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I am reading Strominger's lecture notes on the infrared structure of gravity and gauge theory. I am trying to understand subchapter 2.11, where the author focuses on the notions of "Spontaneous Symmetry Breaking, Vacuum Degeneracy, and Goldstone Bosons" for the case of large gauge transformations.
I will explain my und... |
I have been thinking about this for a while but apparently it is beyond my pop-sci level of understanding:
Imagine a spaceship departing from Earth under constant acceleration of 1g (10 m/s^2) for many years (let's not dwell on how this can be achieved in practice). Since acceleration is absolute, the traveler might do... |
I am implementing thin wire method of moments using W.Gibson's "Method of Moments in Electromagnetics". The approximation for self-term using piecewise sinusoidal basis function is given as
where, sm(x) is the sinusoidal testing function.
In the same book for EFIE, prime operators are used to differentiate terms for s... |
I'm having a hard time understanding the way the energy per electron is calculated in Sommerfeld Theory. From the N.W.Ashcroft book on solid state physics it is done by first calculating the ground-state energy of N electrons in a volume V by adding up the energies of all the one-electron levels inside the Fermi Sphere... |
I'm puzzled as always. In the LHC 2 streams of particles are accelerated in opposite direction and allowed to smash against each other in a controlled accident, then is it classical or quantum mechanically? For classical we can know where the products will end up but for quantum mechanical then we must examine all the ... |
I am trying to understand what an "ideal" lens would look like. Spherical surfaces are not correct, as these produce spherical aberration.
This article here, is really useful. It 'derives' the thin lens equation by using the following reasoning.
Start with a point source at distance $f$ from some plane, explicitly at ... |
When F is applied both m have acceleration F/2m to the right whilst also having an acceleration towards each other. This leads to a kinetic energy gained from the force to the right and the force towards each mass.
If these masses were just connected in series the acceleration from the same force F would be F/2m this... |
Isn't linearly polarised light actually chiral when taking the magnetic field into account?
Just looking at the electric field is just 2D and therefore achiral, obviously.
But with the magnetic field included, the mirror image isn't the same right?
Everywhere I look it is written that linearly polarised light is achir... |
How can the mean life of a radioactive nucleus be derived?
Consider R.dt number of nuclei decaying in the time interval t and t+dt. Then, isn't the lifetime of those R.dt number of nuclei is t? But, I couldn't understand why in many derivations, lifetime is mentioned as tR.dt instead of t and we integrate tR.dt from 0 ... |
I am studying the basics of Nuclear Physics, and just read about the Rutherford experiment.
My question is if we use Negative Ions as probe for nuclear reactions, will they get deflected?
If yes then why?
Because they should be attracted by the coulomb force.
|
In the course of Classical Electrodynamics I learned that in the Lorenz gauge it is easy to prove that the 4-potential $A$ is a 4-vector, that is its components $A^\mu=(\phi/c,\vec{A})$ transform as the component of a 4-vector under Lorentz transformation. The Lorenz gauge is written in a covariant form ($\partial_\mu ... |
Can the electric field vector of an EM wave oscillate in the propagation direction?
In text books the polarisation is always orthogonal to the propagation direction.
I'm wondering specifically because of this paper:
https://doi.org/10.1039/D2CP01009G
On page 17 of the PDF-reader the authors present the concept of sy... |
I am trying to figure out the paper of Asenjo-Garcia et al.: PHYS. REV. X 7, 031024 (2017).
Specifically, in e.g. Equation (5):
$$ \mathcal{H}_{eff} = -\mu_0 \omega_0^2 \sum_{i,j = 1}^N \mathbf{D}^* \cdot \mathbf{G}(\mathbf{r_i}, \mathbf{r_j}, \omega_0) \cdot \mathbf{D} \hat{\sigma}_{eg}^i \hat{\sigma}_{ge}^j. $$
The a... |
For a scenario in which an object is sliding down an inclined plane, its motion opposed by a kinetic friction force, it seems to me that maintaining a constant velocity should be impossible given these assumptions:
The maximum coefficient of static friction is greater than the coefficient of kinetic friction.
