  A fundamental assumption in our understanding of material rheology is that
when microscopic deformations are reversible, the material responds elastically
to external loads. Plasticity, i.e. dissipative and irreversible macroscopic
changes in a material, is assumed to be the consequence of irreversible
microscopic events. Here we show direct evidence for reversible plastic events
at the microscopic scale in both experiments and simulations of two-dimensional
foam. In the simulations, we demonstrate a link between reversible plastic
rearrangement events and pathways in the potential energy landscape of the
system. These findings represent a fundamental change in our understanding of
materials--microscopic reversibility does not necessarily imply elasticity.
