Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why do certain mesons not self-destruct? As I understand it, particles and antoparticles annihilate one another. But some mesons (and pions?) consist of a quark and its antiquark. How can they exist without the two particles annihilating each other?
| But they do decay into the channels available from conservation laws.
Annihilation happens when all the quantum numbers cancel. In the pio the charge and baryon number of the quark antiquark cancel each other, and the decay particles add up to zero quantum numbers.
The $\pi^0$ goes into two photons as soon (electromag... | {
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When only part of the surface an object is in contact with has friction, what is the normal force I should use? I have the following exercise:
A uniform rod of mass $M$ is given a horizontal velocity $v$ on a rough track as shown in the figure. The surface is rough on the right side of the origin $O$ and the surface i... | Imagine there are two objects instead of one. One object has a certain mass, and experiences friction. The other object has another mass, and no friction. If those two objects were joined together, you would have no difficulty figuring out the equation of motion.
But actually the problem is harder than it looks: the wa... | {
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Electric field inside a material I was thinking about the polarisation, and how the electric field behaves inside the material of permittivity greater than one.
I think to have understood what happens to D and P, but is not clear what happens to E.
Is the electric field inside the material bigger, remains constant, or ... | (For completely filled capacitors)
Q = CV
So, C = Q/V
So, C is charge stored per unit Potential Difference applied.
Now,
V = Ed
,where d is distance between plates.
$E = \dfrac{V}{d}$
Case 1) When you apply a constant V of 1V to capacitor
E across capacitor is $ \dfrac{1V}{d}$
which is constant independent of capacitan... | {
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Centripetal force: if radius decreases, does ANGULAR or TANGENTIAL velocity change? Having conceptual trouble with this aspect of centripetal force. Say we have a puck on a frictionless table attached to a string that I am holding through a small hole, so that the puck moves in a circular path. So $F=m\;\dfrac{v^{2}}{r... | As the puck is moving in uniform circular motion the centripetal force is normal to the velocity vector, no work is produced and the total energy of the puck, which is kinetic $\mathcal K=(1/2)mv^{2}$, remains constant.
Pulling the string, even slowly, the string tension becomes oblique to the velocity vector during th... | {
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How black body absorbs light? I learn that black body absorbs light, but couldn't get the mechanism behind it. I wish I could get help.
| In physics one should have clearly defined terms.
Black body radiation is a mathematical model where a function can describe the effects of radiation for an object that radiates off , after absorbing, any radiation that falls on it:
"Blackbody radiation" or "cavity radiation" refers to an object or system which absorb... | {
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Ideal gas law: Will the piston move at all? We have the following experimental setup:
Before the experiment starts: $$p_1=p_2; \space V_1=V_2; T_1=T_2+\Delta T$$
The experiment starts and both the containers are heated so that the temperature difference $\Delta T$ remains constant (Edit: I wanted this to mean that the... | Let $T_{20}$ be the initial temperature of tank 2 and $T_{10}=T_{20}+\Delta T$ be the initial temperature in tank 1. Let $\delta T$ be the equal rise in the temperature of both thanks. Assuming that the piston does not move, we would have $$p_{2f}=p_2\frac{T_{20}+\delta T}{T_{20}}$$and$$p_{1f}=p_1\frac{T_{20}+\Delta ... | {
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When does a liquid 'wet' a solid surface? What is exactly meant when it is said that a liquid wets a solid surface. Has it got only to do with the contact angle ?
| The process of wetting of a solid surface is better explained with cohesive and adhesive forces. Wetting of a solid surface by a liquid means the liquid molecules succeeded in maintaining a contact with the surface through the inter molecular attractive forces. You should see that every liquid may not stick on to a giv... | {
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Why an impact exerts so much force? If an object of velocity $v$ and mass $m$ moves towards a resting object of mass $M$, then if the object which is hit might break. Why?
What is the reason that a collision has more power than a statical force $F$ acting on this object?
I haven't found any literature where such thing... | Although the average force applied during a collision might be small enough that an object can take it, the peak force applied can be much higher. In physics this is called impulse.
Calculating the impulse for real world collisions (like a car crash) is very complicated. This is because cars have many structural member... | {
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Energy conservation around a black hole In the Schwarzschild black hole, the Killing vector "time translation" $k^a$, so that the following quantity is conserved along a geodesic:
$$E = -g_{ab}k^au^b = (1 - \frac{2GM}{r})\frac{dt}{d\tau}.$$
Which is interpreted as the total energy per unit mass measured by a static obs... | The conservation of $\vec{k}\cdot\vec{u}$ only holds in the test particle limit. That is, it considers the metric to be unaffected by the motion of the particle. In this limit, there are no gravitational waves, since the metric has no time-varying quadrupole.
If you want to see gravitational waves, you need to allow th... | {
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How do I find the relation between the accelerations of the ring and the disc (see image)? What is the relation between the accelerations of the ring and the disc (see image)?
Both the ring and the disc have mass $M$. The ring has a radius $R$ and disc has radius $2R$. They are connected by a light inextensible string... | At the instantaneous moment shown in the diagram, we can write:
$$2R\alpha_{ring}=a_{disc}$$
as both are in pure rolling. This also tells us that the point on the ring where the thread is attached has an acceleration $=2R\alpha_{ring}=2a_{ring}$ so we find that:
$$a_{disc}=2a_{ring}$$
Note that when the string moves to... | {
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Rotation of a vector Is a vector necessarily changed when it is rotated through an angle?
I think a vector always gets changed because its projection will change, and also its inclination with axes will always change. However the direction may remain same. Kindly make things clear to me.
| In general it changes although the reason is not exactly because its projections changes.
For example. You start with a vector (let us say the electric field of a parallel plate capacitor) on the plane $xy$. Then you rotate the coordinate system by an angle. The components of the vector on the new coordinate system is ... | {
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Two Robertson-Walker observers, at what time will a light signal be received? Here is a question I have that is inspired by this question here.
The spacetime metric of a radiation-filled, spatially flat ($k = 0$) Robertson-Walker universe is given by$$ds^2 = - dT^2 + T[dx^2 + dy^2 + dz^2].$$Consider two "Robertson-Walk... | In the geometrical optics approximation light ray is represented by a null geodesic. Therefore you only need to find a null geodesic connecting points $(t_0,0,0,0)$ and $(t_1,x,0,0)$ for some $t_1$ (and this condition will determine $t_1$ uniquely). This is probably quite easy to do directly in this case, but in genera... | {
"language": "en",
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What does it mean that a Cooper pair behaves as a boson but respects the obligations of fermions? I refer to the fact that it has integer spin, but antisymmetric wavefunction. How is this possible?
