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

299 | |

313 | |

### Other editions - View all

Mechanistic Images in Geometric Form:Heinrich Hertz's 'Principles of ... Jesper Lützen No preview available - 2005 |

Mechanistic Images in Geometric Form:Heinrich Hertz's 'Principles of ... Jesper Lützen No preview available - 2005 |

### Common terms and phrases

a-priori according to Hertz argued atoms Boltzmann Chapter configuration configuration space connections conservative system considered correctness curvature cyclic coordinates cyclic system defined definition differential equations discussion displacements distance draft electromagnetic empirical equations of constraint ether Euclidean Euclidean geometry experience explained expression fact finite formulated free system function fundamental law Gauss’s geodesics geometry of systems gravitational Hamilton–Jacobi equation Hamilton’s principle Helmholtz Hertz introduced Hertz’s book Hertz’s image Hertz’s mechanics hidden masses hidden system holonomic system ideas image of mechanics image theory inertial mass infinitely small Kantian Kiel Lectures kinetic energy Lagrangian least action line element manuscript Massenteilchen material points mathematical mathematicians matter Maxwell Maxwell’s theory mechanical system mechanistic nature Newton’s non-Euclidean geometry orthogonal parallel transport permissibility philosophical physical physicists possible potential energy principle of least principles of mechanics problem quadratic mean question reduced components Riemannian manifold space straightest path systems of points theorem Thomson vector quantity velocity visible system