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

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OUP Oxford, May 12, 2005 - Mathematics - 318 pages
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) imagesof 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 differentialgeometric 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 andmathematics. 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 somephysicists and mathematicians and its geometric form had a lasting influence on advanced expositions of mechanics.
 

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Contents

1 Introduction
1
2 The principles of mechanics before Hertz
8
3 Mechanization of physics
30
4 Problematization of the concept of force
40
5 A biographical survey
50
6 Hertzs road to mechanics
63
7 Images of nature
83
8 Hertzs earlier ideas about images
97
17 Free systems
202
18 Cyclic coordinates
208
19 Unfree systems Forces
219
20 Cyclic and conservative systems
225
21 Integral principles
235
22 A history of nonholonomic constraints
240
23 Hertz on the Hamilton formalism
247
24 Mathematicians on the geometrization of the HamiltonJacobi formalism
252

9 Images of mechanics
111
10 Kantianism Apriori and empirical elements of images
119
11 Time space and mass
127
The origin of the Massenteilchen
146
13 Hertzs geometry of systems of points
159
14 Vector quantities and their components
173
15 Connections Material systems
187
16 The fundamental law
198
25 Hertz on the domain of applicability of his mechanics
263
26 Forceproducing models
274
27 Reception extension and impact
278
28 List of conclusions
290
Appendix
295
Bibliography
299
Index
313
Copyright

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About the author (2005)


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

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