Mechanistic Images in Geometric Form: Heinrich Hertz's Principles of Mechanics

by Jesper Lutzen, Jesper L. Tzen

Overview

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 images and historians of physics have discussed his forceless mechanics. The present book shows how these aspects, as well as the hitherto overlooked mathematical aspect, form an integrated whole 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 programs was cut short by the advent of relativity theory but it's 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.

Product Details

ISBN-13:	9780198567370
Publisher:	Oxford University Press, USA
Publication date:	07/28/2005
Pages:	332
Product dimensions:	9.30(w) x 6.30(h) x 1.00(d)

About the Author

Jesper Lützen is a Lecturer 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