| Well, $1/2\otimes1/2=0\oplus1$, so a system with two fermions has integer spin. But it is still a two fermion system, and therefore its wavefunction must be antisymmetric, as usual. This is not specific to Cooper pairs, but is basic Quantum Mechanics... [what is specific to Cooper pairs is that their size is $\gg a_0$,... | {
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Intensity fluctuations at the output of a single mode fiber coupled to a He Ne laser I have coupled a Thorlabs HNL050L-EC - HeNe, 632.8 nm, 5 mW, Polarized Laser to a 2 meter long single mode fiber patch chord using a Thorlabs F230-FC-B aspheric lens. While I am certainly able to obtain a pure single mode Gaussian at t... | Check the pointing stability of the laser, which, together with mechanical vibrations, would make the coupling efficiency fluctuate. After making the setup as mechanically stable as possible, try to put small diameter tubes everywhere around the beam before the fiber. And/or enclose everything in a box. Air movement ha... | {
"language": "en",
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Is it true that $\frac{d}{dt}\int_S \mathbf{B} \cdot d \mathbf{a}$ goes to zero if the amperian loop delimiting $S$ contracts indefinitely? I suppose to have an ordinary magnetic field: in the answer I'm not interested to involve Dirac delta: the integral goes to zero. I want to focus on another point: an infinitesimal... | As long as $\mathbf{B}$ is a continuous (once-differentiable) function, when you look at small enough sizes, $\mathbf{B}$ has a Taylor series, the first term of which is a constant. As you let the loop size shrink, only the constant term matters. But then $\int_S \mathbf{B}\cdot d\mathbf{a}\rightarrow \mathbf{B}\int_S ... | {
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Phases and sinusoidal waves When we're talking about a wave, just a singular sinusoidal wave, what exactly is a 'phase'?
I came across a question that gave values of frequency ($550$Hz), and speed ($330$m/s). The question then asked to find how far apart two points are that differ in phase by $\frac{\pi}{3}$ rad. The ... | The clue here is " how far apart". The question is asking for distance which must be in terms of the wave's wavelength. Phase measures fractions of wavelength. And you are given information of the wave's speed and the periodic time in which it propagates (frequency).
The fundamental "distance = rate * time" applies in ... | {
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Conflicting answers gained from different equations First time posting I hope this is the place.
if someone could help me sort out formatting for the equations that would be nice
"As a result of being hit from behind by a toy truck, a 50g toy car rolls 3.0m across a floor that applies a constant retarding force of 1.2N... | The question is inconsistent. At least one of the numbers (mass, force, stopping distance, or stopping time) is wrong. Your calculation of the acceleration from force and mass is correct, but an acceleration of $24$ m/s$^2$ for $2$ seconds means that the toy car was initially traveling at $48$ m/s. This is over $100$ m... | {
"language": "en",
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Why does Special Relativity apply to more than just light? It is my understanding that time dilation is derived from the constancy of the speed of light in vacuum. I would assume this implies that the quirky consequences would therefore apply only to light. But they don't. They apply to all material objects. Why?
| The basic idea is that physical laws are same in all inertial frames. Framing your question in a different way: Why do we generalize a formula(which gives time-dilation) whose derivation is based on a light clock to physical clocks and even the biological clock?
A very interesting argument was given by Feynman in his L... | {
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Wormhole Construction & "Jump Conditions" Throughout the literature Wormholes are typically constructed by "Minkowski" or "Schwarzschild Surgery" (see e.g. Visser, Lorentzian Wormholes...), i.e. under quite simple and/or highly symmetric circumstances.
In the former case, regions are excised from a single manifold and ... | Well general relativity doesn't really have any standard condition on the smoothness of the metric tensor, but generally the metric is assumed to be at least $\mathcal C^2$, so that the Levi Civitta connection will be $\mathcal C^1$ and the Riemann tensor $\mathcal C^0$. Minkowski surgery usually involves a bit of a we... | {
"language": "en",
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Normal reaction Consider a plank on a frictionless surface and a ball from a height H is dropped on this plank. There is no friction between the plank and ball. Can the plank jump up in air for any value of H?
I don't want to know the value of H for which would happen. I just want to know that is this even possible tha... | This is an interesting question.
An ideal plank (rigid, much heavier than the ball) will not rebound, but a real plank has some elasticity - either in the material itself or as a structure (eg if the plank is supported at the ends and the middle is raised off the ground). If a heavy solid object is dropped onto it, ... | {
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Speed of gravitational waves vs speed of light I own an educational YouTube channel on physics and astronomy. I am currently working on a gravitational waves video extension to my "How Fast Is It" video book on relativity theory. I have a question on the speed of gravitational waves. I understand that the field equatio... | A better way to think of it is "speed of causality". That's the fastest any cause-and-effect will spread over space.
With nothing to cause it to go slower, changes to electric and magnetic fields will occur at that speed. No coincidence that changes to spacetime (causing gravity) propigate at the same speed.
You really... | {
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Why doesn't orbital body keep going faster and faster? If we consider the change in velocity during an infinitesimal interval of an orbit:
where body B is orbiting body A, we can see that the magnitude of the resultant vector (the green arrow) is greater than the magnitude of the original tangential velocity. Why does... | You have to consider the limit of infinitesimally short time, in which the (vertical on the paper) component of velocity is infinitely short, and thus also the angle changes for an infinitesimal amount. In this limit, the correction to the length is quadratic in the time step and vanishes exactly in the physical limit ... | {
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Radiation-Glossy Black vs Matte White Well, studying the chapter Heat I know that a matte black body radiates heat more than a glossy white one but can anyone give me an answer about what happens when its a glossy black body and a dull colored white body?
| The spectral radiation rate depends on the material in question and the temperature of the material. You can start to learn about this by Googling "Black Body Radiation" and "Planck" . Your terms "glossy black" and "dull white" are far too vague (in a scientific or engineering sense) to be able to answer. Further, t... | {
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Derivation of Lorentz Transformations How can I derive the Lorentz transformations? I don't want to use hyperbolic functions and the fact that the light waves travel by forming spherical wavefronts. Is there a way to derive the Lorentz transformations applying the conditions I have mentioned. I was unable to understand... | Here's a derivation that uses very basic properties of space and time (isotropy, homogeneity, the fact that two Lorentz boosts should compose into another valid Lorentz boost, etc.). The constant maximum speed through space (i.e., the speed of light) is a derived property, not an assumption.
One more derivation of the ... | {
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Does a box containing photons have more inertia than an empty box? A box containing photons gravitates more strongly than an empty box, and thus the equivalence principle dictates that a box containing photons has more inertia than an empty box. The inescapable conclusion seems to be that we can ascribe the property of... | Yes, both the internal potential energy and the internal kinetic energy of a bound system (in the rest frame of its center of mass) contribute to the bound system's inertial mass according to $E=mc^2$. For a paper discussing the evidence that this is true for internal kinetic energy in particular, see Kinetic Energy an... | {
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Eddy currents in a superconductor Just had a lesson we just had our teacher introduced the concept of eddy currents, and showed us how a magnet moves slowly through a metal tube due to the opposite generated magnetic field.
If you dropped a magnet through a superconductor then, would the magnet just float there? (Becau... | Yes, you are correct. The magnet would just float, perhaps even before entering the tube. You anticipated correctly that the strength and lack of dissipation of the eddy currents keep the magnet in place. This is well illustrated in a clip about levitating superconductors.
| {
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Plane wave shift in a differential operator Does anyone can help me to prove the following equation
\begin{equation}
e^{-i\vec{k}\cdot\vec{x}}f(\partial_{\mu})e^{i\vec{k}\cdot\vec{x}} = f(\partial_{\mu}+ik_{\mu})
\end{equation}
Where $\vec{k}\cdot\vec{x}=k^{\mu}x_{\mu}, \mu = 0,1,2,3$.
| PART 1 : Taylor Expansion ( see @Prahar comment ).
