  Particles that scatter waves interact through the waves they scatter. We
establish that wave-mediated interactions between dissimilar particles are
generically nonreciprocal. This apparent violation of Newton's third law is
allowed because the pair of particles does not constitute a closed system; the
balance of the system's momentum is carried away by the scattered wave.
Nonreciprocal interactions enable collections of scatterers to transduce energy
out of a wave and use it to power their own motion. Such wave-matter composites
therefore are a form of active matter. Their activity, however, is not an
inherent property of the individual particles, nor are the particles simply
driven by the wave. Instead, the particles' collective motion is an emergent
property of their state of organization. This kind of emergent activity should
appear in any context where objects scatter waves. As a concrete example, we
combine analysis, experiment and simulation to demonstrate how nonreciprocity
and emergent activity arise in collections of acoustically levitated spheres.
