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Register a new userEmmy Noether on Energy Conservation in General Relativity
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David E. Rowe
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During the First World War, the status of energy conservation in general relativity was one of the most hotly debated questions surrounding Einsteins new theory of gravitation. His approach to this aspect of general relativity differed sharply from another set forth by Hilbert, even though the latter conjectured in 1916 that both theories were probably equivalent. Rather than pursue this question himself, Hilbert chose to charge Emmy Noether with the task of probing the mathematical foundations of these two theories. Indirect references to her results came out two years later when Klein began to examine this question again with Noethers assistance. Over several months, Klein and Einstein pursued these matters in a lengthy correspondence, which culminated with several publications, including Noethers now famous paper Invariante Variationsprobleme. The present account focuses on the earlier discussions from 1916 involving Einstein, Hilbert, and Noether. In these years, a Swiss student named R.J. Humm was studying relativity in Gottingen, during which time he transcribed part of Noethers lost manuscript on Hilberts invariant energy vector. By making use of this 9-page manuscript, it is possible to reconstruct the arguments Noether set forth in response to Hilberts conjecture. Her results turn out to be closely related to the findings Klein published two years later, thereby highlighting, once again, how her work significantly deepened contemporary understanding of the mathematical underpinnings of general relativity.
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