remark 23.45 Why this is not an analogy

open in the book · parts/03-classical-mechanics/06-hamilton-jacobi.tex:1503 · p. 840

remark -- no derivation owed by its kind

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depends_on proposition 23.44 Relativistic Hamilton–Jacobi equation ¶
- depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶
  - depends_on definition 13.48 Differentiable manifold ¶
    - depends_on definition 13.47 Differentiable structure ¶
      - depends_on definition 13.44 Atlas ¶
  - depends_on definition 13.84 Tensor ¶
    - depends_on definition 13.83 Covector ¶
      - depends_on definition 13.81 Vector on a manifold ¶
    - depends_on definition 13.81 Vector on a manifold ¶ ↺
- depends_on equation 23.2 eq:hj-equation ¶
- depends_on equation 40.5 eq:rdyn-dispersion ¶
- proves proof ch:06-hamilton-jacobi@proof-13 ¶
depends_on theorem 23.40 Eikonal and transport equations ¶
- depends_on definition 23.39 Eikonal ¶
  - depends_on definition 16.103 Optical path length; Fermat's principle ¶
    - depends_on equation 16.89 eq:calcvar-optical-length ¶
    - depends_on lemma 16.100 The ray equation ¶
      - depends_on equation 16.30 eq:calcvar-euler-lagrange-system ¶
      - depends_on equation 16.89 eq:calcvar-optical-length ¶ ↺
      - proves proof ch:14-calculus-of-variations@proof-47 ¶
  - depends_on equation 10.25 eq:pde-helmholtz-equation ¶
- depends_on equation 23.63 eq:hj-helmholtz-medium ¶
- proves proof ch:06-hamilton-jacobi@proof-11 ¶

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type	direction	node	provenance	where
`depends_on`	→	Relativistic Hamilton–Jacobi equation	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1516
`depends_on`	→	Eikonal and transport equations	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1516