The Symbolic Universe Geometry and Physics 1890-1930

Physics was transformed between 1890 and 1930, and this volume provides a detailed history of the era and emphasizes the key role of geometrical ideas. The first part of the book discusses the application of n-dimensional differential geometry to mechanics and theoretical physics, the
philosophical questions on the reality of geometry, and reviews the broad international debate about the nature of geometry and its connections with psychology. The second part then examines the reception of Einstein's theory of special relativity following 1905. It covers Minkowski's reformulation
of the theory, providing the first complete picture of his work, and it describes Einstein's path to formulating general relativity. The chapter on Hilbert's efforts to axiomatize relativity argues against the traditional view of Hilbert as arch-formalist, and the following chapter provides the
first detailed account of Emmy Noether's work on physics. The final section examines the work by Ricci, Levi-Civita, and Weyl to give a new formulation of general relativity in terms of the Riemann differential. This collection will be an invaluable resource for historians and philosophers of
science.

With the development of the theory of relativity by Albert Einstein, physics underwent a revolution at the end of the 19th century. The boundaries of research were extended still further when in 1907-8 Minkowski applied geometrical ideas to this area of physics. This in turn opened the door to other researchers seeking to use non-Euclidean geometrical methods in relativity, and many notable mathematicians did so, Weyl in particular linking these ideas with broader philosophical issues in mathematics. The Symbolic Universe gives an overview of this exciting era, giving a full account for the first time of Minkowski's geometric reformulation of the theory of special relativity.

PART I; Introduction; Geometrizing configurations. Heinrich Hertz and his mathematical precursors; Einstein, Poincar?, and the testability of geometry; Geometry-formalisms and intuitions; PART II; Introduction; The non-Euclidean style of Minkowskian relativity; Geometries in collision: Einstein, Klein and Riemann; Hilbert and physics (1900-1915); The G"ottingen response to general relativity and Emmy Noether's theorems; PART III; Introduction; Ricci and Levi-Civita: from differential invariants to general relativity; Weyl and the theory of connections

Dr Jeremy J. Gray, Senior Lecturer in Mathematics, Faculty of Mathematics and Computing, Open University, Milton Keynes, MK7 6AA. j.j.gray@open.ac.uk