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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