The principle of least action, or more generally the principle of stationary action, is a fundamental concept in classical mechanics and is also employed in quantum field theory. It states that the path taken by a physical system between two points in spacetime is the one for which the action integral is stationary, meaning that small variations in the path do not change the value of the action to first order.
In classical mechanics, the principle of least action has been extensively verified through empirical observations. It provides a concise and elegant formulation of the laws of motion, encompassing Newton's laws as a special case. By minimizing the action, one can derive the equations of motion for a wide range of physical systems.
In quantum field theory, the principle of stationary action is applied within the framework of the path integral formulation. Richard Feynman developed the path integral approach, which involves summing over all possible paths of a particle or field, each weighted by a phase factor. The path with the stationary action contributes most dominantly to the sum.
From a theoretical perspective, the principle of least/stationary action is deeply connected to the mathematical structure of classical and quantum mechanics. It arises as a consequence of variational principles and the mathematical properties of Lagrangian and Hamiltonian formalisms. The principle has been found to be consistent with a wide range of physical phenomena and has yielded successful predictions in various domains.
However, it's important to note that the principle of least/stationary action is based on our current understanding and mathematical models of the universe. As with any scientific principle, it is subject to future refinement or revision if new evidence or theoretical advancements emerge. Nevertheless, its empirical success and mathematical elegance provide strong support for its validity in describing the behavior of physical systems.