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Consider that I'm given the following Lagrangean:
$$L=L_{QED}+\frac{1}{2}\partial_\mu\phi\partial^\mu\phi+\partial_\mu\chi\partial^\mu\chi-\frac{1}{2}m_\phi^2\phi^2-\frac{1}{2}m_\chi^2\chi^2-\frac{1}{2}\mu_1\phi^2\chi-\frac{1}{2}\mu_2\chi^2\phi-g\bar{\psi}\psi\chi$$
where $\phi$ and $\chi$ are neutral scalar fields and... |
The Wikipedia page for "Density Matrix" (https://en.wikipedia.org/wiki/Density_matrix) takes each of a pair of entangled photons as an example of a mixed state:
A radioactive decay can emit two photons traveling in opposite
directions, in the quantum state $|R,L\rangle+|L,R\rangle/\sqrt2$. The
two photons together are... |
In order for a function $f$ to be a probability density, it must satisfy $$\int f dx=1,$$ where $x$ spans the domain of the random variable. If we take the Fermi-Dirac distribution $$\tag{1}f(E)=\frac{1}{e^{(E-E_F)/kT}+1}$$ at $T=0$, we find a step function like this
which is described by $$
f(E) = \left\{
\b... |
I read that the gravitational constant can be expressed in terms of Planck length.
$$G=\frac{\hbar c}{m_\rm{P}^2}$$
What is the derivation of this relationship?
|
The broken line represents the total displacement (i.e line from furthest vertices of the triangles, and the other dotted lines that create a triangle with the solid lines are the hypotenuses, my question is if the sum of those hypotenuses will yield the magnitude of the displacement vector.
|
$\def\b#1{{\mathbf #1}}$
Referring to the following formulae from wiki, it seems like dipole-dipole interactions can be qualitatively described using the formula:
$$H = -\frac{\mu_0}{4\pi|\b{r}|^3}\big(3(\b{m}_1\cdot \hat{\b{r}})(\b{m}_2\cdot\hat{\b{r}})-\b{m}_1\cdot\b{m}_2\big) + \mu_0 \frac{2}{3}\b{m}_1\cdot \b{m}_2 ... |
The Rindler geometry is described by the following line element
$$
\mathrm{d}s^2 = -\alpha^2 \chi^2 \mathrm{d}\tau^2 + \mathrm{d}\chi^2 +\mathrm{d} y^2 + \mathrm{d}z^2 \text{.} \tag{1}
$$
Hence, the Rindler metric (written in matrix form) is
$$
(g_{\mu\nu}) = \begin{pmatrix} -\alpha^2 \chi^2 &0&0&0 \\
0&1&0&0 \\ 0&0&1&... |
I was reading here the paragraph about electromagnets.
It is written that:
"Electromagnets are usually in the form of iron core solenoids. The ferromagnetic property of the iron core causes the internal magnetic domains of the iron to line up with the smaller driving magnetic field produced by the current in the solen... |
Suppose you have set of circular concentric solenoids like so:
How would you calculate the overall inductance of these loops? Would it be the same as this formula:
Or would the formula be modified? Thanks!
|
I'm working through some QFT course notes and I just want to check that my understanding of equal-time commutators is correct.
I don't have much to go on -- the notes rather cryptically insert the statement "Key: equal time commutators $[\hat{p}(t),\hat{q}(t)]$" between the hat-fitting part of canonical quantization $p... |
The following line of reasoning, apart from possible misconceptions in my part, is how instantons are usually (intuitively, at least) introduced:
(i) We look for minimum classical action solution for a pure Yang-Mills theory: these occur for pure gauge fields $A_\mu=\frac{-i}{g}U\partial_\mu U^{-1}$.
(ii) Furthermore, ... |
I am just curious about the above question. It might be helpful for geologists, or meteorite hunters...
|
Physicist John A Wheeler proposed the "Principle of mutability" which said that it could be the case that the universe would eventually shrink in a "Big Crunch" and the be re-born in another Big Bang. He proposed that the laws of physics (even the considered most fundamental ones) would change and therefore, between cy... |
I would like to know if the term: $PdV$, can/should be included in the thermodynamic identity of a solid crystal. Let me clarify that the specific crystal is supposed to be having lost, a small $(\propto 10^{-2})$ proportion of its oscillators. So that its volume has decreased by a small amount.