In the following :
$$
\mathbf{x}=x^{\mu}, \quad \mathbf{k}=k_{\mu}, \quad \partial_{\mu}=\dfrac{\partial}{\partial x^{\mu}} , \quad \mu=0,1,2,3
\tag{1-01}
$$
$$
\mathbf{k}\cdot\mathbf{x}=k_{\mu}x^{\mu}=k^{\mu}x_{\mu}, \quad \text{Einstein's convention on}\: \mu... | {
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Is Bohmian Mechanics incompatible with loop corrections? For those who continue to be unsatisfied with Quantum Mechanics (QM), Bohmian Mechanics (BM) is an alternative worth considering. It is sometimes claimed that BM is equivalent to QM, but Lubos Motl recently argued on his blog that this is true only for a limited... | For some counterarguments against Lubos Motl's argumentation against de Broglie-Bohm theory see http://ilja-schmelzer.de/forum/forumdisplay.php?fid=6 and http://ilja-schmelzer.de/realism/Motl.php
The first proposal for a Bohmian variant of a relativistic quantum field theory has been made in Bohm's original 1952 paper... | {
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Standing wave on a rope fixed at both sides: minus sign in the reflected wave I'm studying stationary waves on a rope fixed at both sides.
In some books I find that the wave function studied is the sum of incident wave $\xi_1(x,t)$ and of the reflected wave $\xi_2(x,t)$.
$$\xi(x,t)=\xi_1(x,t)+\xi_2(x,t)=A \mathrm{sin} ... | If the phase difference between the wave is zero i.e lies in the plane of wave motion the resultant displacement is equal to zero,
Thus, $A = 0$, $(L,t)=0$, due to that fact, you can use $$A\sin(kx−\omega t)\to-A\sin(-(kx+\omega t))=A\sin(kx+\omega t)$$ for progressive wave, but nothing can happen when you use cosine r... | {
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Why do liquids exert pressure on the sides of a container? What makes a liquid push against the walls of a container if the liquid is completely static?
I was thinking a comparable situation would be a bin full of baseballs. Unless the balls were perfectly stacked they would be rolling off one another and the walls of... |
Unless the balls were perfectly stacked they would be rolling off one another and the walls of the bin would stop them.
Even in zero gravity fluids will exert an equal pressure on all walls. In zero gravity the balls would continue to remain stationary without exerting any force on the surroundings. So just thinking ... | {
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Vertical circular motion/How can tension be negative?
This is a rock tied to a string spinning vertically.
Here,
$T+mgsin\theta = mv_1^2/r => T = mv_1^2/r-mgsin\theta$
Suppose I give it a velocity $v$ at the bottom.
1) At what angle $\theta$ will the tension become zero?
2) If the velocity ends up $=0$ at $\theta = ... | Tension in the string will never become zero, as long as rock is moving along the circular path.
Also, speed of the rock also, will never become zero in this case.
| {
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Wave speed derivation
The wave speed derivation approximates the wave as a circle. It uses that to know that $$a=\frac{v^2}{R}$$However, numerous functions can approximate the wave. A straight line, $x^2$, $x^3$, etc. If I used those I would get a different equation for a. So why is a circle the correct approximation ... | A single line isn't very useful for approximating a curve. You could use small segments, but then you'll need several, and the calculation would be more complicated. As noted in the comments, nothing stops you from using any other second order curve, i. e., a plane curve whose rectangular Cartesian coordinates satisfy ... | {
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Why does light act differently in miniatures? When painting miniatures (like RPG fantasy miniature soldiers)... why is it necessary to paint lights and shadows?
Being a 3D object, shouldn't the natural light be enough to create lights and shadows if the figure is simply painted with plain colours?
| When objects are very small, every source of illumination will appear to be "extended" - which softens the shadows and makes it harder to see the contours of the surface.
By painting highlights and shadows, you reduce the impact of the extended source. See for example Why don't fluorescent lights produce shadows?
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/256396",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "41",
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The thickness of a puddled sheet of water If I pour water of different amounts into a puddle on a level surface, it appears by eye that both puddles have the same height. The water seems to retain itself into a puddle by surface tension. I have two questions:
(1) Does the height of a puddle of water on an infinite leve... | Based on the page linked in the comments, the answer seems to be the following:
(1) The height of the puddle does not depend on the material of the surface so long as the surface is nonwetting.
(2) If the amount of water is large then it makes no difference, but if the amount is small, such as a droplet, then the conta... | {
"language": "en",
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Can we "see" into a black hole using gravity? I believe the "no hair" theorem means all black holes settle down into a state only determined by a few parameters, typically listed as mass, charge and angular momentum. But I don't think they can settle down instantly, which means the interior of the black hole may tempo... | Yes. You're exactly right, deviations from no-hair do occur for example after BH mergers --- and hints of the "quasi-normal" mode ("ringdown") were observed in the LIGO detection. The no-hair theorem is constructed for a static, stationary BH (i.e. fully settled). In general, deviations from no-hair (magnetic fields... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Rest mass of phonon: is this concept definable? Phonons are obtaied by non-relativistic quantization of the lattice vibration. The dispersion relation is given by $\omega=c_s k$ where $c_s$ is the velocity of sound. What can we say about the mass of the phonon? I think it is not possible to compare this relation with t... | Phonons are indeed massless, as you can see from their dispersion relation or from the fact that they are Goldstone bosons. The phonon dispersion relation that you wrote down tells us that we can excite a phonon mode, with some finite momentum, using an arbitrarily small amount of energy, hence they have no rest mass (... | {
"language": "en",
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What happens when two wavefunctions meet? Apologies for the over-broad question(s), but I'm having a hard time finding out where to look to answer these myself:
If a particle is a wavefunction describing a probability amplitude distributed through space, what happens when two wavefunctions meet? I imagine that their am... | Wavefunctions combine trough tensor products, which is not the addition that one would expect naively. The reason for this is that a wavefunction contains the description of all possible futures of the system at once, so if there are multiple subsystems, then the wavefuntion of the entire system has to describe all pos... | {
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Fermi energy of electron gas with electrostatic interaction I have been given the following exam question and am unsure how I would go about solving it:
Consider the case of a one-dimensional metal, consisting of a chain of $N$
positive charges $+q$ separated by a distance $2R$ and immersed in a neutralizing backgroun... | Kinetic energy in 1D, method 1. Free electrons. Assume no potential energy at the moment. Zero temperature.
\begin{equation}
n_e=\int_0^{E_F}g(\epsilon)d\epsilon=\int_0^{E_F}\frac{1}{\pi\hbar}\sqrt{\frac{m}{2\epsilon}}d\epsilon=\frac{\sqrt{2mE_F}}{\pi\hbar}
\end{equation}
\begin{equation}
E_F=\frac{\pi^2\hbar^2n_e^2}{2... | {
"language": "en",
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Is there any atom which is dia-electric? Take an atom. Suppose we impose some magnetic field on it. For some atoms, the energy increases---this is a phenomenon of diamagnetism.
The question is, how about an electric field? Can the energy of the atom increase when the electric field is turned on?
