Least Action

I hope that I am not giving you too much information, because I would not want anyone’s head to explode. Nature is thought of as being lazy.  Nature will always choose the path of least action as physical systems perform the minimal amount of work necessary.  Humans are also known to take the shortest and most direct possible route, but I think that has more to do with being smart than being lazy.  Ancient scientists and philosophers observed that every component of nature always followed the grand design and never did anything contrary to that.  They knew that the nearest path for motion was selected, but they were not smart enough to prove it.  The path that an object takes is governed by an important principle of analytical mechanics and this idea of least action is a remarkably theory that helps us to understand motion.  Newton gave us classical mechanics and we got general relativity from Einstein, while Schrödinger added quantum field theory, and all of these major theories have been reformulated by considering the least action principle.  In 1744, the great Leonhard Euler studied projectiles considering mass, speed and momentum over an infinitesimal distance to give us the Euler equation, or the Euler-Lagrange Equation.  In 1746, Pierre-Louis Maupertuis wrote a paper about the laws of motion and rest deduced from a metaphysical principle.  Maupertuis pronounced the Law of the Least Action as a universal principle from which all other principles naturally flow.  Joseph-Lewis Lagrange encountered the principle of Least Action while he was computing planetary orbits.

Albert Einstein came up with the idea that space and time are simply different ways of looking at the same thing, and as a result of this, the action of general relativity can be used for the field equations and equations of motion.  David Hilbert was a much better mathematician than Einstein and he was able to write down the action of general relativity based on discussions that he had with Einstein.  As a high school physics student Richard Feynman learned that when a ball is thrown it seems to choose its path, and somehow it seems to know all the possibilities that it can take toward its target in advance.

Action is an outdated technical term that was utilized before energy and momentum were understood. Action is a rather strange quantity, having the units of energy multiplied by time.  The principal of least action is also outdated and it is now known as stationary action.  Isaac Newton was probably the first to use Action in his three laws of motion, stating that every action will have a equal and opposite reaction.  Max Planck came up with Planck’s constant ћ which consists of units of energy being multiplied by time, so this is an action.  Warner Heisenberg came up with a theory known as Heisenberg Uncertainty Principle which states that, it is impossible to know certain things, such as a particle’s momentum and position, at the same time.  You can know its momentum or its position, but you cannot know both simultaneously, because your knowledge of one of these properties affects the accuracy with which you can learn about the other. Observation effects all kinds of things and Albert Einstein thought the quantum world was so strange that quantum theory must be wrong.  When two quantum particles are entangled, they can perform actions that look as if they are coordinated with each other in ways that defy classical intuition about physically separated particles.  Einstein and his coworkers Nathan Rosen and Boris Podolsky, discovered quantum entanglement in the equations of quantum mechanics, and they realized its utter strangeness and they coined the phrase spooky action at a distance.

Unlike an equation of motion, a principle of least action does not explicitly specify what will happen, it simply asserts that the action will be the least of any conceivable actions.  If the motion of a projectile took any other path than that of least action, than it would encounter destructive interfere.  Finding the least action path will always correspond to the extrema of action, a local minimum or maximum, on a graph, because this is where the amplitude interferes constructively, thus you can ignore all of the other possible paths.  The strange properties of quantum mechanics come from the amazing realization that particles are waves, and the amplitude of the wave reveals how likely we would be able to measure a particle at a given position.  This astonishing revelation allows us to understand fundamental things, like the very of an atom.

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