Additionally, I would ... |
Why do we use virtual displacement to vanish work done by constraint forces instead of the actual displacement?
|
So I have this potential
$$ V(x) = \begin{cases}
-a\delta(x) & -b < x < b \\
\infty & |x| \geq b
\end{cases}
$$
Solving the time independent Schrödinger Equation for bound energy states $(E<0)$ gave me:
$$
\psi_1(x) = Ae^{kx} + Be^{-kx}\mbox{, }-b<x<0 \\
\psi_2(x) = Ce^{kx} + De^{-kx}\mbox{, }0<x<b
$$
Where $k=\sqrt{... |
Suppose we have a center symmetry transformation that acts on the connection as:
$$A \mapsto \ ^gA = \Omega^{-1} (A+d)\Omega $$
and satisfies
$$ \Omega(t+\beta,x) = h\Omega(t,x)$$
Suppose $W[U]$ represents the winding number of $U$ a gauge transformation, which is an integer, and is computed as:
$$ W[U] = \frac{1}{24 \... |
The red circle is being pulled by two gravity points. Assume that the red circle has a given position (x,y) and a given velocity (vx, vy).
I need to calculate the velocity and position of the red circle at time (t) given these two gravity points [(x.a1, y.a1) and (x.a2, y.a2)] with both of them having a force (G) that ... |
The reciprocal lattice vector $\vec{G}=h\vec{b}_1++k\vec{b}_2+l\vec{b}_3$ is perpendicular to the family of planes described by the Miller indices $(hkl)$. This means that if $\hat{n}$ be the unit vector normal to the $(hkl)$ planes, then $\hat{n}\times\vec{G}=0$. So we are taking the cross product of two vectors $\hat... |
Well, let's take the example of a compressible solid. We know that in order to compress a solid we need to apply a force "greater(and not really equal)" than the interatomic/intermolecular repulsions that follow, more precisely, than the internal restoring force that follow. That means in the process of compressing the... |
In computing the variation of the action in Chern-Simons, and in other contexts, we get the following expression that is named the winding number, where $U$ comes from a gauge transformation:
$$ W[U] = \frac{1}{24 \pi^2} \int d^3x \ \epsilon^{\mu \nu \beta} \ \text{Tr}(U \partial_{\mu} U^{-1} \ U \partial_{\nu} U^{-1} ... |
I'm an amateur studying General Relativity. I'm reading some notes of lectures by Susskind. In them, it is written that
"we know that [the covariant derivative of the metric tensor] is zero. Why? Because the ordinary derivative of the metric tensor in Gaussian coordinates is zero. So, in any coordinate system, we... |
I have a mechanics question (Source: Kleppner,Kolenkow; 2nd ed., p.104, problem 2.11), which states the following (along with an answer):
[![One of the classic problems in which a mass attached to a vertically rotating poll with symmetrically strings that are both at 45 degree angle to the rod, and are of the length ... |
When the water is filled up-to the brim the plastic cap can easily stay in the middle (roughly ) of the glass.
When the water is filled till the middle the cap will always come at rest at the corner.
It will be great if somebody can explain why does this happen and also provide me with mathematical proof behind his ... |
Does the superposition principle actually tell us about our inability to predict what happens during the course of the experiment? Does it tell that, since an experiment has multiple outcomes ( i.e , in the case of the double slit experiment , the electron can either pass through slit 1 or 2), all the outcomes have wo... |
It is usually said that the wave function for $N$ particles cannot be imagined in 3 dimensions, but only in $3N$ dimensions. What is the exact argument? Is there a loophole?
Schrödinger, Feynman and many others picture single-particle wave functions in 3 dimensions. So there should be a way to picture many-particle wav... |
When a conducting rod moves in a uniform magnetic field as shown.
By Lorentz force it is easy to explain that EMF induced is BvL and upper end is positive and lower end is negative.
