  Locality imposes stringent constraints on the spreading of information in
nonrelativistic quantum systems, which is reminiscent of a "light-cone," a
casual structure arising in their relativistic counterparts. Long-range
interactions can potentially soften such constraints, allowing almost
instantaneous long jumps of particles, thus defying causality. Since
interactions decaying as a power-law with distance, $r^{-\alpha}$, are
ubiquitous in nature, it is pertinent to understand what is the fate of
causality and information spreading in such systems. Using a numerically exact
technique we address these questions by studying the out-of-time-order
correlation function of a representative generic system in one-dimension. We
show that while the interactions are long-range, their effect on information
spreading is asymptotically negligible as long as $\alpha>1$. In this range we
find a complex compound behavior, where after a short transient a fully local
behavior emerges, yielding asymptotic "light-cones" virtually indistinguishable
from "light-cones" in corresponding local models. The long-range nature of the
interaction is only expressed in the power-law leaking of information from the
"light-cone," with the same exponent as the exponent of the interaction,
$\alpha$. Our results directly imply that all previously obtained rigorous
bounds on information spreading in long-range interacting systems are not
tight, and thus could be improved.
