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In the context of this larger problem, I have a question about the meaning of the matrix $W$ here.
The time reversal operator $\Theta$ can be written $$\Theta = UK$$ and also as $$\Theta = U'K'$$ where $K|n\rangle = |n\rangle$ and $K'|\nu\rangle = |\nu\rangle$. $\{|n\rangle\}$ and$ \{|\nu\rangle\}$ are orthonormal bas... |
While try to understand functional field integral I encountered this problem on Altland & Simons page 184. The question is: Employ the free fermion field integral with action (4.43) to compute the zero temperature limit of the correlation function (4.48) considered in the text (assume $x > 0$).
Setting $v_{F}=1$ and de... |
Consider the following two points, or events as they are more commonly called, in SpaceTime:
Event 1: $(x,t) = (0,0)$
Event 2: $(x,t) = (a,0)$
As you can see they are merely two separate locations, Event 2 could be any point in space. The word 'event' here is a misnomer, because it carries with it the connotation of t... |
Say an object with an initial kinetic energy $\frac12 mv^2$ is launched from the surface of the Earth into an elliptical orbit with area $\pi ab$ without loss of energy. ($a$ is semimajor axis, $b$ is semiminor)
What are the apsides of this orbit?
I know that when an object is at this red point here
the distance betw... |
I have seen time Gravitational time dilation experiments measured using atomic clocks on airplanes, such as the Hafele–Keating experiment. The clocks aboard the airplanes were slightly faster than clocks on the ground. This is measured from the point of view of the clock on the ground.
Is it possible, that the time di... |
Consider a very tall vertical cylinder in a strong gravitational field that is rotating about it's long vertical axis. It is standing on the surface of the gravitational body with suitable bearings to allow it to rotate. The gravitational body is non rotating and uncharged and the Schwarzschild metric applies.
Observer... |
When showing that $\Psi$ stays normalised, we arrive at
$$ \frac{d}{dt} \int_{-\infty}^{+\infty} \lvert \Psi \rvert^2 dx = \frac{i\hbar}{2m} \int_{-\infty}^{+\infty} \frac{\partial}{\partial x} \bigg( \Psi^* \frac{\partial\Psi}{\partial x} - \frac{\partial\Psi^*}{\partial x} \Psi \bigg) dx $$
$$ = \frac{i\hbar}{2m} \B... |
Textbook answer of how radiation is emitted is from the surface. Does the inside of a object also emit infrared?
|
My teacher states that if we apply an external force just equal to the value of limiting friction, then the body will start moving.
But if the external force is just equal to the maximum frictional force will not the net force on the body be zero?
Can I conclude from this that the value of limiting friction can never b... |
After the discovery of the Higgs boson, we were all told that most of a proton's or neutron's mass does not actually come from their three main ('valence') quarks and their interaction with the Higgs, but from non-valence 'virtual' quarks (condensate?), quark kinetic energies and gluons (perhaps something called, myste... |
Either through constant gravity, more simply, or through the changing gravitational field, more accurately. This appears to be a fully determined system, although I found no analytic solutions for this problem online. The best I could find was the rocket equation minus gt: $\Delta v = u \cdot ln(\frac{m_i}{m_f}) - g \c... |
My goal was to attach a trash basket to the side of my butcher block table. It was meant to hang off a cabinet but I wanted it to hang off my table. This did not work well for multiple reasons but did make me realize a hole in my intuition of how magnets work.
Basically I superglued 6 magnets equally spaced in a row un... |
Many books on relativity define "mass" $M$ as the norm of the energy-momentum vector $\pmb{P} := (E, \pmb{p})$, that is, $M = \sqrt{\lvert \pmb{P}\cdot\pmb{g}\cdot\pmb{P}\rvert}$, where $\pmb{g}$ is the metric tensor, and where there may be different sign conventions in these definitions. (The claim in many books is th... |
I'm currently studying physics and contemplating the nature of measurements. It seems to me that in practical scenarios, measurements are often represented using rational numbers. However, I'm curious whether this limitation is inherent to the nature of physical measurements or simply a consequence of our methods of me... |
I always wondered if the electrons superposition is so fragile, why doesn't it interact with the wall or plate with the double slits? Do the slits have to be a certain size?
