  We prove bounds on operator growth and infinite temperature
out-of-time-ordered correlators in many-body systems with $N$
spin-$\frac{1}{2}$ degrees of freedom which interact via two-body all-to-all
interactions. Our results parametrically improve previous bounds, and sharply
constrain when and how quantum simulators, including trapped ion crystals and
cavity quantum electrodynamics, can study quantum gravity.
