  Synchronization of chaos arises between coupled dynamical systems and is very
well understood as a temporal phenomena which leads the coupled systems to
converge or develop a dependence with time. In this work, we provide a
complementary spatial perspective to this phenomenon by introducing the novel
idea of causal stability. We then propose and prove a causal stability
synchronization theorem as a necessary and sufficient condition for
synchronization. We also provide an empirical criteria to identify
synchronizing variables in coupled identical chaotic dynamical systems based on
causality analysis on time series data of the driving system alone.
