What is the principle of least action in physics?

The principle of least action is a fundamental variational principle used to derive the equations of motion for physical systems without relying on vectors or forces. By examining an energy function called a Lagrangian, it evaluates the accumulated value of energy along a path to determine the true trajectory. This powerful concept spans classical mechanics, general relativity, and Feynman's formulation of quantum mechanics.

What we know

• The principle of least action applies the calculus of variations to an accumulated energy function called the action, allowing the derivation of equations of motion without using vectors or forces. [1, 2]
• Action is a mathematical functional taking a system's trajectory as its argument and returning a real number, with units of energy multiplied by time. [3]
• Hamilton's principle states that physical system dynamics are determined by a variational problem based on a single function, the Lagrangian. [4]
• Quantum action principles generalize and justify older classical principles by showing they directly result from quantum interference patterns. [2] · medium confidence

Where to go next

• how it workedHow does the Lagrangian describe a mechanical system?
• the bigger pictureWhat role does action play in Feynman's quantum mechanics?
• whoWho was William Rowan Hamilton?
• a case in pointHow are action principles applied in general relativity?
• whenHow did Joseph-Louis Lagrange develop analytical mechanics?
• an unexpected connectionHow does the Planck constant share units with physical action?The action of a physical system shares the exact same SI units of joule-seconds as the Planck constant, marking the scale where quantum effects become significant.

Sources

• [1]principle of least action (Wikidata Q722799) · CC0 1.0
• [2]Action principles · CC BY-SA 4.0
• [3]Action (physics) · CC BY-SA 4.0
• [4]Hamilton's principle · CC BY-SA 4.0
• [5]Lagrangian mechanics · CC BY-SA 4.0