|
We know that the speed of light in vaccuum can be expressed as $c=\frac{1}{\sqrt{\mu_0\epsilon_0}}$ and thus the speed of light in vaccuum is thus $$v=\frac{1}{\sqrt{\mu\epsilon}}=\frac{c}{\sqrt{\kappa_e\kappa_b}}$$
And by using Snell's law, we also know that $n=\frac{c}{v}$ which turn out to be $v=\frac{c}{n}$. Thus, ... |
I'm studying quantum mechanics and I'm trying to understand the concept of operators. They can be represented in general by the equation:
$$ \hat{A}ψ=ψ'. $$
Here the wavefunction is changed to $ψ'$ after the operator acted on the wavefunction. Since the wavefunction specifies the complete state of a particle, it seems ... |
In 1845 W. R. Hamilton demonstrated [1] by the use of the hodograph representation that the velocity of any Keplerian orbiter is the simple addition of two uniform velocities, one of rotation plus one of translation. Consequently, if we believe the laws of geometry, the derived acceleration from Hamilton's velocity mu... |
Consider the following action for massive scalar as follows
$$S = \int d^4x \left(-\frac{1}{2}\partial^{\mu}\phi\partial_{\mu}\phi-\frac{1}{2}m^2\phi^2\right) \tag{1}$$
with Minkowski signature $(-,+,+,+)$.
Now, I do a Fourier transform of the spatial coordinates to obtain
$$S = \int dt d^3k \left[\frac{1}{2}\dot{\phi}... |
chemical reactions occur spontaneously because they increase the entropy of the universe.
but why does gravitation occur spontaneously? if anything, gravitation decreases the entropy of the universe.
|
I'm trying to derive the dispersion relation of Alfvén waves (AW) by solving analytically the Vlasov-Maxwell equations for a magnetized hot plasma but I'm confused. A simple question, to treat AW using kinetic theory, is it enough to consider only the dynamics of hot electrons, or should ions be included?
|
Exceptional points occur generically in eigenvalue problems that depend on a parameter.
By variation of such parameter (usually into the complex plane) one can generically find
points where eigenvalues coincide. In Weiss' review of exceptional points
I found a demonstration of exceptional points is particularly confusi... |
The gravitational field of the star changes the paths of light rays in space-time from what they would have been had the star not been present. I understand that the light cones are bend slightly inward near the surface of the star.
But what confuses me is - this can be seen in the bending of light from distant star ob... |
I'm looking through Introduction to Supersymmetry by Muller-Kirsten and Wiedemann, along with any other resource I can find. I'm specifically trying to understand the concepts and notations for different representations of $SL(2, \mathbb{C})$, namely the dotted and undotted notation for Weyl spinors. I'm aware there ar... |
When working with the wave function of a particle ($\Psi(\vec{r}, t)$), my professor always makes the assumption that not only does said wave function fulfill $lim_{r\to\infty} \Psi = 0$ but in fact he assumes that this function goes to $0$ faster than its derivatives. This gives rise to two questions:
Under what circ... |
I am confused about the mode expansion in string theory. For instance, for a bosonic closed string, the field describing the string coordinates $X^\mu(\sigma,\tau)$ can be written as: (many thanks to @ACurousmind for writing it in an answer to another question)
$$X_\pm^\mu(\tau\pm\sigma) = \underbrace{\frac{x^\mu + c^\... |
As 1 coulomb electrons go through 1 volt of potential difference, they gain 1 joule of energy. So in s series circuit, do electrons move faster towards the end of the circuit where they went though a larger potential difference? If so, how is the current through a series circuit constant?
|
Why do we have dispersive angle in dispersion without deviation if there is no deviation from the original path?
|
I am learning about Killing Vectors in GR class, and I'm testing my knowledge of them as a start with the Minkowski metric.