But in books, this concept is explained by Faraday's law of electromagnetic induction as the area swapped by conductor is changing and EM... |
Suppose we have a plate capacitor, placed in a uniform background electric field (in a way that the electric field is perpendicular to the capacitors plates.
Without the electric field, the relationship of "voltage" and charge in the electric field would be
\begin{align}
U = \frac{Q}{C}
\end{align}
Here, U denotes the ... |
I wanted to visualize time dilation through Minkowski diagrams but I ended up in a fiasco. Let me show how. Consider two observers $O$ and $O^\prime$ at rest and moving with velocity $-v$ with respect to a clock, respectively. Suppose a one-dimensional boost that transforms the coordinate frame from $x^\alpha$ (in whic... |
"for a strictly classical system in thermal equilibrium can display no magnetic moment, even in a
magnetic field."
The statement is from Introduction to solid-state physics by Kittel (8th edition -Chapter 11), Why a system in thermal equilibrium can't have a magnetic moment? can anyone please give me more insight int... |
In electrostatics we say that charge is quantised. Then my question is how can we integrate them?
|
A block of mass $m$ is attached to one end of a light string which is wrapped on a disc of mass $2\,m$ and radius $R$. The total length of the slack portion of the string is $l$. The block is released from rest. The angular velocity of the disc just after the string becomes taut is:
Solution:
Using the principle of co... |
When I was watching a Youtube video explaining why pressure inside a drop is greater than the pressure of the air outside, surface tension was drawn as acting radially inwards from the spherical surface of the liquid drop. Hence, because there is both the force due to the air pressure acting over the surface area of th... |
In cosmology, the initial perturbations to the metric can be described as $$\mathrm ds^2=-\mathrm dt^2+a(t)^2e^{2\zeta(\mathbf x)}\mathrm d^2x,\qquad(1)$$ where $\zeta(\mathbf x)$ is a gaussian random field with power spectrum $$\frac{k^3}{2\pi^2}P_\zeta(k)\propto k^{n_s-1}.\qquad(2)$$
A power spectrum in which $n_s=1$... |
Suppose you are in radial free fall at some point outside the event horizon of a Schwarzchild metric. The strong equivalence principle implies that locally you would be unable to discern whether you are in fact in free fall near a gravitating body or simply at rest in flat spacetime. The operative word being "locally."... |
Given an asymmetrical coil rotating in a uniform constant magnetic field, does the current flowing in it differ if i change the rotation axis (keeping it on the coil plane), mantaining rotational speed always the same?
|
Question: A long horizontal rod has a bead which can slide along its length and is initially placed at a distance $L$ from one end $A$ of the rod.The rod starts from rest in angular motion about $A$ with a constant angular acceleration $α$.
If the coefficient of friction between the rod and the bead is $μ$ and gravity ... |
I only know the thermodynamic definition that "adiabatic process is a process that doesn't exchange the heat or mass with the surroundings".
Does it mean, that for example "adiabatic waveguide/taper" is just a lossless waveguide/taper? Why won't authors of papers use just the word "lossless"?
Is adiabatic photonic devi... |
I was trying to make sense of color combining and prime colors. I was trying to look at it from an electron orbit and photon perspective. Aside from having an organ that over simplifies things, it doesn't seem to make much sense that I'd be looking for an array of prime blue colored and prime yellow colored photons to ... |
Consider the Fourier transform of a conformal primary $O$
$$\tilde{O}(k) = \int d^dx e^{ik\cdot x} O(x)$$
Now consider the transformation of the momenta $k \to \lambda k$, so that the above reads
$$\tilde{O}(\lambda k) = \int d^dx e^{i\lambda k\cdot x} O(x) = \lambda^{-d}\int d^dx'e^{ik\cdot x'} O(x'/\lambda)$$
where $... |
In my experimental introductory course about Particle-Physics we discussed the deep inelastic scattering of an electron with a proton, where the electron interacts with a parton within the proton by electromagnetic interaction (by "exchanging" a photon).
I am recently studying a process where the parton which is intera... |
Could a similar process be achieved artificially in a laboratory, with the same near perfect efficiency biological systems display.
Is there a sound simple theoretical model on how this works?
|
I was looking into the polarization of patch antennas (for GNSS use).
