Space, Time, Matter

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Courier Corporation, 26.04.2013 - 368 Seiten
"The standard treatise on the general theory of relativity." — Nature
"Whatever the future may bring, Professor Weyl's book will remain a classic of physics." — British Journal for Philosophy and Science
Reflecting the revolution in scientific and philosophic thought which accompanied the Einstein relativity theories, Dr. Weyl has probed deeply into the notions of space, time, and matter. A rigorous examination of the state of our knowledge of the world following these developments is undertaken with this guiding principle: that although further scientific thought may take us far beyond our present conception of the world, we may never again return to the previous narrow and restricted scheme.
Although a degree of mathematical sophistication is presupposed, Dr. Weyl develops all the tensor calculus necessary to his exposition. He then proceeds to an analysis of the concept of Euclidean space and the spatial conceptions of Riemann. From this the nature of the amalgamation of space and time is derived. This leads to an exposition and examination of Einstein's general theory of relativity and the concomitant theory of gravitation. A detailed investigation follows devoted to gravitational waves, a rigorous solution of the problem of one body, laws of conservation, and the energy of gravitation. Dr. Weyl's introduction of the concept of tensor-density as a magnitude of quantity (contrasted with tensors which are considered to be magnitudes of intensity) is a major step toward a clearer understanding of the relationships among space, time, and matter.
 

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Inhalt

NTRODUCTION CHAPTER I
Foundations of Affine Geometry
Conception of wdimensional Geometry Linear Algebra Quadratic Forms 4 Foundations of Metrical Geometry
Tensors
Tensor Algebra Examples
Symmetrical Properties of Tensors
Tensor Analysis Stresses
CHAPTER II
Relativistic Geometry Kinematics and Optics
Electrodynamics of Moving Bodies
Mies Theory
CHAPTER IV
Relativity of Motion Metrical Field and Gravitation
Stationary Gravitational Field Relationship with Experience
Rigorous Solution of the Problem of One Body
Further Rigorous Solutions of the Statical Problem of Gravitation

Note on NonEuclidean Geometry 11 Riemanns Geometry
Riemanns Geometry continued Dynamical View of Metrics 13 Tensors and Tensordensities in an Arbitrary Manifold 14 Affinely Connected Manifo...
Curvature 16 Metrical Space 17 Remarks on the Special Case of Riemanns Space 18 Space Metrics from the Point of View of the Theory of Groups
RELATIVITY OF SPACE AND TIME
Galileis and Newtons Principle of Relativity
Energy of Gravitation Laws of Conservation
World Metrics as the Origin of Electromagnetic Phenomena
APPENDIX I
BIBLIOGRAPHICAL REFERENCES
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Über den Autor (2013)

Along with his fundamental contributions to most branches of mathematics, Hermann Weyl (1885-1955) took a serious interest in theoretical physics. In addition to teaching in Zürich, Göttingen, and Princeton, Weyl worked with Einstein on relativity theory at the Institute for Advanced Studies.

Hermann Weyl: The Search for Beautiful Truths
One of the most influential mathematicians of the twentieth century, Hermann Weyl (1885–1955) was associated with three major institutions during his working years: the ETH Zurich (Swiss Federal Institute of Technology), the University of Gottingen, and the Institute for Advanced Study in Princeton. In the last decade of Weyl's life (he died in Princeton in 1955), Dover reprinted two of his major works, The Theory of Groups and Quantum Mechanics and Space, Time, Matter. Two others, The Continuum and The Concept of a Riemann Surface were added to the Dover list in recent years.

In the Author's Own Words:

"My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."

"We are not very pleased when we are forced to accept mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context."

"A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details." — Hermann Weyl

Critical Acclaim for Space, Time, Matter:

"A classic of physics . . . the first systematic presentation of Einstein's theory of relativity." — British Journal for Philosophy and Science

Bibliografische Informationen