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

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Einstein tensor as a conserved current?

As is well-known, the ``traditional" conserved quantities (energy, momentum...) are Noether currents whose conservation depends on the existence of various Killing fields in Minkowski space. In ...
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0answers
52 views

How can we solve 2D rigid body collision? [duplicate]

I know that usually collision with velocity collinear can be solved by simultaneous equations of both conservation of energy and linear momentum. But my question is when 2D velocity is encountered, we ...
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2answers
736 views

A kind of Noether's theorem for the Hamiltonian formalism

How can I (conveniently?) show that an invariance of the Lagrangian and Hamiltonian (i.e. the kinetic as well as the potential energy are independently invariant) will lead to a conservation law using ...
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5answers
6k views

Spontaneous pair production?

So I've been looking into particle-antiparticle pair production from a gamma ray and don't understand one thing. Let's say I have a 1,1 MeV photon and it hits a nucleus - electron-positron pair with ...
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1answer
75 views

Why particles with certain properties can't exist

This is inspired by a recent post on why a free electron can't absorb a photon, though my question below is about something considerably more general. The argument in the accepted answer goes (in ...
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1answer
56 views

Conserved currents from Noether's theorem

I'm not sure if I understand the concept correctly. Given an infinitesimal transformation $$\phi \rightarrow \phi + \alpha \Delta\phi$$ the change in the Lagrangian density ...
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1answer
166 views

Is my proof of the thought experiment that Walter Lewin proposed in lecture 16 valid? [closed]

A tennis ball bounces off a wall elastically. The momentum of the wall changes, but the kinetic energy of the wall remains zero. How is that possible? Walter Lewin Lecture 16 - Ball bouncing on ...
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3answers
91 views

Why can't we define a potential energy for a non-conservative force? [closed]

We could define potential energies for non-conservative forces too and then we could conserve it with kinetic and potential energy as we know it. But no one does that. Why is this? Please explain. Any ...
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3answers
184 views

Conservation of momentum and mechanical energy in different reference frames

I am a biologist developing an interest in physics. I am struggling with the implications of changing reference frames on momentum, mechanical energy and work done calculations. I invented the ...
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1answer
68 views

Annihilation process and photons [closed]

Why should two photons produced by the annihilation process move in opposite direction? I know you would say for the conservation of momentum but why can't they move in the same direction, I want to ...
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1answer
155 views

Applying conservation of energy on a springs/projectile motion problem

My physics teacher proposed a hypothetical problem to our class as we are nearing the end of the Work-Energy Unit (that will in all likelihood show up on the test). I will probably have various ...
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2answers
247 views

What symmetry is associated with conservation of Lipkin's zilch?

The 'zilch' of an electromagnetic field is the tensor $$ Z^{\mu}_{\ \ \ \nu\rho}=^*\!\!F^{\mu\lambda}F_{\lambda\nu,\rho}-F^{\mu\lambda}\,{}^*\!F_{\lambda\nu,\rho} \tag1 $$ given in terms of the ...
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3answers
472 views

What does it mean to say work is path-independent when pushing an object in different directions?

If I apply a straight upward(perpendicular to ground) force against gravity of $5\ \mathrm{N}$ and lift an object "A" 10 meters, then the work done is: $$ W = F \times S = 5\ \mathrm{N} \times 10\ ...
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3answers
3k 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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1answer
143 views

Conservation of linear momentum and velocity of a system (damper and spring in a series)

This example is from a book on dynamics. Let us consider the system above formed by two blocks (each of mass $m$) connected by a linear damper and spring in a series. They slide without friction on ...
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6answers
4k 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
168 views

Why is only angular momentum conserved for a planet and not linear momentum?

Suppose a planet is moving in an elliptical orbit with the Sun at one of its focii. I know that the forces in existence will be gravity which provides the necessary centripetal force. Now my book ...
11
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1answer
295 views

How do higher-order optical chiralities look like?

