# All Questions

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### How do we find the canonical ensemble density matrix for two spins?

A compound system is constructed by two coupling spins, and the Hamiltonian is $$\hat H = -J\hat\sigma_1·\hat\sigma_2 - \mu_\mathbf{B}\big( \hat\sigma_{1z}+\hat\sigma_{2z} \big)B.$$ So, how ...
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### The criterion to obtain covariant spinor derivatives in superspace

It can be simply said that covariant derivatives in 4d superspace are given by $\mathcal{D}_\mu$, $\mathcal{D}_{\alpha}$ and $\mathcal{D}_{\dot{\alpha}}$, so that they commute with the ...
703 views

### Isentropic and Isothermal Compressibility

Why isentropic compressibility is greater than isothermal compressibility ? While deriving $C_p$ and $C_v$ relation, I got $\frac{Cp}{Cv}$ as $\frac{ke}{Kt}$. Which tells us that $Ke > Kt$. But ...
498 views

### Definition of spatial and temporal coherence in QM?

It is often said that lasers are spatially and temporally coherent. Is there a simple definition of spatial and temporal coherence in the language of quantum mechanics? More specifically, can these be ...
357 views

### Calculate average speed of projectile with air resistance

There's a project that I'm working on that been bugging me for awhile. The project involves this senario: A projectile is released at 1000 feet per second and moves in a straight line infinitely ...
468 views

### making an equation dimensionless

I have a balance of energy equation as following (for a spherical particle that colliding with a spherical fluid droplet) Left hand side is for before collision and RHS for after that: ...
383 views

### Why does an electric field oppose the flow of positive ion?

I'm solving a very interesting problem. Suppose a cell is divided into inside and outside. Inside we have positive ions and outside we also have positive ions in different concentration. Suppose a ...
348 views

### Calculate the equivalent resistance between A and B [closed]

Find the equivalent resistance between A and B. I tried using nodal but there were too many unknown variables. Please help. Thank you!
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### Heisenberg's Unified Field Theory

While searching in the Internet, I came to know about Werner Heisenberg's attempt to obtain an Unified Field Theory (see the book Introduction to Unified Field Theory of Elementary Particles). But ...
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### Evaluating Feynman diagram for coupling between scalar field and dirac particle and anti particle [closed]

If I have a scalar field $\alpha$ and a Dirac particle $\beta$ and its anti particle $\overline{\beta}$, such that the three couple to give a vertex factor of $-ik$ when evaluating the Feynman diagram ...
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### Constant vs increasing acceleration for reference frames

I was reading this webpage created by a professional physicist and was shocked regarding his statement on constant acceleration not being sufficient for producing the old "ball flies into the backseat"...
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### Could you help me understand this paper (PRL 106:136806)?

I'm struggling to understand the paper PRL 106:136806 (2011). It is highly cited, but I cannot reproduce their results. Let me quickly summarize the authors' argument and raise my questions. It is ...
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### Drift velocity of electrons with changing area

What would happen with the drift velocity of a cylindrical resistor's diameter increases, with a given voltage between its terminals? According to the expression: \begin{align} R&=\rho\frac{L}{A}\...
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### If an antenna must be $\frac{1}{4}$ of the wavelength, how can car antennas be so small?

If the transmission antenna has to be $\frac{1}{4}$ of the wavelength, how can the car antennas' size be much less than that and properly receive the radio signal?
266 views

### Does accelerating generate gravitons?

If gravity and acceleration are indistinguishable, then does that mean converting potential energy to kinetic energy generates gravitons... but only temporarily until you stop accelerating?
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### Can a piezo actuator have infinite resolution?

See here: http://www.omega.com/googlebase/product.html?pn=LD400-1&gclid=CjwKEAjw77OhBRCJ7Onfp_HNtwYSJACZqHAWVTfW1BO4RSfSVjz9P3Q4FoPTvZ2r3NIc2W1uEthVhBoCgUHw_wcB I don't think so. Do they just ...
378 views

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### What would happen if one drank only D2O for a long time? [closed]

Would it be lethal ? Would you gain 10% of your body weigth ?
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### Electromagnetic interaction physical interpretation [duplicate]

Why do radio waves, X-ray and gamma rays penetrate through matter? Can anyone explain me this in terms of incident energy or wavelength of the photon and the effective cross-section that these photons ...
105 views

### Projectile motion with drag force of the form $\vec f =-k \vec v$ [closed]

An object is fired with initial velocity $v_0$ at inclination angle $\theta$ above the horizontal. Drag force in the air is taken into account and is of the form $\vec f =-k \vec v$. Knowing that the ...
108 views

### How can monitors display a sharp image, if light travels in all direction?

The question title might be a misnomer, help me improve it. My question is, from my understanding, a light travels in all direction from it's origin point. Also I assume that in the example of a ...
240 views

### Bubbles of Different Size

Suppose that I have 2 bubbles of different sizes located in a liquid, and assume that both of those bubbles are close to one another. What exactly will happen to both of those bubbles? From a ...
202 views

