Questions tagged [conservation-laws]
The statement that a property of a system does not change if the system is isolated.
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Does gravity actually have a ‘reaction force’? [duplicate]
By (my limited knowledge of) Einstein’s theory of General Relativity, as gravity is not a force but rather the effect of an object’s inertial path following a geodesic through curved spacetime due to ...
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How to check conservation laws of particles the quantities are not valid for? [closed]
The question is for all cases where quantities such as strangeness and isospin can't be checked
For example e+ + e- -> photon + photon
In this reaction, we can't check for isospin or its component, ...
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Is there momentum conservation in photoelectric emission? [closed]
There is actually a question in my textbook which I am unable to understand.I didn't understand anything
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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 ...
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What are the conserved quantities in a classical field?
I'm completely new to this. I was trying to derive the conserved current of the following Lagrangian density:
$$
\mathcal L(\phi, \partial_\mu \phi) = \frac{1}{2}\partial_\mu \phi \partial^\mu\phi + \...
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Conservation of Angular momentum for an irregular body rotating about three axes
I am having trouble understanding how conservation of momentum can be used to calculate final angular velocity for a body rotating in multiple axis with an asymmetrical MoI.
Suppose a satellite is ...
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Commutation of the Hamiltonian with the generator of boost
Consider the Hamiltonian $H = (\textbf{P}^2+m^2)^{1/2}$ the generators of rotation and and boost given by $$M^{0i} = tP^i-x^iH \\ M^{ij} = x^iP^j-x^jP^i$$ where $x^i$ and $P^j$ satisfy $\{x^i, P^j\} = ...
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What is the deeper relation between symmetry and the Hamiltonian?
Note:
This question is the same as mine.
After having studied physics decades ago I recently reviewed some basics of symmetry in quantum physics. As a more experimental physicist I never understood ...
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Is the invariance of the Lagrangian under some transformation equivalent to the covariance of the motion equation? [duplicate]
Take the Lagrangian $L=\frac{1}{2}m{{\left( \frac{{\rm{d}}}{{\rm{d}}t}x \right)}^{2}}-\frac{1}{2}k{{x}^{2}}$, for example.
The equation of motion of this system should be given by $m\frac{{{{\rm{d}}}^{...
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Canonical transformations in the covariant phase space formalism
As the title says, I'm looking for an explanation on how to apply canonical transformations when using the covariant phase space formalism. I'm familiar with the topic, but I haven't found a good ...
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Conservation of velocity flux in fluid mechanics
I am currently working through the book Vorticity and Incompressible Flow by Majda and Bertozzi. They define the velocity flux as $\int_{\mathbb{R}^3}udx$, where $u = u(t,x)$ is some smooth vector ...
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How is Law of Conservation of Charge valid if protons and electrons are destroyed in a system?
So I am preparing for an exam with material from openstax books on physics. There in the static electricity chapter I saw this paragraph,
"Because the fundamental positive and negative units of ...
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Three masses connected by a string (momentum conservation) [closed]
Three identical balls each of mass m = 0.5 kg are connected with each other as shown in figure and rest over a smooth horizontal table. At moment t=0, ball B is imparted a horizontal velocity v=9m/s. ...
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Continuity equation in curved space-time: a point particle
Let us consider the action describing a point particle with charge $e$. The interaction term is equal to
$$
S_{int} = e\int A_{\mu}\dfrac{d{x}_e^{\mu}}{d\tau}d\tau = e\int A_{\mu}\dot{x}_e^{\mu}dt
$$
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Vacuum polarization
Interaction vertex of QED are like:
\begin{equation}
e \bar{\psi} {A\mkern-9mu/} \psi
\end{equation}
But we can't write a vertex where a particle-antiparticle pair annihilates in just 1 photon, due to ...
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On the continuity condition of the Klein-Gordon equation
I have to show that $\partial_\mu j^\mu = 0$ for the four-current $j^\mu = \frac{i}{2m}\left(\phi^*\partial^\mu\phi - \phi\:\partial^\mu\phi^*\right)$.
