The Mathematical Structure of Classical and Relativistic Physics: A General Classification Diagram

Description

The theories describing seemingly unrelated areas of physics have surprising analogies that have aroused the curiosity of scientists and motivated efforts to identify reasons for their existence. Comparative study of physical theories has revealed the presence of a common topological and geometric structure. The Mathematical Structure of Classical and Relativistic Physics is the first book to analyze this structure in depth, thereby exposing the relationship between (a) global physical variables and (b) space and time elements such as points, lines, surfaces, instants, and intervals. Combining this relationship with the inner and outer orientation of space and time allows one to construct a classification diagram for variables, equations, and other theoretical characteristics. The book is divided into three parts. The first introduces the framework for the above-mentioned classification, methodically developing a geometric and topological formulation applicable to all physical laws and properties; the second applies this formulation to a detailed study of particle dynamics, electromagnetism, deformable solids, fluid dynamics, heat conduction, and gravitation. The third part further analyses the general structure of the classification diagram for variables and equations of physical theories. Suitable for a diverse audience of physicists, engineers, and mathematicians, The Mathematical Structure of Classical and Relativistic Physics offers a valuable resource for studying the physical world. Written at a level accessible to graduate and advanced undergraduate students in mathematical physics, the book can be used as a research monograph across various areas of physics, engineering and mathematics, and as a supplemental text for a broad range of upper-level scientific coursework. Front Matter....Pages i-xxxvi Introduction....Pages 1-18 Front Matter....Pages 19-19 Terminology Revisited....Pages 21-37 Space and Time Elements and Their Orientation....Pages 39-62 Cell Complexes....Pages 63-87 Analysis of Physical Variables....Pages 89-153 Analysis of Physical Equations....Pages 155-179 Algebraic Topology....Pages 181-220 Birth of Classification Diagrams....Pages 221-238 Front Matter....Pages 239-239 Particle Dynamics....Pages 241-271 Electromagnetism....Pages 273-323 Mechanics of Deformable Solids....Pages 325-354 Mechanics of Fluids....Pages 355-383 Other Physical Theories....Pages 385-412 Front Matter....Pages 413-413 General Structure of the Diagrams....Pages 415-428 The Mathematical Structure....Pages 429-455 Back Matter....Pages 457-514