# All Questions

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### Why are the quantum numbers $n$ and $\ell$ denoted with those letters?

We have 4 quantum numbers: principal, azimuthal, magnetic and spin (denoted $n$, $\ell$, $m$ and $s$ respectively). I assume $m$ and $s$ are simply the initials of 'magnetic' and 'spin'. Is there any ...
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### Wave guide boundary conditions

Why only the normal component of Electric field and the parallel component of Magnetic field exist at the surface of a wave guide or any conductor?
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### Betti Numbers for sphere and torus, cycles and Poincare Duality [on hold]

In the book String Theory and M-Theory by Becker, Becker and Schwarz, the Betti Number $b_p$ is defined as the number of $p$-cycles which are not boundaries. What is a $p$ cycle? Does it have to be ...
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### “Skidding” to Brake on a Skateboard

When people are skateboarding, sometimes they kind of push out their back foot when they turn while carving, causing the board to skid a bit. I was wondering the physics behind this, any details on ...
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### Subluminal speed when going in a circle around someone

Some time ago I thought about such situation: There are two people in the room. Both have synchronized watches on their wirsts. Then the person A starts running around person B with the speed of ...
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### Why is concrete dry around cracks?

On a warm and partly cloudy day this summer, I was sitting in my office and suddenly heard rain on the roof. I went outside to shut my car windows. By the time I did that and was walking back into ...
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### Quantum mechanics, operator commutes with Hamiltonian

My textbook said, if an operator $\hat{O}$ commutes with the Hamiltonian, then we can use the eigen vectors of the Hamiltonian as a basis of the Hilbert space, then express the operator $\hat{O}$ in ...
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### floating human on gas experiment

http://m.youtube.com/watch?v=DzLX96VWTkc&feature=youtu.be I saw this and now I' m wonder is it possible to make this gas to lift human . I read thread about making air dense as water and it is ...
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### Is the future purely a construct of the human mind or is the flow of time an Universe phenomena?

Is it mathematically proven that the future exists already somewhere in the time-space continuum? Do past and present exist in the Universe or is it just one "long thread" of time? Why do we travel ...
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### Changing vector basis in AdS$_3$

I have AdS${}_3$ given as a surface embedded in a 4 dimensional pseudo-Riemannian space $$x^2+y^2-u^2-y^2=-l^2$$ With metric: $$ds^2=dx^2+dy^2-du^2-dv^2$$ I have Killing vectors of that space ...
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### We don't know when a nucleus will decay. Then how can find its half life? [duplicate]

I mean how can we say that in 5730 years, 1/2 the no. of C14 nucleus will decay because in reality we don't know when a particular nucleus will decay
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### Slinky base does not immediately fall due to gravity

Why does the base of this slinky not fall immediately to gravity? My guess is tension in the springs is a force > mass*gravity but even then it is dumbfounding.
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### How does the Universe differentiate objects? [on hold]

So, for example we have 2 objects: Earth and the Moon both exerting equal amount of gravity force on each other. But, I can't help but to wonder, what makes a discrete entity? What makes it whole ...
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I'm reading A simple derivation of the Lindblad equation. It introduces a Hamiltonian for a system consisting of a principal system $S$, a heat bath $B$ and an interaction term: ...
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### Strain energy density in index notation

The strain energy density is defined as $$dU = \int_0^{\epsilon_{ij}} \sigma_{ij} d \epsilon_{ij}$$ (see Reddy "Energy Principles and Variational Methods in Applied Mechanics", 2nd Ed, 4.11). Assuming ...
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### “And God said…and there was light.” What does these equations mean? [duplicate]

Today while I was on the Internet I came across an interesting picture, that caught my eye. It's : I don't have to explain why this picture seems interesting to someone who knows the meaning and ...
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### Parallel axis theorem

For this question we are working in 2-D space. Let's say that we have an arbitrary body. I know the inertia with respect to a perpendicular axis (to the body, that is) that passes through a point (A). ...
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### Newton's Second law of motion: Elevator problem [on hold]

this is a question about newton's second law of motion that I am a bit stuck on. One end of the cable of an elevator is attached to the elevator car,and the other end of the cable is attached to a ...
315 views

### Faster-than-$c$ photons

As far as I know, according to quantum field theory, there are some photons that go faster than c, which is the speed of light in vacuum. However, there seems to be a paper and a corresponding ...
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### Estimate the maximum distance of water spatter

There is a faucet dripping water from height $H$ onto a smooth, horizontal ceramic surface, and I need to give a upper bound of the maximum distance between the water spatter and the point directly ...
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+50

### Symmetrizing the Canonical Energy-Momentum Tensor

The Canonical energy momentum tensor is given by $$T_{\mu\nu} = \frac{\delta {\cal L}}{\delta (\partial^\mu \phi_s)} \partial_\nu \phi_s - g_{\mu\nu} {\cal L}$$ A priori, there is no reason to ...
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### What is a dynamical variable

I see the phrase 'dynamical variable' in several of my texts and they don't really define it. A google search doesn't yield much either. I have gathered that a dynamical variable can be represented ...
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### Why the bosonic part of the superconformal group $SU(2,2|1)$ is $SO(4,1) \times U(1)_R$?

Why in $d=4$ $\mathcal{N}=1$ SCFT the bosonic part of the superconformal group $SU(2,2|1)$ is $SO(4,1) \times U(1)_R$? More generally how can I determine the such a thing in other theories? Is there ...
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### What is the ratio of mass to energy in the universe?

