Geometry, Entropy and Complexity in Quantum Gravity (Part II)
summary
Argues that semi‑classical Euclidean path integrals and saddle points reproduce holographic entropies via Ryu–Takayanagi and recover Hawking area law, shows the thermofield double purifies a thermal CFT into a two‑sided wormhole whose geodesic lengths grow roughly linearly with time, connects that growth to complexity=action/volume proposals, derives a shock‑wave result with delay set by scrambling time ~ β log S, and explains how entanglement wedge reconstruction yields the Page curve while decoding the interior is exponentially hard.
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chapters (9)
- 0:00Introduction
- 1:24Path integrals in quantum gravity
- 6:06Thermal states and wormholes
- 15:39Entropy with Ryu-Takayanagi
- 23:14Penrose diagram structure
- 30:30Wormhole length growth
- 38:44Complexity conjecture and shock waves
- 57:36Entanglement wedge reconstruction
- 1:06:43Future challenges
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