Wormholes and Entanglement Juan Maldacena Institute for Advanced Study Outline • Black holes as quantum systems • Schwarzschild wormhole and entangled states. • Traversable wormholes. • Simple dynamics in Nearly-AdS2 • Traversable wormhole solution in 4d. Black holes as quantum systems • A black hole seen from the outside can be described as a quantum system with S degrees of freedom (qubits). = one reason is AdS/CFT… Hot fluid made out of very strongly Black holeGravity, Interacting particles. Strings Geometry of a Black Hole made from collapse Singularity Oppenheimer Snyder 1939 interior horizon star One exterior, one interior. Full Schwarzschild solution Eddington, Lemaitre, Einstein, Rosen, Finkelstein, Kruskal ER Left Right exterior exterior Vacuum solution. Figure 2: Maximally extended SchwarzschildTwo exteriors, sharing the interior. spacetime. There are two asymptotic regions. The blue spatial slice contains the Einstein-Rosen bridge connecting the two regions. not in causal contact and information cannot be transmitted across the bridge. This can easily seen from the Penrose diagram, and is consistent with the fact that entanglement does not imply non-local signal propagation. (a) (b) Figure 3: (a) Another representation of the blue spatial slice of figure 2. It contains a neck connecting two asymptotically flat regions. (b) Here we have two distant entangled black holes in the same space. The horizons are identified as indicated. This is not an exact solution of the equations but an approximate solution where we can ignore the small force between the black holes. All of this is well known, but what may be less familiar is a third interpretation of the eternal Schwarzschild black hole. Instead of black holes on two disconnected sheets, we can consider two very distant black holes in the same space. If the black holes were not entangled we would not connect them by a Einstein-Rosen bridge. But if they are somehow created at t =0intheentangledstate(2.1),thenthebridgebetweenthemrepresentsthe entanglement. See figure 3(b). Of course, in this case, the dynamical decoupling is not 7 The full Schwarzschild wormhole AdS asymptotics. No need to postulate any exotic matter horizon No matter at all ! left Right exterior exterior Figure 2: Maximally extended Schwarzschild spacetime. There are two asymptotic regions. The blue spatial slice contains the Einstein-Rosen bridge connecting the two regions. not in causal contact and information cannot be transmitted across the bridge. This can easily seen from the Penrose diagram, and is consistent with the fact that entanglement does not imply non-local signal propagation. Wormhole interpretation. Very large distance L R Non travesable (a) (b) L R No signals Figure 3: (a) Another representation of the blue spatial slice of figure 2. It contains a neck No causality violation connecting two asymptotically flat regions. (b) Here we have two distant entangled black holes in the same space. The horizons are identified as indicated.Fuller, Wheeler, Friedman, This is notSchleich an, Witt, Galloway, exact Wooglar Figure 2: Maximally extended Schwarzschild spacetime. There are two asymptotic regions. solution of the equations but an approximateThe blue spatial slicesolution contains the where Einstein-Rosen we bridge can connecting ignore the the two regions. small force between the black holes. not in causal contact and information cannot be transmitted across the bridge. This can easily seen from the Penrose diagram, and is consistent with the fact that entanglement does not imply non-local signal propagation. All of this is well known, but what may be less familiar is a third interpretation of the eternal Schwarzschild black hole. Instead of black holes on two disconnected sheets, we can consider two very distant black holes in the same space. If the black holes were not entangled we would not connect them by a Einstein-Rosen bridge. But if they are somehow (a) (b) created at t =0intheentangledstate(2.1),thenthebridgebetweenthemrepresentstheFigure 3: (a) Another representation of the blue spatial slice of figure 2. It contains a neck connecting two asymptotically flat regions. (b) Here we have two distant entangled black entanglement. See figure 3(b). Of course,holes in the same in space. this The case, horizons the are identified dynamical as indicated. decoupling This is not an exact is not solution of the equations but an approximate solution where we can ignore the small force between the black holes. All of this is7 well known, but what may be less familiar is a third interpretation of the eternal Schwarzschild black hole. Instead of black holes on two disconnected sheets, we can consider two very distant black holes in the same space. If the black holes were not entangled we would not connect them by a Einstein-Rosen bridge. But if they are somehow created at t =0intheentangledstate(2.1),thenthebridgebetweenthemrepresentsthe entanglement. See figure 3(b). Of course, in this case, the dynamical decoupling is not 7 Figure 2: Maximally extended Schwarzschild