Difference between revisions of "Principle of Least Action"
(Mathematical rigor was added to this concept in 1835 by the Irish mathematician and scientist William Rowan Hamilton.) |
(The brilliant and colorful Richard Feynmann devoted one of his famous lectures to this, as "entertainment" separate from his other lectures.) |
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Mathematical rigor was added to this concept in 1835 by the Irish mathematician and scientist William Rowan Hamilton. | Mathematical rigor was added to this concept in 1835 by the Irish mathematician and scientist William Rowan Hamilton. | ||
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| + | The brilliant and colorful Richard Feynmann devoted one of his famous lectures to this, as "entertainment" separate from his other lectures.<ref>https://www.feynmanlectures.caltech.edu/II_19.html#:~:text=%E2%80%9CSo%2C%20for%20a%20conservative%20system,minimum%E2%80%94maybe%20it's%20a%20maximum.</ref> | ||
== See also == | == See also == | ||
*[[Lagrangian]] | *[[Lagrangian]] | ||
Revision as of 03:26, August 21, 2024
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.
| “ | Basically, without outside intervention, objects travel along the path of least resistance and least change. This is called the principle of least action. We know it applies in our everyday world, and now—thanks to a new study—we know it applies in the quantum world as well.[1] | ” |
History
This principle was first proposed in 1744 by the French cosmologist Pierre-Louis Moreau de Maupertuis (1698-1759, after settling in Basel, Switzerland), who declared in Essai de cosmologie (1750; “Essay on Cosmology”) that “in all the changes that take place in the universe, the sum of the products of each body multiplied by the distance it moves and by the speed with which it moves is the least [that is] possible.”[2]
Mathematical rigor was added to this concept in 1835 by the Irish mathematician and scientist William Rowan Hamilton.
The brilliant and colorful Richard Feynmann devoted one of his famous lectures to this, as "entertainment" separate from his other lectures.[3]
See also
References
- ↑ https://www.popularmechanics.com/science/a43981125/principle-of-least-action-demonstrated-in-quantum-realm/
- ↑ https://www.britannica.com/biography/Pierre-Louis-Moreau-de-Maupertuis#ref9124
- ↑ https://www.feynmanlectures.caltech.edu/II_19.html#:~:text=%E2%80%9CSo%2C%20for%20a%20conservative%20system,minimum%E2%80%94maybe%20it's%20a%20maximum.