Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Interacting CFT fixed point of an RG flow Suppose we have a gauge theory defined in the UV and it flows to an interacting CFT in the IR, i.e. the beta function vanishes for some finite value of the coupling. I am confused about the meaning of this. Isn't a CFT by definition scale independent? But we have the CFT only a... | Your confusion arises from the following fact:
In the situation that you describe, the beta function vanishes at some finite value of the coupling. But it does not vanish at a finite value of the energy!
When you go down in energy from the UV to the IR, the coupling increases from zero to its fixed point value. But it ... | {
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Fastest numerical method to solve Lindblad Master Equation? The Lindblad Master Equation is a generalization of the Schrodinger Equation for open quantum systems, given by
$$
\frac{\mathrm{d} \rho}{\mathrm{d}t} = -i \left[ H, \rho\right] + \sum_k \gamma_k \left( L_k \rho L_k^\dagger - \frac{1}{2} \left\{ L_k^\dagger L_... | You can use a Python package called QuTiP which will allow you to solve the LME. It also has different numerical methods to solve your problem, you can take a look at them and compare. Here is some documentation (http://qutip.org/docs/3.1.0/guide/dynamics/dynamics-master.html) There are also plenty of examples to aid y... | {
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How to solve this problem only using the kinematics of rotational motion? This is a problem from my introductory physics textbook:
A wheel of moment of inertia $I$ and radius $r$ is free to rotate about its centre. A string is wrapped over its rim and a block of mass m is attached to the free end of the string. The sy... | To write a more complete answer for other readers: I would use Newton's second law and its rotational equivalent. Use $F= ma$ for the block of mass $m$ (since there is only translation, and no rotation), and then use $\tau = I \alpha$ for the wheel (since there is only rotation about its center, and no translation).
Th... | {
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What does it mean to treat space and time on equal footing? I often read from textbooks that in relativity, space and time are treated on an equal
footing. What do authors mean when they say this?
Are there any examples that show space and time are treated on an equal footing? Conversely, what examples show that space ... | After some thought, this is what I understand:
In Newtonian physics, a particle's path can be specified by $x^i(t)$ where the time $t$ can be seen as an independent parameter. The space coordinates $x^i(t)$ are dependent variables that depend on $t$. We thus say that space and time are not treated on an equal footing.... | {
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Is the torque on a gyroscope a conventional virtual force perpendicular to rotation? So I am having some difficulty understanding gyroscopic precession. I understand that mathematically by convention torque is perpendicular to the force and so is angular momentum but surely that force is a true force acting outwards as... | This is a good question. Gyroscopic precession is also what has baffled me the most of all classical mechanics I've encountered.
The force comes from the inertia of the spinning mass. Gravity tries to make the gyroscope (the top) tilt and fall straight down. But while falling down it also spins. The particles at the lo... | {
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Two Cylinders on Ramp Suppose I have two cylinders: a light one and a heavy one. Now, I let the cylinders roll down a ramp without slipping. My question is, which one will get to the bottom of the ramp first, and why?
| Assuming that the cylenders are identical in appearence and just made of material of different densities. Then the torque about the COM will be unequal but the acceleration would be equal.
Instead ofequation just percieve it as
$$\tau(torque) \propto Mass$$ as gravitational torque and other parameters are equal
$$ \tau... | {
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How could I see the distance light traveled from an airplane? It was nighttime. I was flying on an airplane. As we were landing we passed over a highway. I saw cars below with their headlights on. I could see that the light from their headlights only lit up a certain distance in front of them. Any object that fell past... |
we were never taught anything to clarify this in E&M.
The basic is that our eyes see objects from light reflected from the objects.
Light coming from a source, the headlights of a car are a source, after a certain distance opens up spherically , which means the energy of the beam is dispersed in a wider and wider v... | {
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Why does particle measurement cause quantum wavefunctions to collapse When we attempt to measure a certain property of a particle, how and why does its wave function collapse? I've tried to find answers on my own, but they've been far too complicated for me to comprehend. Would appreciate any answer with limited comple... | A simple way to look at it is to remember that the wavefunction describing a particle or a system of particles is a mathematical function, a solution of a specific quantum mechanical wave equation, with specific boundary conditions . When a measurement is made, an interaction with the system happens that changes the bo... | {
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Picking a direction for currents when doing nodal analysis involving capacitors Let's assume that I was given the following circuit:
Where the capacitor is fully charged at 6V, and a switch (not shown) will be closed at time t=0. From this, let's say that I pick the following directions of my currents in order to do n... | You don’t change the sign because the capacitor is discharging. The fundamental equation presupposes the current flowing into the capacitor (as you have it in your drawing). The negative sign will take care of itself in the solution (discharging).
$$ C \frac{dV_c(t)}{dt} = -\frac{1}{4k} V_c(t) $$
The fundamental capac... | {
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Kinetic energy and curvature In quantum mechanics, the kinetic energy of a particle described by the wave function $\psi$, is related to the curvature of the $\psi$. This is easily seen, but I have confused my self with the negative sign. That is: $\hat{T} = -\frac{\hbar^2}{2m}\nabla^2$, is the kinetic energy operator.... | The "curvature" is a local property of the wave function, but there is no concept in standard QM as "the local value of the kinetic energy" (see e.g. this).
The kinetic energy is one of the eigenvalues of the $T=p\cdot p$ operator (neglecting the factor $1/2$ and setting $\hbar=m=1$).
To understand the minus sign in $T... | {
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Why is the tension on both sides of an Atwood machine identical?
The field forces $F_{g1}$ and $F_{g2}$ push down on Block 1 and Block 2, respectivley, where
$$F_{g1}=m_1g$$$$F_{g2}=m_2g$$
Since the pully system reverses the direction of each force, wouldn't the following be true?
$$T_1 = F_{g2} = m_2g$$$$T_2 = F_{g1}... | Its because the pulley in an atwood's machine is an Ideal pulley. It has no mass and its frictionless. This means that the rope is only going to slip over the pulley freely without rotating it at all. In that case the rope is completely isolated from the pulley and tension should be uniform throughout.
Note that frict... | {
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Can coldness be converted to heat energy? We know that the heat can be converted into heat energy with the help of thermoelectric generators, but why can't we generate energy from coldness?
Like the temperature of the universe in 1 K, can this be used in the near future to be used as an energy resource for probes or sa... | There's a more recent scientific study about this topic, which was then covered in articles like this and this. I also asked a similar question a few months ago.
Basically, this is called "thermoradiative photovoltaics" and involves generating energy by emitting heat (as infrared rays) to a heat sink. The proposed tec... | {
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Spin part of the angular momentum from the Lagrangian For fermions of spin $1/2$ the angular momentum has following form:
$$
\mathcal{J}_z = \int d^{3}x \ \psi^{\dagger} (x) \left[i(- x \partial_y + y \partial_x) + i\sigma^{xy} \right] \psi(x)
$$
Here the first term is orbital part and the latter one is the spin part o... | Your observation is correct. The total angular momentum, integrated over volume, contains both contributions as pointed out in the other answer. However it takes the overall for of an orbital, position dependent, angular momentum while clearly the electromagnetic potential has internal AM as well.
