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

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How is angular momentum conserved if a bullet hits a wheel?

Suppose my system involves: 1) A mounted wheel with some outward flap 2) A bullet already in motion Initially the net angular momentum is 0 and the net kinetic energy is just that of the speeding ...
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1answer
47 views

Particle Physics : Conservation laws

As a whole, is conservation of a Lepton number valid, or is it basically the generalization of conservation of electron and muon numbers?
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1answer
79 views

Additive constants of motion

I've read in a book, that in general case energy $E$, momentum $\textbf{p}$ and angular momentum $\textbf{M}$ of a closed system are the only additive constants of motion, that is, if I have $N$ ...
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3answers
146 views

Rotational invariance and operator-squares

My mind is drawing a blank right now. In systems with spin and orbital angular momentum, I know that rotational invariance implies that $[H, \mathbf{J}]=0$ where $\mathbf J=\mathbf L+\mathbf S$. But ...
2
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1answer
80 views

Are covariant derivatives of Killing vector fields symmetric?

I'm reading the Lecture Notes on General Relativity by Matthias Blau, and in section 9.1 (point 1) he writes: Let $K^\mu$ be a Killing vector field, and ${x^\mu(\tau)}$ be a geodesic. Then the ...
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1answer
77 views

What happens to the acceleration of a body undergoing constant force?

Here's the problem I have, specifically relating to a rocket in deep space: A rocket burns fuel at a constant rate. Assuming its mass remains constant, what happens to its acceleration? I seem to get ...
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1answer
74 views

Need help solving a task - laws of conservation (leptons, baryons, charge)

We got a task from our teacher, a multiple choice task; and here it is: Which of the following reactions is correct, considering the conservation laws? Note: We have only learned to use the ...
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1answer
41 views

How does conservation work in wormholes?

My questions might seem naive as I haven't plunged into the mathematical descriptions, but wormholes are interesting even if I don't actually know them :) First of all, is wormhole making two ...
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3answers
988 views

Noether's current expression in Peskin and Schroeder

In the second chapter of Peskin and Schroeder, An Introduction to Quantum Field Theory, it is said that the action is invariant if the Lagrangian density changes by a four-divergence. But if we ...
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0answers
88 views

Collision of Discs and Snooker Kicks

I woke up this morning thinking about spinning discs. Could someone verify whether my reasoning below is correct? Problem 1 Suppose have two identical uniform discs constrained to move in a plane. ...
0
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3answers
112 views

Why is energy conserved? [duplicate]

From basic principals, how does one prove that energy is conserved? Or a little more specifically - Why does this hold: $$\Delta \mbox{ PotentialEnergy} + \Delta \mbox{ KineticEnergy} = 0 $$ Or, for ...
5
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1answer
165 views

Pion decay in particle physics

I'm taking a particle physics course and we're using Perkins Introduction to High Energy Physics as the text. I am looking at problem 1.7. It asks whether $$\pi^0\rightarrow e^- + e^+$$ is allowed or ...
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0answers
27 views

What is the symmetry associated with electric charge conservation [duplicate]

Is there a kind of symmetry that yields the conservation of charges? and if so , how it works for both type of charges? Electrical Charges
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3answers
1k views

What is the symmetry which is responsible for preservation/conservation 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 ...
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1answer
58 views

Recoil from a shotgun

First of all I'd like to point out that I'm a complete layman when it comes to physics and I apologise if this isn't the correct forum for this. If I were to sit on an office chair on a laminated ...
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1answer
66 views

Could elementary particles join to create bound states?

I recently had question, can 2 elementary particles be "attached" together using Strong and weak nuclear forces to create a bound state. For example can Electron and some other stable elementary ...
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4answers
8k views

Why can't energy be created or destroyed?

My physics instructor told the class, when lecturing about energy, that it can't be created or destroyed. Why is that? Is there a theory or scientific evidence that proves his statement true or ...
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4answers
337 views

Detecting a photon without changing it: Does it break conservation laws?