When the... |
If I want to calculate the electric field inside the $1s$ cloud of an atom. Do I have to consider the protons only or the electrons too? If I take the electric field created by protons only then won't electrons create their own field and distort it?
|
I am currently studying the XXX Heisenberg spin chain using the Bethe ansatz. I am working in the string hypothesis and I am having troubles deriving a simple expression for Fourier transformation of the string-string derivative kernel $A_{mn}(\omega)$. In particular (looking at the screenshot I have added below) i can... |
In the book Field Theories of Condensed Matter Physics by Fradkin:
When discussing the gauge-invariant operators of $Z_2$ lattice gauge theory in Page 299, the author says
Owing to the $Z_2$ symmetry, only the parity of the charge is well defined.
What does "parity of charge" mean? And why only it is well defined?
|
This question is very famous and asked many times, but I want to discuss some another aspect of this question and not something which has been asked before
I want to know if my method of approach is correct?
VfYn0.jpg
I tried to solve the total angular momentum about the origin and I want to know if my method of approa... |
I am trying to compute 2D lindemann parameter to quantify melting in colloidal crystals from particle coordinates obtained in 2D.
The equation I have come across for computing 2D lindemann parameter is as follows
$$L = \frac{\left\langle \left( \Delta u_{i}\left( t \right) -\Delta u_{j}\left( t \right) \right)^{2} \rig... |
I've been doing some reading and came across a simple implementation of the Hadamard gate using Rabi oscillations of an atom in a laser field. However, the author mentions that it required the Rabi frequency $\Omega$ to be taken as purely imaginary.
I know that $\Omega$ is defined in terms of the field amplitude which ... |
I am working through a rigid multibody dynamics problem using this paper as a reference: Newton-Euler Dynamic Equations of Motion for a Multi-body Spacecraft. I am trying to understand the differences in modeling a spherical joint or a gimballed joint or even a more simplified pin joint. Wouldn't a spherical joint and... |
Let $\phi$ denote the Klein-Gordon field. Then its propagator $\langle 0 \mid [\phi(x), \phi(y)] \mid 0 \rangle$ can be calculated as
$$\int \frac{d^4}{(2\pi)^3} \frac{-e^{-ip(x-y)}}{p^2 -m ^2}. \tag{1}$$
Isolating just the $p^0$ part of this integral, which is where the problem is, we get
$$\int \frac{dp^0}{2\pi i} \f... |
Assuming a 2D boundary layer on a flat surface with no pressure gradient (i.e. $dP/dx=0$), suppose the $x$-component of velocity, $U$, has a profile $$\dfrac U{U_e}=\dfrac {2y}\delta -\dfrac{y^2}{\delta^2}$$
where $\delta$ is the boundary layer thickness and $U_e$ is the free-stream velocity.
It can be made non-dimensi... |
In 4 dimensions, arbitrary rotations are usually double rotations (rotations which can be understood as happening independently on two different planes with different rotation angles). It certainly seems like if we take a 4D rigid object (say, a hypercube for simplicity) and apply a series of random torques, then we wi... |
In a Mach Zehnder interferometer if we use one at a time photons and tune it so the first several to arrive in channel D1 after BS2 will all next arrive also in D1? Are there reasons that some will not land on D1 f.e. if BS2 is wide and the probability waves do not overlap at BS2 in some cases. If we turn it to Feynman... |
I am trying to calculate the theoretical imaging performance of a scintillator & camera combination, (scintillator is a plane that emits optical light under X-ray exposure).
