# All Questions

2k views

### Lagrangian to Hamiltonian in Quantum Field Theory

While deriving Hamiltonian from Lagrangian density, we use the formula $$\mathcal{H} ~=~ \pi \dot{\phi} - \mathcal{L}.$$ But since we are considering space and time as parameters, why the formula ...
274 views

### What are the main differences between $p p$ and $p \bar p$ colliders

I know that it is somehow related to the parton distribution functions, allowing specific reactions with gluons instead of quarks and anti-quarks, but I would really appreciate more detailed answers ! ...
179 views

### Momentum Space Renormalization of $\phi ^6$ Model

I'm trying to find the RG flow to lowest order in $\epsilon = 3 -d$ for the energy functional: $$f=\frac{1}{2} \phi ^2 +u \phi ^6 +\frac{c}{2} (\nabla \phi ) ^2$$ where $\ d$ is the dimension ...
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### Energy levels in molecules

I apologize in advance if this turns out to be a duplicate question. As far as I can understand, if you bring two or more atoms together their wave functions begin to interfere and, since there ...
121 views

### Are photon energies conserved in general relativity?

As I understand it, both Maxwell's wave equation and the null geodesics of general relativity are scale invariant. Thus an electromagnetic wave can be shifted along a null geodesic without changing ...
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### Overloading stresses wooden planks beyond their elastic range, causing them to fail? [on hold]

info: In a video on youtube in an unsafe way a car is boarding a ship going over two wooden planks. It looks to me that there two 2x10" wooden boards support a 5,000 lbs car/truck (a not so light ...
193 views

### First order coherence through double slit

The state $$|\Psi \rangle = |0\rangle + \sum_j \int d\omega f_j(\omega)\hat{a}^\dagger_j (\omega) |0\rangle$$ is coming from a far field and incident on a double slit setup. Here j is the index of ...
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### Coulomb barrier in nuclear fusion

Suppose there exists an alpha particle in the nucleus. Within a radius of 2 femtometer, the dominating force is the nuclear force but beyond this radius, the Coulomb force becomes the effective ...
458 views

### How does this chair move?

I have a chair like this(shown in figure). I was kneeling on the part where we sit. I just gave a sudden push to the part where we rest the back, without moving my legs. I found that the chair is ...
21 views

### Central Force - Trajectory [on hold]

There is a central force $\vec{F}(\vec{r})=f(r)\vec{e_r}$. 1.1.: The trajectory/flight path is defined by $r=r(\phi)$, compute $f(r)$. 1.2.: The path is defined by $u=u(\phi)$ with ...
39 views

### 'Doppler redshift' Vs 'Cosmological redshift'

It is not difficult to understand the differences between 'Doppler redshift' and 'Cosmological redshift' conceptually. But how do astronomers distinguish them when doing observations?
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### Derivation of the kinetic energy of decay product [on hold]

By conservation of momentum: $$M_{\alpha }V_{\alpha }+M_{Y}V_{Y}$$ By the conservation of energy: $$(\frac{1}{2})M_{\alpha }V_{\alpha }^{2} + (\frac{1}{2})M_{Y }V_{Y }^{2}$$ Here I begin the ...
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### Question about scalar product of 2 four-vectors

I'm looking for help to prove that $\mathbf{a\cdot b}=-ab\ cosh \ \theta$, where: $a=\sqrt{\mathbf{-a\cdot a}}$, $b=\sqrt{\mathbf{-b\cdot b}}$, and $cosh \ \theta$ is $\gamma$, for a Lorentz ...
847 views

### Causality and how it fits in with relativity

I was talking to my teacher the other day about Einstein's spacetime and there's one thing he couldn't explain about the nature of Cause. I may be being stupid or just unable to comprehend, thanks for ...
288 views

### Quantum field theory meson scattering calculation (scalar yukawa theory)

Please see this question for a clear background of the notation I use. My issue is that I want to use Wick's theorem to calculate the amplitude of meson ...
148 views

### Physical reason why the derivative of a wavefunction has to be continuous?

Question What is the physical reason (i.e. without any maths) that the derivative of a wavefunction (except with infinite potentials) has to be continuous? Other info I know that in the classical ...
21 views

