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

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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 ...
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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 ...
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1answer
91 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., $$ (\Pi _{k} )_{t} - \rm div(j_{k})=0 $$ ...
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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 ...
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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: ...
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3answers
237 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 ...
6
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3answers
107 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 ...
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1answer
89 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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1answer
121 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 ...
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4answers
286 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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4answers
192 views

Is the canonical momentum conserved when a particle moves in magnetic field?

Here is a question about the canonical momentum that I had asked some days ago, but I still have one point that I am not understand. Considering a particle moves in a magnetic field with charge $q$ ...
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2answers
410 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 ...
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1answer
107 views

No valid Feynman diagram for processes

This will likely be easy for anyone experienced in particle physics, but I'm not. I'm asked to explain why it is impossible to construct a valid Feynman diagram using Standard Model vertices for the ...
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1answer
99 views

Quantum explanation of Newton's Third Law of Motion

Newton's law states that for every action there is equal and opposite reaction. This law explains how rockets fly in space and accounts for the the majority of the lift action generated by a ...
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1answer
70 views

How to apply conservation of angular momentum with a shock? [closed]

I got this tricky question, need help. A uniform rod of mass $M$ and length $L$ is attached to an axis at its top, a bullet with mass $m$ traveling at speed $U$ (horizontal) hits the rod at $2L/3$ ...
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1answer
85 views

Angular Velocity after a frictional impulse

I am modelling 2D physics collision into simulations. In Physics for Game Programmers, Grant Palmer book, the velocity Vn1 after collision is mentioned to be independent of the friction coeff. ...
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3answers
144 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 ...
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1answer
183 views

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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1answer
73 views

Symmetry of Minkowksi Metric -> Conserved Current?

My understanding of the Minkowski Metric is that we have the freedom to choose whether to place the negative sign on the time-component or on the spatial-components. That is, either basis should ...
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1answer
722 views

What is happening to rotational kinetic energy when moment of inertia is changed?

I know this question is asked here a lot, but I just had to ask this to finalise the concept. When a system lets say a rod of length $L$ and mass $M$ is rotating with angular speed $omega_1$ its ...
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3answers
411 views

Where does the kinetic energy go?

A uniform cylinder was placed on a frictionless bearing and set to rotate about its vertical axis. After a cylinder has reached a specific state of rotation it is heated without any mechanical support ...
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1answer
108 views

Proof: Conservation of a 4-vector in one frame implies conservation in another

I came across a proof that says if a 4-vector $P$ is conserved in one inertial frame $$P_{before}=P_{after} \text{ (sum)}$$ then Lorentz transforming to another frame gives $$P'_{before}=\Lambda ...
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1answer
58 views

How 4-vector nature of the value is connected with it's conservation law?

In electrodynamics Poynting vector and energy flux of field don't create 4-vector. Also they aren't conserved independently from substance (conservation law includes summand connected with current ...
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1answer
46 views

Conservation laws vs Einsteinian space-time

The way I understand conservation laws - which I am asking you to correct - is that if I observe any slice of the universe perpendicular to the time axis and count up all the mass/energy, momentum, ...
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1answer
74 views

Conservation of mass in fluid flow

When deriving the continuity equation in physics class for two immiscible fluids flowing in succession we used the principle of conservation of mass. My question is, shouldn't volume be conserved ...
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1answer
51 views

Angular momentum of anistropic harmonic oscilator

A potential given by : $$ V(x,y,z) = \frac{1}{2}m(x^2+y^2+\frac{z^2}{2}). $$ Which component of angular momentum is conserved. An attempt: Angular momentum along z, $ L_{z} = m(x\dot{y} - ...
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63 views

Hidden momentum

I'm trying to learn about hidden momentum. After reading what I could find with a google search, I understand that it is equal to the momentum carried by radiation, calculated with the Poynting ...
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8answers
4k views

How can momentum but not energy be conserved in an inelastic collision?