I found this website (http://kempbros.github.io/antennas/Patch_Antenna_Generator/) which gives the geometry of the antenna starting from a couple of parameters (frequency, dielectric constant, etc..).
From what I can see the polarization of the ante... |
In electrostatic case, the charge density and potential at a point is related by:
$$\nabla ^2 \phi = -\frac{\rho}{\epsilon_0}.$$
The same is true for the Magnetic potential $\vec A$ and current density $\vec j$ in magnetostatics.
But in Feynman lectures vol 2, it is mentioned that the equation $\nabla ^2 \psi=-s$ is tr... |
I'm pretty new to the subject of geometric optics so forgive me if what I'm asking has a trivial explanation.
I was trying to find the position of the virtual image of a point object on a convex parabolic-shaped mirror using a ray-tracing method. As far as my knowledge goes, by tracing out at least two of the four prin... |
I can't understand why change in Gibbs free energy must be zero when two ideal gases mix. The differential of $G$ is: $$dG=-SdT + Vdp + \sum_i\mu_idn_i$$ When two ideal gases mix and they are initially at same $T$ and $P$ that is $T_1=T_2=T$ and $P_1=P_2=P$ then the final state will have also same $T$ and $P$. Why we c... |
This is a reference request, to ideally a textbook, monograph, set of lecture notes or lecture videos, on the topics of BRST quantisation and the Lagrangian BV formalism. My constraints are as follows:
Minimal use of the path integral formulation when possible, and minimal use of the category theoretical constructions... |
According to this:
$ E = \frac{-13.6 Z^2}{n^2} $
the energy of an electron is, well, higher the farer it is away from the core. I found this confusing as I need to put less energy to release an electron when it is on the 5th shell than when it is on the 1st shell. Am I right?
Concluding, one would say "The more energy ... |
I'm trying to figure out what determines the energy of the bands, either conduction or valence band. Mostly I can read about the bandgap energy, which is mostly just the difference between $ E_C $ and $ E_V $ but there are also more concise expressions like $ E_g(T) = E_g(0) - \frac{ \alpha \cdot T^2 }{T + \beta} $. Ac... |
I consider a one dimensional waveguide. I study free field propagation on it. I apply periodic boundary condition with periodization length $L$ to describe the physics with Fourier series and not fourier transform.
Within this volume $L$, the total Hamiltonian of the system is:
$$H=\sum_{l} \hbar \omega_k a^{\dagger}_k... |
I have two barrels, each connected to the other by one hose along the bottom and fed by a household hose.
The left is the supply barrel for my irrigation system, the right, a backup (see below for clarity).
If I add one additional barrel on the left, and connect said barrel to the supply barrel in the same manner as t... |
The gravity of the earth or more specifically the gravitational acceleration, $g$, is the acceleration objects with mass experience toward the earth due to gravity.
How much does this vary according to where the moon is, if at all?
In particular what approximate values for $g$ do we get for standing under the moon and ... |
I am trying to understand this paper by Hu, Paz, and Zhang about exact master equation of QBM in general environment. In the paper they used influence functional method introduce by Feynman and Vernon to get HPZ master equation. I am a little bit lost on the derivation they used especially
To get equation (2.18) and (... |
I have many questions (all in bold) around the Carnot cycle. I know I'm not the first one to ask a bunch of questions in the middle of a description of my own understanding, but having read other answers, I really think this is a rather individual process.
I'm using the pebble model : pebbles are resting on a piston wh... |
Imagine you have a small piece of paper in your hand. Your hands are sweaty and due to perspiration, the paper kind of bends up. Can you explain what is happening? Is it the capillary forces?
|
It is well-known, that in superspace formulation of supersymmetric theories auxiliary fields appear. In present of such fields SUSY transformations are linear and independent of model.
Are some non-supersymmetric examples of such phenomena?
|
Many-worlds interpretation says that the wave functions is all there is. And that the entire universe has only one wave function.
But quantum mechanics does not fully reconcile with gravity and there is a possibility that it may have to be tweaked and the wave function would not be all there is?