My answer is written... | {
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Why does ponytail-style hair oscillate horizontally, but not vertically when jogging? Many people with long hair tie their hair to ponytail-style:
Closely observing the movement of their hair when they are running, I have noticed that the ponytail oscillates only horizontally, that is, in "left-right direction". Never... | This phenomenon happens with ear plugs too. I like to think of it by considering what each step of the run does to the motion of the hair. Hair in a ponytail has a fulcrum where it is attached to the head, so it can freely move like a pendulum in its plane.
When someone takes a step forward with their right foot and pu... | {
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Can spacetime be curved even in absence of any source? Einstein's equation in absense of any source (i.e., $T_{ab}=0$) $$R_{ab}-\frac{1}{2}g_{ab}R=0$$ has the solution $$R_{ab}=0.$$
But I think $R_{ab}=0$ does not imply that all components of the Riemann-Christoffel curvature tensor $R^c_{dab}$ be zero (or does it?). F... | This is a simple answer:
I would view this in the same light as the following question:
Does
$$ {\bf \nabla \cdot E} = \frac{\rho}{\epsilon_0} $$
imply zero electric field in region with no charge density?
To which the answer is clearly, "No".
And as an example: The astronauts on the moon. They were there in a pretty g... | {
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Are we using a hybrid coordinate system to define four velocity? Ordinarily in Newtonian physics, velocity is defined as $${\vec v}=\frac{d{\vec x}(t)}{dt}$$ where we use the coordinates of an observer and the universal time $t$.
When we dive into special relativity, we define the spatial components of the four-velocit... | In Newtonian mechanics, $t$ is the time for the object that is moving, as it is in SR. The difference is that any inertial frame believes that it is also their own time. It is an approximation that is corrected by SR.
Only after that correction some important quantities are conserved. For example, momentum before and a... | {
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Physical meaning of $\frac{π}{8}$ in Poiseuille's equation Recently I read about the Poiseuille's equation which relates the flow rate of a viscous fluid to coefficient of viscosity ($\nu$), pressure per unit length($\frac{P}{l}$) and radius of the tube ($r$) in which the fluid is flowing. The equation is
$$\frac{V}{t}... | The appearance of the irrational $\pi$ comes from the assumption, that the pipe is perfectly circular.
This in itself is of course a nonphysical assumption, so it is not surprising to get a irrational result.
| {
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Relation between uncertainty in measurement of mean and standard error on the mean I have a series of individual (time) measurements with a certain uncertainty each per measurement, which is the same for all the measurements (±one frame). I have understood that the uncertainty on the arithmetic mean of these measuremen... | In order to understand what is happening it is helpful to know the true distribution. Thus, I simulated $N=100$ data points from a normal distribution with mean value $\mu=21$ and standard deviation $\sigma=3$. The data looks like this
The red line is the average value, and the blue line is a Gaussian (least square) f... | {
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How to transform velocity 4-vectors to Zero Momentum Frame I have a particle $p$ with speed $u$ in lab frame approaching a stationary particle $q$.
The $p^{\mu}$ and $q^{\mu}$ velocity 4-vectors are:
$$p_{LAB}^{\mu}=\gamma_u(c, u, 0, 0)$$
$$q_{LAB}^{\mu}=(c, 0, 0, 0)$$
To get to ZMF, I need a standard lorentz boost wit... | Your intuition is correct, in the zero momentum frame you'd assume both objects to be moving towards you at the same speed. (I'm assuming, of course, that the two objects are identical.) So the first question to ask yourself is "What should this speed be?" The assumption you made ($v=u/2$) is incorrect, as while $q$ wi... | {
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Applications of representation theory of finite group in physics? Well, I have just finished my study on basic representation theory of finite group from a pure math course. After tortured a lot by abstract constructions, I would like to know the real application of this theory, however, it seems to me not many topics ... | In the study of equilibrium configurations and vibrational properties of molecules, clusters and solids, finite groups representations play a key role to extract all consequences of point symmetries of the average atomic positions.
Also electronic states in molecules, clusters and solids provide a different example o... | {
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Finding the metric tensor from a 2D line element A 2D space has coordinates $x^1$ and $x^2$ with line element
$$\mathrm{d} l^{2}=\left(\mathrm{d} x^{1}\right)^{2}+\left(x^{1}\right)^{2}\left(\mathrm{~d} x^{2}\right)^{2}.$$
I'm looking to find the metric tensor and its dual metric. I understand the basics of summing ove... | Your question is a bit unclear but as I understand it you want to derive the metric tensor of this line element and its inverse. You have to remember that $dl^2 = g_{i j}dx^i dx^j$. So your metric is $\text{diag}(1,(x^1)^2)$. And so its inverse is $\text{diag}(1,(x^1)^{-2})$.
Edit for clarity :
\begin{equation}
dl^2=g_... | {
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Unruh particles When we accelerate, an event horizon forms behind us resulting in Unruh radiation. In this kind of scenario, the existence of the radiation particles themselves is observer dependent.
My question is: If the existence of the particles is observer dependent, then what do the particles, themselves as obser... | A photon is not an observer, and can't be because its proper time is always zero and it has no frame of reference in which it is at rest. However, Unruh radiation is black body radiation, so it does include particles with charge and mass. To get an observer from this, you can get low-probability interactions among thes... | {
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How come the formula $W=Fd$ doesn't apply for energy stored in springs? I always thought that work is like the energy transferred and it is given by $W=Fd$, but this concept gets problematic for springs.
If the force $F$ is applied to a spring which compresses it by a length $d$, then apparently the energy stored in th... | Because $W = Fd$ only holds for a very special case. The general definition of work
is given via
$$W = \int_\gamma \vec F (\vec r) \cdot \text{d}\vec r$$
where $\gamma$ represents a trajectory in $\mathbb{R}^3$ and $\vec F (\vec r )$ represents a vector field.
The case where $W=Fd$ holds is when $\vec F (\vec r)$ is co... | {
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Angular velocity of a particle moving in 3D I have a particle trajectory where particle position is available at discrete time steps with respect of (0,0,0) in 3D. Time step is 0.05 sec. For reference, positions are shown in following image.
Particle velocity can be computed easily. My goal is to calculate angular vel... | You have a time series $\mathbf r (n\Delta t)$ where $\Delta t = 0.05$ seconds. To apply the formula
$$\mathbf \omega = \frac {\mathbf r \times \mathbf v}{r^2}$$
at time $t=n\Delta t$ start with
$$\mathbf v(t) \approx \frac{\mathbf r(t+\Delta t) - \mathbf r(t)}{\Delta t} = 20(\mathbf r(t+\Delta t) - \mathbf r(t))$$
so
... | {
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Relativistic energy of harmonic oscillator What is the relativistic energy of an harmonic oscillator:
$$\frac{m_0 c^2}{\sqrt{(1-\frac{v^2}{c^2})}}+\frac{1}{2}kx^2$$
Or
$$\frac{{m_0 c^2}+\frac{1}{2}kx^2 }{\sqrt{(1-\frac{v^2}{c^2})}}$$
I think the first one is true but I need an exact logic or derivation.
| The energy in special relativity (SR) is defined to be $\gamma m_0c^2$ via the scalar product between 4-momenta. So... I think that $kx^2/2$ would then be encompassed in $\gamma m_0c^2$. You should be able to answer this with an application of math by using Hamilton's action principle and the Euler-Lagrange equations.
| {
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Mathematical Definition of Power I am a high school student who was playing around with some equations, and I derived a formula for which cannot physically imagine.
\begin{align}
W & = \vec F \cdot \vec r
\\
\frac{dW}{dt} & = \frac{d}{dt}[\vec F \cdot \vec r] = \frac{d\vec F}{dt} \cdot \vec r + \vec F \cdot \frac{d\vec... | Work is defined as $W = \int_{}^{} \vec F \cdot d \vec r = \int_{}^{} \vec F \cdot \vec v \enspace dt$. Power, P, is dW/dt = $\vec F \cdot \vec v$.
