# Tagged Questions

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

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### 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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### 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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### Noether's theorem for space translational symmetry

Imagine a ramp potential of the form $U(x) = a*x + b$ in 1D space. This corresponds to a constant force field over $x$. If I do a classical mechanics experiment with a particle, the particle behaves ...
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### 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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### No diffusion term in conservation of mass in Navier-Stokes equations?

I have followed derivations of the Navier-Stokes equations and I can see how the various terms arise in the "main equation", the momentum conservation equation. However I don't understand why the ...
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### 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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### 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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### 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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### Translational invariance implying diagonal representation in momentum space

I have just come across something in my reading of Peskin and Schroeder that claims that because a function, in this particular case a two-point correlation function, is translationally invariant, it ...
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### 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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### 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 SchrÃ¶dinger equation, show that ...
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### Are there conserved quantities in field theory which don't arise from Noether's Theorem?

In some QFT texts one writes down the number operator $N$ for free theories, such that when acting on an $n$-particle state $|n\rangle$ we have $$N|n\rangle=n|n\rangle$$ In free theories this is a ...
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### 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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### Why do wheels spin?

I'm pretty sure this is probably a stupid question but it is annoying me a lot. In my physics textbook it says, cars move because the wheels exert a backward force on the ground and the ground exerts ...
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### Does the Inertia of a Cue Ball Affect its Reflection Angle off a Resting Billiard Ball?

Consider the following Diagram in which a Cue Ball (A) of mass M is shot twice at another pool ball with identical mass M. When the force with which the cue ball (A) is hit (v1) is increased (v2) ...
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### Determine path of point mass using the Hamilton's principle

I am very new in this field but I try to solve a problem by using the Hamilton's principle and afterwards I want to compare the solution by solving the same problem using conservation laws. What I ...
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### 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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### 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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### Confusion regarding rotational motion!

Let us assume I have a rod of some mass m, moment of inertia I, length l and center C. If I apply a force F on C for a duration of time t, it will accelerate forward. If I apply it elsewhere, the ...
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### 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 airplane'...
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### Why can't I push myself in a chair? [duplicate]

If I am sitting in a chair with wheels and someone pushes on the back of my chair with sufficient force it will role along the ground. However, if I push on the back of the chair with the same force ...
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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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### Light and momentum question? [duplicate]

Each photon of light bulb carries momentum. Why does the light bulb not recoil from conservation of momentum?
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### Why isn't momentum conserved in this pulley problem?

I have some conceptual doubt about method of solving this problem. 24. A block of mass $m$ and a pan of equal mass are connected by a string going over a smooth light pulley as shown in figure (9-...