Zenith Grant Awardee

Adam Brown

Stanford University

Co-Investigators

Leonard Susskind, Stanford University

Project Title

Complexity, Black Holes, and Observers

Project Summary

There are some things that no single observer can know, even in principle. Thanks to Heisenberg\'s uncertainty principle, they can know both the position and momentum of a particle; thanks to the finite speed of light, they can observe two causally disconnected points. What do we make of this? You might think these are just accidental inconveniences. But the principle of complementarity — in the first case quantum complementarity, in the second case causal complementarity — says these are essential obstacles, required for the consistency of the laws of nature. Some paradoxical thought experiments may be resolved by restricting attention to only that which is actually observable. In this proposal, I explore a third, more radical, proposed complementarity principle. Some computations are easy, but some computations are hard. If the computation required to exhibit a would-be inconsistency in the laws of physics is sufficiently complex as to be impossible without dramatically transforming the system under study, perhaps that is reason enough to say that there is no inconsistency. I investigate moving computational complexity from an epiphenomenon to a central role in understanding the physics of the observer.

Technical Abstract

Quantum complexity theory classifies quantum computations by how hard they are; for example, whether the required computing resources are polynomial or exponential. Until recently, high-energy theoretical physics has not had much use for computational complexity–we may ask whether a certain operation is possible or impossible, but rarely whether it is easy or hard. In this project, I explore tantalizing hints that the application of computational complexity theory is essential to describing the experience of an observer falling into a black hole. In classical general relativity, an observer falling through the horizon of a black hole experiences no abrupt shocks. In quantum gravity, thanks to the \"firewall\" argument, the observer\'s fate is less clear. I argue that computational complexity holds the key to understanding the emergence of spacetime in quantum gravity. First I look at holographic complexity, and what it says about the transparency of horizons. Second I argue that implementing the firewall experiment requires a calculation so complicated that enacting it has ontological consequences.