Gravity from Optimized Computation

Inspired by the universality of computation, I advocate for a notion of spacetime complexity, where gravity arises as a consequence of spacetime optimizing the computational cost of its quantum dynamics. This principle is realized in the context of holography, where complexity is understood in terms of state preparation via Euclidean path integrals, and the linearized equations of motion, for any theory of gravity, emerge from the first law of complexity. This suggests gravity has a computational origin. When the leading $1/N$ bulk quantum corrections are included, the holographic first law is modified by an additional term which could be interpreted as “bulk complexity”, leading to a derivation of semi-classical gravitational equations of motion.