Using the Leibniz rule, one gets to
$$\partial_\...
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Pendulum attached to a cart: is momentum conserved?
Both the cart and the pendulum have velocity=0 at time=0, pendulum is held at that angle θ and then released.Frictions are negligible.
Is there an axis along which linear momentum is conserved? I've ...
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Using Galilean transformation to solve a question with a block-spring-block system [closed]
I am currently practicing for my PHYS 101 major test and encountered this question:
In Figure 11, block 1 (mass 2.50 kg) is moving rightward at 10.0 m/s
and block 2 (mass
6.20 kg) is moving rightward ...
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How is the momentum conserved in the case of recombination in direct bandgap semiconductor?
In the case of a direct bandgap semiconductor, the recombination of an electron and a hole generates a photon that has energy equal to the bandgap of the semiconductor, accounting for energy ...
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What is the intuitive reason why Ampere's law is incorrect?
I don't understand why Ampere's Law for magnetic fields is wrong. So initially, we got taught it as the following:
$$\vec\nabla\times\vec{B}=\mu_0\vec{J}$$
and this turns out to be wrong. I also ...
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Total bound charge equal to zero (proof)
I always see the assumption that the total bound charge is always zero, but is it not clear for me why is it true for every dielectric material, and I haven't find it in a textbook.
I know that $\...
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Calculate the speed of a rifle bullet as a result of shooting a bullet, should we use momentum or kinetic energy?
Say a rifle fires a bullet. We know the mass of the bullet, the velocity of the bullet (upon exiting the barrel) and the mass of the rifle. The rifle shoots hanging from a string, and we want an ...
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Translation Invariance and Conserved Momentum for scalar fields
In my Quantum Field Theory Notes, the professor said that the Hamiltonian of the scalar field lattice $\sum_{x} w \big[a_x^\dagger a_x +h/2 \big]$ is translation invariant. This implies that there is ...
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Information conserved applied to time
So it's said that information in the universe is conserved. So does that also mean that anything that happened in the past is also conserved and can be accessed?
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Conservation of Angular Momentum, why does person rotate only one way?
As seen from the video that i linked, when the wheel is spinning then he doesnt rotate, but as soon as he flips the wheel he will start to rotate. Why he doesn't rotate both counter and anticlock wise?...
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What is the connection between matter in the universe and the baryon number not being conserved?
Towards the end of "Quarks, the Stuff of Matter", the author discusses the implications of the proton is not stable and ultimately decays. He states, that if the proton decays, then the ...
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Conservation of momentum with antiparticle annihilation
I'm confused about how momentum can be conserved when a particle and its antiparticle collide. For example, if an electron and positron collide and annihilate to form two photons, then there should be ...
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How to obtain the continuity and Euler equations by taking moments of the Vlasov equation in Cosmology?
In a set of notes about cosmology, I have found the following claim:
The 0th moment of the Vlasov equation yields the continuity equation. For that, upon integrating over the momentum, we have to ...
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Is there any mathematical equation for Kirchhoff's Junction law for complicated electrical circuits? [closed]
Is there any mathematical equation for Kirchhoff's junction law? As far as I know, the junction law states :
The total current entering the junction must be equal to the total
current leaving the ...
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Conservation of energy/momentum doubt in bullet embedding into block
A bullet of mass 10$\,$g travels horizontally with speed of 100$\,$m/s and is absorbed by a wooden block of mass 990$\,$g suspended by a string. Find the vertical height through which the block rises, ...
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Diffusion without mass conservation?
I'm looking for the physical description of a certain diffusion process, but I don't know how to precisely express it, making the search fruitless. I'd like to have some help formulating, or rather ...
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Confusion about the conservation of momentum of a ball and an angled wall [duplicate]
Say we have a ball that is traveling to the right at some velocity $v = v_x$. Say there is a completely immobile or infinitely heavy wall that is angled such that the normal vector of the wall is ...
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Bernoulli's equation in a conical pipe
Question
A stream is rushing from a boiler through a conical pipe, the diameter of ends of which are $D$ and $d$; if $V$ and $v$ are the corresponding velocities of the stream and if the Bernoulli's ...
