David Hilbert and the Axiomatization of Physics (1898-1918): From Grundlagen der Geometrie to Grundlagen der Physik by L. CorryDavid Hilbert and the Axiomatization of Physics (1898-1918): From Grundlagen der Geometrie to Grundlagen der Physik by L. Corry

David Hilbert and the Axiomatization of Physics (1898-1918): From Grundlagen der Geometrie to…

byL. Corry

Paperback | December 6, 2010

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David Hilbert (1862-1943) was the most influential mathematician of the early twentieth century and, together with Henri Poincaré, the last mathematical universalist. His main known areas of research and influence were in pure mathematics (algebra, number theory, geometry, integral equations and analysis, logic and foundations), but he was also known to have some interest in physical topics. The latter, however, was traditionally conceived as comprising only sporadic incursions into a scientific domain which was essentially foreign to his mainstream of activity and in which he only made scattered, if important, contributions. Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert's intense, original, well-informed, and highly influential involvement with physics, that spanned his entire career and that constituted a truly main focus of interest in his scientific horizon. His program for axiomatizing physical theories provides the connecting link with his research in more purely mathematical fields, especially geometry, and a unifying point of view from which to understand his physical activities in general. In particular, the now famous dialogue and interaction between Hilbert and Einstein, leading to the formulation in 1915 of the generally covariant field-equations of gravitation, is adequately explored here within the natural context of Hilbert's overall scientific world-view.This book will be of interest to historians of physics and of mathematics, to historically-minded physicists and mathematicians, and to philosophers of science.
Title:David Hilbert and the Axiomatization of Physics (1898-1918): From Grundlagen der Geometrie to…Format:PaperbackDimensions:530 pagesPublished:December 6, 2010Publisher:Springer NetherlandsLanguage:English

