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An Approach to Quantum Gravity

An Approach to Quantum Gravity. Causal Dynamical Triangulation in 1+1 Dimensions. Norman Israel The College of Wooster. Outline. Quantum Gravity Theory Gauss-Bonnet Theorem CDT Simulation. Quantum Gravity. Singularities: Big Bang Black Holes

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An Approach to Quantum Gravity

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  1. An Approach to Quantum Gravity Causal Dynamical Triangulation in 1+1 Dimensions Norman Israel The College of Wooster

  2. Outline • Quantum Gravity • Theory • Gauss-Bonnet Theorem • CDT • Simulation

  3. Quantum Gravity • Singularities: • Big Bang • Black Holes • Quantum Mechanics meets General Relativity at small distances and large energies • Quantum Gravity Problem NASA/WMAP Science Team

  4. Quantum Gravity • Approaches: • String Theory(M) • Loop Quantum Gravity(LQG) • Causal Dynamical Triangulation(CDT) • Microcausality implies classical spacetime • Recovers classical spacetime at large scales • Predicts fractal spacetime at small scales • Potentially testable

  5. BACKGROUND THEORY

  6. Metric • Riemannian (non-negative) - • Pseudo-Riemannian (relaxes non-negative property) - Includes Riemannian metric and spacetime metric.

  7. GR: Spacetime Metric

  8. GR: Einstein-Hilbert Action

  9. QM: Path Integral What is the probability amplitude to go from a to b?

  10. GR + QM: Geometric Propagator

  11. CDT: Causal dynamical triangulation

  12. t x Deficit angle

  13. Deficit Angle

  14. Gauss-Bonnet Theorem on Polyhedra For cube: genus (sphere = 0, torus = 1)

  15. Regge Calculus Because:

  16. Wick Rotation Assures convergence Action Propagator Partition function

  17. Simulation

  18. Monte Carlo Simulation • Random walk in triangulation space to compute expectation values (periodic boundary conditions). • Move and Anti-move • This is believed to be ergodic

  19. Monte Carlo Averaging • Averaging N measurements of observable O

  20. Simulation Screenshot

  21. Simulation Results: Critical cosmological constant

  22. Simulation results: Spatial fluctuations

  23. Acknowledgements • Copeland Funding • My advisors John Lindner and John Ramsay • AbhayAshtekar, William Nelson, Miguel Campiglia • Karen Lewis

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