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<body><div style="font-family: sans-serif;"><div class="plaintext" style="white-space: normal;"><p dir="auto"> I don’t see that there is any problem here. Suppose at some point the ball reasons as follows: I’ve gotten to this point, and my trajectory so far is the one with the least action. What is the vector I should follow for the next</p>
<p dir="auto">On 12 Mar 2025, at 11:44, Pieter Steenekamp wrote:</p>
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<div dir="ltr">There's a *"nice"* layman’s explanation of the principle of *least action* (<a href="https://www.youtube.com/watch?v=qJZ1Ez28C-A)">https://www.youtube.com/watch?v=qJZ1Ez28C-A)</a>—though I don’t quite agree with it. (It does, however, include a rather neat explanation of quantum mechanics that I find useful—but that’s another discussion.) <br>
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Back in engineering school, when calculating trajectories, we relied entirely on Newtonian mechanics, applying it so relentlessly in problem-solving that it became second nature. Later, I encountered the principle of *least action* and its claim to be more fundamental than Newton’s laws. <br>
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A common example used to illustrate this principle goes like this: <br>
If someone throws a ball from point A to point B, the ball *evaluates* all possible paths and then follows the one of least action. <br>
<br>
This framing presents a problem. Here’s my perspective: <br>
If a person throws a ball from point A and it *happens* to land at point B, a post-mortem analysis will confirm that it followed the path of least action. But that’s an observation, not a mechanism. <br>
<br>
The distinction is subtle but important. In both cases, when the ball leaves the thrower’s hand, it has no knowledge of where it will land. Throw a thousand balls with slightly different angles and velocities, and they’ll land in a distribution around B. Yet the layman’s explanation suggests that each ball somehow *knows* its endpoint in advance and selects the least-action trajectory accordingly. <br>
<br>
I don’t buy that. <br>
<br>
My view (and I welcome correction) is that the ball simply follows Newton’s laws (or the least action laws) step by step. It doesn’t *choose* a trajectory—it merely responds to the local forces acting on it at every instant. Once it reaches its final position, we can look back and confirm that it followed the least-action path, but that’s a retrospective conclusion, not a guiding principle. <br>
<br>
Ultimately, in this context, Newton’s laws and the least-action principle are equivalent descriptions of the same physics—neither requires the system to "know" its endpoint in advance.<br>
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