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

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If there are 4 dimensions, shouldn't objects appear and disappear in 3D space?

If there are 4 (or more) physical dimensions, and physical objects can move through the 4th dimension in paths perpendicular to our 3 dimensions, the physical objects must pass through our ...
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2answers
41 views

Can momentum be distributed to multiple objects which travel in different vectors?

This is a question about the conservation of momentum: If there were a cluster of billiard balls floating in space and the cluster was struck by one moving ball, the cluster balls would scatter in ...
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98 views

Trying to show that the current is conserved

$ \newcommand{\p}{\partial} $ I am trying to show that the current $J^{\mu} = (\gamma_{\nu}\partial^{\nu} \phi - m\phi)\gamma^{\mu}\psi$ is conserved for all fields that satisfy the Klein-Gordon and ...
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2answers
112 views

Particle number conservation equals $U(1)$-symmetry?

If have by now frequently read the above but never really understood it. It is said that the particle number conservations is related to the phase of the wave function, but how?
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2answers
112 views

Color-charge conservation in proton decay

In some extensions of the Standard Model of particle physics (Supersymmetry with R-parity violation being a prominent example), the proton is allowed to decay, e.g. via $p\to e^+\pi^0$: While this ...
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138 views

Translations and Noether's Theorem

I'm fine with $U(1)$ symmetry and Noether's Theorem, but struggling with the translations of the field; namely $$\phi'(x^{\mu})=\phi(x^{\mu}-a^{\mu}),$$ where $a^{\mu}$ constant four-vector ...
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303 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
1k views

Can the velocity of the center of mass of two spheres change after a collision?

I'm curious as to whether or not the velocity of the center of mass of a system comprised of two spheres can change after the two spheres collide. Looking at the equation for the velocity of the ...
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1answer
159 views

Ghost Number Conservation

I've been reading about gauge theory quantization, and understand it mostly. The only thing I don't get is why people talk about "ghost number conservation". As far as I can tell, the ghost number is ...
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2answers
254 views

A kind of Noether's theorem for the Hamiltonian

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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3answers
376 views

Where do the conservation laws come from?

I know the conservation of energy comes from Noether's theorem via the time-translational symmetry, and if I remember correctly, the conservation of momentum comes from space-translational symmetry. ...
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1answer
132 views

Paradox: electric current in a coil on a disc - will this disc spin if the circuit is opened?

I encountered this problem in a book, but there were no solution written there. The setup: there is a plastic (insulator) circular disc, that is suspended in a way, that can very easily rotate (so ...
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73 views

Why does matter gather as discs around massive objects? [duplicate]

Why do discs, like rings of Saturn and the spiral shape of our galaxy form around massive objects, instead of just a (spherical?) cloud of matter?
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2answers
186 views

Confused about elasticity and collisions

I was solving the following problem and the explanation to it confused me. There are two objects with mass $m$ and $M$, respectively. The object with mass $m$ has a velocity of $\sqrt{2gl}$ and ...
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1answer
2k views

Elastic collision of rotating bodies

How would you explain in detail elastic collision of two rotating bodies to someone with basic understanding of classical mechanics? I'm writing simple physics engine, but now only simulating ...
3
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1answer
628 views

Can we explain physical similarities between Black Scholes PDE and the Mass Balance PDE (e.g. Advection-Diffusion equation)?

Both the Black-Scholes PDE{*} and the Mass/Material Balance PDE have a similar mathematical form of the PDE which is evident from the fact that on change of variables from Black-Scholes PDE we derive ...
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3answers
1k views

Is there more energy in the collapse of a cavitation bubble than the energy required to create the bubble in the first place?

The following does not include all scientific details and parameters, only a common summary of "thoughts". What is scientifically wrong with this summary? When you take your beer and tap the top ...
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4answers
852 views

Why Does Angular Velocity Increase as Radius Decrease?

Suppose a child were to ask you why a tetherball (picture below) seems to speed up as it wraps around the pole. How would you explain this to them? Certainly you wouldn't say something like, "Angular ...
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1answer
120 views

How does conservation of energy manifest itself quantum mechanically?

We know that classically, if we have some theory $\mathcal{L}$ such that the action $\int d^4 x \mathcal{L}$ is invariant under time translation, then we can use Noether's theorem to find that (the ...
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569 views

If a truck collides with a car, can the truck experience a larger force?

I am confused, here is a question: A large truck and a mini bus both have same velocity V and they collide and stop. The collision lasts for 1 second. A) Which one of the two will experience ...
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1answer
119 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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2answers
353 views

Can a neutron be created from pure energy

Is it possible to create a neutron out of pure energy, i.e. not by bringing a bunch of already-existing quarks together? (A quick calculation using E = mc2 shows the energy required would be about 1.5 ...
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Is it possible to lift yourself off from the ground?

