Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Is the Lagrangian density of electromagnetism half-blind? The Lagrangian density of electromagnetism is
$$
\mathcal{L}_{EM}=\frac{1}{4\mu_0}F^{ab}F_{ab}
$$
This represents one of two fundamental Lorentz invariants of electromagnetism. The second one is:
$$
\frac{1}{2}\epsilon_{abcd}F^{ab}F^{cd}
$$
Since $\mathcal{L}_{E... | You can add this to the Lagrangian if you want, but it will have no effect whatsoever. Try running the Lagrangian with the extra term through the Euler-Lagrange equation; it's a bit tedious, but you'll see it has no effect on the equations of motion. The reason why is that this term can be written as a total derivative... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Describing forces in rolling Consider a wheel on a frictionless horizontal surface. If we apply a horizontal force (parallel to the surface and above the level of the center of mass), what happens to the wheel? Does it roll or slide forward or rotate only or does any other phenomenon happen? Please guide me. Also draw ... |
The equation of motions are:
$$\sum_M F_y=m\frac{d}{dt}\,v-F=0$$
$$\sum_M \tau_x=I\,\frac{d}{dt}\,\omega-F\,d=0$$
Thus :
$$\dot{v}=\frac{F}{m}\tag 1$$
$$\dot{\omega}=-\frac{F\,d}{I}\tag 2$$
Roll condition:
$$v=\omega\,R$$
Slide condition :
$$v \lessgtr \omega\,R$$
$\Rightarrow$
$$\dot{v}\lessgtr \dot{\omega}\,R\tag 3$... | {
"language": "en",
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Why does the entanglement of quantum fields depend on their distance? When watching Seans Carrol's "A Brief History of Quantum Mechanics", he mentioned around the 50th minute (the video I linked to starts at that point) that
[about quantum fields in vacuum] ... and guess what! The closer they are to each other, the mo... | I don't think you should pay any attention to this. Entanglement refers to quantum states, not to quantum fields.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/560399",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Is the question asking for the primitive translation vector of simple cubic or reciprocal lattice?
Can anyone please give me a clue on what the question wants? Based on the question, I am clueless if it asks for primitive translation vector of simple cubic or reciprocal lattice?
Because the form of the given $\mathbf ... | From what you wrote I understand the question as follows.
You first need to determine what the Brillouin zone is for a simple cubic lattice. I recommend you try to do this yourself, and you should find that for a simple cubic lattice of lattice parameter $a$, then the Brillouin zone is also simple cubic with reciprocal... | {
"language": "en",
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Why doesn't the ergodic hypothesis hold for most systems? Is there a physical (intuitive) explanation for why most systems are not ergodic? As my book states, it is a natural assumption that a system is at least quasi-ergodic; it then proceeds to state that this hypothesis is, in fact, false, and that we need a differe... | I'm not sure how to quantify "most" systems, but off the top of my head, there are many processes that we encounter in our daily lives that break ergodicity within the timeframe under which we consider them.
*
*Symmetry breaking in general breaks ergodicity. Take, for example, a magnet. Ergodicity would imply that a ... | {
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What is the difference between a force and a net force? I read in Newton's first law, it states that an object will continue to have a constant velocity unless acted upon by a force whilst for other articles, it states "unless acted upon by a net force." Which one is correct? Are they both interchangeable? Is there any... | Force is a vector quantity. The first law talks of a single object and a force, without going in the details.
A net force means a vector addition of forces, two equal and opposite forces add up to zero net force . This is expressed more clearly here.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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"answer_id": 7
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Harmonic oscillator partition function via Matsubara formalism I am trying to understand the solution to a problem in Altland & Simons, chapter 4, p. 183. As a demonstration of the finite temperature path integral, the problem asks to calculate the partition function of a single harmonic oscillator. The coherent state ... | OP's partition function for the harmonic oscillator
$$\begin{align}Z^{-1}
~=~&\prod_{n\in \mathbb{Z}}\left[ -\frac{2\pi i n}{\beta} + \omega\right] \cr
~=~&\omega\prod_{n\in \mathbb{N}}\left[\left( \frac{2\pi n}{\beta} \right)^2 + \omega^2\right] \cr
~=~&\omega\left[ \prod_{n\in \mathbb{N}}\frac{2\pi }{\beta}\right]^... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Invariance of Lagrangian under rotations in a constant magnetic field
The Lagrangian for the motion of a particle with mass $m$ and charge $q$ in a constant magnetic field $B$ is given by $$\mathcal{L}(x,v)=\frac{m}{2}\left|v\right|^2-\frac{q}{2c}\left(v\cdot[x\times B]\right).$$
Show that rotations around the $B$-axi... | Write your Lagrangian in cylindrical coordinates. You will see that the Lagrangian doesn't depend on $\theta$, where $\theta$ is the angle that measures the rotatión about the z-axis.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is this synthetic molecular motor and what is the energy source? In the "Molecular dynamics" entry of 2018 version of Wikipedia (it have been removed for the current version), there is such a synthetic molecular motor:
You can also find this image by searching "MD_rotor_250K_1ns" for image on Bing.
(1) Any refere... | The wiki article still exists, with the simulation too.
Molecular dynamics simulation of a synthetic molecular rotor composed of three molecules in a nanopore (outer diameter 6.7 nm) at 250 K
In the wiki article:
The basic requirements for a synthetic motor are repetitive 360° motion, the consumption of energy and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/561609",
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Current and conductance from the Landauer formula The Landauer formula for a one dimensional quantum system (potential step scattering) can be written as
$$
I(V)=\frac{2e}{h}\int_{-\infty}^\infty dE T(E) (f_S(E) - f_D(E)),
$$
where $T(E)$ is the transmission probability and $f_i(E)$ is the Fermi function of source $S$ ... | In general, the relationship $I(V)$ for arbitrary voltages is nonlinear in the voltage difference $V$, and the assumption of low voltage allows one to write the linear approximation $I \approx GV$ by expanding at first order the difference of the Fermi-Dirac functions.
At zero temperature, the relationship $I(V)$ is st... | {
"language": "en",
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How does an up quark decay into products more massive than itself? According to https://en.wikipedia.org/wiki/Up_quark the up quark can decay into a down quark plus a positron plus an electron neutrino. The problem is that the mass of the by-products is greater than the original particle. This would violate conservat... | The most common example of this is beta plus decay. In this process one of the up quarks in a proton decays into a down quark and a $W^+$, and the $W^+$ then decays into a positron and electron neutrino. As a result of the decay the proton converts to a neutron.
As you say, the process violates conservation of energy a... | {
"language": "en",
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Do atoms absorb the same amount of light? I'm currently working on a project on my own where I'm interested in finding information about an object based on a spectrum. Namely, I want to use the spectrum that I input into my program to be able to analyze what atoms are present in the analyzed object. (I know this is pro... | Different materials will absorb different amounts. You cannot rely on two materials to absorb the same number of watts per mole, or anything like that.