I used the simple 2d Minkowski metric:
$$ds^2 = -dt^2 + dx^2$$
and got 3 killing vectors:
$$\xi_{(1)} = \left[ \begin{array}{} 1 \\ 0 \end{array} \right] \ , \xi_{(2)} = \left[ \begin{array}{} 0 \... |
The fact that if we place a jar full of gas in a moving train won't change its temperature , and that the temperature isn't really affected by the motion ( even though kinetic energy of gas molecules is increased ) is something I am confused with.
Temperature is related to motion of the molecules and it's kinetic energ... |
Well, my doubt's pretty elementary.
Firstly I wanted to confirm whether both the cases, as illustrated in the picture, are correct. I've darkened the part of each coil that faces us. Using the clock-rule both are right. Even on the net I've seen these two variations.
In the practical sense, can we say that one of thes... |
I know this question has been asked a myriad different times, but nowhere can I seem to find a definitive, final resolution to it.
Is a body in uniform circular motion in equilibrium?
|
SO, I think we define temperature as something related to the average translational kinetic energy of a molecule.
Is temperature dependent on the rotational and vibrational energy of the molecules.
If so, why??
|
I personally don't get a feel when I study Debye's model, maybe because I am not well-versed in continuum mechanics, even after studying both theories i.e. of Einstein and Debye, I still feel Einstein's theory(although a bit inaccurate) takes into account things more intuitively while Debye uses out of the box approach... |
Quick review (skip it):
In the formula from 8th grade, you figured out the length of the long side of the triangle
using this equation:
And in three dimensions:
This gives the length of the line between two opposite corners of a cube (it passes through the center).
Einstein said that time is a 4th dimension that you... |
Since a wavelength, $\lambda$, is the length of a entire cycle
How many $\lambda$ (complete cycles) can a composed wave have? I mean, for $n \lambda$, how big can $n$ be? And what does it mean, physically?
I'm not necessarily talking about an electromagnetic wave, it can be an 'electron wave' since particles can be in... |
Suppose you wanted to calculate the electric potential of a uniformly charged sphere with radius $R$ at a point $r$ inside the sphere. In Griffith's EM this is done by integrating $\frac{1}{4 \pi \epsilon_0} \int_V \frac{\rho}{(r-r')}d \tau$ over the region of the sphere where $\rho$ is the uniform charge density and $... |
The study of geometric aspect of Special Relativity is all about the geometry of Minkowski spacetime $(M,\langle,\rangle)$, a flat spacetime whose curvature vanishes at everywhere. The (Minkowski/Lorentz) inertial frame is defined based on Einstein's 2 postulates of Special Relativity, which in term of mathematic can b... |
When thinking of gauss laws, it states that the net outflow of the electric field through a closed surface is proportional to the enclosed charge.
This for the most surfaces is understandable, but not for the following:
The closed "volume" shall be the area within the green line, the green line shall be the enclsoing ... |
Fix $4$-dimensional Minkowskian spacetime $(\mathbb{R}^4, \eta)$. As in my previous posts, a reference frame is then simply a choice of basis vectors $\{e_{\mu}\}\subset \mathbb{R}^4$ such that $\{e_0\}$ is timelike, while $\{e_1, e_2, e_3\}$ are spacelike. Then every $4$-vector $v\in \mathbb{R}^4$ can be uniquely writ... |
Imagine a traveling, EM wave passing through some plasma. The waveform is given by the vector potential:
$A = (0, -\frac{cE_0}{\omega_0}\cos\eta, 0)$
where $\eta = \omega_0t-k_0x$ is the phase. From what I understand about ponderomotive forces, it arises from inhomogeneous fields and proportional to the field gradient ... |
I am reading a popular article and in one of the lines it says that :
"To illustrate this point, consider the familiar gas-and-piston
setup, in which the gas of N = 10^23 molecules begins in a state of thermal equilibrium inside
a container enclosed by adiabatic walls. If the piston is rapidly pushed into the gas and t... |
I understand that liquids are understood to be virtually incompressible, and so when a force over an area is applied to a liquid in a fixed volume container, the pressure change is even throughout the fluid—otherwise the internal pressure differences would cause movement and compression. However, what I don't understan... |
In classical mechanics it is known that a certain model is solvable exactly (integrable) if it posses a sufficient amount of "well behaved" conserved charges.
