| 21. | The previous derivatives are consistent with the energy operator, corresponding to the time derivative,
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| 22. | Then the two terms which contain time derivatives can be combined into a single term.
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| 23. | Let \ dot { x } denote the time derivative of the constant mode x.
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| 24. | Another result from the Legendre transformation relates the time derivatives of the Lagrangian and Hamiltonian:
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| 25. | Where the dot represents a time derivative.
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| 26. | The above inner product can also be written in terms of and its time derivative.
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| 27. | And taking the total time derivative of the second equation and equating to the first.
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| 28. | The remaining 3 Einstein equations contain only first order time derivatives of the metric tensor.
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| 29. | When talking about a time derivative, a better analogy would be velocity and acceleration.
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| 30. | This wave equation incorporates fractional time derivatives:
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