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

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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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3answers
4k views

Proving angular momentum is conserved for a particle moving in a central force field $\vec F =\phi(r) \vec r$

A problem I am trying to work out is as follows: A particle moves in a force field given by $\vec F =\phi(r) \vec r$. Prove that the angular momentum of the particle about the origin is constant. ...
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2answers
459 views

Would a sneeze by a cosmonaut in a spacesuit affect his movement?

Naive question; feel free to shoot me down It is a truism that any motion in space would continue indefinitely unless it is opposed by an external force. If a cosmonaut were to sneeze within his/her ...
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203 views

In QED, why is the $e^- + e^+\leftrightarrow\gamma$ process forbidden on-shell?

QED has a vertex that couples a single photon to two fermions. This vertex describes the annihilation of an electron-positron pair into a photon. Why is this process forbidden for all three particles ...
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635 views

How to apply Noether's theorem

Say I have a point transformation: $$x' ~=~ (1 +\epsilon)x,$$ $$t' ~=~ (1 +\epsilon)^2t,$$ and Lagrangian $$ L ~=~ \frac{1}{2}m\dot{x}^2 - \frac{\alpha}{x^2}.$$ How do I go out about showing ...
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What causes a force field to be “nonconservative?”

A conservative force field is one in which all that matters is that a particle goes from point A to point B. The time (or otherwise) path involved makes no difference. Most force fields in physics ...
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355 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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225 views

Why does the pion half-life differ between the charged and uncharged species?

Why does the uncharged pion have much shorter half-life than the charged pion despite the fact that the uncharged pion has a little bit less mass than the charged one, so that according to the ...
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91 views

Pass to globally conserved currents from locally conserved currents in curved spacetime

Let us begin with a Lagrangian of the form $$\mathscr L= \frac 12 \sqrt{-g}g^{\mu\nu}\partial_\mu\phi(x)\partial_\nu\phi(x)+\mathscr L_g,$$ where $$\mathscr L_g=\frac 1{16\pi k}\sqrt{-g}R.$$ ...
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785 views

Symmetry of Euler-Lagrange equations and conservation laws

Continuous symmetry of the action implies a conservation law, but what if equations of motion have a continuous symmetry? Does it imply a conservation law? Also is symmetry of equations of motion ...
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Quantum Mechanics: Show that the expectation value of angular momentum does not change with time

The potential is given by $V\left(\left\|(x,y,z)\right\|\right)$, so $[\hat{L}, \hat{H}] = 0$. Using the definition of $\langle \hat{L} \rangle$ and the time-dependent Schrödinger equation, show that ...
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818 views

How does Delta baryon decay conserve angular momentum?

I'm a chemist so bear with me: I understand the Delta baryons $\Delta^{+}$ and $\Delta^{0}$ to be in some sense spin (and isospin) quartet states of the proton and neutron. These can decay straight ...
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1answer
105 views

When I move my arm forward in vacuum, will my body move backward?

Let's say I stay at point $x=0$ in vacuum. When I move my arm forward such that it will have a positive $x$ position (say $x=5$) will the rest of my body move backward such that it will have a ...
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1answer
231 views

Question on conserved quantities and Noether's theorem

I have a question about Noether's theorem in the context of QM, which I'll state in the context of the weak interaction but the basic point could be generalized. According to Noether's theorem, given ...
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1answer
127 views

Is it possible to project a problem of mechanics in a lower dimensionality?

I had the intuition that, in classical mechanics, when the trajectory of a body is known, then analysis of its motion can be done in the linear space of that trajectory, if all forces are projected on ...
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1answer
269 views

Firing machine question

Suppose we have a firing machine on a frictionless surface at point $x=0$. It fires a bullet of mass $m$ every $T$ seconds. Each bullet has the same constant velocity $v_0$. There's a body of mass ...
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170 views

Parity of a decay

If a particle of unknown intrinsic parity decays into 2 particles each with negative intrinsic parity, does that necessarily imply that the original particle also has negative parity?
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257 views

Crystal Momentum in a Periodic Potential

I'm working through some basic theory on periodic potentials, and I would appreciate help in understanding the crystal momentum. Suppose we have a Bravais lattice with lattice vectors $\textbf{R}$. ...
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1answer
71 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 ...
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274 views

Two-body problem questions

I am self studying the two body problem and I'm stuck on the following: I have given $$\ddot{\vec{x}}_1= - G m_2 \frac{\vec{x}_1-\vec{x}_2}{|\vec{x}_1-\vec{x}_2|^3}$$ and $$\ddot{\vec{x}}_2= - G ...
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Why is momentum conserved in an inelastic collision and kinetic energy is not conserved?

We know that in an inelastic collision that total momentum of the system before collision equals the total momentum after collision. But total kinetic energy before collision is not equal to total ...
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555 views

Differential or integral form of the conservation equations?

Is there a 'rule' for when it is best to use either the differential or integral form of the continuity and momentum equations in calculations?
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391 views

Thrust center in space

I have this dilemma: Suppose you have a space ship somewhere in deep space, where there is no drag force or substantial gravity. If the ship has a single engine situated in such a way that the center ...
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1answer
368 views

Is momentum conservation for the classical Schrödinger equation due to non-relativistic or due to some more exotic invariance?

