A main theme of the book outlines the role of the quantum potential in quantum mechanics and general relativity and one of its origins via fluctuations formulated in terms of Fisher information. Another theme is the description of various approaches to Bohmian mechanics and their role in quantum mechanics and general relativity. Along the way various approaches to, for instance, the Dirac equation, the Einstein equations, the Klein-Gordon equation, the Maxwell equations and the Schrodinger equations are described. Statistics and geometry are intertwined in various ways and, among other matters, the aether, cosmology, entropy, fractals, quantum Kaehler geometry, the vacuum and the zero point field are discussed. There is also some speculative material and some original work along with material extracted from over 1000 references and the work is current up to April 2005.

Table of Contents:
Preface. 1: The Schrodinger Equation. 1.1. Diffusion and Stochastic Processes. 1.2. Scale Relativity. 1.3. Remarks on Fractal Spacetime. 1.3.1. Comments on cantor Sets. 1.3.2. Comments on Hydrodynamics. 1.4. Remarks on Fractal Calculus. 1.5. A Bohmian Approach to Quantum Fractals. 2: DeBroglie-Bohm in Various Contexts. 2.1. The Klein-Gordon and Dirac Equations. 2.1.1. Electromagnetism and the Dirac Equations. 2.2. Bertoldi-Faraggi-Matone Theory. 2.3. Field Theory Models. 2.3.1. Emergence of Particles. 2.3.2. Bosonic Bohmian Theory. 2.3.3. Fermionic Theory. 2.4. DeDonder, Weyl and Bohm. 2.5. QFT and Stochastic Jumps. 2.6. Bohmian Mechanics in QFT. 3: Gravity and the Quantum Potential. 3.1. Introduction. 3.2. Sketch of DeBroglie-Bohm-Weyl Theory. 3.2.1. Dirac-Weyl Action. 3.2.2. Remarks on Conformal Gravity. 3.3. The Schrodinger Equation in Weyl Space. 3.3.1. Fisher Information Revisited. 3.3.2. The KG Equation. 3.4. Scale relativity and KG. 3.5. Quantum Measurement and Geometry. 3.5.1. Measurement on a Biconformal Space. 4: Geometry and Cosmology. 4.1. Dirac-Weyl Geometry. 4.2. Remarks on Cosmology. 4.3. WDW Equation. 4.3.1. Constraints in Ashtekar Variables. 4.4. Remarks on Regularization. 4.5. Pilot Wave Cosmology. 4.5.1. Euclidan Quantum Gravity. 4.6. Bohm and Noncommutative Geometry. 4.7. Exact Uncertainty and Gravity. 5: Fluctuations and Geometry. 5.1. The Zero Point Field. 5.1.1. Remarks on the Aether and Vacuum. 5.1.2. A Version of the Dirac Aether. 5.1.3. Massless Particles. 5.1.4. Einstein Aether Waves. 5.2. Stochastic Electrodynamics. 5.3. Photons and EM. 5.4. Quantum Geometry. 5.4.1. Probability Aspects. 6: Information and Entropy. 6.1. The Dynamics of Uncertainty. 6.1.1. Informaion Dynamics. 6.1.2. Information Measures for QM. 6.1.3. Phase Transitions. 6.1.4. Fisher Information and Hamilton's Equations. 6.1.5. Uncertainty and Fluctuations. 6.2. A Touch of Chaos. 6.2.1. Chaos and the Quantum Potential. 6.3. Generalized Thermostatistics. 6.3.1. Nonextensive Statistical Thermodynamics. 6.4. Fisher Physics. 6.4.1. Legendre Thermodynamics. 6.4.2. First and Second Laws. 7: On the Quantum Potential. 7.1. Resume. 7.1.1. The Schrodinger Equation. 7.1.2. DeBroglie-Bohm. 7.1.3. Geometry, Gravity, and QM. 7.1.4. Geometric Phases. 7.1.5. Entropy and Chaos. 7.2. Hydrodynamics and Geometry. 7.2.1. Particle and wave Pictures. 7.2.2. Electromagnetism and the SE. 7.3. Some Speculations on the Aether. 7.3.1. Discussion of a Putative PSI Aether. 7.4. Remarks on Trajectories. 8: Remarks on QFT and Tau Functions. 8.1. Introduction and Background. 8.1.1. Wick's Theorem and Renormalization. 8.1.2. Products and Relations to Physics. 8.2. Quantum Fields and Quantum Groups. 8.3. Renormalization and Algebra. 8.3.1. Various Algebras. 8.4. Tau Function and Free Fermions. 8.4.1. Symmetric Functions. 8.4.2. PSDO on a Circle. 8.5. Intertwining. 8.6. Vertex Operators and Symmetric Functions. Appendix A: DeDonder-Weyl Theory. Appendix B: Relativity and Electromagnetism. Appendix C: Remarks on Quantum Gravity. Appendix D: Dirac on Weyl Geometry. Appendix E: Biconformal Geometry. Bibliography. Index.