Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Do photons lose energy after radiation pressure is applied to a perfect reflector? I was readng Wikipedia article (English one) about radiation pressure because there is something I still cannot figure out. As I understand it, radiation pressure emerges from conservation of momentum. Photons or electromagnetic waves po... | There will be a recoil momentum ($2p$ and energy ($2p^2/M$ of the mirror. The photon energy will therefore be $pc-2p^2/M$. For a mirror of one mole of glass (60g) and a photon of 500 nm (~2eV) that is a relative frequency change of $2p/Mc= 2/(6\cdot 10^{23}\cdot 10^9 \approx 3\cdot10^{-32}$. However this is not what wi... | {
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"timestamp": "2023-03-29T00:00:00",
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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... | The thing missing from your picture is the steep pressure gradients (and associated acceleration) at the inlet of the pipe. Far from the pipe inlet at the bottom of the tank, the pressure will be approximately hydrostatic; near the pipe inlet, it is anything but. The same thing can be observed at the drain of an emptyi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/576012",
"timestamp": "2023-03-29T00:00:00",
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Solving a momentum problem without the assumption I encountered the problem in Physics HRK:
A stream of bullets whose mass m is each $3.8$ g is fired horizontally
with a speed v of $1100 \frac{m}{s}$ into a large wooden block of mass that is
initially at rest on a horizontal table. If the block
is free to slide withou... | You will have to consider a series of incidents taking place.
When the first bullet strikes
*
*$$P_{f 1} = (M+m)V1=mv$$
After this as the mass adds to the block
*
*$$P_{f2} = (M+2m)V2=mv+(M+m)V1$$
.....`v is initial velocity of bullet
And so on you can calculate
`
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/576134",
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Can rolling without slipping occur without friction? If a body is rolling without slipping is it necessary that there is friction acting on it ? I encountered a question in which there is a spherical body and a force is being applied on its top point ...so if there is only force then it should do translation motion on... | As outlined in my answer here this is definitely possible.
If you have an object with moment of inertia $I=\gamma mR^2$ on a horizontal surface and you apply a constant horizontal force $F$ some distance $\beta R$ above the center of the object, then for rolling without slipping to occur we need a friction force
$$f=\f... | {
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Wave motion in a transverse wave I was learning about wave motion and how in transverse waves, each particle executes SHM up and down. If that is the case, how is it so that energy is still transferred onto the next particle? The logical answer should be that it disturbs the other particle, but if it moves up and down ... | In the case of transverse waves, the oscillations are at right angles to the direction of propagation of the wave. The wave itself is the transfer of energy from one point to another. Say the wave moves to the right (e.g., x-direction). Then the particles in the medium of the wave are moving "up and down" (y-direction)... | {
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Probability of measuring state $|+\rangle$ and state $|-\rangle$ given a state and a basis I am given a basis $|+\rangle = \frac{1}{\sqrt 2}(|0\rangle + |1\rangle)$ and $|-\rangle = \frac{1}{\sqrt 2}(|0\rangle - |1\rangle)$ and i am given a three qubit state $|\phi\rangle = \frac{1}{\sqrt 3}|1\rangle |0\rangle |1\rangl... | So I don't think your state is normalized and probably what was meant was $$|\phi\rangle = \sqrt{\frac13}|101\rangle + \sqrt{\frac23}|010\rangle.$$(But as written you can also normalize it by multiplying by $\sqrt{3/5}$ and converting the denominator to 5.)
There are several ways to do this problem. Possibly the easies... | {
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How is it possible that combustion of coal releases similar energy as TNT explosion while intuitively we would not expect that? According to Wikipedia, the energy released in a TNT explosion is 4 × 106 J/kg.
https://en.wikipedia.org/wiki/TNT
According to web, combusion of coal is around 24 × 106 J/kg.
https://www.world... | You’re basically talking about the difference between power and energy. A TNT explosion has vastly more power than the combustion of an equivalent amount of coal (in normal circumstances), because it happens over a vastly shorter timescale. And it’s the power that you notice, not the energy.
| {
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Do bodies radiate energy by emitting gravitons? As gravitons are formulated in current theories, are bodies supposed to radiate energy as they emit gravitons?
I thought that if bodies radiate energy, for big bodies this would be difficult to measure, as they emit a lot more energy in the form of heath, and smaller bodi... | Yes bodies radiating gravitons do radiate energy. That's why we were able to detect gravitational waves a few years ago, as you can see from the Wikipedia article on gravitational waves:
On 11 February 2016, the LIGO collaboration announced the first observation of gravitational waves, from a signal detected at 09:50:... | {
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Transformers: How does current in primary coil change? I was doing a question on transformers and found this really confusing question:
A 100% efficient transformer converts a 240V input voltage to a 12V
output voltage. The output power of the transformer can be a maximum
of 20W. The output is connected to two 0.30A b... | So the first thing we need to do is find the "step-down ratio". Due to how a transformer works, a small change in the secondary coil/output current will result in an even smaller change in the primary coil current.
*
*Ratio = $\frac{\text{Output Voltage}}{\text{Input Voltage}}$
= $\frac{12V}{240V}$
= $0.05A$
*Use t... | {
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Are distributions of position and momentum assumed to be independent in quantum mechanics? Given a wave-function of a single particle we can calculate probability density for positions. We can also calculate probability density for momenta. Are these probability densities assumed to be always independent?
Or, in other ... |
if we measure position and momentum of a particle (for example electron in hydrogen being in the ground state), should we expect that these two random quantities independent?
No. The momentum probability distribution and the position probability distribution have an inverse relationship with each other, which is a di... | {
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Direction of flow of Electrons during an Electric Shock Question:
What is the direction of the flow of electrons during an electric shock?
I was studying electrostatic force, suddenly a question struck my mind “What will be the direction of flow of electrons when I touch a live bare wire standing barefoot on the grou... | You are correct that if the wire has a lower voltage than the ground, then electrons would flow from the wire to the ground. If the wire has a higher voltage than the ground, then electrons would flow the other way. This completely depends on the voltage of the wire relative to the ground, which can be pretty much anyt... | {
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Why does metal change its color under polarized light? I've taken two photos of a metal in an experimental setup.
The first image shows the metal illuminated by a halogen-lamp from above. The second image shows the same metal illuminated by the same lamp but there are two additions: There is a linear-polarizing filte... | I’ll venture a guess at what’s going on. Take it with salt.
Aluminum is not a perfect conductor, but I do not see how how the variation of reflection coefficient with wavelength or the slight difference between HH and VV reflections could be responsible.