Your relationship for work is incorrect, so your relationship for power (boxed-in relationship in your question) is not correct.
| {
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Is any particle allowed within the laws of physics? In the same way wormholes are possible but not guaranteed to occur naturally, is a theoretical particle possible such as one with a mass of a tonne and a charge of -3, or are there upper and lower limits of a particle's properties?
Related: Is there a theoretical uppe... | I'm not sure I understand what you mean by lower bounds, since there are massless, and also chargeless particles, like the photon. Let's stick to upper bounds.
When it comes to charge, hadronic resonances have some pretty high charges like 2, and nuclei go on and on... Don't get started on elementary versus composite.
... | {
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Why do low-energy waves produce heat, but high-energy waves do not? Radio waves, microwaves and infrared are known to produce heat and even cause burns, while visible light and ultraviolet are not. This seems counterintuitive to me, as the latter contain the highest amount of energy.
Why is this? Does it have to do wit... | The amount of heat generated by an EM radiation source depends on many factors, including how much of it is absorbed by the material. Of course in the microwave and infrared, absorption is high in liquids and solids and those sources rapidly produce heating by rotational and vibrational excitations being rapidly conve... | {
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Gravitational Binding energy of a sphere of 2 uniform densities So I know that the gravitational binding energy of a sphere of uniform density can be given by:
$$U=-\frac{16}{3}G\pi^2\rho^2\int_0^Rr^4dr$$
Which if integrated gives:
$$U=-\frac{3GM^2}{5R}$$
As desired. But say I had a density function given by:
$$\rho(r)... |
Could I then write that...
No, it's more complicated than that. You didn't show how you got your first integral, but one way to do it is as in Wikipedia:
Imagine that it is pulled apart by successively moving spherical shells to infinity, the outermost first, and find the total energy needed for that.
The mass $dm$ o... | {
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Does PIXE only measure external composition? When performing X-ray spectroscopy, say with PIXE, do atoms inside the metal have vacancies induced or only the outer layer?
For example, a quarter has a shell of 75% copper and 25% nickel, but a bulk composition of 8.33% nickel and 91.67% copper. If I perform X-ray spectros... | Typical Particle-Induced X-ray Emission (PIXE) uses an incident proton or alpha particle of a few MeV. Electronic stopping of this particle transfers energy to electrons in the sample, exciting them up from valence states. Electrons relaxing back down into those empty states release the characteristic x-rays.
So, the f... | {
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Law of refraction In my textbook it is given that "The refractive index of a substance does not depend on the angle of incidence"
But
Refreactive index =sine of angle of incidence/sine of angle of refraction
It is clear from above relation that refractive index depends on angle of incidence.Where am I wrong?
| The accepted answer is great. Just wanted to distill it down to the most basic statements that could be made.
Refractive index is a property of a material.
Angle of incident is a property of a light ray.
| {
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Difference in the equlibrium of the buckets Let there be a bucket of mass on earth resting on floor with water reaching the brim. And now consider another identical bucket with water till brim in outer space with no gravitational influence, and also a 3rd identical bucket with water till brim falling freely near Earth'... | Well, the second bucket in outer space is in static equilibrium and the third one (that's freely falling) is in dynamic equilibrium. And according to my knowledge, the first one, on the ground, is also in static equilibrium. It would be helpful if you could explain what you meant by "pressure difference pattern in the ... | {
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Does the Earth's magnetic field reversal and the corresponding magnetostrictive stress and strain make any contribution to the Earth's oblateness? If the changing magnetic field in a power grid's transformer can induce stress and strain on the transformer core, then can the changing magnetic field of the Earth, similar... | As far as I know, magnetostrictive materials are unusual. I doubt there are enough to be noticeable.
Also, Earth's magnetic field is weak, and shape changes even in strong fields are generally small.
Even so, it might not make any difference. Magnetic fields change over long times. Rocks flow over long times, especiall... | {
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Dark standard model linked though Higgs is it possible to have a dark std model (ie image of the std model) linked to the std model only through the Higgs? That would allow dark matter condensation, dark galaxies, stars, planets and biology.
Is there any astronomical evidence for (or search for) large condensed dark ma... | Yes. Actually, it is also possible to have such a Dark Standard Model that is linked to the Standard Model only through gravity.
Original theories for the nature of dark matter assumed all of the dark matter to be made of a single particle. WIMPs and Axions are the two prototype examples. Since these have not yet been ... | {
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Formula for centripetal acceleration: simple proof that does not use calculus? I teach physics to 16-year-old students who do not know calculus and the derivates. When I explain the formula for centripetal acceleration in circular uniform motion, I use this picture:
Here,
$$\vec{a}_{\text{av}}=\frac{\Delta \vec{v}}{\D... | A very simple derivation that requires no calculus is the following. We use the fact that there is a perfect mathematical analogy in which the velocity vector is to the radius vector as the acceleration is to the velocity. Writing $r$, $v$, and $a$ for the magnitudes, the analogy allows us to infer that if $v=2\pi r/T$... | {
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Lorentz transformation of continuity equation In a particular reference frame with coordinates $x^\mu$, we can define a current density 4-vector $J^\mu=(c\rho,\vec{J})$ where $\rho$ is the charge density and $\vec{J}$ is the current density.
The continuity equation in this frame is then $$\frac{\partial J^\mu}{\partial... | From $J'^\mu=\Lambda^\mu_\nu J^\nu$ take derivative on both sides
$$\frac{\partial J'^\mu}{\partial x'^\mu}=\Lambda^\mu_\nu \frac{\partial J^\nu}{\partial x'^\mu}$$
Note that $\frac{\partial}{\partial x'^\mu}=\Lambda^\sigma_\mu\frac{\partial}{\partial x^\sigma}$ Then we have
$$\frac{\partial J'^\mu}{\partial x'^\mu}=\L... | {
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Why is it easier to handle a cup upside down on the finger tip? If I try to handle a tumbler or cup on my fingertip (as shown in fig), it is quite hard to do so (and the cup falls most often).
And when I did the same experiment but this time the cup is upside down (as shown in fig), it was quite stable and I could han... | Dr jh has explained by taking torque about the center of mass but it could be explained better if we take it about the point of contact of your finger and the cup.
When the cup is upright gravity provides a torque by a force acting on its center of mass which is above your finger. Small perturbations will cause rotatio... | {
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Please explain the meaning of below statement Newtons second law is a local law.
(In the book,it says that it means that it applies to a particle at a particular instant without taking into consideration any history of the particle or its motion.)
