Collective behavior is widespread in biological systems across many different scales and organisms. As physicists, our hope is that the (complex) details of the individuals are not important when looking at collective properties, and that large scale behavior can be characterized in terms of general laws, much as we do in condensed matter. However, this assumption cannot be given for granted and must be experimentally justified.
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.