Your material is polycrystalline, so the surface is never truly ... | {
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Time transfer from proper to coordinate: apparent Special / General Relativity mismatching in theory In SR we've learned that the time dilation for an observer moving clock w.r.t one fixed in a frame at rest is
$$\tau = \gamma \tau_0 = \frac{\tau_0}{\left(1-v^2/c^2\right)^{1/2}}$$
ref: "Special Relativity - A.P. French... | Using bionomial approximation, French's equation equals:
$$\tau = \gamma \tau_0 = \frac {\tau_0} {\left(1-v^2/c^2\right)^{1/2}}\approx{\left(1+\frac{v^2}{2c^2}\right)\tau_0}$$
The second equation introduced by you, substituting $U=0$, also implies:
$$\Delta t\approx{\left(1+\frac{v^2}{2c^2}\right)\Delta\tau}$$
There is... | {
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Representation of homogeneous Lorentz transformation In Page 63, Section 2.5 of Weinberg's QFT Volume 1, on "One-particle states", he considers the representation of homogeneous Lorentz transformation, $U(\Lambda, 0) \equiv U(\Lambda)$
$$
U(\Lambda) \Psi_{p, \sigma}=\sum_{\sigma^{\prime}} C_{\sigma^{\prime} \sigma}(\L... | This is an example of induced representation. Consider two groups, $K < G$. Let a representation $D(K)$ act in a vector (usually, Hilbert) space ${\mathbb{V}}$. Based on this, we now wish to construct a representation of $G$. In mathematics, this (so-called "induced") representation is denoted with $\operatorname{Ind}_... | {
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Why can we see light further than it shines? This is a question I’ve been thinking about for a while. If I’m standing in the middle of a straight road, during night, I can see a car coming towards me because of its lights even if it is kilometers away. Notwithstanding, the driver can not see me because the car will bri... | Strictly speaking the following statement is wrong:
the car will brighten the road only few hundred meters further
The fact that you can see the light emitted by the car is evidence for the light illuminating all the way between you and the car.
Two main reasons can be named why you see the car but the driver does no... | {
"language": "en",
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"source": "stackexchange",
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Application of Noether Theorem I attempt to understand one of the examples of the application of Noether theorem given in Peskin & Schroeder's An Introduction to Quantum Field Theory (Page no. 18, Student Economy Edition). The relevant portion of the text is given below.
If I understand the derivation and the correspo... | The Euler-Lagrange equation is not automatically satisfied by $\mathcal{L}$. It's the other way around. Given $\mathcal{L}$, you can find the classical equation of motion satisfied by the field $\phi$. This is like giving you a formula for the force in Newtonian mechanics. Even if you know $F$, you still need to know N... | {
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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... | Rather than thinking of the plates as solid line charges, think of them as lines of infinitely many point charges.
2 point charges will have a straight field-line directly between them, and weaker curved field-lines outside of that. If you place 2 pairs of point charges next to each other — positive with positive, an... | {
"language": "en",
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Particle as wave, stable? I've started reading about the wave-particle duality but, after a few steps, reached a dead end:
*
*Schrodinger equation solutions for a free particle is a sum of terms of the form:
$$\psi(\mathbf{r}, t) = Ae^{i(\mathbf{k}\cdot\mathbf{r}-\omega t)}$$
however, a single element of this form c... | It's right, you cannot normalize a plane wave.
But... remember that plane waves cannot exist in nature, because nothing is actually infinite. Plane waves do not exist, no matter what waves we're talking about.
But! They are a nice approximation for many situations. You can approximate many usual waves to be plane, and ... | {
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A photon scatters an electron at an angle... Does it imply electron having an area greater then the photon's? Even we don't know much about scattering areas of photons and electrons does the fact that a photon scattering an electron at an angle mean that the photon cross-section area hits only a small lateral area of t... | Photons and electrons are elementary particles in the standard model of particle physics, SM , a quantum field theory model.
They are by axiomatic definition point quantum mechanical particles and their behavior is perfectly described by the SM. Their scattering can only be described within this quantum mechanical fra... | {
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Am I understanding the equivalence principle correctly? So Einstein stated that gravity and acceleration are the same things in a local reference frame (please correct me if I misstated that).
Here is what I think I understand and want you to verify if it is correct:
In Special Relativity, the faster you go, the more t... |
Because gravity and acceleration are the same thing, does that mean that the time dilation when near a gravitating mass is the same time dilation as when you are at a very high speed? Are these two things connected/the same?
No. In fact concerning GPS satellites SR effects and gravitational effects can compete each o... | {
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How to measure the force produced by a finger? If I push my finger onto a weighing balance and it reads 100g, then how do I calculate the force produced by my finger? Do I just use F = mg? Or is this even possible?
| Yes, You are correct. A balance actually measures force, but the readout is conveniently scaled to tell you how many grams of mass would feel that same force from gravity near the surface of the Earth.
All you have to do is reverse that scaling to get the force in Newtons.
| {
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Force exerted by blocks on an angled rail I'm trying to figure out the force exerted on blocks positioned on an angled rail due to gravity. This is the scenario I have (apologies for the poor graphic):
where each block (red square) is equipped with a wheel (black circle) which is fitted on a rail (black lines). The to... | In this situation, the vertical component of the (normal) force of the track acting on the upper block supports part of the weight of the upper block. The problem is to find that normal force. To keep the upper block from rotating there must be a horizontal friction force from the block below acting on the bottom of th... | {
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Why do aluminium sheets wrinkle easily but are hard to un-wrinkle? I notice when I buy aluminium sheets (the kind used for wrapping food) they come in straight, smooth rolls. Once I use them though, they become wrinkled, and they are impossible to un-wrinkle. Image of a wrinkled sheet:
Why is this the case? Only thing... | When the Aluminium sheet has been deformed beyond the elastic limit the bonds between the Aluminium atoms have been broken/deformed irreversibly.
This is called plastic deformation.
So a small amount of deformation (elastic) will allow the Aluminium sheet to revert to its original condition when the deforming force is ... | {
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"url": "https://physics.stackexchange.com/questions/579314",
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What does $\hat{\phi}$ mean in cylindrical coordinates? When talking about the unit vectors in cylindrical coordinates, $\hat{\phi}$ often comes up. However, I cannot find a straightforward meaning for it. However, I do know that it is perpendicular to $\hat{\rho}$. How is that significant?
| From the linked article it shows exactly what the vector $\hat{\theta}$ means
There it is, a unit vector pointing around the "hoop" direction, tangent to the surface and perpendicular to the axial direction $\hat{z}$.
| {
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Is it possible to bend light without changing its color? It seems to me that whenever you change the direction of a wave it also affects frequency. Would this not also be true of light waves bending from, for example, gravity?
| You are specifically asking about gravitational lensing, that is a distribution of matter between a distand lightsource and the observer, that is capable of bending the light from the source as the light travels towards the observer.
If the (light) source, the massive lensing object, and the observer lie in a straight... | {
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How do astronomers detect the spin of the black holes? There are various theoretical models for accretion disks and relativistic jets from black holes that considers the black hole to be either rotating (Kerr geometry) or non-rotating (Schwarzschild geometry). But when astronomers detect a source, they detects whether ... | Here is from the abstract of a paper about theory and observation of the spin of a black
..non-zero spin leaving an indelible imprint on the space-time closest to the black hole. As a consequence of relativistic frame-dragging, particle orbits are affected both in terms of stability and precession, which impacts on th... | {
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Why do waves, specifically light, diffract through a slit? I've been wondering this for a while now, and have thus far only come across answers that seem to use an equation as an explanation. I've also looked at Huygens' principle (albeit not in-depth), but this doesn't make much logical sense to me.