Um, I couldn't understand what do they mean by " taking into considerati... | Yeah, it's quite confusing to read that. Even me, myself couldn't understand it first. Newton's second law is the relation between force and acceleration. It says that " the acceleration is directly proportional to the applied force, with the mass of the body being constant ".
And I guess this is what your NCERT Textbo... | {
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Why is acceleration directed inward when an object rotates in a circle? Somebody (in a video about physics) said that acceleration goes in if you would rotate a ball on a rope around yourself.
The other man (ex Navy SEAL, on YouTube too) said that obviously it goes out, because if you release the ball, it's going to fl... | A moving object continues in a straight line unless a force is applied to it.
If a ball is whirled in a circle at the end of a string, it is caused to move in a circle by the pull of the string. If the string breaks the ball proceeds in a straight line unless gravity pulls it downward. The ball's straight line is a ... | {
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Superconducting energy storage and voltage I've been reading up on superconducting magnetic energy storage, and while I know how the energy is stored ($E=\frac12LI^2$) I have no idea how the discharging works. Specifically, as per this paper 1 a voltage is applied across the superconducting coil, and the power output i... | Normally a superconducting magnet (a coil) is closed. If a resistor is connected at two points on the coil and the coil is opened between those points, current will flow through the resistor. The back EMF caused by the current through the resistance will cause a voltage between the ends of the coil. This in turn caus... | {
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Work done when you bring an bringing an object down from a height I am going to explain this question through an example.
Suppose I lift an object I apply a force $mg $ then I apply additional force, that would be $ma $ so total force would be $m(g+a)$. My doubt is that the work done by a person in lifting a box by app... | That is correct. Also, since the gravitational PE increases by $mgh$ it is clear that the kinetic energy increases by $mah$
| {
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Is there an accepted Lagrangian for the transport equation? Perhaps because it is so simple, I have not seen a lagrangian form of the transport equation
$$(\partial_t + a \partial_x)q = 0.$$
This equation is first order, which makes obtaining it from the Euler-Lagrange equation a bit tricky.
It would appear that the la... | I may be wrong, but it seems to me, that lagrangian, satisfying this equation is not possible in principle, at least classically.
Consider the Euler-Lagrange equation:
$$
\frac{d}{dt} \left(\frac{\partial L}{\partial \dot{x}}\right) -\frac{\partial L}{\partial x} = 0
$$
Note, that it is invariant under the time reversa... | {
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Would there be any gravity inside a hollow planet made of a spherical shell of basalt crust? I am writing a science-fiction story, which contains a 'crazy' planet. I would like some input into the consequences of this physics according to standard physics.
The planet in question is Earth-sized and it orbits a Sun-like ... | If you neglect the gravity of the nitrogen gas, there is no net gravitational force anywhere inside. This is a result of the famous “Shell Theorem” for inverse-square forces. At any point, you are attracted by all the atoms in the shell, but the vector sum of all these forces — in different directions, and having diffe... | {
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Why don't opaque objects reflect light? My sister was doing a quiz and I tried to point her in the right direction by giving her scenarios to imagine. One of the questions in the quiz was:
Which of the following objects do not reflect light:
*
*Polished metal
*Mirror
*Undisturbed water
*Book
She suggested that ... | The question is asking "which of the following objects will you not see a reflection?".
A distinction (albeit poorly) is being made between specular reflection and diffuse reflection.
The objects in options 1-3 will exhibit specular reflection, while option 4 "a book" will exhibit diffuse reflection. So the correct opt... | {
"language": "en",
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Example of an infinite volume Lindblad system What is an explicit example of a Lindbladian
\begin{align*}
L(\rho) = - i \lbrack H_A, \rho \rbrack + G \sum_{j} V_j \rho V_j^* - \frac{1}{2}(V_j^* V_j \rho + \rho V_j^* V_j)
\end{align*}
acting on the space of trace class operators on some Hilbert space $\mathcal{H}$ such... | In the following paper https://arxiv.org/abs/2206.09879 (work I did in connection to asking the question) several examples of infinite volume Lindblad systems are discussed.
In the single particle sector, consider the Hilbert space $l^2(\mathbb{Z})$ and some space of operators on that Hilbert space, e.g. trace-class, H... | {
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Analytic solution to Kepler's Problem, exegesis From 'Solving Kepler's Problem' by Colwell, the first analytic solution to Kepler's Problem used a theorem of Lagrange, and later Burmann, to invert Kepler's equation. When you look on the internet for a proof you find these lines that begin the section on Burmann's theo... | Basically you suppose that $z\in B_\epsilon(a)\subseteq S$
($S$ in Wolfram), for small $\epsilon$. In other words you suppose that the distance (The metric for this case) $|z-a|$ is small enough (which you would have to anyways if you neglect the higher order Terms of the Taylor-Series). It follows that
$$
\phi'(a)={\r... | {
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Which graph shows how the power $P$ dissipated in the load resistor varies with the resistance of the load resistor?
^ question
Which graph shows how the power P dissipated in the load resistor varies with the resistance of the load resistor?
The answer is A but what I need help in understanding is why. From what I un... | Seems like I've got an answer (if the working is incorrect that would invalidate this answer, in that case please leave a comment, thanks).
Power dissipated:
$P = I^2R$
$I = V/R_{T} = 12/(2+R)$
$P = 12/(2+R) * R$
choosing values 0.5 through 4 for $R$ we can infer by the results that the gradient should increase and tha... | {
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How can I make sense of the work-energy theorem in the situation of a force applied on a disk? Pretend that we are in space and that gravitational attraction is negligible. Now, imagine that there are two disks that are exactly the same. However, on the first disk, a force is applied tangentially and on the second disk... |
However, on the first disk, a force is applied tangentially and on the second disk, the same force is applied to its center of mass. The force is exerted over the same distance for both.
It is not possible for the force to be applied for both the same amount of time and over the same distance. The tangentially applie... | {
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Why does air pressure decrease with altitude? I am looking to find the reason: why air pressure decreases with altitude? Has it to do with the fact that gravitational force is less at higher altitude due to the greater distance between the masses? Does earth’s spin cause a centrifugal force? Are the molecules at higher... | I edited this question on the first day, in response to a few comments that pointed out a misunderstanding, but it didn't register. I sincerely apologize for that.
As pointed out by other answers, the pressure due to any fluid, compressible or not, increases with depth. This is due to the greater mass and thus weight o... | {
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Magnetic dipole moment of volume current derivation The multipole expansion of the magnetic potential yields the dipole term :
$$\mathbf A_{dipole}(\mathbf{r}) =\frac{\mu_0}{4\pi r^{2}}\int (\hat {\mathbf r} \cdot {\mathbf r}') \mathbf J {dV}'$$
How do I get from this expression to the final expression :
$$\mathbf A_{d... | There is in identity for the triple product:
$$
\mathbf{r}^{'} \times (\mathbf{J} \times \hat{\mathbf{r}}) =
\mathbf{J} (\mathbf{r}^{'} \cdot \hat{\mathbf{r}})
-\hat{\mathbf{r}} (\mathbf{r}^{'} \cdot \mathbf{J})
$$
Substitutring it in the exprerssion, one is left with the integral:
$$
\int dV^{'} \hat{\mathbf{r}} (\m... | {
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Effect of gravity in space According to general relativity, I know that time flows at a different rate in the presence of gravity which is nothing but the curvature of spacetime. And is called time dilation.