So what is the justific... |
Let's consider the Abelian Higgs model in 1+1 dimensions in Euclidean space-time:
$$L_E=\frac{1}{4e^2}F_{\mu\nu}F_{\mu\nu}+D_\mu\phi^\dagger D_\mu\phi+ \frac{e^2}{4}(|\phi|^2-\zeta)^2$$
where $\zeta>0$ and $D_\mu\phi= (\partial_\mu-iA_\mu)\phi$.
We are looking for finite action field configurations, i.e instantons.
Bec... |
I had this question while I was reading the differences between pressure and stress.
As I have read:
Pressure is the intensity of external forces acting on a point, and it always act normal to the surface.
Stress is the intensity of internal resistance force developed at a point, and it could be either normal or parall... |
Is the magnetic field of a neutron star generated by the minuscule amount of protons and electrons left or the spin of the neutrons?
If its because of the spin of the neutrons, how come they are all lined up?
|
Moved to materials stackexchange.
I'm compiling the mathematical expression of SCAN (Strongly Constrained and Appropriately Normed) functionals' constraints, but apparently they are not very obvious from their paper (at least for me).
I have compiled some constraints from the SCAN paper, the PBE paper, and Perdew's pre... |
Is the force on a wire zero if the direction of some net magnetic field is in the direction of the current. If not what would be the orientation of the wire such that the force is 0?
|
I have a wave function $\Psi (x,t)$. According to the Max Born postulate, $\lvert\Psi (x,t)\rvert ^2$ is the probability density. This quantity specifies the probability, per length of the $x$ axis, of finding the particle near the coordinate $x$ at time $t$.
If at $t=0$ I make a Fourier transform for the momentum spac... |
I am looking to determine the relative mass flow rate resulting from a puncture in a high-pressure cylinder for hydrogen and natural gas:
Note that the Outside Pressure (P2) is not necessarily atmospheric pressure.
I am struggling to get my head around the problem. The flow rate will reduce over time I think since the... |
The path integral's action $W_{ij}$ as a function of a pair of sources and sinks $J = J_1 + J_2$ can be written
$$W_{ij} = -\frac{1}{2} \int \frac{d^4k}{(2 \pi)^4}J_j^*(k)\frac{1}{k^2-m^2+i\epsilon}J_i(k)$$
so that for $J_1 + J_2 := \delta^{(3)}(\vec{x}-\vec{x_1}) + \delta^{(3)}(\vec{x}-\vec{x_2})$, we have $W_{12} = W... |
If we have a magnetic dipole moment $\vec{m}$ in a non-homogeneous magnetic field $\vec{B}$, how is torque $\vec{\tau} = \vec{m} \times \vec{B}$ related to force $\vec{F}_{\text{dipole}} = -( \vec{m} \cdot \vec{\nabla}) \vec{B}$?
|
The Bayes theorem simply states:
$$ P(B | A) P(A) = P(A | B) P(B) $$
I wonder if there is something that can be meaningfully said as generalization of this relationship when the probabilities in question arise from applying the Born rule to a quantum system. Is there an expression akin to Bayes that applies directly to... |
I came across an advertisement that said this juice is this because of anti-gravity formula.
|
This question is about getting to understand better what the Dual Resonance (DR) model actually managed to successfully predict or model from the nuclear interactions, in the context of understanding what aspects of the DR are expected to be emergent from QCD
My summary and very brief understanding of the whole affair ... |
When an electron is brought close to an proton I understand the math why energy drops and we have to provide energy to move the electron similar to a battery. Now I'm looking for a more conceptual answer. Why do we have to provide energy? Won't the proton attract the electron?
|
When doing QFT in curved spacetime we do Bogoliubov transformation to find one set of annihilation and creation operators in terms of others. In the paper Particle creation by black holes
Hawking states following:
One could still require that the $\{f_i\}$ and $\{\bar{f_i}\}$ together formed a complete basis for solu... |
My question is about the generators of the Lorentz group: signature $(-,+,+,+)$. I have found the well known Lorentz generators (intended as elements of its algebra evaluated in the identity element of the group)
Boosts:
\begin{equation*}
K_{1} =\begin{pmatrix}
0 & 1 & 0 & 0\\
1 & 0 & 0 & 0\\
0 & 0 & 0 & 0\\
0 & 0 & 0 ... |
Why we cannot express Generalized coordinates as a vector like we do with Cartesian coordinates $x$ , $y$ ,$z$ ?
