Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Converting heat into energy I'm currently building a custom desk. In this desk I will also build-in a small part with a custom electronic panel to provide power to USB devices.
As my gaming pc generates a lot of heat and the panel will generate some too, I was thinking about doing something with this heat. I read anoth... | Ok, never mind. After checking some videos of homemade thermo electric generators, it's obvious my situation will never provide enough current and voltage for my USB. One created a voltage of arround 0.5V with a flame but with hardly enough current. Maybe I will create one for fun to check if it could light up some LED... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/90548",
"timestamp": "2023-03-29T00:00:00",
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Why is a vacuum cleaner not as good heater as an electric radiator? I've read this question and answer: How efficient is an electric heater?
, but still don't understand.
If I have an electric radiator it heats the room with 1000 Watts of power. And I feel the room's getting warmer.
In contrast, if I turn on a vacuum c... | A more creative answer involves knowledge of statistical physics:
Using the vacuum cleaner will transfer the system (your room) in a state of less entropy (if the rising temperature is neglected) as the dust is compressed in a smaller volume (just like the mixed state of two gases has more entropy then the state where... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/90612",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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At what frequency does the medium of air change from acoustic to light? I'm calculating the max doppler frequency of a fading channel in an in-room environment and looking at different carrier frequencies. Calculated as follows:
F = vf/c
Where
F -> max doppler shift
v -> Velocity of object
f -> carrier freq
c -> speed... | Acoustic and electromagnetic waves are totally different. There is no overlap whatsoever. You can obviously have very long EM waves, but best example I can think of would be old long wave radio. In my country they still transmit at 225 kHz which is quite easy to achieve with sound wave too, but their nature is differen... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/90743",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Observations in the cathode ray tube experiement
1.One of the observations I learned was that the glass tube begins to glow with a brilliant green light. Many websites I read through refer to a fluorescent material. However, as shown in the above diagram there was no fluorescent material in the experiment carried out ... | In this experiment discharge glass tube was taken and at both end of glass two metal plate were placed. they were connected with high voltage battery(10000 volt.) the H2 WAS filled at high pressure and at anode end a layer of ZnS WAS placed.
1) At high pressure i.e. 1atm when high voltage current passed then no chang... | {
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"timestamp": "2023-03-29T00:00:00",
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Photons traveling backwards in time? Imagine that two widely separated charged particles $A$ and $B$ exchange a photon.
Because they are far apart one can imagine that there is a major contribution to the photon propagator that travels at the speed of light from $A$ at a time $T_0$ to $B$ at a time $T_1$ where $T_1 > T... | Suppose $A$ is at the space-time origin $0$, and $B$ is at space-time event $x$. You suppose that a real photon could go from $A$ to $B$, so this means that $A$ and $B$ are separated by a light-like interval, that is $x^2 = (x^0)^2- \vec x^2=0$. This means that $x^0>0$, too.
Now, the propagator $D_{\mu\nu}(x)$ represe... | {
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Angular Momentum of a rigid, extended object: When we see a rotating object, is the state of rotation is totally relative? Angular momentum of an object is a physical quantity that depends on the chosen point about which to calculate the angular momentum.
It is often said that an object that has been thrown up in the a... |
So when we see an object rotating, its state of rotation is totally relative, as it happens for many other physical quantities...
Is that correct?
The state of rotation is not $totally$ relative; for example, the angular velocity of rotation is the same for all points of reference. It is true that you can use diff... | {
"language": "en",
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What does 99.9% speed of light mean when there is no absolute velocity? So when people say: 'I am approaching the speed of light, and to get to 100% light I would need infinite energy' they are essentially saying that this situation is impossible?
I read this in Hawking's book and confused me because I assume when he s... | It means 99.9% of the speed of light in a vacuum.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Quantum eraser double slit experiment In the quantum eraser double slit experiment, does the photon (or wavefunction) pass through one slit or both slits when different polarizers are placed over the slits?
| Quantum mechanics is a theory that can only predict probability distributions. It cannot predict trajectories. It is ruled by differential equations which have as solutions the wavefunctions, and the complex conjugate square of the wavefunction gives the probability of a specific, photon, electron, to be at (x,y,z,t) g... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/91317",
"timestamp": "2023-03-29T00:00:00",
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Is the spin 1/2 rotation matrix taken to be counterclockwise? The spin 1/2 rotation matrix around the $z$-axis I worked out to be
$$
e^{i\theta S_z}=\begin{pmatrix}
\exp\frac{i\theta}{2}&0\\
0&\exp\frac{-i\theta}{2}\\
\end{pmatrix}
$$
Is this taken to be anti-clockwise around the $z$-axis?
| For your example, we have $e^{i\theta S_z}\mathbf{S}e^{-i\theta S_z}=\begin{pmatrix}\cos\theta & -\sin\theta&0\\\sin\theta & \cos\theta&0\\0&0&1\end{pmatrix}\mathbf{S}$, with $e^{i\theta S_z}=\begin{pmatrix}e^{i\frac{\theta }{2}} & 0\\ 0 & e^{-i\frac{\theta }{2}}\end{pmatrix}$ and $\mathbf{S}=\begin{pmatrix}S_x\\ S_y\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/91483",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Placatory motion of more than two bodies Recently in a documentary I heard that Newton's law of gravitation very well explains motion of two bodies such as sun and earth. And when applied to three bodies the answer is chaotic and not stable.
Then how do physicists explain the motion of higher number of bodies such as t... | Here is an example of a (relatively) recent paper to deal with the many-body gravitational problem in regards to the orbit of Mercury. The upshot is that big masses are only slightly perturbed by smaller masses, but small masses can be strongly influenced by the behavior of larger masses. So think of it this way: the d... | {
"language": "en",
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Is it possible to "cook" pasta at room temperature with low enough pressure? It is known fact, that boiling point of water decreases by decreasing of pressure. So there is a pressure at which water boils at room temperature.
Would it be possible to cook e.g. pasta at room temperature in vacuum chamber with low enough p... | Starches in the durum wheat flour will only activate at boiling temperature. Hydration is irrespective and can be achieved under vacuum.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "36",
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"answer_id": 6
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Why does a "speed of sound" exist? I've recently read that wind cannot be faster than the speed of sound (german source).
But why is there a speed of sound? I understand (well, mostly accept to be honest) that the speed of light in vacuum is a maximal speed for all matter. And I understand that you need more energy the... |
I've recently read that wind cannot be faster than the speed of sound
This is false. Wind can go faster than Mach 1. However, the wind present in nature usually doesn't, so the Fujita scale doesn't cross Mach 1.
But why is there a speed of sound?
Sound is, after all, a propagating vibration of air molecules. Molec... | {
"language": "en",
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"source": "stackexchange",
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Realistic calculation of heat loss for pipe Good day everyone,
I am new on this site and I hope to find here help, since I am not going anywhere with the literature I have found.