Put in a different wa... | No, there can't be atoms like that, at least not in the real world.
In the magnetic case, diamagnetism means that the magnetic susceptibility may be negative (so the permeability may be lower or higher than in the vacuum, the magnetic susceptibility may have both signs).
But in the electric case, the electric susceptib... | {
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Transversal wave speed derivation for small amplitudes
The above is a derivation for the wave speed equation in my physics textbook. However, I've read online that this equation is only true for waves with small amplitudes. I do not see where this assumption is made in the derivation, so why is the equation only true ... | The explanation is not a very full one. As you correctly note, you're taking a limit, so the assumption $\sin\theta \to\theta$ as $\delta z\to0$ becomes exact. So Eq 16-23 contains no approximation.
The assumption creeps in subtly when one assumes that the force calculated in Eq 16-23 is at right angles to the $z$ axi... | {
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Analysis of a system consisting of a leaking tank of water The departure point is this problem:
A water tank on wheels is moving over an horizontal trail with negligible friction. There is a small opening in one of the walls, at a depth of $h$ below the tank's water level. The cross-section area of the opening is $A$. ... | For a particular setup, the equations may get very simple: the tank should be massless ($M=0$) and the hole is all the way at the bottom of the container. Then $h$ is proportional to the mass of the water in the container: $m=m_0 h/h_0$, with $h_0$ the initial height. It's straightforward to derive that the force gener... | {
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A Question about a $U(1)_{B-L}$ I know I can write the QCD lagrangian like this:
$$ \mathcal{L} = (i\bar{q}_{R} \gamma_{\mu}\partial_{\mu} {q}_{R} + i\bar{q}_{L}\gamma_{\mu}\partial_{\mu} {q}_{L}) + \text{other terms} $$
When written this way we say it is invariant under $SU(3)_{R}\times SU(3)_{L} \times U(1) \times U... | I searched through the whole book and didn't find a single instance of "$U(1)_{B-L}$", so a page number reference would be helpful. But for the purposes of pure QCD, $U(1)_V$ is the same as $U(1)_B$, because all quarks carry the same baryon number, and that's the same as $U(1)_{B-L}$ since nothing carries lepton number... | {
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Can air be considered incompressible as long flow velocities are less than 100 m/s (Ma = 0.3)? Multiple sources state that steady air flow (in open systems) can be considered incompressible at velocities less than 100 m/s (Ma = 0.3). Example:
Deborah A. Kaminski, Michael K. Jensen, "Introduction to Thermal and Fluids ... | As far as I catch the question (without going digged in math), pressure doesn't go instantly from a point to a point, but has certain speed, that is sound speed. No matter if your system is opened or closed, the air is the same. If you compress air in cylinder slowly, then the air well compressible, but if you try to m... | {
"language": "en",
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Parity conservation in second harmonic generation? The second harmonic arises from susceptibility of third rank tensor $X^{(2)}$ which have (-1) parity.
page 28
Let say two photons are absorbed and one is emitted, so the total change in parity is $(-1)^{(2+1)}$. The initial state equals the final state so $(-1)^0=1$.
... | The requirement is that $\chi^{(2)}$ be non-centrosymmetric. That's a bit different than having a particular parity. The states involved must be neither odd nor even; the parity must be mixed. That way the dipole matrix element exists between all three intermediate states involved in calculation of the susceptibil... | {
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Two contradictory groups of statements from two different books on quantum physics There are two contradictory groups of statements from two different famous books on quantum physics.
Which one is correct?
Group (1) : Following statements are from Berkeley Physics Course Vol. 3, "Quantum Physics" by Wichmann, 1967
Page... | It's neither a classical wave nor a classical particle. I think any attempts to describe it as either of those need to be qualified like this. It might look like one or the other, but both are only approximations.
The best theories we have describe quantum fields, and a particle is a field quantum. I don't really know ... | {
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How to calculate number of degenerate states? For example if we need to get number of degenerate states for a particle confined in a 3D box that have energy
$$E=41\frac{\pi ^2 \bar{h}^2}{2m_e L^2}$$
I know that
$$E=\frac{n^2 \pi ^2 \bar{h}^2}{2 m_e L^2} $$
and $$n^2=n_x ^2+ n_y ^2 +n_z ^2$$
$$\Rightarrow n_x ^2+ n_y ^2... | What you have here could be described as a subset sum problem. Given $n$ can take any integer value (not including zero), you have the set of squares up to $36$,
$S = \{1,4,9,16,25,36\}$
and you wish to find subsets of three which sum to $41$. Looking at the subset sum problem this can not be solved analytically but al... | {
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What type of instrument can I use to determine my current distance from the center point of Earth? Immediately, I think of a scale, but is there better way? I can only imagine weighing an object of known mass with an extremely precise scale.
I am asking because I would like to be able to address absolute elevations rel... | Sounds like GPS is best here. The position of the antenna is determined first in coordinates relative to the center of the earth, and then translated onto the ellipsoid and geoid. So finding the position relative to the center of the earth should actually be more accurate than finding its altitude relative to sea lev... | {
"language": "en",
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Why does time-independent Hamiltonian not depend on angle variable? In Landau and Lifshitz Mechanics, $\S50$ Canonical variables a time-independent Hamiltonian is considered, and a canonical transformation is done such that adiabatic invariant $I$ becomes the new momentum. Then the angle variable is found as
$$w=\frac{... | This is more or less an exercise in chasing definitions. The adiabatic invariant $I$ is defined as
$$ I\equiv \oint p \frac{\mathrm{d}q}{2\pi}\tag{49.7}$$
where the integral is taken over the path for given $E$ and $\lambda$. The external parameter $\lambda(t)$ is a slowly varying function of time $t$ in $\S49$, but i... | {
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How much noise is in the Cosmic Background Radiation, especially from Cosmic Rays Do we have an estimate of how much noise, if any, say caused by cosmic rays in particular, is present in the CMB datasets and the maps based upon them?
Can we extrapolate a figure from the cosmic ray flux estimated to enter our atmosphere... | Cosmic Rays are most often high-energy particles, mostly protons and alpha particles accelerated to high velocities by cosmic magnetic fields.
They do not show up in the microwave wavelength range that comprise the CMB.
As @ACuriousMind says in the comment, there is contamination in the CMB, but this is mainly due to ... | {
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Why do quasi-free states satisfy the positivity condition? In LQFT, a state, $\omega$, is a linear map $\omega:A=:CCR({\cal{S}},\Omega)\rightarrow \mathbb{C}$ satisfying:
*
*$\omega(aa^{*})\geq 0$ for all $a\in A$.
