Questions tagged [conservation-laws]
The statement that a property of a system does not change if the system is isolated.
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questions with no upvoted or accepted answers
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Penrose's Zig-Zag Model and Conservation of Momentum
I was reading through Penrose's Road to Reality when I saw his interesting description of the Dirac electron (Chapter 25, Section 2). He points out that in the two-spinor formalism, Dirac's one ...
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Conservation of Komar mass
The definition of Komar mass in GR is associated with one asymptotically flat end. However, a hypersurface may contain more than one end, such as the spacelike Einstein-Rosen bridge in Kruskal ...
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Gauge symmetry implies global symmetry and quantum gravity
It is folklore that quantum gravity cannot have any exact global symmetry (see Global symmetries in quantum gravity). This follows for example from thought experiments involving black holes (no-hair). ...
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Does an evaporating black hole violate conservation of angular momentum?
Angular momentum is supposed to be conserved, but when a rotating black hole evaporates the Hawking radiation comes out in straight lines. Doesn't this violate conservation of angular momentum?
Does ...
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Is there a Noether's theorem for approximate conservation and approximate symmetries?
It is my impression that verifying a symmetry in physical laws often takes the form of verifying the corresponding conservation law instead. But since experimental verification must allow for ...
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Conserved Charge in Conformal Field Theory
I am reading Introduction to Conformal Field Theory by Blumenhagen and Plauschinn, and do not quite understand how eq. 2.33 for the conserved charge
$$
Q = \int dx^1 j_0
$$
is converted to eq. 2.34:
$$...
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How does cobalt-60 beta decay experiment also violate charge conjugation?
I understand why the cobalt-60 decay experiment shows that parity is violated in the weak interaction.
However, my lecture notes also say that 'Note that the outcomes of this experiment can also be ...
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What is information the generator of?
According to the no-hiding theorem (see https://en.wikipedia.org/wiki/No-hiding_theorem), information is truly and generally conserved within any isolated system. According to Noether's theorem (https:...
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Infinite number of conserved charges for the Sine-Gordon Lagrangian
I recently came across a paper of Witten that talks about the S-matrix of the supersymmetric non-linear sigma model. In the beginning part of the paper, he mentions that theories like the non-linear ...
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Inelastic collisions in different frames of reference: regarding thermal energy loss
I am currently reading Introduction to Special Relativity by James H. Smith, and I am attempting to complete the exercise problems for chapter 1 before moving on.
The 4th problem asks
Show ...
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Uses of the Angular Momentum 4-Tensor
The angular momentum 4-tensor has 6 independent components, three angular momentum components and three new guys. Some call these new guys the 'boosts', but since they are the conjugate momentum of ...
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If weak isospin is not conserved in time, what does the Noether theorem tell us?
As far as I understand weak isospin is only conserved in interactions but not as time evolves. Nevertheless, we get from Noethers theorem, because of global $SU(2)$ invariance a conserved quantity ...
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Why must SUSY be broken?
Background
One usually claims that supersymmetry must be spontaneously broken.
The reasoning is roughly the following:
Since $M^2=P^{\mu}P_{\mu}$ is a casimir operator of the supersymmetry algebra, ...
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How does the Hong-Ou-Mandel (HOM) effect conserve photon momentum?
HOM is a two-photon interference effect where temporally overlapped identical photons coming perpendicular to a beam splitter must leave it in the same direction.
How is momentum conserved in this ...
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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-...
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Current conservation in Yang-Mills equations?
In electromagnetism, the equations of motion are
\begin{align}
dF &= 0 \\
*d*F &= J
\end{align}
From this, we can easily derive current conservation $d*J = 0$.
The Yang-Mills equations appear ...
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Can the full set of II. Bianchi identities be derived from the symmetries of the action?
In pseudo-Riemannian geometry we can derive the II. Bianchi identities by considering, e.g. the expression of the Riemann tensor in Riemann normal coordinates. They read
$$R_{\mu\nu\kappa\lambda;\...