My doubt is, are there similar effects in space as well? I mean, when there is a curve in space-time, it's not j... | If you are talking about gravitational time dilation and length contraction yes there are analogous formulations like in special relativity.
But in this case, they are rather more complicated since you are no longer working on flat spacetime. You need to define the metric. For simplicity if you choose a non-rotating bl... | {
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Why is the net force acting on a massless body zero? I know that massless bodies can accelerate (in theory) even with the net force equaling to zero. But, why cannot there be a net force on a massless object? Why does it always have to be zero as a resultant in the end?
I'm talking about object whose mass is assumed to... | If we start from Newton's Second Law
$$F=ma,$$
then we can see that if the mass is zero, then the total force must be as well:
$$F = ma = (0)a = 0.$$
Then again, this leaves acceleration completely undefined since $a = F/m = 0/0.$ This is why every massless object in a physics problem--whether rope, spring, or pulley--... | {
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How does a capacitor get charged instantly in AC whereas it takes infinite time in DC? I have seen when a capacitor is connected to a dc source it takes infinte time to charge, but when connected to ac it takes the potential of the source instantly,
probably the approach in the books is not adequate, please clarify,
He... | Capacitors always take time to charge. In practice, when a capacitors is ~99% charged , we can call it fully charged. The exponential which is used to describe the charging of a capacitors does not make sense when time is very large because charge can never be less than charge of an electron while in the exponential e... | {
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Can magnetic loops with no source current knot or link? The answer to this question is obviously no. I would like to pose a variation of that question. Suppose a simply connected domain of a 3-d vacuum space has no source current. Does there exist a case where two closed loops of magnetic field residing in that domain ... | As @benrg mentioned in his comment, there are papers on exactly this topic, e.g.,
*
*Carlos Hoyos, Nilanjan Sircar and Jacob Sonnenschein, New knotted solutions of Maxwell’s equations.
*Hridesh Kedia, Iwo Bialynicki-Birula, Daniel Peralta-Salas,
and William T.M. Irvine, Tying knots in light fields.
There, the elect... | {
"language": "en",
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Is inertia and gravity determined by relativistic mass or invariant mass? As far as I know, mass fundamentally determines inertia and the gravitational force. But since there are two types of mass, which mass determines which? From what I have read so far, and correct me if I'm wrong, the relativistic mass determines t... | As stated is not advised to call the relativistic energy $m\gamma$ relativistic mass. Mass these days strictly refers to total energy in the rest frame divided by $c^2$.
$m\gamma$ is indeed the source of gravity and it determines inertia, as the relativistic momentum is $m\gamma \vec v$. Newton's second law is replaced... | {
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Why different methods to solve this question gives different values of time While solving the following question.Why do we get different values of time by different approaches.
An elevator whose floor to ceiling distance is $2.7m$ starts ascending with a constant acceleration of $1.2m/s^{2}$.Two sec after it starts, a... | In approach 1 which is from the lift frame, you are doing the calculation as if the frame is inertial. Meaning, you are using only the gravitational acceleration $g$ and are ignoring the centrifugal part, namely the presence of the lift acceleration.
$$\text{Inertial frame:}\qquad a=g$$
This is how the bolt will fall i... | {
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Why is the $i\epsilon$-prescription necessary in the Klein-Gordon propagator? When evaluating the Klein-Gordon propagator, in the book by P&S, p. 31, I see that, it is customary to shift the poles and add $i\epsilon$ in the denominator. I don't understand, why this is necessary. Why can't we just use complex analysis? ... | Note that the original integral you are trying to compute is over the real line, not over a closed contour, so the Cauchy theorem does not apply until you find a suitable way to close the contour. Due to the presence of the exponential factor $e^{ibz}$, as you have written it, one can close the contour in the upper hal... | {
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What is the non-relativistic limit of the quantised electromagnetic field? I’m not a physicist so this question may be naive ... For a real scalar field, quantisation yields the Klein-Gordon equation and the non-relativistic limit of this gives the Schrödinger field. What is the equivalent equation or field starting fr... | As electromagnetic fields in vacuum always move at speed $c$ there is no nonrelativistic approximation to electromagnetism. In other words photons have zero rest mass and therefore no rest frame.
| {
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Number of variables in the Hamilton-Jacobi equation In Goldstein's Classical Mechanics, while introducing the Hamilton-Jacobi equation, he argues that the equation $$H(q_1, ... , q_n; \frac{\partial S}{\partial q_1}, ..., \frac{\partial S}{\partial q_n}; t) + \frac{\partial S}{\partial t} = 0$$ is a partial differentia... | the action function in the HJ formalism is dependent on time through the upper bound.
$$S(q_i,t,\alpha_i,t_0)=\int_{t_0}^tL(q_i,\partial_tq_i,t')dt'$$
in cases of Lagrangian that is independent (explicitly) of time then the constant of integration conjugate to $t$ let's call it $\alpha_t$ is simply the Energy.
read mor... | {
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Will this spaceship collide with the star? (time dilation) I thought of the above thought experiment and arrive on 2 conflicting conclusions. I can't seem to identify the flaw in my reasoning.
Suppose there is a star 4 light years from earth that has will explode and turn into a white dwarf in 3 years (as measured in t... | $t=0$, $x=0$
B: $t=3$, $x=4$
C: $t=4/v\approx 4.62$, $x=4$
*Lorentz transform to the ship frame:
| {
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Why don't radio waves sent by electronic devices intefere with each other? You know how phones, computers and other electronic devices that use wireless communication use radio waves to communicate?...well since almost everyone has gotten a smart phone wouldn't radio waves from different smart phones interfere with eac... | For a significant and stable interference pattern, two such waves would have to be of the same frequency and of comparable amplitude. There is an area in North Miami where I get poor reception on my car radio. I think the several radio and TV transmitters in the area are over-driving the circuits in my radio.
| {
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Is the brick-concrete connection the 'weakest link' in brick made buildings? When an earthquake strikes,do buildings made of bricks and concrete break mostly on concrete-brick connection spots?If Yes does the brick on the picture prevents this from occuring?
| As far as I know, yes, brick-concrete connection is the weakest link. The connection would break if torque about the interface surpasses the the limit to which the interface is designed/expected to bear the torque.
The above design provied a counter torque about the interface due to normal force from the inclines at th... | {
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Why is there a specific negative sign in front of the $m_{12}$ term of the 2HDM Higgs potential? Why is there a specific negative sign in front of the $m_{12}$ term of the 2HDM Higgs potential?
(but not for the $m_{11}$ and $m_{22}$)
See for example: https://arxiv.org/abs/1106.0034
Eq. (2) Page 6:
$$
V = m_{11}^2\Phi_1... | The authors are writing down the most general potential consistent with the symmetries of the problem. The constants $m_{ij}^2$ are free parameters, and the sign is purely conventional. For example, if I were to write the most general linear function of $x$, I could write $f(x)=\alpha+\beta x$ for some parameters, or $... | {
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How does universe expand when cosmological constant is zero? From what I learned, Einstein believed in a static universe but from his general relativity equations universe must collapse under gravity. Hence Einstein adjusted this gravity with cosmological contact which is a kind of anti-gravitational effect. But later ... | The universe can expand just without a cosmological constant.
