# All Questions

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### woven appearance of water-streams by the side of the street

It's pretty rainy in Boston now, and there are streams of water by the sides of the street. Why do they have a 'woven' appearance? What's the formal name for this kind of fluid flow? With lots of ...
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### What's the purpose of the speed of light in $E = mc^2$?

Is $E=mc^2$ not just $E=m$. What does the speed of light have to do with this other than to give it a really big number so it looks cool? What spectrum of light is used? How can we test the speed of ...
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### Imaginary number for extinction coefficient in complex refractive index

In complex refractive index on a material, $n=n'+ ik$, the imaginary part $k$ is physical meaning, as it shows absorption in the material but it is an imaginary. How we measure an imaginary values in ...
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### Sphere between two parallel plates [on hold]

I'm stuck on the following physics question; I'm not sure how much, if any, of what I'm doing is right: A small sphere of mass 1.0 × 10−6 kg carries a total charge of 2.0 × 10−8 C. The sphere hangs ...
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### Speed=mass=time? [on hold]

I was wondering why objects gain mass with speed? How can we measure speed if there is no truly stationary point to measure from? And if an object comes to a stand still will it loose its mass? ...
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### About accelerating particles

Can a particle moving below the speed of light be accelerated more and more until it is travelling at c? IF so does it behave like electro-magnetic radiation?
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### Would an Object Near a Pre-Blackhole Star Experience the Same Gravity as Post-Blackhole?

My question was inspired by this question, which got me thinking. According to Newton's Law of Gravitation, $$F = G\frac{m_1m_2}{r^2},$$ the gravity of an object is inversely proportional to the ...
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### Photon Angular Momentum

Essentially I am wanting to evaluate $$\langle j\, m \mid a^\dagger(\mathbf{k}, \lambda) \mid 0 \rangle \,,$$ where $\lambda$ indicates the circular polarization (about $\mathbf{k}$). We have that ...
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### Does the unit of Inertia include radians? [duplicate]

The unit for angular acceleration $\alpha$ is: $$\mathrm{rad/s^2}$$ The unit for torque is $\mathrm{Nm}$: $$\mathrm{kg\ m^2/s^2}$$ And their relationship with Inertia is: $$I = \tau/\alpha$$ So ...
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### Our universe the surface of a 4-dimensional sphere?

The cosmic microwave background that we observe uniformly around us is usually explained by assuming that our universe is the surface of a four dimensional sphere. That way the uniformity makes sense ...
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### Probability distribution of two particle types system

Suppose that particles of two different species, A and B, can be chosen with probability $p_A$ and $p_B$, respectively. What would be the probability (and distribution) $p(N_A;N)$ that $N_A$ out of ...
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### Calculating the electrostatic energy per unit length of a cylindrical shell surrounded by a coaxial cable

Suppose an infinitely long cylindrical shell of radius $a$ carries a surface charge density $\sigma_0$ and is surrounded by a coaxial cable of inner radius $b$ and outer radius $c$ with uniform charge ...
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### Acceleration is zero, for non-zero net force

I understand a problem like this has already been asked, but I have not found an answer that makes it clear. A force is applied to a box on a table(lets ignore friction), and the box moves with some ...
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### Energy in an electromagnetic wave

A radio antenna creates EM waves through switching the polarization in the antenna at a certain frequency. I assume the the energy of the photons produced in this process amount to E=hf for each ...
118 views

### 2D Gauss law vs residue theorem

I used to have a vague feeling that the residue theorem is a close analogy to 2D electrostatics in which the residues themselves play a role of point charges. However, the equations don't seem to add ...
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### I need help with angular and linear kinematics ASAP! [on hold]

I am writing a paper for kinesiology about the biomechanics of cutting a pizza and one of the sections has to deal with measuring angles and angular and linear kinematics. Is there anyone who can help ...
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### Green Function for Proca Equation

I have tried to find a retarded and advanced Green function for Proca field equation. $(\Box - \mu^2)A^{\mu}=J^{\mu}$ where $\mu$ is the mass term. How I did it: first: I made Fourier ...
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### Waveguide in TE mode. Power guided [on hold]

I have the following problem and don't know where to begin. Could someone give me a hand with it? A waveguide is formed by two conducting parallel plates spaced apart a distance $d=3cm$, and width ...
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### Why doesn't gravity ruin satellites?

Recently I watched a documentary about Io, a moon around Jupiter. Io has volcanic activity even though it is small and can't retain heat well because gravity from Jupiter and a nearby moon cause it to ...
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### Intuitively what's the relationship between forces and connections?

In Einstein's General Relativity we relate the effects of gravity with the curvature of the Levi-Civita connection on the spacetime manifold. Also, when we get the electromagnetic tensor $F = dA$ ...
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### Where does this term “shell” with prefix “on-/off-” come from?

Is there some historical reasons or is there a specific reason behind it? This question is connected to: Why on-shell vs. off-shell matters?
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### Entropy of Reeh-Schlieder correlations

Any state analytic in energy (which includes most physical states since they have bounded energy) contains non-local correlations described by the Reeh-Schlieder theorem in AQFT. It is further shown ...
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### water pressure in the oceans or great lakes

Is there a way to create energy from water depth pressure? Convert the pressure to any type of energy? Does there need to be movement? Can someone comment on this process? Thanks
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### Rewriting $\langle {\bf k} \vert E,l,m \rangle$ as $\langle {\bf k} \vert ~k,l,m \rangle$ Spherical Harmonics

From Sakurai eq. 6.4.21a we have that $$\langle {\bf k} \vert E,l,m \rangle=\frac{\hbar}{\sqrt{M k}}\delta\left(E-\frac{\hbar^2 k^2 }{2M}\right) Y_l^m({\bf\hat k}),$$ where $M$ is the mass of the ...
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### How to derive the schwarzchild metric?