*$\omega(I)=1$ where $I$ denotes the identity element of $A$.
where $CCR({\cal{S}},\Omega)$ is the... | The condition on the modulus of $\Omega$ ensures that the complex bilinear form $\mu_c$ defined as $\mu_c(\cdot,\cdot)=\mu(\cdot,\cdot)+i\Omega(\cdot,\cdot)$ is a scalar product. Therefore $(\mathscr{S},\mu_c)$ is a complex pre-Hilbert space. Denoting by $\mathscr{H}_{\mu_c}$ its completion, it is then possible to defi... | {
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Tractrix - velocity pointing to pulling point It is said the tractrix is the curve described by a mass being pulled by a string, where the end of the string being pulled moves with constant speed, and the mass suffers a friction force. What is the physics explanation for why in the tractrix the velocity is always align... | UPDATE:
Many thanks for the update, Miguel. I am sorry, I misunderstood the description of the curve, which is misleading. The "mass" has no inertia (now I understand what philip_0008 meant in his comment) and is pulled infinitessimally slowly. So the "pulling" here is a "quasi-static" process, not a dynamic one. ... | {
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How much of water's surface tension is entropic? Water molecules on the surface of an air-water interface have preferred orientations that lower their energy. This implies that these molecules are not uniformly distributed in orientation space, implying that the entropy is somewhat reduced when molecules are on the sur... | If the water-air system is a closed system, when surface tension reshapes the interface shape between water and air, entropy of air increases due to increasing in volume and entropy of water decreases due to decreasing in volume. The heat to make this happen will reduce the air temperature. The water pressure will incr... | {
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Calculating eigenvalues for operator Given relation $[a,a^\dagger]=I$. Operator $K$ is defined as $K=a^\dagger a+\lambda a^\dagger+\lambda^* a$. I need to find the eignevalues of operator $K$. How realtion that involves commutator could help me? Thanks for any suggestions.
| You may just complete the square:
$$ K = (a^\dagger+\lambda^*)(a+\lambda) - \lambda\lambda^* $$
Expand the product and subtract the last term to see that you get the same three terms. One may define $b=a+\lambda$. Then
$$ K = b^\dagger b - \lambda \lambda^* $$
and $[b,b^\dagger]={\bf 1}$, so these $b$ operators are i... | {
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Relativity paradox with mirrors and light pulses
Consider two very short light pulses emitted from the centre (C) of two mirrors A and B (as shown in the diagram).
From the point of view of the lab frame, the apparatus is all moving to the left at velocity v.
Imagine there is also an electron near the centre of the ap... | If $t_{CA}$ refers to the time it takes in the lab frame for the light to reach C from A, and the same with $t_{AC}$, $t_{CB}$ and $t_{BC}$ then we have:
$t_{CA}=\frac{L/2+v t_{CA}}{c}$
$t_{AC}=\frac{L/2-v t_{AC}}{c}$
$t_{CB}=\frac{L/2-v t_{CB}}{c}$
$t_{BC}=\frac{L/2+v t_{BC}}{c}$
Thus $t_{CA}=t_{BC}$ and $t_{AC}=t_{CB... | {
"language": "en",
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How can I measure the amplitude of a light wave? Suppose I have a light wave and I want to measure its amplitude, or check to see if it has an amplitude of a certain value: how would one go about doing this?
| Direct measurement of the amplitude of the optical field requires interferometric techniques. One that works is the FROG - Frequency Resolved Optical Grating. There are many variations on it today, including from the original developers: Trebino Research Group.
These devices were designed for ultrafast pulses. For C... | {
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Can we write the wave function of the living things? If yes then how? In quantum mechanics we studied that everything has a wave function associated with it.My question is can we write down the wave functions of things. Then how we can write down the wave functions of the things like animals, human eye, motion of snake... | My answer will be very non-technical, but hopefully will convey some basic ideas about what the quantum state (or wavefunction) is about.
One intuitive way to picture the nature of the quantum state of a system is to see it as the interference (hence the "wave" idea) of every different changes it could possibly undergo... | {
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Why does $\prod^n_{j=1}\sigma^{(j)}_x$ commute with this adiabatic Hamiltonian? In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring.
The adiabatic Hamiltonian is defined as
$$
\tilde{H} (s) = (1-s) \sum^n_{j=1}(1-\s... | The first term (sum) in $\bar H$ obviously commutes with all $\sigma_x$ variables because it's a function of $\sigma_x$ only and they commute with each other.
The second term (sum) in $\bar H$ also commutes with the product of all $\sigma_x$ because the first term in the summand is a $c$-number and the second term $\si... | {
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Merging black holes makes them less dense, so According to What is exactly the density of a black hole and how can it be calculated? (more specifically, John's answer here made me think: if you merge a whole load of chunks of an element heavier than iron (to prevent them from fusing), the resulting object would either ... | There is nothing wrong in having something more dense than a black hole, large black holes can have densities less than water. If you put a lot of iron together it might or not become a black hole. An object of any density can be large enough to fall within its own Schwarzschild radius. The larger the black hole the lo... | {
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Check dimensions of the integral of a function I and a colleague are arguing about the dimensions of:
$$\int_0^x f(x) dx $$
in this particular case $[f(x)]=m^2/s^3$ and $[x]=m$.
Does it follow that $[\int_0^x f(x) dx]=m^2/s^3$ or $[\int_0^x f(x) dx]=m^2/s^3m$?
| It will be the latter case, $m^2/s^3m$ which is just $m^3/s^3$.
Remember that the integral is the sum of all the products $f(x)\;\text{times}\; dx$. $dx$ is a tiny piece of the path from $0$ to $x$, so it is in units of $m$ as well. Each of the products $f(x)dx$ have units $m^3/s^3$, and the sum of all these products k... | {
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How to pour water from a bottle as fast as possible? When one pours water out of a bottle, it first flows smoothly but then a pressure 'blockage' develops and the pouring becomes interrupted and turbulent, so that the water comes out in splashes. This seems to slow down the flow of water from the bottle.
What is the op... | A few years after asking this question I stumbled upon this super interesting video tweet, which is relevant for this question: link to tweet video.
The video shows two ways of emptying a certain water bottle. In one case, the bottle is simply flipped upside down. In the other case, the bottle is also flipped upside do... | {
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Friction-free rolling/sliding on an inclined plane Suppose a sphere is rolling down an inclined plane. There is no friction. The body will not roll and undergo just a translation. But why is this so?
If we consider the axis to be along the point of contact, then there would be a torque which will cause it to rotate bu... | The question answered by @SatwikPasani is related but not quite a duplicate.
The apparent paradox is resolved by realising that using a frame of reference relative to the sphere which is accelerating down the slope is a non-inertial frame of reference.
If there is friction and the no slipping condition is satisfied t... | {
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Uniformly charged rod electric field A uniformly charged rod of length $L$ and total charge $Q$ lies along the $x$ axis as shown in in the figure. (Use the following as necessary: $Q$, $L$, $d$, and $k_e$.)
(a) Find the components of the electric field at the point $P$ on the $y$ axis a distance $d$ from the origin. $E... | First I have to ask: does the question mention anything about the distance d? The reason why I am asking is because if d is large enough, we can say that it is in the far-field and we can easily approximate the field values using electrostatic theory treating the rod as point charge Q. I will provide an edit later if y... | {
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Nuclear bomb power - myth? I'm not experienced in physics yet (if it helps I've covered as much as acceleration, momentum and energy transfer/chemistry ionic and covalent bonding) but I've heard that the way people compare destructive force of nuclear weapons by megatonnes or kilotonnes is wrong. This does seem to make... | The so-called TNT equivalent of a nuclear weapon is an unambiguous way of quantifying how much energy is released by the nuclear weapon. There's nothing 'wrong' about it.