My question is I found some equations that express the light-collection efficiency based on geometric optics for a point source or Lambertian surf... |
I'm trying to ascertain the original source and author of this picture:
which can be found in this section ("An Einsteinian Experiment") of
Einstein’s Theories of Relativity and Gravitation
A Selection of Material from the Essays Submitted in the Competition for the EUGENE HIGGINS PRIZE of $5,000
compiled and edited,... |
In another question evaluating the reality of length contraction, the circular motion was involved and some answers argued that centrifugal force would negate any possible length contraction. A famous paradox called "The Ehrenfest Paradox" analyses a similar situation with relativistic motion in a circle and it suffers... |
What is the physics behind this mechanism? What would be the free body diagram be like regarding all the magnitudes of the tension forces present in the chains?
|
What is the physics behind this mechanism? What would be the free body diagram be like regarding all the magnitudes of the tension forces present in the chains?
|
In Shankar Chapter 8, there is a section at the end of the chapter on the path integral formulation for a potential of the form $$V(x,\dot{x}) = a + bx + cx^{2} + d\dot{x} + ex\dot{x}.$$ I follow the arguments given related to the propagator, but I am wondering how this problem would be approached in the Schrödinger pi... |
Why does the resultant force in centripetal force act towards the center of the circle in uniform circular motion and not at any other point, why only the center, always?
|
Can I understand spatial coherence in the following way (I'm not sure if it's correct)?
As shown in the diagram:
Each wavefront or wave surface on the left is irregular, so it is spatially incoherent.
The wavefront on the right is uniform, such as concentric circles or parallel lines, representing spatial coherence.
T... |
I can't see any reason it shouldn't.
However, Wikipedia says:
Negative exponents reflect a process where work and heat flow simultaneously in or out of the system. In the absence of forces except pressure, such a spontaneous process is not allowed by the second law of thermodynamics.
First and foremost, is that part
... |
The divergence theorem connects the flux (through surface) and divergence (in a volume) for any vector field.
This theorem expresses continuity. It isn't clear (to me) whether there is a conserved quantity associated with the continuity equation. It appears that this theorem would be equivalent to mass conservation, if... |
Recently, I read a Wikipedia article regarding the paradox that made this statement about the reference frame:
The reference frame is fixed to the stationary center of the disk. Then the magnitude of the relative velocity of any point in the circumference of the disc....
How is it possible that the center of a rotati... |
In what sense, there are only three independent rotations (i.e., rotations $R_x, R_y$, and $R_z$ about $x$, $y$, and $z$ axes, respectively)? Is it because any infinitesimal rotation about an arbitrary axis can be written as a sum of three rotations $R_x, R_y$, and $R_z$?
But then, in what sense, there are only three i... |
My question is about parts (e) and (f). I have found the matrix to equation of motion to be $\frac{d}{dt}\begin{bmatrix} x_1 \\ x_2 \\ p_1 \\ p_2\end{bmatrix} = \begin{bmatrix} 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & \frac{1}{2} \\ -400 & 500 & 0 & 0 \\ 500 & -\frac{1900}{3} & 0 & 0 \end{bmatrix}\begin{bmatrix} x_1 \\ x_2 \\ p_... |
In a talk The enigma of black hole horizons, (at 24:37), it is said that
"Raychaudhuri equation implies, if the flux into H is positive, area increases and horizon is spacelike".
How increase in area implies spacelike horizon? Similarly, how constant area implies null and decrease in area implies timelike horizon?
|
I am looking for an example of a clean, local $d=2$ classical model that undergoes a continuous phase transition on varying temperature that satisfies two properties:
The phase transition is resilient to quenched "energy"-like uncorrelated disorder (i.e. satisfies the Harris criterion that the critical exponent $\nu>1... |
when doing problems i have seen that only $V=kq/r$ has been used. while for electric fields many other different formulas have been used. Does potential not matter with shape of body, if yes then why not?
|
In the photoelectric effect, accordingly to the classical theory, if the electrons' energies depend on the intensity of the incident light, then on what does the electrons' number depend? I mean, how can one increase the number of emitted electrons according to the classical theory?
|
All solutions online I could find to this question takes it as a preconceived fact that as the mass winds, its motion will be perpendicular to the acceleration provided by the thread and hence the speed won't change.