Assuming the universe to be spatially homogeneous and isotropic, and combining this with the Einstein field equations produces the two Friedmann equations$$\frac{\dot{a}(t)}{a(t)} = \frac{8\pi G}{3}\rho - \frac{k}{a^2(t)}+\frac{\Lambda}{3}$$ and $$\frac{\ddo... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to compute gauge potential $A$ from the field strength $F$? Let $F=dA+A \wedge A$ be the field strength that solves vaccum Yang-Mills equation.
The question is: how to recover the gauge potential $A$? Is there any standard way? or any theorem stating the solvability? Suppose the metric is $g=g_{\mu \nu}dx^{\mu}dx^{... | You can't recover the gauge potential uniquely without specifying more information, because of gauge invariance. $A$ is not uniquely defined by $F$. For any gauge transformation $g: \Sigma \to G$, the transformed connection $A^g = g^{-1}A g + g^{-1}dg$ has curvature $F_{A^g} = g^{-1}F_A g$.
It's physically a bit weir... | {
"language": "en",
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Can an electron have a spin opposite to the hole? Consider the simplest case - a gapped system where the electron in the valence band is excited to the conduction band. In this process, is the spin conserved? Or to word it differently, can the excited electron have a different orientation of spin compared to the hole?
| Yes, the Spin of the electron will be the same (as it is essentially the same electron of the same shell).
[
Moreover, the spin of the electron will not matter at all, as the other electron of different atom 'lives' in splited subshell (different).
So, Auf Bau'S principle will not be violated
]
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can $1/V$ be equal to $0$ in Boyle's Law? In relation to ideal gases, Boyle's Law states that pressure is inversely proportional to volume under constant temperature. In other words,
$$P \propto 1/V$$
Below is a graph that plots pressure, $P$, against inverse volume, $1/V$.
How can $1/V$ ever equal zero? How is th... | You've got to start with the ideal gas law
$$pV=mRT$$
Where, in this version, $m$ is the mass of the gas, $R$ is the specific gas constant and $T$ is the temperature. If $m$ and $T$ are constant, then $mRT$ = constant = $C$.
$$p=\frac{C}{V}$$
It is important to note that Boyle's law only applies to a closed system, i.e... | {
"language": "en",
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Period behavior near separatrix in Hamiltonian system Given the periodic potential Hamiltonian $H=\frac{p^2}{2} - \omega_0^2 \cos(q)$ I would like to show that near the separatrix the period has this behavior: $T(E)\sim |\log(\delta E)|$ with $\delta E=|E-\omega_0^2|$.
More generally given an Hamiltonian system of the ... | The period is calculated by the integral
$$
\sqrt{2}\int_0^{2\pi} \frac{d q}{ \sqrt{\omega_0 ^2 \cos (q)+E}}
$$
which can be represented by special functions. After applying a replacement $E\to \delta E+\omega^2_0$, you need to expand this integral around separatrix $\delta E=0$, the leading term is $-2\omega_0^{-1}\ln... | {
"language": "en",
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Speed, acceleration, accelerating acceleration, etc. How do we know where to stop? I am not a physicist.
Suppose a body A is falling towards body B in a vacuum. We know that A's speed will increase. However, as A draws near to B, the force of gravity will increase so the rate at which A accelerates will increase. Also ... | In your question, you are tracking both ${\bf r}_A$ and ${\bf r}_B$ (the position vectors in a fixed coordinate system), with something like:
$$ m_a\ddot {\bf r}_A = km_am_b\frac{{\bf r}_A - {\bf r}_B}{||{\bf r}_A - {\bf r}_B||^3}$$
$$ m_b\ddot {\bf r}_B = km_am_b\frac{{\bf r}_B - {\bf r}_A}{||{\bf r}_A - {\bf r}_B||^3... | {
"language": "en",
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Net force on links in chain? Suppose there is a chain with 5 links in it where each link has a mass of $m=0.1kg$, and the chain is being accelerated upward at $2.5 m/s^2$. I want to find the net force on each link in the chain.
I would have thought that the net force is the sum of the force from gravity (i.e., its wei... | The reason each link will have the same net force is because:
*
*Each link has the same acceleration, and;
*Each link has the same mass.
Since the net force is $\Sigma F=ma$ and $m$ and $a$ are the same for each case, the net force on 1 link is the same as the net force on each other link.
So yes, each link will ha... | {
"language": "en",
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Peskin and Schroeder, where is the mass in the denominator of the simple harmonic oscillator Hamiltonian? This relates to page 20 of Peskin and Schroeder.
They state that the Fourier transform of the Klein-Gordon field satisfies the following:
$$\left[\frac{\partial^2}{\partial t^2}+(|\vec p|^2+m^2)\right]\phi(\vec p,t... | Neither does it have a mass in the numerator for the $\phi^2$ term! Peskin & Schroeder just do not bother with a constant $m$ is this context. As you can see, this part introduces you to the ladder operators, in order to apply the formalism to the Klein-Gordon hamiltonian. No need to worry about $m$'s, which are irrele... | {
"language": "en",
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Where does the law of conservation of momentum apply? Take the scenario of a snowball hitting a tree and stopping. Initially, the snowball had momentum but now neither the snowball nor tree have momentum, so momentum is lost (thus the law of conservation of momentum is violated?). Or since the tree has such a large mas... | Let give a bigger picture. Assume the snowball appears (due to atmospheric processes) at some height "h". From this moment, gravity accelerates it against earth (discard wind forces). In the same way, earth is accelerated towards the snowball. Gravitational forces are the same for snowball and earth in modulus but oppo... | {
"language": "en",
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Can thermodynamics be considered logical? One of the laws says that heat won't flow from cool to warm and at the same time this same theory claims that there is a finite (albeit tiny) chance that it will, because there is always such a microstate.
We can also have a situation where all air molecules in the room can be ... | I think it is a matter of probabilities. The macrostate that is seen when the system is in equilibrium has enormously large number of microstates than the macrostate where all gases are on one side of the system.