The optical chirality of the electromagnetic field is a conserved quantity, analogous to the energy density, linear momentum density, and angular momentum density, which describes how chiral the EM ...
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2answers
70 views

At what speed is the conservation of angular momentum carried out?

If the sun suddenly slowed down would pluto's orbit immediately speed up? If so, then isn't the information pertaining to the sun's angular momentum change being carried to Pluto faster than light? ...
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3answers
138 views

General Definition of Steady State

According to many sources (including Wikipedia, Stephani&Kluge, D.J. Acheson) a steady state ist: In systems theory, a system in a steady state has numerous properties that are unchanging in ...
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1answer
50 views

How do I solve for $v_2$ where $mv_1^2 + MU_1^2 = mv_2^2 + M U_2^2$ and $MU_1 - Mv_1 = MU_2 - mv_2$ by eliminating $U_2$?

I was trying to solve the head on collision slingshot problem where the rocket moving with speed $v_1$ approaches a planet which is moving with speed $U_1$. I wanted the final speed of the rocket ...
3
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2answers
162 views

Constant of motion

An exercise from Goldstein (9.31-3rd Ed) asks to show that for a one-dimensional harmonic oscillator $u(q,p,t)$ is a constant of motion where $$ u(q,p,t)=\ln(p+im\omega q)-i\omega t $$ and ...
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1answer
267 views

Angular momentum paradox with 2 identical gears

Consider two identical gears touching each other. The system is friction less. One has a handle that you use to apply a torque on the entire system. If you turn the handle, there will be a non-zero ...
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1answer
337 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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0answers
71 views

A mysterious conserved quantity for a central potential

In teaching a course in classical mechanics and I have come across (from my predecessor) a to me mysterious conserved quantity. We are considering a gravitational (or electric) potential with the ...
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1answer
99 views

What is the different between a dark state and a ground state?

In a atomic quantum system, typically discussing in quantum optics, there is something called dark state. A dark state is a state of a quantum system that does not emit any photon. A ground state also ...
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2answers
340 views

Number conservation of bosons and fermions

Why is the number of bosons not conserved while the number of fermions is conserved? Does it have something to do with the Pauli exclusion principle?
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4answers
185 views

How is angular momentum conserved

from a classical perspective, what is it about angular momentum fundamentally that means it has to be conserved? Surely if I have a rod about a fixed axis and a moving particle hits the end it will ...
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3answers
90 views

Can a neutron decay to the gravitons?

Is it possible that a bunch of neutrons totally decay to the graviton? In other words, does the baryon number conserve in the quantum gravity interactions?
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0answers
58 views

First law of thermodynamics with additional term

I read in a paper that a "known expression for the heat received by a body" is $$dQ=dU+pdV-\mathbf{v}\cdot d\mathbf{P}$$ where $\mathbf{P}$ is the linear momentum of the body, $p$ is the pressure, ...
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2answers
163 views

Is the reaction force for a stone hitting a wall infinite?

Let us assume a rigid stone which moves in empty space with a constant speed of $v$. (Or in the air with no friction and drag or you can imagine a free fall with friction). This stone hits a rigid ...
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1answer
121 views

Explain this contradiction of violation of “ energy conservation ” using classical mechanics

Consider a rocket moves upward with some acceleration for a very small time say '$dt$' then the kinetic energy increases (for acceleration). as well as as the potential energy increases (due to height ...
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0answers
17 views

Motion in Spaces [duplicate]

How does a shuttle move in the space as, the whole mechanism of a rocket is based on 3rd law of newton but, we can not apply 3rd law of newton in space because there is no reactive force in space?
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4answers
495 views

Gravity between two unequal masses. Do both masses move?

