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AIMS-GHANA & RESEARCH ON QUANTUM GRAVITY Prince K. Osei - PowerPoint PPT Presentation

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AIMS-GHANA & RESEARCH ON QUANTUM GRAVITY Prince K. Osei AIMS-Ghana & University of Ghana Next Einstein Initiative and Rural Prenatal Care in Ghana October 20, 2014 Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on

  1. AIMS-GHANA & RESEARCH ON QUANTUM GRAVITY Prince K. Osei AIMS-Ghana & University of Ghana Next Einstein Initiative and Rural Prenatal Care in Ghana October 20, 2014 Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 1 / 43

  2. Outline Research on Quantum Gravity 1 Motivation Research Focus Others... AIMS-Ghana 2 Neil’s vision = Our goal Academics Research Outreach Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 1 / 43

  3. The universe as described by GR Taken from hubblesite.org Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 2 / 43

  4. Einstein’s General relativity Phenomena at large scales are governed by gravitational interactions Gravitation is inherent in the dynamic Riemannian geometry of spacetime Gravity is a property of spacetime Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 3 / 43

  5. Formulation of GR Gravity = curvature of spacetime ⇒ curvature of spacetime is directly related to the energy = and momentum of whatever matter and radiation are present. Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 4 / 43

  6. Evidence of GR Taken from Wikipedia Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 5 / 43

  7. General relativity Led to Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 6 / 43

  8. General relativity Led to cosmology relativistic astrophysics GPS Leading us towards gravitational wave astronomy Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 6 / 43

  9. General relativity Predicts Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 7 / 43

  10. General relativity Predicts black holes gravitational waves expanding universe etc... Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 7 / 43

  11. Quantum mechanics A theory for the microscopic world Shows that Phenomena at small scales are dominated by strong and electroweak interactions Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 8 / 43

  12. Quantum mechanics A theory for the microscopic world Shows that Phenomena at small scales are dominated by strong and electroweak interactions Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 8 / 43

  13. Quantum mechanics Gave rise to Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 9 / 43

  14. Quantum mechanics Gave rise to particle physics atomic physics nuclear physics semiconductors computers Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 9 / 43

  15. Formulation of QM Quantum mechanics uses an external time variable or a fixed, non-dynamical background spacetime requires that any dynamical field be quantized, i.e. at small scales it manifests itself in discrete quanta governed by the laws of probability. Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 10 / 43

  16. Formulation of QM Quantum mechanics uses an external time variable or a fixed, non-dynamical background spacetime requires that any dynamical field be quantized, i.e. at small scales it manifests itself in discrete quanta governed by the laws of probability. Formulation incompatible with general relativity! Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 10 / 43

  17. Quantum gravity quantum gravity = quantum theory of spacetime Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 11 / 43

  18. Quantum gravity quantum gravity = quantum theory of spacetime Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 11 / 43

  19. Quantum gravity QUESTION: Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 12 / 43

  20. Quantum gravity QUESTION: what then is the quanta of spacetime? how then does one describe a quantum spacetime? Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 12 / 43

  21. Quantum gravity Technical challenges: Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 13 / 43

  22. Quantum gravity Technical challenges: Einstein’s general relativity is mathematically complicated Einstein’s equations of motion which governs the theory of gravity are a set of highly non-linear differential equations which cannot be solve exactly. Even is a relatively simple case, one would require numerical techniques. Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 13 / 43

  23. Approaches to quantum gravity perturbative quantum gravity canonica quantization & path integrals loop quantum gravity string theory Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 14 / 43

  24. Approaches to quantum gravity perturbative quantum gravity canonica quantization & path integrals loop quantum gravity string theory noncommutative geometry Spin Foam Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 14 / 43

  25. Research Focus Noncommutative structures in quantum gravity Spin Foam Models Others... Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 15 / 43

  26. Noncommutative structures Proposal Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 16 / 43

  27. Noncommutative structures Proposal quantum gravity will require or predict a new mathematical framework for differential geometry. Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 16 / 43

  28. Noncommutative structures Proposal quantum gravity will require or predict a new mathematical framework for differential geometry. A candidate for such a framework is provided by noncommutative geometry Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 16 / 43

  29. Noncommutative structures Our focus a more general notion of geometry that by its noncommutative nature should be the correct setting for the phenomenology and testing of first next-to-classical quantum gravity corrections. the mathematical constraints of NCG may give us constraints on the structure of quantum gravity itself Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 17 / 43

  30. Noncommutative structures Our focus a more general notion of geometry that by its noncommutative nature should be the correct setting for the phenomenology and testing of first next-to-classical quantum gravity corrections. the mathematical constraints of NCG may give us constraints on the structure of quantum gravity itself in particular the role of quantum groups or Hopf algebras as the most accessible tool of NCG. Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 17 / 43

  31. Some Results P . K. Osei and B. J. Schroers, On Semiduals of local isometry groups in 3d gravity, J. Math. Phys. 53, (2012) 073510, arxiv: 1109.4086v3 [gr-qc]. P . K. Osei and B. J. Schroers, Classical r-matrices via semidualisation, J. Math. Phys. 54 (2013) 101702. P . K. Osei and B. J. Schroers, Classical r-matrices 3d gravity, in preparation. Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 18 / 43

  32. Implications of Results This should lead to a coherent and precise scenerio of quantum gravity Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 19 / 43

  33. Spin Foam Models Aimed at providing a non-perturbative and background independent quantisation of gravity via an auxiliary discretization. Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 20 / 43

  34. Spin Foam Models Our focus Study analogue spin foam and spin net models with q − deformed quantum groups understand the relation between them. Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 21 / 43

  35. Spin Foam Models Our focus Study analogue spin foam and spin net models with q − deformed quantum groups understand the relation between them. Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 21 / 43

  36. Others Quantitative Risk Analysis Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 22 / 43

  37. Others Quantitative Risk Analysis Credit and Operational risk Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 22 / 43

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