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# Topic: Principle of least action

 Action (physics) - Wikipedia, the free encyclopedia In physics, the action is an integral quantity that is used to determine the evolution of a physical system between two defined states using the calculus of variations. The action is usually an integral over time, but may be integrated over spatial variables as well (for action pertaining to fields); in still other cases, the action is integrated along the path followed by the physical system. The action corresponding to the various paths is used to calculate the path integral, that gives the probability amplitudes of the various outcomes. en.wikipedia.org /wiki/Action_(physics)   (1781 words)

 Principle of least action - Wikipedia, the free encyclopedia In physics, the principle of least action or principle of stationary action is a variational principle by which, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system. The principle remains central in modern physics and mathematics, being applied in the theory of relativity, quantum mechanics and quantum field theory, and a focus of modern mathematical investigation in Morse theory. By contrast, the action principle is not localized to a point; rather, it involves integrals over an interval of time and (for fields) extended region of space. en.wikipedia.org /wiki/Principle_of_least_action   (1482 words)

 The Principle of the least action, the universal law of motion and posology. By Bernhardt FINCKE Nay, the very principle of conservation of forces itself is only another impersonation of the principle of the least action, for its equivalent nature shows clearly that the conseration is as in all equivalence the least possible action in the given case. We infer from that circumstance, that the universal character of the principle of the Least Action, given to it by its discoverer, is not yet properly understood. The least action in natural processes produces the phenomena which are the objects of Physics, and the least action depending upon the assimilability of substances within infinitesimal limits, belongs to the department of chemics. www.homeoint.org /cazalet/fincke/leastaction.htm   (7254 words)

 Edwin F. Taylor - Principle of Least Action The principle of least action has wide applicability in undergraduate physics education, from mechanics in introductory classes through electricity and magnetism, quantum mechanics, special and general relativity—and it provides a deep foundation for advanced subjects and current research. Heuristic derivations of the Euler-Maupertuis abbreviated action and the Hamilton action. The principle of least action is a powerful addition to upper undergraduate courses for physics majors, modifying the selection of topics and presenting advanced topics in a more contemporary way. www.eftaylor.com /leastaction.html   (998 words)

 Principles of Nature: the principle of least action In my view, Least Action is curiously more powerful as a concept than the concepts of energy it entails (potential and kinetic energy) and perhaps one day the principle of Least Action will be understood in simpler visual mathematical terms and patterns that do not require this 'qualification' mandated by Einstein's theory. There is a fundamental difference in the way Least Action interprets the orbits of planets for example: not as a moment-by-moment thing (as in the Calculus), but as a holistic consideration and summation of all possible paths. Just as in least action, in which time is considered globally (all at once) with a bird's-eye perspective, so resonant scale structures arise through a multiple integrative interactive process in which past and future are equal players.... www.principlesofnature.net /principle_of_least_action.htm   (956 words)

 Principle of Least Action Interactive The worldline you have constructed satisfies the condition of least action for this special case of a worldline of four straight segments equally spaced along the time axis. When the action stops changing as the program hunts, record the value of the action for this worldline and the value of the maximum height of the trajectory. Therefore the principle that the whole path gives a minimum can be stated also by saying that an infinitesimal section of path also has a curve such that it has a minimum action. www.eftaylor.com /software/ActionApplets/LeastAction.html   (1657 words)

 PhilSci Archive - The Principle of Least Action as the Logical Empiricist's Shibboleth The Principle of Least Action as the Logical Empiricist's Shibboleth Stöltzner, Michael (2002) The Principle of Least Action as the Logical Empiricist's Shibboleth. Principle of Least Action, calculus of variations, Hilbert's axiomatic method in physics, Mach-Planck controversy, Logical Empiricism, Moritz Schlick, Hans Hahn, Philipp Frank. philsci-archive.pitt.edu /archive/00000616   (285 words)

 Principle of Least Action (part 4) The uncertainty principle follows from the interplay between the absolute value of the wave function (which describes the density distribution of the particle) and its phase (which describes the time evolution of the particle). The least action principle could be regarded merely as a technique that allows one to incorporate all equations characterizing the theory in a single formula. The reason for that is that we actually know very little about the first principles and so far we have discovered very few fundamental concepts like the principle of least action itself. physics.ucsd.edu /~epivovar/action4.xml   (1344 words)

