All Questions
166
questions
130
votes
10
answers
41k
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Why the Principle of Least Action?
I'll be generous and say it might be reasonable to assume that nature would tend to minimize, or maybe even maximize, the integral over time of $T-V$. Okay, fine. You write down the action ...
- 8,540
48
votes
5
answers
4k
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Is the principle of least action a boundary value or initial condition problem?
Here is a question that's been bothering me since I was a sophomore in university, and should have probably asked before graduating:
In analytic (Lagrangian) mechanics, the derivation of the Euler-...
- 1,350
36
votes
3
answers
25k
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Deriving the Lagrangian for a free particle
I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading "Mechanics" by Landau and Lifshitz recently and hit a few roadblocks right away.
Proving that a free ...
- 463
31
votes
4
answers
6k
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How do I show that there exists variational/action principle for a given classical system?
We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's ...
- 955
24
votes
4
answers
4k
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Confusion regarding the principle of least action in Landau & Lifshitz "The Classical Theory of Fields"
Edit: The previous title didn't really ask the same thing as the question (sorry about that), so I've changed it. To clarify, I understand that the action isn't always a minimum. My questions are in ...
- 28.3k
23
votes
3
answers
2k
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What makes a Lagrangian a Lagrangian?
I just wanted to know what the characteristic property of a Lagrangian is?
How do you see without referring to Newtonian Mechanics that it has to be $L=T-V$?
People constructed a Lagrangian in ...
- 1,880
19
votes
3
answers
2k
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In what sense (if any) is Action a physical observable?
Is there any sense in which we can consider Action a physical observable? What would experiments measuring it even look like? I am interested in answers both in classical and quantum mechanics.
I ...
- 1,289
16
votes
3
answers
6k
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Hamilton-Jacobi Equation
In the Hamilton-Jacobi equation, we take the partial time derivative of the action. But the action comes from integrating the Lagrangian over time, so time seems to just be a dummy variable here and ...
- 921
16
votes
5
answers
6k
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Why can't any term which is added to the Lagrangian be written as a total derivative (or divergence)?
All right, I know there must be an elementary proof of this, but I am not sure why I never came across it before.
Adding a total time derivative to the Lagrangian (or a 4D divergence of some 4 ...
- 1,263
16
votes
7
answers
4k
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In the Principle of Least Action, how does a particle know where it will be in the future?
In his book on Classical Mechanics, Prof. Feynman asserts that it just does. But if this is really what happens (& if the Principle of Least Action is more fundamental than Newton's Laws), then ...
- 504
14
votes
6
answers
2k
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Does universal speed limit of information contradict the ability of a particle to pick a trajectory using Principle of Least Action?
I'm doing some self reading on Lagrangian Mechanics and Special Relavivity. The following are two statements that seem to be taken as absolute fundamentals and yet I'm unable to reconcile one with the ...
user297575
13
votes
3
answers
2k
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In a Lagrangian, why can't we replace kinetic energy by total energy minus potential energy?
TL;DR: Why can't we write $\mathcal{L} = E - 2V$ where $E = T + V = $ Total Energy?
Let us consider the case of a particle in a gravitational field starting from rest.
Initially, Kinetic energy $T$ is ...
- 255
13
votes
2
answers
2k
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Is Action Always "Locally" Least?
In general, I know it's true that the Principle of Least Action is more properly called the Principle of "Stationary" Action. However, there are results which seem to suggest that for sufficiently ...
- 255
11
votes
3
answers
12k
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Physical meaning of the Lagrangian function [duplicate]
In Lagrangian mechanics, the function $L=T-V$, called Lagrangian, is introduced, where $T$ is the kinetic energy and $V$ the potential one. I was wondering: is there any reason for this quantity to be ...
- 307
10
votes
2
answers
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Deriving the action and the Lagrangian for a free massive point particle in Special Relativity
My question relates to
Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action.
As stated there, to determine the action ...
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