I had no problem appliying the Neothers theorem for translations to the non-relativistic Schrödinger equation $\mathrm i\hbar\frac{\partial}{\partial t}\psi(\mathbf{r},t) \;=\; \left(- ...
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329 views

Lepton Number Conservation

What is the global symmetry of the electroweak Lagrangian that gives rise to lepton number conservation? As I understand it, electric charge is some linear combination of the conserved quantities ...
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543 views

Conservation of momentum in collision of two bodies

Suppose we have some ramp on wheels of mass $M$, standing on a frictionless surface. A cart of mass $m$ moves with a certain velocity $v$ towards the ramp. The cart moves up the ramp ...
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Energy conservation in Electrodynamics

Let us suppose that we have a known electromagnetic wave-train of finite size propagating in a certain direction. There is a probe charge on its way. This EMW is an external field for the charge. The ...
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800 views

Can conservation of momentum be violated?

The law of the conservation of momentum has been established for hundred of years. Even in Quantum field theory every particle collision must be momentum-conserving if there is homogenity in space. ...
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Conservation of momentum but not kinetic energy in inelastic collisions

In inelastic collisions, the kinetic energy of the system is not conserved but the momentum is. Kinetic energy is: $0.5 \times \text{mass} \times \text{velocity}^2$. Momentum is: ...
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503 views

Rocket/Thrust/Gas/Free Expansion of Gas

We know, the rockets in space use Newton's 3rd law to increase their velocity and hence move. What I don't understand is how it is possible in space aka vacuum-state without air? From what I know, ...
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Newton's 3rd Law: How can I break things?

If I punch a wooden board hard enough and it breaks in two, has the board still exerted a force of equal magnitude on my fist? When the board breaks in two due to my force, the halves have a ...
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4answers
435 views

Is the principle of Conservation of Energy empirically verifiable?

Before I am inundated by myriad and vociferous claims that conservation of energy is the single most well-attested and experimentally verified principle in all of science, let me say that I am well ...
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225 views

What barriers exist to prevent us from turning a baryon into a anti-baryon?

At present the only way we can produce anti-matter is through high powered collisions. New matter is created from the energy produced in these collisions and some of them are anti-matter particles ...
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126 views

Classical EM : clear link between gauge symmetry and charge conservation

In the case of classical field theory, Noether's theorem ensures that for a given action $$S=\int \mathrm{d}^dx\,\mathcal{L}(\phi_\mu,\partial_\nu\phi_\mu,x^i)$$ that stays invariant under the ...
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231 views

Two components of angular momentum conserved $\Rightarrow $ All three components are conserved?

I was wondering whether it is correct to say that if two components of the angular momentum are conserved, then all three Cartesian coordinates of the angular momentum are conserved? I would regard ...
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How is Angular Momentum Conserved when Mass is Released?

I am not a physicist (math/comp-sci) but I understand that Angular Momentum is supposed to be conserved. I find this confusing because there seems to be many simple, common cases where a restrained, ...
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100 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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987 views

What is difference between the different 'flavours' of neutrinos?

Moreover, how-come scientist know that muon-neutrino are different from electron-neutrino when they didn't even know what the difference was? Did they interact differently with other particles?
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188 views

Any case of a particle seemingly decaying into copies of itself?

Is there any case reported that seems to resemble the following: there is a particle and at some moment, the particle seems to break down into two or more particles that are all identical to the ...
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75 views

Why is $p_\phi$ conserved in a Schwarzschild orbit?

This arises from the question What is the relationship between $a$ and $m$, which I'm afraid I answered just by looking it up in Schutz's book. However Schutz (as he frequently does) glosses over ...
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88 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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460 views

If angular momentum corresponds to linear momentum, what corresponds to energy?

Angular momentum is defined from linear momentum via $\vec L = \vec r\times\vec p$, and is conserved in a closed system. Since energy is the time part of the linear four-momentum, is there a quantity ...
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1answer
400 views

What conservation law corresponds to this local $U(1)$ symmetry of the CCR?

It is known that canonical commutation relations do not fix the form of momentum operator. That means that if canonical commutation relations (CCR) are given by ...
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3answers
187 views

Trilinear gauge couplings: Spin

In non-abelian gauge theories self interaction of gauge fields is permitted, allowing coupling such as $WWZ$ (i.e. $Z$-boson decaying to $W^+W^-$) or ggg (i.e. gluon splitting into two new gluons). ...
3
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1answer
189 views

In a Sterling Engine, does heat from the hot side transfer to the cold side?

A Sterling Engine is a closed system. The "hot" side oscillates between higher temperature with higher pressure and lower temperature with lower pressure. Does Nature switch back and forth between ...
3
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1answer
186 views

Intuitive meaning of a special case of the Bernoulli equation

In the Bernoulli equation, if $h$ equals zero, it reduces to $$P_1+\frac12\rho v_1^2 = P_2+\frac12\rho v_2^2$$ The equation does not have an intuitive meaning other than the fact that it is a bare ...
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286 views

Conservation of momentum and energy in an explosion

One simple problem is physics is to determine the mechanical energy difference after an explosion. To do this, you must assume that momentum is conserved because in a explosion you have internal ...
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1answer
152 views

Euler Equations, Sod shock tube & conservation

Conservation of momentum? I am considering the Euler equations in conservative form and solving the Sod shock tube problem I have written a Godunov finite volume type solver. It solves for density ρ, ...
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1answer
235 views

Conservation of total angular momentum in $\Phi$-meson decay

I am looking into the decay of a $\Phi$-meson decaying into $K^+$, $K^-$. My problem is, the $\Phi$-meson has a total angular momentum of 1 and the two Kaons have a total angular momentum of 0. On the ...
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262 views

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 ...