'Enormously large' still does not feel large enough, its actually mind bogglingly large. Thus, the probabil... | {
"language": "en",
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What makes a standing wave a wave? Well, this is my physics professor's question and it really made me think a lot about standing waves, realising I don't actually understand it. What makes a standing wave a wave? How could I explain it? What actually makes wave a wave?
| As John Rennie says, a wave is defined in physics to be a function which satisfies a wave equation. I just want to add that what makes this a wave in common-speak is that the solutions are cyclic (i.e. repeating) functions. This is of course already clear to anyone familiar with the maths in John Rennie's answer which ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What experiment confirms $\mathbf{J}^2 = \hbar^2 j(j+1)$? I learned that if we measure the spin angular momentum of an electron in
one direction $J_z$, we get $\pm \frac{1}{2} \hbar$. But if we measure
the magnitude of the angular momentum $\mathbf{J}^2$, we should get
$\frac{3}{4} \hbar^2$. What experiment gives the... | The Zeeman effect, discovered in the 19th century, was understood in quantum theory by Lande and Sommerfeld early on. Essentially, in a magnetic field, the energy levels of atoms are split by differences of magnetic moments, which are proportional to $J_z$, or the corresponding S and L components comprising J. This the... | {
"language": "en",
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$P=\epsilon_o \chi E$ or $\epsilon_o \chi E_o$ Suppose the polarisation inside a dielectric is given by $P$, then is it related to the electric field as $\vec{P}=\epsilon_o \chi \vec{E}$ where $E$ is the field inside the dielectric or is is $E$ the original field that would have been present in that region in absence o... | $E$ is the field inside the dielectric. "Original field" is called "electric displacement" and usually denoted by $\mathbf D$, not $\mathbf E$.
| {
"language": "en",
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What causes pain when experiencing a static shock? What exactly causes the pain in my fingertip when I get a static shock from touching something? Is it the current flowing through my nerves or is it a localized thermal burn from the spark itself?
| It is the flow of tiny amounts of current through the nerve endings that creates the pain of a shock. The brevity of the (tiny) heat pulse is not detectable by your nerves unless the current is really big (which does not happen with shocks caused by static electric discharges)- which current might also be big enough to... | {
"language": "en",
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Plotting the Bethe-Bloch Formula We had in our scriptum the following formula for the Bethe-Bloch formula:
$$-\frac{dE}{dx} = K\frac{\rho Z}{A} \frac{z^2}{\beta^2} \left[ \ln\left( \frac{2m\gamma^2\beta^2}{I} - \beta^2 \right) \right], $$
where I set $c = 1$ for convenience, $K$ is a constant, $I$ is the average ionisa... | If you know $\beta$ you can compute $\gamma = (1 - \beta^2)^{-1/2}$, so it is just a matter of calculating $\beta \gamma$ for each value of $\beta$ you are interested in. And if you know $\beta\gamma$, you can extract $\beta$ from it, e. g. by plotting $\beta\gamma$ versus $\beta$ (again, $c = 1$):
When you know $\bet... | {
"language": "en",
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Mutual inductance - induced magnetic flux in the primary Let there be two coils, L1 (with self inductance L1), and L2, with self inductance L2.
The first coil is connected to a sinusoidal supply, and the second one is connected to a resistor load, as shown in the image:
As we know There is a changing current in coil 1... | The infinite process you suggest exists but only for non-zero intervals of time. At a single time instant, there are only two induced effects on coil 1: that due to the coil 1, and that due to coil 2. That is what the equation
$\varepsilon_2 =-L_2\frac{\mathrm{d}I_2 }{\mathrm{d} t} - L_{21}\frac{\mathrm{d} I_1}{\mathrm... | {
"language": "en",
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Does Schwarzschild metric in Kruskal-Szekeres coordinates admit asymptotic ($r \to +\infty$) timelike observers? I thank in advance whoever will answer my question.
Schwarzschild metric in Schwarzschild coordinates in $\mathbb{R}^{1,3}$ is [1]:
$$ds^2=-\bigg(1-\displaystyle\frac{2M}{r}\bigg)dt^2+\bigg(1-\frac{2M}{r}\bi... | I don't think there are any $r\to\infty$ asymptotic timelike observers. There seems to be a limit of that sort in some coordinates, like Eddington-Finkelstein $(u,r)$, but it's an illusion. Conformal spatial infinity is a single point with no time dimension, and its causal past only contains past infinity.
The $r\to\in... | {
"language": "en",
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Partial derivative in Newtons Second law Newton's second law states Force is the time derivative of momentum. But is it a total derivative or partial derivative? What is the reason behind it?
| Newton second law
$$\frac{d}{dt}(m\,\vec v)=m\,\frac{d\vec v}{dt}=\vec{F}\tag 1$$
the velocity $~\vec v$ is in general depending on the generalized coordinates $~\vec q~$ the velocity of the generalized coordinates $~\vec{\dot{q}}~$ and the time $~t$
$\Rightarrow$
the total derivative is
$$d\vec v=\frac{\partial \vec v... | {
"language": "en",
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Polarity in a magnetized Möbius strip When a flat iron or Alnico washer is magnetized one of the faces develops a north polarity and the other, south. The geometric shape here is simple.
However, when a standard Möbius strip (or one of given thickness, radii of curvature and torsion of edges) is magnetized, which regi... | For a 'uniformly' magnetized material, the longitudinal (down the length) component can be continuous around the loop, but both the transverse (across the width) and perpendicular (through the thickness) components must encounter a 180-degree change somewhere around the loop.
If the magnetic anisotropy is high, the m... | {
"language": "en",
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If a jet engine is bolted to the equator, does the Earth speed up? If a jet engine is bolted to the equator near ground level and run with the exhaust pointing west, does the earth speed up, albeit imperceptibly? Or does the Earth's atmosphere absorb the energy of the exhaust, and transfer it back to the ground, cancel... | As other answers have stated there would be a small change in the Earth's rotation rate and a change in the opposite direction to the atmosphere's rotation rate. The size of the change would be limited by the increased friction between the earth and the atmosphere, and so the length of a day would settle to a new value... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If the sea surface were absolutely calm should the Sun reflection be the area of a circle instead a ribbon? Although waves produced on the sea can cause different points of the sea surface to reflect sunlight towards the same observer, how is that kind of ribbon image produced? Why isn't the reflection stretched also p... | First off, some terminology: the 'ribbon' is known as sun glitter (and, when observed from space, as sunglint). A good explanation is at this NOAA page, but the basic dynamics is that the light reflects specularly off of the water, but the variable angles of the surface deflects it in different directions.
If you we... | {
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Lorentz indices to label rotation irreducible representations Consider the $A_\mu\in\left(\frac{1}{2},\frac{1}{2}\right)$, the vector representation of the restricted Lorentz group. One can decompose this vector under spatial rotations as $A_\mu\in 0\oplus 1$ where $A_0$ transforms as a 3D scalar and $A_i$ transforms a... | This is a close duplicate.
$\psi_{\mu~\alpha}$, in $$\left(\frac{1}{2},\frac{1}{2}\right)\otimes\left[\left(\frac{1}{2},0\right)\oplus\left(0,\frac{1}{2}\right)\right],$$ has 16 components; so you project out the spinor piece, $\gamma\cdot \psi_\alpha =0$, $ \left[\left(\frac{1}{2},0\right)\oplus\left(0,\frac{1}{2}\ri... | {
"language": "en",
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Normalization Constant in Time Evolution of Density Matrix Given the Hamiltonian:
$$%H = \omega \left(|0\rangle \langle1| + |1\rangle \langle0| \right) = \begin{bmatrix}
0 & \omega \\
\omega & 0
\end{bmatrix}$$, I want to find the final state $\rho(t_f)$of the given density operator:
$$\rho(0) =|0\rangle \langle0|... | Additionally to Norbert Schuch's answer and comments, where he points out your problem of normalization, I want to add a brief note about the exact calculations that can be performed in this example.
