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Unformatted text preview: Chapter 1 Physics in Flat Spacetime: Geometric Viewpoint Version 0201.2, September 2002 Please send comments, suggestions, and errata via email to [email protected], or on paper to Kip Thorne, 130-33 Caltech, Pasadena CA 91125 1.1 Overview This is a book about classical physics. It is a book about the interpretation of physical phenomena on the large scale, when the particle nature of matter and radiation is secondary to the behavior of these particles in bulk, when their statistical as opposed to their individ- ual properties are important and when their inherent graininess can be smoothed over. We shall take a journey, through spacetime and phase space, though statistical and continuum mechanics, through optics and relativity, to comprehend the fundamental laws of classical physics in their own terms and in relation to quantum physics. Through carefully chosen ex- amples, we shall show how these laws are being applied to important contemporary problems and we shall uncover some deep connections between the fundamental laws and between the practical techniques that are used in different subfields. In order to bring out these connections, we shall adopt a different viewpoint on the laws of physics than that found in most elementary textbooks. In elementary texts, the laws are expressed in terms of quantities (locations in space or spacetime, momenta of particles, etc.) that are measured in some coordinate system or reference frame. For example, Newtonian vectorial quantities (momenta, electric fields, etc.) are triplets of numbers [e.g., (1 . 7 , 3 . 9 ,- 4 . 2)] representing the vectors’ components on the axes of a spatial coordinate system, and relativistic 4-vectors are quadruplets of numbers representing components on the spacetime axes of some reference frame. By contrast, in this book, we shall express all physical quantities and laws in a geometric form that is independent of any coordinate system. For example, in Newtonian physics, momenta and electric fields will be vectors described as arrows that live in the 3-dimensional, flat Euclidean space of everyday experience. They require no coordinate system at all for their existence or description—though sometimes coordinates will be useful. We shall state 1 2 Special Relativity Classical Physics in the absence of gravity Arena: Flat, Minkowski spacetime vanishing gravity General Relativity The most accurate framework for Classical Physics Arena: Curved spacetime weak gravity small speeds small stresses Newtonian Physics Approximation to relativistic physics Arena: Flat, Euclidean 3-space, plus universal time low speeds small stresses add weak gravity Fig. 1.1: The three frameworks and arenas for the classical laws of physics, and their relationship to each other....
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