principle of least action
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The principle of least action is a fundamental concept in physics that describes the motion of a dynamic system. It posits that for a spontaneous process without change in total energy, the system will follow a path where the "action" is minimized. Action can be understood as a quantity related to the system's energy and the time or distance it travels.12
This principle is a generalization of earlier ideas, such as Fermat's principle of least time for light, which states that light travels between two points along the path that requires the least time. In mechanics, the principle of least action, more accurately described as stationary action, implies that a system's actual motion between two configurations is one where the action is either a minimum or a maximum. This concept became even more significant with the advent of quantum theory, where actions are restricted to whole-number multiples of Planck's constant.32
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mathematicsMathematical physics…extremal principles (such as the principle of least action). The extremal principle usually yields information about an integral involving the sought-for function, hence the name integral equation. Hilbert’s contribution was to bring together many different strands of contemporary work and to show how they could be elucidated if cast in…
Read More…extremal principles (such as the principle of least action). The extremal principle usually yields information about an integral involving the sought-for function, hence the name integral equation. Hilbert’s contribution was to bring together many different strands of contemporary work and to show how they could be elucidated if cast in…
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principles of physical scienceManifestations of the extremal principle…extremal principle in mechanics, the principle of least action, was proposed by the French mathematician and astronomer Pierre-Louis Moreau de Maupertuis but rigorously stated only much later, especially by the Irish mathematician and scientist William Rowan Hamilton in 1835. Though very general, it is well enough illustrated by a simple…
Read More…extremal principle in mechanics, the principle of least action, was proposed by the French mathematician and astronomer Pierre-Louis Moreau de Maupertuis but rigorously stated only much later, especially by the Irish mathematician and scientist William Rowan Hamilton in 1835. Though very general, it is well enough illustrated by a simple…
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Richard Feynman…quantum mechanics governed by the principle of least action. This approach replaced the wave-oriented electromagnetic picture developed by James Clerk Maxwell with one based entirely on particle interactions mapped in space and time. In effect, Feynman’s method calculated the probabilities of all the possible paths a particle could take in…
Read More…quantum mechanics governed by the principle of least action. This approach replaced the wave-oriented electromagnetic picture developed by James Clerk Maxwell with one based entirely on particle interactions mapped in space and time. In effect, Feynman’s method calculated the probabilities of all the possible paths a particle could take in…
Read More- Pierre-Louis Moreau de Maupertuis
In 1744 Maupertuis enunciated the principle of least action, later published in his Essai de cosmologie (1750; “Essay on Cosmology”). It states simply 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…
Read MoreIn 1744 Maupertuis enunciated the principle of least action, later published in his Essai de cosmologie (1750; “Essay on Cosmology”). It states simply 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…
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