I try to calculate realistically the heat loss of a hot, uninsulated pipe. Let's say,
it is $170\,\,C$, 1 meter long, $8" (=0,203\,\,m)$ of d... | The natural convective heat transfer coefficient can be estimated through correlations and depends on geometry and its orientation.
There is a calculator which does this for a horizontal pipe here:
https://www.poppyi.com/app_design_form/public_render/free%20convection-%20horizontal%20cylinder
Hope this helps.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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General relativity in terms of differential forms Is there a formulation of general relativity in terms of differential forms instead of tensors with indices and sub-indices? If yes, where can I find it and what are the advantages of each method? If not, why is it not possible?
| It was Cartan who developed General Relativity in his book "ON MANIFOLDS WITH AN AFFINE CONNECTION AND THE THEORY OF GENERAL RELATIVITY " relying only on "Affine Connections", it is not clear to me what to be called a "formulation of General relativity in terms of differential forms", but I take it granted from the que... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/91867",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 4,
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Is it possible to estimate the speed of wind by the sound emitted by a cable of an overhead power line? I was near ($\approx40m$) an overhead power line and I heard a sound coming from the cables of the power line; I think the sound was made by the vibrations of the power cables due to the wind but I am not sure. The w... | In the design of aeolian vibration dampers the frequency of oscillation is given empirically by $$ f = 3.26 V/d $$ where $f$ is in $\rm Hz$, $V$ wind speed in $\rm mph$ and $d$ the cable diameter in $\rm in$. The problem is that beyond $15 \,{\rm mph}$ the wind is too choppy to excite one frequency and the vibration a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/91978",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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How can space and time arise from nothing? Lawrence Krauss said this on an Australian Q&A programme.
"...when you apply quantum mechanics to gravity, space itself can arise from nothing as can time..."
Can you elaborate on this please?
It's hard to search for!
| Space and time, as ordinarily understood, came into being after the Big Bang and after the temperature of the universe decreased to the point that the particles (matter) created could not revert back to energy.
When two "permanent" particles were created, space (distance between the particles) was created, and the re... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/92037",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
"answer_count": 7,
"answer_id": 5
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Does a sound at 50dB at 1m have the same intensity of a sound of 51dB at 10m? Does a sound at 50dB at 1m have the same intensity of a sound of 51dB at 10m, and also the same intensity of a 52dB sound at 100m?
| The scale of sound pressure (decibel) is logarithmic
$$
L_p=20\log_{10}\left(\frac{p}{p_{ref}}\right)
$$
With $p_{ref}$ a reference pressure, with a commonly used value of $20\mu Pa$ according to Wikipedia, because it is roughly the threshold of human hearing.
Due to this definition the intensity/pressure roughly doubl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/92088",
"timestamp": "2023-03-29T00:00:00",
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What exactly is a bound state and why does it have negative energy? Could you give me an idea of what bound states mean and what is their importance in quantum-mechanics problems with a potential (e.g. a potential described by a delta function)?
Why, when a stable bound state exists, the energies of the related station... | It means the same thing it means in classical mechanics: if it is energetically forbidden to separate to arbitrarily large distance they are "bound".
The Earth is gravitationally bound to the Sun and the Moon to the Earth. Electrons in a neutral atom are electomagnetically bound to the nucleus. A pea rolling around in ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/92244",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "35",
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Lax-Pair for principal chiral model This question concerns Eq. (2.10) of the paper https://arxiv.org/abs/hep-th/0305116 by Bena, Polchinski and Roiban.
In section 2.1 they are showing that the infinite number of conserved quantities for the principal chiral model
\begin{equation}
L = \frac{1}{2\alpha_0} \mathrm{Tr}(\p... | To simplify, take the notation : $U_y(x)= U(y,t;x,t)$, $U^{-1}_z(x)= U(x,t;z,t)$, $a_i(x) = a_i(x,t)$
Note that you have (on the spatial choosen path $ C = \int dx^1 = \int dx $) :
$\partial_x U^{-1}_z(x)=-a_1(x) U^{-1}_z(x)$, and $\partial_x U_y(x)= U_y(x)a_1(x)$
The minus sign difference can be understood because... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/92316",
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"source": "stackexchange",
"question_score": "4",
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Collision between a photon and a massive particle Just a small question regarding collisions.
Imagine a head-on collision between a photon and a particle with mass that moves with a non-relativistic speed, the particle was on its ground state, completely absorbs the photon, and moves to its next energy level. Is it alw... |
Is it always the case that the particle ends up with a non-relativistic speed after the collision?
No - it depends on the total energy of the particle after the interaction, which (given that the particle is initially non-relativistic) depends on the mass of the particle and the energy of the photon. Compare the ener... | {
"language": "en",
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Elementary particles That's what Wikipedia says about Elementary Particle:
In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus it is not known to be composed of other particles.
Assumed the above sentence:
Can we ever know the structure of an elementa... | Well it turns out that all particles in the standard model are maybe made of particles called "preons". However this is not a well supported theory. The theory that is trying to answer what particles are really made of is string theory. They say that all particles are made of one dimensional "strings".
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/92623",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Finding the Schwarzchild radius of a star of solar mass 30 I am currently trying to determine the Schwarzchild radius of a star with solar mass 30. I am calculating it both with respect to solar mass, and w.r.t kilograms, however I am getting conflicting answers. (of a factor of 10)
$$
1 \text{ solar mass} \sim 1.9891 ... | Your method is correct, but you've got lost in the numbers. This is a good opportunity to use some neat web tools.
Google: 30 solar masses
Answer:
30 solar masses =
5.9673 × $10^{31}$ kg
So you have miscalculated your solar masses in kg.
Secondly, there is a neat WolframAlpha tool:
Given Mass = 30 solar masses
Answe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/92990",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How to get a $\mathcal{N}=2$ SuperYang-Mills Lagrangian from a quiver How can one write down the $\mathcal{N}=2$ SuperYang-Mills Lagrangian given a quiver graph?
For concreteness consider the quiver
$$(2)-(4)-[6]$$
where the node $(2)$ corresponds to a $U(2)$ factor of the gauge group, the $(4)$ node is a $U(4)$ facto... | A quiver is a neat way of representing the field content of a large class of supersymmetric field theories. One also needs to specify the amount of supersymmetry to understand what a node or an edge stands for.
$\mathcal{N}=2$ supersymmetry implies that that the complete action can be written in terms of a holomorphi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/93170",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Do electromagnetic waves always move in straight lines? When we send an electromagnetic short wave to the sky, it reflects due to the ionosphere effects. But if we send it horizontally, is it correct that it moves around the surface of the earth, and if it has enough energy, it can return to its first position?
