All Questions
Tagged with classical-mechanics noethers-theorem
117
questions
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0
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Is there a straightforward simplified proof of energy conservation from time translation symmetry?
Electric charge conservation is easily proven from electric potential gauge symmetry, as follows:
The potential energy of an electric charge is proportional to the electric potential at its location.
...
3
votes
1
answer
82
views
Does quasi-symmetry preserve the solution of the equation of motion?
In some field theory textbooks, such as the CFT Yellow Book (P40), the authors claim that a theory has a certain symmetry, which means that the action of the theory does not change under the symmetry ...
-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
vote
1
answer
59
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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 ...
6
votes
1
answer
78
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How do I formulate a quantum version of Hamiltonian flow/symplectomorphisms in phase space to have a "geometric", quantum version of Noether's theorem
I'm currently exploring how Noether's theorem is formulated in the Hamiltonian formalism. I've found that canonical transformations which conserve volumes in phase space, these isometric deformations ...
3
votes
5
answers
938
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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 ...
5
votes
1
answer
592
views
Does the Hamiltonian formalism yield more Noether charges than the Lagrangian formalism?
In Lagrangian formalism, we consider point transformations $Q_i=Q_i(q,t)$ because the Euler-Lagrange equation is covariant only under these transformations. Point transformations do not explicitly ...
1
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0
answers
54
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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
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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 ...
15
votes
5
answers
3k
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Why does time-translational symmetry imply that energy (and not something else) is conserved?
I'm trying to understand Noether's theorem from an intuitive perspective. I know that time-translational symmetry implies the conservation of energy. Is it possible to convince oneself that time-...
13
votes
6
answers
1k
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(A modification to) Jon Pérez Laraudogoita’s "Beautiful Supertask" — What assumptions of Noether's theorem fail?
I am curious about the following (physically unrealizable) scenario involving a supertask described here: https://plato.stanford.edu/entries/spacetime-supertasks/#ClasMechSupe. The original paper is ...
1
vote
1
answer
135
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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+...
1
vote
0
answers
27
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Analytical mechanics: Noether charge as a generator with variating fields to time direction [duplicate]
Summary
I want to clarify how can I prove the fact that "the Noether charge generates the corresponding transformation" when the infinitesimal transformation of the fields contain the ...
2
votes
1
answer
293
views
Geometrical intuition for Noether's Theorem
I have been reading some questions about the relation between Noether's Theorem and Lie Algebras and I wanted to get some intuition on it, but I didn't find what I really wanted. Also, the majority of ...
4
votes
0
answers
170
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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-...
0
votes
4
answers
374
views
Is Feynman correct when he suggests that Noether's Theorem requires quantum mechanics?
I'm reading the Feynman lectures on physics. In 52-3 he discusses how for each of the rules of symmetry there is a corresponding conservation law. I'm assuming he is referring to Noether's Theorem, ...
1
vote
0
answers
195
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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. ...
5
votes
2
answers
775
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Intuition behind the definition of Continuous Symmetry of a Lagrangian (Proof of Noether's Theorem)
Suppose there is a one-parameter family of continuous transformations that maps co-ordinates $q(t)\rightarrow Q(s,t)$ where the $s$ is the continuous parameter. Also, for when $s=0$ the transformation ...
1
vote
1
answer
179
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Goldstein's derivation of Noether's theorem
This is a followup to my previoucs question: Translation invariance Noether's equation
In Goldstein's derivation of the Noether's theorem in chapter 13,
we have the infinitesimal transformation $$...
0
votes
3
answers
633
views
Translation invariance Noether's equation
In chapter 13 of Goldstein's classical mechanics, on page 591 when talking about Noether's theorem, Goldstein says we need condition 3, which is
$$\tag{13.133} \int_{\Omega'}\mathcal{L}(\eta_\rho'(x^\...
0
votes
2
answers
85
views
How did Noether use the total time derivation to get her conservation of energy? [duplicate]
I was informed by @hft that by combining the total time derivation:
$$\frac{dL}{dt} = \frac{\partial L}{\partial x}\dot{x} +
\frac{\partial L}{\partial \dot{x}}\ddot{x} +
\frac{\partial L}{\partial t}$...
-1
votes
2
answers
620
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Conservation theorem for cyclic coordinates in the Lagrangian
Suppose $q_1,q_2,...,q_j,..,q_n$ are the generalized coordinates of a system.
$q_j$ is not there in the Lagrangian (it is cyclic).
Then $\frac{\partial L}{\partial\dot q_j}=constant$
In Goldstein, it ...
1
vote
1
answer
73
views
Are there non time-symmetric systems that increase total energy over time?
According to Noether's theorem, systems that are not time-symmetric have $\frac{\mathrm{d}E}{\mathrm{d}t}\neq0$. I have essentially two questions, then:
Are there any real systems (discovered or ...
2
votes
3
answers
480
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Lagrangian first integral
I want to extremize $$\int dt \frac{\sqrt{\dot x ^2 + \dot y ^2}}{y}.$$
I have thought that, since the Lagrangian $L(y, \dot y, \dot x)$ is $t$ dependent only implicitly, that i could use the fact ...
2
votes
3
answers
191
views
Noether‘s theorem: Why can function be dependent of $\dot{q}$?
We define a continuous symmetry in Lagrangian mechanics as follows:
$$\delta L\overset{!}{=}\epsilon\frac{\mathrm{d}}{\mathrm{d} t} f(q,\dot{q}, t)$$
Where $\epsilon\in\mathbb{R}$ is a parameter in ...
1
vote
0
answers
70
views
Symmetry of a time-dependent Lagrangian
How do I get the group of symmetries and the constant of motion of $L=\frac{\dot{x}^2}{2}m+V(x+ct)$ where c is a constant?
When I tried to solve it, it was to look for shifts in $x$ and $ct$ under ...
5
votes
6
answers
1k
views
How is energy conservation & Noether's theorem a non-trivial statement?
Noether's theorem says that energy conservation is a result of temporal translation symmetry of the laws of physics. This is implied to be - and I'm not saying it's not - a very non-trivial statement. ...
4
votes
3
answers
269
views
Newtonian vs Lagrangian symmetry
Suppose we have a ball of mass $m$ in the Earth's gravitational field ($g=const.$). Equation of motion reads as:
$$
ma = -mg
$$
From here we can conclude that we have translational symmetry of the ...
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 ...
1
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0
answers
188
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Physical interpretation of the symmetry for the Runge-Lenz vector
In the post What symmetry causes the Runge-Lenz vector to be conserved?, and based on the results of https://arxiv.org/abs/1207.5001, it was it was discussed that the Runge-Lenz vector is the ...