The ultimate case study would be the white paint used to coat roofs and charcoal. They both obviously do have an absorption spectra, in different frequencies. Howeve... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562229",
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Individual particle states in Fock space I am currently learning QFT, and after watching the wonderful lectures by Leonard Susskind (https://theoreticalminimum.com/courses/advanced-quantum-mechanics/2013/fall), I am still struggling to see the connection between multi-particle (Fock) states and harmonic oscillators. Wh... | Fock space description and second quantization are not specific to harmonic oscillators - this is simply counting how many particles are in each state, whatever is the nature of the states. Creation/annihilation operators serve here to increase or reduce the number of particle in a state.
What often serves as a source ... | {
"language": "en",
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"source": "stackexchange",
"question_score": "4",
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In metals, the conductivity decreases with increasing temperature? I am currently studying Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edition, by Max Born and Emil Wolf. Chapter 1.1.2 Material equations says the following:
Metals are very good conductors, bu... | In metals, increase in temperature decreases average time between collision of charge carriers which increases the resistivity and therefore conductivity decrease.(also increase in temperature don't affect the no of charge carriers in metals).
| {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
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If mass is homogeneously distributed why would there be gravitational attraction between bodies? Assuming the mass of the universe was spread completely evenly throughout space why would gravitational attraction happen? All bodies in the universe would feel gravitational tug equally in all directions so why would they... | If one assumes the question in Newtonian dynamics (as distinct from gr) then the answer is that Newtonian gravity for an infinite uniform matter distribution in flat space is inconsistent. This can be shown from the equations of Newtonian gravity, in which the problem is that the integrals over all space do not converg... | {
"language": "en",
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Velocity of the touching point between 2 rotating circles I'm trying to solve the following problem that I'm having a hard time with:
We have circle ${\Sigma}_1$ with center $O_1$ and radius $a_1$. The center $O_1$ is also the center of the static orthonormal coordinate system $R_0 (O_1, x_0, y_0, z_0)$. ${\Sigma}_1$ r... | When ${\omega}_1=0$, ${\omega}_2=(\frac{a_1}{a_2}+1){\omega}_3$ (the factor $1$ appears because ${\Sigma}_2$ makes one extra turn after having rolled one turn around ${\Sigma}_1$ in the $R_0$ coordinate base).
So ${\omega}_3=\frac{{\omega}_2}{(\frac{a_1}{a_2}+1)}$. When ${\omega}_1\neq0$, we have to add this to ${\omeg... | {
"language": "en",
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Electric field energy density In vacuum, the energy density of the electric field is given by $\mathcal{E}=\epsilon_0\frac{E^2}{2}$ with $E$ the total electric field present. So, if you have a static $E_0$ and dynamic $e(t)$ field, the energy density becomes
$$\mathcal{E}=\epsilon_0\frac{\left[E_0+e(t)\right]^2}{2} = \... | The cross term represents interference. It is the term that makes it so that the energy density is reduced when the two fields are in opposite directions and so that the energy density is increased when the two fields are in the same direction.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562817",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Standing waves in optical cavities an optical cavity is "an arrangement of mirrors that forms a standing wave cavity resonator for light waves" (wikipedia).
The possible standing wave patterns for such structure are like these:
As you can see, the vertical black lines (which are the mirrors) are the nodes of the stand... | The reflected wave obtains a phase shift of $\pi$. If 100% of the light is reflected, the amplitude at the mirror vanishes, because the phase shift flips the sign, $e^{i \pi}=-1$.
Refering to the comments:
The following graph shows the situation, where the mirror reflects only 50% of the incident light:
The blue point... | {
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How is the frequency of a wave defined if it propagates on three different directions? Let's consider a wave which propagates on 2 or three directions, like for instance an electromagnetic wave inside a rectangular waveguide totally closed on two ideal conductor surfaces:
The walls of the guide force the wave to assum... |
So, three different wavelenghts. What does it mean? In physics I have
always studied that frequency corresponds to wavelength, if the
propagation medium is fixed. What is the definition of frequency in
this case?
The $\text{2D}$ or $\text{3D}$ solution to the wave equation doesn't have a single frequency, it has a sp... | {
"language": "en",
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Any boundary conditions missing from this problem? Recently I was solving some boundary value problems in Electrostatics. I stumbled upon a problem with an infinitely long cylinder (axis along the $z$-direction and radius $a$) with a plate inside it (centered at $z=0$). The plate is perpendicular to the axis of the cyl... | Correct me if I'm missing something @HeyDosa, but for the Laplace equation, $\nabla^2 \phi =0$, $\phi$ has the uniqueness property that if it is specified for the boundary of the region(volume) where you want to find it, then it is uniquely determined. Your region of interest is (in cylindrical coordinates), $S = [0,a]... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Meaning of the Planck Temperature I don't understand what makes the Planck Temperature the "absolute hot". To my understanding Temperature is just a measure of the kinetic energy of the particles, so is the Planck Temperature the temperature at which the particles are moving at a speed so close to the speed of light th... | The short answer is "We don't know" if there is an "absolute hot" or if there is, what it is.
This column by Peter Tyson : https://www.pbs.org/wgbh/nova/zero/hot.html
is what I point people to when they want to know why I can't explain it better.
But here goes my attempt: as the thermodynamic temperature rises from ab... | {
"language": "en",
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Sound Horizon in cosmology I was trying to write the sound horizon in terms of the scale factor, however I don't understand all the steps in the derivation.
I know that I should get:
$$r_{s}=\int_{0}^{a_{d}}\frac{da}{a^{2}H(a)}$$
What I tried
$$c_{s}dt=a(t) dr$$
Where $a(t)$ is the scale factor as the function of time,... | The equation for the sound horizon is simply the equation for the particle horizon, with the speed of light replaced by the speed of sound, there's nothing more to it. Nevertheless, you have to keep in mind that the speed of sound also changes with time, since the matter density dilutes with a growing scale factor, so ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/563567",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What do $\ell$ and $A$ precisely mean in the formula for electrical resistance? The formula for resistance is
$$R=\rho\frac{\ell}{A}$$
Generally in most of the textbooks it simply written that $\ell$ is the length of the conductor and $A$ is it’s cross-sectional area. But my question is which length and area do we need... |
Textbooks simply take an example of a solid cuboid whose opposite faces are supplied with potential difference. But what if I change the faces across which potential difference is applied(for example if I choose two adjacent faces of same cuboid)
It depends all on the direction of current flow.
Let's take a cuboid wi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/563802",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Which force is doing the work here? My text book (Fundamentals of Physics by Halliday, Resnick, and Walker) mentions the following about the work done in internal energy transfers:
An initially stationary ice-skater pushes away from a railing and then slides over the ice. Her kinetic energy increases because of an ext... | Let's make a simple example. A block with a compressed spring attached to it is on a frictionless horizontal surface against a stationary, immovable wall. The spring is released, and the block is then pushed away from the wall, thus gaining kinetic energy.