If yes,... | Due to the refraction index dependence on the air density, optical (and radio) rays bend in the atmosphere. It turns out that an atmospheric layer with temperature inversion (temperature increasing with height) can create conditions where the curvature of the ray would match the curvature of the Earth surface. This is ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/93243",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Basic geometric optics question - how come we don't have to have exact focus to capture objects clearly? The top frame of the image below shows an image formed on the screen (at right) of an object (pencil on the left) located at some distance $D$ from the lens. The lens focuses all the light rays hitting it from the t... | This is because usually you are taking pictures of objects that are in much greater distance from the lens than the focal length. In this case the photographed objects are all almost in "infinity" and the rays do not diverge that substantially.
In your drawings here you have the object in the same distance as the focal... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/93306",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Do centripetal and reactive centrifugal forces cancel each other out? In order for a body to move with uniform velocity in a circular path, there must exist some force towards the centre of curvature of the circular path. This is centripetal force. By Newton's Third Law, there must exist a reactive force that is equal ... | NO, They do not cancel out each other, while centripetal (center seeking force) is generally provided by some other agency/force, like for revolution of planets it is provided by gravitational force, centrifugal force(outward force) is a pseudo force which is felt in the reference frame of the revolving/rotating body. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/93599",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Will density of a metal increases during forging? This question is metallurgical engineering, but I had a similar doubt regarding density of liquids and what causing it.
Forged parts refines defects, dislocations will be moved strengthening the metal. But will the density of forged metal change?
My earlier question was... | Forging inevitably compresses the mass and therefore increases the density. In a perfect metal, forging would make little or no difference but no metals are perfect and most contain unwanted substances and voids. During the forging process voids are compressed and it is also possible that the impurities also are dimini... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/93745",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Could quarks be free in higher-dimensional space than 3D? Reading this answer, I now wonder: if quarks are confined by $r^2$ potential, could their potential allow infinite motion in higher-dimensional space?
To understand why I thought this might be possible, see what we have with electrostatic potential: in 3D it is ... | If you take the classical analogy of a charge generating field lines then the force at some point can be taken as the density of field lines at that point. In 3D at some distance $r$ the field lines are spread out over a spherical surface of area proportional to $r^2$ so their density and hence force goes as $r^{-2}$ -... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If a material is built to handle tension, would removing the tension damage it? If an object is designed to cope with large forces such as tension, would removing these forces risk damaging the object?
For example: The neck of a guitar is built to handle the tension of steel strings (~800 Newtons),
if you removed/reduc... | This answer is specifically about guitars because I have guitar building and repair experience.
The strings and the truss rod are under tension so the neck itself is mainly under compression. There is some tension on the back side of the neck due to neck relief (forward bow of neck) but not much. Necks are made from ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/94222",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Potential energy curve for intermolecular distance
(source: a-levelphysicstutor.com)
I'm trying to understand this curve better, but I can't quite figure out what "negative potential energy" means.
The graph should describe a molecule oscillating between $A$ and $B$, however where I'm stuck in reasoning this is that ... | It seems you are equating value of potential energy and repulsion/attraction. Identical values of potential energy do not mean identical behavior of the particle/system in question. Recall that force $F_r=-dU/dr$. If you want to find out whether there is attraction ($F_r<0$) or repulsion ($F_r>0$), you should look at t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/94281",
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"question_score": "1",
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During reflection does the emitted photon have same properties? When light (photon) is reflected the the original photon is absorbed by an electron and then emitted again. Does this "new" photon have the same wavelength, frequency etc. as the original?
|
During reflection does the emitted photon have same properties?
During reflection the color does not change and the phases do not changes otherwise the reflected images would be fuzzy.
I will complete the other answers by examining the mirror material.
Not all materials reflect. Reflecting materials are materials whe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/94359",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Angular speed of the planets Do all the planets in our solar system have the same angular speed? Physics teacher says yes, my research is not crystal clear. I want to make sure I have the right information for future reference.
| I would guess there is something missing in this question. Are you sure you have the teacher's statement correct? If the planets all had the the same angular speed (about the Sun) they would all complete an orbit in the same amount of time.
If it is angular speed about their axis, again clearly not true. Mercury rotate... | {
"language": "en",
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"source": "stackexchange",
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Gravitational collapse and free fall time (spherical, pressure-free)
A very large number of small particles forms a spherical cloud. Initially they are at rest, have uniform mass density per unit volume $\rho_0$, and occupy a region of radius $r_0$. The cloud collapses due to gravitation; the particles do not
intera... | A partial answer only.
Given a spherical collapse, and ignoring relativistic effects, the time is the same as the time taken for a particle at the edge of the cloud to fall to the centre.
As all the mass is inside the edge, we can determine the mass pulling that edge in as the volume of the sphere of radius $$r_0$$ tim... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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"answer_id": 1
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What is the center of Earth's landmass? I have read, several times, that the Great Pyramid is located at "the center of Earth's landmass".
How do we define "Earth's landmass"? And once defined, how do we find the center of it?
| This Wikipedia article has a quick discussion and finds the center to be near Ankara, Turkey. I would think a better point would be well inside the earth, the CM of the thin shell discussed in the article. Finding an average point on the surface of a sphere(oid) is problematic. It depends on your definition.
| {
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White light diffraction I have a hard time understanding why light waves of different wavelengths diffract in a different manner. According to Huygens' principle, every point on the wavefront is a source of a secondary wave. So if we have a white light going through, say, a single slit (light rays parallel to each othe... | Diffraction effects depend on the wavelength of the light. Considering a single narrow slit with monochromatic light, light with wavelengths much larger than the slit will not be transmitted and light with wavelengths much shorter than the slit will be transmitted without significant diffraction effects, but light wit... | {
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Measuring background radiation We tried to measure background radiation using a geiger counter for a experiment at school. The meter showed $0.12$-$0.21$ microSv/h during the day averaging at about $0.14$ mcSv/h.
As we tried to see ways how to shield incoming radiotion nothing seemed to work. Taking a cue from nuclear... | If you are not living close to a uranium mine or other natural sources of radioactivity the main radioactivity that your geiger counter measures outside is cosmic radiation. At sea level this is composed mainly by muons , which are weakly interacting and will not be stopped by a meter of water. This is also true f... | {
"language": "en",
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Can we calculate the frame dragging force of the Earth? Although clearly this force would be significantly greater with a rotating black hole, is it still possible to calculate this drag for say a satellite orbiting the Earth?
| This is really an add-on to the excellent answer by Pulsar. Sarah Jayne never got her units worked out fully because she had the wrong "g" and used "r" in km instead of meters. I solve the equation that she has posted using the universal constant G = 6.67e-11 m3/kgs2 as:
radian/second = 6.67e-11*8.02e37*7.29e-5/(2*3e... | {
"language": "en",
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Centre of instantaneous rotation problem Is there a point of Centre of Instantaneous Rotation (CIR) for every type of motion or only for cases of rolling?
| I assume you are talking about a rigid body in motion in a plane.
Consider any two different points on the body, A and B.
At any point in time, each one has a velocity vector $\vec{v_A}$ and $\vec{v_B}$ (assuming neither one is, itself, the center).
