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

Oxford University Press, 2005. — 318 p.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.The principles of mechanics before Hertz.
Mechanization of physics.
The concept of force.
A biographical survey.
Hertz's road to mechanics.
Images of nature.
Hertz's earlier ideas about images.
Images of mechanics.
Kantianism. A priori and empirical elements of images.
Time, space and mass.
The line element: the origin of the Massenteilchen.
Hertz's geometry of systems of points.
Vector quantities and their components.
Connections. Material systems.
The fundamental law.
Free systems.
Cyclic coordinates.
Unfree systems. Forces.
Cyclic and conservative systems.
Integral principles.
A history of non-holonomic constraints.
Hertz on the Hamiltonian formalism.
Mathematicians on the geometrization of the Hamilton-Jacobi formalism.
Hertz on the domain of applicability of his mechanics.
Force-producing models.
Reception, extension and impact.
List of conclusions.
Appendix.