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Continuity equation derivation in statistical mechanics
I was reading my professor's slides (a sort of Introduction to Statistical Mechanics) and unfortunately, they do not seem to be as clear as I'd want them to be, therefore I've come here for help.
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Does the flow rate of a falling water column increase further down the column?
Suppose you have a faucet that expels water at a rate r Liters/second. Will the rate at which water flows through some ring beneath the faucet be greater than r or equal to r?
On one hand, if the rate ...
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What does conservation of color charge mean for mixed states in QCD?
In quantum chromodynamics, in an interaction in which a quark and an anti-quark exchange a gluon, the color charge must be conserved. When we are talking about base states like $r\bar{b}$ it seems ...
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Calculating the recoil mass of an atom after absorption of a photon [duplicate]
I'm solving a problem 4.11 in <Introducing Einstein's Relativity, Ray D'Inverno>. The problem states as follows:
An atom of rest mass $m_0$ is at rest in a laboratory and absorbs a photon of ...
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Gauge invariance in QED with just fermion transformations
I've got myself confused about a basic question. If we have a gauge-invariant operator $\mathcal{O}$ whose expectation value is
\begin{equation}
\left\langle\mathcal{O}\left(x_1, \ldots, x_n\right)\...
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The time derivative term in the continuity equation
The integral form of the continuity equation is written as:
$$\frac{dq}{dt} + \oint_{S} \textbf{j} . d\textbf{S} = \Sigma$$
where $q$ is the amount of quantity in a certain volume $V$, $t$ is the time,...
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Compressible fluid equation
We know the continuity equation of a continuum (in this case I want to discuss fluids, equation reference):
$$\frac{\partial \rho}{\partial t} + \nabla . (\rho u) = 0$$
where $\rho$ is the mass ...
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Energy conservation and Lorentz invariants [closed]
In relativistic collision theory,How can we deduce energy is conserved by using Lorentz transformation?
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How is it that underground nuclear tests create huge caverns without violating conservation of mass?
If a multi-megaton underground nuclear test 500m down in deep hard rock detonates, we’re told that it will leave a rather radioactive cavern in its wake (I’m just using Gnome as an example, I’m not ...
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Definition of conserved quantities in integrable system
This question is about the definition of conserved quantities integrable systems.
Using Algebraic Bethe ansatz,a family of commuting operators $F(\lambda)$ can be contructed by taking a partial trace (...
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What referential should I use? Ping pong and water cup
I'm trying to modelise the ping pong and water cup experiment.
They were already questions on stackexchange about this:
Why does a ping pong ball bounce higher when it is dropped together with a cup ...
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Electron momentum in a one-dimensional lattice and conservation issue
A one-dimensional lattice is a periodic array of atoms or ions where any two adjacent ions are separated by a fixed distance, the lattice spacing $a$. The Hamiltonian of an electron moving in this ...
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Necessity and Sufficiency of Yang-Baxter Equation for Integrability
Yang-Baxter Equation (YBE) seems to be a sufficient condition for integrability, i.e. if you have an $R$-matrix satisfying YBE, then the model is integrable. But how about the reverse? More ...
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Is colour the conserved charge of global $SU(3)$ color symmetry?
Consider the Lagrangian consisting of three Dirac fields
$$ \mathcal{L} = \sum_{a=1}^3 \bar{\psi}_a ( i \gamma^\mu \partial_\mu - m ) \psi_a$$
where $a$ is an internal index labelling the colour ...
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Equation in Noether's paper
When I was reading the paper by Emmy Noether about the famous Noether Theorem, there is an equation I don't know its meaning and why it holds on page 5.
$$\phi\frac{\partial^{\sigma} p(x)}{\partial x^{...
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Proof that if the 3-momentum is conserved then so is energy. (Weinberg's Gravitation and Cosmology)
In section 4 chapter 2 of his book "Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity", Weinberg argues that if the 3 momentum is conserved in a '...
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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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