Mechanistic Images In Geometric Form: Heinrich Hertzs Principles of Mechanics

Hardcover | May 15, 2005

byJesper Lutzen

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This book gives an analysis of Hertz's posthumously published Principles of Mechanics in its philosophical, physical and mathematical context. In a period of heated debates about the true foundation of physical sciences, Hertz's book was conceived and highly regarded as an original andrigorous foundation for a mechanistic research program. Insisting that a law-like account of nature would require hypothetical unobservables, Hertz viewed physical theories as (mental) images of the world rather than the true design behind the phenomena. This paved the way for the modern conceptionof a model. Rejecting the concept of force as a coherent basic notion of physics he built his mechanics on hidden masses (the ether) and rigid connections, and formulated it as a new differential geometric language.Recently many philosophers have studied Hertz's image theory and historians of physics have discussed his forceless mechanics. The present book shows how these aspects, as well as the hitherto overlooked mathematical aspects, form an integrated whole which is closely connected to the mechanisticworld view of the time and which is a natural continuation of Hertz's earlier research on electromagnetism. Therefore it is also a case study of the strong interactions between philosophy, physics and mathematics. Moreover, the book presents an analysis of the genesis of many of the central elementsof Hertz's mechanics based on his manuscripts and drafts. Hertz's research program was cut short by the advent of relativity theory but its image theory influenced many philosophers as well as some physicists and mathematicians and its geometric form had a lasting influence on advanced expositionsof mechanics.

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This book gives an analysis of Hertz's posthumously published Principles of Mechanics in its philosophical, physical and mathematical context. In a period of heated debates about the true foundation of physical sciences, Hertz's book was conceived and highly regarded as an original andrigorous foundation for a mechanistic research prog...

Jesper Lutzen is a Professor in the Department of Mathematics at the University of Copenhagen.

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Format:HardcoverDimensions:331 pages, 9.21 × 6.14 × 0.88 inPublished:May 15, 2005Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198567375

ISBN - 13:9780198567370

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Table of Contents

1. Introduction2. The principles of mechanics before Hertz3. Mechanization of physics4. The concept of force5. A biographical survey6. Hertz's road to mechanics7. Images of nature8. Hertz's earlier ideas about images9. Images of mechanics10. Kantianism. A priori and empirical elements of images11. Time, space and mass12. The line element: the origin of the Massenteilchen13. Hertz's geometry of systems of points14. Vector quantities and their components15. Connections. Material systems16. The fundamental law17. Free systems18. Cyclic coordinates19. Unfree systems. Forces20. Cyclic and conservative systems21. Integral principles22. A history of non-holonomic constraints23. Hertz on the Hamiltonian formalism24. Mathematicians on the geometrization of the Hamilton-Jacobi formalism25. Hertz on the domain of applicability of his mechanics26. Force-producing models27. Reception, extension and impact28. List of conclusionsA. Appendix