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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