2
votes
0answers
134 views

Resonance condition in confocal cavity

In a confocal cavity, a beam traverses the length of the resonator 4 times between two transmissions along the same ray. . For example, in the above figure, path difference between two beams that ...
0
votes
0answers
84 views

Deduce magnetic field based on electric field

I'm learning Maxwell's electromagnetic equations and i can't wrap my head around this problem: Given the volume $x\in [0,1], y\in [0,1], z\in [0,1]$, electric field $\vec E(x,y,z,t)$ and material ...
2
votes
1answer
62 views

All angle dependence in $\mathrm{d}LIPS_2$?

Recall that $\mathrm{d}LIPS_2$ (one particle decaying into two particles of the same mass) is given by $$\mathrm{d}LIPS_2 = \frac{\vert{\bf k_1'}\vert}{16\pi^2\sqrt{s}}\mathrm{d}\Omega_{cm}.$$ In a ...
3
votes
1answer
431 views

Question on index notation and metric tensor

I found this expression in my SR notes: $$ (\Lambda^{-1})^{\lambda}_{\ \ \ \sigma} = g^{\lambda\mu}~\Lambda^{\rho}_{\ \ \ \mu} ~g_{\rho\sigma} = \Lambda_\sigma^{\ \ \ \lambda}$$ I know where it ...
2
votes
1answer
49 views

Director field fluctuations in a liquid crystal in a magnetic field

If we consider the Frank elastic free energy in the equal constants limit (for more details, see here Chapter 4.1.) with an external magnetic field, we have $$ F = \frac{1}{2}\int \text{d}^3 r\left ( ...
1
vote
1answer
229 views

How much smaller will be human body, when we hypothetically get of every space between particles [closed]

I had an interesting dream, where advanced civilization compress their body with technology, that turn off space betweens atoms/particles. They travel in small spaceship with billions citizens very ...
1
vote
1answer
812 views

Duration of Satellite orbit in the shadow of the Earth

I want to determine how many minutes a satellite is in a circular orbit around the Earth at about $1000 km$ altitude. I assumed that the Sun-Earth vector lies exactly in the orbital plane of the ...
1
vote
2answers
116 views

What is the principle of equivalence in thermodynamics?

I've been searching for this for a while. There is a principle of equivalence in general relativity: http://en.wikipedia.org/wiki/Equivalence_principle But I need the principle of equivalence in ...
1
vote
0answers
46 views

Which power should a radio transmitter have to overcome attenuation of 100 km thick ice crust?

Imagine I put a floating probe inside the subglacial ocean of Encelado or Europa: how much power should my radio have to be able to communicate from external surface with the probe? Or, in different ...
1
vote
1answer
156 views

Moment of inertia of a sphere

I'm looking at sample calculations of moment of inertia of a sphere here. In the first example (disc method), it has the integral as $dI = \frac{1}{2}r^2 \,dm$, while in the second example (shell ...
0
votes
5answers
530 views

Relation between shm and circular motion

I recently read in a book that combination of two simple harmonic motions of equal amplitude in perpendicular directions differing in phase by pi/2 is circular motion. I don't seem to understand this ...
4
votes
2answers
1k views

Why does pitch in a helicopter take effect 90 degrees later?

In a helicopter if you want to give it a forward pitch, you change the angle of the blades when it is in this position ---- So the two blades experience unequal lift and because o gyroscopic ...
1
vote
0answers
30 views

How can a pion with neutral charge exist? [duplicate]

A $\pi^0$ consists of an up and anti-up quark. However, I also learned that when a particle and its anti-particle meet, energy is produced. So, my question is that how can $\pi^0$ exist? Won't it ...
0
votes
3answers
234 views

What happens when one of the photons in entangled state gets destroyed?

Consider two entangled photons with two mutally conjugate circular polarization. What happens when one photon which is, say, left hand polarized gets destroyed. Will the other photon retains its right ...
2
votes
1answer
507 views

How to use specific heats and temperature change in a system to calculate mass?

In a system where multiple liquids and solids are mixed together with different specific heats at different initial temperatures, reaching an equilibrium temperature, how do all of these things relate ...
1
vote
3answers
1k views

What is a linear probability density function?