On the other hand in quantum mechanics we say that a model described by Hamiltonian $H$ is integrable if it can be solved using the algebraic Bethe ansatz (look ... |
Is there a way to prove that the second derivative of enthalpy with respect to entropy is always positive? If we are using the specific heat capacity at constant pressure do show how that is positive without using the above condition.
Thank you
|
I was looking at some stuff online about Spider Man in the famous scene from the comics where he accidentally breaks Gwen Stacy's neck, because as he shoots his web down to stop her falling from the Brooklyn Bridge, she stops too quickly and basically suffers whiplash.
If we assume the Brooklyn Bridge, and that she fel... |
In QED, on general grounds one can expect that there are mixed electron-photon Fock components contributing to the Lamb shift at 2 loops and beyond—i.e. states of the form $a^{\dagger} c^{\dagger} |0\rangle$ where $a^{\dagger}$ is the creation operator of the photon. These contributions presumably do not arise at 1 loo... |
Just as in electrostatics we can expand in a Taylor series the electrostatic potential as the infinite sum of the contributions of a monopole, a dipole, a quadrupole, etc., could we apply the same reasoning to the gravitational field? More importantly, even if we could, would this be of any interest? I'm assuming it wo... |
From an online lecture, I heard that $d$ orbitals cause metals to have a peak in their reflectivity curve at some wavelength. This is generally the case for most metals. However, the peak lies mostly in the ultraviolet region which makes them still appear silver-greyish. But for copper and gold this peak lies in the bl... |
I'm wondering if there's a region where the star density in the galaxy create the conditions in outer space where the galactic temperature is between 0 and 200°F. This may cause a ring shaped where liquid water exist in interstellar space. This is question comes from the fact the center of the galaxy is around 1,000,00... |
We know that gravitational fields are attractive. Their direction is inward. So if we go from a nearer point to a farther point the potential energy should increase, and the work done should be negative. But why is the work done positively, and the potential energy becoming more negative?? In the case of the electric f... |
How does one know that a uniform solid sphere rolling purely on a smooth surface does so about an axis passing through its CENTRE OF MASS and not any other axis? Is there a mathematical or intuitional proof to show that it rotates about CENTRE OF MASS ?
|
While I'm reading Hong Liu's notes, it says:
Now we have introduced two theories:
(a)$$\mathcal{L}=-\frac{1}{g^2}Tr[\frac{1}{2}(\partial \Phi )^2+\frac{1}{4}\Phi^4]$$
(b)$$\mathcal{L}=\frac{1}{g^2_{YM}}[-\frac{1}{4}Tr F_{\mu\nu}F^{\mu\nu}-i\bar{\Psi}(\not{D}-m)\Psi]$$
(a) is invariant under the global $U(N)$ transform... |
There has been extensive discussion in the literature and on this forum regarding the question of "whether a given system has a Lagrangian" (e.g. post1, post2, post3, and paper1, paper2).
The fundamental approach involves framing this question as the "inverse problem of the calculus of variations", wherein, given a se... |
Is there a theoretical limit for the wavelength of light that can pass through a solid? It appears that some borosilicate glasses can transmit UV light, but could any solid material act transparent to x-rays? or $\gamma$-rays?
|
What is potential energy of an electric dipole without any external field?
If its 0 then why? Wouldn't the charges get attracted thus do work so they must have some potential energy.
|
Water droplets gathered and formed into cloud which gets heavier then does the entropy of the system decreases? If so why 2nd law of thermodynamics allowed it?
|
(very amateur) physics student/enthusiast here. While reading Griffith’s textbook on electrodynamics I came across this line about separation of variables solutions for Laplace’s equations, assuming azimuthal symmetry. The $\ell(\ell+1)$ is the separation constant between the functions of $\theta$ and $r$ that come abo... |
This question concerns mainly a few statements from the following article https://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.063839.
