1 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.
1.0.1 Minimum Action Principles in Electromagnetism and Quantum Theories