The relevant forces here are 1) the force between the spring an... | {
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The differential cross section and cross section As we know the total cross section can always be obtained from the differential cross section:
$$\sigma = \int_0 ^{2 \pi } \int_{0}^{\pi } \frac{d \sigma}{ d \Omega} d \Omega $$
I understand how the integration is done.
For example, sometimes I see the differential cros... | Your first formula makes no sense. You're integrating over the solid angle, which is ok but then you're integrating another time over no variable in the $[\pi,\pi]$ interval, which again makes no sense.
In general the differential cross section can be given in a number of different ways depending on how one treats the ... | {
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Why is internal resistance of battery considered outside the terminals although it is present between the terminals inside the battery In ideal battery the internal resistance is zero whereas in non-ideal battery there is some internal resistance now this internal resistance is due to the battery material (electrolyte)... | Because there is no potential difference inside of the cell due to the fact that the battery does not form a closed circuit. The circuit is internally separated, or 'terminated', at the posts. Voltage is defined as the difference between the electric potential at two points, or the work required per unit of charge to m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564196",
"timestamp": "2023-03-29T00:00:00",
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How does one (physically) interpret the relationship between the graviton and the vielbein? One can naturally think of the vielbein $e_\mu^a$ as a gauge field corresponding to local translation invariance. Moreover, the metric may be written
$$g_{\mu\nu}=e_\mu^a e_\nu^b \eta_{ab}.$$
I have always seen the graviton $h$ ... | So your first equation is more general than the linearised version of the second equation, so let's focus on the most general relation.
In general your vielbein $e^\mu_a(x)$, depend on the coordinates of your manifold. So vielbein represent a local frame transformation away from flat space. And this phenomenon, after u... | {
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Why does glass, in spite of being amorphous, often break along very smooth surfaces? When a crystalline material breaks, it often does so along planes in its crystalline structure. As such this is a result of its microscopic structure.
When glass breaks however, the shapes along which it breaks are typically very smoot... | As PM 2Ring has mentioned in a comment, if the crack is due to a mechanical impact (as opposed to gradually increasing stress beyond a critical value), then the shape of the crack is defined by the shape of the shock waves / vibration patterns, in addition to the structure of the material.
In crystalline materials with... | {
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Do Maxwell's equations contain any information on the time evolution of the current density $J$? The answers to Can the Lorentz force expression be derived from Maxwell's equations? make clear that Maxwell's equations contain only information on the evolution of the fields, and not their effects upon charges; the Loren... | Maxwell's equations place a constraint on the current, namely that it be conserved. To see this, take the divergence of Ampere's law for
$$0 = \mu_0 \nabla \cdot \mathbf{J} + \mu_0 \epsilon_0 \nabla \cdot \frac{\partial \mathbf{E}}{\partial t}$$
which is equivalent to
$$\nabla \cdot \mathbf{J} = - \epsilon_0 \frac{\par... | {
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Newtonian Limit of Schwarzschild metric The Schwarzschild metric describes the gravity of a spherically symmetric mass $M$ in spherical coordinates:
$$ds^2 =-\left(1-\frac{2GM}{c^2r}\right)c^2 \, dt^2+\left(1-\frac{2GM}{c^2r}\right)^{-1}dr^2+r^2 \,d\Omega^2 \tag{1}$$
Naively, I would expect the classical Newtonian limi... | Carroll is merely matching the Schwarzschild solution to the linearized weak field solution, treated as a consistent truncated Laurent series in $c^{-1}$, cf. this Phys.SE post. The main point is that the spatial components of the metric are subleading in an $c^{-1}$ expansion and may receive non-trivial contributions ... | {
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Are there any quantum effects which we can see in every day life? I am wondering if there are any natural phenomenon in every-day life that cannot be explained by classical physics but can only be explained by quantum mechanics. By classical physics, I mean Newtonian mechanics and Maxwell's electromagnetic theory.
I kn... | The whole "color temperature" notion and the finite speed of the radiative heat exchange.
A classical blackbody has an infinite power of electromagnetic radiation at any non-zero absolute temperature (see UV catastrophe). One needs a quantized light in order to understand the thermal radiation.
The whole "chemistry" th... | {
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Vacuum polarization or electron with structure? Is it possible to construct some charge density $ρ(r)$ to get the Uehling-Potential?
$${\displaystyle V_{\text{Uehling}}(r)\approx -Z\alpha \hbar c{\frac {1}{r}}\left(1+{\frac {\alpha }{8\pi ^{2}{\sqrt {2}}}}\left({\frac {\lambda }{r}}\right)^{3/2}e^{-4\pi {\frac {r}{\lam... | The entire theory (quantum electrodynamics) used by Uehling to derive this potential, is based on the assumption that the electron is a point particle. So the mainstream interpretation of the extra charge density “outside” the electron is that it is polarization of the vacuum by the point electron. Any other conclusion... | {
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Probability current density confusion As we all know, the probability current density in quantum mechanics is defined as: $$\textbf{J}=\dfrac{\hbar}{2mi}(\Psi^* \nabla \Psi-\Psi \nabla \Psi^*)$$ For simplicity let us work in one dimension and let us suppose a wave function $\Psi= A\ \text{cos}\ {kx}$. Applying the abov... | A solution of the free one-dimensional Schroedinger equation:
$$ i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial^2 \psi}{\partial x^2}\,\,\,\quad \text{(1)} $$
is:
$$\psi = A e^{i(kx -\omega t)} \quad\quad\quad \text{(2)} $$
where $\omega$ fulfills the condition $\hbar \omega = \frac... | {
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Why does higher frequency sound dampen faster in air? I know as a general fact that higher frequency sound dampens quicker in air so when music is heard from a distance only the bass part is audible.But I don't know what the physical reasoning behind this is. I couldn't find an answer anywhere on the internet (or they ... | Recall that wave equations will usually have a damping term and acoustic waves are no different. Wave damping is usually modeled with a velocity dependent term. The faster you try to distort the medium, the higher the damping. The viscosity of the fluid through which the sound wave is traveling plays a large role in... | {
"language": "en",
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What is meant by the transverse nature of gravitational waves? Gravitational waves, like the electromagnetic waves, are also transverse. By transversality of the EM waves, we mean that ${\vec E}\cdot\vec{k}={\vec B}\cdot\vec{k}=0$ i.e., the accompanying electric and the magnetic field (which are two $3$-vectors) vibrat... | The typical image of transverse gravitational waves is that as the wave travels thru spacetime, space itself stretches perpendicular to the direction of travel ($\hat{k}$). So space starts out "square", then get stretched vertically, goes back to square, gets stretched horizontally, goes back to square, etc.
You can G... | {
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I'm unable to wrap around the concept of antennas and more specifically microstrip antennas. How does a microstrip antenna which is bended work? So, I had come to the agreement that to understand how antennas work, it is best to assume light/electromagnetic waves act like photons/particles in the presence of recieving ... | The simplest way to think about a transmitting antenna is a surface (or linear shape) with an electric field oscillating at fixed frequency every on it. Then add in a position dependent phase offset (possibly zero) that remains fixed, too
| {
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Electron Capture or K-Capture and Heisenberg's Uncertainty principle I read about Electron Capture or K-Capture in radioactivity. There I found that the electron in the K shell is captured by the nucleus and as a result the atomic number of the element decreases by 1 unit.
