  Microscopic speed limits that constrain the motion of matter, energy, and
information abound in physics, from the "ultimate" speed limit set by light to
Lieb-Robinson speed limits in quantum spin systems. In addition to these
state-independent speed limits, systems can also be governed by emergent
state-dependent speed limits indicating slow dynamics arising, for example,
from slow low-energy quasiparticles. Here we describe a different kind of speed
limit: a situation where complex information/entanglement spreads rapidly, in a
fashion inconsistent with any speed limit, but where simple signals continue to
obey an approximate speed limit. If we take the point of view that the motion
of simple signals defines the local spacetime geometry of the universe, then
the effects we describe show that spacetime locality can be compatible with a
high degree of non-local interactions provided these are sufficiently chaotic.
With this perspective, we sharpen a puzzle about black holes recently raised by
Shor and propose a schematic resolution.
