Einstein, Hilbert, and the Theory of Gravitation: Historical Origins of General Relativity Theory

ISBN-13: 9789027704405 / Angielski / Miękka / 1974 / 96 str.

Jagdish Mehra; J. Mehra

Opis

Some time ago I published a small piece * dealing with a charming little essay on 'the state of ether in magnetic fields', which the sixteen-year-old Einstein had written while he was awaiting admission to the E. T. H. in Zurich. This paper sought to trace the continuity between Einstein's early interest in electrodynamics and his later work on the special and general relativity theories. On reading this paper, Professor Eugene Wigner asked me whether David Hilbert had not independently discovered the field equations of gravitation. ** His impression from his stay in Gottingen (where Wigner had been Hilbert's assistant for one year in the late nineteen-twenties) was that Hilbert had indeed done so, and he asked me if it was true. I replied to Professor Wigner about Hilbert's contribution to the theory of gravitation. t He kindly encouraged me to expand my account to deal with the intricate and exciting details of the early years in the formulation of the general relativity theory of gravitation. This is what I have sought to do in this study. Albert Einstein created the general relativity theory of gravitation and dominated its development through the rest of his life. His early work on the theory of gravitation, from 1912 to 1916, had the drama of high adventure. It culminated in the establishment of its foundations which have remained unassailed by the theoretical and experimental work of succeeding decades.

Spis treści

1. Introduction.- 2. Steps Towards a New Theory of Gravitation.- 2.1 The Principles of Equivalence and Relativity.- 2.2 Abraham’s Objections.- 2.3 Nordström’s Theory.- 2.4 Einstein and Grossmann: Search for the Mathematical Tools of General Relativity.- 2.5 The Foundation of General Relativity.- 3. Physics and Geometry.- 3.1 The Role of Axiomatization in Hilbert’s Work.- 3.2 Concepts of Space and Geometry.- 3.3 Space-Time and Invariants.- 3.4 Mie’s Field Theory of Matter.- 3.5 Hilbert’s Communication to the Göttingen Academy.- 3.6 Axioms of Hilbert’s Theory of Matter.- 3.7 Hilbert’s Fundamental Theorem, Energy Conservation and the World Function.- 4. Completion of the Theory of Gravitation.- 4.1 General Covariance and the Equivalence Principle.- 4.2 Theory of the Gravitational Field.- 4.3 Consequences and Applications of the Theory of Gravitation.- 4.4 The Cosmological Term.- 5. Physical Interpretation of General Covariance.- 5.1 Axiom of Physical Interpretability.- 5.2 Restrictions due to Causality.- 5.3 Hilbert’s Conclusion.- 6. Hamilton’s Principle and the Conservation Laws.- 6.1 Lorentz and the Hamilton Principle in Einstein’s Theory.- 6.2 Einstein and the Hamilton Principle.- 7. General Covariance and Conservation Laws.- 7.1 Energy Conservation and the Theory of Invariants.- 7.2 Identities from General Covariance.- 7.3 Bianchi Identities and Hilbert’s Constraint Conditions.- 8. Extension of General Relativity.- 8.1 Generalization of Riemannian Geometry.- 8.2 Weyl’s Unified Theory.- 8.3 Five-Dimensional Relativity.- 9. ‘Ein Bleibender Kern’ — An Enduring Core.- References and Notes.- Index of names.