In the following question, what is meant by linear probability density function? Is it a uniformly distributed variable or triangularly distributed? Thanks in advance. The kinetic energy of any ...
5
votes
1answer
880 views

Mandelstam variables 1 positive 2 negative

The three Mandelstam-variables are defined as: $$s=(p_A+p_B)^2=(p_C+p_D)^2,$$$$t=(p_A-p_C)^2=(p_B-p_D)^2$$$$u=(p_A-p_D)^2=(p_B-p_C)^2.$$ Where A and B are the incoming particles and C and D are the ...
2
votes
1answer
89 views

Is polarization of a wave just a description of its motion in three dimensions?

Since a polarization of the wave is described by complex numbers, we can try to give that mathematical formalism geometrical meaning. With having two different axes, one imaginary and other real, it ...
1
vote
1answer
7k views

Characteristic length for the diffusion equation (temperature)

The background: I'm doing some simulation work involving the diffusion equation in 1D. Specifically I have some temperature profile, constant thermal conductivity and fixed temperature at each end of ...
3
votes
1answer
124 views

De Broglie Wavelengths

I have a working knowledge of wave-particle duality, I think. I know the de Broglie wavelength is a sort of probability of finding a particle in a specific position, and is calculated by ...
2
votes
0answers
289 views

Statistical mechanics of a coin toss

I'd like to ask some questions about flipping two coins related to statistical mechanics, e.g. microcanonical distribution, phase space distribution function etc... after I rephrase the coin flipping ...
3
votes
1answer
1k views

Diagonalization of Hamiltonian

Typically, one way of understanding the physics of an interacting quantum system is by diagonalizing the Hamiltonian. In principle, can we always diagonalize a Hamiltonian, such that it is expressed ...
2
votes
0answers
181 views

Relativistic Transverse Doppler Effect

In Minkowski spacetime, two observers, A and B, are moving at uniform speeds u and v, respectively, along different trajectories, each parallel to the y-axis of some inertial frame S. Observer A emits ...
3
votes
1answer
205 views

Why does not my power stop when alternating current goes at 0 between positive and negative?

I am having some trouble understanding three-phase alternating current. I realize that most houses are not three-phase but single phase. Would that not mean that at some point when the flow of ...
1
vote
1answer
102 views

Circuits and Power [closed]

"The diagram below represents a simple circuit composed of 5 identical light bulbs and 2 flashlight batteries. Which bulb (or bulbs) would you expect to be the brightest? a) V only b) V and W ...
2
votes
1answer
816 views

What is the pressure at the top of a sealed tube being drawn out of water?

Is the atmospheric pressure in a closed container the same as that of the surroundings (1 bar at sea level)? Consider a tube with both ends open with one end dipped into water (like a pipette in ...
1
vote
1answer
916 views

Normalized Projection Operator

What is meant by normalized projection operator? What is its physical meaning in quantum mechanics? I am pretty confused regarding the physical interpretation of both projection operator and ...
3
votes
1answer
486 views

Naive questions on the ground states of Kitaev model

I got some naive questions on the ground states of honeycomb Kitaev model (with open boundary conditions): (1) Consider a simple case that $J_x=J_y=0$, then the model reduces to $$H=J_z\sum_{z\text{ ...
1
vote
0answers
45 views

What can I say about compatibility between predictions and results?

If I have these theoretical predictions: \begin{align} \omega_{p_1} = 4.5132 \pm 0.0003~\text{rad/s} && \omega_{p_2} = 4.5145 \pm 0.0002~\text{rad/s}\\ \omega_{b_1} = 0.0707 \pm ...
1
vote
1answer
530 views

How do projectors work?

So, objects are certain colors because they are absorbing every color except for that one. So why is it that if I take a projector and project a blue image on a red wall, the red wall still reflects ...
8
votes
1answer
107 views

Very short decay: A bare quark?

I keep reading the same phrase about the very short life time of the top quark: Because the t-quark decays on a shorter than the characteristic QCD interaction-time it cannot hadronize. ...
2
votes
0answers
89 views

One question about Weinberg's derivation of arbitrary spin fields expressions

In his book "QFT" (vol. 1) Weinberg writes the expression for an arbitrary spin massive field: $$ \hat {\Psi}_{a}(x) = \sum_{\sigma = -s}^{s} \int \frac{d^{3}\mathbf p}{\sqrt{(2 \pi)^{3}2 ...
1
vote
2answers
17k views

Difference between angular frequency and angular velocity?

