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Euler As Physicist Dieter Suisky Euler as Physicist Dieter Suisky Euler as Physicist 123 Dr. Dr. Dieter Suisky Humboldt-Universitat¨ zu Berlin Institut fur¨ Physik Newtonstr. 15 12489 Berlin Germany [email protected] ISBN: 978-3-540-74863-2 e-ISBN: 978-3-540-74865-6 DOI 10.1007/978-3-540-74865-6 Library of Congress Control Number: 2008936484 c Springer-Verlag Berlin Heidelberg 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper 987654321 springer.com Preface In this book the exceptional role of Leonhard Euler in the history of science will be analyzed and emphasized, especially demonstrated for his fundamental contri- butions to physics. Although Euler is famous as the leading mathematician of the 18th century his contributions to physics are as important and rich of new methods and solutions. There are many books devoted to Euler as mathematician, but not as physicist. In the past decade, special attention had been directed at the development of science in the 18th century. In three distinguished tercentenary celebrations in oc- casion of the births of Pierre Louis Moreau de Maupertuis (1698–1759), Emilie du Chateletˆ (1706–1749) and Leonhard Euler (1707–1783) the merits of these scholars for the development of the post-Newtonian science had been highly acknowledged. These events were not only most welcome to remember an essential period in the past, but are also an opportunity to ask for the long lasting influence on the further development of science until present days. Euler’s contributions to mechanics are rooted in his program published in two volumes entitled Mechanics or the science of motion analytically demonstrated very early in 1736. The importance of Euler’s theory results from the simultaneous de- velopment and application of mathematical and physical methods. It is of particular interest to study how Euler made immediate use of his mathematics for mechanics and coordinated his progress in mathematics with his progress in physics. Euler’s mechanics is not only a model for a consistently formulated theory, but allows for generalizations of Euler’s principles. Though his pioneering work on mechanics had an essential influence in the 18th century, its impact on the 19th century was obscured by the overwhelming success of his mathematical writings. Euler anticipated Mach’s later criticism of absolute motion and Einstein’s assumption on the invariance of the equation of motion in in- ertial systems. It will be demonstrated that even problems in contemporary physics may be advantageously reconsidered and reformulated in terms of Euler’s early uni- fied approach. The interplay between physics and mathematics which appeared in the 18th century will be compared to the development of physics in the 20th century, especially to the development of quantum mechanics between 1900 and 1930. The reader of Euler’s works benefits from his unique ability to preserve math- ematical rigour in the analytical formulation of physical laws. The principles and v vi Preface methods found in the original sources may be advantageously compared to later developments, interpretations and reformulations. The extraordinary power of Eu- ler’s program and legacy is due to the successful frontier crossing between different disciplines presented in an exemplarily clear terminology. I am grateful to those individuals who draw my attention to Euler’s original work and its contemporary interpretation. I would like especially to thank Dr. Hartmut Hecht (Berlin-Brandenburgische Akademie der Wissenschaften), Dr. Peter Enders (Berlin), Dr. Peter Tuschik (Hum- boldt University, Berlin), Dr. Rudiger¨ Thiele (University of Leipzig), Prof. Robert E. Bradley (Adelphi University, Garden City), Prof. C. Edward Sandifer (Western Con- necticut State University), Prof. Heinz Lubbig¨ (Berlin), Prof. Eberhard Knobloch (Technical University Berlin), Prof. Ruth Hagengruber (University of Paderborn), Dr. Andrea Reichenberger (University of Paderborn) and Prof. Brigitte Falkenburg (University of Dortmund) for many stimulating and encouraging discussions. In particular, I am indebted to Prof. Wolfgang Nolting (Humboldt University, Berlin) for stimulating support over a period of years. Finally, I would like to thank my wife Ingrid Suisky for rendering every help in preparing the manuscript. Berlin Dieter Suisky Introduction Read Euler, read Euler, he is the master of us all. Laplace Euler began his extraordinary scientific life in the third decade of the 18th cen- tury and spent most of his career working in St. Petersburg and Berlin.1 His first paper was published in 1726, the last paper of his writings only in the mid of the 19th century. For his scientific career he was well prepared