I'd sincerely appr... | Light diffracts primarily because there is an interaction of the EM field of the aperture material with the EM field of the photon or wave. Diffraction is interesting in itself but it is also the diffraction pattern or "interference" pattern that results which causes a lot of discussion. The word
"interference" is hi... | {
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Why are the capacitors in this circuit in parallel but not in series?
In the circuit, the capacitors are said to be connected in parallel. Why is that so?
Edit: The switch will be closed and C2 is fully charged by C1 and no more current will flow between C1 and C2. The question asks for the voltages and charges hold b... | They are in series, one end of the first capacitor contacts one end of the other. They are also parallel when the switch is on, because they both connect two ends.
Parallel connection means both ends of the two elements are connected together. This happens when you turn the switch on. Both ends of C1 becomes connected ... | {
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Electric Potential Energy - How a charge can be brought from infinity to a point without accelerating it? Question:
My Book says:
ELECTRIC POTENTIAL ENERGY: Electric potential energy of a charge($q_o$) at a point(A) in the electric field due to any charge is given by the work done by an external force to displace $q_o... | You can assume that in the beginning you have a very, very small acceleration resulting in v, from then on you have no force so your last equation ist true, at the end you still have m/2v^2 left for your energy balance.
| {
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What is the polarization of an EM wave after it suffers scattering? If a linearly polarized classical monochromatic electromagnetic radiation undergoes a scattering, does the scattered electric field have the same polarization as the incident electric field? I am looking for an answer (or deduce the conclusion mathemat... | It depends on what the wave is scattered from. The simplest case to study (as an exercise to get intuition) is scattering of a monochromatic EM wave in vacuum from an infinite metal plane: in this case the boundary condition is that the component of the electric field along the surface should be zero. This may add a ph... | {
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How the matrix representation of a Hamiltonian affects the eigenvalues? Suppose we're given the following Hamiltonian: $$\hat{H}=\frac{\omega}{\hbar} \left(\hat{S}_+^2+\hat{S}_-^2\right)$$ Suppose also that we measure $\vec{S}^2$ and get $6\hbar^2$, i.e. reduced to the $s=2$ subspace, and want to find all the possible ... | Your 2 matrices only differ by the same rearrangement of rows and columns, which does not change the eigenvalues. To be precise, let $P$ be the permutation that takes $\{|2,2\rangle,|2,1\rangle , |2,0\rangle , |2,-1\rangle , |2,-2\rangle)\}$ to
$\{|2,1\rangle , |2,-1\rangle , |2,2\rangle, |2,0\rangle , |2,-2\rangle)\}... | {
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Why is the mean density the same for all nuclei? Tell me if this is a correct theory? So the radius $R$ of the nucleus is directly proportional to $A^{1/3}$ (the nucleon number).
As $$V = \frac 43 \pi r^3,$$ this makes $V$ directly proportional to $R^2$. Also, as the nucleon number increases, the mass also increases an... | Density is $$\rho = \frac mV$$
Expressing for nuclei mass and volume, gives :
$$ \rho = \frac{A\,\mu}{4/3 \,\pi \left(r_o A^{1/3}\right)^3} $$
Simplifying gives :
$$ \rho = \frac{\mu}{4/3 \,\pi~ r_o^3 } $$
Where $r_o = 1.25 ~\text{fm}$ and $\mu$ is typical nucleon mass. Thus nuclei density is constant.
| {
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Eddy current confusion Every source tells that eddy currents are produced by change in magnetic flux in conductor, but according Gauss' law for magnetism net flux over a closed surface is 0, then how magnetic flux will change to produce eddy current?
| Gauss' law for magnetism net flux over a closed surface is 0.
The polarity of static fluxes balances out to 0.
Static magnetic fields do not create eddy current losses because of the lack of motion of charges. You either need a moving magnetic material or a dynamic/alternating current or both.
The external flux is red... | {
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"url": "https://physics.stackexchange.com/questions/580696",
"timestamp": "2023-03-29T00:00:00",
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Ceiling fans with just one large winglet? I am from India and in India ceiling fans have generally three wings.
Today while laying on my bed a question came in my mind.
First of all, I know that if we use just a single wing at a time of same dimensions as each wings of a three winged fans have then it will reduce the a... | @trula comment is correct. The fewer the blades the more unbalanced the air load on the fan putting more stress on the bearings. It is similar to what happens to a top loading washing machine in the spin cycle if the clothes are concentrated on one side of the tub as opposed to being distributed around the center of ro... | {
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Find the emf in the loop by two methods In the Figure below assume the magnetics are shaped such that the magnetic field is in
the $z$ direction and varies as
$$
B_0 = B_m\left(1-\frac{x^2}{a^2}\right)\hat{z}
$$
Find the emf in the loop by two methods, a) the rate of change of flux b) the motional
emf method.
My try:
$... | Ok, we want to calculate the emf induced in the rotating coil. The B magnitude in the z direction (horizontal) depends on x (vertical position) as shown below:
$$emf = \oint \mathbf{E} \cdot \mathrm{d}\boldsymbol{l} = - \frac{\mathrm{d}}{\mathrm{d}t} \int \mathbf{B} \cdot \mathrm{d}\mathbf{a}$$
In other words, the e... | {
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Magnetic, geographic and geomagnetic poles
Can someone explain me in simple terms where and what are the magnetic, geographic and geomagnetic poles?
Some sites say that magnetic north pole is in the south and thus it attracts the south pole of the magnetic needle while some say the north pole of the needle points sou... | The North geographic pole is where the effective axis of rotation meets the surface at the North end of the earth. The North (seeking) pole of a magnet is the end which swings toward the North (if its mount allows it to turn). The magnetic field of a magnet emerges from the North (seeking) pole, loops around, and ree... | {
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Newtonian approximation of the metric tensor I was reading Dirac's General Theory of Relativity. In chapter 16, the Newtonian approximation, we start with
Let us consider a static gravitational field and refer it to a static coordinate system. The $g_{\mu\nu}$ are then constant in time, $\frac{\partial g_{\mu\nu}}{\pa... | I think the key phrase is "and refer it to a static coordinate system."
It isn't so much that a static spacetime implies the metric takes a particular form, but that you can choose a coordinate system such that $g_{m0}=0$.
A good exercise would be to start with with a metric where every component was time independent, ... | {
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Will energy in an LC circuit become 0 if its is disconnected when the capacitor is fully discharged? In a recent test I had a question in which there was an LC circuit with an inductor a capacitor and a switch. According to the answer key
If switch is opened when capacitor is fully charged energy of LC system remains ... | When the capacitor has no charge, the energy is in the magnetic field of the inductor, which is associated with a current flow. If the switch is open, the current cannot flow. The magnetic field collapses, leaving no energy. (The collapse of the field will cause a large voltage spike, and probably an arc across the op... | {
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Will the sky be full of rainbows? I saw this article and something really wierd came in my mind.