What is the difference between angular frequency and angular velocity? I think one is used for SHM and the other for circular motion? Also can both be used for centreptal accelartion? I think angular ...
3
votes
1answer
312 views

Epsilon Tensor in FeynCalc

A few days ago I started to use the Mathematica package FeynCalc and one thing confuses me: Assume we have a four-vector $p_\mu$ and we contract it with the epsilon tensor. FeynCalc produces ...
3
votes
1answer
167 views

Dirac operator Feynman propagator

Is it true that the following identity holds for the Feynman prescription Dirac propagator: $$ S_F(x) \stackrel{?}{=} \gamma^0[S_F(-x)]^\dagger\gamma^0 $$ where $S_F$ is defined as the Green's ...
1
vote
1answer
970 views

Why does diffraction depend on wavelength? [closed]

We've all heard of the diffraction of radio waves over a mountain and the diffraction of water waves through a gap, but why does this effect depend on wavelength? I'm looking for as simple answer as ...
5
votes
3answers
1k views

Why cannot fermions have non-zero vacuum expectation value?

In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory ...
0
votes
1answer
832 views

Latent heat of vaporization

The molecular weight of water is 18.015 gram. The number of moles of water in one liter (1000 gram) will be: $3.34\times 10^{25}$ molecules (in 1kg). We know that latent heat of vaporization of water ...
4
votes
4answers
203 views

why do the electroweak vacuum have to be charge and color neutral?

My question is why the electroweak vacuum of the Standard Model have to electroweak charge and QCD color neutral? What goes wrong if electroweak vacuum has either non-zero charge or color quantum ...
0
votes
2answers
960 views

Types of circular acceleration?

To my knowledge there are three types of acceleration when a body (e.g. a rod) is moving in a circle about an axis. These are: Angular acceleration : this is the rate of change of angular velocity. ...
0
votes
1answer
73 views

What is the resolution to this apparent contradiction?

Momentum is defined as $$p = \gamma m_0 v$$ And here is another law $$E^2=(m_0c^2)^2+(pc)^2$$ And this website says the energy of a red photon is $1.9074 eV$. Also, light has a rest mass of $0$. The ...
4
votes
3answers
4k views

Why does an electric motor burn up when you physically stop it?

As an electric motor spins, the energy from the electricity is 'conducted' to the rotor by the magnetic fields. However, when the motor is stopped, the energy becomes heat and burns up to motor. ...
1
vote
0answers
74 views

Radiation heat transfer

I'm looking at the radiosity equations for heat transfer http://en.wikipedia.org/wiki/Radiosity_(heat_transfer)#Radiosity_method Specifically, I'm hesitant to accept the equation: $$ \dot Q_i = ...
0
votes
3answers
101 views

Is “atmospheric geostationary satellite” feasible with current technology?

Meaning by "atmospheric geostationary satellite" a vehicle capable of hovering 30 km above Earth surface, hence insde atmosphere, for unlimited time, making use of air propellers, solar panels and ...
4
votes
1answer
570 views

Simple & intuitive explanation of 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 ...
0
votes
3answers
454 views

Why is energy conserved? [duplicate]

From basic principals, how does one prove that energy is conserved? Or a little more specifically - Why does this hold: $$\Delta \mbox{ PotentialEnergy} + \Delta \mbox{ KineticEnergy} = 0 $$ Or, for ...
0
votes
1answer
92 views

Expectation value of Hamiltonian on number state [closed]

Hamiltonian is defined by $H_I = \hbar \omega (\hat{a}^+ \hat{a} + 1/2)$ What is the expectation value of the energy on the number state $$\vert \psi \rangle = \frac{1}{\sqrt{2}} ( \vert 1 \rangle ...
3
votes
0answers
117 views

Relation between holography and matrix models

Let's consider a 0-dimensional $N \times N$ Hermitean one matrix model. It is defined by a potential V(M). Its partition function is $Z = \int_{H_{N}} dM e^{-\frac{1}{g}V(M)}$ where $H_{N}$ is the ...
1
vote
0answers
39 views

Regulating a particular function

I am interested in computing the integral of this function: \begin{align} \int_0^\infty\frac{2du(u^2+1)}{(1-e^{2\pi u})}, \end{align} which of course at first sight, does not converge. But in QFT ...
0
votes
1answer
2k views

Ball thrown in a moving train [duplicate]

A ball is thrown upward in a train moving with a constant velocity. Where will it land? My intuition tells me that the ball will fall at my back. But my book says that it will return back to the ...

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