This is about an article published on ScienceMag: Nondestructive Detection of an Optical Photon. I don't have access to full text, but you can see a brief transcription in this link. Basically, it ...
1
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1answer
123 views

Hamiltonian conservation

Lagrangian formalism does not involve forces that doesn't come from a potential and Hamiltonian formalism says that even though energy is not conserved due to a force like this, the Hamiltonian is ...
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1answer
381 views

Energy conservation limited by uncertainty principle

The way I learned it from practicing Fourier analysis and signal processing besides quantum mechanics, is that Energy conservation cannot be achieved in short time scales, and that limits energy ...
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1answer
77 views

Energy/Momentum required to deflect earth from its orbit

This question occurred to me when thinking about the firepower people have on earth. How hard is it to change the characteristics of the orbit of the earth when an explosion happens on its surface, ...
0
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1answer
47 views

Thrust to Weight ratio in Space with an off set CoM

With regards to this thread, Thrust center in space My question is, if the thrust to weight ratio was increased so that it was much higher than the weighted mass of the sphere (ship), would the ...
0
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1answer
53 views

Regarding derivation of Probability Current

The question for the full derivation of Probability Conservation -> Probability Current was already asked here: Probability current. I apologize for not retyping it out, but it's already beautifully ...
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0answers
58 views

Conservation laws in vacuum phase transition

Let's consider a bubble nucleation phase transition between different vacua via quantum tunnelling .For my understanding a particle must penetrate the potential barrier and find herself in an another ...
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0answers
72 views

Oscillations and Majorana Neutrino

In neutrino oscillations, neutrinos can convert from one flavor to another. This implies individual lepton number is not conserved. Doesn't it also imply that, if the neutrinos have mass, the mass ...
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0answers
77 views

How are symmetries defined mathematically? [duplicate]

I have started working on differential geometry very recently. I am little bit familiar with mathematical concepts such as manifolds, differential forms and associated concepts. As I was speeding ...
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1answer
1k views

Probability current

Conservation of probability: Suppose a wavefunction has ${\partial \mathbb P \over \partial t} = -t f(x,t)$ and ${\partial j \over \partial x} = i f(x,t)$. How does it follow that ${\partial \mathbb P ...
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6answers
819 views

A paradox to Lenz's law

I have read that in simple words, Lenz's law states that: The direction of current induced in a conductor is in such a fashion, that it opposes its cause. This validates law of conservation of ...
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1answer
92 views

How do I calculate stopping power?

Malcolm Gladwell made a claim in a recent talk that a sling with a stone going at 30m/s has the same stopping power as a .45 calibre handgun. How would I verify whether or not this claim is true - ...
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2answers
83 views

Equal and opposite reaction - forces coming in pairs - or just common sense?

I've never understood why the conservation of momentum law is taught in schools as "every force has an equal opposite reaction". To me a gun's recoil is self explanatory; the explosion sits ...
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0answers
17 views

Change in Angular momentum of a spinning superball

I throw a superball towards the ground and when I do I intentional induce a spin on the ball so that the ball is spinning towards me on the descent. As soon as the ball hits the ground and comes back ...
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0answers
95 views

Orbital angular momentum selection rules for three identical particles

I'm trying to figure out if there are selection rules for the total orbital angular momentum for a system of three identical particles, say bosons. For two identical bosons one can argue that the ...
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3answers
68 views

Confused about Impulse

Encountered a problem that involves impulse while studying for my exam and I'm not sure how to even approach it. I know that momentum is conserved, but I'm not sure how to relate that to avg force. ...
2
votes
1answer
60 views

Linearized mass conservation equation

I'm working on global seismology and I'm currently facing troubles understanding how an equation is obtained. The equation concerned is the following one : $$ \rho^{E1} = -\nabla \cdot ...
4
votes
1answer
68 views

What is the difference between the process in which energy converts to matter and that in which it converts to antimatter?