Consider the line normal to $\vec{v_A}$, call it $n_A$, and likewise $... | {
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Is the frequency/wavelength of light modified when multiple light sources are combined? Let's say I light a wall with two spotlights: One red and one green one. Where they overlap, I'll see a yellow area at the wall.
My question is, whether this is caused by an modification of the frequency/wavelength or simply by my e... | The bottom picture is correct. Your eye is only made up of red, blue, and green cones. This is what your eye uses to see all colors. When a yellow light enters your eye, the red and green cones activate, and you perceive yellow. This is the same as if red and green light enters your eye. Your mind perceives this as yel... | {
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Can a liquid insulator be electrically charged by touching a charged conductor?
Can a liquid insulator be electrically charged by touching a charged
conductor?
I understand that solid insulator will only be charge on the surface where it is touch, but the case is different from liquid which it circulates, so I imag... | It is certainly possible to charge insulators. I have personally charged ping pong balls and rubber balloons, and a certain Robert A. Millikan earned himself a Nobel prize by charging oil droplets.
But to get to the point of your question, you are correct that a liquid object (like Millikan's oil drops) will disperse t... | {
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Why is $U(\Lambda)^{-1} = U(\Lambda^{-1})$ for a unitary representation? This is from the beginning of Srednicki's QFT textbook, where he writes (approximately):
In QM we associate a unitary operator $U(\Lambda)$ to each proper orthochronous Lorentz transformation $\Lambda$. These operators must obey the composition r... | I'd like to add a something to V. Moretti's (correct) answer. You may be wondering
Where does the property $U(I) = I$ come from?
This property and the original one you asked about, generally hold for any group representation and, in fact, for any group homomorphism.
Let $\mathrm{SO}(1,3)^+$ denote the proper, orthoc... | {
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How do photons 'connect' during wireless connection? So wireless router broadcasts a signal and then your device searches. So what actually happens when the photons 'meet' it's kind of like saying, 'ah your one of us, so we will follow you, show us the way'
It's so bizarre, how do photons connect during wireless connec... | I'm not 100% sure, but I suppose photons are identified by its frequency.
WiFi routers have usually 12 or 14 channels, whose frequency depends on the local laws for telecommunications. They are supposed to be the only photons in each channel.
Any photon of a different frequency just will not be absorbed by the antenna.... | {
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If one is travelling at a significant fraction of $c$, will the length of the trip be shortened? Assuming two stars are 1 light year apart and a traveler is travelling at 0.75 of $c$, from the point of view of the traveler what would be the observed time en route? Also, if a vehicle is constantly accelerating, will it ... | Suppose to have an observer at rest with respect to the star and assume that their distance remains constant (1 light year). A spaceship traveling at $0.75 \, c$ with respect to this observer will cover 1 light year in $1.33$ years (16 months). However, for an observer inside the spaceship the length is contracted by a... | {
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Wavefunction of a Baryon How to write the total wavefunction of a Baryon including space part, spin part, isospin part and color part such that the net wavefunction is antisymmetric? What is the difference in wavefunctions of two different baryons but of same quark content say proton $p$ and $\Delta^+$ baryon?
| You can think of $\Delta^+$ as just the energized state of $p$, due to the spin configuration of the three quarks, and therefore different total spin ($3/2$ vs. $1/2$). This is much the same as the hydrogen atom, where different angular momentum states lead to different energy states.
| {
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Energy of an inductor I know that for an inductor having self inductance $L$ energy stored in its steady state when a current $I$ has been established is given by $U = \frac{LI^2}{2}$.
But after this current has been established, if we suddenly cut the wires attaching the inductor to the potential source or short the c... | The place where you cut the wire acts as a temporary Capacitor where a huge potential difference is formed. This potential difference causes an intense electric field to develop, which is where the energy is initially stored. If the potential difference developed exceeds the dielectric breakdown voltage of the interven... | {
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Phonon-phonon interaction I have been told that phonon-phonon Interaction is an anharmonic effect so only arises if terms of third and higher order in the displacement of the ions the Hamiltonian for the nuclii is taken into account.
So how do I see the there is no phonon-phonon interaction in the harmonic approximatio... | When you solve for such Hamiltonian for the harmonic oscillator you get a set of eigenstates which by definition are orthogonal and thus you have phonons that don't interact.
When you include a non harmonic term to the Hamiltonian and treating it as a perturbation you get new eigenstates that are a mixture of those the... | {
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Why does a picture of a person seem to be looking in the same direction irrespective of the angle of observation? If you observe a picture of a person hanging on a wall who seems to be looking directly towards you always seems to be looking at you even though you change your angle of observation to the extremes.
The s... | A picture has only two dimensions. Ultimately all depth created through perspective and light and shadow is a trick, similarly eyes in a painting following you is also an illusion. The light, shadow and perspective depicted in a painting are fixed, meaning they don't shift. in a painting also it don't change, they look... | {
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Which electron gets which energy level? Electrons sit in different energy levels of an atom, the farther the higher energy is. Every electrons have the same structure, they can gain energy from environment, electrons which gained energy could jump to a higher energy level and will finally fall back again.
I'm wonderin... | Pauli's exclusion Principle requires no two electrons to occupy the same quantum state. Based on spin, it is decided which electron 'sits' where it does. As far as the 'jumping' to the higher energy is concerned, it depends on the way the electron gains energy. If say, light of energy which matched the energy differenc... | {
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Branching lemon drop "smoke rings" This might be hard to ask, but here goes nothing.
I recently poured a cup of water into a black coffee cup. There was a light source--not very bright--above the cup. Anyways, I was squeezing a lemon into my water mindlessly, and to make sure I got every last drop of lemon juice into... | The smokering is the epitomy of perfect turbulence as is the 'smokering' described in this question. The fluid through which the smokering is passing flows laminarly against the circumference of the rotating ring as the smoke ring travels. The energy imparted to the molecules of the ring is stored in the circular rotat... | {
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Propagator of Maxwell-Chern-Simons theory I need to compute the "topologically massive photon" propagator.