It states: "Early studies of two-level quantum systems used two-level atoms or ions isolated in high vacuum. The upper-state population decays at a rate $1/T_1 = \Gamma_1$, while t... |
I have read Hawking's famous paper Particle creation by Black Holes (Ref. 1) and I have some doubts about the geometric optics approximation and its implications in the argument being made. The derivation has been repeated a number of times in the literature, with some variations; Ref. 2-3-4 are the ones resembling the... |
Let $\mathscr{H}$ be a complex Hilbert space, and $\mathcal{F}^{\pm}(\mathscr{H})$ be its associated bosonic (+) and fermionic (-) Fock spaces. Given $f \in \mathscr{H}$, we can define rigorously the creation and annihilation operators $a^{*}(f)$ and $a(f)$ (see, e.g. Bratteli & Robinson). These operators are densely d... |
I'm familiar with the equation for the sag of a cable:
$$x = \frac{wx(L-x)}{2T}$$
Where w = the weight per length, T = the tension and L = the length of the span between supports. I'm wondering if there is a similar equation for the sag of a cable that has two different weights. For instance, if two cables with differe... |
In my introduction to Thermodynamics, my lecturer has described the Saturated Vapor Pressure (SVP) as an "equilibrium condition" in which the number of particles condensing and evaporating are equal. However, this doesn't click for me, since under this condition, it seems that during boiling, which occurs at SVP, the a... |
I am reading Closed universes in two dimensional gravity by Usatyuk1, Wang and Zhao. The question is not too technical, it is about the solutions to the equations of motion that result from the variation of the JT action with respect to the dilaton field. The action given in this paper is
$$I[g,\Phi]=\frac{1}{2}\int d^... |
I'm trying to derive an expression for the total energy of a compressible viscous fluid. I know that the energy per unit volume of a compressible inviscid fluid is given by the sum of its kinetic energy and internal energy:
$$E = \frac{1}{2} \rho v^2 + \frac{P}{\gamma-1}$$
where $\rho$ is the fluid density, $v$ is the ... |
I'm working on analyzing the viscoelastic behavior of a elastomer using time-temperature superposition (TTS) techniques based on stress relaxation experiments. I've come across various conditions for checking the validity of TTS plots created through the application of frequency, such as the smoothness of Van-Gurp Palm... |
Last night I couldn't sleep for some time because of thinking this problem. The starting point of this problem was actually "If we were to jump perfectly vertically on earth, would we land on the same spot as we jumped?". However, I would like to ask a simplified version:
Suppose that there is a spherical rotating body... |
I have seen the following dispersion relation as a differential equation:
$$
\frac{ \partial \mathbf{k} }{ \partial t } + \left( \mathbf{V}_{g} \cdot \nabla \right) \mathbf{k} = 0 \tag{1}
$$
in the page number 135 of the textbook Holton, J. R., & Hakim, G. J. (2013). An introduction to dynamic meteorology (5th ed., Vol... |
I would like to ask you some questions I have about some interesting work I was reading (https://arxiv.org/abs/1205.4238 & https://academic.oup.com/mnras/article/527/4/11962/7457744) where the authors analysed the effects of dark energy in the shape and evolution of voids
Apparently, they established a relation between... |
Given a Hermitian operator $A$, Sakurai (in his book "Modern Quantum Mechanics") defines $\Delta A$ as follows:
$$\Delta A = A - \langle A\rangle$$
Where I believe $\langle A\rangle\vert\psi\rangle = \langle A\rangle_\psi\vert\psi\rangle$ is the definition of the operator.
He then goes on to define dispersion as
$$\lan... |
Let us have a system which consists of $N$ electrons with the spin (i. e. fermionic subspace has a dimension of $4^N$) and $K$ bosonic modes (let us consider $K=1$ for simplicity). Let us say, we obtained (numerically) the density matrix of the system. One can easily obtain the Wigner (or Husimi) quasi-distributions fo... |
I have been studying how light behaves in dielectric and conductive media, and now I was about to study it in anisotropic media. The introduction to the subject is: "From Maxwell's equations it is shown that the direction of propagation of the energy (rays) and the wave do not coincide in anisotropic mediums, and in a... |
One consequence of electromagnetic duality (see e.g., https://doi.org/10.1038/s41467-023-36420-4) is that if we have a system described by permittivity and permeability profile $(\varepsilon, \mu)(\mathbf{r})$ that has an eigensolution with associated electric and magnetic fields $(\mathbf{E}, \mathbf{H})(\mathbf{r})$,... |
I want to preface by saying I'm not a physicist, I'm a hardware designer at an R&D center trying to wrap my head around temperature measurements, so please forgive me if my questions are stupid or don't make sense.
