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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 … Mehr…

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

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 Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert's intense, original, well-informed, and highly influential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.

Detailangaben zum Buch - David Hilbert and the Axiomatization of Physics (1898-1918): From Grundlagen der Geometrie to Grundlagen der Physik L. Corry Author


EAN (ISBN-13): 9781402027772
ISBN (ISBN-10): 140202777X
Gebundene Ausgabe
Erscheinungsjahr: 2004
Herausgeber: Springer Netherlands Core >2 >T
532 Seiten
Gewicht: 0,953 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2007-06-01T11:27:40+02:00 (Vienna)
Detailseite zuletzt geändert am 2024-02-02T01:15:24+01:00 (Vienna)
ISBN/EAN: 9781402027772

ISBN - alternative Schreibweisen:
1-4020-2777-X, 978-1-4020-2777-2
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: corry, david hilbert, leo per, einstein
Titel des Buches: grundlagen der geometrie, archimedes, physik, 1898 1918, david hilbert and the axiomatization physics


Daten vom Verlag:

Autor/in: L. Corry
Titel: Archimedes; David Hilbert and the Axiomatization of Physics (1898–1918) - From Grundlagen der Geometrie to Grundlagen der Physik
Verlag: Springer; Springer Netherland
513 Seiten
Erscheinungsjahr: 2004-11-01
Dordrecht; NL
Gewicht: 2,040 kg
Sprache: Englisch
299,59 € (DE)
307,99 € (AT)
330,50 CHF (CH)
POD
XVII, 513 p. 36 illus.

BB; History and Philosophical Foundations of Physics; Hardcover, Softcover / Physik, Astronomie/Allgemeines, Lexika; Wissenschaftsphilosophie und -theorie; Verstehen; Albert Einstein; Ludwig Boltzmann; axiomatization; electrodynamics; probability; science; History of Mathematical Sciences; Mathematical Methods in Physics; Philosophy of Science; Philosophical Foundations of Physics and Astronomy; History of Mathematical Sciences; Mathematical Methods in Physics; Philosophy of Science; Physik; Geschichte der Mathematik; Mathematische Physik; BC; EA

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 EmpiricalConsiderations. 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

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