First, for convenience, I want to take the factor $\omega$ out of the definition of the Hamiltonian. Now we have to noti... | {
"language": "en",
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Identifying inertial system without already having an inertial system? Learning some basic physics principles via Spivak's Physics for Mathematicians, and he rephrases Newton's first law as
Newton's First Law: There is at least one coordinate system — an inertial system — in which any object not acted upon by any forc... |
In practice, do we have a way to measure forces that doesn't rely on choice of coordinate system?
Yes, we use accelerometers (more properly inertial measurement units which measure acceleration on three axes and rotation about three axes).
Regardless of your coordinate system, if your accelerometer reads 0 then the o... | {
"language": "en",
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Why do we not observe a greater Casimir force than we do? I am very new to quantum field theory, so forgive me if this question is a bit silly. The Casimir force is usually explained by the zero point energy of the field. You assume that the frequencies of the field are quantized between the two plates, perform some re... | Metal plates impose a boundary condition on the electromagnetic field, because metal is made of charged particles which interact with an electromagnetic field. But those metal plates do not impose a boundary condition on the Higgs field, which extends through conductors.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/609676",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
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In QFT why does the degree of the interaction terms in Lagrangian start from 3? I'm new to QFT so it's not obvious to me why there is no quadratic interaction terms in Lagrangians.
For example, the Lagrangian for a real scalar field is
$$L=\frac{1}{2}\partial_\mu \phi \partial^\mu \phi-\frac{1}{2}m^2\phi^2-\sum_{n\geq ... | Given that an interaction of the $n^{th}$ order implies the existence of an $n$ pointed vertex.
ex. $L_1 = g \phi^3$ in a real scalar field theory gives rise to a $3$ pointed vertex.
If the interaction term had form $$L_1 = g\phi^2$$ this would just be a $2$ pointed vertex. If we allow conservation laws in this theory ... | {
"language": "en",
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Einstein's light speed postulate I have seen two statements of Einstein's 1905 light speed postulate; for instance, in Andrew Steane's Relativity Made Relatively Easy:
*
*There is a finite maximum speed for signals.
*There is an inertial reference frame in which the speed of light in vacuum is independent of the mot... | I like this, so I'm going to try. I'm going to add in "light transmits signals", since it seems like that equivalency is not what the OP is getting at. Also, I'm going to say "there is a maximum speed for everything". I think those two things come from reasonable definitions of signals, light, and what a "source" is:
1... | {
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Have anyone seen an unbound electron absorb/emit a photon via Bremsstrahlung process? I know free electron cannot absorb or emit photon as it cannot satisfy both the conservation of energy and momentum at once but how about in Bremsstrahlung process? The presence of a positively charged particle is used to deflect the ... | Bremsstrahlun photons were used in order to identify electrons when studyig elementary particle interactions in cloud chambers and bubble chambers.
Strong magnetic fields were imposed so that charged particles would bend and their momentum measured. The photon from the bending electrons pair-produces in the chamber ... | {
"language": "en",
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Question regarding Lorentz Transformation and Space Contraction- Contradiction I stumbled upon this question regarding Special relativity- and have seemed to reach a contradiction.
I am trying to find the distance that the ball travels
I am obviously not looking for the numerical answer, but I'm trying to understand wh... | When dealing with problems in Special Relativity its best to deal with individual events. So let's consider two events here: the ball leaves the "back end" of the train, and the ball arrives at the "front end" of the train.
Now let's see what we know: The ball leaves the back end ($x=0=x'$) at $t=0=t'$, and the front e... | {
"language": "en",
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Is there a correlation between the Earth's spin, the moon, and temperature? Based on NASA's arcticle, changes to land, ice sheet, ocean, and mantle flow affect Earth's spin.
Does the moon's elliptical orbit around Earth also affect Earth's spin? What effect does distance play?
The moon has also been drifting away conti... | This is a change that's happening over bullions of years. So the changes exist, but are so small they have little relevance on a timescale of years or centuries, probably not millennia either.
| {
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Calculation of time for electronic transitions How do we determine the time for electronic transitions in atoms or in semiconductor devices, from one energy level to another?
| For an absorption process, the transition time (in order of $femto second$) is usually estimated using uncertainty principle:
$$
\Delta t = \frac{\hbar}{\Delta E} = \frac{\hbar}{E_2 - E_1};
$$
Where $E_1$ and $E_2$ are the energies of the two levels.
For emision process, the life time of electron is much longer (in t... | {
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Amount of matter in two infinite universes I don't know exactly where to find any other information on this question so I thought I would ask here. If there were two infinitely large universes one where 20% of the space in the universe was taken by matter and nothing else and one with 30% of its space taken up by matte... | Because percentages are dimensionless numbers (each representing only a portion of the particular object of which it is a percentage), they are not what the mathematician Cantor (extremely important in astronomy and cosmology) called "countably infinite": As a result, the information you may be seeking, which I'd imag... | {
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"answer_id": 0
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Why does a body in SHM have more probability (of being observed) at the extreme positions and not at other positions? There is a question on the number of times a body comes to a place in a simple harmonic motion. Have a look:
I thought that the answer was B because in each oscillation a body is at the extremes only o... | At the ends, the oscillator slows down. So the probability of finding it at ends is high.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/611154",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 2
} |
Why is the tension equal to the spring force here?
Here the block is oscillating and to solve this question I took the tention in the string to be equal to the spring force
But if that's the case a particle in the junction of the spring and the rope will expirence a net force of zero yet it still it goes up and down e... | As you seem to be having trouble with a general concept rather than asking for a homework solution, I will attempt an explanation. In an ideal situation they are equal. It takes more force, as the mass's weight carries it downwards, to stretch the spring further therefore more tension on the string. So as spring force... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/611416",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
What information is sufficient for describing a thermodynamic system? For a single-component system, why are the energy, volume, and number of particles sufficient for describing the thermodynamics of the system? Why just three variables and those three variables in particular?
In the book that I am using (Callen, $\te... | A flippant, but not entirely inaccurate, answer is that those three variables were chosen because it was convenient.
From the Wikipedia page for Thermodynamic State:
A thermodynamic system is a macroscopic object, the microscopic
details of which are not explicitly considered in its thermodynamic
description. The numb... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/611534",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Validity of Ampère's law in terms of $H$ We know that the auxiliary magnetic field $\bf{H}$ is
$$\mathbf{H}=\frac{1}{\mu_{0}} \mathbf{B}-\mathbf{M}$$
and
$$\mathbf{\nabla} \times \mathbf{H}=\mathbf{J}_{f}$$
but this differential equation is generally not valid at the boundary of a magnetized body due to an abrupt chan... | Just use Ampère's law for $\mathbf B$ to get the total current. Then subtract the bound current from the result to get the free current, if needed.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/611662",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 3
} |
Converting energy from units of joules into units of wavenumber If we have an expression for energy $E$ in Joules why is it that if we wish to convert the energy into wavenumber we divide the expression by $hc$?
I know that $$E = \frac{hc}{\lambda}$$
So surely this implies that $$\frac{E}{hc} = \frac{1}{\lambda}$$
and ... | From the Planck relation
$$E=h\nu = \frac{hc}{\lambda} = hc\tilde{\nu} $$
where in spectroscopy $\tilde{\nu}$ is the wavenumber and it has the following relation with angular wavenumber $k$
$$\tilde{\nu}=\frac{k}{2\pi}$$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/611777",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
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