Why Does Nature Favor the Principle of Least Action?

  • Thread starter Thread starter dEdt
  • Start date Start date
  • Tags Tags
    Least action
AI Thread Summary
Hamilton's principle states that the action for a system's true path is stationary, typically resulting in the least action. The preference for least action over greatest action raises questions about the underlying reasons in nature. While the action can be stationary, it cannot be a maximum since faster, more complex paths can increase action. This leads to the possibility of saddle points, though the term "Principle of Least Action" is more widely recognized. The discussion highlights the nuances of action in physics and the terminology used to describe these principles.
dEdt
Messages
286
Reaction score
2
Hamilton's principle says that the action for the true path that a system follows will be stationary. As I understand it, the action is almost always least. Is there a reason why nature prefers least action rather over greatest action?
 
Physics news on Phys.org
Hamilton's principle says that the action will be stationary but we can certainly say that it won't be a maximum because we can always increase S by taking a faster, wiggly path with T>>0 so you know it won't be a maximum.

However it could still be a saddle point but "Principle of stationary action" doesn't sound as cool as "Principle of Least Action"
 
Thread 'Gauss' law seems to imply instantaneous electric field'

Thread 'Gauss' law seems to imply instantaneous electric field'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »

Thread 'Highway: Deriving speed from Doppler shift'

I passed a motorcycle on the highway going the opposite direction. I know I was doing 125/km/h. I estimated that the frequency of his motor dropped by an entire octave, so that's a doubling of the wavelength. My intuition is telling me that's extremely unlikely. I can't actually calculate how fast he was going with just that information, can I? It seems to me, I have to know the absolute frequency of one of those tones, either shifted up or down or unshifted, yes? I tried to mimic the...
View full post »

Similar threads

I Principle of minimum action and application to real problems
Replies
10
Views
1K
Why is Hamilton's Principle assumed to be valid for non-holonomic systems?
Replies
25
Views
3K
I Variational operator in the least action principle
Replies
4
Views
1K
I Is the Action Always a Minimum in the Principle of Least Action?
Replies
3
Views
2K
I Action in Lagrangian Mechanics
Replies
5
Views
2K
Principle of least action ...some confusion
Replies
7
Views
3K
I What is the motivation for principle of stationary action
Replies
31
Views
7K
I Intuition for Hamilton's Principle
Replies
4
Views
2K
What does it mean to "minimise" an action ?
Replies
6
Views
4K
B Lagrangrian and Hamiltonian mechanics: A historical picture
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top