### How can we be sure that a new frequency standard is better than the old one?

Lets assume for this question that at one point in scientific history everyone was running along well with their cesium frequency standards, and someone has a brilliant idea and builds an active ...
168 views

### Dielectric constant of water

I need the dielectric constant of water from $10^{-2}$ Hz to $10^4$ Hz. As stupid as it may seem, I cannot find much info. I've googled for days. All I can find is close to GHz. And the only info ...
19 views

### Notation of polarization of light

Upon my research of polarization of light I stumbled upon the following formula: What do the three dots mean? I have never seen them before. Edit: Found this notation in the book "Nonlinear fiber ...
54 views

### Minimizing the Lagrangian action of an impossible problem

I'm working my way through Structure and Interpretation of Classical Mechanics (SICM), and am stuck on an exercise in Section 1.4: Exercise 1.6. Minimizing action: Suppose we try to obtain a ...
393 views

### Explaining a quote by Weinberg about the signifcance of symmetry groups in physics

When skimming through a book, I found this quote: The universe is an enormous direct product of representations of symmetry groups. —Steven Weinberg I am a mathematician (so I know only basic ...
28 views

### Seeking Reference on Transport of Momentum by Diffusion of Mass

I'm looking at continuum mechanics from the perspective of De Groot and Mazur's "Non-Equilibrium Thermodynamics" - the first reference that I've come across that seems to do a good job of bringing ...
47 views

### Getting to spins of arbitrary direction

Let me rephrase this question: Let us assume we know that symmetry transformations always look like this: $$U(s)=e^{iKs}$$ with a hermitian Operator K. This tells us that for very small $s$: ...
34 views

### Is the light from the stars within our galaxy redshifted?

I know that metric expansion does not happen within a galaxy. But is the light from stars in our galaxy somehow redshifted? Also, everyone says that our galaxy isn't expanding. But is there a slight ...
20 views

### Does the electron confinement energy vary with temperature?

I was introduced the electron confinement energy. At room temperature thermal energy of a particle is about $k_B T$, where $T=298K$, giving about $25meV$. I was told that $E_\text{confinement}=50emV$, ...
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### On Thermodynamics of Spontaneity of the Reduction-Oxidation Chemical Reactions

According to the first and second law for a closed system containing different chemicals we have \begin{align} &\delta Q - \delta W = dU = T dS - p dV +\sum_i \mu_i d N_i\\ ...
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### What are the quantum dimensions of the primary fields for SU(N) level k Kac-Moody current algebras?

The CFT of the $\mathrm{SU}(N)$ level $k$ Kac-Moody current algebra has many Kac-Moody primary fields. I wonder if any one has calculated the quantum dimensions of those Kac-Moody primary fields. I ...
30 views

### Time dilation: reference frame [on hold]

So I'm calculating how long it will take for half of some muons to decay for in a stationary observers frame of reference. They have a half life of 2.2 * 10^-6 and are moving at a speed of .98c ...
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### What is the energy levels of 1d hydrogen by using WKB? [on hold]

I need to find the energy levels of 1d hydrogen using WKB and $V(x)=-1/x$? can you help me please?
54 views

### Are spherical coordinates distances or angles?

I've become confused about spherical coordinates when dealing with electric fields. The way I always understood spherical coordinates is something like the below picture. To define a vector, you give ...
94 views

### Solution of simple problems using only Maxwell equations in differential form

Solve simple electrostatic or magnetostatic problems using only Maxwell equations. For example: In every book there is an excercise to find a magnetic field outside a thin wire of radius $a$ with ...
244 views
+100

### Black Body Golf Balls

The surface of a golf ball has about 35% more surface area (than a similar sphere) due to its dimples. So my question is simple, given identical radius, ideal black body material, and temperature: ...
25 views

### Concentrations of carriers in semiconductor

For a given semiconductor at a given temperature $T$ with doping levels of acceptors $N_A$ and donors $N_D$ and intrinsic carrier concentration $n_i$ without any external biases, how can I calculate ...
500 views

### Force required to move a fluid out of piston at depth

I have a cylinder filled with water in it at the bottom of the ocean. Say 100 meters down. In this cylinder is a piston that moves up and down. Its job is to squish the water out the bottom of the ...
17 views

