All Questions
45
questions
-3
votes
1
answer
116
views
Noether's theorem by a taste of logic [closed]
I am a mathematician and I asked this question briefly and my question became closed, may be - I don't know - because physicists don't used to apply the method of "proof by contradiction". ...
- 1,409
1
vote
1
answer
59
views
Designing a thought experiment on Noether's Theorem [closed]
By Noether's theorem, in classical physics, conservation of total momentum of a system is result of invariance of physical evolution by translation.
So logic says "if" there exists closed ...
- 1,409
3
votes
5
answers
938
views
What is the point of knowing symmetries, conservation quantities of a system?
I think this kind of question has been asked, but i couldn’t find it.
Well i have already know things like symmetries, conserved quantities and Noether’s theorem, as well as their role in particle ...
- 311
1
vote
0
answers
54
views
Doubt Regarding Noether's theorem for time-dependent systems
I'm having problems showing Noether's theorem when the lagrangian is time dependent. I'm trying to do it not using infinitesimal transformations from the beginning, but continuous transformations of a ...
2
votes
1
answer
72
views
Some doubts about action symmetry
We know that Symmetry of the Lagrangian ($\delta L = 0$) always yields some conservation law.
Now, if $\delta L \neq 0$, that doesn't mean we won't have conservation law, because if we can show action ...
- 525
1
vote
1
answer
135
views
In a simple case of a particle in a uniform gravitational field, do we have translation invariance or not?
Consider a system where a particle is placed in a uniform gravitational field $\vec{F} = -mg\,\vec{e}_{z}$. The dynamics of this are clearly invariant under translations. When we take $z\rightarrow z+...
- 8,640
4
votes
0
answers
170
views
Noether's Theorem in non-conservative systems
In most books on classical mechanics, Noether's Theorem is only formulated in conservative systems with an action principle. Therefore I was wondering if it is possible to also do that in non-...
- 470
1
vote
0
answers
195
views
Dynamics of particles and fields on the torus: references
In some situations (e.g. molecular dynamics situations, Euclidean QFT, cosmology), a common trick to eliminate boundary effects or to provide an infrared cutoff is to use periodic boundary conditions. ...
-1
votes
2
answers
620
views
Conservation theorem for cyclic coordinates in the Lagrangian
Suppose $q_1,q_2,...,q_j,..,q_n$ are the generalized coordinates of a system.
$q_j$ is not there in the Lagrangian (it is cyclic).
Then $\frac{\partial L}{\partial\dot q_j}=constant$
In Goldstein, it ...
- 293
5
votes
6
answers
1k
views
How is energy conservation & Noether's theorem a non-trivial statement?
Noether's theorem says that energy conservation is a result of temporal translation symmetry of the laws of physics. This is implied to be - and I'm not saying it's not - a very non-trivial statement. ...
- 20.6k
4
votes
3
answers
269
views
Newtonian vs Lagrangian symmetry
Suppose we have a ball of mass $m$ in the Earth's gravitational field ($g=const.$). Equation of motion reads as:
$$
ma = -mg
$$
From here we can conclude that we have translational symmetry of the ...
- 1,795
17
votes
6
answers
3k
views
What symmetry is responsible for the amplitude independence of the period of a simple harmonic oscillator?
In the ICTP lectures of Y. Grossman: Standard Model 1, in about minute 54:00, he leaves an informal homework for the students. He ask to find the symmetry related to the conservation of the amplitude ...
- 5,568
1
vote
1
answer
156
views
Number of conservation laws
I saw a discussion about the relation of symmetries of Lagrangian and conservation laws on a textbook of analytical mechanics. A part that was counterintuitive to me was that all the discussion was ...
- 63
0
votes
0
answers
71
views
Conservations for time or space translational invariance, why $\delta L\vert_{\text{time trans}}\neq 0$? but $\delta L\vert_{\text{space trans}}= 0$?
To summarize my question first,
Given a classical mechanics Lagrangian,
$L=L(x(t), \dot{x}(t); t)$,
Why the conservation law for time $t$-translational invariant system, under time variance $\delta ...
- 4,336
3
votes
2
answers
628
views
Noether's Theorem: There are conserved quantities corresponding to symmetries of position, orientation, and time, but why not velocity?
Noether's Theorem seems to be one of the most fundamental and beautiful results in all of physics. As I understand it, the fact that the laws of physics are the same independent of position, ...
- 2,403