8.3 Conclusions
The subject of this note has been a small historical thread in the long and complex story of the status of energy conservation in General Relativity, concerning two related claims made by Klein and Hilbert: that the energy conservation law is an identity in generally covariant theories, and that this marks a contrast with other (earlier) theories. Both these claims were disputed by Einstein. We have seen how three theorems proved by Noether and Klein can be brought to bear on this disagreement, showing that:
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Klein’s worry over the physical significance of the energy conservation law in General Relativity was perhaps not adequately addressed by Einstein, even though in the end we side with Einstein against Klein, and
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the possibility of re-writing the energy conservation law in the form that so worried Klein does indeed depend upon the local symmetry structure of General Relativity.
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References
Barbashov, B. M., and Nesterenko, V. V. (1983). Continuous Symmetries in Field Theory. Fortschritte. der Physik 31, 535–567.
Brading, K., and Brown, H. R. (2003a). Symmetries and Noether’s theorems. In Symmetries in Physics: Philosophical Reflections. Katherine Brading and E. Castellani, eds. Cambridge University Press.
Brading, K., and Brown, H. R. (2003b): Noether’s Theorems, Gauge Symmetries, and General Relativity. Manuscript.
Brown, H. R. and Brading, K. (2002). General Covariance from the Perspective of Noether’s Theorems. Diálogos 79, 59–86.
Deser, S. (1972). Note on current conservation, charge, and flux integrals. American Journal of Physics 40, 1082–1084.
Earman, J. (2003). Tracking down gauge: an ode to the constrained Hamiltonian formalism. In Symmetries in Physics: Philosophical Reflections. Katherine Brading and E. Castellani, eds. Cambridge University Press.
Einstein, A. (1916). Die Grundlagen der allgemeinen Relativitätstheorie. Annalen der Physik 49, 769–822. Translated as The Foundation of the General Theory of Relativity in The Principle of Relativity. H. A. Lorentz et al. Eds. Dover, New York, 111–164.
Einstein, A. (1998). The Collected Papers of Albert Einstein, vol. 8, R. Schulmann et al. eds. Princeton University Press, Princeton, New Jersey.
Hilbert, D. (1916). Die Grundlagen der Physik. (Erste Mitteilung.). Königliche Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-physikalische Klasse. Nachrichten, 395–407.
Klein, F. (1917). Zu Hilberts erster Note über die Grundlagen der Physik. Königliche Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-physikalische Klasse. Nachrichten, 469–82.
Klein, F. (1918). Über die Differentialgesetze für die Erhaltung von Impuls und Energie in der Einsteinschen Gravitationstheorie. Königliche Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-physikalische Klasse. Nachrichten 171–89. Translated by J. Barbour as “On the Differential Laws for Conservation of Momentum and Energy in Einstein’s Theory of Gravitation,” ms.
Noether, E. (1918). Invariante Variationsprobleme. Königliche Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-physikalische Klasse. Nachrichten, 235–57. Translated by M. A. Tavel (1971) as “Noether’s Theorem” In Transport Theory and Statistical Physics. 1, 183–207. Page numbers refer to the English translation.
Rowe, D. (1999). The Göttingen Response to General Relativity and Emmy Noether’s Theorems. In The Symbolic Universe: Geometry and Physics 1890–1930. J. Gray, ed. Oxford University Press, Oxford.
Sauer, T. (1999). The Relativity of Discovery: Hilbert’s First Note on the Foundations of Physics. Archive for History of. Exact Sciences 53, 529–75.
Trautman, A. J. (1962). Conservation Laws in General Relativity. In Gravitation: an Introduction to Current Research. L. Witten, ed. Wiley, New York.
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Brading, K. (2005). A Note on General Relativity, Energy Conservation, and Noether’s Theorems. In: Kox, A.J., Eisenstaedt, J. (eds) The Universe of General Relativity. Einstein Studies, vol 11. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4454-7_8
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