In this book, a central theme will be a Geometric Principle: The laws of physics must all be expressible as geometric (coordinate-independent and reference-frame-independent) relationships between geometric objects (scalars, vectors, tensors, . . . ) that represent physical entities. There are three different conceptual frameworks for the classical laws of physics, and correspondingly, three different geometric arenas for the laws;
see Fig. 1. General relativity is the most accurate classical framework; it formulates the laws as geometric relationships among geometric objects in the arena of curved 4-dimensional spacetime. Special relativity is the limit of general relativity in the complete absence of gravity; its arena is flat, 4-dimensional Minkowski spacetime.1 Newtonian physics is the limit of general relativity when . gravity is weak but not necessarily absent, . relative speeds of particles and materials are small compared to the speed of light c, and . all stresses (pressures) are small compared to the total density of massenergy.
Its arena is flat, 3-dimensional Euclidean space with time separated off and made universal (by contrast with relativity’s reference-frame-dependent time).
In Parts II–VI of this book (covering statistical physics, optics, elasticity, fluid mechanics, and plasma physics), we confine ourselves to the Newtonian formulations of the laws (plus special relativistic formulations in portions of Track Two), and accordingly, our arena will be flat Euclidean space (plus flat Minkowski spacetime in portions of Track Two).
In Part VII, we extend many of the laws we have studied into the domain of strong gravity (general relativity)—the arena of curved space time. …….DOWNLOAD