What would the sky look like on those planets of our solar system where rainfall of diamonds occur? Will it be full of rainbows? Has it been ever captured?
I don't know whether it will be full of rainbows or not but there ... | Unlikely. The strong primary rainbow on earth happens because the sun location and the water locations are limited. If you tried to make a sky full of rainbows, it would just smear together into white.
Ice crystals commonly form in earths atmosphere. Like diamonds, and unlike water droplets, these disperse light in ... | {
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Ordering ambiguity in the Feynman propagators obtained using Wick's theorem Applying Wick's theorem to a string of four field operators, $\phi_a\equiv\phi(x_a)$:
$$T(\phi_1\phi_2\phi_3\phi_4)=\{...\}, \tag{1}$$
we obtain several terms, three of which are fully contracted fields: $$\phi_1^{\bullet}\phi_2^{\bullet}\phi_3... | In Wick's theorem, it is usually assumed that contractions supercommute with all pertinent operators, cf. e.g. my Phys.SE answer here. With this assumption there are no ambiguities in operator-ordering as long as one observes the sign rule for manipulating Grassmann-graded objects.
| {
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Increase in internal energy and temperature of a thermodynamics system A banquet hall ($150 m^3$) is to be used for a formal dinner for 20 persons. Each person occupies $0.075 m^3$ of space and has an average heat transfer rate of $500 \frac{kJ}{hr}$. If the AC system fails, determine the increase in the internal energ... | If the walls are rigid then the system is isolated the total change in internal energy of the system (humans +room air) would be zero.
But when we consider the air in the room as the system the humans are then the surroundings. Any work done by or on the air in the room is due to the expansion and contraction of the hu... | {
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Solutions of the Harmonic Oscillator are $not$ always a Combination of Separable Solutions? Are there solutions of the Schrödinger equation that are not a linear combination of separable solutions and how do we find them?
In Griffiths, Quantum, Prob. 2.49, there is a solution of the (time-dependent) Schrödinger equatio... | Sometimes the expansions are not obvious. For example The harmonic oscillator time-dependent Schr"odinger equation
$$
i\partial_t \psi = -\frac 12 \partial^2_x \psi +\frac 12 \omega^2 x^2 \psi
$$
has a ``breathing'' solution
$$
\psi(x,t)= \left(\frac{\omega}{\pi}\right)^{1/4}\frac 1{\sqrt{e^{i \omega t} +R e^{-i\om... | {
"language": "en",
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How does light, which is an electromagnetic wave, carry information? We see an object when light from a source strikes the object and then reaches our eyes. How does light, which is an electromagnetic wave, gets encoded with the information about the object? Do the individual photons get encoded with this information o... | Assume Light is a being.
Light doesn't carry information. All it does is, just pass through, if the object it hits, allows it to pass through or it gets reflected back.
Example 1 :
Infrared Laser in Scanning barcodes.
Barcodes are nothing but alphanumerics shrinked in size. When infrared laser is allowed to hit it. Eac... | {
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Doubt on net acceleration during non-uniform circular motion During non-uniform circular motion, the direction of net acceleration is not in the direction of the centripetal acceleration, then why does a particle still move in a circular path, please explain.
| Think of a car going round a circular track. At an instant when it has speed $v$ it has an acceleration of magnitude $\frac{v^2}{r}$ towards the centre of the circle. The car is gaining velocity towards the circle centre. But suppose that, at this instant, the driver is making the car go faster. The car will also be ga... | {
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If an electron-hole pair is formed, where does the electron "go"? I've seen the explanation before that holes are basically electron deficiencies in an atom and that the hole "moves around" by electrons from surrounding atoms shuffling to fill that spot which is a very spatial way of viewing what a hole is. However, wh... | It is also not very clear to me. I try below an explanation.
For a single piece of doped semiconductor, I agree that there is no meaning in talking about holes "moving" from place to place in the k-space.
But in a junction, the band structure is not constant due to the diffusion of the dopants atoms. It can be thought ... | {
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Understanding the Functional Poisson Bracket In classical field theory (for a single field $\psi$) the dynamical variables are defined to be functions of the fields $\psi$, $\pi$, $\partial_{x_{i}}\psi$ and maybe $\mathbf{r}$, where $\pi$ is the conjugated field to $\psi$.
For $F=\int\mathcal{F}\,d\mathbf{r}$ and $G=\i... | You are on the right track, but some clarification is needed. First as you mentioned, the Poisson bracket is defined over functionals of the local fields, i.e. an object of the form $F=\int d^n x {\cal F}[\psi(x),\pi(x)]$. Note that here we integrate over $x$, so $F$ is not a function of $x$. Accordingly, your last equ... | {
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In turbulence what to we mean that an eddy has a wavenumber k? In turbulence what to we mean that an eddy has a wavenumber k?
|
In turbulence what to we mean that an eddy has a wavenumber k?
Not all eddies are created equal, if you will. That is, they need not be all the same spatial size. Different wavenumbers correspond to different length scale fluctuations. One of the basic ideas of turbulence is that energy cascades from large to smal... | {
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Are there Interpretations of Classical Mechanics, Classical Electrodynamics, and/or Relativity (either Special or General) Just like Quantum Mechanics has many interpretations (Copenhagen, Many-Worlds etc.), do any other theories in Physics have multiple interpretations? For example, does Classical Mechanics, Classical... | Classical theories do not have multiple interpretations in the same way quantum Mechanics does. All theories require some sort of interpretation - i.e. a way to tie the mathematics back to the "real" world, however classical theories use concepts such as mass, position, time, EM fields about which there is little real ... | {
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Does the oscillating electric and magnetic field of a photon generate gravitational waves? From my understanding, little as it may be, because photons have energy they warp spacetime. The energy is expressed as an oscillating electric and magnetic field. Would this mean that the energy is also oscillating and would gen... | A “photon” is a quantum entity while “gravitational wave” is an entirely classical (non-quantum) concept. Generally, a good classical description of a quantum physical system could only be achieved when the number of quanta is large. Consequently, question about a single photon generating a (classical) gravitational wa... | {
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Perpetual motion: Conditions for rolling a wheel sliding on a bar This is a basic question about energy conservation and classical mechanics:
Question: Under what situations can this motion be perpetual?
*
*Without gravity and without frictions.
*Without gravity and with frictions.
*With gravity and without fri... | Yup, perpetual motion. The playground for physics hobbiests. Inside a proton, perhaps..But nowhere else. So your question, to spite the conditions you established, is moot.
