All Questions
26
questions
14
votes
6
answers
2k
views
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
10
votes
2
answers
4k
views
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 ...
- 737
9
votes
2
answers
983
views
Why does the 'metric Lagrangian' approach appear to fail in Newtonian mechanics?
A well known derivation of the free-space Lagrangian in Special Relativity goes as follows:
The action $\mathcal{S}$ is a functional of the path taken through
configuration space, $\mathbf{q}(\lambda)...
- 91
8
votes
2
answers
614
views
How is the Hamiltonian & Lagrangian non-relativistic & relativistic respectively?
I have read from the textbook of Matthew Schwartz on page 49 of the PDF viewer (or page 30 of the textbook) where he says:
I am interested in the last sentence of this paragraph where he says that ...
- 1,896
7
votes
1
answer
169
views
Modifying Feynman-Wheeler absorber theory to work with arbitrary potentials?
I'm trying to consider relativistic multi-body dynamics in special relativity. In classical mechanics, it's easy to write a simple $n$-body system with arbitrary potential $V$:
\begin{equation}
m \...
- 716
6
votes
2
answers
766
views
Deriving special relativity free particle Lagrangian using infinitesimal boost?
At the very beginning of Landau and Lifshitz Mechanics they derive the form of the Lagrangian for a free particle in Newtonian mechanics.
I want to see how to do the analogous derivation in special ...
- 866
4
votes
2
answers
2k
views
Why do we consider Lagrangian densities in field theory (as opposed to Lagrangians as in point mechanics)?
My question is: Why do we consider Lagrangian densities in field theory (as opposed to Lagrangians as in point mechanics)?
Is it simply because of the following?
We wish the theories to be Lorentz ...
- 3,063
4
votes
2
answers
213
views
Does locality emerge from (classical) Lagrangian mechanics?
Consider a (classical) system of several interacting particles. Can it be shown that, if the Lagrangian of such a system is Lorenz invariant, there cannot be any space-like influences between the ...
- 34.4k
4
votes
1
answer
386
views
Does the negative sign in the Lagrangian $L=T-V$ relate to the $(+,-,-,-)$ Minkowski signature of relativity?
I've read many derivations of the Euler-Lagrange equation, but this is more of a physics-philosophical point.
Kinetic energy $T$ involves time derivatives, while potential involves spatial location. ...
- 568
3
votes
0
answers
141
views
Relativistic configuration space in classical mechanics
Okay so a couple of questions. Firstly I realise that in order to study the dynamics of one particle (classically), we define the Lagrangian and Hamiltonian to be the maps from the tangent and ...
- 504
2
votes
2
answers
2k
views
Lagrangian for free particle in special relativity
From definition of Lagrangian: $L = T - U$. As I understand for free particle ($U = 0$) one should write $L = T$.
In special relativity we want Lorentz-invariant action thus we define free-particle ...
- 171
2
votes
1
answer
187
views
Inconsistency in Goldstein’s Lagrangians for Relativistic Point Particles?
In Goldstein’s Classical Mechanics (3rd edition), section 7.10 focuses on covariant lagrangians for point particles. Here, we begin by stating
$$L=-mc\sqrt{x’_{\nu} x’^{\nu}}, \tag{7.162}$$
with ...
- 109
2
votes
1
answer
226
views
In classical mechanics, can the Lagrangian be thought of as a metric?
I know that there are some other discussions on this on physics stack exchange, but the other day I was playing with the expression for the Lagrangian and thinking about it's connection with ...
- 281
2
votes
1
answer
3k
views
What is a Lagrangian of a photon? [duplicate]
In sense of classical mechanics+special relativity what is lagrangian of a photon?
Lagrangian of a relativistic massive particle is as follows:
$$ L_{massive}= -mc\sqrt{c^2-v^2} $$
So is it a zero?
- 529
2
votes
0
answers
161
views
Problem understanding something from the variational principle for free particle motion (James Hartle's book, chapter 5)
I am currently studying general relativity from James Hartle's book and I have trouble understanding how he goes to equation (5.60) from equation (5.58). It's about the variational principle for free ...