Say for instance a person who was strong enough to lift double his body weight. If he placed his hands under his bottom and tried to lift$^1$ himself$^2$ off the ground, could he? -- $^1$In a ...
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721 views

Conservation of angular momentum for a nonrigid body

Question: The sun is not a rigid body but a hot ball of gas. The period of rotation varies from 37 days at the pole to 26 days at the equator. The mean radius of the sun is $7\times 10^8\text{ ...
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555 views

Substance like quanties and conserved quantities, Karlsruhe physics course

In the Karlsruhe physics course one defines the term "substance-like" quantity: Let my cite the definition from a paper by Falk, Herrmann and Schmid: "There is a class of physical quantities whose ...
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Why is only the third component of weak isospin used as a conserved quantity?

Using Noether's theorem \begin{equation} \partial_0 \int d^3x \left(\frac{\partial L}{\partial(\partial_0\Psi)} \delta \Psi \right) = 0 \end{equation} we get three conserved quantites $Q_i$ from ...
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68 views

Relationship of multiple particles under collision [closed]

Consider 3 particles. All 3 particles travel along the x-axis. The 1st particle possesses some mass, m, and its initial position is somewhere on the negative x-axis. It has some (positive) velocity ...
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63 views

What's the corresponding symmetry of enstrophy conservation?

In fluid mechanics, especially 2D turbulence study, people talk about conservation of enstrophy. But I can't really understand enstrophy very well, and what's the corresponding symmetry of enstrophy ...
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1answer
346 views

Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
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1answer
87 views

What's the conserved quantities correspond to the generator of conformal transformation

What's the conserved quantity corresponding to the generator of conformal transformations?
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514 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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58 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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Videos of changing the orientation of an astronaut in space

Kane, Headrick and Yatteau describe in their paper "Experimental investigation of an astronaut maneuvering scheme" possible maneuvers to change the orientation in space without external torque. Is ...
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Does Newton's third law apply to momentum or to forces?

I read all the previous answers concerning the 3rd law and I have seen that it is definitely not universal, (Edit: but conservation of momentum is. If it is not universal it should be not a problem to ...
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Kinetic energy and momentum conservation in an explosion?

My physics book says, "A firecracker sliding on ice has the same total momentum before and after it explodes." I understand this part. This is because of Newton's 3rd law, and no external forces. This ...
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372 views

Thermal expansion is an expression of which conservation laws?

Many objects get larger as they heat up and contract as they cool down. Which conservation laws are applied to describe this phenomenon? How do they interact with each other to produce this effect?
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488 views

Rotation, cats landing on their feet, and conservation of angular momentum

Let θ be the orientation (angle) of a body (such as a cat), and let ω be its angular velocity. It is well-known that θ can change even when the body is not rotating, using the conservation of angular ...
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2answers
2k views

Angular momentum conservation while internal frictional torque is present

So this appears in a problem which looks simple enough in its context; It's something like this: Two discs, A and B, are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ ...
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2answers
208 views

Is there any law that prevents an object with mass to become massless?

I got into a discussion with my physics teacher about the speed of light and I asked What if an object with mass was to lose mass as it gained speed-- would that allow for an object to eventually ...
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1answer
2k 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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2answers
489 views

How do you find conserved quantities for linear second order ODEs?

I have a differential equation of the form $ \frac{d^2 y}{dt^2} + f(t) \frac{dy}{dt} + g(t) y = 0 $ where $f$ and $g$ are known functions of time. Is there a systematic (or otherwise) way of ...
2
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1answer
109 views

Total divergence term and corresponding Feynman Diagram

A total divergence term added to the Lagrangian doesn’t affect the action because the integral of a total divergence vanishes. But if one attempts to derive the Feynman rules from the Lagrangian with ...
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981 views

Simple elastic collision

If a particle with mass $m$ collides with a wall at right angles, and the collision is perfectly elastic. The particle hits the wall at $v\ ms^{-1}$. There is no friction or gravity. So the particle ...
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Why do some satellites fall to Earth?

In another question How does Newtonian mechanics explain why orbiting objects do not fall to the object they are orbiting?, one can read an affirmative answer. They how do you explain satellites ...
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2answers
132 views

What motion can emerge in a still universe? [duplicate]

I consider a very large non homogeneous cloud of dust in isolation. No external gravitational interactions. It is initially completely still and start collapsing under the its own gravity. Can the ...
2
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2answers
148 views

Question relating to energy transfer in between two particles

How would I go about calculating the maximum kinetic energy transferred from one particle when it forms an elastic collision with another particle. For example, if I had two billiards one with mass m ...
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4answers
508 views

Application of Kirchhoff's laws in circuits with inductors

As we know,the Kirchhoff circuit laws are applicable for conservative electric fields. Now it is applicable for circuits where inductors are present but the field there is not conservative. So how ...
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3answers
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When is momentum not conserved?

What are some common examples where momentum is not conserved? This question arose in my mind when I read that a ball dropped from a height penetrates into a bed of sand and that momentum is ...
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423 views

How to calculate a collision which is partly elastic and partly inelastic?

(For the purpose of this question, "calculating a collision" means: given the velocities and masses of two objects in a collision, figuring out the new velocities of both objects after the collision). ...