# All Questions

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### Why is orbital angular momentum quantized according to $I= \hbar \sqrt{\ell(\ell+1)}$?

I simply have no idea how this result is found $$I=\hbar \sqrt{\ell(\ell+1)}.$$ The result seems to just be dumped in textbooks rather than explained. I can get the result that $I_z=\hbar m_j$. ...
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### Amount of entanglement in terms of greatest eigen value for hermitian matrices?

I was reading the paper No Universal Qubit Flipper. In this the paper they show inability to create a universal flipping machine. The method they follow is they take an entangled state between Alice ...
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### Spinors and asymmetry of wave function

A spinor is a mathematical entity which changes sign if it is rotated by $2\pi$. Is this connected to the asymmetry of the spinor wave function?
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### Do quasiparticles have antiparticles?

Bosons (except for W) are their own antiparticles, since they have no electric charge. Charged fermions have antiparticles differing from the particles. Now my question is: has a charged ...
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### second variation of the action for 1-d lagrangian

i know that the first variation of the action integral yields to the euler lagrange equation by setting $\delta S [y(x)]=0$ however given a Lagrangian in the form $$\frac{1}{2}mv^ {2}-V(x)$$ how ...
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### How do these factors affect the free fall of objects?

Take an example of two balls of different masses being dropped from about 250 meters from the ground. How do the following factors affect free fall: Air resistance. Absence of air resistance. ...
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### Self-made air pump - What does it take to pump up a balloon?

We are building a simple altitude-controlled balloon (idea borrowed from Google Loons). As part of that, we need an air pump to inflate a balloon acting as ballast (which is called a Ballonet in ...
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### Space-time translations and Propagator

Let us assume to have the following scalar field theory $${\cal A}=\int d^4x\left[\frac{1}{2}(\partial\phi)^2-\frac{\lambda}{4}\phi^4\right]$$ where I used a quartic potential to fix the ideas. ...
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### Effect on Q factor and resonant frequency when scaling down a damped oscillator to micro / nano scales

I've always just accepted that as you scale down a mechanical system the frequency and Q factor both increase. But how exactly do they scale? Linearly? With the square of reduction in size? Or maybe ...
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### Pressure change in throttling & flow rate reduction in a water circulation

If the pressure in a water pipe line is reduced from 7kgf/cm2 to 4 kgf/cm2, what is the % reduction in flow rate?
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### Linear Perturbation theory in General Relativity, what to do with products of derivatives?

I'm trying to do a problem in which I am given the Einstein tensor for the following metric: $$ds^2 = -e^{2\Phi}(d{x^0})^2 + e^{2\Psi}\delta_{ij}dx^idx^j,$$ And then asked to find the Einstein ...
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### Why does red light travel faster than blue light?

I know that light of all frequencies travel at the same speed in vacuum. But I wonder why their speed differ in any other medium, why does red light travel faster if it has less energy than blue ...
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### A free axis of rotation [duplicate]

It is claimed that the free axes of rotation of a rigid body are the ones with the smallest and the largest moment of inertia. Why? How can we determine which free axis of rotation will be used?
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### Name for the transformation into an accelerated frame?

A transformation into a frame that looks at an experiment from a rotated perspective is called a rotation. A transformation into a frame that moves with a different constant velocity is called a ...
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### Potential in uniform fields

First in a book I found that the electric field strength $\mathrm{E}$ of a uniform electric field from a charged plate is equal to $\frac{q}{2\times \epsilon_0 \times S}$ where $q$ is the charge of ...
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### Radian Zeno-version paradox: Can a particle moving in the circular path reach the angular position of non-terminating decimal form radian value?

Consider a particle P moving in a circle of radius r as shown in the figure. Premise 1: Position of the particle can be described by the angle $\theta$. Premise 2: Particle reaches the position ...
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### Oscillation of a vertical rod supported by horizontal spring [closed]

The system seems to oscillate with $\omega = \sqrt{\frac{\frac{3}{2}mgl + 3k a^2}{ml^2}}$ for small angle $\theta$, and in particular for whatever stiffness $k$ chosen relative to gravitational ...
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### SR: constant acceleration wordline simultaneity

A worldline $W$ with constant acceleration $a$ is given parametrically by $$t=\frac{c}{a} \sinh(\frac{a \tau}{c}), \quad x=\frac{c^2}{a} \cosh(\frac{a \tau}{c}).$$ Let $E=(0,0,0,0)$. I showed that for ...
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### Interaction rates from cross sections in a thermalized gas

Consider a target particle embedded in a gas with a thermal distribution of velocities. If we know the cross section $\sigma$ for interactions between the target particle and a gas particle, how do we ...
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### Fire: Why is Carbon combustible and Why is Oxygen needed?

This question is about the requisites of fire and combustion. My physics learning is only high school level. In a nutshell, why are certain elements more susceptible to combustion while others are ...
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### When was Electromagnetically Induced Transparency first introduced?

The oldest paper I know regarding this topic was published in 1997 by Stephen E. Harris. But I am not sure if he is the first to introduce this idea. Could you tell me when and by who did introduce ...
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### What are non-local charges?

In integrable systems, for example in the XXX spin chain, one encounters non-local charges (that form a Yangian). They are fine since the Yangian generate an infinite number of them, which gives us ...