But by Heisenberg's-Uncertainty-principle stat... | The electrons are not in fixed obits around the nucleus, the Bohr model is a semi-classical model of the real quantum mechanical solutions. The electrons are in orbitals, probability loci. Have a look , for simplicity, of the orbitals of the energy levels available to the electron of the hydrogen atom.
Note that there... | {
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Why we add the individuals quantities to find the total amount of a system's "quantity"? Is this by definition of "total"? Why to find e.g. the total energy of a system of particles (non-interacting) we add their individual kinetic energies? Is total kinetic energy defined to be that sum? It may seem obvious for scalar... | In short: yes it's by definition.
The longer explanation is:
In physics we postulate that certain quantities behave like vectors and other behave like scalars ecc. This allows us to develop mathematical models to understand and predict phenomena.
But why are we allowed to postulate such claims? It is simply on the base... | {
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Impulse operator on real wave function The impulse operator in quantum mechanics is given by
\begin{align}
\hat{p} = \frac{\hbar}{i}\nabla
\end{align}
As a Hermitian operator, the expected value of this operator $\langle{p}\rangle = \langle \psi|\hat{p}\psi\rangle$ should be real. However, for a real wave function $\ps... | If your wavefunction $\psi$ is real, as is the case when you are dealing with a solution to the time-independent Schrodinger equation, then indeed the expectation value is automatically $0$ since the expectation value must be real and the integral $-i/\hbar\int dx \psi^* (\nabla)\psi$ is necessarily complex unless it ... | {
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Measuring the Hubble constant in a curved universe In an article from the University of Chicago, July 17, 2020, it is stated that
"Judging cosmic distances from Earth is hard. So instead, scientists measure the angle in the sky between two distant objects, with Earth and the two objects forming a cosmic triangle. If... | What appears to be a sufficient answer to the question can be found in this SE answer by @JohnRennie, combined with a few other articles. I had confused "flat space" with "flat spacetime". As John Rennie said in that answer, spacetime is not flat in an expanding universe, but space can be flat. So, indeed, it is nece... | {
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What is 'covariant variation'? What is 'covariant variation'? As opposed to the usual variation with respect to a gauge parameter?
| Briefly, Ref. 1 considers generalizations of Yang-Mills-type gauge theories based on a Leibniz algebra structure. Concretely, Ref. 1 defines a covariant variation as
$$ \Delta {\cal A}~:=~e^{-{\cal A}}\delta e^{\cal A}. \tag{3.33}$$
In physics jargon, ${\cal A}$ is a gauge field; $\Lambda=\delta {\cal A}$ plays the rol... | {
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Why does critical temperature exist? This question has been previously asked over here and the comment and answer there has already answered my original question (the one that I had in my mind), but the following question arises:
*
*Why isn't it possible for the for a fluid to form the persistent structure$^{\dagger}... | For "persistent structure" read "bound structure by quantum mechanical potential sollutions".
At the atomic and molecular level structures arise because the number of atoms can settle at a lower energy level, than when free. This means there is a binding energy that has to be payed for the atoms to be freed from the s... | {
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Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges on them repel each other with a force $F$ Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges on them repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having s... | Call the new spherical conductor D.
As Michael Seifert implies, the charge on D and the remaining charge on C will depend on where C and D touch.
When they touch, if the distance from B to D equals the distance from B to C, then half of C's charge will flow to D.
If D is between B and C when they touch, then D will hav... | {
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Will cutting sand paper with scissors make the scissors sharper or duller? This is a little question that I have been wondering when I need to cut sand paper with scissors.
Sand paper can be used to sharpen knives etc. when applied parallel with the blade surface. Also it can be used to dull sharp edges when applied no... | Duller
Scissors are sharpened by honing the narrow "chisel" edges, not the broad flat edges where the two blades sandwich together. Here's an image of someone sharpening tiny scissors with an even tinier file:
So, cutting sandpaper will abrade the point between the chisel edge and flat edge.
*You can use the sandpaper... | {
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Does the absorbtion of photons from the Sun decrease with distance for a point charge? Let's suppose we have a point charge with no dimensions (zero volume and surface area) absorbing photons from Sun. Does it change the amount of photons and energy absorbed when we move the point charge close to, or far from the Sun? ... | Quantum mechanics: although the energy of the individual photons does not change with distance, the density of photons (the number of photons per volume) does. This is because every spherical shell around the sun must have the same number of photons, but ones with bigger radius have a greater surface, so the photons ar... | {
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Is energy required in generating magnetic field in simple resistance circuit? Consider a simple resistance circuit with a cell and a resistor. It is stated that energy stored in cell appears as heat in resistance as current flows in ideal circuit (neglecting EM radiation) as whole.
POWER/RATE OF HEAT GENERATION = POWER... | *
*Yes, energy is needed to create the magnetic field. Once the field has been created, no further energy is needed. The electric current in the circuit preserves the magnetic field. 2. The chemical energy in the cell is converted to electrical energy that moves the charges in the current, and as the charges start ... | {
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What is the point of a voltage divider if you can't drive anything with it? The voltage divider formula is only valid if there is no current drawn across the output voltage, so how could they be used practically? Since using the voltage for anything would require drawing current, that would invalidate the formula. So w... | You don't have to draw significant current to "use" a voltage. For example, if you want to measure the output voltage, which is a perfectly useful thing to do, then you can just attach a voltmeter. And ideally, voltmeters don't draw current at all.
If you wanted to drive something at a lower voltage than the input, you... | {
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Is magnetic field due to current carrying circular coil, zero everywhere except at its axis?
Consider a current ($I$) carrying circular coil of radius$ R$ of $N$ turns.Consider a rectangular loop $ABCD$,where length $AB=CD=\infty$
Performing the integral for axial points,
$$\int_ {-\infty}^{\infty}\vec{B}\cdot \vec{dx... | They say more than the sum of those three line integrals being $0$. They correctly say that $\mathbf B$ is $0$. This is because, as stated on your diagram, those ends of the rectangle are at an infinite distance away from the circular loop, and $\mathbf B$ must go to $0$ infinitely far away from the circular loop.
| {
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Photon description of quantum-optical interference experiments I am currently studying the textbook The Quantum Theory of Light, third edition, by R. Loudon. In the introduction, the author says the following:
In the customary photon description of quantum-optical interference experiments, it is never the photons them... | There is no difference between the two interpretations that you list. Photons do not interfere with themselves or other photons. The wave function should not be identified with photons. It gives the probability of detecting photons. It can be seen as the average of a poisson distribution describing the number of photon... | {
"language": "en",
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Conservation Laws and What Happens if they go Wrong? I read this excellent article on the Conservation Laws and also I was taught in Schools that Conservation Laws cannot be proven and only verified. I was wondering what would actually happen if a Conservation Law turned out to be false?
