Relativity and the Question of Discretization in Astronomy

ISBN-13: 9783642880865 / Angielski / Miękka / 2012 / 188 str.

Dominic G.B. Edelen;A.G. Wilson

Opis

Theoretical researches in general relativity and observational data from galactic astronomy combine in this volume in contributions to one of the oldest questions of natural philosophy: Is the structure of the physical world more adequately described by a continuous or a discrete mode of representation? Since the days of the Pythagoreans, this question has surfaced from time to time in various guises in science as well as in philosophy. One of the most bitterly contested and illuminating controversies between the continuous and the discrete viewpoints is to be found in the wave versus corpuscular description of optical phenom- enae. This controversy was not resolved to the satisfaction of most of its protaganists until the development of the quantum theory. However, several obscurities that still becloud the question suggest that some deeper formulation may be necessary before more satisfactory answers can be given 1. The firm establishment of the validity of quantized structure and discrete energy distributions on the atomic scale following the ideas of Max Planck, together with the apparent absence of quan- tization effect in astronomical and cosmic structures leaves uncertainties concerning the role played by the scale of the observer in perceiving or not perceiving discrete distributions. Some of the metaphysical inter- pretations and implications of the quantum mechanics that have been made in recent years 2 would be subject to revision if the existence of discretized descriptions were to be established in astronomical and cosmic structures.

Spis treści

Prologue.- One Theoretical Considerations.- I The Environment for Cosmic Structures.- A. The External or Cosmological Enveloping Environment.- 1. The Classical Models.- 2. Inhomogeneity as a Similarity Construct.- 3. The Momentum-Energy Tensor.- 4. The Governing Equations.- 5. The Dispersion Vector.- 6. Approximation: Prestructures.- 7. The Condition of Bounded Potential in the Classical Models.- 8. The Future State with Bounded Potential.- 9. Solution of the Prestructure Equation and the Resulting Inhomogeneities.- B. Internal Consistency Structure: The Locally Induced Environment.- 10. Observation Operators.- 11. From the Local to the Macroscopic.- 12. Implication and Inference.- II An Equilibrium Theory of Galactic Isopleths.- A. Geometric Equilibrium.- 13. Isopleths and Timelike Hypersurfaces.- 14. Geometric Equilibrium.- 15. Implications of Geometric Equilibrium.- B. Physical Isopleths and Jump Discontinuities.- 16. Surface Quantities and Continuity Assumptions.- 17. Jump Strengths and Existence Conditions.- 18. Differential Relations.- 19. The Continuation Problem.- 20. Solution of the Continuation Problem.- 21. Physical Identification of the Isopleths.- C. Physical Isopleths in Geometric Equilibrium.- 22. Determination of {S??}.- 23. More about {S??}.- 24. The Tsoplethic Condition and the Perfect Fluid Approximation.- 25. The Trace Condition and the Discretization Equation.- III Galactic Morphology and Scale.- A. The Underlying Geometry of S* and the Equations of the Isopleth.- 26. Interpretation of the ? Function.- 27. The Subsidiary Space T.- 28. The Metric Tensor of T.- 29. The Embedding Problem.- 30. Spacelike Quadrics.- 31. Equations for the Isopleths.- B. The Discretization Equation.- 32. Normalization.- 33. Evaluation D.- 34. The Linearized Discretization Equation.- C. Equilibrium Morphology of E and SO Galaxies and the Scale Question.- 35. The Resulting Morphology of E and SO Galaxies.- 36. The Linear Scale.- 37. Galactic Scale Discretization.- Two Observational Considerations.- IV Observational Problems of Macroscale Discretization.- A. Epistemological Viewpoints.- 38. The Discrete and the Continuous.- 39. Paradigmatic Inference.- B. Design of Observational Tests.- 40. Tests for Discretization Hypotheses.- 41. Remarks on Statistical Tests.- V Observational Evidence for Discretization Phenomena.- A. Diameters of Galaxies.- 42. Measurement of Diameters.- 43. Discretization in Bright Galaxies.- 44. Discretization in Cluster Galaxies.- B. Redshift Discretizations.- 45. Prediction of Discretized Redshifts.- 46. Redshift Discretization of Clusters of Galaxies.- 47. Other Redshift Discretizations.- 48. Atomic-Cosmic Relations.- Appendix A. Curvature Conventions and Signs.- Appendix B. The Spherically Symmetric Case.- Appendix C. On Conformally Related Metric Spaces, One of which Admits an Irrotational Isometry.- 3. Lemma and Relations.- Appendix D. Analysis of the Complete Nonlinear Discretization Equation.- 1. Statement of the Problem.- 2. Conditions for Nontrivial Solutions.- 4. The First Approximation.- 5. The Second and Higher Order Approximations.- Author Index.