I'm having trouble differentiating the following when making a change of co-ordinates to determine the Schwarzchild metric. $$r'^{2}=r^{2}C(r)$$ Then taking the total derivative of both sides, the ...
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### Three-plate capacitor [on hold]

What is the total capacitance of this capacitor? Is it analogous to the case of inserting a plate into a capacitor (essentially creating two capacitors in series)?
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### Calculate speed of proton at infinity [on hold]

I have this problem to solve: Two protons are on the x axis at x=-1 and x=0. An alpha particle is placed at x=2, and the proton on the left is released, find its speed at infinity. I know that this ...
168 views

### Does the mass of a star change as it collapses into a black hole?

I know (I think!) that when a really big star collapses on itself it creates a black hole. My question: When a star collapses, is the mass equal to the mass of the star when it's not a black hole? Or ...
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### The Spin Connection

Why do we need to introduce the spin connection coefficients $\omega_{\mu \space \space b}^{\space \space a}$ in General Relativity? To me, they just look (mathematically) like the Christoffel ...
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### What is the shape of the Sun's orbit around the Milky Way? [on hold]

Here is a question for you really bright folks. How does the motion of the sun along the midpoint of the plane of the galaxy look like? I suspect it to travel above and then below the plane but I ...
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### Polar Decomposition of a Complex Scalar Field

People often write a complex scalar field via polar decomposition. What does this parametrization precisely mean? To be more explicit consider the following Lagrangian of a complex scalar field with ...
51 views

### What are the eigenvalues of the Lorentz matrix?

The Lorentz matrix defines the transformation of a four-vector between different frames of reference, such that $$p^{'\mu} = \Lambda^{\mu}_{\ \ \nu}p^{\nu}$$ where in this example $p^{\mu}$ is the ...
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### Why does my eardrum feel strange inside a car?

When I was riding a car (I was not the driver), my eardrum felt a little similar to the case when I was in a plane that was taking off, and little loss of hearing. Nothing was played inside. The ...
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### Why won't this reactionless drive idea work (motor with a moving weight in space)

I know people will say it violates many laws of motion and conservation but could anyone explain why it is so? It's NOT a question about free energy. Imagine a motor in space. It has an arm (rod) ...
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### Intuitive explanation for superfluidity?

I know that superfluidity is caused by the fluid having zero viscosity. This only happens at very low temperature, so the fluid (e.g. Helium-4) is a Bose-Einstein condensate. I also know that in a ...
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### Calculation of the electric field from a cube of charge with charge density proportional to radial distance [on hold]

I have a cube of side length $L$ centered at the origin and total charge $Q$; the charge density is $\rho(r)\propto r^n$ for some integer $n$, where $r$ is the radial distance in spherical ...
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### How can current be a smooth curve?

The following is a graph of the current across some circuit element: Note how the current is treated like a smooth continuous function. Even in the analysis of things (i.e. analysis of the ...
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### Why does Gauss's law work for a charge off center in a spherical surface?

CASE 1: Consider an enclosed spherical surface with a charge $q$ at its centre. From Gauss' law we can say that the flux through this sphere is $q/\epsilon_0$. CASE 2: The charge is inside but off ...
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### From a cross section to a probability

This is homework problem: Given the cross-section of a neutrino-electron scattering, what is the probability for a solar neutrino to scatter with a electron as it goes through the center of the Earth? ...
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### Quantum Mechanics - Observable

If $O$ represents an operator corresponding to an observable why does the following equality hold? $$\langle f(x)\, |\, O g(x)\rangle = \langle g(x) \,|\, O f(x) \rangle$$ It is used on the last ...
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### Approximation of skeleton diagrams

I'm studying the diagrammatics for a Bose system (in the superfluid phase) developed by Gavoret and Nozieres (Annals of Physics 28 349 (1964)). In this paper, they show how to solve the problem using ...
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### If two objects collide, will the collision force be twice as big as the original force? [duplicate]

Say, if we have two trucks travelling towards eachother at 60m/s, and those two trucks carry the same payload, and are the same model (aka they're exactly the same), will the collision force be as if ...
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### 'Warp'- type travel; is it possible?

I just re-read an article about space travel, and the same article claimed that Star Trek-type 'warp' nuclear engines ARE theoretically possible, but that it will take around 500 years for humans to ...
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### Inertia matrix of a rod rotating about an axis [on hold]

I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, ...
34 views

### group and phase velocity of free particle [duplicate]

If Schrödinger wave equation is for matter waves then for a free particle Group velocity $V_g =2$ Phase velocity $V_p$ But matter waves satisfy the relation $V_g V_p = C^2$ where $V_p>C$ Does this ...
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### Franck and Hertz graph function

I need a function whom graph is the following (the Frank and Hertz experiment graph): Currently I wrote the following function: ...
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### Is there just one fundamental frequency?

I read simple definitions of the terms frequency, and fundamental frequency, which defined them thus, Frequency: the number of occurrences of a periodic wave during a second Fundamental Frequency: ...
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### Chemical potential of Bose-Einstein condensation

This is a problem in An Introduction to Thermal Physics. (a)(b) is easy to work out. In (c), I use the formula $N_{excited}=(\frac{T}{T_c})^{3/2}N, \ (T<T_c)$ to calculate how many atoms are ...
Say I build a perfect rectangle. Side lengths $l_1$ and $l_2$ and perfect right angles. I am on earth and the metric is given by the Schwarzschild metric. Setting $dt=0$ leads to the spatial ...