The only caveat is that the damage caused by, say, Little Boy versus 15 kilotons of TNT would not be identical despite having an equivalent yield (fo... | {
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Special relativity: is this a known paradox, or one at all? Two ships of the same proper length $L$ move towards each other, as in the diagram below (which shows it in the reference frame where the ship at the left is at rest). The fronts (noses) are pointing to each other.
Now, when both noses pass each other, they s... | The argument by Symmetry is correct and the argument of time-dilation is flawed. Time-dilation suggests that if the two events will have the least temporal interval in the proper frame. But none of the frames in this scenario is a proper frame and not just that, they are equally far off from being the proper frame (i.e... | {
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Particle sliding on a sphere I believe most of you probably solved the following problem using energy conservation as shown here. It states
A particle starts from rest at the top of a frictionless sphere of radius R and slides on the sphere under the force of gravity. How far below its starting point does it get befo... | @dvij gave the equation $$g\sin \theta =R\frac{d^2\theta}{dt^2}=R\frac{d\omega }{dt}$$
If we multiply this by omega, we obtain:
$$g\sin \theta \frac{d\theta}{dt}=R\omega\frac{d\omega }{dt}$$
If we integrate this equation between 0 and t, we obtain:
$$g(1-\cos \theta)=\frac{R}{2}\omega^2$$
So we have $$mg\cos\theta-2mg... | {
"language": "en",
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Vlasov equation, Maxwell distribution I have the Maxwellian distribution:
$$f(v)=n\left(\frac{m}{2\pi kT}\right)^{\frac{3}{2}}\exp\left(-\frac{mv^2}{2kT}\right)$$
I have to show that it is a solution to the Vlasov equation:
$$\frac{\partial f}{\partial t}+\vec{v}
\cdot \text{grad}(f)+\frac{q\vec{E}}{m}\cdot \text{grad}... | A property of the Vlasov equation is that any distribution that is only a function of constants of motion is its solution. So if the velocity of the case you present is not a function of time, the distribution would trivially be a solution of Vlasov.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/262447",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Double-Slit Experiment: Effect of Intensity Reduction on Fringes
Monochromatic light passes through a double-slit arrangement. The intensity of the monochromatic light passing through one of the slits of the double-slit arrangement is reduced. State, and explain, the effect of this change on the appearance of the brig... | Suppose the amplitude of the wave from slit $1$ arriving at a point is $A_1$ and the amplitude of the wave from slit $2$ arriving at the same point is $A_2$ and let $A_2>A_1$.
The relative phase between the waves from the two slits arriving at that point depends on the path difference between the slits and the point an... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Can I recirculate water from an open reservoir to the bottom of a bigger, closed one, without a pump? A fountain head pumps water out of the main tank into a 'pond' reservoir. Can the water recirculate back into the main tank without the help of another pump?
I'm sorry if this a dumb question. I'm guessing it would not... | How about:
open valve 2 to transfer water from the reseroir to the tank. Close valve 2 to create the 'fountain' feature. Open valve 3 to transfer water from tank to reservoir.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/262838",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why must a physical theory be mathematically self-consistent? I always read in modern physics textbooks and articles about the need for physical theories to be mathematically self-consistent, which implies that the theories must not produce contradictions or anomalies. For example, string theorists are proud of the fac... | To put it in a short way: Self-consistency is required because we expect nature to stick to laws that can be described mathematically. Mathematical descriptions by definition have to be self-consistent.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/262917",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "88",
"answer_count": 11,
"answer_id": 6
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Does momentum increase with out of phase photons? This paper speculates that the EM drive produces thrust with out of phase photons:
http://scitation.aip.org/content/aip/journal/adva/6/6/10.1063/1.4953807
My question is this, do out of phase photons have more momentum than the same set of photons traveling in phase?
Ed... | The momentum of the photon is $p=h\nu/c$, so it only depends on its frequency, not its phase. At constant frequency, all photons will have the same $p$ regardless of phase.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/263011",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is exactly the "progenitor bias"? I am taking a course in astrophysics and my teacher mentioned different biases that are present when taking a sample of galaxies: the progenitor bias and the Malmquist bias. I understand very well the Malmquist bias but I think that I don't yet really understand the progenitor bia... | The progenitor bias arises in attempts to study early-type (elliptical) galaxies at higher redshift. The desire is to choose a sample of galaxies at high $z$ that are the analogs of the galaxies that evolved to form the low $z$ sample. The bias arises if one chooses a sample of only early-types at high $z$. Because som... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do we know that an electron "spins"? As far as I know, you can't necessarily isolate an electron to observe it, you can only observe its effects on other particles due to fields. Moreover, we can't know an electron's exact location or how much space it occupies, although it has finite mass. It seems that the genera... | Electrons And Spin From Scientific American
Unfortunately, the analogy breaks down, and we have come to realize that it is misleading to conjure up an image of the electron as a small spinning object. Instead we have learned simply to accept the observed fact that the electron is deflected by magnetic fields. If one ... | {
"language": "en",
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On the Stability of Circular Orbits Bertrand's Theorem characterizes the force laws that govern stable circular orbits. It states that the only force laws permissible are the Hooke's Potential and Inverse Square Law. The proof of the theorem involves some perturbation techniques and series expansion.
The most natural t... | What you just did was to find a condition for attractive power-law forces to have stable orbits where stable means they remain bounded when perturbed around the circular orbit. You got the correct result.
The Bertrand's Theorem though says something different: the only forces whose bounded orbits imply closed orbits ar... | {
"language": "en",
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"source": "stackexchange",
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The analytical result for free massless fermion propagator For massless fermion, the free propagator in quantum field theory
is
\begin{eqnarray*}
& & \langle0|T\psi(x)\bar{\psi}(y)|0\rangle=\int\frac{d^{4}k}{(2\pi)^{4}}\frac{i\gamma\cdot k}{k^{2}+i\epsilon}e^{-ik\cdot(x-y)}.
\end{eqnarray*}
In Peskin & Schroeder's bo... | The calculation of the propagator in four dimensions is as follows.
\begin{eqnarray*}
\int\frac{d^4 k}{(2\pi)^4}e^{-ik\cdot (x-y)}\frac{1}{k^2}
&=& i\int \frac{d^4 k_E}{(2\pi)^4}e^{ik_E\cdot (x_E-y_E)}\frac{1}{-k_E^2} \\
&=& \frac{-i}{(2\pi)^4} \left( \int_0^{2\pi}d\theta_3 \int_0^{\pi}d\theta_2 \sin \theta_2 \righ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/263846",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Accessibility by reversible processes and the Second Law of Thermodynamics One common way of motivating the existence of Entropy as a state function is the following. Let us take the Clausius/Kelvin-Planck statement of the second law, from which we can deduce Clausius' theorem
$$\oint \frac{\delta Q}{T} \le 0,$$
where ... | So, you want to prove that between any arbitrary two states of a system, it exists at least one reversible path. You can prove this if you accept continuity of properties of substances. I.e. for example, if we have an ideal gas in equilibrium at initial state $(P_i,T_i)$ and final state $(P_f,T_f)$; then certainly ther... | {
"language": "en",
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"source": "stackexchange",
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Resistor in series We know that when a resistor is connected in series , the current flowing through that resistor will be constant.But how do we use a resistor to limit the current flowing through a circuit ,when resistor is connected in series with the circuit ?
| Resistance can be interpreted in various ways depending on the circuit. It can be used to cause a potential drop, or it can be used as a heating device, etc.
