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Lectures on Gravity and Entanglement (1609.00026v1)

Published 31 Aug 2016 in hep-th, gr-qc, and quant-ph

Abstract: The AdS/CFT correspondence provides quantum theories of gravity in which spacetime and gravitational physics emerge from ordinary non-gravitational quantum systems with many degrees of freedom. Recent work in this context has uncovered fascinating connections between quantum information theory and quantum gravity, suggesting that spacetime geometry is directly related to the entanglement structure of the underlying quantum mechanical degrees of freedom and that aspects of spacetime dynamics (gravitation) can be understood from basic quantum information theoretic constraints. In these notes, we provide an elementary introduction to these developments, suitable for readers with some background in general relativity and quantum field theory. The notes are based on lectures given at the CERN Spring School 2014, the Jerusalem Winter School 2014, the TASI Summer School 2015, and the Trieste Spring School 2015.

Citations (113)

Summary

  • The paper demonstrates that spacetime geometry emerges from the entanglement structure of quantum states via the AdS/CFT correspondence.
  • It derives linearized Einstein equations from the entanglement first law, linking gravitational dynamics directly to quantum information.
  • It explores thermofield double states and black holes, offering insights into wormhole connectivity and advancing the quest for quantum gravity.

Overview of "Lectures on Gravity and Entanglement"

The lecture notes entitled "Lectures on Gravity and Entanglement" by Mark Van Raamsdonk present an informal yet comprehensive exploration of the intricate relationship between quantum entanglement and spacetime geometry, primarily through the framework of the Anti-de-Sitter/Conformal Field Theory (AdS/CFT) correspondence. This work synthesizes several years of research that points to the profound conclusion that spacetime itself may be emergent from more fundamental quantum mechanical degrees of freedom.

AdS/CFT Correspondence and Holography

The AdS/CFT correspondence postulates a duality between a gravity theory in a (d+1)-dimensional AdS space and a conformal field theory (CFT) on its d-dimensional boundary. This duality not only exemplifies the holographic principle, which suggests that bulk gravitational dynamics may be encoded in lower-dimensional boundary theories, but also implies that spacetime itself emerges from the entanglement properties of quantum states in the CFT.

Entanglement as the Cornerstone of Spacetime Geometry

One of the central insights provided by Van Raamsdonk is the idea that the geometry of spacetime is intricately linked to the entanglement structure of the boundary CFT. Through the Ryu-Takayanagi formula, which equates the entropy of a boundary region to the area of a minimal surface in the bulk, these lectures illustrate how changes in entanglement lead to modifications in spacetime geometry. This perspective aligns with the conjecture that quantum entanglement is the "glue" that holds the fabric of spacetime together.

Linearized Einstein Equations from Quantum Entanglement

The notes articulate a remarkable result: the linearized Einstein equations in the bulk AdS space can be derived from the entanglement first law for the CFT. This implies that gravitational equations might be a consequence of the quantum informational properties of the underlying quantum theory. The approach taken by Van Raamsdonk highlights a reverse engineering of gravity's fundamental principles from quantum mechanics, supporting the view that quantum information is fundamental.

Thermofield Double States and Black Holes

A significant portion of the notes is dedicated to understanding the dual description of black holes through thermofield double states. This description provides a framework for comprehending the emergence of wormholes as a manifestation of entangled states across non-interacting systems, emphasizing the dual role of thermal states in CFTs as black holes in AdS space. The connectivity of spacetime in such models further illustrates the indispensable role of entanglement.

Implications for Quantum Gravity

The explorations encapsulated within these lectures have profound implications for theoretical physics, particularly in the quest for quantum gravity. By reinterpreting gravity as an emergent property arising from quantum mechanics, Van Raamsdonk's work suggests that spacetime, with its inherent geometric and topological properties, may not be fundamental. This paradigm shift could provide new directions for resolving longstanding puzzles such as the quantum nature of black hole horizons and the information paradox.

Closing Thoughts on Future Developments

While the notes provide a robust framework connecting entanglement with spacetime geometry, they also indicate directions for future research. Questions such as the complete characterization of holographic states, the reconstruction of bulk geometry from entanglement data, and the full non-linear extension of the derived Einstein equations remain open. The path forward lies in exploring deeper into the entanglement structure and seeking new principles guiding the emergence of spacetime. As quantum gravity continues to develop, understanding these principles may lead to a more unified theory encompassing all fundamental forces.

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