There is no perpetual motion.
| {
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How can a 2-sphere exist in Euclidean 3-space? I don't know if this is a simple question to answer however, I have trouble understanding how a spherical object (such as a planet) with positive curvature can exist in Euclidean 3-space with no curvature. From my understanding Euclidean geometry seems to be the most likel... | I think you are confusing the positive-curvature of the object's surface with the curvature of the ambient space.
We can draw a 2D sphere in 3D Euclidean space. the curvature of the surrounding space would be 0, but the induced curvature on the sphere would be positive.
Just as a comment, a physical massive object does... | {
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Similarity of particle in a box and free particle It can be shown that particle in a box and free particle have the same energy at certain wavenumbers (at an integer multiple of $\pi/L$ , where $L$ is the length of the box)
I am aware that the general wavefunctions of the two particles spoken of are different, but I ca... | The particle in a box is simply a free particle which lives in a compact interval $[0,L]$ rather than $\mathbb R$, and whose energy eigenstates are chosen to vanish at the endpoints. In other words, the free-particle energy eigenfunctions$^\dagger$ satisfy $-\frac{\hbar^2}{2m}\psi''(x) = E\psi(x)$, while the particle-... | {
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If objects in motion experience time differently, how does my body stay synced when I move my legs or arms? If I move my swing my arm really fast, the matter in my arm should experience time slower than the matter in my body.
So how does my body still sync with each other?
And a more general question that derives from ... |
If I move my arm really fast ...
We humans think we can move quickly. We can't. When compared with the micro-machines that make up our bodies, we are actually huge giants moving incredibly slowly on a low-gravity planet. We only think we move fast because our brains are slow. Luckily they are fast enough to keep our ... | {
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Many-world interpretation of double slit experiment Different interpretations of young's double slit experiment is available, I read Copenhagen and Feynman's path integral interpretation of double slit experiment; former uses the idea of wave function and later uses the idea of infinite paths and sum over the weight f... |
It would be great helpful if someone give a nice explanation that, how famous double slit experiment is explained using Many world interpretation of quantum mechanics?
In the "one photon double slit experiment" an infinite number of photons leave the light source, go through an infinite number of screens, and hit an ... | {
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Why is the isotope Nitrogen-14 formed preferentially to Nitrogen-15 in the CNO-cycle in stars? Most of the universe's nitrogen is formed in larger, main sequence stars using the CNO Cycle, right?
But I cannot find a good, specific explanation as to why $^{14}$N, with both an odd number of neutrons and protons, is forme... | Both $^{14}$N and $^{15}$N are produced as part of the CNO cycle during the hydrogen-burning main sequence phase of stars more massive than the Sun. However $^{15}$N reacts rapidly with protons to (re)form $^{12}$C and an alpha particle, whereas the much slower $^{14}$N$(p,\gamma){}^{15}$O reaction allows $^{14}$N abun... | {
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How the classical linear correlation of spin is derived?
I found this image on Wikipedia under Bell's theorem. I understand the blue curve generated by quantum mechanics, but couldn't understand how the classical curve (red curve) is generated (I don't understand how correlation changes with angle, classically). This ... | The classical correlation is obtained by averaging the measurement results depending on the direction of measurement and the incoming photon polarization (physically, but the lambda could be any data, provided all of them are averaged) :
$$C(a,b)=-\int A(a,\lambda)A(b,\lambda)d\lambda$$
The case of linear correlation ... | {
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Why do the Dirac-Maxwell Lagrangian and the QED Lagrangian look the same? I know that QED is some kind of second quantized version of the Maxwell-Dirac theory. But why is it that this modification to a second quantized version is just to replace the scalar function $\Psi$ by a field operator $\hat{\Psi}$?
| Your observation is that the field operator $\hat\Psi$ is supposed to satisfy the field equation of the classical field $\Psi$, i.e. the Dirac-Maxwell equation derived from the classical Lagrangian $$\mathcal{L}=\Psi (i\gamma^\mu D_\mu - m) \Psi \quad+\quad ...$$ where $D_\mu = \partial_\mu -i e A_\mu$ is the covariant... | {
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Why Bose-Einstein condensate is superconducting Im looking into Quantum Computing, where the BCS Theory is used to build Qubits with a BEC.
Why does the Bose-Einstein Condensate not interact with other particles and hence has no dissipation?
In other words how does the BEC form a superconducting material. Why is there ... | So I assume you know in the BCS theory, fermions form Cooper Pairs (bound electrons) at very low temperatures. Since their paired state has a lower energy than the Fermi energy, they are bound. So the pair is now a composite boson with spin 0 or 1 instead of the fermions spin 1/2.
This allows them to "condense" into th... | {
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How to convince myself that capacitance cannot be a function of voltage? My textbook states that:
...The capacitance $C$ depends only on the geometrical configuration (shape, size, separation)of the system of two conductors. [As we shall see, later, it also depends on the nature of the insulator (dielectric) separatin... | Capacitance does depend on the applied voltage.
I think what the author means is that for many substances, capacitance will not change regardless of the potential differences between the plates. He could also mean that for the same voltage different substances will cause different capacitance.
Consider two plates with ... | {
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Why doesn't planet Earth expand if I accelerate upwards when standing on its surface? According to General Relativity I am being accelerated upwards by planet earth while writing this question. But a curious person on the the other side of the planet relative to me would have the same experience. That means we are acce... | That is because we are just accelerating radially outwards and not "moving" radially outwards. This case is analogous to circular motion where there is radial acceleration but no radial movement.
You can refer to my article in the link below for detailed explanation:
https://paribeshregmi.medium.com/a-soft-intro-to-gen... | {
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What is the difference between Luminous intensity and intensity of illumination? What is the difference between the Luminous intensity and intensity of illumination? Please explain with units and dimensions as well! I googled but I partially understood it!
| From this Wikipedia article:
The luminous intensity for monochromatic light of a particular wavelength λ is given by:
$$I_{\nu}=683\cdot \bar y(\lambda)\cdot I_e,$$
where
$I_{\nu}$ is the luminous intensity in candelas (cd),
$I_e$ is the radiant intensity in watts per steradian (W/sr),
$\bar y(\lambda)$ is the standar... | {
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How to determine the power of a magnifier lens empirically when no values are given? I have several magnifiers/magnifying-glasses of varying quality with either nothing inscribed on them, or power ratings that I think are wrong.
How can the power of a magnifier be determined when no values are given?
Kyle Downs at quo... | The power of a magnifying glass is relative to the near-limit distance of the standard human eye (25 cm). The lens makes it possible to bring the object closer to the eye, so that it subtends a larger angle than at the near limit. The ratio of the (tangent of the) angles is proportional to the ratio of these distances.... | {
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Rotating current carrying loop Consider a circular loop of wire fixed on the rim of a wheel. This wire carries a current 'i' in it. When the wheel is at rest, which basically means that the current carrying loop is at rest, the magnitude of magnetic field at the center is, say B1. If I set the wheel in motion with a co... | The situation resembles alot to a rotating loop. So I'm using this as a hint .The formula for calculating magnetic field at the centre of a current carrying loop is directly proportional to i/R. We see that when the ring rotates the current in a small area remains constant.