The task we have is the following: we need to measure extremely fast temperature changes in human body ti... |
I'm trying to understand the Poincaré invariance of the vacuum state in Minkowski spacetime, how it implies the uniqueness of the vacuum state, and why there's no unique vacuum state in general spacetimes. For Poincaré invariance I found the following demonstration:
Under a Lorentz transformation $\Lambda$ a generic fi... |
Let there be a cylindrical pipe through which a fluid is flowing.
Between 2 points at the same height:
$$p_1+\frac12\rho(v_1)^2 = p_2+\frac12\rho(v_2)^2$$
Thus,
$$p_1 - p_2 = \frac12\rho[(v_2)^2 - (v_1)^2] = \frac12\rho[(v_2+v_1)(v_2-v_1)]$$
Now, if I am using the same equation from the frame of an observer moving oppo... |
I have a question I am sticking around and can't find a satisfying answer. Say I have an intrinsic semidonductor at zero Kelvin (no electrons in conduction band). I apply a DC voltage across it. Can the electron get excited from the valance band to the conduction band just by the DC voltage? There is band gab for i.e l... |
Regarding de Broglie formula
$$\lambda= h/mv$$
here m is relative mass or rest mass?
|
If a mass is attached to a spring(hanging from a wall) with spring constant $k$, causing an expansion $x$, then the potential energy stored by the spring is $\frac{1}{2}kx^2$. However, the potential energy stored by the spring is just the potential difference of the mass caused by its descent, isn't it? So why isn't th... |
Recently I came across the following problem:
Suppose $\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ is an ellipse with surface charge density $\sigma=\sigma_0\sin(\theta)\cos(\phi)$ where $\theta$ is the angle with the $z-$ axis and $\phi$ is with the $x-$ axis. Find the potential and multipole moments at a point... |
My teacher taught us the concept of inertial frames in a manner not usually presented in books. So I wish to confirm if his approach to the concept is valid.
Firstly he makes some points clear :
Acceleration has two causes, one being Force and other being the reference frame itself. He defines force outside atomic nuc... |
I'm trying to find a formula for (or some sort of direction towards approximating) the energy lost by a ultra relativistic positron when traveling through a cherenkov detector but I can't seem to find anything
|
In the pic, you see a sphere freely hanging from the ceiling by a string. According to the simple definition of a pendulum, it seems to be okay to call it a pendulum.
An instantaneous force, shown by the red arrow, is applied to the sphere.
The sphere swings and eventually passes points A,B and C. ( I am aware that the... |
I’m considering a fully connected Ising model with a Hamiltonian of the form:
$$ H = \sum_{i<j} J_{ij} S_i S_j $$
where $S_i = \pm 1$ represents the spin of each particle, and the sum is over all pairs of particles. The interaction matrix $J_{ij}$ is given by
$$J_{ij} = (i + j)(1 - \delta_{ij}) $$
which means that the ... |
Referring to Plasma Astrophysics, Part 1, author: Boris V Somov, 4.1.1,
We have the kinetic equation with Landau collisional integral,
$$
\frac{\partial f}{\partial t} + v_{\alpha} \frac{\partial f}{\partial r_{\alpha}} + \frac{q}{m} \left[ E_{\alpha} + \frac{1}{c} [ v \times \left( B + B_{0} \right) ]_{\alpha} \right]... |
Sigh.
So I've scoured the internet for many many hours, on many many occasions... aaand, yeah.
Is light:
just ONE photon which acts like a physical wave as those seen in classical mechanics (if so, where does one begin and the next stop)
a stream of MULTIPLE photons, each an individual, quantized, packet of energy (i... |
I was told in a lecture the following relationship, where $Y_{\ell}^m$ are the spherical harmonics and the eigenfunctions of the two following operators:
$$ L^2 Y_{\ell}^m = \ell(\ell + 1) \hbar^2 Y_{\ell}^m $$
$$L_z Y_{\ell}^m = m \hbar Y_{\ell}^m $$
We were also told that these two operators $L^2$ and $L_z$ show sph... |
I want to do a short practice to see how mass evolve space and how space curvature evolve mass distribution.