I'm myself uncertain how this is true. This might be an intuitive hunch to solve this question but I c... |
The momentum of particles in pilot wave theory is dependent on the phase of the spatial wave function, which is 0 for stationary states. This means that electrons in all excited stationary states of a hydrogen atom would have a momentum of 0. However actual measurements reveal a nonzero momentum. I have read that pilot... |
I have a 3-dimensional density field from a big N-body simulation, and I would like to compute the matter power spectrum $P(k)$ to see how it compares with the one observed by Planck etc. I know that the process involves computing the FFT of the over-density field, $\hat{
\delta}(k)$, and then average $|\hat{
\delta}(k... |
My friend from physics who doesn't know whistling says he is good at whistling, but the resonant frequencies are ultrasonic so others cannot hear it.
Could this be right, or is he just bluffing?
Excuse my unscientific language here, but when you whistle, initially there is just a hollow windy sound, and then you sudden... |
When we heat a metallic beam, it expands and we observe that for small ranges of temperature the change in length is proportional to the original length and the change in temperature. I do understand how this works for a beam, but what about someother objects.
Consider an isotropic donut shaped object. Upon heating I w... |
Objective: I am trying to familiarise myself with quantum entropy for squeezed vacuum states.
Context: As a previous excercise, I have evaluated von Neumann entropy $\mathcal{S}(\widehat{\rho})=-\text{Tr}(\widehat{\rho}\log(\widehat{\rho}))$ for thermal states, since the density matrix for thermal states is known resu... |
Does anyone have an idea how the authors of this paper https://www.nature.com/articles/s41598-021-81722-6#additional-information
solved the equation 10? Thank you in advance
|
The system of electrons in a box, i.e. in a rectangular infinite potential well, with length of 0.5 nm is described by the wave function $$\Psi = \frac{1}{4\sqrt{2}}(2\psi_1 + \psi_2 - 3\psi_3 + 4\psi_4 - \psi_5 + \psi_6),$$ where the vectors $\psi_n$ are eigenvectors of the Hamiltonian for the system of particles in t... |
I'm trying to get a deeper understanding of this particular form of the ideal gas law I have seen. That form is $P=\rho R T$. I believe this form is not valid when mass or volume is changing. Am I correct? Below, I put a derivation of $P=\rho R T$ and some of my reasoning as to why I think it doesn't hold under changin... |
I have a simple pendulum of length $l$,
(The string is massless)
What is its time period?
Simple, you say, it's $2 \pi \sqrt{(l/g)}$.
Are you sure about that?
Well, for a small angle that's true
Is it?
The limit as amplitude approaches $0$?
Sure that's better, but really is it?
What if the ball of the pendulum wasn't a... |
In QED we like to define the (differential) cross section for a scattering process as follows:
$$d\sigma \ \dot= \ \frac{w_{fi}dN_f}{|j_{inc}|}\tag{1}$$
where $w_fi$ is the probability of transition between the initial and the final state per unit time (so the probability per unit time that a scattering event will happ... |
I have found a discrepancy in the way different sources define surface gravity (or derive) via the non-affine geodesic equation satisfied by the a Killing vector $\xi$ on a Killing Horizon (KH), up to a sign. That is, on the one hand Ref. 1, Ref.2, Ref. 3 (and many others) claim that on the KH
$$\xi^{\mu}\xi_{\nu;\mu}=... |
I have seen many different derivations of the second virial coefficient, but none of them explains how they turn a double integral into a single integral.
The second virial coefficient is:
$$
B_2=-\frac{1}{2} \int d^3q_1 d^3q_2 \ f(|\vec{q}_1-\vec{q}_2|)
$$
with
$$
f(|\vec{q}_1-\vec{q}_2|) = e^{-\beta U(|\vec{q}_1-\v... |
In this circuit, the sum of the charges on both the plates is 0.The sum of the charges present on the negative terminal and positive terminal of the battery is also 0 (I think). Is it possible for the sum of the charges on the 2 terminals of the battery to not be 0, so that the net charge on the two plates is also not... |
Since the valence or free electrons and doing the flowing guided by electromagnetic field, what about the protons that are still stuck in the nucleus inside the wire, battery, resistor what have you those protons are they doing any work at all?
|
They mention that Rutherford's model of an atom was wrong as in a circular orbit the electron would accelerate and hence radiate energy along with electric and magnetic fields. But why does the electron accelerate and how would it spend energy?
