A theorem that relates continuous symmetries (continuous transformations that don't affect the value of the lagrangian) to quantities conserved in time.
11
votes
3answers
549 views
Swimming in Spacetime - apparent conserved quantity violation
My question is about the article Swimming in Spacetime.
My gut reaction on first reading it was "this violates conservation of momentum, doesn't it?". I now realize, however, that this doesn't allow ...
11
votes
4answers
940 views
If all conserved quantities of a system are known, can they be explained by symmetries?
If a system has $N$ degrees of freedom (DOF) and therefore $N$ independent1 conserved quantities integrals of motion, can continuous symmetries with a total of $N$ parameters be found that deliver ...
13
votes
6answers
2k views
Can Noether's theorem be understood intuitively?
Noether's theorem is one of those surprisingly clear results of mathematical calculations, for which I am inclined to think that some kind of intuitive understanding should or must be possible. ...
8
votes
3answers
843 views
What is the symmetry which is responsible for preservation of electrical charges?
Another Noether's theorem question, this time about electrical charge.
According to Noether's theorem, all conservation laws originate from invariance of a system to shifts in a certain space. For ...
1
vote
0answers
557 views
Do symmetries increase the number of conserved quantities? [closed]
Let us consider a classical mechanical system of N particles in a constant external field. We have 3N coordinates and 3N velocities, so totally 6N unknown variables. We have 6N ordinary differential ...
26
votes
7answers
2k views
Is there something similar to Noether's theorem for discrete symmetries?
Noether's theorem states that, for every continuous symmetry of a system, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...
16
votes
1answer
209 views
Why does charge conservation due to gauge symmetry only hold on-shell?
While deriving Noether's theorem or the generator(and hence conserved current) for a continuous symmetry, we work modulo the assumption that the field equations hold. Considering the case of gauge ...
12
votes
2answers
4k views
Why can't energy be created or destroyed?
My physics instructor told the class, when lecturing about energy, and that it can't be created or destroyed. Why is that? Is there a theory or scientific evidence that proves his statement true or ...
4
votes
1answer
281 views
Noether theorem and classical proof of electric charge conservation
How to prove conservation of electric charge using Noether's theorem according to classical (non-quantum) mechanics?
I know the proof based on using Klein–Gordon field, but that derivation use ...
12
votes
5answers
1k views
What is the conserved quantity of a scale-invariant universe?
Consider that we have a system described by a wavefunction psi(x). We then make an exact copy of the system, and anything associated with it, (including the inner cogs and gears of the elementary ...
8
votes
2answers
829 views
What's the interpretation of Feynman's picture proof of Noether's Theorem?
On pp 103 - 105 of The Character of Physical Law, Feynman draws this diagram to demonstrate that invariance under spatial translation leads to conservation of momentum:
To paraphrase Feynman's ...
4
votes
1answer
512 views
invariance of lagrangian in Noether's theorem
Noether's theorem needs the lagrangian to be invariant.
However, given a lagrangian $L$, we know that the lagrangians $\alpha L$ (where $\alpha$ is any constant) and $L + \frac{df}{dt}$ (where $f$ is ...
17
votes
5answers
811 views
Is the converse of Noether's first theorem true: Every conservation law has a symmetry?
Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law.
Is the converse true: Any conservation law of a physical ...
8
votes
2answers
222 views
Translation Invariance without Momentum Conservation?
Instead of the actual gravitational force, in which the two masses enter symmetrically, consider something like $$\vec F_{ab} = G\frac{m_a m_b^2}{|\vec r_a - \vec r_b|^2}\hat r_{ab}$$ where $\vec ...
8
votes
2answers
76 views
More general invariance of the action functional
I will formulate my question in the classical case, where things are simplest.
Usually when one discusses a continuous symmetry of a theory, one means a one-parameter group of diffeomorphisms of the ...
1
vote
1answer
144 views
Improved energy-momentum tensor
While still dealing with this issue, I've stumbled upon this answer to a question asking about the conserved quantity corresponding to a scaling transformation. It mentions that in accordance with ...
3
votes
1answer
316 views
Noether current for the Yang-mills-higgs lagrangian
I am trying to calculate the Noether's current, more specifically, the energy density of the Yang-mills-Higgs Lagrangian. Please refer to the equations in the Harvey lectures on Magnetic Monopoles, ...
2
votes
2answers
137 views
Does a constant factor matter in the definition of the Noether current?
This is a very basic Lagrangian Field Theory question, it is about a definition convention. It takes much more time to typeset it than answering, but here it is:
Consider a field Lagrangian with only ...
2
votes
2answers
849 views
Noether's theorem vs. Heisenberg uncertainty principle
In continuation of another question about Noether's theorem I wonder whether there exists some kind of relationship between this theorem and the Heisenberg uncertainty principle.
Because both the ...
-3
votes
2answers
234 views
why is dark matter the best theory available to explain missing mass problems?
Why is dark matter the best theory to explain the missing mass problem?
Why is dark matter mathematically necessary to explain the missing mass problem?
On a side not I believe dark matter is ...