and educated by Johann Bernoulli who introduced him in mathematics by personal supervision2 since 1720. His close relations to the Bernoulli family, especially to the older sons of Johann Bernoulli, let him finally settle in St. Petersburg3 in 1727. In this time, the scientific community was involved in controversial debates about basic concepts of mechanics like the nature of space and time and the measure of living forces, the priority in the invention of the calculus and the application of the calculus to mechanics. The promising Newton-Clarke-Leibniz debate between 1715 and 1716 was truncated by the death of Leibniz in 1716. The letters on the basic principles of natural philosophy exchanged by him with Clarke published in 1717 [Leibniz Clarke] can be considered as a collection and listing of solved and 1 Euler lived from 1707 to 1727 in Switzerland. In Basel, he studied mathematics under the su- pervision of Johann Bernoulli (1667–1748). From 1727 to 1740 Euler worked in St. Petersburg. Euler grew up together with Daniel Bernoulli (1700–1782), Nikolaus II Bernoulli (1695–1726) and Johann II Bernoulli (1710–1790) Bernoulli, the sons of Johann Bernoulli. The change of Euler to St. Petersburg was mainly stimulated by the leave of Daniel Bernoulli who went to St. Petersburg as a professor of mathematics in 1725. After a successful and fruitful period in St. Petersburg Euler spent the decades from 1741 to 1766 in Berlin before he went back to St. Petersburg (1766–1783). Essential contributions of Euler to mechanics were published during Berlin period between 1745 and 1765. 2 “A. 1720 wurde ich ich bey der Universitat¨ zu den Lectionibus publicis promovirt: wo ich bald Gelegenheit fand, dem beruhmten¨ Professori Johanni Bernoulli bekannt zu werden, welcher sich ein besonderes Vergnugen¨ daraus machte, mir in den mathematischen Wissenschafften weiter fortzuhelfen. Privat Lectionen schlug er mir zwar (...) ab: er gab mir aber (...) alle Sonnabend Nachmittageinen freyen Zutritt bey sich, und hatte die Gute¨ mir die gesammlete Schwierigkeiten zu erlautern,¨ (...).” [Fellmann (Row)] Euler dictated the autobiography to his son Johann Albrecht in the second Petersburg period. 3 “Um dieselbige Zeit wurde die neue Akademie (...) in St. Petersburg errichtet, wohin die bey- den altesten¨ Sohne¨ des H. Johannis Bernoulli beruffen wurden; da ich denn eine unbeschreibliche Begierde bekam mit denselben zugleich A. 1725 nach St. Petersburg zu reisen.” [Fellmann (Row)] vii viii Introduction unresolved problems in mechanics and philosophy. One of the crucial points is the debate on the nature of time, space and motion. This listing will be completed by the problems originating from the controversy on the priority of the invention of the calculus which had been initiated by British scientists in 1690’s and continued until 1711 [Meli]. Furthermore, the scientific community was involved in the long-lasting debate on the true measure of living forces and, as a consequence, split into differ- ent schools. The post-Newtonian scientists were confronted with a legacy rich of new methods and solutions of old problems, but also rich of open questions and had to struggle with a collection of most complicated problems which were, moreover, closely interrelated preventing from the very beginning a merely partial solution. Nevertheless, such partial solutions were constructed by the several schools which had been appeared, established and settled preferentially in France, England and Germany.4 The debate was dominated by these schools, the Cartesians, the Newto- nians and the Leibnizians, respectively. The common problem was to find a way out from the merging of scientific and non-scientific problems. All the scientists were involved in the controversies as Euler reported 30 year later [Euler, E343].5 The leading scientist decided it is necessary to reconsider the legacy of their predecessors without prejudice, i.e. independently of the country where it was produced (compare [Chatelet,ˆ Institutions]). Voltaire did a great work to accustom people in France to the ideas of Newton [Voltaire, El´ emens].´ Wolff was interesting in that his system becomes popular in France. The profound education Euler received from Johann Bernoulli is not the only long lasting influence on his thinking and life. There is also the personal and sci- entific relation to Daniel Bernoulli which was of great influence on the scientific biography of Euler. The concept of his program for mechanics published in the Mechanica may be related to the discussion on the status of the basic law of me- chanics which had been later called Principe gen´ eral´ et fondamental de toute la mecanique´ by Euler [Euler E177].
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