|
I calculated an expression for a decay rate of a decay of Higgs boson into two $W$ bosons. The expression is as follows
$$
\Gamma = \frac{g^2\sqrt{1-4\frac{M_W^2}{M_H^2}}}{64\pi \hbar} \frac{M_H^3}{M_W^2}\left [ 1-4\frac{M_W^2}{M_H^2}+12\frac{M_W^4}{M_H^4}\right ].$$
What I want to get is a number. I can use known mass... |
I've been asked a question by a student - it's off the beaten track, and I am struggling to get a definitive answer, even off other physics teachers...
If we have an open tube, so open at both ends, how can we end up with a standing wave being formed in this tube?
How can the initial wave reflect back and cause the for... |
Ok So please forgive me for my weird doubts and obviously stupid doubt but we (a grade 10 student) study that solid, liquid, gas is sometimes defined according to the distance between the molecules and atoms i.e. really close, far, far away. According to me this definition seems a bit incomplete, I mean if I get a micr... |
I have hard time understanding why Gibbs-Helmholtz equation holds for finite changes. That is why we can write:
$$\Delta \left(\frac{\partial{G/T}}{\partial{T}}\right)_p=-\frac{\Delta H}{T^2}$$
We differentiate $f=G/T$ which must be a function of $(T,p)$ as is denoted in partial derivative operator. Therefore:
$$\left(... |
I'm trying to get an upper bound to the neutrino mass with kurie plot.
In order to do that I need to make a linear fit in order to get energy value that corresponds to $y=0$.
($y$ the kurie plot). The thing is, the range of the fit is rather arbitrary, and for each range I get slightly different values, so I was wonder... |
I know what trace is in matrix algebra, but does it have any intuitive physical significance when acted on a quantum mechanical operator? What aspect of an operator $A$ does ${\rm Tr}(A)$ capture? Or is it just a convenient mathematical tool and nothing more?
|
For linear molecules with two atoms, I understand that the rotational energy is:
$$\frac{1}{2} \mu \omega^2R^2$$
Where $\mu$ is the reduced mass and $R$ the bond length.
However, consider a rotating asymmetric linear molecule of 3 atoms with the heaviest atom being at one of the two edges. The rotating axis will theref... |
Based on Newton's third law of motion I understand how waves reflect pi out of phase off of hard boundaries (see gif 1), but what would be the reasoning as to why waves reflect in phase off of free boundaries?(see gif 2),
I theorize that because the ring moves higher up than the amplitude of the free boundary (like sho... |
I was wondering if we can predict the rotational velocity due to dark matter in this way:
Consider that we theoretically derived the rotational velocity of a galaxy ($v_{the}$). Then from experiment we got some other rotation velocity ($v_{obs}$). Then can we subtract these two velocities to obtain the rotational velo... |
This is the reason that suction pipes of centrifugal pumps are most of the times much wider than the discharge pipes and that restriction of blood flow in arteries is always an alarming event.
Does anybody know any mathematical proof or explanation why friction losses depend on fluid velocity squared?
|
Suppose we're interested in (minimally) coupling a heavy scalar particle to the electromagnetic field. In quantum field theory, we describe the particle as an excitation of a complex scalar field $\phi$. Including the simplest possible coupling leads to the theory of scalar QED, with Lagrangian
$$\mathcal{L} = - \frac1... |
Ok hear me out.
One thing I have always liked about Dirac notation is that it visually displays where expressions expect inputs/outputs. For example $\langle\psi|$ expects an input to the right to form a complete expression like $\langle\psi|\phi\rangle$. The angle brackets indicate the expression is 'complete'. Things... |
I am interested in a gravitational actions of this form:
$$
S=\iiiint d^4x\sqrt[4]{\left( R\sqrt{|\det g|} + L_m\sqrt{|\det g|} \right)^2 +L_a}
$$
where $L_m$ is a matter Lagrangian and $L_a$ is an additional contribution.