 13.4.1.2 Hamilton's principle of least action Hamilton's principle of least action states that the trajectory, The ``least'' part of Hamilton's principle is actually a misnomer. It is technically only a principle of ``extremal'' action because (13.130) can also yield motions that maximize the functional. msl.cs.uiuc.edu /planning/node699.html   (534 words)

 bader   (Site not responding. Last check: 2007-10-01) At any particular moment the action might rise or fall, but when the ball arrived at its destination, the path it had followed would always be the path for which the total action was least. It is almost impossible for a physicist to talk about the principle of least action without inadvertently imputing some kind of volition to the projectile. Fermat, in plucking his principle of least time from a pristine mathematical landscape, had found the same law of nature. www.physics.utoledo.edu /~ljc/bader1.html   (663 words)

 sciforums.com - Principle of Least Action? The principle of least action is a well-establish principle in classical mechanics, and has also been applied to quantum mechanics, most notably by Richard Feynman. Action is just another one of these qualities. The amount of 'action' in any action is defined as the object's momentum multiplied by the distance it travels. www.sciforums.com /showthread.php?t=22566   (196 words)

 Whewell on the Principle of Greatest Resulting Good The import of the principle was, that the body would select such a path, and move in such a manner, that the total action which took place in consequence of the body's motion would be smaller than if the body had moved in any other line or in any other manner. The truth and the meaning of this principle were the subject of a long and angry controversy; and, as is usual in such controversies, the meaning of the principle was so modified as to ensure its truth. The principle then was precarious, for every mechanical principle is precarious so long as it rests upon metaphysical reasonings alone, though these may, perhaps, convert known truths into necessary truths:--the principle was of doubtful meaning if true, for its real meaning was only established when its universal truth was proved. branemrys.org /pages/WWPaley.html   (1236 words)

 THE PRINCIPLE OF THE LEAST ACTION, THE UNIVERSAL LAW OF MOTION AND POSOLOGY, By B. FINCKE, M.D. THE PRINCIPLE OF THE LEAST ACTION, THE UNIVERSAL LAW OF MOTION AND POSOLOGY, By B. Bernhardt Fincke. In 1751 Professor Koenig of Franeker, the former pupil of Maupertuis, published in the Acta eruditorum of Leipzig, a letter from Leibnitz to Hermann, which was said to contain already the principle of the least action. The least action in organic bodies by which their organs carry on life is the prerogativ e of Biology. www.minimum.com /reviews/artfin01.htm   (7319 words)

 the principle of least action/time, and geodesics of spacetime the principle of least time for light, which states that light always travels in paths of least time. given the priciple of least action/time, derive that light always travel in geodesics of the space to which it is confined. I think it is interesting that the least action principle for light applies equally well when light moves from one medium to another. www.physicsforums.com /showthread.php?t=1740   (1812 words)

 Principle of Least Action   (Site not responding. Last check: 2007-10-01) One of the fundamental principles of physics which justifies human laziness. Which, BTW, reads "the variation of action must vanish", for all of you that want to spread the secret of inner workings of the Universe to your friends. To say that the page which, dear visitor, you are reading, is created according to the Principle, is to say nothing at all, since (as has been previously been explained) the whole Universe has automatically been created according to the Principle - things simply work in this way. www.princeton.edu /~gtkacik/principle.html   (260 words)

 text5   (Site not responding. Last check: 2007-10-01) It was based on the minimal principle, which was thought to govern the behavior of physical systems from beginning to end by minimizing a certain quantity. Fermat's principle of least time for reflection was the same as Hero's minimal principle. They proposed that all motion and change in matter are ruled by the principle of least action and that everything that happens at the physical level is the expression of a basic unity in Nature. www.scientific-religious.com /text5.html   (983 words)

 Answer 10/02   (Site not responding. Last check: 2007-10-01) In analytical mechanics Newton's laws are reformulated as Hamilton's Principle of Least Action. But the term "Least Action" seems to imply that the path must be a minimum of the functional. On the other hand, if we allow the midpoint to move in the direction perpendicular to the original long arc, the action integral can be made smaller (together with the length of the path). star.tau.ac.il /QUIZ/02/A10.02.html   (470 words)

 HYLE 3 (1997): Ockham's Razor and Chemistry Whoever rechristened the principle of parsimony as Ockham's Razor (the earliest reference appears to be to Etienne Bonnot de Condillac in 1746)[6] was creating an easily imagined image. On the molecular level the mechanism includes, in principle, knowledge of the geometry and relative energy of all structures involved, including isolable or potentially isolable intermediates and transition states, the latter representing the turning points along the minimal energy paths connecting all interconverting species. The forced choice between such descriptions is, at least in some cases, a consequence of drawing a potential energy profile in which there is only a single dimension assigned to the reaction coordinate. www.hyle.org /journal/issues/3/hoffman.htm   (9512 words)

 Refraction Let us postulate that the particles of light follow paths that minimize the time it takes to arrive wherever they are going. This is called the principle of least action. One must keep in mind that this behaviour is very natural for lifeguards, who know where they wish to go and why, but is, to say the least, a bit strange when applied to particles of light. theory.uwinnipeg.ca /mod_tech/node123.html   (521 words)

