<div dir="ltr">Hi Nick,<br><br>Exercise caution when attempting to grasp the principle of least action, particularly if you desire an intuitive comprehension of it.<br><br>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.<br><br>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.<br><br>Therefore, at present, the following points can be made:<br>a) When applied to the laws of motion, the principle of least action and Newton's laws of motion are equivalent.<br>b) The reason for their acceptance lies in their agreement with empirical evidence and experimental results.<br>c) The principle of least action carries more depth as it applies across several other fields of physics, such as electromagnetism and quantum physics.<br>d) The fundamental formulation of the principle of least action is also simpler than that of Newtonian physics.<br><br>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.<br><br>Moreover, for practical mechanical engineering calculations involving forces and motion in the real world, Newtonian physics surpasses the principle of least action.<br><br></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, 3 Jul 2023 at 05:12, Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>So the difference is at a positive max when the ball hits the ground and at a negative maximum when the ball reaches its highest altitude? So how am I to understand positive and negative? vectors? <br></div><div><br></div><div>Instantaneious Action is at a minimum when the two terms are equal? <br></div><div><br></div><div>I have no intuitive sense of what is going on here. <br></div><div><br></div><div>But thanks for trying, Frank. <br></div><div><br></div><div>N<br></div><div><br></div><div><br></div><div><br></div><div>N<br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, Jul 2, 2023 at 12:27 PM Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com" target="_blank">thompnickson2@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>Frank, <br></div><div><br></div><div>Thanks SO MUCH for forwarding this to me. To any other defrocked english majors on Friam, who have listened to these guys blather on about LaGrangians for all these years, I highly, HIGHLY recommend the video. Pretty short, AND, you might possibly, conceivably understand Steve Guerin when you get to the end. Yeah. Really. <br></div><div><br></div><div>Nick<br></div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">---------- Forwarded message ---------<br>From: <b class="gmail_sendername" dir="auto">Frank Wimberly</b> <span dir="auto"><<a href="mailto:wimberly3@gmail.com" target="_blank">wimberly3@gmail.com</a>></span><br>Date: Thu, Jun 29, 2023 at 2:53 PM<br>Subject: Fwd: Watch "The Most Important Idea in Physics: The Principle of Least Action - Ask a Spaceman!" on YouTube<br>To: Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com" target="_blank">thompnickson2@gmail.com</a>><br></div><br><br><div dir="auto"><br><br><div>---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">---------- Forwarded message ---------<br>From: <b class="gmail_sendername" dir="auto">Frank Wimberly</b> <span dir="auto"><<a href="mailto:wimberly3@gmail.com" target="_blank">wimberly3@gmail.com</a>></span><br>Date: Thu, Jun 29, 2023, 12:51 PM<br>Subject: Watch "The Most Important Idea in Physics: The Principle of Least Action - Ask a Spaceman!" on YouTube<br>To: Thompson, Nicholas <<a href="mailto:nickthompson@earthlink.net" target="_blank">nickthompson@earthlink.net</a>>, Barry MacKichan <<a href="mailto:barry.mackichan@mackichan.com" target="_blank">barry.mackichan@mackichan.com</a>><br></div><br><br><div dir="auto"><a href="https://youtu.be/UuqpCBZoX3M" rel="noreferrer" target="_blank">https://youtu.be/UuqpCBZoX3M</a><br><br><div>---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM</div></div>
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