  Collective behaviour in biological systems pitches us against theoretical
challenges way beyond the borders of ordinary statistical physics. The lack of
concepts like scaling and renormalization is particularly grievous, as it
forces us to negotiate with scores of details whose relevance is often hard to
assess. In an attempt to improve on this situation, we present here
experimental evidence of the emergence of dynamic scaling laws in natural
swarms. We find that spatio-temporal correlation functions in different swarms
can be rescaled by using a single characteristic time, which grows with the
correlation length with a dynamical critical exponent z~1. We run simulations
of a model of self-propelled particles in its swarming phase and find z~2,
suggesting that natural swarms belong to a novel dynamic universality class.
This conclusion is strengthened by experimental evidence of non-exponential
relaxation and paramagnetic spin-wave remnants, indicating that previously
overlooked inertial effects are needed to describe swarm dynamics. The absence
of a purely relaxational regime suggests that natural swarms are subject to a
near-critical censorship of hydrodynamics.