 Action (and the principle of least of which) Action (and the principle of least of which) is the difference between the perturbed action (the time integral of the above equation) and the reference one, which is just the equation you're asking about. Finding a path of extremal action is just finding a function (or a point in function space) that is an extreme value of the functional (the definite integral). www.physicsforums.com /showthread.php?threadid=98156   (853 words)

 Path Integrals in Quantum Mechanics This is called the Principle of Least Action: for example, the parabolic path followed by a ball thrown through the air minimizes the integral along the path of the action T-V where T is the ball’s kinetic energy, V its gravitational potential energy (neglecting air resistance, of course). If this is the case, then the observed path followed will be just that of least action, for only near that path will the amplitudes add constructively, just as in Fermat’s analysis of light rays. If this action is of order Planck’s constant h, then the phase factor will not oscillate violently on moving to different paths, and a range of paths will contribute. galileo.phys.virginia.edu /classes/752.mf1i.spring03/PathIntegrals.htm   (2178 words)

 CiteULike: Maximum path information and the principle of least action for chaotic system   (Site not responding. Last check: 2007-10-01) On the basis of the assumption that the paths are differentiated by their actions, we show that the maximum path information leads to a path probability distribution as a function of action from which the well known transition probability of Brownian motion can be easily derived. This suggests that the principle of least action, in a probabilistic situation, is equivalent to the principle of maximization of information or uncertainty associated with the probability distribution. An interesting result is that the most probable paths are just the paths of least action. www.citeulike.org /article/497   (271 words)

 No. 2101 Maupertuis In fact, his Principle of Least Action actually gave the same result as Newton's mechanics. He spent the rest of his years trying to apply the Principle of Least Action to explain biology, and life itself. But when the Principle was used in straightforward calculations, it solved real problems. www.uh.edu /engines/epi2101.htm   (594 words)

 UK manifesto: Economy: Principle of least action The same principle applies for all systems and all types of activity, however complex. When this principle was first stated by Maupertius in 1747, he exclaimed at the "divine economy" that nothing in the universe, not even "action", is squandered. This theme of economy in Nature's administration of the universe may be termed the principle of "automation in administration". www.natural-law-party.org.uk /UKmanifesto/economy9.htm   (248 words)

 From counting to abstraction in maths The abstract concept of the unit was a key that opened up thinking as we understand it today. It formed a principle of connection among things that, superficially at least, appeared to be unrelated. The notion of assigning unitary value to each of the members of a heterogeneous set simultaneously spawned the notion of plurality or 'the many'. www.principlesofnature.net /from_counting_to_abstraction_in_maths.htm   (1377 words)

 Math Forum Discussions   (Site not responding. Last check: 2007-10-01) action at a distance I have shown you can get away without it. the least possible number, however, and that is the route that the The Math Forum is a research and educational enterprise of the Drexel School of Education. mathforum.org /kb/thread.jspa?threadID=1139063&messageID=3730553   (1291 words)

 LEAST ACTION PRINCIPLE OF CRYSTAL FORMATION OF DENSE PACKING TYPE AND KEPLER'S CONJECTURE   (Site not responding. Last check: 2007-10-01) Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that 18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques and in the tradition of classical geometry. www.worldscibooks.com /mathematics/4741.html   (246 words)

 Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations   (Site not responding. Last check: 2007-10-01) Principle of least action ; some possible generalizations In this article we draw the attention to an important variational principle in dynamics: the Maupertuis-Jacobi Least Action Principle (MJLAP).^This principle compares varied paths with the same energy h. are 1 (Hamilton`s principle) and 1/2 (Maupertuis-Jacobi Least Action Principle). www.osti.gov /energycitations/product.biblio.jsp?osti_id=6424737   (157 words)

 Find in a Library: The principle of least action in geometry and dynamics Find in a Library: The principle of least action in geometry and dynamics The principle of least action in geometry and dynamics WorldCat is provided by OCLC Online Computer Library Center, Inc. on behalf of its member libraries. worldcatlibraries.org /wcpa/ow/03ba0d36c37e12f9a19afeb4da09e526.html   (65 words)

 Principle of Least Action The reader should have an idea about integrals and derivatives, minima and maxima of the functions, and differential equations. I start with basic motivation for the need of such a principle, then I give a classical example of a problem that can be solved using the calculus of variations, and finally, I describe the action integrals in classical, relativistic and quantum physics. To view mathematics on these pages, you have to use a browser that supports MathML standard, such as Mozilla or physics.ucsd.edu /~epivovar/action.htm   (105 words)

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