Most of the GR simulations were rather complicated but I think the black hole binary had become quite standard especially with LIGO's success, and I did saw some PPTs from the early 2000s about the topic.
Is the... |
It is said that the equations of motion of a theory are those whose solutions give the coordinates/trajectory of the system.
I was wondering ¿which is the correct equation of motion in the theory of general relativity?
The einstein field equations
$ R_{\mu\nu} - \frac{1}{2} Rg_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi... |
Assumptions:
Indestructible variable-pitch aircraft propeller
Arbitrary motor torque and velocity
Standard pressure and atmospheric conditions at sea level
Low, near-zero relative airspeed
This may be a question better suited for XKCD's "what if" but I'm wondering if there is a theoretical limit to the thrust that a ... |
I'm reading "Lectures of Quantum Field Theory" by Ashok Das, where I encountered for the first time the normal ordering of an Hamiltonian (Chapter 5.5). In the book, the Hamiltonian for the Klein-Gordon equation (in second quantization) is
$$
H = \int d^3k \frac{E_k}{2} \left(a\left(\vec{k}\right)a^\dagger\left(\vec{k}... |
I have already constructed the tangent space to a manifold, denoted $T_pM$, and I have a good basis for it $\{\hat e_{(\mu)}\}$. (I followed the method of equivalence classes of curves tangent at $p$.) I have also shown that the space of directional derivative operators at $p$ forms a vector space, which I denote $D_... |
The generally quoted formula foe resistance is
\begin{equation}
R = \rho \ell/A
\end{equation}
some special cases are easy to solve. For example the case where the current flowing along the z-axis and $\rho$ or $A$ only depend on $z$ can be easily solved and is commonly mentioned in introductory textbooks.
Usually, the... |
Can anyone advice how to perform some sort of Taylor series approximation to compute the inverse of the following expression for $t(v)$ i.e. to obtain $v(t)$. Thanks!
$$
t(v) = t_0 - \frac{5M}{256\eta v^8} \left[ 1 + \left( \frac{743}{252} + \frac{11}{3}\eta \right)v^2 \right]
$$
Where $t_0, M$ and $\eta$ are all const... |
Section 12 of Dirac's book "General Theory of Relativity" is called "The condition for flat space", and he is proving that a space is flat if and only if the curvature tensor $R_{\mu\nu\rho\sigma}$ vanishes; he has just defined the curvature tensor (in the previous section) as the difference between taking the covarian... |
My understanding of QFT is quite elementary. I'm reading through Kevin Costello's book on Renormalization and effective field theory, which is based on Wilsonian low energy theory.
The integral for an $n$-point function can be made to converge by imposing a (say length scale) cutoff (regulator), and this $n$-point func... |
I have read this:
Yes, single neutron stars can emit gravitational waves if they have sufficient asymmetries.
For some background, an object symmetric about its axis of rotation does not produce gravitational waves. A quote from Hartle's An Introduction to Einstein's General Relativity in the example "A Little Rotatio... |
Let $(M,g)$ be a (Lorentz) spacetime, i.e a connected smooth manifold $M$ with a metric tensor field $g$ and a time orientation called future direction which is defined by a smooth timelike vector field $T:\ M\longrightarrow TM$.
The chronological relation $\ll$ is defined as $\forall p,q\in M,\ p\ll q $ iff there exis... |
For over a year me and a friend have been working on a Kerr Black Hole renderer. We are close to the finish line and get renders like these;
These renders show aberration of light due to the cameras moment, encapsulated in the four velocity vector $\vec{u}$.To make a long story short, what we take the 3 component ve... |
Famous Astrophysicist Dr Neil DeGrasse Tyson, explains that whenever we observe a rainbow it appears exactly semi-circle to us. If another person is observing the same rainbow from a slightly different position, the rainbow still appears 'face-on' semi circle to him/her, not inclined. So he concludes that for every per... |
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