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 is information conserved over time?

From what I've learned, information seems to be the knowledge of the past and it suggests that it is preserved by specific aspects of particles. But considering time isn't an issue, it suggests that ...
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Non-conservation of angular momentum example but is an external torque really required?

Say a man is twisting his body using internal body muscle contractions and torque interactions between his feet and ground (no slipping). From the answers of a previous question I raised, these ground ...
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Where does this formula come from? [closed]

I am doing revision for my module stellar & galactic astrophysics and have come upon this formula which I cannot seem to derive. Could someone please explain where it comes from? "For an ...
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Where does the law of conservation of momentum apply?

Take the scenario of a snowball hitting a tree and stopping. Initially, the snowball had momentum but now neither the snowball nor tree have momentum, so momentum is lost (thus the law of conservation ...
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Additional term in the Noether current

I've seen this same question before Why is there an extra term in definition of Noether current for spacetime translations? but I didn't understand the answer that was given so I would like to ask ...
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Is it easier to apply angular momentum to a rocket with the engine off?

Let's say I've got a rocket that I need to rotate for my next maneuver. Assuming it's flying through full vacuum, I can turn off my engine first, and then use reaction control thrusters to rotate, or ...
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Can a lone photon disintegrate?

While studying the very basics of QFT, I became aware of scattering interactions. After some research, it seems that a massive particle can give two new particles. However, I cannot find anything ...
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Do we include momentum conservation factors in amplitudes?

Let $\phi$ be a real scalar field and $$\mathcal L = \frac{1}{2}(\partial_\mu \phi)^2 + \frac{1}{2}m^2\phi^2 - \frac{\lambda}{4!}\phi^4.$$ Given the standard Feynman diagrams and Feynman rules for $\...
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How Would a Feynman Diagram Look Like for a Proton-Proton Collision?

The LHC is a proton-proton collider. If I wanted to draw a leading order Feynman diagram for a two-quark production in proton-proton collisions, would it be correct to draw sth like this, or would ...
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How does cobalt-60 beta decay experiment also violate charge conjugation?

I understand why the cobalt-60 decay experiment shows that parity is violated in the weak interaction. However, my lecture notes also say that 'Note that the outcomes of this experiment can also be ...
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Demonstrate why conservation of momentum stems from invariance to translation - in Newtonian mechanics [duplicate]

I know that conservation of momentum is caused by invariance (symmetry) of the laws of mechanics to translation - this is an example of Noether's theorem. However, I'm looking for an explanation, ...
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Question about Conservation of Momentum

I have what I believe is a simple question about the conservation of momentum, but I'm not sure what the answer is. I'm wondering when a stationary ballistic pendulum collides perfectly inelastically ...
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Three body problem + spring + center of mass (classical mechanics)

Given three bodies with mass $m$ each - body $1$ moves (to the right) towards the stationary body $2$ with velocity $v_1=7v$ and collide with it. On the other side of body $2$, body $3$ moves (to the ...
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How impulse is fundamentally different than momentum?

Are impulse and momentum really different quantities? Is there a conservation law of Impulse too just like momentum conservation. And lastly, will impulse be conserved for the cases where body (say a ...
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An application of Conservation of Angular Momentum

One of the applications of the law of conservation of angular momentum involves a helicopter with a single propeller. A/c the book, a helicopter with one propeller would rotate itself in the opposite ...
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Conserved charges for complex scalar fields

I have been studying complex scalar fields, and in Peskin and Schroeder, An Introduction to Quantum Field Theory, (chapter 2, problem 2, part d— on page 34) they ask you to compute the conserved ...
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Centre of a black hole

In a text intended for people without background in general relativity or quantum mechanics, I read two statements which are false or do not make sense, if I'm correct. Am I correct, and why (not)? ...
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A doubt regarding Maxwell correction for Ampere's law [duplicate]

I am reading the book Introduction to Electrodynamics by David J Griffiths. Given a magnetic field $\bar{B}$ and volume current density $ \bar{J}$ by Ampere's law we have $$ \nabla \times \bar B = \...
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Why are there two pressures acting on a body in opposite direction during free fall on earth?

This is how my sir explained this to me: There are more than billions of atoms present in the earth's atmosphere. All those atoms have their force acting downwards. When he explained this diagram to ...
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On elastic collisions and calculating velocities

I am teaching a PHY class at the high school level. I wanted to check that this is a valid way to get the relative velocities of objects after an elastic collision to wit: -- Usually we are told (for ...
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How is rotational information transferred to a singularity? [duplicate]

If some mass spirals into a black hole the conservation of angular momentum means that the result will have to spin (at least to my albeit limited understanding). But if the singularity is a point, ...
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Integrating an equation of motion

My physics book says that the equation of motion $ 2 \dot{r} \dot{\varphi} + r \ddot{\varphi} = 0 $ can be integrated once to give the equation $ mr^2 \dot{\varphi}= \text{const} $, assuming constant ...
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Velocities in an elastic collision

My teacher keeps saying that, in a head-on elastic collision of two bodies of equal masses, the velocities get exchanged. But consider two balls of equal mass moving with the same velocity in the ...
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A simple mechanics problem

The problem says: A bullet hits a block kept at rest on a smooth horizontal surface and gets embedded into it. Which of the following does not change? A. Linear momentum of the block B. Kinetic ...
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Why can't a photon decay into to pions $\gamma \to \pi^+ + \pi^-$?

