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<p dir="auto">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.</p>
<p dir="auto">Some comments.</p>
<ol>
<li>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.</li>
<li>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.</li>
<li>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.</li>
</ol>
<p dir="auto">Just sayin’</p>
<p dir="auto">—Barry</p>
<p dir="auto">On 3 Jul 2023, at 2:51, Pieter Steenekamp wrote:</p>
</div><div class="plaintext"><blockquote><p dir="auto">Hi Nick,</p>
<p dir="auto">Exercise caution when attempting to grasp the principle of least action,
<br />
particularly if you desire an intuitive comprehension of it.</p>
<p dir="auto">It is essential to recognize the significance of the principle of least
<br />
action, as it applies to various areas of physics and could potentially
<br />
hold a closer answer to the "why" question than Newtonian physics regarding
<br />
the laws of motion.</p>
<p dir="auto">However, based on our current knowledge, the best explanation for why the
<br />
principle of least action holds true is that it aligns with the
<br />
observations and experiments conducted in the real world. Although a
<br />
breakthrough might be on the horizon, a consensus has not yet been reached
<br />
regarding the "why" question.</p>
<p dir="auto">Therefore, at present, the following points can be made:
<br />
a) When applied to the laws of motion, the principle of least action and
<br />
Newton's laws of motion are equivalent.
<br />
b) The reason for their acceptance lies in their agreement with empirical
<br />
evidence and experimental results.
<br />
c) The principle of least action carries more depth as it applies across
<br />
several other fields of physics, such as electromagnetism and quantum
<br />
physics.
<br />
d) The fundamental formulation of the principle of least action is also
<br />
simpler than that of Newtonian physics.</p>
<p dir="auto">However, if you are aiming to develop an intuitive understanding of the
<br />
motion of objects in the real world, it is advisable to adhere to Newtonian
<br />
physics. The principle of least action lacks inherent intuitiveness. Let me
<br />
rephrase that: I have personally constructed an intuitive understanding
<br />
that I find useful, but I cannot present it as the definitive answer.
<br />
Perhaps someone else has a compelling intuitive explanation? I am open to
<br />
hearing different perspectives.</p>
<p dir="auto">Moreover, for practical mechanical engineering calculations involving
<br />
forces and motion in the real world, Newtonian physics surpasses the
<br />
principle of least action.</p>
<br /></blockquote></div>
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