Inertia and Gravitation

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This book delves into inertia and gravitation, aiming to illuminate the laws of gravitational interaction and the nature of spacetime. Chapter 1 offers a comprehensive analysis of the law of inertia, presenting the mathematical and geometrical framework of Newtonian spacetime from a four-dimensional perspective. It critically examines historical challenges related to free particles and straight lines, while also connecting to projective geometry. Chapter 2 explores the relativistic extensions of gravitation, building on the works of Weyl, Ehlers, Pirani, and Schild, and emphasizes Mach’s critique of Newton’s notions of ‘absolute space’ and ‘absolute time’ as a key influence on Einstein’s general relativity. The chapter highlights how Einstein’s equivalence principle reshaped the understanding of inertia. Chapter 3 focuses on the unique mathematical structure of Einstein’s field equations, showcasing some of their notable physical predictions. In Chapter 4, different types of dragging phenomena are analyzed to assess the realization of the equivalence principle in general relativity. This discussion is closely tied to the concept of gravitomagnetism, a 'new force' theorized by Einstein and Thirring, which has gained attention following recent experimental confirmations.