Spin Foam Model and Emergent Gravity Muxin Han (韩慕⾟) （in collaboration with Zichang Huang (⻩⼦⾿) and Antonia Zipfel） General Relativity: Gravity = Curved Spacetime Geometry Quantum Gravity = Quantum Spacetime Geometry What is a Quantum Spacetime? ( In this talk, the spacetime dimension is 4 = 3+1 ) !2 Wheeler & Hawking’s Quantum Foam J.A. Wheeler, Geometrodynamics and the issue of the final state, in Relativity, groups and topology, C. DeWitt and B.S. DeWitt eds., Gordon and Breach, New York U.S.A. (1964). S.W. Hawking, Space-time foam, Nucl. Phys. B 144 (1978) 349. !3 Quantum Mechanics: If we localize too much a particle in spacetime, its energy and momentum grow. Quantum Mechanics: If we localize too much a particle in spacetime, its energy and momentum grow. General Relativity: If energy and momentum grow too much, it collapses and forms a black hole. Singularities, infinities, difficulies Quantum Mechanics: If we localize too much a particle in spacetime, its energy and momentum grow. General Relativity: If energy and momentum grow too much, it collapses and forms a black hole. Singularities, infinities, difficulies Resolution: There is a minimal scale (Planck scale p) in spacetime against localization. Quantum Spacetime is Foam-like A minimal cell of quantum spacetime A Complementary Point of View: Emergent Gravity Quantum Gravity as an Ocean of Entangled Qubits Xiao-Gang Wen, Zhenghan Wang 2018 Zheng-Cheng Gu, Xiao-Gang Wen 2009 !8 A Complementary Point of View: Emergent Gravity Quantum Spacetime is a Tensor Network Swingle 2009, Evenbly, Vidal, 2014 Pastawski, Yoshida, Harlow, Preskill, 2015 Hayden, Nezami, Qi, Thomas, Water, Yang 2016 Qi, Yang 2018 !9 Question Quantum of Emergent Spacetime is Foam-like Gravity (Semiclassical Consistency of QG Model) A minimal cell of quantum spacetime Foam-like spacetime Ocean of entangled qubits Quantum, Discrete, and Algebraic (fundamental) Classical Gravity: Smooth Spacetime Geometry (emergent low energy excitations) !10 Spin Foam Model (SFM) and Emergent Gravity The definition of SFM as a State-Sum Model and a Tensor Network Large Spin Asymptotics and Emergent Geometry Continuum limit and Emergent (vacuum) Einstein Equation Gµ⌫ = 0 <latexit 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!11 Spin Foam Model and Covariant Loop Quantum Gravity Quantum Spacetime is Foam-like Foam-like discrete spacetime: a triangulation of 4-manifold (simplicial complex) A MinimalA spacetime minimal Cell cell in Loop of Quantumquantum Gravity spacetime 4-simplex4-simplex:: the simplest cell in 4dminimal cell in 4d triangulation (10 triangles and 5 tetrahedra) 4-dimensional analog of tetrahedron in 3d and triangle in 2d.