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Conservation law relating magnetic geodesics and certain Killing fields
This is going to be somewhat math-heavy, but I'd like to make physical sense of this. Consider the following setup.
$(Q, g)$ is a Riemannian manifold.
$A \in \Omega^1(Q)$ is a magnetic potential ($1$-...
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Is there a theorem about "Electromagnetic Miracles"?
I listened to a lecture several years ago in which the speaker claimed that there is a theorem that shows that violation of charge conservation under classical electrodynamics is impossible in the ...
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Where do the intrinsic parities of particles come from?
It is known that some particles have negative intrinsic parity - for example pion $\pi$. I was wondering if this parity can be understood. I read somewhere that parity of quarks is defined to be ...
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Additions to the stress-energy tensor that leave equations of motion the same
In short:
For a stress-energy tensor $T^{\mu\nu}$, what are possible additions that will leave the tensor equations of motion $\nabla_\nu T^{\mu\nu} = 0$ unchanged?
Context:
Any modification, $T^...
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Why particles with certain properties can't exist
This is inspired by a recent post on why a free electron can't absorb a photon, though my question below is about something considerably more general.
The argument in the accepted answer goes (in ...
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Conserved quantities in overdamped dynamics
I have an implementation of over-damped Brownian dynamics, with particles that follow the version of the Newtons law where the inertia is absent. This is a common thing to do at micrometer scale.
$m x'...
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Generalised hydrodynamics and the Dirac delta potential
Generalised Hydrodynamics is a theory of hydrodynamics for Quantum integrable systems. Those system are integrable in the sense that one can find an infinite number of conserved charges i.e. ...
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Intuitive explanation on why velocity = 0 for a inverted pendulum on a wheel system
I believe I have solved below problem. I am not looking for help on problem-solving per se. I am just looking for an intuitive explanation.
Problem statement: wheel mass = $m_1$, even mass rod BC mass ...
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What is the difference between objectivity and symmetry?
I encounter this question when reading a paper about continuum mechanics (Kumar and Parks, 2015, Proc.R.Soc.A. refer to eq.3.1 and eq.3.3)
Speaking of the objectivity of strain energy density ${\psi}$,...
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On including conserved charges when maximizing entropy of a statistical system
One approach towards constructing the probability of a state in a system is by maximizing the constrained entropy
$$
S[p(n);\alpha,\beta] = -\sum_np(n)\log(p(n))\;+\;
\alpha\big(\sum_nE_np(n) -\langle ...
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Global symmetry in gravity
There exists "folk-theorem" about the impossibility to have global symmetries in a consistent theory of quantum gravity. For example, see Global symmetries in quantum gravity .
Typical argument ...
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Symmetries and conservation laws for a falling cat
For Hamiltonian systems, symmetries and conservation laws are defined and related to each other by Noether's theorem. Symmetry means the invariance of the Hamiltonian for a transformation group, and ...
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Does Noether's theorem show that electric charge (and other charges) are not fundamental? (LAYMEN)
Just to clarify, I am just a laymen so go easy on me.
I was looking into where electric charge comes from, and apparently it comes from $U(1)$ symmetry. But what does that mean?
Does it mean that ...
user164839
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Spontaneous symmetry breaking and conservation of Noether's charge, classically
This is an old question to which I previously posted an answer. I later found that answer to be unsatisfactory and is now deleted. It is newly edited on $01.05.2020$.
Classical conservation laws are ...
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What is internal space translation?
While I was reading the paper named "Classical time crystals," by A. Shapere and F. Wilczek, I found the following transformation.
$$f(x) \to f(x+e) - \frac{df}{dx}*e$$
It says the transformation is ...
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What does Newton's third law actually look like with a finite speed of causality?
Newton's third law of motion states (as quoted on wikipedia):
When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction ...
