Abstract
The symmetry of time reversal is one of the basic symmetries considered in the natural sciences. It occurs in many physical dynamic systems, in particular, in classical and relativistic mechanics and electrodynamics. These consider the time conception, time translation invariance, and time-reversal symmetry. It was shown that the symmetry under time translation, which is a manifestation of the time homogeneity, is stipulated by the law of conservation of total energy of a closed system. This is proved in the Lagrange formalism of classical mechanics, as well as on the basis of Nöether’s theorem in the case of Einstein’s special relativity.
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Notes
- 1.
Lagrangian \(\mathcal {L}\) is a functional, so (strongly speaking) its dependence on generalized coordinates \(q_{k}\), generalized velocities \( \overset{\cdot }{q}_{k}\)and time t should be notated as \(\mathcal {L}[q_{k}, \overset{\cdot }{q}_{k}, t]\).
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Geru, I.I. (2018). Time Reversal in Classical and Relativistic Physics. In: Time-Reversal Symmetry. Springer Tracts in Modern Physics, vol 281. Springer, Cham. https://doi.org/10.1007/978-3-030-01210-6_1
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DOI: https://doi.org/10.1007/978-3-030-01210-6_1
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Online ISBN: 978-3-030-01210-6
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