In physics, action is a fundamental concept in the formulation of mechanics, especially in Lagrangian mechanics. It is defined as the integral of the Lagrangian (kinetic energy minus potential energy) over time:
Action (S) = ∫ L dt
According to the principle of least action, the actual path taken by a physical system between two states is the one that minimizes (or extremizes) the action. This principle determines the system’s dynamics and leads directly to the Euler–Lagrange equations, which govern the motion.
Key Ideas:
- Action is a scalar quantity with units of energy × time.
- The “least” action doesn’t always mean the absolute minimum—it refers to a path where the action is stationary (no small variation changes it).
- Provides a unified approach to classical mechanics, optics, quantum mechanics, and relativity.
Examples:
- In optics, light takes the path of least time (Fermat’s principle), which is a special case of the principle of least action.
- In quantum mechanics, the action appears in Feynman’s path integral formulation, where all possible paths are summed, but those near the classical path contribute most.
The concept of action lies at the heart of modern theoretical physics, revealing how nature optimizes motion and connecting deeply to symmetry, conservation laws, and quantum behavior.