The displacement of the electron is perpendicular to the force so wouldn't ... |
Suppose there is a non-stationary diffusion process in 2D rectangular plane. Component diffuses from the outside through all four faces of the plane.
When I think about the simulations of the non-stationary diffusion in Matlab for example (finite difference numerical solution), I remember how time change in concentrati... |
In the Venturi tube the sum of static and dynamic pressure is kept constant along a streamline. A reduced cross section leads to a reduced static pressure.
$$p_1+\rho v_1^2/2 = p_2 + \rho v_2^2/2$$
But on the other hand, the velocity in a pipe is zero at its wall. So, following a streamline close to the wall, I would g... |
I'm watching this lecture on introductory Supersymmetry (Clay Cordova, 2019 TASI lecture 2 on Supersymmetry). My question relates to the first 20minutes or so. The lecturer is introducing Superfields in the context of Quantum Mechanics.
He supposes we have $\mathcal{N} = 2$ supersymmetry, and we have a single complex s... |
I am making a sound dampening box for a vacuum pump. It’s loud almost 96dB. I have an ultra quiet fan to vent heat out of the box. I want to calculate how to make a couple small inlet holes while still giving the fan the ability to pull maximum air if needed. How do I find how many holes I need and how big those holes ... |
When we write $j=\sigma E$ in a conductor, is $E$ here the net electric field produced by the electrons and the source that drives the current? For example, inside an electrolytic cell (let us assume it is ohmic), the electric field produced in the electrolyte must have 2 components; (i) the electric field produced by ... |
This is a relatively simple question, but I cannot find a clear answer:
Given the multipole expansion of a real scalar function,
$$
f(r,\theta,\phi) = \sum_{\lambda\mu} f_{\lambda\mu}(r) Y_{\lambda\mu}(\theta,\phi)
$$
do the coefficient functions $f_{\lambda\mu}(r)$ necessarily form spherical tensors of rank $\lambda$?... |
In fluid mechanics, consider a liquid with a free surface denoted by $z=h(x,t)$ (e.g. sessile droplet on a substrate). Suppose the free surface is subject to external forces acting in the normal direction, e.g. we apply an external electric field to a liquid metal so there is an electrostatic stress acting in the norma... |
Just wanted to understand how I would go about calculating the effective focal length of these different lens configurations.
There's the combined focal length formula, but I'm struggling to apply it to this setup, and how would I account for the different lens types other than the bog standard concave and convex ones ... |
Ok so I was going through this question:
Two small spheres of masses
m1 and m2 are connected by a light right rod.The system is placed between a rough floor and smooth vertical wall as shown in Fig. The co-efficent of friction between the floor and the sphere of mass m2 is μ .Find the minimum value of θ so that the sy... |
Well basically title. The characteristic / discrete radiation from an x-ray tube comes from electrons falling down into a vacancy which was created by an incoming electron from the acceleration voltage. This electrons always comes from an upper shell and emits some radiation in the length of a few dozen pm.
My question... |
Is it sensible to say about "linear" YM theories with tiny YM fields, thus removing the nonlinear YM self-interaction terms from the Lagrangian which therefore only contains the linear YM field interaction with matter?
|
Suppose positive and negative charges are separated into different objects by friction in some inertial lab frame. Those objects are then moved to opposite directions along the $x$ axis, with an initial velocity big enough to balance the electrostatic attraction, so that they will get zero velocity at infinity.
