# Questions tagged [conservation-laws]

The statement that a property of a system does not change if the system is isolated.

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### How do conservation of energy and relativity hold if spacetime is discrete?

I understand the principle of conservation of energy and momentum in classical physics. I am aware of the fact that such conservation laws arise due to fairly deep mathematical symmetries in the ...
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### Probability current density confusion

As we all know, the probability current density in quantum mechanics is defined as: $$\textbf{J}=\dfrac{\hbar}{2mi}(\Psi^* \nabla \Psi-\Psi \nabla \Psi^*)$$ For simplicity let us work in one dimension ...
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### Why does the speed of a ping pong ball increase when the space in which it can bounce decreases?

I was playing table tennis the other day when I my ball fell off the table. I placed my paddle above it in order to slow it down, and then I brought the paddle to the ground so that the ball would ...
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### Conservation of Momentum on Noether's Theorem for Relativistic Classical Fields

Consider an infinitesimal translation (α = 0, 1, 2, 3) $$x'^{\mu} = x^{\mu} + \frac{\delta x^{\mu}}{\delta a^{\alpha}} \delta a^{\alpha}$$ where $\delta a^{\alpha}$ is a parameter from transformation ...
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### In a closed system (body), is it possible to stop fast moving body with internal forces? [closed]

We know closed system cannot generate unidirection motion of itself. is it possible for system to stop or slow by itself with internal motion when it is moving very fast. Example: A space ship is ...
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### Do Maxwell's equations contain any information on the time evolution of the current density $J$?

The answers to Can the Lorentz force expression be derived from Maxwell's equations? make clear that Maxwell's equations contain only information on the evolution of the fields, and not their effects ...
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### Is conservation of angular momentum responsible for rotating a rigid body when it slows down an internal wheel?

Suppose that there is a rigid body, such as a satellite, which contains inside it a wheel that is spinning at a constant rate. This means that the satellite has a certain, constant, angular momentum ...
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### Covariance of Noether's charge in GR

If we consider a theory of GR (the standard Einstein-Hilbert action) and a complex scalar field, we can easily see that we have a global $U(1)$ symmetry for the scalar field. Now, via Noether's ...
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### How to identify internal and external forces acting on a system of particles?

In my Physics textbook there is sample problem in which a firecracker placed inside a coconut of mass M, initially at rest on a frictionless floor, blows the coconut into three pieces (A, B and C) ...
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### Interpretation of Gauss's theorem applied to Maxwell's equations: $\dfrac{d}{dt} \int \rho \ dV + \int \mathbf{j} \cdot \mathbf{n} \ dS = 0$

Using Maxwell's equations and Gauss's theorem, we get $$\dfrac{d}{dt} \int \rho \ dV + \int \mathbf{j} \cdot \mathbf{n} \ dS = 0,$$ where $\rho$ is the electric charge density and $\mathbf{j}$ is the ...
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### Conserved quantity associated with Permutation Symmetry?

Based on my crude understanding of Noether's Theorem, for each symmetry in physics, there is a conserved quantity associated with it. If so, what is the conserved quantity associated with permutation ...
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### Conservation laws in Newtonian mechanics

Newton's third law is equivalent to conservation of momentum. Assuming conservative systems, we get conservation of (mechanical) energy. Assuming central forces, we get conservation of angular ...
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### Is it possible to change the momentum of a system without actually doing any work on the system?

Consider a rigid wall somewhere in free space. Now imagine two balls of the same mass and same speed headed towards the wall from two opposite directions. Now they go on to hit the wall and rebound ...
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### Conserved quantities for the system consisting of an uniform spinning top

A uniform top of mass $M$ with its lower end fixed to the ground is rotating on its axis of symmetry with angular velocity $\Omega$, initially in a vertical position ($\theta=0, \dot \theta=0$). The ...
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### Definition of charge with Hodge star

I understand the definition of charge given by $$Q = \int_{\mathbb{R}^{D-1}} \text{d}^{D-1}x J^0. \tag{1}$$ In Carroll’s Spacetime and Geometry book (pg. 455) he writes Start by imagining that we ...
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### Do waterfalls conserve momentum? If so, how?

I understand that waterfalls conserve energy, given the fact that the top of a waterfall possesses gravitational potential energy, and as the water is falling from top to bottom, this potential energy ...
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### Finding mass ratio from the collision of two bodies

I am currently studying Clssical Mechanics, fifth edition, by Kibble and Berkshire. Problem 1 of chapter 1 is as follows: An object $A$ moving with velocity $\mathbf{v}$ collides with a stationary ...
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### Is there any deeper reason behind the conservation of mass?

I have read that behind the conservation of energy or momentum is the Noether theorem with its intimidating maths. Is there any similar deeper foundation behind the conservation of mass?
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### Conservation of spin in Non-relativistic limit

Consider electron-positron interaction : $$e^-e^+\rightarrow\mu^+\mu^-$$ when peskin book come to compute Non relativistic limit of this process said that, because we are in Non relativistic limit we ...
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### How do I know which Feynman diagram is right? ($s,t,u$-channel)

Following the Lagrangian: $$\tag{1} \mathcal{L} = \mathcal{L}_{initial}-M^2 \varphi^* \varphi - g\varphi^*\varphi -g\phi^3$$ where $\phi$ is a particle associated with a real scalar field, and \$\...
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### Is the exchange of momentum between two interacting objects always the same? [duplicate]

The rule is that the total momentum of an isolated system is constant. I am interested in one question. If you imagine a closed system, there will be two planets, for example: Earth and Mars. They ...
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### Why can we still assume momentum is conserved in an inelastic collision?

This is very similar to this question: How can momentum but not energy be conserved in an inelastic collision? However, I feel as though an important caveat was not resolved for me which is why I am ...
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### Is there a formal distinction between Lorentz boosts and the others types of transformations of the Poincaré group?

The doubt arises as space translations can be associated to homogeneity of space, time translations to homogeneity of time and classical rotations to isotropy of space. These properties of space leads ...