I've started with:
$$
\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{\mu}{4}\epsilon^{\mu\nu\lambda}A_\mu\partial_\nu A_\lambda
$$
$$
=A_\mu\underbrace{[\frac{1}{2}g^{\mu\lambda}\partial^2+\frac{\mu}{2}\epsi... | The following is a rough calculation. If the operator,
$$\triangle^{\mu\lambda} = \eta^{\mu \lambda} \partial^2 + \mu \epsilon^{\mu\nu\lambda}\partial_{\nu},$$
is the one you wish to invert, then we must solve the differential equation
$$ \triangle^{\mu\lambda} G = \left[\eta^{\mu \lambda} \partial^2 + \mu \epsilon^{\m... | {
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Admixtures of longitudinal and timelike photons! In the quantization of electromagnetic field the physical states $|\psi\rangle$ are found to obey the following relation:
$[a^{(0)}(k)-a^{(3)}(k)]|\psi\rangle=0$
It is explained as the physical states are admixtures of longitudinal and timelike photons. What do longitudi... | It seems to me that longitudinal photons are not unphysical. They are responsible for the Coulomb interaction between charged particles.
| {
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Frequency of rotating coil Given a coil initially in the x-y plane, rotating at angular frequency $ \omega $ about the x-axis in a magnetic field in the z-direction. This uniform time varying magnetic field is given by $B_z (t)=B(0)cos(\omega t) $ I am required to show that there is a voltage of frequency $2\omega $ ac... | The angle $\theta$ between the normal($\hat n$) to the surface of the coil is given by $\theta=\omega t$ at any instant $t$. Also The magnetic field $B_n$ in the direction of $\hat n$ is given by $$B_n=B_z(t) \cos\omega t$$. calculation of flux through the coil of area $A$ is easy.
$$\Phi = B_n(t)A$$
$$\Phi = B_z(t)cos... | {
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What makes a rainbow happen? A rainbow is formed when a raindrop refracts light, but why then does the whole sky not become a huge rainbow when it rains? Would the light not be dispersed into ordinary white light? What causes it to look as if each end is nearly touching the ground?
| The best is probably to give you an insightful link. You will find there an applet which illustrates the following, which is your intuition:
*
*Coming from the sun, light rays hit the droplet and enter it with refraction air to water
*They reflect internally in the droplet
*They come to your eye, following a secon... | {
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Is using a swing an example of normal or of parametric resonance? Parametric resonance is a situation where the driving frequency is a multiple of the eigenfrequency. Various people say that using a swing and propelling it oneself is such a case, with the driving frequency being the double of the eigenfrequency. But wh... | In the case of a father pushing a child, it's normal resonance.
In the case of a child driving the motion itself it's parametric resonance. The Wikipedia article you mentioned states: For example, a well known parametric oscillator is a child pumping a swing by periodically standing and squatting to increase the size o... | {
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Why can you make two repelling positively charged rods touch? Shouldn't the Coulomb force become infinite? For a physics lab on the Triboelectric effect, we rubbed two rods with fur which gave both of them a positive charge.
We then brought them close together, and they obviously repelled. We then held one rod down fir... | The reason is that Coulomb's law is only directly valid for point charges, i.e. for charges, sizes of which are much smaller than distance between them. For particular symmetry reasons it appears to also be applicable to spherically symmetric balls of charge - but note that the distance you should take is not between t... | {
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When to use the Boltzmann distribution and the chemical potential? How do you know when to use the Boltzmann distribution for a particular problem?
I have many polymers connected together in many different possibilities by connector agents. All are in a solvent. I wrote the partition function of the system and used the... | The chemical potential is needed if you have an open system, that is able to exchange matter with another system. For instance, when water condensates, the liquid phase can exchange matter with the gaseous phase.
In polymer solutions, one usually needs to take the chemical potential into account because the monomers ca... | {
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Is crystal momentum an operator? My teacher has for Bloch waves the notation $\langle \vec{r}|\vec{k} \rangle = e^{i\vec{k}\cdot \vec{r}}u_{\vec{k}}(r)$ and uses it consistently. However, does this not assume that there is an operator that has eigenstates $|\vec{k} \rangle$? If so, how would such an operator be defined... | I was confused when I wrote that question... The answer, trivially, is that $|\vec{k} \rangle$ is just a state, not necessarily an eigenstate of any operator.
| {
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Can zinc nitride be used as light emitting material? I cannot manage to find any journal papers about the applicability of zinc nitride as active layer of an light emitting diode (LED). But certain papers got mention that zinc nitride with a direct bandgap can be fabricated with potential applications in optoelectronic... | In principle yes. But to make a good $\text{Zn}_3\text{N}_2$ homojunction LED you need the capability to incorporating both p-type and n-type dopants (normally oxide materials are naturally n-type) which might not be possible.
From what I have read, this material has been proposed as a way of making p-type ZnO (which i... | {
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Definition of quantum anharmonicity I have been reading research papers in mathematical physics for some months now, and I've seen the the term "anharmonic oscillator" quite frequently. At first I assumed that given a Schrodinger equation
$$\frac{d^2u}{dx^2}+(E-V(x))u=0$$
where $E$ is the energy, and $V(x)$ is the pote... | I've always treated anharmonic oscillators to mean the potential has the form
$$
V(x)=\gamma x^2 + \beta_ix^i
$$
with $i$ being any value except 2, including negative values as well. Anharmonicity then follows as the deviation of the eigenvalue of $V(x)$ above from the harmonic solution.
For example, the paper you link... | {
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Do photons and cosmic rays radiate energy through gravitational waves? If not, why not? Due to the mass-energy equivalence, both matter and EM radiation bend spacetime, and both are capable of forming singularities (black hole, white hole/kugelblitz). In light of this, why do photons traveling from the most distant rea... | Photons or cosmic rays don't (normally) emit gravitational waves.
Consider the comparison with radio waves. A moving electron doesn't emit radio waves. It has to be accelerating to emit EM radiation. Specifically radio waves are only emitted when there is a changing dipole moment.
So you wouldn't expect a particle movi... | {
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While holding an object, no work done but costs energy (in response to a similar question) I read the answer to Why does holding something up cost energy while no work is being done?
and wanting to know more, I asked my teacher about it without telling him what I read here. Instead of referring to muscle cells and biop... | Put the object on a table. Nothing happens, table or object. Your meat is metabolizing about 2000 Calories/day basal metsbolism, 8.4 million joules/day. "There is only about 0.1 mole of ATP in the body, but daily energy needs require 100 to 150 moles, or about 50 to 75 kg. The average human adult will use their body... | {
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Number of Parameters of Lorentz Group We embed the rotation group, $SO(3)$ into the Lorentz group, $O(1,3)$ : $SO(3) \hookrightarrow O(1,3)$ and then determine the six generators of Lorentz group: $J_x, J_y, J_z, K_x, K_y, K_z$ from the rotation and boost matrices.
From the number of the generators we realize that $O(1... | It's the same way you know there are three parameters in $SO(3)$. The equation $\Lambda^T \eta \, \Lambda = \eta$ has $(n^2+n)/2$ independent scalar equations. To see this, write the equation in component form: $\Lambda^{\mu\nu} \Lambda_\mu{}^\rho = \eta^{\nu\rho}$. Now we see there are $n^2$ scalar equations equations... | {
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How do wind turbines cause lightning? I saw this paper about Lightning discharges produced by wind turbines
More lightning strikes wind turbines than comparable non-moving structures.
What would be the physical cause of this? Does it depend upon the motion of the wind turbine blades or is it because these are connected... | I don't think that the fact that they are connected to the grid has anything to do with that. In fact, the generator part of the turbine is one of the most expensive parts, so it is protected against impacts from the outside.