The cha... |
Matthew D. Schwartz in his QFT and the Standard Model subsection 10.1.2, shows that $SO(1,3) \cong SU(2) \times SU(2)$ which according to this PhysicsSE post is actually untrue. I was confused about this because of the usage of direct product to actually mean tensor product in texts such as, for eg., Wu Ki Tung's Group... |
I was trying to understand the Earth's frame of reference. You stick a coordinate system on the surface of the Earth and due to the Earth's rotation the coordinate rotates with respect to the axis of the Earth. It is also obvious that the coordinate axes have some rotation around the origin for example if you stick the... |
Does the following make sense? And has anyone else come
across this odd ~’cosmological coincidence’ before?…
…If we posit that our total universe mass is:
(1) $$M_{U}=\frac{{M_{pl}}^4}{{M_{p}}^2M_{e}},$$
where $Mpl$, $Mp$ and $Me$ are the Planck, proton and electron masses
respectively, yielding a total mass of ~8... |
I am reading "An Introduction to the Theory of Piezoelectricity" 2nd edition by Jiashi Yang
I am trying to understand a derivation for an equation that uses multiple Levi-Civita symbols.
The Levi-Civita symbol is defined as:
\begin{equation}
\varepsilon _{ijk} = \hat i_i \cdot \left( {\hat i_j \times \hat i_k } \ri... |
In either case I was thinking their curl is cero since they're homogenous. But that only leaves with
$- \frac{\partial B}{\partial t}=0$ for example, but then?
|
I am not able to wrap my head around this. Why does taking average pressure and multiplying it with the area given total hydrostatic force? In many books, the reason was because pressure is linearly varying with height but I don't see the connection. I can find this by integrating but what is the proof to this?I can pr... |
The canonical derivation for the $1/r$ potential due to a point charge is as follows:
We consider an electric field of the form $$\mathbf{E}=\frac{q}{4\pi\epsilon_0 r^2}\hat{\mathbf{r}},$$ and integrate along a straight path from $r'=\infty$ to $r'=r$: $$V_\infty(r)=-\int_\infty^r\mathbf{E}(r')\cdot\mathrm{d}\mathbf{r... |
The work energy theorem states that for a given object
∆ Kinetic Energy = Work done by all forces ( Conservative, Non Conservative, External )
Here ,
Suppose if ∆KE = 0 , Potential energy has changed
Ie. For example the ∆ kinetic energy of a body being brought up to a height by a crane , say x , is 0
This means the obj... |
If supernovas can be predicted depending on the mass of the a star, (If its more than about 8 times the mass of sun it will eventually go supernova - https://www.space.com/23756-white-dwarf-stars.html), can we use that data to predict if a neutron star will later form from this supernova and if that neutron star will t... |
I was reading a book on thermodynamics when I came across the following:
"Any closed thermodynamic cycle can be approximated by infinitely many Carnot cycles".
I realize that because the adiabatic legs of the cycle "cancel" each other out, such that the isothermal legs all add up along the boundary of the cycle. This... |
I have several questions regarding the definition of planar spin.
I was reading the big yellow book (by Di Francesco et. al.)
Section 5.1.5 looks a little mysterious. Look at 5.25, which is the two-point correlation function:
$$<\phi_1(z_1,\bar{z}_1)\phi_2(z_2,\bar{z}_2)> = \frac{C_{12}}{(z_1-z_2)^{2h}(\bar{z}_1-\bar{z... |
I get very confused about the concept of inner product. When an inner product is defined in a vector space, $\mathbb{V}$, don't we define it as an operation between two vectors from $\mathbb{V}$ itself?
But very often, I hear that people [cannot give a reference, :-(] say it is an operation between a vector from $\math... |
I am exploring the one axis twisting (OAT) hamiltonian $\hat{H}=\chi S_z^2$ with $S_z=\sum_{i=1}^N\frac{\sigma_z^i}{2}$ and considering the initial state to be $\left|\psi(0) \right>=\left|+x\right>^{\otimes N}$, where +x means that the state is pointing along the x direction in the Bloch sphere, i denotes the index of... |
I'm studying for an exam called Introduction to QFT. One of the main topics in this class is the quantized free fields.
I can now find the fields that solve the Klein-Gordon equation and the Dirac equation, but I don't really know what they do.
For example: if we are considering a Klein-Gordon scalar-free field, we wou... |
I am conducting an experiment in which I am measuring how the internal pressure in a balloon varies with its circumference. To explain the relationship (shown in the graph below) I decided to calculate stress & strain values of the balloon's membrane.