What is the difference between the process in which energy converts to matter and the process in which it converts to antimatter? In colliders, for instance, is the product (either being the matter or ...
3
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0answers
154 views

Practice AP Physics B Exam Question regarding Momentum

I am trying to review momentum for the AP exam coming up. I will be taking the AP Physics C exam for Mechanics, but I was just practicing on any free response questions I could find and I came across ...
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3answers
239 views

Continuum limit for solid mechanics

Is there a rigorous derivation of the limits for continuum properties in solid mechanics? For instance, the stress-strain relationship may be linear for large samples (the slope being the Young's ...
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0answers
38 views

Particle physics conservation law checking tool

I'm just starting out with simple particle physics, and I'm doing a ton of exercises where I have to check if a certain reaction is allowed, from the point of lepton/baryon/energy conservation and ...
3
votes
1answer
92 views

Nonlinear Klein Gordon equation

For the Klein Gordon nonlinear equation, $$ u_{tt}- \Delta u +f(u)=0,$$ how could I use Noether's theorem to prove that there is a conserved quantity? I.e., $$ (\Pi _{k} )_{t} - \rm div(j_{k})=0 $$ ...
0
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1answer
32 views

Equation of conservation of mass for isotropic fluid considering external forces [closed]

I have trouble doing the following problem: Consider a fluid isotropic in three dimensions such that one can ignore all dissipative forces effect, as would be the viscosity. By analyzing the flow ...
3
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0answers
55 views

Property of stress-tensor in flat spaces

Let $T_{ab}$ be a stress-tensor in a flat space satisfying conservation equations. Define $$ P^i=\int T^{oi}d^3x, \;\; D^i=\int T^{00}x^id^3x $$ Can anyone show me how to prove $$ \frac{dD^i}{dt}=P^i ...
5
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1answer
111 views

Is this a valid proof that the four-current is conserved?

The four-current of a particle moving along a worldine $X^\nu(s)$ is defined as $$j^\mu(x^\nu) = ec \int u^\mu(s)\, \delta^4(x^\nu - X^\nu(s)) \, ds$$ So here's my proof that this is conserved: ...
2
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0answers
28 views

Doppler -D'Alembert laws

I have found a document refering to the following two equations \begin{align*} &\frac{\partial^2 a\left(x,t\right)}{\partial t^2}+2u\left(x,t\right)\frac{\partial^2 a\left(x,t\right)}{\partial x ...
6
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3answers
108 views

Movement in outer space via Newton's law of every action has an equal and opposite reaction

What is more effective for travel in outer space ignoring all other factors like air radiation etc. I have a 10 kg bag of rice would I travel faster throwing the whole bag at once or throwing a grain ...
0
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1answer
93 views

Is there such a thing as instantly stopping?

I'm sorry if this is a stupid question, but I've never taken a physics class and I was curious about something. But anyway, my question is, is there such a thing as instantly stopping? For example, if ...
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4answers
293 views

Does the action and Lagrangian have identical symmetries and conserved quantities?

From the book Introduction to Classical Mechanics With Problems and Solutions by David Morin, page 236 states: Noether's Theorem: For each symmetry of the Lagrangian, there is a conserved ...
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1answer
124 views

What's a good book for an advanced undergraduate/early graduate student to learn about symmetry, conservation and Noether's theorems?

What's a good book (or other resource) for an advanced undergraduate/early graduate student to learn about symmetry, conservation laws and Noether's theorems? Neuenschwander's book has a scary review ...
0
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2answers
438 views

Why is electric charge conserved?

We have long been taught that electric charges are neither created nor destroyed. But somehow it is okay to destroy two oppositely charged particles at once ! Why is that so? Let's just take a look ...
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2answers
123 views

What are the correct initial conditions for the moon (in a simulation)?

So I've modeled the interactions between the sun and all the planets (and the interactions between the planets) using Verlet integration. I've used data from Wikipedia for masses, distance from the ...