You are asking how resistance can change the current flowing through the circuit when connected in series. In that context, the resistance can be used to alter th... | {
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How much realistically usable energy can be obtained from matter/antimatter interaction? The high energy density of a matter/antimatter system is well known. However, depending on the nature of the material, most of the energy from the interaction is released in the form of photons (gamma rays), which are difficult to... | There was a lot of hype $10$ to $15$ years ago over the hydrogen economy. It was of course rather odd that anyone could take this seriously. How much free hydrogen gas is available? Answer: virtually none. The problem is that you have to either put electrical energy into water to split it into $H_2$ and $O_2$, or if yo... | {
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Two qubits system in polar co-ordinates I know that I can write a single qubit state in terms of polar co-ordinates $(r,\theta,\phi)$ on a Bloch sphere.
\begin{equation}
\rho =
\begin{pmatrix}
\frac{1+r \cos\theta}{2} &\frac{r \exp(-i\phi)\sin\theta}{2} \\
\frac{r \exp(i\phi)\sin\theta}{2} &\frac{1-r \cos\theta}{2} \... | A valid density operator is any Hermitian, trace 1, matrix (with complex entries) and all eigenvalues between 0 and 1. Any two qubit system may be represented therefore by a Hermitian, trace 1 4x4 matrix.
Your qubit representation could be rewritten, more suggestively as:
\begin{align}
\rho &= \frac{1}{2}\left(\oper... | {
"language": "en",
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Projection of a tensor Consider the following tensor (abstract index notation, e.g. Wald's) $B_{ab}$ and timelike vector field $X^{a}$ such that $X^aX_a=-1$ and
\begin{equation}
B_{ab}=\nabla_bX_a
\end{equation}
Then one claims that $B_{ab}$ is purely spatial, i.e. $B_{ab}X^a=B_{ab}X^b=0$. I do not quite understand ho... | Take the covariant derivative of the equation $X^aX_a=-1$. The RHS becomes zero so we have $$2X_a\nabla_b X^a=0\implies X^aB_{ab}=0.$$
The other equation, $X^bB_{ab}=0$, is the geodesic equation, so it doesn't hold for just any $X^a$.
Let's consider the situation at some point $p\in M$. Then $X^a$ is a prime candidate ... | {
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Prove that an electron in a hydrogen atom doesn't emit radiation According to electrodynamics, accelerating charged particles emit electromagnetic radiation.
I'm asking myself if the electron in an hydrogen atom emits such radiation. In How can one describe electron motion around hydrogen atom?, Murod Abdukhakimov says... | The existence of hydrogen atoms is enough to demonstrate that the electrons don't emit radiation.
If they did, that energy would have to come from somewhere. The only place it could come from would be a reduction of orbital radius until the electron finally reaches the nucleus.
If you accept that electrodynamics applie... | {
"language": "en",
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Does curved spacetime change the volume of the space? Mass (which can here be considered equivalent to energy) curves spacetime, so a body with mass makes the spacetime around it curved. But we live in 3 spatial dimensions, so this curving could only be visualized in a chart with 4 dimensions, and the living being will... | Within the Schwarzschild metric, the volume does change.
It is the rectangle formed by the radial dimension and time which is invariant:
The dilating effect of the Schwarzschild metric
$$ \mathrm ds^2 = -\left(1 - \frac{2GM}{c^2 r}\right) c^2 ~\mathrm dt^2 + \frac{1}{1 - \frac{2GM}{c^2 r} }~\mathrm dr^2 + r^2 (\mathrm... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/265071",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Physical meaning of enthalpy I've been reading about thermodynamics and reached the topic about enthalpy . I've understood its derivation but I don't understand its physical meaning ... Also I don't understand why they have divided by the mass of gas to get to the specific enthalpy equation . what's the use of it? I kn... | Enthalpy is heat at constant pressure:
$ dH = dU + pdV + Vdp $
$ dU = \delta Q - pdV $
$ \delta Q = dU + pdV $
$ dH = \delta Q + Vdp $
$ dp = 0 $ for constant pressure
So on a psychrometric chart of air, enthalpy is heat (energy) content per unit weight.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why don't the magnetic dipole moments in a neutron cancel out? This may be a silly question. I thought magnetic dipoles were dependent on electric charge, so why in a neutron do the dipole moments not just cancel each other out?
| I am presenting this classical description for simplistic understanding of the process.
In general (not for elementary particles) the Magnetic dipole moment is generated by a current loop. If you consider a current loop with current $I$ then the charge exiting from loop is same as charge entering into loop and hence t... | {
"language": "en",
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How does the uncertainty product $\Delta x \Delta p$ behave for the bound states of the triangular potential? As has been remarked earlier, if you take an unbounded potential $V(x)$ (so that all the eigenstates are bound) and you look at the uncertainty product $\Delta x\Delta p$ as a function of the index $n$ of the e... | The cone potential $V(x)$ is exactly solvable, with eigenstates of the form
$$
\psi(x)\propto\mathrm{Ai}(|x|-b)
$$
in terms of the Airy $\mathrm{Ai}$ function, so this is rather easy to test. It is probably possible to produce explicit analytic expressions for the uncertainty product, but simple numerical evidence is p... | {
"language": "en",
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Electric field dependence on distance How can it be proved that for a point charge, $E$ is proportional to $$1/r^2$$ using the concept of Electric field lines (or lines of force)? I tried to show that if field lines are close, then magnitude of Electric field is higher. But, I couldn't show the given dependence.
| As Anthony B said,the number of field lines cutting any sphere surrounding a point charge is the same(because any field line which passes through a sphere of radius 1 also Passes through a sphere of radius 200) given that, the flux = E 4pir^2 should be constant. That explains the 1/r^2 dependance theoretically
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/265816",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Question in Lagrangian formalism In lagrangian mechanics,
where $L=T-U$
and the lagrangian formulation is $ \frac{d}{dt}\big( \frac{\partial L}{\partial \dot{q_i}}\big)-\frac{\partial L}{\partial {q_i}}=F_i$,
where $F$ is the non-conservative force.
My question is if I want to find out the above equation for a given p... | No, you get a separate Euler-Lagrange equation for each individual degree of freedom, i.e. a system of simultaneous equations. So in your example,
\begin{align}
\frac{d}{dt}\left(\frac{\partial L}{\partial \dot{\theta}}\right)-\frac{\partial L}{\partial \theta} &= 0, \,\mathrm{and} \\
\frac{d}{dt}\left(\frac{\partial L... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/265957",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can the energy released when bonds formed be harnessed to do work? I'm trying to understand how living organisms get energy from food. I've heard that "energy is released when bonds form", but what exactly does "released" mean?
If the energy dissipates in the form of heat, then how can the cell use it for things?
