[FRIAM] Watch "The Most Important Idea in Physics: The Principle of Least Action - Ask a Spaceman!" on YouTube
Roger Critchlow
rec at elf.org
Mon Jul 31 20:04:53 EDT 2023
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.mackichan at 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.
>
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