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Conservation of momentum in statistical physics in presence of a potential
Imagine a number of particles, all confined in a parabolic potential. The particles initially have a random velocity and are let free to bounce off each other (say, it's rigid spheres). Does ...
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Number of Independent postulates in Electrodynamics
We know that there are two ways to get charge conservation in electrodynamics by using the following action:
$$S[A]~=~\int\! d^4x {\cal L},$$
$$ {\cal L} ~=~{\cal L}_{\rm Maxwell} + {\cal L}_{\rm ...
user121238
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How obtain conserved quantities in integrable models in accordance with Liouville's theorem, via Sklyanin Poisson algebra?
In classical integrable models, in the discrete case we have the Sklyanin algebra, $$\lbrace T_{a}(u),T_{b}(v)\rbrace =[r_{ab}(u,v),T_{a}(u)T_{b}(v)].$$ How to prove that the conserved quantities are ...
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Noether's Theorem For Functionals of Several Variables
My question is on using a form of the single variable Noether's theorem to remember the multiple variable version.
Does Noether's theorem, for functionals of a single independent variable, just say ...
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Does electron go through a forbidden state when annihilate with positron?
Let's consider an electron-positron pair with total spin equal to zero. When it annihilates it can not emit only one photon because it would have zero momentum and nonzero energy. The pair emits two ...
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Does energy conservation implies the mass conservation?
According to Noether's theorem, every symmetry implies and conserved quantity. And, from Einstein's equation, every mass have an amount of energy associated.
Can it say that the mass conservation is ...
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When is the time derivative of the electric dipole moment 0?
While reading Introduction to Electrodynamics by David J. Griffiths I encountered a problem regarding the time derivative of the electric dipole moment. I wanted to find the conditions when the time ...
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Photon momentum in Snell's law of refraction
In the drivation of Snell's law for light as EM waves, we have the wave vector components parallel to the interface $k1\parallel$ = $k2\parallel$ as shown in the picture.
From $k_{1x} = k_{2x}$, we ...
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Early E&M problem revisited
In my first electromagnetism class we were given this problem: Suppose you take two electrons and bring them within a distance $d$ of each other. Then release them. What is their final velocity?
Early ...
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Conservation of angular momentum in LSZ reduction formula
I recently solved a problem involving calculating an LSZ reduction formula for the decay of a polarized photon into two pions. Specifically, I wrote an expression for the matrix element $\langle p_+,...
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Can linear frame dragging cause gravitational dipole radiation?
I have just learned that linear frame dragging exists in General Relativity. I have also seen simulations where a periodically accelerated and decelerated mass causes a sort of gravitational dipole ...
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Why a spinning top bounces in a direction vertical to the surface that it hits?
When a spinning top slowly advances and hit a surface (a wall), intuitively one would expect that the top gets bounced mostly along the wall, due to the friction between the top and the wall. But the ...
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Some doubts about action symmetry
We know that Symmetry of the Lagrangian ($\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 ...
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What is the conserved flux corresponding to center symmetry?
I understand the one-form symmetry of $U(1)$ gauge theories as related to the conservation of magnetic and electric flux, given by integration of two-form electromagnetic field tensor and its dual, ...
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Conservation of Extensive Quantities
Thermodynamic quantities are usually divided into two categories: extensive and intensive. The extensive category is sometimes modified to be an extensive density measured relative to unit mass or ...
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Charged particle in a purely radial magnetic field, is the canonical angular momentum conserved?
Let $ \vec{B} = k \dfrac{\vec{u_r}}{r^2}$ (assuming magnetic monopoles exist) and let $q$ be a charged particle. The associated hamiltonian is $H = \dfrac{(\vec{p} - q \vec{A})^2}{2m}$ and the ...
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Relativistic conservation of momentum in an elastic collision
I am reading from Townsend's Quantum Physics (not Mechanics).
In frame $S'$ there are two masses of mass $m$ that elastically collide along the $x$-axis. The masses rebound perpendicular to their ...
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