# All Questions

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### When is entanglement entropy the same as free energy?

I am given the feeling that there exists scenarios when this equality holds. Can anyone state/refer to the situations? One case that I hear of is that for $2+1$ CFTs the entanglement entropy ...
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### Asymmetry in muon energies of public CMS dimuon event data

CMS published for educational purposes (caveat) 100.000 dimuon events: https://cms-docdb.cern.ch/cgi-bin/PublicDocDB//ShowDocument?docid=11583 As one easily sees, column 4 shows the first muon's ...
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### Nonlocal games: The CSCH game

The problem that I am having is that I don't see how they come up with the probabilities mentioned on Slide #7 here: https://www.ipam.ucla.edu/publications/opws1/opws1_9367.pdf first I don't ...
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### How do the Einstein's differential equation of the curvature of spacetime come out of Einstein's field equation?

The classical theory of spacetime geometry that we call gravity consists of the Einstein equation, which relates the curvature of spacetime to the distribution of matter and energy in spacetime. ...
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### Free body diagram of rod in sphere

I was finding the free body diagram part of dynamics quite easy until I found this question , Here's how it goes : A rod AB is placed inside a spherical shell, whose inside surface is rough. Draw ...
202 views

### Energy of a string

What is the correct definition of the energy of a string ? I suddenly get confused with the definition of the energy of a string. Considering, for instance, a bosonic open string in the light-cone ...
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### The basic equation of bosonization

[..quoting from Page 11 of Polchinski Vol2..] Given $1+1$ conformal bosonic fields $H(z)$ one has their OPE as, $H(z)H(0) \sim -ln(z)$ Then from here how do the following identities come? ...
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### Do permanent magnets emit virtual photons?

Is the magnetic field propagated by photons or by virtual photons? If it is by photons, then doesn't that mean that magnets lose energy and eventually become non magnets?
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### Some complex-number manipulation when calculating coefficients

I am going through Sakurai's quantum mechanics, and at one point the solution to a problem says: $(\sin(\beta)\cos(\alpha)-i\sin(\beta)\sin(\alpha))b+\cos(\beta)a=a$ ...
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### Potential of a Body

I have a doubt about the electric potential of a body. Well, I know that given a continuous distribution of charge we can find the potential at a point $a$ using the following relation: ...
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### Scattering Amplitude in second Born Approximation for the Yukawa potential

Does anyone know where I can find the analytical expressions of the scattering amplitude in second Born Approximation for the Yukawa potential? I need it for the both cases of the method of partial ...
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### Derivation of Pressure/Kinetic Therory problem involving hole in box

A box of volume $V_0$ has a small hole of area $A_0$. The box initially has one mole of an ideal gas at $t = 0$, which is at an initial temperature $T (t = 0)$. Find the rate of energy flow through ...
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### Infinite quon statistics/Quantum Boltzmann statistics: models and hamiltonians

I learned long ago that there are some exotic classes of statistics. One of them is calleq $q$-on or quon statistics. It is given by $$a_ia^+_j-qa^+_ja_i=\delta_{ij}$$ Infinite statistics (Quantum ...
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### What is known about the trace of two copies of a channel / four copies of an isometry

Let $\mathcal{E} : \mathcal{L}(A) \to \mathcal{L}(B)$ be a completely positive trace preserving map. By the Choi–Jamiołkowski isomorphism there is an isometry $J : A \to B \otimes C$ such that ...
286 views

### Shape of the rainbow

I have watched Walter Lewin's lecture(http://www.youtube.com/watch?v=6QVbE_tU2sA) which was about the rainbows. But there is still a question bothering me. I understood the first part of the ...
2k views

### Path of least resistance vs. short circuit

Some sources on the web claim that "electricity follows the path of least resistance" is not true, e.g. this physics SE question. However, in every explanation of "short circuits", the author says ...
606 views

### What is the maximal height for a water rocket's flight?

A water rocket works like this: there is a circular slot of area $A_1$ at the bottom centre of a cylinder of cross-sectional area $A_0$ and height $L$ that is filled with water to an initial height ...
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### Beyond WKB approximation for energies

In the first term the energies are given by the Wentzel–Kramers–Brillouin (WKB) formula $$\oint p dq = 2\pi \left( n+\frac{1}{2} \right)$$ However, can this formula be improved to include ...
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### Fundamental question about the Buckingham $\pi$ theorem (dimensional analysis)

I have a rather fundamental question about the Buckingham $\pi$ theorem. They introduce it in my book about fluid mechanics as follows (I state the description of the theorem here, because I noticed ...
690 views

### What's the altitude of the flat base of Cumulus clouds?

Is there a formula that describes the altitude of clouds with respect to the local temperature? I think of the flat bases of Cumulus clouds. Thanks...
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### Magnetic moment of electron

Since magnetic moment come from the circulation of charge, what is the origination of the electron's magnetic moment? Because spin of electron is not the classical spin of particle. Can we say that ...
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when we approach a charged rod (+) to a neutral metal rod ( not touching) a number of electrons to that side ( lets call it side B) negating the effect of the introduced electric field, reaching ...
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### Equation for the equipotential lines? [closed]

What is the equation for the equipotential lines in $x$-$y$ plane for a dipole oriented along the $x$ axis?
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### Induced metric on a null hypersurface

Consider a metric $g_{\mu\nu}(x)$ and a hyper surface ${\cal H}$ defined by $~f(x) = c$. One (or at least I) usually finds the "induced metric" on ${\cal H}$ by solving$~f(x) = c$ for one of the ...
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### Additional merits to Wetterich's “Universe without expansion” compared to standard cosmological redshift interpretation?

A recent news item in Nature promotes Wetterich's preprint "A Universe without expansion". All sounds very exciting but hard to judge for non-experts. As I understand from the Nature's article, the ...
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### Eigenvalue Postulate and Experiment Outcomes in QM

In Nielsen and Chuang's text on Quantum Information and Computation, the measurement postulate is stated by using a collection of measurement operators and the outcomes are the indices of the ...
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### How does a state vector be projected onto an eigenspace after measurement

In http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Degenerate_spectra, it is said that If there are multiple eigenstates with the same eigenvalue (called degeneracies),..., The ...
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### Is there any quantum analogs of three body problem?

IS there any quantum analogy where a three state (or three body) system shows chaotic dynamics as three body problem in classical mechanics?
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### Information Preservation and Burning Books

I recently read an article in the NY Times called A Black Hole Mystery Wrapped in a Firewall Paradox. I really liked the article, but reading one quote immediately made me think of asking Physics.SE a ...
14k views

### Difference between current and voltage sources

I am confused about the current and voltage. My intuitive example would be that of a pipe of say water. The diameter of the pipe determines the amount of water flowing per second but the pressure is ...
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### How scientists could say that such meteorite comes from Mars

How could scientists affirm that a meteorite comes from Mars and not from another source ? This is a probability or an absolute certainty ? How much percent ?
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### Need to weigh a sack of kittens

Hypothetical brain teaser here, no real kittens involved! - For some bizarre reason I have a sack of kittens, I need to find the total weight of the kittens and the sack but I'm only allowed to use ...
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### Newton's gravitational constant $G$, the reduced Planck constant $\hbar$, the speed of light $c$: the Dream Team of moderators?
The three great constants of Nature are well known: the speed of light $c$ (special relativity), the reduced Planck constant $\hbar$ (quantum mechanics), Newton's ...