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Questions tagged [conservation-laws]

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

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Confusion over use of contravariant notation in Noether's theorem and Lagrangian filed theory

The variational principle clearly gives $$\frac{\partial \rho}{\partial t} + \overrightarrow{\nabla}\cdot \mathbf{J} = 0.$$ So the sign is positive. However in my lecture notes it is claimed that ...
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1answer
19 views

Conservation of bound charge?

It is intuitively obvious that free charge is conserved in vaccum. But when is bound charge conserved? I tried to find this by formula: The charge conservation law in microscopic view (Assuming there ...
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3answers
47 views

A doubt related to Sound

According to laws of conservation of energy energy can neither be created nor be destroyed. We all know that sound is energy. But according to law of conservation of energy- sound can neither be ...
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0answers
27 views

When a rocket applies a force to a mass (a gas) in one direction does the rocket experiences a force in the opposed direction? [on hold]

When I fire a gun the exploding charge applies a force to the bullet. I feel a recoil force on my shoulder in the opposed direction. This conserves momentum? The total momentum was zero before the gun ...
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Are all of chiral primary operators conserved currents in 2D CFTs?

On the page 95 of this lecture note[https://mcgreevy.physics.ucsd.edu/s14/239a-lectures.pdf], it says "a current in a d-dimensional critical theory always has scaling dimension d: you have to ...
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475 views

Car and truck collision

When a car and a truck crash, the car seems to get damaged a lot more. Why does the car get more damaged then the truck in the collision?
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2answers
49 views

Do internal forces cause change in velocity?

For the earth sun system, the force of gravitation is an internal force ( forces* a newtons third law pair) and this INTERNAL force is causing the earth to accelerate. . it is providing the ...
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1answer
47 views

Proof of overall momentum conservation

In $\phi^4$ momentum conservation at each vertex comes from integration in the vertex. How can from momentum conservation at each vertex proof overall momentum conservation that is if $k_1,k_2 ,k_3,...
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3answers
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Elementary argument for conservation laws from symmetries *without* using the Lagrangian formalism

It is well known from Noether's Theorem how from continuous symmetries in the Lagrangian one gets a conserved charge which corresponds to linear momentum, angular momentum for translational and ...
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1answer
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How would you calculate the force of a hammer hitting an anvil? [duplicate]

If I were to hit an anvil with a hammer (let's say a 1 kg hammer at 1 m/s) how would the force of the impact be calculated? So, where I'm at with this is that I know the deal with f = mv, so the ...
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1answer
25 views

Understanding Noether's second theorem

Wikipedia writes that "if the action has an infinite-dimensional Lie algebra of infinitesimal symmetries parameterized linearly by $k$ arbitrary functions and their derivatives up to order $m$, ...
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1answer
50 views

On-shell and off-shell transformations in Noether's theorem

For any transformation of the fields, $$\varphi\to\varphi'=\varphi+\delta\varphi$$ the change in the Lagrangian can be written as $$\delta\mathcal L = \text{EoM} + \partial_\mu j^\mu\tag{1}$$where "...
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2answers
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Can a particle radiate in vacuum without external forces applied?

I was reading about possible and forbidden processes involving photons. First of all, the annihilation process of a pair electron and positron cannot result into a single photon because it would be ...
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2answers
71 views

Noether's Theorem in Classical Field theory Confusion

Consider $N$ independent scalar fields $φ_i (x)$ in 4D space. Also consider a lagrangian density $$\mathcal{L} = \mathcal{L}(φ_i, \partial_μφ_i).$$ Suppose we perform the following infinitesimal ...
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0answers
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Collision of light with light [duplicate]

Photons have momentum. So when a light passes through another light what happens? Do they collide and conserve momentum? If they collide they should deviate (move away from the straight line at a ...
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2answers
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Why is force related to acceleration instead of velocity?