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ISBN - 10:9048167191

ISBN - 13:9789048167197

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Table of Contents

Preface. Acknowledgements and Credits. Introduction. 1: Late Nineteenth Century Background. 1.1. Hilbert's Early Career. 1.1.1 Algebraic Invariants. 1.1.2 Algebraic Number Fields. 1.1.3 Deep Roots in Tradition. 1.2. Foundations of Geometry. 1.2.1 Riemann. 1.2.2 Projective Geometry. 1.2.3 Nineteenth-Century Axiomatics. 1.2.4 Pasch and the Italian School. 1.3. Foundations of Physics. 1.3.1 Kinetic Theory, Mechanistic Foundations. 1.3.2 Carl Neumann. 1.3.3 Heinrich Hertz. 1.3.4 Paul Volkmann. 1.3.5 Ludwig Boltzmann. 1.3.6 Aurel Voss. 1.4. Mathematics and Physics in Göttingen at the Turn of the Century. 1.4.1 Felix Klein. 1.4.2 The Physicists. 2: Axiomatization in Hilbert's Early Career. 2.1. Axiomatics, Geometry and Physics in Hilbert's Early Lectures. 2.1.1 Geometry in Königsberg. 2.1.2 Geometry in Göttingen. 2.1.3 Mechanics in Göttingen. 2.2. Grundlagen der Geometrie. 2.2.1 Independence, Simplicity, Completeness. 2.2.2 Fundamental Theorems of Projective Geometry. 2.2.3 On the Concept of Number. 2.3. The 1900 List of Problems. 2.3.1 Foundational Problems. 2.3.2 A Context for the Sixth Problem. 2.4. Early Reactions to the Grundlagen. 3: The Axiomatic Method in Action: 1900-1905. 3.1. Foundational Concerns - Empiricist Standpoint. 3.2. Hilbert and Physics in Göttingen circa 1905. 3.3. Axioms for Physical Theories: Hilbert's 1905 Lectures. 3.3.1 Mechanics. 3.3.2 Thermodynamics. 3.3.3 Probability Calculus. 3.3.4 Kinetic Theory of Gases. 3.3.5 Insurance Mathematics. 3.3.6 Electrodynamics. 3.3.7 Psychophysics. 3.3.8 A post-1909 addendum. 3.4. The Axiomatization Program by 1905 - Partial Summary. 4: Minkowski and Relativity: 1907-1909. 4.1. The Principle of Relativity. 4.2. The Basic Equations of Electromagnetic Processes in Moving Bodies. 4.2.1 Three Meanings of "Relativity". 4.2.2 Axioms of Electrodynamics. 4.2.3 Relativity and Mechanics. 4.2.4 Relativity and Gravitation. 4.3. Space and Time. 4.3.1 Groups of Transformations. 4.3.2 Empirical Considerations. 4.3.3 Relativity and Existing Physical Theories. 4.4. Max Born, Relativity, and the Theories of the Electron. 4.4.1 Rigid Bodies. 4.5. Minkowski, Axiomatics and Relativity - Summary. 5: Mechanical to Electromagnetic Reductionism: 1910-1914. 5.1. Lectures on Mechanics and Continuum Mechanics. 5.2. Kinetic Theory. 5.3. Radiation Theory. 5.3.1 Hilbert and Kirchhoff's Law: 1912. 5.3.2 Reactions and Sequels: Early 1913. 5.3.3 Pringsheim's Criticism: 1913. 5.3.4 Hilbert's Final Version: 1914. 5.3.5 Kinetic and Radiation Theory: General Remarks. 5.4. Structure of Matter and Relativity: 1912-1914. 5.4.1 Molecular Theory of Matter - 1912-13. 5.4.2 Electron Theory: 1913. 5.4.3 Axiomatization of Physics: 1913. 5.4.4 Electromagnetic Oscillations: 1913-14. 5.5. Broadening Physical Horizons - Concluding Remarks. 6: Einstein and Mie: Two Pillars of Hilbert's Unified Theory. 6.1. Einstein's Way to General Relativity. 6.2. Mie's Electromagnetic Theory of Matter. 6.2.1 First and Second Installment: Early 1912. 6.2.2 Third Installment: November 1912. 6.3. Contemporary Debates on Gravitation. 6.4. Born's Formulation of Mie's Theory. 6.5. The Background to Hilbert's Unified Theory - Summary. 7: Foundations of Physics: 1915-1916. 7.1. Einstein in Göttingen - Summer of 1915. 7.2. Hilbert's Unified Theory - General Considerations. 7.3. Hilbert's Communication to the GWG - November 1915. 7.3.1 Axioms and Basic Assumptions. 7.3.2 The Hamiltonian Function and the Field Equations. 7.3.3 Summary and Additional Considerations. 7.4. The Hilbert-Einstein Correspondence and Einstein's Four Communications - November 1915. 7.5. Hilbert's Unified Theory: First Printed Version - March 1916. 7.6. Foundations of Physics - Summary. 8: Hilbert and GTR: 1916-1918. 8.1. Mie's Reaction. 8.2. Einstein's Reaction. 8.3. Hilbert Teaches GTR - 1916-1917. 8.4. Hilbert's Second Communication - December 1916. 8.5. Göttingen Debates on Energy Conservation in GTR - 1918. 8.6. Later Talks and Writings on GTR. 8.7. Last Versions of Hilbert's Theory. 8.8. Hilbert´s Way to GTR - Summary and Concluding Remarks. 9: Epilogue. 9.1. Foundations of Quantum Theory. 9.2. The Culture of "Nostrification" in Göttingen. 9.3. General Relativity and Geometry. 9.4. Hilbert and Participant Histories of GTR. 9.5. Hilbert and Physics - Concluding Remarks. Appendix 1: General Chronology of Events Mentioned in the Text. Appendix 2: Hilbert's Göttingen Courses on Physics. Appendix 3: Seminars, Miscellaneous Lectures. 3.A. Advanced Seminars Taught by Hilbert. 3.B. Public Lectures by Hilbert. 3.C. Physical lectures at the GMG and GWG by Hilbert. 3.D. Lectures on Physical Issues at the GMG by Others. Appendix 4: Hilbert's Physics Assistants and Doctoral Students. 4.A. Assistants for Physics. 4.B. Doctoral Students on Physical Topics. Appendix 5: Letters Quoted in the Book. Appendix 6: Items from the Hilbert Nachlass referred to in the Book. Appendix 7: Hilbert's Axioms for Radiation Theory. References. Commonly Used Abbreviations. Published and Unpublished Sources. Index.

Editorial Reviews

From the reviews:"This is a massive scholarly book on the work of David Hilbert on physics. In more than 400 pages the author provides us with an in-depth analysis of the fundamental contributions of this mathematician-born scientist to many branches of physics . . the historical reconstruction, which was the main aim of the author is . done with extreme competence and care, and it is, I think, of the highest quality." (Daniele Oriti, Mathematical Reviews, Issue 2006 i)"The main message of the book is that physics played in Hilbert's research . a much larger role than is commonly recognized. . It is written in a lively but at the same time in a very careful academic style. . Throughout the book the reader is confronted with many interesting . facts. . Leo Corry's book is a significant contribution to Hilbert studies and will be a major reference source . . I enjoyed reading the book and can recommend it to everyone." (Lev Beklemishev, Studies in History and Philosophy of Modern Physics, Vol. 37, 2006)