spacetime. There are two asymptotic regions. The blue spatial slice contains the Einstein-Rosen bridge connecting the two regions. not in causal contact and information cannot be transmitted across the bridge. This can easily seen from the Penrose diagram, and is consistent with the fact that entanglement does not imply non-local signal propagation. Wormhole and entangled states Connected through the interior (a) = (b) W. Israel J.M. Figure 3: (a) Another representation of the blue spatial slice of figure 2. It contains a neck connecting two asymptotically flat regions. (b) Here we have two distantEntangled entangled black holes in the same space. The horizons are identified as indicated. This is not an exact solution of the equations but an approximate solution where we can ignore the small force βE /2 TFD = e− n E¯ E between the black holes. | i | niL| niR n X (in a particular entangled state) All of this is well known, but what may be less familiar is a third interpretation of the eternal Schwarzschild black hole. Instead of black holes on two disconnected sheets, we can consider two very distant black holes in the same space. If the black holes were not entangled we would not connect them by a Einstein-Rosen bridge. But if they are somehow created at t =0intheentangledstate(2.1),thenthebridgebetweenthemrepresentsthe entanglement. See figure 3(b). Of course, in this case, the dynamical decoupling is not 7 ER = EPR J.M. , Susskind Figure 2: Maximally extended Schwarzschild spacetime. There are two asymptotic regions. The blue spatial slice contains the Einstein-Rosen bridge connecting the two regions. not in causal contact and information cannot be transmitted across the bridge. This can easily seen from the Penrose diagram, and is consistent with the fact that entanglement A forbidden meeting does not imply non-local signal propagation. Romeo Juliet (a) (b) Figure 3: (a) Another representation of the blue spatial slice of figure 2. It contains a neck connecting two asymptotically flat regions. (b) Here we have two distant entangled black holes in the same space. The horizons are identified as indicated. This is not an exact solution of the equations but an approximate solution where we can ignore the small force between the black holes. All of this is well known, but what may be less familiar is a third interpretation of the eternal Schwarzschild black hole. Instead of black holes on two disconnected sheets, we can consider two very distant black holes in the same space. If the black holes were not entangled we would not connect them by a Einstein-Rosen bridge. But if they are somehow created at t =0intheentangledstate(2.1),thenthebridgebetweenthemrepresentsthe entanglement. See figure 3(b). Of course, in this case, the dynamical decoupling is not 7 Figure 2: Maximally extended Schwarzschild spacetime. There are two asymptotic regions. The blue spatial slice contains the Einstein-Rosen bridge connecting the two regions. not in causal contact and information cannot be transmitted across the bridge. This can easily seen from the Penrose diagram, and is consistent with the fact that entanglement does not imply non-local signal propagation. (a) (b) Figure 3: (a) Another representation of the blue spatial slice of figure 2. It contains a neck connecting two asymptotically flat regions. (b) Here we have two distant entangled black holes in the same space. The horizons are identified as indicated. This is not an exact solution of the equations but an approximate solution where we can ignore the small force between the black holes. All of this is well known, but what may be less familiar is a third interpretation of the eternal Schwarzschild black hole. Instead of black holes on two disconnected sheets, we can consider two very distant black holes in the same space. If the black holes were not entangled we would not connect them by a Einstein-Rosen bridge. But if they are somehow created at t =0intheentangledstate(2.1),thenthebridgebetweenthemrepresentsthe entanglement. See figure 3(b). Of course, in this case, the dynamical decoupling is not 7 Is there a better way ? • Traversable wormholes • Quantum teleportation Gao, Jafferis, Wall, … Bennett, Brassard, Crepeau, Jozsa, Peres, Woetters Quantum teleportation Bob Alice • Bob and Alice share an entagled pair of qubits. Classical • Charlie gives Bob a qubit and he wants to send it to Alice. information • Bob does a joint measurement of Charlie’s qubit and his qubit. • Sends the the result to Alice as classical information Charlie’s qubit Entangled • Alice does an operation on his qubit that depends on Bob’s result. • Alice gets the qubit. • Resources needed to send a qubit: One entangled qubit and 2 bits of classical information. How does the qubit travel ? Would you like to be teleported ? Teleportation through the wormhole Bob Alice horizon Positive Bob Alice energy Classical Negative information energy left Right exterior exterior Entangled Gao, Jafferis, Wall Quantum teleportation through the wormhole • What does the message feel ? • A shock wave.