[FRIAM] Least Action

[Barry MacKichan]

  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

On 12 Mar 2025, at 11:44, Pieter Steenekamp wrote:

> There's a *"nice"* layman’s explanation of the principle of *least 
> action* (
> https://www.youtube.com/watch?v=qJZ1Ez28C-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.)
>
> 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.
>
> A common example used to illustrate this principle goes like this:
> 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.
>
> This framing presents a problem. Here’s my perspective:
> 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.
>
> 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.
>
> I don’t buy that.
>
> 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.
>
> 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.

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