I know it would question our me... | Noether's theorem is the thing to pay attention to here. This theorem basically says that if there is a symmetry in the underlying physics, there is also a conserved quantity. Traditionally the best-known symmetries are:
*
*Time invariance, i.e. the laws of physics do not change with time. If this is the case, then e... | {
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Work done on object being carried upwards If you carry a book in your hands, and you walk up stairs with a change in height of $h$, the net work on both you and the book would be $-M_{\mathrm{total}}gh$ since $W = - \Delta U$. This would be due to gravity.
However, when considering the book alone, the work done by the ... |
This means that the net work done on the book through the process of
walking up the stairs is 0.
That is correct, because gravity does negative work of $-m_{book}gh$ equal to the positive work done by you of $+m_{book}gh$ for a net work of zero. All that means, per the work energy theorem, is the change in kinetic en... | {
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Effect of Earth's Rotation on Time According to Wikipedia:
Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's rotation. Atomic clocks show that a modern-day is longer by about 1.7 milliseconds than a century ago, slowly increasi... | For the speed at which the earth rotates, relativistic time dilation would be pretty much unnoticeable. For the satellites in the GPS system, it does have to be taken into account in order to predict accurate positions on the earth.
| {
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Are resistors, inductors, capacitors the only possible passive components in this universe? I wonder whether or not there is a possibility to find another passive component (with value either $X$ or $Y$) that will change the well known RLC circuit equation below
$$
L\; \frac{\mathrm{d}^2 \; i}{\mathrm{d}\; t^2} + R\; ... | Look at it this way: what possible forces can be applied to an electric current in a constrained environment, e.g. a wire? Or, more specifically, to the value of the voltage at any location along the wire. About all you can do is apply a lead, a lag, or an attenuation (and all of those as a function of $\omega$ ) ... | {
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Do adjacent sarcomeres oppose each other during contraction? A sarcomere is the contractible portion of the muscle cell. And here is a figure of three sarcomeres in series before and after contraction:
I was taught that the thick fiber, myosin, pulls on the thin fiber, actin. I am confused as to how contraction can ha... | Yes, there is a tug of war, which results in tension being developed in the muscle fibre. As it has the ability to contract, increased tension will cause it to do so. Once the muscle contracts, the muscle has no mechanism to provide an outward force, thus a compressed muscle has to rely on the compression of another mu... | {
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Different variations of covariant derivative product rule This is a follow-up question to the accepted answer to this question: Leibniz Rule for Covariant derivatives
The standard Leibniz rule for covariant derivatives is $$\nabla(T\otimes S)=\nabla T\otimes S+T\otimes\nabla S$$
so for $T\otimes\omega\otimes Y$ this wo... | Use that tensor product is associative, so $\nabla(T\otimes \omega \otimes Y)=\nabla[(T \otimes \omega ) \otimes Y]$
Thus you have the Leibniz rule $$\nabla(X\otimes Y)=\nabla(X)\otimes Y+ X\otimes \nabla(Y)$$
that gives you
$$ [\nabla(T\otimes\omega)]\otimes Y + T\otimes \omega \otimes \nabla Y$$
Using again in first ... | {
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Why do complex number seem to be so helpful in real-world problems? Complex numbers are often used in Physics especially in Electrical Circuits to analyze them as they are easy to move around like phasors. They make the processes easy but it seems kind of amusing to use something which has no other real world analogous... | How do you describe a rotation? One approach is to do
$$x' = x\cos\theta - y\sin\theta$$
$$y' = x\sin\theta + y\cos\theta$$
That's unwieldy. Another approach is to declare: I use a complex coordinate $r$ where $x$ equals the real part, and $y$ equals the imaginary part. Now we can write the rotation much more simply:
$... | {
"language": "en",
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What do I need to build special relativity? If I postulate the principle of relativity and the constancy of the speed of light for every inertial observer can I then prove all SR?
Or do I need some other postulate?
For example: do I need to also postulate the structure of the Lorentz transformations or the Lorentz tran... | You can not prove all of SR. You can derive the Lorentz transformation using those two postulates plus linearity. The Lorentz transformation then gives you time dilation, length contraction and relativity of simultaneity. But this is not all of SR. You can not get the relativistic formula for momentum and the well-know... | {
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What makes the electron, as an excitation in a field, discrete? In standard quantum mechanics, the wave function have discrete energy-values due to a potential. However, my very limited understanding of QFT is that electrons are excitation in the Dirac field, and the number of electrons is discrete even in free space. ... | There are two facts to be distinguished. Electrons are what we loosely call particles, so they only ever occur in discrete numbers. Millikan demonstrated the discreteness of charge. Secondly, localised states in general have discrete energies. Examples of these are atomic and molecular states. Free electrons have conti... | {
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Maxwell Coexistence from Entropy Considerations As explained by Maxwell, (1875), a realistic thermodynamical system will, at low temperature, have pressure vs. volume curve that is non-monotonic. In practice, though, the observable states of the system will lie along a straight line of constant pressure, where part of ... | The vapor and liquid phase coexist along the straight line. Call the left and right intersection with the original curve $v_A$ and $v_B$ and the vapor pressure $p_v$.
Coexistence implies the equality of chemical potentials between the phases. Because if the phases were at different chemical potentials, particles would ... | {
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Work done by normal force on a block placed on movable inclined wedge A block placed on movable smooth inclined wedge placed on a smooth surface. Both are released and allowed to move.
I was told that
If the center of mass of wedge and block system is fixed (in the horizontal direction I assume, otherwise there won't ... | The normal force indeed does work on the block.However, it does zero work on the block + wedge system:
Suppose the block gets displaced by $\vec{dr}$ relative to the wedge, and the wedge gets displaced by $\vec{dx}$. Then the block, as seen from the ground , is displaced by
$\vec{dr}$+$\vec{dx}$. The work done on the b... | {
"language": "en",
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How to determine the result of 2D elastic collision
As shown by the image, a disk of radius $R_1$ mass $M_1$ and initial velocity $V_0$ collides with another still disk of radius $R_2$ mass $M_2$. Both disks has no rotation initially. The direction of $V_0$ is indicated by $\theta$. For three situations there are un... | Friction acts only so long as there is relative slipping between the surfaces of the sphere. For smaller angles, $\mu$ is sufficient for the relative slipping to cease by the end of the collision. For larger angles $f=\mu N$ may not be sufficient to reconcile the tangential velocities of the surfaces by the end of the ... | {
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Why can't photons cancel each other? The textbook argument against photons canceling each other draws upon the conservation of energy. Does this mean that energy conservation is a "stronger" principle than superposition? Waves in other media than the EM field, e.g., sound or water, do cancel out---presumably by passing... | It is a curious thing, because in the early days of quantum mechanics it was thought that wave interference effects (which is what I think you mean by cancelling) were only possible for a particle and itself (Dirac said exactly that, although I would have to put in a fair amount of work to find a reference).
This is in... | {
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Ward identity of QED - whether the fields are all $c$-number fields I am following Sidney Coleman's lectures of Quantum Field Theory.
