The Language of Physics: The Calculus and the Development of Theoretical Physics in Europe, 1750-1914

ISBN-13: 9780817640392 / Angielski / Twarda / 1998 / 399 str.

Elizabeth Garber; E. Garber

Opis

This study began as an attempt to understand mechanics in the nineteenth century. The terms mechanics and mechanical world view were being used as general descriptions of nineteenth-century physicists' assumptions and interpretations of nature. However, there were no studies of the particulars of these assumptions or the range and content of these interpretations. Rene Dugas' work on classical mechanics focused on France. The search for the particulars of these forms of "mechanics" led me to explore precisely what mechanics meant to physicists of a century and more ago. However, none of Lagrange's, Hamilton's, or Jacobi's "mechanics," while ele gant, fits easily within the history of physics. Lagrange reduced mechanics to an exercise in analysis; Hamilton and Jacobi used mechanics to explore solutions to partial differential equations. They were mathematicians doing mathematics. As I went deeper into the matter it became obvious that, in the nineteenth century, there were two kinds of mechanics, each containing a variety of forms, one physical, the other mathematical. There were a group of men using mechanics to understand nature and another group using the equations of mechanics to explore the calcu lus. However, when tracing these two traditions back into the eighteenth century, physics disappeared altogether."

Recenzje

"Garber discusses an interesting part of scientific development, using examples of theoretical physics and their historical steps."

---Mathematical Reviews

"Garber argues her case convincingly... A very valuable addition to the existing literature on the history of modern physics. The book is also well written... Those who make an effort to follow the argument will gain many new insights and obtain a fresh outlook at the mathematization of physics in the 18th and 19th centuries."

---Physics World

Spis treści

I: Introduction.- Mathematics and Modern Physics.- Modern Physics.- Earlier Historical Approaches to Modern Physics.- Mathematics as Language.- Organization of the Text.- I: Eighteenth-Century Science.- II: Vibrating Strings and Eighteenth-Century Mechanics.- Mathematics from Physics.- Ignoring Physics.- Eighteenth-Century Mechanics and the History of Physics.- III: Eighteenth-Century Physics and Mathematics: A Reassessment.- Physics as Experimental Philosophy.- The Practice of Mathematics.- The Intellectual Geography of Physics and Mathematics.- The Social Geography of Physics and Mathematics.- II: Transitions, 1790–1830.- IV: “Empirical Literalism”: Mathematical Versus Experimental Physics in France, 1790–1830.- Changes in Social Geography, 1790–1830.- Experimental Physics.- Electricity and Magnetism.- Heat.- Light and Elasticity.- French Mathematics and Physics c. 1830: Some Conclusions.- V: On the Margins: Experimental Physics and Mathematics in the German States, 1790–1830.- Prologue.- Physics and Mathematics in the German States, 1790–1830.- University Reform and Career Opportunities.- Changes in Physics in the 1820s.- Changes in Mathematics in the 1820s.- VI: On the Margins: Experimental Philosophy and Mathematics in Britain, 1790–1830.- Social Institutions.- Natural Philosophy and the Universities.- Intellectual Organization of Research, 1800–1820.- Mathematics in Britain, 1790–1820.- Natural Philosophy and Mathematics in the 1820s.- III: Transformations, 1830–1870.- VII: From Natural Philosophy and “Mixed Mathematics” to Theoretical and Experimental Physics: Britain, 1830–1870.- Keywords.- The Crucial Turn: the 1830s.- Cambridge University, the Cambridge Mathematical Journal, and Theoretical Physics.- William Thomson.- George Gabriel Stokes.- James Clerk Maxwell.- VIII: Physics and Mathematics in the German States, 1830–1870.- Mathematical Physics as Mathematics.- The Transformation of Physics: The First Generation.- Franz Neumann.- Wilhelm Weber.- Clausius and Helmholtz.- IV: Conclusions and Epilogue.- IX: Physics About 1870 and the “Decline” of French Physics.- The “Decline” of French Physics.- Some Conclusions.- X: Epilogue: Forging New Relationships: 1870–1914.- The Limitations of Autonomy.- Mathematics in Physics.- Beyond the Calculus.- Physicists Versus Mathematicians.

Blurb

This work is the first explicit examination of the key role that mathematics has played in the development of theoretical physics and will undoubtedly challenge the more conventional accounts of its historical development. Although mathematics has long been regarded as the "language" of physics, the connections between these independent disciplines have been far more complex and intimate than previous narratives have shown.

This study encompasses engagements across discipline boundaries and many nations rom the ear of Euler and Bernoulli o that of Hilbert and Einstein. At all times physicists and mathematicians retained their distinct sets of disciplinary standards and goals. Interactions within historical ears are handled using the standards of the time to define mathematics and physics. In this context, the works of Lagrange, Laplace, Fourier, Jacobi, William Thomson, Maxwell, Helmholtz, and many others are discussed, and by 1870, it is evident that the essentials of modern theoretical physics are in place. The epilogue, spanning the decades from 1870 to the First World War, deals with the decline of these interactions and the building of new connections. It is particularly significant that these new patterns of interactions became paradigmatic for the rest of the twentieth century.

The unique perspectives concerning the history of theoretical physics will undoubtedly cause some raised eyebrows, as the author convincingly demonstrates that practices, methods, and language shaped the development of the field, and are a key to understanding the mergence of the modern academic discipline. Mathematicians and physicists, as well as historians of both disciplines, will find this provocative work of great interest.