PlanetPhysics/Fermat's Principle

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Fermat's Principle

Initially conceived in optics, Fermat's principle was stated as the principle of least time for traveling light waves, that is the path or paths taken between two points by light which can be traversed in the least time; in an Euclidean space or a flat Minkowski space, this is the straight line defined by a single ray of light. This can be thought as the trajectory of an emitted photon traveling at the universal maximum speed $c$ in vacuum. In a Riemannian or Minkowski spacetime this corresponds to the surface of a light cone.

In general relativity, however, a point particle path is a geodesic curve in a Riemannian space that can be curved, for example, by the presence of intense gravitational fields. One such effect was observed and reported by modern astrophysicists and is called gravitational lensing .