This is because when the loop rotates the pa... | {
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When a sphere is in pure rotation, will all particles in its surface have same linear speed? Imagine this sphere to rotate about its diameter, from the centre to the point of surface if we take all of them have equal distance that is 'r(radius of the sphere)'.So same linear speed right? I looked up many sites but they ... | The distance to be considered is axial. You have various slices wich give different circumferences (varying radius) with a maximum at the equator.
Take for instante a cylinder: then you have only one axial radius. But the sphere has different level curves
| {
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Is spin necessary for electromagnetism? I know that spin is needed for defining the magnetic moment of any particle, and I have also read that the spin actually is the reason why some materials are magnetic. What I want to know is whether spin is necessary for the some interactions in the electromagnetic field.
Let me ... | Classical electrodynamics is formulated in terms of macroscopic (i.e. averaged over many atoms/particles) fields and sources (currents and charges). It is fully condensed in Maxwell equations and supporting material equations (describing how the sources respond to the fields). As such it does not need spin, simply beca... | {
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Are wormholes evidence for traversal of a higher dimension? Warning, pop science coming.. please correct what I’m getting wrong. Einstein’s equations of relativity showed the potential for existence of wormholes that can connect different points in space time. I understand the mechanisms for their practical implement... | Agree to Rd Basha. Embedding spaces are only necessary for the mathematical constructions. They don't necesserily have physical reality.
Like the mathematics of a 2-sphere is easier if it's embedded into a 3-dimensional Euclidean space.
But the 2-sphere happily exists without a third physical dimension.
| {
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Why does light hitting a charged particle cause it to oscillate? I am trying to study the classical Physics interpretation of light hitting a charged particle.
Why does light hitting a charge particle, such as an electron, cause it to oscillate?
Is it because the light hitting it produce an electromagnetic wave, which ... | In classical electromagnetism, light is an electromagnetic (EM) wave. Photons are quantum objects that are absent in classical physics.
EM-waves are composed of oscillating electric and magnetic fields. Charged particles are sensitive to EM fields, which make them move in a definite direction. Then if the EM fields osc... | {
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Skyrmion number The skyrmion number is defined as
$$n=\frac{1}{4\pi}\int\mathbf{M}\cdot\left(\frac{\partial\mathbf{M}}{\partial x}\times\frac{\partial\mathbf{M}}{\partial y}\right)dxdy$$
where $n$ is the topological index, $\mathbf {M}$ is the unit vector in the direction of the local magnetization within the magnetic... | It is not a curl. This can be seen by expressing the curl in vector components.
$$\nabla \times \mathbf M=\begin{pmatrix}
\partial_yM_z-\partial_z M_y\\
\partial_zM_x-\partial_x M_z\\
\partial_xM_y-\partial_y M_x
\end{pmatrix}$$
Here $\partial_x$ denotes the partial derivative with respect to $x$. The quantity $\partia... | {
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Is $U^\dagger(R)\hat{H}U(R)=\hat{H}$ always true? Consider a Rotation transformation on momentum state,
$$U^\dagger(R)\hat{\mathbf{p}}U(R)=R\hat{\mathbf{p}}$$
Now the question is whether,
$$U^\dagger(R)\hat{H}U(R)=\hat{H}\,?$$
Here, $\hat{H}$ is the Hamiltonian of a free particle. Is it always true? Is there any counte... | Base transformations of a scalar operator (H) and the vector operator's spatial rotation are confused here, I think. Try to rewrite it in bra-ket notation.
Coordinate -> momentum space transformations also done in $ UHU^{-1} $ way and it really changes H.
| {
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Why is the potential not infinite? One way to calculate potential (using infinity as our reference point) is to sum all the contributions of charges that are around.
Let's say I want to calculate the potential at some point on charged surface.
At that point, there is some charge (can be infinitesimal) and that charge s... | No, it would not necessarily mean infinite. This is a classic mathematical misunderstanding regarding limits.
If you have a fraction,
$$\frac ab,$$
and you let the numerator tend to zero, $a\to 0$, then the fraction might tend towards zero:
$$\frac ab\to\frac 0b=0\; \text{ for } \;a\to 0.$$
If you instead let the denom... | {
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Curl of electric field is not zero in the case of a steady current in a loop Say we got conducting circular loop connected to a battery . The electric field inside the loop obeys equation $\vec{J}=\sigma \vec{E}$.
Since the current flows in a circumferential way around the loop the electric field will be circumferenti... | You can easily see that for a stationnary circuit the curl of the electric field should be $0$ (as you mentionned, this comes from the Maxwell-Faraday equation).
However, this is not contradictory with the fact that $\overrightarrow{E}$ seems to be circumferential. $\overrightarrow{J}$ is indeed circumferential but $\o... | {
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Can we apply Stefan's law to find how much energy a body absorbs? Stefan's law tells gives an expression for thermal radiation emitted per unit time by a body of surface area A and temperature $T$
$$ u = \sigma A e T^4$$
In my book, it is written that in thermal equilibrium the energy of a body radiated out by stefa... | If the question is why the energy absorbed per unit time is the same irrespective of the body's temperature, then the answer is: this is not strictly true, because emissivity $\epsilon$ and area of the surface of the body $A$ depend on temperature. But if the temperature changes are small, this effect may be too small ... | {
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Angular momentum operator for Dirac equation The orbital angular momentum operator is given by
$$L_i=\epsilon_{ijk}x_j p_k$$
where $x$ and $p$ are the position and momentum operators.
In the Dirac equation, the hamiltonian operator is a 4x4 matrix. Will $L_i$ then also be a 4x4 matrix, which is given by $$L_i=\epsilon_... | Formally all linear operators are $4\times 4$ matrices,
because they need to transform Dirac-spinors to Dirac-spinors.
Therefore all those operators, which don't mix the components of Dirac-spinors
(like $x_i$, $p_i$, $L_i$), contain $I$ (the $4\times 4$ identity matrix)
as a factor.
| {
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If you keep the center of gravity of two objects on each other would you never be able to separate them? To find the attractions between planets and stuff like that, you use the center of gravity/mass to apply to Newton's equation. So even if those planets collided into each other, you could separate them if you give e... | No. When centered, your two concentric hoops don’t exert any net force at all on each other. There is a net force in other positions, but never an infinite force. You can separate them.