The reason is simple: the turbine blades are being charged as a result of rubbing against the... | {
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Hydrogen atom: potential well and orbit radii I happened to open up an old solid-state electronics book by Sah, and in it he says:
"it is evident that the electron orbit radius is half the well radius at the energy level En"
The orbit radius is $r_n=\frac{4\pi\epsilon_0 ℏ^2 n^2}{mq^2}$ and the potential well $V(r_n)=\f... | Express V and E as explict functions of r.
$$V = \frac{-q^2}{(4\pi\epsilon_0)r}$$
$$E = \frac{-q^2}{2(4\pi\epsilon_0)r}$$
Also, the previous page of Sah emphasizes that 2E = V.
| {
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Are the axial electric field lines of a dipole the only ones that extend to infinity? Consider an electric dipole and its electric field lines.
There will be many field lines that do not extend to or originate from infinity, but rather begin at the positive charge and loop back around to terminate at the negative cha... | Dipole
$\def\vp{{\vec p}}\def\ve{{\vec e}}\def\l{\left}\def\r{\right}\def\vr{{\vec r}}\def\ph{\varphi}\def\eps{\varepsilon}\def\grad{\operatorname{grad}}\def\vE{{\vec E}}$
$\vp:=\ve Ql$ constant $l\rightarrow 0$, $Q\rightarrow\infty$.
\begin{align}
\ph(\vr,\vr') &= \lim_{l\rightarrow0}\frac{Ql\ve\cdot\ve}{4\pi\eps_0 ... | {
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Why is the moment of inertia (wrt. the center) for a hollow sphere higher than a solid sphere (with same radius and mass)? Why is the moment of inertia (wrt. the center) for a hollow sphere higher than a solid sphere (with same radius and mass)? I have completely no idea and I am inquiring about this as it is an intere... | A hollow sphere will have a much larger moment of inertia than a uniform sphere of the same size and the same mass.
If this seems counterintuitive, you probably carry a mental image of creating the hollow sphere by removing internal mass from the uniform sphere. This is an incorrect image, as such a process would cre... | {
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Center of rotation and trajectory of a rigid body in a plane with applied *fixed* forces This is my first question so please excuse me if my format is a bit off.
Given a 2D rigid body with forces applied to it in such a way that the angle the force vector makes with the surface of the object remains constant (think of ... | The problem as is stated is somehow ambiguous, but using some simplifications we can manage to get something: if we assume that forces don't change depending of the angle (i.e. there is no "correcting trayectory rocket" that acts depending of its orientation), and that the center of mass is fixed, then you can express ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/100481",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
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Relativistic fomulae for energy and momentum? I know that the relativistic formulae for energy and momentum are:
$E = \gamma mc^2$ and $\textbf{p} = \gamma m\textbf{v}$;
Can we derive these formulae?
If yes, where from?
| Once we have the position 4-vector
$$x^\mu=
\left(
\begin{array}{c}
ct\\
\vec{x}\\
\end{array}
\right)
$$
It is natural to define the momentum and energy in a fashion which is analogous to the Newtonian case (and reduces to it in the frame of the particle itself, when $\vec{v}=0$:
$$
p^\mu \equiv
m\frac{d}{d\tau}
\left... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/100638",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
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What is decay associated spectra? What is decay associated spectra?
Suppose we measure the fluorescence intensity over different wavelengths and over time, we get:
$$I(\lambda,t) = \sum_i^n \alpha_i(\lambda) \exp(\frac{-t}{\tau_i}).$$
The assumption is that there are n component,species, in the $I(\lambda,t)$. If we fi... | Sure it can be negative. It simply means that there is a dynamics (reaction, energy transfer, ...) between species, so that there is an exponential rise at some wavelengths
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/100710",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
Explain the microscopic nature of Electric current? Explain the microscopic nature of Electric current?i.e
What is is average current and Instantaneous current? A microscopic view what really happens?
| From a microscopic point of view you can image metal (conductors) in a lot of different ways. The easiest model is the Drude model in which atoms are fixed in the space and everyone have one or two (in a metal) free electrons. When you apply an external electric field this particles move as a consequence of Coulomb for... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/100782",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
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Linearized mass conservation equation I'm working on global seismology and I'm currently facing troubles understanding how an equation is obtained. The equation concerned is the following one :
$$
\rho^{E1} = -\nabla \cdot (\rho^0\mathbf{s})
$$
(From the book Theoretical Global Seismology, Princeton Press : Google Book... | If you substitute the decomposition in, you get:
$$ \partial_t \rho^0 + \partial_t \rho^{E1} + \nabla \cdot (\rho^0 \mathbf{u}^E) + \nabla \cdot (\rho^{E1} \mathbf{u}^E) = 0 $$
Typically the decomposition used assumes that $\rho^0$ is constant in time and that $\rho^{E1}$ is random in time, such that it's mean value is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/100839",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
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Bulk flow of air in a long tube between Antarctica and Australia? I have a 5km diameter clear plastic tube which is open at each end and runs from the center of Antarctica to Lake Eyre in Australia. The tube is on the ground where it can be and at sea level on the ocean.
Will there be bulk flow of the air in the tube? ... | any flow is driven by pressure gradient, which must overcome the friction of flow through the tube. It's a very long way, hence huge pressure drop relative to the initial pressure gradient. No flow
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/100920",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 4,
"answer_id": 3
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States of Matter and Equilibrium Can I say that, matter generally when cooled decreases in volume because, when it is cooled,i.e., we lower the temperature of the surroundings, then the avg. energy of our sample will be higher than the surroundings and hence, the molecules coming out will be more, therefore, the volume... | No, you should not refer to molecules coming out or going in, unless there is more than one phase (such as in evaporation, sublimation, condensation, etc.). The volume decreases (or increases) because the space between molecules or atoms decreases (or increases), even though the number of molecules or atoms is constan... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/100961",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Do exact beta functions exist in (super)gravity theories and string theory? An exact beta function exists for Super-Yang-Mills theories in 4D without matter - the so-called NSVZ beta function.
Does a similar exact beta-function exist in gravity or supergravity theories? In string theory? Please provide references too.
| @Ten The NSVZ beta function exists for theories with matter as well. Just read the scholarpedia article carefully. What happens is that the NSVZ beta function for the gauge coupling constants depends on the anomalous dimensions of the matter fields.
A very nice example is to consider $\mathcal{N}=4$ SYM theory and wri... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101011",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
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Neutrinos and anti-neutrinos in the Standard Model In standard model neutrinos and the left handed electron forms SU(2) doublet.
*
*What about the anti-neutrinos in the standard model? Do they also form some doublet?