### Polchinski equation 11.2.7

In Polchinski's string theory volume 2, when discussing the GSO projection for the heterotic string he says: In the IIA and IIB superstrings the GSO projection acted separately on the left- and ...
44 views

### How do I calculate the energy flux for this toroid?

My question is how do i calculate the total energy flux through the walls of the torus in this situation? The Poynting flux is given by $\vec{N} = \frac{1}{\mu} ( \vec{E} \times \vec{B})$ but the ...
16 views

### What is the value (order of magnitude) of electric charge density of the atom and the nucleus?

The mass density of the nucleus is constant. But what is the electric charge density of the nucleus and the atom (any order of magnitude)?
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+50

### single photon/electron double slit experiment, resetting the detector material after each impact

What is the experimental (*) outcome of a single photon/electron double slit experiment under the constraint that after each detection the detector material is reset to the original state ie, in the ...
120 views

### Far Field Diffraction of EM waves: what does the zero frequency signify?

If you have a system of independently radiating electrons/point-charges, the far field distribution of the EM waves can be approximated by the fraunhoffer diffraction integral, or simply by the ...
151 views

### Reduction of Nambu Goto action to true degrees of freedom

First consider the particle $$S=m\int\sqrt{-\dot{X}^2}d\tau$$ if you choose the static gauge $\tau=X^0$ and replace it in the action you get $$=m\int\sqrt{1-\dot{X}^j\dot{X}^j}d\tau$$ So now, you ...
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### With what frequency triangle swings if it shuns from equilibrium? [on hold]

Guide V-shaped is with no friction in the swivel bearings A and B (see Fig.) Of the magnet with a vertical magnetic field of 0.8 T. The weight of the guide is 50 g, the length AB 4 cm, and the length ...
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### Speed of light paradox [duplicate]

If I send two rockets from the Earth in opposite directions, at, say, 60% of the speed of light relative to the Earth, then relative to each other they are travelling at 120% of the speed of light. ...
9 views

### What voltage is induced between the endpoints of bar, if we swing it by an amplitude [on hold]

After a long horizontal conductor carrying current of 10 A is vertically suspended 2m long insulated conductive rod. We swing it by an amplitude of 10 cm. (a) in the direction of the wire; (b) in ...
21 views

### How to count the symmetric wavefunctions made by 6 (u, d, s, $\bar{u},\bar{d},\bar{s}$) quarks to form Baryons (i.e., 3 particle state)?

Peskin said 6 (particles + Anti-Particles) guys make (6($\Rightarrow$particles) x7x8)/(3x2)= 56 total symmetric state. How?
40 views

### How do vinyl records work?

I know that vinyl records save the sound as ups and downs on the record plate surface. Let's say two people with different voice timbers say "I like vinyl records" with the same level of voice. It ...
10 views

### does the internal energy and enthalpy of the GAS changes in a free expansion process?

when a balloon kept in an evacuated room is punctured and the ideal gas in the balloon goes on to fill the entire room,does the gas perform any work in this expansion, and is there in any change in ...
180 views

### Mean-free-time between collisions and drift-velocity

In a physics text book I need help to make sense of the part highlighted in yellow: This is out of context of course, so just to make it clearer: $\tau$ is the mean free time of the electrons in a ...
235 views

### Motivation to introduce von Neumann algebras in addition to $C^*$algebras?

Observables are self-adjoint elements of a $C^*$algebra. As such, this structure seems sufficient to describe physics. A theorem by Gelfand and Naimark says that a $C^*$algebra can always be ...
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### What are the latest findings on the topology and size of the universe?

The paper G. Aslanyan & A.V. Manohar, The Topology and Size of the Universe from the Cosmic Microwave Background, JCAP 06 (2012) 003, arXiv:1104.0015, uses the 7-year WMAP data. Has any ...
49 views

### Explanation of Interference of Electromagnetic Waves

There is a question on a test which goes like this: "Given two electromagnetic waves, one of wavelength 6.0 X 10-7 m and the other of wavelength 7.0 X 10-7 m, travelling in space. When the two ...

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