So far, I have derived the equations of motions as follows:
$$
\begin{align}
\delta S&=\iiiint \... |
The equation with the highest exponent I could find was the coefficient of energy loss of light scattered in an optical fiber:
$$
{\displaystyle \alpha _{\text{scat}}={\frac {8\pi ^{3}}{3\lambda ^{4}}}n^{8}p^{2}kT_{\text{f}}\beta }
$$
which has a power of $8$ on $n$, the index of refraction.
My question is why is this ... |
Electronegativity decreases with period in in the periodic table. The explanation for that is because the distance to the nucleus decreases with each orbital shell of electrons, if I got that right. What about the ability to attract over distance, how is it affected? Is it instead increased (given the higher positive c... |
So this random question popped up in my mind. As we know the photons get deflected if they pass in the vicinity of a black hole. At the event horizon(right before it), they form the photon sphere. The point where they start orbiting the black hole in circles. In fact they are travelling straight, it's just the space-ti... |
In my thermodynamic's course, this equation was presented as the Sackur-Tetrode equation:
$$\frac{S}{n}=R\log{\left(\frac{V/n}{V_{0}/n_{0}}\right)} +c_v^{*}\log{\left(\frac{T}{T_0}\right)} + \frac{S_0}{n_0}$$
An expression for entropy when $N$ is not constant.
However, researching on the Internet I discovered that, in ... |
I have come across the following stress-energy tensor and I was wondering if anyone know of a physical system this could correspond to?
$$
T^{\mu\nu}=\pmatrix{(X^0)^2 & X^0X^1 & X^0X^2&X^0X^3 \\ X^1X^0&(X^1)^2&X^1X^2&X^1X^3\\X^2X^0&X^2X^1&(X^2)^2&X^2X^3\\X^3X^0& X^3X^1&X^3X^2&(X^3)^2}
$$
where $X^0,X^1,X^2$ and $X^3$ ... |
Solving second order inhomogenous PDE by separation of variables requires homogenization of the boundary conditions. Let's say we are looking at 1D heat equation. From intuition, if we have fixed temperature on both sides(inhomogeneous Dirichlet-Dirichlet boundary conditions), there is no heat coming in or out of the 1... |
Why telescopes before event horizon telescope were not possible to take such picture of black hole that EHT taked?
|
We have a compact lattice gauge theory if we let $A_{i}(n)\in[-\pi,\pi]$, and if we identify $A_{i}(n)\sim A_{i}+2\pi$. A simple lattice gauge theory in 2+1D then has an action
$$S=\sum_{x}1-\cos(F_{\mu\nu})$$
Here, the compactness of the gauge field is provided by the periodicity of the action with respect to $A$. It ... |
As far as I know:
The gravitational force occurs due to curve in spacetime. A curve in spacetime occurs due to energy. So my question is the increase in angular momentum is also increase in gravitational force? For example a spinning blackhole would apply more gravitational force compared to a non spinning one. Because... |
In some books on QFT and particle physics, the $-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$ term (which arises in field theories with a coupling to electromagnetism) referred to as "the kinetic energy of the photon".
I know that this tensor invariant is related to the classical EM fields via $F_{\mu\nu} F^{\mu\nu} = 2 \left( B^2... |
In Schrodinger's theory of the atom, an electron does not move on a circular path. Its motion is in 3D and its random. It could be anywhere in space. How come they named it to wave form? If it's random, how can we talk about wave here?
|
BTZ black holes are defined for the case of 1+2D gravity theory because of closed form computation. I’m wondering if there exist a $1+3D$ analogue black hole?
Edit: What I'm actually looking for is the black hole solution of Einstein-Maxwell equation with a negative cosmological constant but in $1+3D$ dimension instead... |
We know quantum mechanics gives a random result when we observe a particle that's in a superposition, but why is it random? One of the explanations I've heard is that because light comes with those discrete energy packets called photons, when a photon is passing through a polarized filter, it must either all pass throu... |
When we say waves, we usually imagine soothings like a sin wave, with a crest and a trough. But we can't use the same logic with gravitational waves, can we?
Because if gravitational waves had a crest, would that not mean that space-time is being curved one way (down lets say) and another way later (up lets say).
Would... |
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