Building up spacetime with quantum entanglement

Building up spacetime with quantum entanglement

March 31, 2010 | Mark Van Raamsdonk
In this essay, Mark Van Raamsdonk argues that the emergence of classically connected spacetimes is closely linked to the quantum entanglement of degrees of freedom in a non-perturbative description of quantum gravity. He begins by discussing the gravity/gauge theory correspondence in string theory, which posits an equivalence between certain quantum gravitational theories and ordinary quantum field theories. Despite the correspondence's validity, the mechanism by which spacetime emerges from these field theories remains poorly understood. Van Raamsdonk explores the idea that classical connectivity in spacetime can arise from quantum superpositions of states corresponding to disconnected spacetimes. He provides an example where a quantum state that appears to be a superposition of disconnected spacetimes (in the field theory description) is interpreted as a classically connected spacetime (an eternal AdS black hole). This connection is established through the entanglement properties of the state, specifically the entanglement entropy and mutual information between subsystems. In a disentangling experiment, Van Raamsdonk demonstrates that decreasing the entanglement entropy between two regions in the field theory leads to an increase in the proper distance between the corresponding spacetime regions. This is quantified by the Ryu-Takayanagi proposal, which relates the entanglement entropy to the area of the minimal surface in the dual spacetime. As entanglement decreases, the minimal surface area decreases, and the regions of spacetime pull apart and pinch off from each other. The essay concludes by highlighting the fascinating role of quantum entanglement in the emergence of classical spacetime geometry, suggesting that this quantum phenomenon is crucial for understanding the non-perturbative nature of quantum gravity.In this essay, Mark Van Raamsdonk argues that the emergence of classically connected spacetimes is closely linked to the quantum entanglement of degrees of freedom in a non-perturbative description of quantum gravity. He begins by discussing the gravity/gauge theory correspondence in string theory, which posits an equivalence between certain quantum gravitational theories and ordinary quantum field theories. Despite the correspondence's validity, the mechanism by which spacetime emerges from these field theories remains poorly understood. Van Raamsdonk explores the idea that classical connectivity in spacetime can arise from quantum superpositions of states corresponding to disconnected spacetimes. He provides an example where a quantum state that appears to be a superposition of disconnected spacetimes (in the field theory description) is interpreted as a classically connected spacetime (an eternal AdS black hole). This connection is established through the entanglement properties of the state, specifically the entanglement entropy and mutual information between subsystems. In a disentangling experiment, Van Raamsdonk demonstrates that decreasing the entanglement entropy between two regions in the field theory leads to an increase in the proper distance between the corresponding spacetime regions. This is quantified by the Ryu-Takayanagi proposal, which relates the entanglement entropy to the area of the minimal surface in the dual spacetime. As entanglement decreases, the minimal surface area decreases, and the regions of spacetime pull apart and pinch off from each other. The essay concludes by highlighting the fascinating role of quantum entanglement in the emergence of classical spacetime geometry, suggesting that this quantum phenomenon is crucial for understanding the non-perturbative nature of quantum gravity.
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