I... | In most reactions the energy is released as kinetic energy of the reaction products. If you consider some reaction:
$$ A + B \rightarrow C + D $$
then if you add up the kinetic energies of $A$ and $B$ before the reaction and add the kinetic energies of $C$ and $D$ after the reaction you'll find that the kinetic energy ... | {
"language": "en",
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Measuring different components of spin simultaneously I'm reading Griffiths Introduction to QM and I'm having trouble understanding why you can't simultaneously measure the x,y and z components of spin. I know that the uncertainty principle prevents this but I still don't see why.
Griffiths' example is that if we have ... | In general you are getting it right: Non-commuting operators do not share eigenstates, thus measuring $S_x$ on an eigenstate of $S_z$ will result in a state that is not an eigenstate of $S_z$ anymore. The spin operators do not commute because they are defined via the Lie-algebra relation $[S_i, S_j] = i \hbar \varepsil... | {
"language": "en",
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What means that a pendulum system having saddle points? What means that a pendulum system having saddle points? I know when it haves drain, source but I can't find any information of when it has saddle points
| Very simply put: a saddle point is an unstable equilibrium. Without solving the equations, you can probably guess where there is an unstable equilibrium for a simple pendulum system: if the pendulum is above right the pivot, it will stay there. But give it even a the slightest notch, and it will not go back to this pos... | {
"language": "en",
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Two Rolling logs Suppose we have two logs rolling down a hill, one of gold and the other of wood; the acceleration for both will be equal, something which is unclear to me; I get that this may be due to their form, which is the same, but how come the mass of the objects doesn't matter?
| $$F = M A$$
Simply, more mass doesn't mean more acceleration, but more force. The logs will accelerate at equal speeds, but the heavier one will carry more force with it.
So, the gold one would have much more force behind it, and would take more force to stop it. If you put up bowling pins down the hill to attempt to ... | {
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Why do we not use the SI system for distance in space? One of the closest stars to Sol is Alpha Centauri at 4.367 Ly according to wikipedia. Why do we not say that it is 41.343 Peta-meters rather? (4.367 Ly = 41.343 Pm)
Why does Light-years or Parsecs seem to be the standard rather than SI?
|
Why does Light-years or Parsecs seem to be the standard rather than SI?
In the solar system astronomy, the astronomical unit is much more widely used rather than meters for distance, days (86400 seconds), Julian years (365.25 days), or Julian centuries (36525 days) are used rather than seconds for time, and the solar... | {
"language": "en",
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What is the difference between a physical constant, a scalar, an invariant, and a conserved quantity? I don't really know how to properly articulate this question. This question popped into my mind when pondering why the fact that a physical constant like the speed of light doesn't have an associated symmetry even thou... | *
*A conserved quantity is a quantity whose value remains the same over time.
*An invariant, or scalar quantity is a quantity whose value is the same in all reference frames.
These two properties are completely independent. Energy is conserved but not invariant. Mass (i.e. $E^2 - c^2 \mathbf{p}^2$) is invariant but... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/267041",
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"source": "stackexchange",
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Scattering from a step potential barrier Suppose a potential barrier of the form
$$
V(x) = \begin{cases} V_0 & x>0 \\ 0 & x<0 \end{cases}
$$
Then, for energy $E$ such that $E < V_0$, we have that the transmission and reflection coefficients for the probabilities are $R = 1, T = 0$. In case where $V_0$ is not enormously... | $T$ and $R$ are transmission and reflection coefficients for waves. They refer to the probability that an incident wave will penetrate the barrier and continue propagating infinitely far. Physically, you should think of it as sending a constant sine wave in from the far left and looking to see what amplitude of constan... | {
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Why Do Glueballs Have Mass, When Individual Gluons Are Massless? From Wikipedia Glueballs
Glueballs are predicted by quantum chromodynamics to be massive, notwithstanding the fact that gluons themselves have zero rest mass in the Standard Model. Glueballs with all four possible combinations of quantum numbers P (parit... | Because glueballs have energy, and $E = m c^2$ says that energy is equivalent to mass. (Or another way to say it is that if you "zoom out" far enough that you can't see the constituent gluons that form the glueball, than you just lump all their energy into an effective glueball mass.) The energy can be thought of as ... | {
"language": "en",
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Principle of Maximum Work for Different Paths The principle of maximum work states that for any process between two states, the work done by the system is maximised for a reversible process (and heat transfer is minimised), and that the work done by any reversible process between these two states is equal.
I don't see ... | It doesn't seem possible for the original premise to be correct. If you start at a certain state, and carry out a reversible Carnot cycle ending up at the same original state, you can design a great big Carnot cycle and you can design a tiny little Carnot cycle. Certainly the reversible work for these two cycles will... | {
"language": "en",
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Sliding sphere wear shape Please refer to the figure attached. Consider a normal force is acting on the top of sphere. A constant coefficient of friction causes frictional force throughout the sliding. I want to know after this sphere slides (pure sliding no rolling) for sometime and assuming that it wears as it slides... | It depends. Assuming the lower surface is much harder than the sphere then :
If the sphere does not rotate at all as it slides then the answer is (a).
If the sphere rotates, ie rocks to and fro, as well as sliding, then it is (b).
On the other hand, if the sphere is harder than the lower surface, or the two surfaces h... | {
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"answer_id": 0
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Does the speed of light in vacuum define the universal speed limit?
*
*Is light the thing causing the universal speed limit to be $299\,792\,458\,\mathrm{m/s}$? So the universal speed limit would be different if light travelled faster or slower?
*Or, is $299\,792\,458\,\mathrm{m/s}$ the universal speed limit anyway ... | There is quite a bit of ambiguity in the question(s), so let me start by substituting electro-magnetic (EM) wave for "light." Then, the "universal speed limit," is the speed at which EM waves propagate in "space." The reason I use space (not vacuum), is because it is the characteristics of space ($u_o, \epsilon_o$) th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/267852",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "32",
"answer_count": 6,
"answer_id": 4
} |
Conceptual doubt in Tension force I recently studied that Tension in a string is a kind of force originated from electrostatic attraction between the atoms of the string in which the force is originating. My doubt was that:
Assume that I am pulling a rope with a force $F$, and the rope will develop a tension $T$ in its... | If the rope is in static equilibrium then $T=F$. If $T\neq F$ then that section of the rope (where tension is $T$) must be accelerating, which may happen if the rope is slack or if it is extensible.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/267987",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Wouldn't a photon disappear because of length contraction? I was experimenting with the formula for length contraction, when I realized that anything traveling at the speed of light shrinks out of existence. This is the formula for length contraction:
$$T=T'\sqrt{1-\frac{v^2}{c^2}}$$
Where $T$ is the observed length an... | I am only a layman, so don't take this answer seriously.
This length contraction formula, and the whole Special Relativity in its original form, is for macro-sized, non-quantummechanical objects. Thus, the formulas work if you want to calculate the size of a spaceship nearing the speed of the light. And not if you want... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/268142",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Can we know the tension of the string that is connected to a pully?
If the pulley have mass, I learned that T1 and T2 isn't same. then what about the circled part of the string? can we calculate the tension with given T1 and T2?
| Somewhere in between $T_1$ and $T_2$ -- but exactly what depends on details about how the friction between the string and the pulley varies, how the string stretches under tension and the pulley deforms while being accelerated by the string ... All of these are things that cannot be deduced from an idealized picture su... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/268230",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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