will be "asymptotically integrable", that is to say, if we displace a vector parallel to itself along a closed curve whose total length is proportional to r, then, as we remove the curve to infinity, the change of the vector that results from the circuit about the curve will tend to zero. In the presence of gravitational radiation the total energy will not be con served, because the waves carry some energy with them; analogous statements apply to the linear momentum, etc. But that is not all; if there is no coordinate 2 system in which the field strengths drop off as 1/r , then there is no possibility to generate out of one vector" at infinity" a whole field of parallel vectors" at infinity". Thus we are unable in the presence of radiation to define, even at infinity, a "rigid displacement", the type of coordinate transformation that is presumably generated by the energy integral. Under these circumstances it is very difficult to see how one can define the "free vector" energy -linear momen tum in a convincing manner. These ambiguities of course do not imply that general relativity lacks quan tities that obey equations of continuity; rather, general relativity suffers in this respect from an embarras de richesse. There is an infinity of such quantities, and our difficulty is to single out a subset and to present these as the "natural" l expressions for energy, linear momentum, etc.
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Three quarters of a century elapsed between Ampere's definition of electrodynamics and Einstein's reform of the concepts of space and time. The two events occurred in utterly different worlds: the French Academy of Sciences of the 1820s seems very remote from the Bern Patent Office of the early 1900s, and the forces between two electric currents quite foreign to the optical synchronization of clocks. Yet Ampere's electrodynamics and Einstein's relativity are firmly connected through a historical chain involving German extensions of Ampere's work, competition with British field conceptions, Dutch synthesis, and fin de siecle criticism of the aether-matter connection. Olivier Darrigol retraces this intriguing evolution, with a physicist's attention to conceptual and instrumental developments, and with a historian's awareness of their cultural and material embeddings. This book exploits a wide range of sources, and incorporates the many important insights of other scholars. Thorough accounts are given of crucial episodes such as Faraday's redefinition of charge and current, the genesis of Maxwell's field equations, and Hertz's experiments on fast electric oscillations. Thus there emerges a vivid picture of the intellectual and instrumental variety of nineteenth-century physics. The most influential investigators worked at the crossroads between different disciplines and traditions: they did not separate theory from experiment, they frequently drew on competing traditions, and their scientific interests extended beyond physics into chemistry, mathematics, physiology, and other areas. By bringing out these important features, this book offers a tightly connected and yet sharply contrasted view of early electrodynamics. Olivier Darrigol is a Research Director at the Centre National de la Recherche Scientifique, Paris. His research focuses on the history of quantum theory and of electrodynamics.