
reheating. We use these two methods in a popular liquid model of polydisperse
particles. Such polydisperse models are known to capture the hallmarks of the
glass transition and can be equilibrated efficiently up to millisecond time
scales. The analysis reveals that cooperative effects do not control the
fragility of such liquids: the change of energy of local barriers determines
the change of activation energy. More generally, these methods can now be used
to measure the degree of cooperativity of any liquid model.
