Contents -- Preface -- Chapter 1 Why Quantum Fluctuations of Spacetime? -- 1.1 Quantum Fluctuations and Spacetime -- 1.2 Detecting Quantum Gravity Fluctuations -- 1.3 Connections to Strings and Membranes -- 1.4 Beyond Standard Constructions -- Chapter 2 Quantum Fluctuations and Spacetime -- 2.1 Introduction -- 2.2 Fluctuations in Quantum Mechanics -- 2.3 ADM Relativity, the Wheeler-DeWitt Equation and Torsional Flucutations -- 2.4 Thermalized Torsional Fluctuations -- 2.5 Squeezed States, Wormholes and Nascent Cosmologies -- 2.6 Spacetime Fluctuations and Wormholes -- 2.7 The Geometry of Quantum Mechanics -- 2.7.1 Projective Structure in Spacetime and Quantum Mechanics -- 2.7.2 Bell's Inequality, Metrics and Expectation -- 2.7.3 The Hibert Space CP2 and Lorentz Group PSO(5,1) -- 2.7.4 Quantum Geometry and Extended Field Theories -- 2.8 Quantum Computing Backwards in Time and P NP -- 2.9 Summary on Spacetime Fluctuations -- References -- Chapter 3 Detection of Quantum Gravity Fluctuations -- 3.1 Can Quantum Gravity Be Experimentally Tested? -- 3.2 Atomic Detection of Quantum Spacetime Fluctuations -- 3.3 Detecting Virtual Black Holes -- 3.4 Quantum Optical Detection of Quantum Gravity Induced Decoherence -- 3.5 Ring Gyro Test of the Holographic Principle -- 3.6 Measurement of Unruh-Hawking Physics with Bose-Einstein Condensates -- 3.7 Testing Gravitational Squeezing of the Vacuum State -- 3.8 Cosmological Gravity Waves -- 3.9 The Universe as a (all ) = 0 -- References -- Chapter 4: Quantum Gravity Fluctuations, Strings and Two Dimensional D-Branes -- 4.1 Quantum Gravity Fluctuations in Modern Physics -- 4.2 Finite Temperature Theory of Rotating Strings -- 4.3 Nonlinear Spacetime Transformations, Quantum Theory and Gravity -- 4.4 Overview of Basic Topological Field Theory -- 4.5 Supersymmetry and Cohomology of the Horizon Algebra.

4.6 Moduli Space Constructions of Horizons -- 4.7 Brane Dynamics and Black Holes -- 4.8 Supersymmetric Moduli Space -- 4.9 Moduli Spaces With Non-Hausdorff Zariski Topology -- 4.10 Modularity and Fractal Aspects of Moduli with Zariski Topology -- 4.11 Julia Sets and NonHausdorff Measures over Moduli Spaces -- References -- Chapter 5 Topology, Extra Large Dimensions and the Higgs Field -- 5.1 Extra Dimensions and the Horizon D2-Brane and D5-Brane -- 5.2 Time Symmetry and Violations of Topological Quantum Numbers -- 5.3 TEV Physics From D-Branes and the Higgs Field -- 5.4 Quantum Group Structure With Ricci Flows and Three-Manifold Surgery -- References -- Chapter 6 Zeta Functions, Topological Quantum Numbers and M-Theory -- 6.1 Wrapped Spaces and Internal Symmetries -- 6.2 Instantons Between String Types, Topology, and Vacuum Ambiguity -- 6.3 String Types, M-Theory and Octonions -- References -- Chapter 7 The Generalized Uncertainty Principle -- 7.1 The Vacuum Problem -- 7.2 Differential Structure of Fields in Spacetime -- 7.3 Nonlocalizability of Energy and Noncommutative Geometry -- 7.4 Quantization of Fields in Spacetime and Noncommutative Geometry -- 7.5 Connections to One-Loop Quantum Gravity -- 7.6 The Noncommutative Algebra -- 7.7 General Relativity and Quantum Mechanics as Subsets of a Single Theory -- 7.8 A Proposed General Mathematics for the B* Algebra -- 7.9 Concluding Words -- References -- Chapter 8 Octonionic Quantum Gravity -- 8.1 Algebra and Basis Elements -- 8.2 Triality and Right/Left Eigenvectors Over -- 8.3 Quantum Mechanical Interpretation -- 8.4 Eigenvalues, Clifford Algebras and Quaternions -- 8.5 Holographic Principle from the Quantum Theory of Spin -- 8.6 Associative and Co- Associative SubAlgebra and Spacetime -- 8.7 Polyhedra and Jordan Algebraic Representations of Octonions.

8.8 Nonassociative Fields and Topological Supersymmetry -- 8.9 Bohr's Gravitixation of the Quantum -- 8.10 Quantum Black Holes as Strings and Error Correction Algorithms -- 8.11 Quantum States for Hamming and Golay Error Correction Codes -- 8.12 Phase Structure of Black Holes -- 8.13 Higher Polyhedral Representations -- References -- Chapter 9 Physical Law from No Law -- 9.1 Universal Computation In Quantum Cosmology and the Decidability of Cosmic Censorship -- 9.2 PreGeometry and Mathematical Undecidability -- 9.3 Recovering Geometry From PreGeometry -- 9.4 Godel's Theorem In Quantum Mechanics -- 9.5 The Anthropic Cosmological Principle? - Maybe -- References -- Index.