Geometric and physical interpretation of the action principle An open access article from Nature.
https://www.nature.com/articles/s41598-023-39145-y -- rec -- On Mon, Jul 10, 2023 at 12:01 PM Barry MacKichan < barry.mackic...@mackichan.com> wrote: > This is late since another ISP cut my fiber connection a week ago. Living > with only cell service plus $15 per gigabyte is not pleasant. > > Some comments. > > 1. I believe that the fact that photons travel on geodesics (least > distance betwee2 points on a surface (manifold)) gives a fingerhold on > trying to grasp least action. > 2. I read the wikipedia artice, and it hints that the application to > electromagnetism and quantum physics requires some tweaks, so it is not as > straightforward as the video implied. > 3. Granted that Newton’s laws are simpler, my understanding is that > problems involving constraints are easier to set up than integrating the > constraints into the setup of the equations. > > Just sayin’ > > —Barry > > On 3 Jul 2023, at 2:51, Pieter Steenekamp wrote: > > Hi Nick, > > Exercise caution when attempting to grasp the principle of least action, > particularly if you desire an intuitive comprehension of it. > > It is essential to recognize the significance of the principle of least > action, as it applies to various areas of physics and could potentially > hold a closer answer to the "why" question than Newtonian physics > regarding > the laws of motion. > > However, based on our current knowledge, the best explanation for why the > principle of least action holds true is that it aligns with the > observations and experiments conducted in the real world. Although a > breakthrough might be on the horizon, a consensus has not yet been reached > regarding the "why" question. > > Therefore, at present, the following points can be made: > a) When applied to the laws of motion, the principle of least action and > Newton's laws of motion are equivalent. > b) The reason for their acceptance lies in their agreement with empirical > evidence and experimental results. > c) The principle of least action carries more depth as it applies across > several other fields of physics, such as electromagnetism and quantum > physics. > d) The fundamental formulation of the principle of least action is also > simpler than that of Newtonian physics. > > However, if you are aiming to develop an intuitive understanding of the > motion of objects in the real world, it is advisable to adhere to > Newtonian > physics. The principle of least action lacks inherent intuitiveness. Let > me > rephrase that: I have personally constructed an intuitive understanding > that I find useful, but I cannot present it as the definitive answer. > Perhaps someone else has a compelling intuitive explanation? I am open to > hearing different perspectives. > > Moreover, for practical mechanical engineering calculations involving > forces and motion in the real world, Newtonian physics surpasses the > principle of least action. > > -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. . > FRIAM Applied Complexity Group listserv > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > https://bit.ly/virtualfriam > to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: 5/2017 thru present > https://redfish.com/pipermail/friam_redfish.com/ > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ >
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