I know that the internal pressure balances the surface tension of th... |
I had always understood that the well-known effects of SR- such as time dilation, length contraction and so on- were properties of the geometry of spacetime so that they applied to spacetime in an abstract sense. For example, the spatial distance between two parallel worldlines in one inertial frame could be length-con... |
While I'm reading an article, I get confused by why and how we study different limits in quantum limit.
In this paper, the author introduced four limits in D0-brane quantum mechanics: the DKPS (Douglas–Kabat–Pouliot–Shenker) limit, the SSS (Susskind–Seiberg–Sen) limit, the BGLHKS (Balasubramanian–Gopakumar–Larsen–Hyun–... |
When an car moves forward we go back and we have always read that the reason was that our legs stay in contact with the ground and our body goes back since it was at rest and with sudden motion it still has a tendency to stay at rest . But shouldn’t pseudo force apply too ? I did asked someone that and they said that p... |
In the system shown below, the floor is frictionless.
The question of the exercise is as follows: What will be the acceleration of point P?
I am a bit confused because I just can't understand the meaning of acceleration of a point. Can someone explain?
|
This is the diagram drawn for analysis of laminar flow in a pipe. While I understood that pressure difference is the main reason behind the flow, I can't understand how two cross-sections in flowing fluid can have different pressures? Since we must have same pressure at all point at same altitude. Can I get help findi... |
I have a lot of confusion understanding the concept that a mass creates a curvature in the space time and other small masses gets attracted towards big masses since they starts falling inside that curvature and we feel that it got attracted towards the bigger mass.
But if we let say dig a curved whole in the ground an... |
I Googled up some things in thermodynamics, but I'm still confused about a few basic one.
If I mix warm and cold water in a tank the mixture will have the potential and kinetic energy of atoms, but that energy won't be useful to do work. If warm up the top of the water in a tank, but the bottom part not, as it won't mi... |
Ok, I am very rusty in thermodynamics. In fluid mechanics books, you can find the heat transport equation in terms of temperature $T$:
$$
\rho c_p\left(\frac{\partial T}{\partial t}+\boldsymbol{u}\cdot\nabla T\right)=\nabla\cdot(\kappa\nabla T),
$$
where $\rho$ is the density, $c_P$ the specific heat at constant pressu... |
Given an incompressible vector field $b$ in $\mathbb{R}^2$ or $\mathbb{R}^3$, it holds that $b= \nabla \times \Phi$ for some vector field $\Phi$. I would be interested in the simple situation where $b$ is the velocity induced by a point force in a Stokes flow (also called "stokeslet"). I'd need a precise representation... |
I have been trying to derive snell's law in the case of a monochromatic harmonic plane wave at a planar interface. By the same derivation I also wanted to derive how the frequency of the wave does not change at the interface. Here's the context:
We solve the planar wave helmholtz equation in both regions and get phaso... |
I am self-studying Optics by Pedrotti and I'm on the subject of geometric optics, specifically ideal Cartesian surfaces. These are reflecting or refracting surfaces that form perfect images. I was able to derive the equation for an ellipsoid using Fermat's principle, but I'm struggling with the algebra for a paraboloid... |
I am trying to understand if gaps contract in the same way as solid objects in SR and casually the answer seems to be yes, but there seems to be circumstances where this is not always true.
Consider the following thought experiment. A galactic battleship is firing shells at a rate of once per second at a velocity of $v... |
In Fetter and Walecka Many Particle Physics we see a sketch for a quantum system how the limit of a quantum system embedded in a bath of harmonic oscillators can give rise to a pole off of the real frequency axis. My understanding is that a finite system will have all its poles on the real frequency axis, yet as the sy... |
In quantum dynamics folks often examine the imaginary part of the Green's function to understand the response of a system. in classical mechanics / mechanical engineering folks often study the Bode plot which instead separates the transfer function into magnitude and phase. Why does one community focus on the imaginary... |
If we have a gas or liquid described by the van der Waals gas law with negative pressure, does that lead to a negative stress energy tensor?
Does a stretched liquid for example have a negative stress energy tensor?
|
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