[Colloquium] The Quantum Mechanics of Geometry – Xi Dong

Speaker: Xi Dong

Title: The Quantum Mechanics of Geometry

Abstract:

A quantum theory of gravity must accommodate different spacetime geometries and their superpositions within a single quantum framework. Holography provides a precise setting for this task by describing gravity in terms of a quantum system in fewer dimensions. Work with my collaborators showed that this holographic description can be understood as a quantum error-correcting code. Quantitative analyses of these codes have largely focused on states describing small fluctuations around a single classical spacetime.

I will discuss recent work extending this framework beyond a single classical background, with explicit bounds on the approximation errors. This extension lets us compare modular flow — quantum evolution determined by a reduced density matrix — with geometric flow generated by an area operator. An idealized black hole with two exterior regions provides a concrete setting for comparing the relative time shifts produced by these flows, showing when they agree and when they differ at leading semiclassical order.