*If neutrinos have tiny masses will it not imply indirectly and conclusively that right-handed neu... | The antineutrinos do indeed form a doublet. The particle-antiparticle conjugation operator is usually denoted by $\hat{C}$ and is defined through:
\begin{equation}
\hat{ C}: \psi \rightarrow \psi ^c = C \bar{\psi} ^T
\end{equation}
where $ C \equiv i \gamma _2 \gamma _0 $. So given a neutrino you can always get its c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101114",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Confused about Impulse Encountered a problem that involves impulse while studying for my exam and I'm not sure how to even approach it. I know that momentum is conserved, but I'm not sure how to relate that to avg force. Maybe someone can help point me in the right direction? I know that it's in quadrant III, through i... | Alternatively, and qualitatively, think about the components of velocity (in the x y directions) have changed. Along the x axis, velocity has reduced, so the re has been a force in the -x direction. In the y axis, velocity has changed sign, so there must have been a force in the -y direction. Hence the total force... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101226",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why does foam dull knives? I have recently taken up prop making and just started my first foam-built costume from a video game. These kinds of costume armour builds are often built out of the various foam floor mats you can buy in say Home Depot or BJ's or Five Below for around $1 for 4 sq. foot tile.
The one thing tha... | My guess is that the foam has some type of sillica in it which may stick to the knife having a detremental effect on its cutting ability possibly cleaning the blades regularly with alcohol could help this but i'm no chemist, hopefully this is helpful
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101341",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 4,
"answer_id": 1
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Which angle should it be? in the formula
$$dB = \frac{\mu_0l ~|dl \times r|}{4 \pi r^3} $$
and the image
where dl is in y-z plane and dB is in x-y plane. the ring conductor is in y-z plane carrying current I in direction as mentioned
EDIT: also point p can move in the circular ring
EDIT 2:To clear the confusion...T... | The angle between $\vec {dl}$ and $\vec r$ is $2n\pi \pm\dfrac{\pi}{2}$ because the angle between them is the angle between the x-r plane and y-z plane.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101424",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Does the equation of continuity hold for turbulent flows? My textbook mainly deals with laminar flows. The book derives the equation of continuity, which states that the cross-sectional area times the velocity of a flow is always constant. But nowhere in the derivation does the textbook explicitly assumes that the flow... | In order to have such a relation, your flow needs to be be stationary, which is never the case for turbulent flows.
The conservation of the mass gives you the local continuity equation.
$$\partial_t \rho+ \nabla . (\rho \vec{v})=0 $$
For a stationary problem without sources, Ostrogradsky's theorem allows you to reach:
... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101555",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Does a mirror help a near-sighted persion see at a distance clearer? A near-sighted person without eye-glasses can not clearly see things at distance.
If he takes a photo of the things at distance, he can see the things from the photo much clearer, because he can place the photo much closer to his eyes.
If he turns his... | Edit: Reading other people's answers, I forgot to mention I assumed a flat mirror.
Excellent question, but the answer is no. The reason is because the object (in the strict optics meaning) in the case of the photograph is actually on the paper whereas in the case of the mirror it is still at the same place, far behind:... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101627",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "22",
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Wrong positioned Ampere-meter and Voltmeter I'm dealing with a problem here and even that I'm trying to solve it i can't
It says:
In what figures the voltmeter and ampere-meter are wrong positioned?
I think that all the the others are correct except the second one.
Can anyone help me?
| The ammeter actually creates a short across the battery in the second figure (so that one is certainly wrong). Very likely, this would cause damage to the ammeter, or at least result in a blown input protection fuse.
I think the other diagrams are OK, depending on what it is you are trying to measure (which is open t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101701",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Would there be fringe pattern in this arrangement? Figure shows a standard two slit
arrangement with slits S1, S2. P1, P2 are the two
minima points on either side of P.
At P2 on the screen, there is a hole and behind P2
is a second 2- slit arrangement with slits S3, S4
and a second screen behind them.
Would there be ... | In interference and diffraction, light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe. There is no gain or loss of energy, which is consistent with the principle of conservation of energy.
If you consider a point where there is de... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101872",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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The best way to cool the teapot My professor today in the class made us a question:
"Lets say we have a teapot with water in it.The water is hot.Now we want to cool the water.
Will it cool faster if we put an ice cube above the teapot or under the teapot."
My answer was the it will cool faster if we put the ice cube ab... | Put the ice cube atop. Poorer air and water conductive and convective heat transfer kinetics are more than compensated by meltwater and cooled air dribbling down the pot, further cooling it by heat capacity as they warms from 0 C. If the ice cube is touching the bottom, meltwater and cooled air flow away from the pot... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101915",
"timestamp": "2023-03-29T00:00:00",
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Valley meaning explanation for foreigner English is not my native language and I have some hard time translating this word.
I was searching in couple dictionaries(both paper and online) and could not find it.
Could anyone provide me definition of word "Valley".
example usage:
Suggest using only the valley degree of f... | Sounds like graphene physics or something similar. You won't find it in a dictionary.
In the band structures of many materials, it is common to find multiple similar points in reciprocal (momentum) space. For example, in silicon's band structure there are six distinct conduction bands that all have similar behaviour. T... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101972",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Deriving commutation relations in second quantisation I am trying to start from:
\begin{align*}
[\phi(x),\pi(x')] = i\hbar\delta(x-x') \\
[\phi(x),\phi(x')] = [\pi(x),\pi(x')]=0
\end{align*}
to derive:
\begin{align*}
[a(k),a(k')^\dagger]=\delta_{kk'}\\
[a(k),a(k')]=[a(k)^\dagger,a(k')^\dagger]=0
\end{align*}
So startin... | I believe in the last line, the plane-wave functions $u_k(x)$ should carry different coordinates and momenta, e.g
$$ [a(k)^\dagger,a(k')]u_k(x)u_{k'}(x') $$
You may note that the commutator $[\phi(x),\pi(x')]=i\hbar\delta(x-x')$ holds if one choses $[a_k,a_{k'}^\dagger]=\delta_{kk'}$. However, this indirect reasoning ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Aerosol size distribution When the size distribution of particles in an aerosol is obtained, there is always a bimodal distribution. The small peak accounts for the particles that are in sub-nanometer size range and the larger peak accounts for the particles that are in nanometer to micrometer size range. Why does it s... | There may be several reasons for this.
In general the bimodal character of atmospheric aerosols is the owed to different lifetime of particles. These are dependent on the particle size and loss mechanisms predominantely associated with the respective sizes.
Usually atmospheric aerosols consist of four size modes. From ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102174",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 1,
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How does a half-life work? Carbon-14 has a half-life of 5,730 years. That means that after 5,730 years, half of that sample decays. After another 5,730 years, a quarter of the original sample decays (and the cycle goes on and on, and one could use virtually any radioactive isotope). Why is this so? Logically, shoul... | The mass of radioactive materials follows the ordinary differential equation:
$$
m'(t)=-am(t),
$$
where $m$ is the mass and $a$ a positive constant - i.e., constant relative rate of decay.