At the end of ch.32, he derived the Ward identity for the 1PI generating functional $\Gamma[\psi,\bar{\psi},A_{\mu}]$ for QED:
\begin{equation}
ie \bar{\psi} \frac{\delta \Gamma}{\delta ... | No, $\psi$ and $\bar{\psi}$ are $a$-number fields, while $A_{\mu}$ is a $c$-number field. The above Ward-Takahashi identity (WTI) is a supernumber-valued identity.
The WTI is often used by differentiating it a number of times wrt. the fields, and then set the remaining fields to zero.
See also this related Phys.SE post... | {
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Why are the positive charged particles moving the the right direction?
The following is the description for this figure provided by my textbook:
The paths of different types of radiation in a magnetic field. Using the right-hand slap rule, we see that positively charged particles are forced to the right. [...]
Why a... | The hidden assumption is that the particles enter from the bottom of the diagram and are moving (initially) towards the top. That gives the direction of $\vec v$. You've correctly read the direction of $\vec B$, so you're ready to find $\vec v\times\vec B$.
| {
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Feynman rules for interactions with derivatives: How exactly do the momentum factors appear? I know how to treat Feynman interactions without derivatives by Wick contraction. But now, take for example $$\mathcal{L}_{int}=\lambda \phi (\partial_{\mu}\phi)(\partial^{\mu}\phi).$$
Now many books write that in momentum spac... | For your case, starting with this interaction term, let us substitute the expansion of $\phi$ in Fourier modes:
$$
\phi = \sum_k \phi_k e^{i kx}
$$
The action of derivative produces a factor of $ik$. Then, in the action you sum(integrate) over all $x$ :
$$
\sum_x \sum_{k_1, k_2, k_3} (ik_{2 \mu}) (ik^{3 \mu}) \lambda \... | {
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What is the difference between the specific heat capacities of water under isobaric and isochoric conditions Can the difference of specific heat capacity of water under isochoric and isobaric conditions be explained in terms of the internal energy of the system? Most of the videos I have watched base their explanation ... | The specific heats diverge mainly after 100 C when at 1 atmosphere water changes phase and begins acting like a gas approaching ideal gas behavior.
Based on the first law the internal energy explanation for the specific heat at constant pressure (isobaric) $C_P$ being greater than the specific heat at constant volume ... | {
"language": "en",
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Would a moving elementary particle follow the Heisenberg's Uncertainty Principle with respect to itself? An observer at rest or in motion different from the particle cannot determine its momentum and position to great accuracy at the same time. But what if the observer is on the particle itself or moving with the same ... | As elementary particles are point particles, there cannot be an observer "on them" . The only observation can happen with interactions with other particles, and yes, the envelope of the Heisenberg uncertainty has to be obeyed, whether the system is at rest ( studied in its center of mass) or moving.
In mathematical cal... | {
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How is melting time affected by flow rate and temperature of surroundings? Suppose you have a solid sphere of m, where m is an element with freezing point of 0 degrees Celsius.
In one scenario, you place your sphere in a (“static”) 25 degree Celsius environment and measure time, t, until melting. The sphere is fixed an... | In the static case, you need to give a better definition of the problem. How big is the container that the ice sphere resides in? Are the walls of the container insulated, or can they exchange heat with the environment? If heat exchange occurs with the environment, what are the container walls made of, what is their... | {
"language": "en",
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Gibbs free energy, Helmholtz free energy and their contribution to expansion and non-expansion work In the book "An Introduction to Thermal Physics" by Daniel Schroder, I got the following expressions Helmholtz free energy : F = U - TS
and Gibbs Free energy : G = H - TS = U + PV - TS
The author explained the intuitio... |
But in the definition of Gibbs free energy there is a pressure-volume term which Helmholtz free energy does not have. Therefore, my intuition is that it should be the other way around.
The Gibbs free energy definition $G=U+PV-TS$ doesn't add an expansion term, it removes it. The internal energy $U$ is $U=TS-PV+\Sigma... | {
"language": "en",
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Why is curved space able to change an object's velocity (vector)? I don't really understand what is meant by curved space. Why does mass warp space? Why does curved space alter the velocity of a massive object? Normally to change an object's direction you have to apply some force to overcome inertia. So how does curved... | As far as I know, it is not known why mass warps space (one of the biggest problems in physics, uniting general relativity with quantum mechanics). It is just a model, and all observations so far support this model. As for the second question, as far as I understand spacetime does not change an object's velocity, it ju... | {
"language": "en",
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Can a single-slit experiment demonstrate the particle nature of light? Young's two-slit experiment is generally credited for demonstrating the wave nature of light. But what about a similar experiment with just one slit? My understanding is that this will create an interference pattern. Shouldn't that be enough to demo... | I believe you have that backward. The two-slit experiment demonstrates the wave nature of light.
Light must be quantum because it interacts with single atoms and either has an effect or does not have an effect. It has to do that in a single place. It is established that this is because of the quantum nature of light an... | {
"language": "en",
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Why is QED renormalizable? My understanding of renormalizability is that a theory is renormalizable if it the divergences in its amplitudes can be cancelled out by finitely many terms. I see that by adding counterterm (in the MS-bar scheme)
$$L_{ct}=-\frac{g^2}{12\pi^2}\left(\frac{2}{\epsilon}-\gamma+\ln4\pi\right),$$
... | We get infinite number of counterterms, but that will all be the same form (or in a closed set), it is just that the coefficients in front of the term will be expanded in a power series of the coupling constant. What it means by "infinite number of counterterm -> non-renormalizable", at least from my understanding, is ... | {
"language": "en",
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How big (in meters) could the difference be between ECI and ECEF coordinates at midnight UTC? Is the only difference due to leap seconds, etc. or other differences between UTC and updated forms of universal time, such as UT1? In other words, are all earth-centered inertial (ECI) coordinate frames constructed on purpos... |
In other words, are all earth-centered inertial (ECI) coordinate frames constructed on purpose so they match at approximately midnight each day?
No, they are not.
There are multiple Earth centered inertial frames. All have one thing in common: An Earth-Centered, Earth-Fixed rotates more or less about the ECEF frame's... | {
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Could gravity be much stronger (or weaker) at the atomic scale? If gravity is mediated by particles and you are at a scale where those particles are relatively much larger does that perhaps imply that gravity can't work exactly the same way at very small scales as it does at much larger (like planetary, galactic) scale... | Regarding the broad question which you bring up, yes, it is possible for gravity to have a different strength from expected at extremely small scales. But it doesn't have to do with the size of particles. It involves what's called the ADD model, or the theory of "large extra dimensions" ("large" being a bit of a misnom... | {
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Why does the spring constant not depend on the mass of the object attached? It is said that:
$$ F = -m\omega^2 x = -kx, $$
so $k=m\omega^2$. Since $k$ is the spring constant it doesn't depend on the mass of the object attached to it, but here $m$ signifies the mass of the object. Then how is $k$ independent of the mass... |
Then how $k$ is independent of mass attached?
