[FRIAM] Least Action

[Pieter Steenekamp]

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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