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Mechanistic Images in Geometric Form Jesper Lutzen (, Department of Mathematics, University of Copenhagen, Denmark)

Mechanistic Images in Geometric Form By Jesper Lutzen (, Department of Mathematics, University of Copenhagen, Denmark)

Mechanistic Images in Geometric Form by Jesper Lutzen (, Department of Mathematics, University of Copenhagen, Denmark)


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Summary

This book presents an analysis of Heinrich Hertz's posthumously published 'Principles of Mechanics' in its philosophical, physical and mathematical context. It is the first book to comprehensively examine Hertz's important ideas on mechanics and the author draws on the original manuscripts to reveal the creative process of Hertz throughout the writing of his book.

Mechanistic Images in Geometric Form Summary

Mechanistic Images in Geometric Form: Heinrich Hertz's 'Principles of Mechanics' by Jesper Lutzen (, Department of Mathematics, University of Copenhagen, Denmark)

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 and rigorous 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 conception of 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 mechanistic world 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 elements of 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 expositions of mechanics.

Mechanistic Images in Geometric Form Reviews

...the book is very well-written and well-presented...the book is the best thing ever written on Hertz's mechanics and, as such, is strongly recommended to all philosophers and historians of science. J. Preston, Studies in History and Philosophy of Science, 38 (2007) 260-267.
... very clearly written and well organised. * Jeremy Gray, Open University *
... interesting, thorough, well-documented and well-presented. * Leo Corry, Tel Aviv University *

About Jesper Lutzen (, Department of Mathematics, University of Copenhagen, Denmark)

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

Table of Contents

1. Introduction ; 2. The principles of mechanics before Hertz ; 3. Mechanization of physics ; 4. The concept of force ; 5. A biographical survey ; 6. Hertz's road to mechanics ; 7. Images of nature ; 8. Hertz's earlier ideas about images ; 9. Images of mechanics ; 10. Kantianism. A priori and empirical elements of images ; 11. Time, space and mass ; 12. The line element: the origin of the Massenteilchen ; 13. Hertz's geometry of systems of points ; 14. Vector quantities and their components ; 15. Connections. Material systems ; 16. The fundamental law ; 17. Free systems ; 18. Cyclic coordinates ; 19. Unfree systems. Forces ; 20. Cyclic and conservative systems ; 21. Integral principles ; 22. A history of non-holonomic constraints ; 23. Hertz on the Hamiltonian formalism ; 24. Mathematicians on the geometrization of the Hamilton-Jacobi formalism ; 25. Hertz on the domain of applicability of his mechanics ; 26. Force-producing models ; 27. Reception, extension and impact ; 28. List of conclusions ; A. Appendix

Additional information

NPB9780198567370
9780198567370
0198567375
Mechanistic Images in Geometric Form: Heinrich Hertz's 'Principles of Mechanics' by Jesper Lutzen (, Department of Mathematics, University of Copenhagen, Denmark)
New
Hardback
Oxford University Press
2005-05-12
334
N/A
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