Changes

The '''Principle of Least Action''' was orginally formulated by Pierre Louis Maupertuis, who believe that nature must always operate in the most efficient way possible, so all laws of nature should be described as the minimization of a certain [[quantity]].  Pierre Louis Maupertuis considered the Principle of Least Action as a proof that God exists.{{fact}}

The '''Principle of Least Action''' was originally formulated by Pierre Louis Maupertuis, who believe that nature must always operate in the most efficient way possible, so all laws of nature should be described as the minimization of a certain [[quantity]].  Pierre Louis Maupertuis considered the Principle of Least Action as a proof that God exists.{{fact}}

In [[classical mechanics]], the Least Action Principle states that the motion of a particle along some path always minimize the difference between its [[kinetic energy]] and its [[potential energy]].  Mathematically, the motion of a particle always minimizes the Lagragian action functional.

In [[classical mechanics]], the Least Action Principle states that the motion of a particle along some path always minimize the difference between its [[kinetic energy]] and its [[potential energy]].  Mathematically, the motion of a particle always minimizes the Lagrangian action functional.

In [[General Relativity]], the Least Action Principle states that the motion of a particle on a [[surface]] M must be a [[geodesic]] of M, so it must minimize the geodesic functional. Additionally, the [[Einstein]] field equations follow from applying the principle of least action to the action functional <math>\int R_{g}d\mathrm{vol}_g</math>, where the minimization takes place over the space of [[metric]]s <math>g</math> on spacetime, and <math>R_g</math> denotes the scalar [[curvature]] of the metric.

In [[General Relativity]], the Least Action Principle states that the motion of a particle on a [[surface]] M must be a [[geodesic]] of M, so it must minimize the geodesic functional. Additionally, the [[Einstein]] field equations follow from applying the principle of least action to the action functional <math>\int R_{g}d\mathrm{vol}_g</math>, where the minimization takes place over the space of [[metric]]s <math>g</math> on spacetime, and <math>R_g</math> denotes the scalar [[curvature]] of the metric.