In inelastic collisions, kinetic energy changes, so the velocities of the objects also change. So how is momentum conserved in inelastic collisions?
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0answers
61 views

Collision Between Two Particles: Writing the Mass As A Function of The Angle [duplicate]

Suppose we have two masses, $m_1$ and $m_2$, where $m_2$ is at rest, and $m_1$ is headed directly towards $m_2$. I would like to write the ratio of the masses as a function of the angle. Using ...
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1answer
92 views

How is the current for the Dirac equation derived?

Why is it that the derivative of the current $j^\mu$ is the difference between the Dirac equation and its adjoint?
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1answer
78 views

Noether's theorem for more interesting transformations of the time co-ordinate

According to Wikipedia, Noether's theorem (for the mechanics of a point particle) says that if the following transformation is a symmetry of the Lagrangian $$t \to t + \epsilon T$$ $$q \to q + ...
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1answer
27 views

Is using water in a charcoal smoker less efficient than not using water?

I have a charcoal smoker that uses water. My understanding is that the water serves as a buffer and as a way to add moisture to the cooking environment. Some say that using water wastes fuel because ...
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2answers
224 views

Noether's theorem and time-dependent Lagrangians

Noether's theorem says that if the following transformation is a symmetry of the Lagrangian $t \to t + \epsilon T$ $q \to q + \epsilon Q$ Then the following quantity is conserved $\left( ...
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2answers
250 views

Emmy Noether's theorem in simpler terms

I'd like to understand Noether's theorem and its contents as to what it implies in a bit simpler terms. I am familiar with mathematics unto Calculus 1,2,3 and some linear algebra and group theory. I ...
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0answers
41 views

Experimental information: is momentum conserved?

Could I say that it is conserved during the time, or instead there is a slight decrease?
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1answer
121 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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2answers
203 views

How to calculate velocities after collision?

I'm currently writing a program for a particle simulator. One of the requirements is that the particles collide in a realistic way. However, I don't know how to calculate the final velocities. For ...
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2answers
140 views

What is the symmetry associated with the local particle number conservation law for fluid?

According to Noether's theorem, every continuous symmetry (of the action) yields a conservation law. In fluid, there is a local particle number conservation law, which is ...
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2answers
129 views

Proof of conservation of information [duplicate]

After listening of some lectures of Leonard Susskind about black holes, he mentioned that conservation of information is one of the foundations of physics. After searching the web I cannot seem to ...
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2answers
373 views

Angular momentum conservation in pion decay?

I have seen the charged pion decay $$\pi^{-}~\to~ \bar{\nu}_{\ell} +\ell^{-}$$ represented with diagrams containing a $W^-$ in the $s$-channel. The $\pi^-$ and $W^-$ have angular momentum $0$ and $1$ ...
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1answer
119 views

Is it useful to geometrically represent conservation laws?

In my physics class, we just studied collisions. We learned that momentum is conserved in collisions. I decided to examine a one dimensional collision in which two objects collide - object 1 and ...
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3answers
275 views

Conservation of energy and continuity equation

When physicists say energy is conserved, do they mean that energy satisfies the continuity equation: $$\triangledown \cdot j+\dot{\rho}=0$$ On the internet there is plenty of talk of how the ...
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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 ...
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6answers
2k views

Is there a way for an astronaut to rotate?

We know that if an imaginary astronaut is in the intergalactic (no external forces) and has an initial velocity zero, then he has is no way to change the position of his center of mass. The law of ...
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1answer
118 views

Conservation of Hamiltonian vs Conservation of Energy

What is the difference between conservation of the Hamiltonian and conservation of energy?
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2answers
77 views

Conservation of ang. momentum for paths reaching a rotation axis

My question is the following: if we had the trajectory of a particle eventually reaching a point of a rotation axis $ \vec{u} $ (take that as being the z-axis for convenience) by an angle $ s $, ...
4
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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 ...
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1answer
168 views

Deriving $p = mv$ from translational symmetry (momentum conservation law)?

"In classical mechanics, momentum is defined as the quantity which is conserved under global spatial translations or, alternatively, as the generator of spatial translations." (G.Parisi, ...
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2answers
144 views

Tension in vertical circular motion

In vertical circular motion we conserve energy for calculating velocities at a point (if initial velocity given). But, energy can only be conserved when forces are conservative. Tension is not a ...