| {
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How to use Ampère's law in this problem? I want to prove that the magnetic field inside a cylindrical cavity in a long, cylindrical conductor carrying uniformly distributed current i and having radius R is uniform. The radius of cavity is 'a' and it's axis is parallel to the main conductor axis. However the axis of cav... | This is a standard "trick" question. You compute the field due inside the fat conductor carrying a uniform current I amps per unit area and ignoring the cavity. This is a standard Ampere law calculation and gives you circumferential field proportional to the distance from center of the fat conductor. You then comput... | {
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Is the Green function of electromagnetism a scalar or a tensor? When I check classical electromagnetism books Maxwell equations
\begin{equation}
\Box A^\nu (x)=\frac{4\pi}{c}j^\nu (x)
\end{equation}
can be solved using a scalar Green function $G(x,x')$
\begin{equation}
A^\nu (x)=\int G(x,x')j^\nu (x')d^4x'
\end{equatio... | It is a scalar or a second rank unit tensor, which amounts to the same. The boundary condition argument does not hold because physically a boundary condition can only be realised by additional charge-current distributions, that is, the boundaries are sources of field themselves.
| {
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Why don't we use the concept of axis of mass in place of center of mass? Being a high school student, I read the concept of center of mass and it was written in my book that
When a spinning ball is projected with some velocity , then all the points on the ball have complicated paths except the center of that ball whic... | Take a globe. Spin it around its normal axis, the polar axis the way the Earth spins. Then pick the globe up and while it is still spinning the first way, flip it north to south the way you would a coin. There you have a sphere spinning over two axes at the same time and your axis of mass makes no sense. The center ... | {
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Can quantum measurements be the origin of thermodynamic arrow of time? We can practically consider that the microscopic interactions are symmetric with respect to time(as we can neglect weak force for many cases which is the only interaction that can violate $T$ symmetry). So I thought that the asymmetry might be due t... |
Do they mean that the universe had a very low entropy at the beginning?
Yes, the universe had a very low entropy immediately after the Big Bang. It was filled with a very uniform distribution of very energetic (very "hot") fundamental particles. Due to the effect of gravity, this uniform distribution is actually a hi... | {
"language": "en",
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How is a free theory defined? In field theory, I've seen a free theory described as
*
*A field with the specific Lagrangian density ${\cal L}=|\partial\phi|^2+m^2\phi^2$
*A field whose equation of motion yields a linear set of solutions
*A field with non-interacting i.e. free normal modes
The first seems too speci... | I think these might all be equivalent up to change-of-basis. The definition I have heard is "Lagrangian is bilinear in the fields", which I think is also the same.
In the basis in which the bilinear operator is diagonal, the equations of motion are linear, so (2) and (3) are the same up to change-of-basis.
If the field... | {
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How is torque transmitted between inclined surfaces? In the picture below, in a), a body K1 is pivotably attached to a bearing. My question is about the torque that results from a force exerted onto a surface of the body K1.
A first force F1 applied orthogonally onto the surface should result in a torque M1 in clockwis... | I think friction is required for any torque to be applied CCW, which be definition works against torque being applied CW. So with no friction it would be net torque CW, but with "infinite" friction (i.e. no slipping) it would be net torque CCW (and also locked up and not spinning). I don't think this question can be so... | {
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Does the Bell test preclude localism, realism, both, or just one of either (indeterminate)? I saw this excerpt from the wikipedia article on EPR paradox
They postulate that these elements of reality are, in modern terminology, local, in the sense that each belongs to a certain point in spacetime. Each element may, aga... | The violation of Bell inequalities proves that quantum mechanics is incompatible with the assumption of local realism (rather than with the assumptions of locality and realism), in the sense that either the one or the other or even both turn out to be false.
| {
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Reduced density matrix: Derive or postulate? Let us consider a quantum mechanical system of interest S that interacts with the environment E. Then, the reduced density matrix
$$
\hat \rho_\mathrm{S} = \mathrm{Tr}_\mathrm{E} \{ \hat \rho \}
$$
is the partial trace over the environment, where $\hat \rho$ denotes the ... | As indicated in the answer by @Vadim the expression you give is a definition of the reduced density matrix. From this definition, the Born rule and some probability you can prove that the reduced density matrix carries information about the marginal probability distribution for the subsystem which it describes.
| {
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Why is the electrostatic force felt in straight lines? When two positive charges are kept close, they get repelled in the direction of a line joining both the charges. Why is it so?
Also, why is the repulsion in a straight path?
In both the cases, the potential energy of the charge which gets repelled decreases. What... | Great question!
Perhaps you're familiar with the idea that the force on an object is the negative gradient of the potential energy created by that force*:
$-\vec{\nabla} PE(x,y,z) = \vec{F}(x,y,z)$
Now, imagine any slope. The gradient vector at any point on that slope points in the direction that you would step to incr... | {
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I Need the Z-Machine's Circuit Diagram Where can I find a copy of the circuit diagram for Sandia Lab's Z-Machine, or indeed for any pulse forming network that outperforms the ordinary Marx bank (if such a thing exists)? Google has let me down in my search for this information. TIA.
| A recent Physics of Plasmas on the Z Machine has a high level overview with copious references to the fundamental technology. However, it is not clear just how detailed of a 'circuit diagram' you want. Simulations using standard electrical engineering analysis tools, while useful as rapidly calculated analogs of the ma... | {
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Describing small, NRQM systems purely in terms of photons Is there a canonical way to describe an open, non-relativistic quantum system with density matrix $\rho(t)$ entirely in terms of the light that it emits and absorbs (and vice versa?) Or is it possible in general for a density matrix trajectory $\rho(t)$ to be in... | For Markovian systems, this is possible in a certain sense. If the quantum system is linearly coupled to the bath (which is usually the case, e.g. in light-matter interaction, in cavity-bath interaction etc.), one can write an input-output relation
$$\hat{b}_\mathrm{out}(t) = \hat{b}_\mathrm{in}(t) + i\kappa\hat{a}(t)$... | {
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Confusion about the dimension of a Hilbert Space in Quantum Mechanics In Quantum Mechanics, the quantum state of the physical system lives in an infinite-dimensional Hilbert space and can be written in terms of two different bases, the position basis (uncountably infinite) and the energy basis (countably infinite). App... | Note that the "position basis" is not a basis, because its elements $|x\rangle$ are not elements of the Hilbert space. It is a useful structure to work with, but making mathematically rigorous statements about it can be quite tricky.
| {
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Higgs Lagrangian and massive/massless fields In QFT yesterday we were talking about Higgs/SSB and mass terms in Lagrangian. Our professor wrote down some lagrangians
and asked us to explain certain things and also if it is for massive or massless field. One of them was this
Lagrangian (not a realistic one I think)
$\ma... | In this case you can
demonstrate that this Lagrangian represents a massive field. You do this by looking at the exponential term $e^{m\phi}$ in
$\mathcal{L} = \frac{1}{2} (\partial_\mu \phi )^2 - e^{m \phi} + \lambda \phi^4$
and performing a Taylor expansion. That is
$e^{m\phi} = 1 + m \phi + m^2 \large \frac{\phi^2}{2... | {
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Is Penrose's CCC consistent with Penrose's singularity theorem? According to Penrose's Conformal Cyclic Cosmology (CCC), there were universes prior to ours, prior to the singularity of our universe.