I know $F=ma$, but it's never really made sense to me. Here's an example: Hypothetical scenario- I push a bowling ball ($m = 4\,\rm kg$) sitting on the floor with $5\,\rm N$ of force. (Assume no ...
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1answer
35 views

In the derivation of Noether theorem, why do we subtract the same quantity to obtain Noether current? [closed]

In a general approach derivation of Noether theorem, we have $$ \alpha \mathcal{L} = \alpha \partial _{\mu} \left( \frac{\partial \mathcal{L}}{\partial \left( \partial _{\mu} \phi \right)} \Delta \...
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1answer
37 views

Using a ball on a string for propulsion in space

My friend presented a bit of a puzzle to me, and I can't remember enough physics to say whether it would work, and more importantly, why. It goes like this: Imagine you are an extremely dexterous ...
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1answer
43 views

Continuity equation in the Lagrangian flow picture approach

In deriving continuity equations using Lagrangian. We consider the element of fluid which occupied a rectangular parallelopiped having its centre at the point $(a,b,c)$ and its edges $\delta a$ , $\...
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1answer
24 views

Completely inelastic collisions & center-of-mass acceleration

The system can be isolated, or non-isolated, and comprises of, say, two carts. If these two carts undergo a completely inelastic collision, will they then accelerate together at the center of mass ...
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0answers
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Does “Quantized Inertia Theory” violate conservation of momentum? [closed]

This recent news article reports that DARPA is doing work with "quantized inertia", despite their claim that it's not widely accepted by physicists: The Defense Advanced Research Projects Agency (...
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2answers
55 views

Conservation of momentum on moving charge

The forces of attraction or repulsion between two stationary charges are the action and reaction forces between them. So when we move one of the charges then the other charge also gets affected. But ...
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1answer
81 views

Physically, what is the Fabri-Picasso theorem really trying to say?

The Fabri-Picasso (FP) theorem states that if a symmetry is spontaneously broken the corresponding conserved charge operator $Q$ does not exist in the Hilbert space. The state $Q|0\rangle$ will have ...
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2answers
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Are these collisions equivalent?

Similar to the question if two cars with a velocity of 50 mph each colliding is the same as one car colliding with wall at 100 mph, I was wondering if the same amount of energy is produced when ...
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5answers
143 views

Newton's Third Law and conservation of momentum

I was looking through some reference material, and I came across this: In the situations in which we cannot follow details, we need to know some general properties, that is, general theorems or ...
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2answers
75 views

Why does current conservation involve an arbitrary function?

In section 6.1 of Peskin's quantum field theory introduction, right after equation 6.3, the four current density $j^{\mu}$ is said to be conserved because for any function $f \left( x \right)$ that ...
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4answers
876 views

Reason for inertia of motion of Earth orbiting the Sun [duplicate]

We all know the following universal truth since childhood. Earth (and other planets) orbits around the Sun. And, while I was reading this post, I found that the reason behind Earth revolution is ...
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0answers
32 views

Newtonian Mechanics - Regarding Conservation of Momentum in Collisions

In the question, it is given that all three balls are identical and are connected by a massless, ideal string (on a horizontal plane), and initially, the ball at the centre is given a velocity $v$. If ...
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2answers
50 views

What is possible intuitive explanation of inelastic relativistic collsion?

In classical mechanics, we say an inelastic collision happens when some energy is transferred to heat and noise without changing the total sum of momentum. However, in special relativity, every ...
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2answers
912 views

Conservation of angular momentum on Earth

If I start spinning while standing on the floor, conservation of angular momentum says something needs to start spinning in the opposite direction but what's that?
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2answers
261 views

Infinitely many conserved currents in any QFT?

So I have the following curiosity: Consider for example, in QED, the quantity $$ j^\mu\equiv\partial_\nu (\lambda(x) F^{\mu \nu}) $$ where $\lambda(x)$ is an arbitrary scalar function of spacetime, ...
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1answer
31 views

Difference between conserved quantities and constants of motion?

In Hamiltonian mechanics, consider extended phase space, the trajectory followed by a particle in that space is formed by an intersection of different 2n dimensional surfaces, all of these surfaces ...
3
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1answer
57 views

Gauge transformations with varying phase give us conservation of the charge density. Hence charged particles cannot move?

I stumbled upon the following paragraph in Quark confinement and Topology of gauge theories by Polyakov "Gauge invariance with constant phase $\Psi \to e^{i \alpha}$ lead to conservation of the ...
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1answer
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Is this Feynman diagram possible?

