Entanglement and Complexity: Gravity and Quantum Mechanics

Stanford Institute for Theoretical Physics・2 minutes read

A secret conference discussed dualities in physics, quantum states, and tensor networks, impacting theoretical physics through AdS/CFT duality and black hole experiments involving entangled particles and Einstein-Rosen bridges. The complexity of quantum states, black holes, and information spreading links gravity, quantum mechanics, and general relativity, revealing new insights through entanglement, scrambling, and system behavior dynamics.

Insights

  • The concept of entanglement, where systems share information without direct connection, plays a crucial role in simplifying the description of quantum states by focusing on patterns of entanglement, aiding in calculations and understanding of complex quantum systems.
  • The growth of complexity in tensor networks, crucial for understanding the AdS/CFT duality connecting gravity and quantum field theory, mirrors the growth of complexity in black holes, with the formation of entangled black holes leading to the creation of Einstein-Rosen bridges that pose challenges for reuniting separated individuals, showcasing the intricate relationship between quantum mechanics, gravity, and spatial connectivity.

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Recent questions

  • What is entanglement in quantum mechanics?

    Entanglement involves shared information between systems, adding complexity.

  • How do tensor networks simplify quantum states?

    Tensor networks represent entanglement structures, aiding in calculations.

  • What is the AdS/CFT duality?

    AdS/CFT duality connects gravity with quantum field theory.

  • How do black holes relate to quantum scrambling?

    Black holes are fast scramblers, spreading information rapidly.

  • What is the EPR connection in physics?

    EPR connects entanglement with spatial connectivity.

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Summary

00:00

"Quantum Entanglement and Tensor Networks in Physics"

  • A secret conference was held off-campus at a military site to discuss video recording and travel to Mr. Simon's compound in New York.
  • Dualities in physics involve two equivalent descriptions of the same thing, one involving fluctuating variables and the other simpler and classical.
  • A special duality emerged between highly quantum mechanical systems and systems described by gravity, impacting various areas of theoretical physics.
  • General relativity and Quantum information Theory are central to the explosion in theoretical physics, influencing fields like Quantum field Theory, string theory, and more.
  • Quantum mechanical systems are exponentially complex, making them hard to describe on classical computers due to the vast number of complex coefficients needed.
  • Entanglement in quantum mechanics, where systems are not connected but share information, adds to the complexity and difficulty in understanding quantum mechanics.
  • Entanglement can help navigate through the complexity of quantum states by focusing on patterns of entanglement to simplify the description of systems.
  • Entanglement is not limited to particles but also exists in the vacuum, with entanglement entropy proportional to the area of the boundary separating regions.
  • Tensor networks, introduced by physicist Vidal in 2006, use entanglement patterns to describe the wave function of systems like spin lattices in condensed matter physics.
  • Tensor networks help navigate the complexity of Hilbert space by representing entanglement structures in systems, aiding in calculations and understanding of quantum states.

17:13

Tensor Networks: Key to Quantum Complexity and Duality

  • The real geometry lies in the tensor network on the boundary, not in the bulk geometry.
  • The complexity of a state is determined by the minimal tensor network needed to describe it.
  • Tensor networks can measure entanglement between different parts of a system.
  • Entanglement can be destroyed by feeding energy into the system, breaking the tensor network connections.
  • The concept of tensor networks is crucial in understanding the AdS/CFT duality discovered in 1998.
  • AdS/CFT duality connects gravity in anti-de Sitter space with quantum field theory on the boundary.
  • Excited quantum states require larger tensor networks than ground states to describe their complexity.
  • The complexity of quantum states increases over time, reflected in the growth of tensor networks.
  • Adding energy to anti-de Sitter space can lead to the formation of black holes.
  • Inside a black hole, the space grows rapidly, resembling the growth of complexity in tensor networks.

34:48

"Love Across Black Holes: Quantum Connection"

  • Alice and Bob, Space Cadets in love, are separated 10 billion light years apart due to an accident.
  • They consider creating a pair of black holes to reunite, leading to two experiment versions.
  • In the first experiment, they create two independent black holes by jamming particles together.
  • The second experiment involves entangling particles before creating the black holes, resulting in entangled black holes.
  • Entangled black holes form an Einstein-Rosen bridge, allowing for a shortcut connection between them.
  • The complexity of the Quantum State causes the Einstein-Rosen bridge to grow over time.
  • The growth of the bridge poses a challenge for Alice and Bob to meet inside the black holes.
  • The possibility of using quantum computers to prevent the bridge's growth is considered.
  • The equivalence between entanglement and spatial connectivity is termed EPR, discovered in 1935.
  • The connection between gravity, quantum mechanics, and general relativity opens new avenues for solving complex physics problems.

52:36

"Fast Scrambling Theory and Black Holes"

  • The game involves blindfolding participants every 10 seconds, where they find a partner and shake hands.
  • The black ink on Pierre's hand spreads exponentially through handshakes.
  • In a linear chain of interactions, the ink spreads slower than in a free interaction scenario.
  • The time to infect everyone in a room is logarithmic to the number of people.
  • The rate of interaction is linked to temperature, affecting the speed of infection spread.
  • Fast scrambling theory suggests that no system can scramble faster than the contagion model.
  • Black holes are proven to be fast scramblers, smearing out information at a specific rate.
  • Perturbations in black holes lead to shock waves that spread information rapidly.
  • The time for a shock wave to reach the horizon aligns with the conjectured bound on scrambling time.
  • Complexity theory plays a role in understanding black hole interiors and quantum entanglement.

01:10:25

Complexity in Black Hole Field Theories

  • Field theories that encompass entangled black holes and bridges between them must be complex and chaotic to meet the requirements of gravity, indicating a strong coupling and the presence of fast scramblers.
  • The study of black holes and anti-de Sitter space (AdS) focuses on non-dynamical aspects, contrasting with cosmology's exploration of exponentially expanding universes without boundaries, raising questions about the implications of these different approaches.
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