The clue is in :
$$F=kx$$
It states simply that the spring, when extended by $x$, will provide a restoring force $F=kx$.
The force needed to affect the extension (displacement) $x$ can be provided by almost anything. A mass (its weight) can do it but is just one way, one ... | {
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Why do electrons flow in the opposite direction to current? I'm 15 and just had a question about physics and electric fields.
I've read that electrons flow in the opposite direction to current. Isn't current the flow of negative charge and therefore the flow of electrons?
Or are they referring to conventional current?... | We can safely say, that you are talking about electric current. It is defined as the "electric charge, which flows trough some point or region in given amount of time" (by Wikipedia):
$$
\textbf{I}=\frac{de}{dt}\hat{a}
$$
Bear in mind, that differential $d$ mrans small change, eg. small amount of charge divided by time... | {
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When can the velocity of a car exceed the limit imposed by the static friction? My physics mentor was teaching about circular motion. To explain it, he used an example of a car moving in a circle with constant speed $v$ having mass $m$. Then he talked about a situation when the car would go out of the track. He calcula... | "Maximum speed" here isn't related to the absolute top speed of the car. Rather, it's the maximum speed at which the car can maintain its circular course. The maximum possible force that friction can exert is governed by the normal force and coefficient of friction - if you try to push off the pavement with greater for... | {
"language": "en",
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What will happen if we try to take a voltage reading by keeping it in current mode in a multimeter? There are different modes present in a multimeter. one is
the current mode and voltage mode for their respective measurements. what
will happen if one try to take a voltage reading by keeping it in current mode?
| Whenever a multimeter measures a current it is actually measuring the voltage drop across the so called shunt resistor. A shunt resistor is a resistor with a very low resistence so that whenever it's placed in series with the circuit, and so when you try to measure the current of said circuit, it does not effect, to an... | {
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Effects of the discrete quotient of chiral symmetry group For a theory of $N_f$ massless Dirac fermions coupled to a Yang-Mills field, the usual story is that we have a $U_L(N_f)\times U_R(N_f)$ symmetry, which is then expressed as
$SU_L(N_f)\times SU_R(N_f) \times U_V(1) \times U_A(1)$.
However, since $U(n)\cong \left... | Keeping track of discrete chiral symmetries is important for discrete anomaly matching, see here. In QCD discrete anomaly matching can be used to exclude the option that spontaneous chiral symmetry does not lead to a chiral condensate $\langle\bar{q}q\rangle$, but is signaled by the vev of a higher dimension operator, ... | {
"language": "en",
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Interpreting the Negative Sign in Simple Harmonic Motion What I Know:
$$ \vec F = -k \vec x $$
where the negative sign indicates the Force acts in the opposite direction to the displacement.
If we were to take the integral so...
$$\int_{x_i}^{x_f} Fdx = -\Delta U$$
What would the negative sign in this instance represen... | See first of all Potential Energy arises when work is done against a conservative force.This means that:
Change in Potential Energy = - Work done against conservative force
$$ΔU = - W$$
Thats where the negative sign comes from
What would the negative sign in this instance represent?
This means that work done against... | {
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Energy Conservation in Rolling without Slipping Scenario
A solid ball with mass $M$ and radius $R$ is placed on a table and given a sharp impulse so that its center of mass initially moves with velocity $v_o$, with no rolling. The ball has a friction coefficient (both kinetic and static) $μ$ with the table. How far do... | Hi there mister Radek Martinez! Good to see you've joined the game! And with a good question too!
Here's what I think:
The energy loss due to kinetic friction makes the ball move slower, thus the change in linear kinetic energy is equal to the loss in friction-induced loss of energy. Energy is left for linear and rotat... | {
"language": "en",
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Does Energy & Momentum also Dilate & Contract respectively? Does energy and momentum also dilate and contract as time and length do respectively, since energy and time and momentum and length are complementary quantities both in relativity & QM?
| In a way, yes, one can roughly say so. This can be seen from the way their formula "change". The non-relativistic momentum (dropping vector signs)
$$P=mv$$
turns into
$$P=\gamma mv$$
and the non-relativistic (kinetic) energy
$$E=1/2mv^2$$
turns into
$$E=(\gamma-1)mc^2.$$
These changes in the formulas for momentum and e... | {
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Why do fluids not accelerate? A fluid flowing in a horizontal pipe must be flowing at a constant velocity because of the conservation of mass.
However, considering how there would be a pressure and hence force acting behind the fluid, for it to have a constant velocity, there must be an equal force slowing it down (dep... | Yes you have basically constant velocity once you get into the pipe.
The pressure difference between bottom of tank (pipe inlet) and the atmosphere (pipe outlet) will drive flow fast enough that viscous-drag force equals pressure-difference force:
$$A~(P_i-P_f) = F_{\mu}$$
But $F_{\mu}$ is a function of flow rate. The ... | {
"language": "en",
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How does a Foucault pendulum work? How exactly does a Foucault pendulum work? The usual explanation says that the plane of the oscillation of the pendulum is fixed while the earth rotates underneath. On Wikipedia, there is a demonstration of this effect, showing what it's like on the north pole. But surely that can't b... | Yes, the point is Coriolis force. If you want to study the motion of the Foucault's pendulum you have to consider the fact that it oscilates in a non inertial frame, which is Earth's surface, so apparent forces have to be taken into account.
Wouldn't the Coriolis force just be too miniscule?
If you want to restrict y... | {
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Why should the particles meet at a common point? I saw a question in my physics book asking for the time when all the three particles (each at the corner of an equilateral triangle and each having constant velocity v along the sides of the triangle) meet at a common point.
I can't find the reason why these particles s... | I think it's possible that you either misunderstood the problem or that it was badly phrased. I think you're right that if the particles were simply moving in straight lines with a constant velocity, they would never meet.
I believe, however, that the problem was probably intended as a Pursuit Curve-type problem: the p... | {
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Confusing conceptual question An observer $A$ standing on the circumference of a disc rotating with an uniform angular velocity $\omega = 1$ units , and radius $r=1$ units observes a person $B$ at rest w.r.t ground.Given the $\angle \theta = 30^\circ $ as shown in the figure
Find out the,
*
*relative velocity of $A$ ... | Let's fix a Cartesian co-ordinate system that is at rest w.r.t the ground and has origin at the centre of the circle. Let's call the co-ordinates of $A$ and $B$ in this co-ordinate system $\vec r_A(t)$ and $\vec r_B(t)$. At time $t=0$ we have
$\vec r_A(0) = (0, -1) \\ \vec r_B(0) = (\sqrt 3, -1)$
At a general time $t$,... | {
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Can rockets fly without burning any fuel with the help of gases under extreme pressure only? Why is it necessary to burn the hydrogen fuel coming out of the engine for the lift of rockets?
If it is done to create a greater reaction force on the rocket then why can't we get the same lift with just adjusting the speed of... | Releasing compressed gas will produce some thrust. But when the gasses are combusted they expand much more. This produces a much higher exhaust velocity which gives a much greater thrust.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Acceleration transformation in special relativity I am having a hard time understanding the transformation of acceleration when it is not parallel to the instantaneous displacement of the particle, in particular the its dimension.