### Is fluorescence from a single atom/ion visible with the naked eye (e.g. in a strongly coupled trap or cavity)

I remember sitting in on a conference talk by a person (possibly Rainer Blatt) doing research with trapped ions (or single atoms strongly coupled to light in an optical cavity), and the person showed ...
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### Finding 3-Sphere Christoffel connection coefficients using variational calculus, Sean Carrol problem

I have A 3-Sphere with coordinates $x^{\mu} = (\psi,\theta,\phi)$ and the following metric: $$ds^2 = d\psi^2 + \text{sin}^2\psi(d\theta^2 + \text{sin}^2\theta d\phi^2)$$ ...
262 views

### Simple estimation of the critical temperature of water

I'm trying to develop fermi estimation skills and I came up with a question for which I don't even know where to start from. Here goes: Is it possible to estimate the critical temperature (say in ...
22 views

### Mechanism of Current flow in Metals [duplicate]

I do not fully understand the mechanism of current flow in conductors. It cannot be that a current starts only when an electron from one terminal of the electric supply physically reaches the other ...
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### Change in line density of electrons

We're proving that electricity and magnetism are essentially two manifestations of the same underlying phenomenon by using the toy example of a positive charge moving parallel to an infinitely long ...
163 views

### Distance as a function of time where acceleration changes with respect to distance

I was thinking the other day about gravity. I know that acceleration in a magnetic field changes with respect to distance from the center of the field. So I was thinking, how would one find the total ...
103 views

### Dependence of the Capacitance on the Material and Geometry of the Plates

I have two questions concerning capacitors: 1) We know that the capacitance of a capacitor also depend on the dielectric material inside as $C=$ $\dfrac{K \epsilon_0 A}{d}$ But what if the ...
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### Energy Stored In A Capacitor (Slowly Moving Parallel Plates Together)

I think this is a canonical problem with capacitors, but I'm having difficulty understanding the paradox. In Purcell's Electricity And Magnetism, problem 3.16 reads: Calculate the electrical ...
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### Is the stability matrix of a linearised RG flow always diagonalisable?

This is a follow up on "Why are the eigenvalues of a linearized RG transformation real?". My question is simple: Is there some physical (or mathematical) reason for the stability matrix of ...
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### I am looking for a good primer on Special relativity [duplicate]

I am starting a course in Gravity and Quantum Field Theory this year, and I have all of the prerequisites except for a few topics in Special Relativity. I have had some SR, but only the 1-dimensional ...
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### Casimir effect with super conductors

Do the plates in the Casimir effect need to be metal? What if one uses super conductors? Is there any difference theoretically/experimentally?
112 views

### Effect of Motion on Capacitors

What will happen if a capacitor is accelerated or rotated very very fast? Will its capacitance decrease? Will one of the plates be able to hold the electrons which is providing the Potential ...
994 views

### Power dissipation in circuits:Why is high voltage used in power lines?

I know this question has been asked before, but there is one doubt I still cannot clear. Power dissipation is proportional to $I^2R$. Does this not mean that it is also proportional to $V^2/R$? If ...
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### How thin a practical capacitor can be?

According to the formula of a $parallel$ $plate$ capacitor... $C$ $=$ $\dfrac{\epsilon_0 A}{d}$ The thinner the capacitor, more the charge it will be able to store... And hence the graph should ...
730 views

### What would we see if we looked at our Solar system from 2,000 light years away with our current technology?

Assuming the tables were turned and we would live in a system like Kepler-422/423/424, some 2,000 ly away. If we'd look at the Solar system with a telescope like Kepler and using techniques like ...
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### Weighing with One-Foot Scale

I stand with left foot on a scale and the other on a piece of effectively incompressible material at the same initial height at the scale's top surface. The weight shown is WL. I repeat with right ...
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### Unstable equilibrium in a pendulum

Consider a pendulum with a bob and a massless, rigid, hinged rod attached to the bob. The bob is at rest at the bottom most position. Neglecting friction, is it possible to impart such a velocity (...
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### Special relativity and missing factors of $c$

I am doing problems in a textbook called 'Introduction to Classical Mechanics' by David Morin. In one of the questions it says the following: In the lab frame, two particles move with speed $v$ ...
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### Vector fields and tensors in E&M

I'm confused by a very basic property of electric fields. The electric field is a vector field. Vectors are tensors. Wikipedia has the following statement in the article about the electromagnetic ...
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### Open string 4-tachyon amplitude for cylinder/annulus topology in bosonic string theory

One knows the formula for the open string $4$-tachyon amplitude for the disk topology in the bosonic string theory : it is proportional to the $s \leftrightarrow t \leftrightarrow u$ symmetrisation ...
Consider a database $\cal D$ containing $N$ entries $A_0, A_1, ... A_{N-1}$, which are some fixed and unknown strings of $k$ bits; you can access this database sending a coherent superposition of ...
In quantum mechanics, we can show that $$\langle r \rangle^{-1} \neq \langle r^{-1} \rangle$$ I can understand this mathematically as the integrals are different but can anyone explain physically - ...