Principle of Least Action

The Principle of Least Action is an assumption of efficient motion in physics whereby a particle of fixed overall potential and kinetic energy follows the path that minimizes its action. This principle is remarkably productive in modern physics because it does not depend on vectors or forces, and tends to be independent of coordinate systems. The Parable of the Vineyard Workers is Biblical scientific foreknowledge by foreshadowing this powerful principle of modern physics.

The principle predicts behavior based on energy, not forces, and actions rather than points. A central equation to this approach integrates over time, for a particular path, the difference between kinetic and potential energies.

Variations on this principle include the following insights that:

• a multi-body system will come to rest at a position that minimizes overall potential energy.
• light takes the shortest path to travel between two points

This principle is a physical extension of the Euclidean theorem that the shortest distance between two points is a straight line.

The doctoral thesis of physicist Richard Feynmann applied the Principle of Least Action to quantum mechanics, and later built on that work to generate "Feynman diagrams," for which he won a shared Nobel Prize.

See also

• Lagrangian
• Stationary Action explained