I've been watching videos about gravity and I have a question My understanding is that mass have gravity and gravity is a force which attract other object with mass. For example, I jump up and the ...
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0answers
61 views

Dirac equation in the algebra of physical space and conservation laws

I have the following question: I was thinking, is it possible to obtain the conservation laws for the Dirac equation in the algebra of physical space? If yes, how? Can anyone show me a book for these ...
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2answers
188 views

Energy conservation in electrodynamic system

Consider two charged particles initially at rest in the configuration below. Let us assume the following: Starting at time $t=0$, we apply a constant force $f$ to the the bottom particle so that ...
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1answer
82 views

When are energy, mechanical energy, momentum, and angular momentum conserved?

I am in AP Physics and my only real hangup is knowing when the said quantities are conserved. Please define what is the SYSTEM in your answer. I kind of have the basic idea. For example, if there ...
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1answer
129 views

Noether's Theorem for Hamiltonians and Lagrangians

Looking around I see one version of Noether's Theorem that creates conserved quantities from symmetries that preserve the Lagrangian (e.g. http://math.ucr.edu/home/baez/noether.html), and another ...
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1answer
46 views

Applying conservation of energy to a railgun problem?

When a projectile is lunched due to the Lorentz force($F_L$), how can I apply the conservation of energy that the electrical energy inputted to generate the Lorentz force & magnetic field equals ...
2
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1answer
50 views

Simple frame of reference problem (conservation of momentum?)

I'm having trouble wrapping my head around a particular concept. Suppose we have a machine that fires balls of speed $u$ at some mass rate $\sigma$ (of units $\frac{kg}{s}$) directly at a car of mass ...
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3answers
7k views

Relationship between height and velocity in conservation of mechnical energy

I'm a high school physics student, and we recently did a lab on the conservation of energy where we measured the speed of a marble at varying heights on a rollercoaster track. We were supposed to ...
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2answers
172 views

Conservation of energy and Killing-field

In general relativity we have no general conservation of energy and momentum. But if there exists a Killing-field we can show that this leads to a symmetry in spacetime and so to a conserved quantity. ...
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1answer
37 views

Conservation of momentum in inelastic conservation

Why does momentum and velocity change along contact normal but not contact tangent In in elastic collision? Suppose a ball strike an inelastic surface. It's velocity component does not change along ...
0
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1answer
32 views

momentum conservation in particle-antiparticle creation

It's understood that the PRESENCE of a heavy nucleus is necessary for conservation of linear momentum in pair creation. What I can't understand is why it must occur in ADJACENCY of the nucleus. Is ...
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2answers
192 views

Is there something more to Noether's theorem?

From the definition of Lagrangian mechanics, Noether's theorem shows that conservation of momentum and energy comes from invariance vs time and space. Is the reverse true? Are Lagrangian mechanics ...
2
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1answer
62 views

Does third law of motion apply to light or EM waves? [duplicate]

Third law of motion - "For every action there is an equal and opposite reaction" I was considering the situation, where I may be motionless in space with only a flashlight and no forces acting on me. ...
0
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1answer
26 views

The equation of continuity in isothermal system in spherical axis(transport phenomena)

My homework is about finding the equation of continuity in isothermal systems in spherical axis, I can't imagine a workaround for that since its a little complicated for me to understand velocities ...
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0answers
29 views

Momentum and Collision of a ball head on? [closed]

I'm stuck on a question with momentum and collision of two balls. Two balls move toward each other. Ball one is moving in the positive direction, has a mass of m1, and a velocity of v initially. ...
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1answer
70 views

Conservation of momentum homework problem [closed]

A 2-stage rocket travels $1200 \text{ m/s}$ relative to earth. When the first stage runs out of fuel, the explosive bolt separates the first stage from the second with a velocity of $35 \text{ m/s}$ ...
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1answer
125 views

Difference between $dM/dt = 0$ and $\partial M/\partial t=0$ [duplicate]

$\frac{dM}{dt} = 0$ represents a constant of motion $M.$ Why not $\frac{\partial M}{\partial t}$ represent a constant of motion $M$?