Principle of Least Action

The Principle of Least Action is the foundational variational principle of physics, stating that the actual path taken by a system between two states is the one for which the action integral is stationary. First formulated by Pierre-Louis Moreau de Maupertuis in 1744 and later refined by Euler, Lagrange, and Hamilton, the principle unifies classical mechanics, electromagnetism, and general relativity under a single mathematical framework. It reveals that physical systems do not follow laws step by step but select entire trajectories by optimizing a global quantity — a formal echo of teleology in the heart of physics. The principle was Richard Feynman's starting point for the path integral formulation of quantum mechanics, in which all possible paths contribute to the quantum amplitude, with the classical path emerging as the dominant contribution.