Suppose a particle is in projectile motion. Acceleration is downward because of gravity b... | If by projectile motion, you mean falling only under action of gravity, the acceleration in the frame of the object is zero. It is in free fall, and any test particle in that frame has no acceleration.
But we can suppose a rocket making a curve by using its engines, so that the crew will feel an acceleration.
The compo... | {
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Why are voltage and volt both are denoted by $V$? Why are voltage and volt both are denoted by $V$? Won't it cause confusion?
| For this same reason some texts denote Voltage by $v$ and Volt by $V$.
Historically Volt was named after Alessandro Giuseppe Antonio Anastasio Volta to honour his remarkable work.
Further I think the denoted of Voltage by $V$ was started by Sir Pierre-Simon Laplace. Since then $V$ has been used for denoting Voltage.
I... | {
"language": "en",
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Are there examples of dark matter at intra-galactic scales? In articles I've read, evidence of dark matter (rotation of galaxies / gravitational lensing / galaxy collisions etc) is presented at galactic scales.
Are there examples of dark matter at smaller scales than this?
One possibility I could think of, would be a m... | One could argue that the rotation curves of galaxies are intra-galactic evidence, since it requires the somewhat continuous presence of dark matter across the galaxy.
If you want smaller scales, the smallest systems where dark matter is firmly established are dwarf galaxies; these are dark matter dominated.
Finally, th... | {
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Kleppner and Kolenkow, 2nd edition, problem 4.23 - Suspended garbage can I am working through Kleppner and Kolenkow's An Introduction to Mechanics on my own and have a question about the solution of the mentioned problem.
Problem Statement: An inverted garbage can of weight $W$ is suspended in air by water from a geyse... | The Two equations you started with in the question, seems incorrect to me! Have a Look at my approach.
| {
"language": "en",
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Proof of a vector calculus identity In https://arxiv.org/abs/hep-ph/0010057 the following vector calculus equality is claimed without proof although in note [4] the cryptic comment is made that "The relation is essentially the momentum space identity $(\mathbf{k}\times\mathbf{A})^2=\mathbf{k}^2\mathbf{A}^2-(\mathbf{k}\... | As @flevinBombastus has suggested here is a sketch of the proof of the equality in Equation $(6)$ based on [1].
Start with $$\nabla^2\frac{1}{|\mathbf x - \mathbf x'|}=-\delta(\mathbf x - \mathbf x')$$ and
$$\nabla \times (\nabla \times \mathbf v)=\nabla (\nabla\cdot \mathbf v) - \nabla^2 \mathbf v$$
Then $$\mathbf{A}(... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/577619",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does gravity act at the centre? Why does gravity act at the centre of earth and how does that happen?
| Given a spherically symmetric Earth and a point $P$, the gravitational field vector at $P$ can be determined in two steps:
*
*Why does the field point toward the Earth's center $C$? Consider rotational invariance about the axis passing through $C$ and $P$. The mass distribution of the Earth is unchanged by this rotat... | {
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Maximizing entropy with Lagrange multipliers This is a problem I saw in a stat mech textbook, and I think it is a fairly common problem.
Given the entropy function: $$S = - \sum_{i=1}^N p_i \log p_i$$
Maximize $S$ subject to constraints:
$$ \sum_{i=1}^N p_i = 1 \\ \sum_{i=1}^N p_i e_i = c$$
It was suggested to solve th... | One may apply a following trick, let $f(\mu) = \sum e^{-\mu e_i}$, then:
$$
\frac{\partial f}{ \partial\mu} = -\sum e_i e^{-\mu e_i}
$$
the constraints lead to following differential equation:
$$
\frac{\partial f}{ \partial\mu} = -cf \qquad f(0) = N
$$
Where $N$ is number of operands in $e_i$. Which has a solution:
... | {
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What is the centripetal force when instead of a mass point we have a physical rotating body? I was wondering what is the centripetal force of a body rotating in a circular motion. I know that the centripetal force of a point mass is $mv^2/r$. I only have done an introductory physics class so I can not find the answer.
| you probably come to that in your cours later.
for short: you take all masses with the same r for them its just your formula, then you have to add all the forces for the masses with different r. If you know what integrating is you integrate over all radii. For simple forms of bodies you calculate their "moment of ine... | {
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Gravitational potential energy of an $n$-body In my CIE A level course, the gravitational potential energy of a mass in a gravitational field is defined as the work done in bringing the mass from infinity to that point without changing it’s k.e. energy.
I thought about the gravitational potential energy if a system of ... | The gravitational potential energy of a system of $n$ bodies is calculated by the formula, similar to the formula of potential energy of the two bodies. You just need to apply the two-bodies-formula for all pairs of bodies and sum up the results: $$ E = - \sum_{i=0}^n{\sum_{j=i+1}^n}Gm_im_j/r_{ij}$$
Why is it so? Suppo... | {
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Why do electric field lines curve at the edges of a uniform electric field? I see a lot of images, including one in my textbook, like this one, where at the ends of a uniform field, field lines curve.
However, I know that field lines are perpendicular to the surface. The only case I see them curving is when drawing fi... | These are so-called edge effects. The straight electric field lines connecting two surfaces is a solution for the infinite charged plates. In practice, no plates are infinite: they have edges. Far from the edges (close to the center of the plates) one can still think of the plates as infinite, but at the edges this is ... | {
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Can we Predict the Trajectory of a hypersonic missile? I read in a newspaper that we can't predict the trajectory of a hypersonic missile and that this property renders the missile undetectable.
However, what I could not understand is why can't we predict it's trajectory? What factors do we have to look at for predicti... | I'll deal here with "classic" hypersonic missiles which travel through the upper reaches of the atmosphere and stay aloft by generating lift and operate under continuous thrust.
Such missiles are maneuverable, unlike ballistic missiles whose post-boost phase coasting trajectories can be mapped in real time and for whic... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Can we represent 4D graphically? Actually I know that axes are always perpendicular but after three axes we cannot draw any other axis that is perpendicular to all the other three axes.
can any one say how can we draw another axes which is mutually perpendicular
| This cannot be done. Humans can only perceive three dimensions and the axis that you are asking for would imply that we can vision a fourth spatial dimension which cannot be done. However, it is not impossible that there could be other spatial dimensions in a addition to the three we have. We just cannot see or sense t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/578728",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Is there anything such as gravitational field-lines in GR similar to the electric/magnetic field lines in electromagnetism? I sometimes mistake space-time curvature for gravitational field lines. Do geodesics in some ways represent $g$-field lines? Why is not it traditional to show $g$-field lines around a massive obje... | I would encourage anyone to draw any lines that help either them or others to get a good understanding. But the reason field lines are so much used in electromagnetism, and much less used in gravity, is because they nicely capture a mathematical property of a field whose divergence is zero (on a flat spacetime backgrou... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/578862",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
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