I was looking at this statement (found in a problem set online): The decay $\gamma \longrightarrow \pi^+ + \pi^-$ is impossible according to special relativity So I considered the following method ...
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Conservation of mass in nuclear reactions

I've read that the law of conservation of mass doesn't hold in nuclear reactions, but I think it does hold. Consider the following reaction: $$\require{mhchem} \ce{ A -> B + C}$$ I can write $m_{A} ...
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Conservation of momentum in a newton’s cradle with inelastic collisions

Let's consider that we have a Newton's cradle in vacuum: Considering that each ball has a mass of 100g or 0.1 kg we release the ball and at the time of contact, the ball has a final velocity of 1 m/s....
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Does: capillary_action * surface * distance = (force*surface) / area*distance == capillary_energy?

I'm trying to get the hang of the conservation of energy. Looking for that aha moment when it makes more sense that energy is conserved than not. When reading it seems to be a consensus that energy is ...
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Why is angular momentum conserved if we keep a ball on rough surface with only translational velocity after it attains pure rolling motion

Assume a ball to be kept on a rough surface with intial translational velocity V and no rotation. After some time it aquires pure rolling. It is acted upon by an external torque due to friction still ...
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Earth's unimpeded rotation for billions of years [duplicate]

My nephew (7th grade) has stumped me with this question. If I spin a top, it eventually stops, because of friction, air resistance etc. How come the Earth has been spinning non-stop for 4.5 Billion ...
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Why is it difficult to define conserved quantities in general relativity as in special relativity?

How exactly are conserved quantities, i.e. mass, energy and momenta of a system computed in special relativity and why doesn't it work in general relativity? I know that the curvature of the spacetime ...
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What is information the generator of?

According to the no-hiding theorem (see https://en.wikipedia.org/wiki/No-hiding_theorem), information is truly and generally conserved within any isolated system. According to Noether's theorem (https:...
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Does Conservation of Four-Momentum imply Conservation of Energy in Particle Physics?

In Particle Physics processes, we always assume four-momentum conservation. Does this automatically lead to energy conservation, since the four-momentum conservation must be fulfilled for every ...
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What is the mathematical justification for introducing the surface traction/stress tensor in the derivation of the momentum balance?

In fluid dynamics and continuum mechanics it is common to derive the the momentum balance by the following argument: For some open domain $V$, use the Reynolds Transport Theorem to show: $$\frac{d\...
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Why is $g_{\mu\nu}\frac{dx^\mu}{d\lambda}\frac{dx^\nu}{d\lambda}$ a constant for geodesics in GR?

In Sean Carroll's spacetime and geometry chapter 5 Carroll states the following In addition we always have another constant of the motion for geodesics: the geodesic equation (together with metric ...
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Why don't mirrors violate conservation of momentum/do they get warm? [duplicate]

Imagine you have a photon with momentum $p$ which hits a mirror $M$ and is reflected back. Since $M$ is at rest in your frame of reference the total momentum of the system pre-reflection is $p$ and ...
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Continuity Conditions at a General Wave Boundary:

is there some general approach to deducing the continuity conditions at a wave boundary for any type of wave - quantum, string, pressure etc. that works for you in your physics. I find it difficult to ...
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Is momentum conserved in the rocket equation? If so, why is there force? [closed]

I'm studying the rocket equation and from what I get from it the momentum between the fuel and the rocket is conserved. But if that happens, how come the calculated force is not zero? The rocket ...
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Electric Current in Classical Electrodynamics derived as Noether current [duplicate]

I'm looking for a derivation of the often quoted fact that the conservation of electric(!) current $j^{\mu} = (c \rho, \vec{j})$ in relativistic classical electrodynamics is an explicit consequence of ...
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What keeps the cookie in my coffee from moving when I rotate the cup?

I dropped a browny cookie in my coffee cup, it sank at first but then surfaced after a couple of minutes. I tried to rotate the cup to lure the cookie out, but it got stuck in place. Please check out ...
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The conditions under which a stress tensor $T^{\mu\nu}$ exists

I used to believe that the existence of the stress tensor in a QFT has to do with translation invariance: "If a theory is translation invariant, then one can construct a conserved $T^{\mu\nu}$ by ...
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Angular momentum conservation in semiconductors

In elementary quantum mechanics, we know that when the system possess continuous rotation symmetry, the angular momentum is conserved, and the Hamiltonian of the system commutes with angular momentum ...
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Law of conservation of energy and law of conservation of momentum cannot both be true?

For example, lets assume there is an elastic collision between two balls. The first ball has a mass of 2 kg and an initial velocity of 4 m/s. The second ball has a mass of 4 kg and is at rest so it ...
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Calculating new velocities of $n$-dimensional particles after collision

I am working on a particle simulation where there is no gravitational force exerted on particles, they simply travel through space and, upon collision, change trajectories accordingly. There isn't a ...
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Verification of Faradays law of EMI

What is the verification for Faraday's law of EMI which involves the change in current and voltage produced by the generator with change in speed of the rotor?
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Follow-up on “Conservation of electric charge in Feynman diagram”

I took the following Feynman diagrams from page $5$ of this document: For the right diagram, I drew the circled $1$ and $2$ myself. What I unfortunately don't understand yet is: (i) This question is ...
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Random Direction of Spontaneous Emission, and Conservation Laws

I'm trying to imagine how/why the direction of a spontaneously emitted photon is random, and how that works and reconciles with the conservation of momentum and kinetic energy. For intuition, I was ...
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Deriving conserved charges from the equations of motion

It is very well established how to derive conserved charges associated to the symmetries of Lagrangian using the Noether's theorem. Also in the Hamiltonian formulation, we know how to derive the ...
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Do all Noether theorems have a common mathematical structure?

I know that there are Noether theorems in classical mechanics, electrodynamics, quantum mechanics and even quantum field theory and since this are theories with different underlying formalisms, if was ...
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What is the energy integration constant from time symmetry in general relativity?

If the metric components $g_{\mu\nu}$ are independent of the time coordinate $x^0=t$, then it's common to say there is a constant of motion called "energy" begotten from considering the ...

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