"Stuff" exists either in the shape of mass or energy. Can one estimate the ratio of energy to mass in the universe? What shapes does energy exist in, maybe photons or molecular vibrations? Does mass ...
108 views

### QFT and violation of Heisenberg uncertainty principle

In some QFT books is said that a free electron can emit a virtual photon as long as it reabsorbs the photon and returns to its original state within a time: $$\Delta t<\dfrac{\hbar}{2\Delta E}$$ ...
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### Connection between quantum error correction and entropic quantities

Can the requirement of a quantum code to be error correcting be expressed in terms of a relation involving only entropic quantities (von neumann entropy, mutual information etc)? For example, a lot ...
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### Can we draw analogy between em power flow through free space and ac power flow through a transmission line?

Knowing that the free space has a characteristic impedance (which is purely resistive, measured in ohms) I was wondering if I can model the free space as an infinitely long transmission line- ...
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### How to get the linear and angular acceleration generated by a force vector field?

I am working on a physics simulation and I have to calculate the angular acceleration in degrees per seconds squared around the point on the object located relatively to the center of a vector field ...
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### If you were able to get rid of Hydrogen from a weather balloon as it were rising and expanding would the weather balloon rise further than usual?

I know that the weather balloon will eventually be stopped because of the atmosphere no longer being buoyant but would the balloon be able to go farther than it regularly would?
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### 3 pulley and 2 masses,relation between their accelerations [on hold]

I want to find acceleration of each mass in this system. lets take length of rope between three pulleys as $L$. then we can use this relations ...
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### How to treat partially polarized light with Jones vectors?

I have to calculate the degree of s-polarization (perpendicular) of a transmitted unpolarised light ray when it goes through a glass plate ($n=1.5$) at Brewster's angle (Brewster's window). ...
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### How to convert candela into joule?

How to convert candela into joule? What equation can we use? Is this site useful? http://en.wikipedia.org/wiki/Photometry_%28optics%29
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### Point group symmetries and unit cell

I was wondering if the unit cell (of a given lattice) had to have every point group symmetries of the lattice it defines ? I guess there is no unique way to define a unit cell and that it may not have ...
159 views

### Calculating the magnetic field from rectangular conductor?

I want to apply the Biot-Savart law to calculate the magnetic field at a point created by current flowing through a square/rectangular conductor. More specifically, a trace on a printed circuit board. ...
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### Flashing a fluorescent light bulb with high voltage

My son and I built a Wimshurst machine (our second try) over the last couple of weekends. It works -- not terribly well, as it only makes 2cm sparks with 20 cm disks (something like 60 kVolt when it ...
286 views

### Do all the particles acquire mass in the Standard Model due to the Higgs mechanism only?

I know that a mass term for an intermediate boson is not compatible with the gauge symmetry. But in principle a mass term for the electron field does not violate a gauge symmetry. However to build an ...
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### Earth-Sun Lagrange points L4/L5 existence

Why do Lagrange points L4 and L5 exist at all? Consider the mass of Jupiter equals 320 Earth masses, and distance from Lagrange point to Jupiter is about 4-6 A.U. We get that the gravity of Jupiter ...
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### Path integral method for harmonic oscillator [on hold]

Use the path integral method to calculate the transition $\langle x(f),t(f) \rvert x(i),t(i) \rangle$ for a harmonic oscillator.
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### Why are there dead zones near an antenna using the sky-wave propagation system?

I have heard in my class that there are dead zones near the antennas which use the sky-wave propagation system. I have also been told that cell phones are unable to receive signal near the antennas. ...
197 views

### Boundary conditions on current carrying wire

I'm trying to simulate by finite elements method Maxwell equations for a current carrying wire. My 3d geometry consists of a cylinder and a box containing it. I will use a mixed formulation and ...
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### An unwinding cable problem [on hold]

Suppose a light cable is wrapped around a solid cylinder with mass $M$ and radius $R$. The cylinder rotates with no friction about a stationary horizontal axis. The free end of the cable is attached ...
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### What arguments and examples did Newton give in support of Absolute time and space?

As everyone knows, Sir Newton advocated the Absolute Space & Time theory. But what examples and arguments did he confer to establish his theory? I read the wiki page where it was written that he ...
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### Why is there a voltage drop across a superconducting inductor?

If there is no electric field inside a perfect conductor, then why is there a potential difference across an (superconducting) inductor?
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### Can the Higgs condensate be described in terms of creation operators?

In superconductivity, the BCS condensate can be described in terms of 2 creation operators (the 2 electrons of the pair) acting on the vacuum. I'm wondering whether a similar description can be given ...
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### Dirac bracket and second class constraints in first-order gravity formalism

In the first order formulation of general relativity, the frame field $e_{\mu}^a$ and $\mathrm{SO}(3,1)$ spin connection $\omega_{\mu c}^b$ are independent variables. In the Hamiltonian formulation of ...
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### $e^{\mp i \pi \hbar S_z } S_{ \pm} e^{ \pm i \pi \hbar S_z} = -S_{\pm}.$ [on hold]

I am supposed to show that $$e^{\mp i \pi \hbar S_z } S_{ \pm} e^{ \pm i \pi \hbar S_z} = -S_{\pm}.$$ I tried things like the Hadamard equation, but did not really get close to this equation. Does ...
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### Why the bulb glows brighter?

If the total current is divided into the branches in a parallel configuration and it is constant in series. How come the bulbs glow brighter when connected in parallel than when connected in series?
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### Leptogenesis with singlet neutrinos

(i) The Lagrangian of electroweak model extended with right-chiral singlet neutrinos $N_{iR}$ contains the Yukawa coupling term+ the bare Majorana mass term f_{\alpha ...
Consider a cantilever beam AB in equilibrium: End A is fixed and B is free. Force $P$ is applied at free end B. I know that at the fixed end horizontal and vertical reactions act and a reacting ...