I have been introduced to Feynman diagrams in a particle physics University module and I just created this diagram to practice checking conservation laws: I have been told that charge, baryon and ...
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0answers
35 views

Hamilton-Jacobi theory vs Hamiltonian formalism

I'm writing some notes on Hamilton-Jacobi Theory and I'd like to find an example of a system that is quite difficult to integrate in the usual Hamiltonian formalism, but quite easy in the Hamilton-...
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4answers
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How is momentum conserved in this example? [duplicate]

Suppose a sticky substance is thrown at wall. The initial momentum of the wall and substance system is only due to velocity of the substance but the final momentum is 0. Why is momentum not conserved?
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1answer
27 views

High spin for $Δ^{++}$ resulting from angular momentum of pion in relation to proton

When a pion (Spin 0) collides with a proton (Spin 1/2) the result can be a Δ++ (Spin 3/2). When I tried to look up how the resulting Spin is possible, I came about an answer I do not understand. It ...
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1answer
73 views

How did the Moon get into orbit?

It's the accepted theory that Moon was formed when an object collided with Earth, throwing off a lump of matter which became the Moon. But also, an object cannot be launched into orbit from a planet ...
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1answer
28 views

Is angular momentum conserved in case of a vehicle turning?

When a vehicle takes a turn is the sharpness viz radius of turn related to the velocity by conservation of angular momentum ? If it is so then while going on a straight a line it has infinite radius ...
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1answer
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COM frame in Relativistic particle physics

I have a home work: Consider a head-on collision of a 'bullet' of rest mass $M$ with a stationary 'target' of rest mass $m$. Prove that the post-collision γ-factor of the bullet cannot exceed:$$(m^...
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Question on hard spheres collision

My question is very simple: is it true that if I have a collision of two hard spheres, then the vectore of change of the momentum lies on the line connecting the two centers? Thank you!
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1answer
72 views

Why does pair production produce an electron and positron with opposite spin?

So I was trying to understand quantum entanglement and the example that was used to describe an entangled pair of particles was of an electron and positron after it is formed from a photon in pair ...
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4answers
56 views

Newton’s Third Law Intuition Example Question and Clarification

Assume that I was in space, where there is no friction. Also assume that there were two objects at rest: myself and a matchbox. Does this mean that, by Newton’s Third Law, since there is no friction, ...
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1answer
51 views

Is it possible to model elastic collision of two rotating bodies (rotating rods hitting each other)?

If I understand it correctly the laws of conservation linear and angular momentum and kinematic energy isn't enough since these are just three equations and four unknown values. Another thing is there ...
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1answer
25 views

Is translational/rotational KE conserved when diatomic molecules collide?

When two diatomic molecules of a gas collide, is the collision elastic or inelastic? Is rotational KE also conserved/not conserved? My guess is that translational KE is conserved while rotational KE ...
3
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1answer
66 views

What is the Noether charge associated with the the color $SU(3)$ symmetry of QCD?

A version of the Noether's theorem applies to local gauge symmetries. What is the Noether's charge associated with a non-abelian gauge symmetry such as the color $SU(3)$ and how is that derived? I ...
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3answers
65 views

Force during collision between a body moving with a constant velocity and an accelerating body [closed]

Lets us assume that a train of huge mass is approaching me with a huge constant velocity of the order of hundreds of kilometres per hour. And little me is standing on the tracks but moving with ...
3
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1answer
67 views

Parity conserving QFT

I was reading Peskin's QFT text and in Chapter 6 (Radiative Corrections), there is a line in section 6.2, page 185 which I am quoting below. The passage is about the $\Gamma^{\mu}(p^{'},p)$ and its ...
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1answer
38 views

Can an energy-momentum four vector include the quantities of all objects in a closed system?

Say I have a particle moving along the $x$-axis in the Earth's reference frame. It decays into an upsilon and a proton, each of which has an energy of 60 GeV. They are traveling in opposite ...
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1answer
55 views

Momentum and conservation of momentum [closed]

If an object that is moving collides with an object that is at rest and then they both move together what are the momentum and speed changes that take place