But how is this claim compatible with his famous singularity theorem, according to which spacetime geodesics cannot be ex... | Long story short, the Big Bang is a singularly unique singularity which is mathematically no different than the massively expanded universe in the far, far future. Because they are the same, one infinitely expanded universe becomes the infinitely small start of the next.
The mathematics he uses to demonstrate this com... | {
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Why does power increase as a constant force accelerates a body? If a constant force is being applied to a body, without any other external forces, F = ma says that that body will accelerate at a constant rate. This acceleration will continuously increase the body's velocity.
According to P = Fv, since the force is cons... | Suppose the body starts from rest at time $0$ and accelerates at a constant rate $a$. At time $t$ it has speed $v=at$ and kinetic energy $E=\frac 1 2 ma^2t^2$.
At time $t+\delta t$ it has speed $a(t+\delta t)$ and energy $E + \delta E = \frac 1 2 ma^2(t+\delta t)^2$. So
$\delta E = m a^2 t \delta t + \frac 1 2 ma^2 (\d... | {
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Orbit with crash Let's assume I shoot an object from a high tower horizontal to the earth's surface. As far as I understand, depending on the velocity I will get different types of orbits. With decreasing velocity I will go from
*
*hyperbolic orbit where the focal point is the earth's center
*parabolic orbit where t... | The answer is yes, even though it doesn't make sense to talk about "orbit" in your case as the object crashes on the surface of the planet.
As a thought experiment, though, you can think of the Earth as a point particle, and your object being shot in space far from the surface. Then, as its trajectory starts "bending" ... | {
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What is the equivalent to $\Box A^\alpha =- \mu_0 J^\alpha$ using differential forms? The set of equations $$\Box A^\alpha = -\mu_0 J^\alpha$$
can be found in section 12.3.5 of Griffiths's book. From what I understand, the real-valued functions on both side of the equations are the coefficients of some $1$-forms with r... | If $$\delta \equiv *d*$$
then the Maxwell equations amount to
$$\delta d A = J$$ with $\mu_0 =1$.
Starring the above equation, you get conservation of current. Taking the dual twice will get you to the form you started with, that is modulo some signs. Taking the dual of the above equation you get conservation of curren... | {
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Understanding of electric potential's integration form I already known that the potential difference when a charge moves from A to B is
But I still have confusions about what does the infinitesimal of vector $s$ refers. I mean when you change the movement of the charge from B to A, the $\Delta V$ should be opposite nu... | If I understand your question, I think you are assuming that when you integrate from B to A two things change: the direction of ds (and therefore the dot product of E and ds) and the integral (because you changed the limits) and therefore you end up with the same as when you integrated from A to B. But integrating from... | {
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Precise zero energy bound for supersymmetry Usually we can shift the energy $E$ by any amount $\delta$ to redefine the lowest energy as
$$
E + \delta.
$$
However, in supersymmetry, there is a precise $E=0$ must be true, so that the supercharge $Q$ annihilates some state $|\psi_{min}\rangle$ to give the minimal energy
$... | I will offer two arguments to try to exhibit what the problem with ground states with non zero energy in a supersymmetric theory is.
The case of gauged supersymmetry: Energy backreacts on the geometry.
If the energy of the ground states of a supersymmetric theory were non exactly zero the underlying geometry of the bac... | {
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What exactly means "local"? How local (and memoryless) is "local"? Local and memoryless are easily defined in quantized space and time:
Local: What happens from one time step to the next in one "cell" of quantized space is only influenced by the state of neighboring cells.
Memoryless: The state in the next time step is... | Local may have different meaning depending on the context. One common use of this term is in describing the equations of physics as local, because a value of a function/field is determined only by the values of this and other functions/fields at the the same point (or infinitesimally close points), as reflected by the ... | {
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Shouldn't We modify the field in force equation $\mathbf{F}=q\mathbf{E}$? Consider charge particle $q$ in electric field $\mathbf{E}$. The force on the charge is given by
$$\mathbf{F}=q\mathbf{E}$$
Now we know that charge $q$ will also produce an electric field. Due to this field, the field already present in the space... | The electric field that appears in this expression (and in Lorentz force equation more generally) is the total electric field, meaning the field as contributed from all sources. The reason the field due to the point particle in question (which would make it interact with itself) is usually ignored because the field of ... | {
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Why not consider rate of change of acceleration? Why do we not consider rate of change of acceleration in the study of linear motion?
| Sometimes we do need to consider the rate of change of acceleration - sufficiently often for it to have been given a name. The rate of change of acceleration is called jerk. Limiting the magnitude of jerk is an important consideration in the real world design of railway tracks, elevators and roller coasters.
The initia... | {
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Differential operators in QM whose domain is a subspace of $L^2$ act on equivalence classes - How is that even defined? As far as I know, differential operators in Quantum Mechanics (for example the momentum operator) are defined on a subspace of $L^2$ (if $L^2$ is the Hilbert space). This means that they act on equiva... | Each equivalence class in the domain must contain a differentiable element. The differential operator acts on those representatives. Notice that each such representative is necessarily unique, since two continuous functions which are different on a zero measure set are actually everywhere equal. So the action is well ... | {
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A Loop Quantum Gravity question Can someone answer this question, I have chosen this from Bodendorfer's article on 'An Elementary Introduction to Loop Quantum Gravity' from section 3 General relativity in the connection formulation and quantum kinematics exercise 3.6.10
Ashtekar-Lewandowski Vaccum
A Cylindrical Functio... | Well, the answer is in the question – you need to evaluate the flux operator!
It's not that hard to see actually. Draw an arbitrary auxiliary graph, and note that the Ashtekar-Lewandowski vacuum state corresponds to a spin network on this graph with all spins equal to zero (because the spin-0 representation of $SU(2)$ ... | {
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Matsubara sum with log term How do I compute the Matsubara sum
$$\sum_n \log\left(-i\omega_n +\frac{k^2}{2m}+\mu\right)?$$
If I have sums like
$\sum_n \frac{1}{i\omega_n -m}$, I can sum it up by calculating the sum of residues of the function $\frac{1}{z-m}g(z)$ at the poles where $g(z)=\begin{cases}
\frac{\beta}{\exp... | For this kind of stuff you usually integrate by parts.
First change your sum to an integral:
$$\sum_n \log\left(-i\omega_n +\frac{k^2}{2m}+\mu\right) \Rightarrow \int \mathrm{d}\omega \, \log(f - \mathrm{i}\omega), $$
where $f$ here is $k^2/2m+\mu$ which I am assuming are not functions of $\omega$.
Then integrate by ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/592802",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Problem with the proof that for every timelike vector there exists an inertial coordinate system in which its spatial coordinates are zero I am reading lecture notes on special relativity and I have a problem with the proof of the following proposition.
Proposition. If $X$ is timelike, then there exists an inertial coo... | The matrix you wrote will take the standard basis $\{(1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1)\}$ into the basis constructed from $\mathbf{X}$. Therefore, to take $\mathbf{X}$ into something proportional to $(1,0,0,0)$, you need to use the inverse matrix.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/592938",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
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