This implies
$$
m(t)=m(0)\mathrm{e}^{-at}. \tag{1}
$$
If $T_h$ is half life, then $$m(T_h)=m(0)\mathrm{e}^{-aT_h}=\frac{1}{2}m(0),... | {
"language": "en",
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"source": "stackexchange",
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Prove identity of partial derivatives I can not do the following problem:
Prove the identity:
$$\left( \frac{\partial x}{\partial y} \right)_{z}\left( \frac{\partial y}{\partial z} \right)_{x}\left( \frac{\partial z}{\partial x} \right)_{y}=-1$$
State the properties that must be $x=x(y,z)$, $y=y(x,z)$, $z=(x,y)$.
The t... | The way I always thought about this was to pick one of the variables to be thought of as the dependent variable. Here I will pick $z$. Then we think of $z(x,y)$ to be a function which has partial derivatives $\partial_x z = \frac{\partial z}{\partial x}$ and $\partial_y z = \frac{\partial z}{\partial y}$.
Now we must ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why are free electrons free? This is what I understand so far: in a conductor, the ions have a weak pull on the valence electrons. So when an electric field is applied, the free electrons are able to easily move about. Makes sense.
In a neutral conductor with no electric field, the free electrons aren't bound to any io... | The intuition is that the valence electrons are so far away from their nucleus that when they combine to form metals, they feel the attraction of all the other nuclei as strongly as from theirs.
In a more rigorous description, the orbitals for the valence electrons fully overlap with their neighbouring atoms, so their ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"answer_id": 2
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Naive visualization of space-time curvature With only a limited knowledge of general relativity, I usually explain space-time curvature (to myself and others) thus:
"If you throw a ball, it will move along a parabola. Initially its vertical speed will be high, then it will slow down, and then speed up again as it appro... | You have the right basic idea. But it gets simpler to visualize if you just drop the ball, or throw it vertically. Then there is just one spatial dimension to consider, and you can directly compare the paths in space and in space-time, like shown here:
http://www.youtube.com/watch?v=DdC0QN6f3G4
But note that this doesn... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102409",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
"answer_count": 5,
"answer_id": 1
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Auto-refrigeration I'm reading about the auto-refrigeration effect and can't find a really good explanation. Is the idea that when you have your condensed liquid, and then release it into a low pressure environment, some of it evaporates instantly, leaving behind a cold liquid?
Let me explain what I'm thinking again: p... | If you want to separate hot and cold gas streams from a common stream, use a Ranque-Hilsch vortex tube,
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102495",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
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A paradox to Lenz's law I have read that in simple words, Lenz's law states that:
The direction of current induced in a conductor is in such a fashion, that it opposes its cause.
This validates law of conservation of mass-energy.
I arranged the following thought experiment:
Let there be a pendulum with its bob being ... | As the magnet approaches the solenoid, a current is induced. The current generates a magnetic field. The field repels the magnet, slowing it's approach. The amplitude of the oscillations diminish.
If there was no resistance, this would work in reverse as the magnet receded from the solenoid. The magnetic field would a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102556",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 7,
"answer_id": 4
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Why do we have a TeV scale? When model building we don't want to introduce any new scales into our theory. We usually try to have new particles at the Higgs (TeV) scale (to solve the hierarchy problem), at the GUT scale, or at the Planck scale.
However, if the Higgs VEV already gives us a new scale, why would there no... | If you want the new physics to solve the hierarchy problem, it's best if it is close to the weak scale, or else you will be left with a residual little hierarchy.
You are describing the "big desert" between the weak and GUT scales. I think it was motivated by the idea that SUSY lived at the weak scale, solving the hier... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102703",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
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electron levels in a high voltage conductor what is the electron energy level in a 300,000 volt power line? This voltage is way above the ionisation potential but electrons are not emitted from the wire.
| The electron energy in the line is $300kV$ * the electron charge $q$. Whether or not electrons are emitted depends on the gradient of the voltage, i.e the electric field, at the surface of the wire, which determines the force on the electron. See the wikipedia article on field electron emission.
A well-designed hig... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
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Schrödinger's Equation and its complex conjugate I would like to know why there is a minus sign on the right-hand side of the Schrödinger's complex conjugate equation, whereas in the Schrödinger's equation there isn't. I know it is a simple question, but I don't know where this comes from.
$$
-\frac{\hbar^2 }{2m}\frac{... | I personally (maybe wrongly) see this feature as an early sign of the $CT$ symmetry where $C$ is the charge conjugate symmetry operation and $T$ is the time-reversal symmetry operation. Having no explicit charge in your equation, the charge conjugate symmetry operation would be simply taking the complex conjugate of th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102838",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 1
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Bogoliubov transformation with a slight twist Given a Hamiltonian of the form
$$H=\sum_k \begin{pmatrix}a_k^\dagger & b_k^\dagger \end{pmatrix}
\begin{pmatrix}\omega_0 & \Omega f_k \\ \Omega f_k^* & \omega_0\end{pmatrix} \begin{pmatrix}a_k \\ b_k\end{pmatrix}, $$
where $a_k$ and $b_k$ are bosonic annihilation operators... | The Hamiltonian can be written as
$\sum_k \psi^\dagger M \psi$
where $\psi=\begin{pmatrix}a_k \\ b_k\end{pmatrix}$ and $M=\begin{pmatrix}\omega_0 & \Omega f_k^* \\ \Omega f_k & \omega_0\end{pmatrix}$.
We introduce a new set of operators $\phi=\begin{pmatrix}c_k \\ d_k\end{pmatrix}$, via $\psi=U \phi$ where $U$ is necce... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102967",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 4,
"answer_id": 2
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Electric field near surface of a conductor?
If the electric field on a positive charge is non-zero, then the charge accelerates in the direction of the field.
The field at the surface of a conductor is perpendicular to the surface. Why don't the surface charges accelerate away from the surface of the conductor then?
| In a conductor the electric field within itself is always equal to 0 and therefore all of the charge is found on the surfaces of the conductor, forming an equipotential. We are left with a surface charge density $\sigma$ and an electric field (close to the surface):
$$\vec{E}\approx \frac{\sigma}{2\varepsilon_{0}}\hat{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103049",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Superconducting wire in a Magnetic Field? A superconducting wire($SC$) is moved rapidly in a magnetic field( $1$ $Tesla$), what would happen to the wire? Are there any forces induced of attraction or repulsion?
In a typical conductor, we know that if it is moved around a magnetic field $-V$ is induced within the wire ... | The induced current will flow in such a way that the flux produced will tend to cancel the change in flux. According to traditional classical electrodynamics, the magnetic field does not do any work and it is the electric field and the charge carriers which do the work and ultimately limit Faraday's law in extreme case... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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"answer_id": 0
} |
Step in a proof that $\textrm{div} \ \mathbf{B} = 0$ from Biot-Savart's law Notation: The magnetic field $\mathbf{B}$ generated by a point charge $e$ moving with velocity $\mathbf{v}$ is given by Biot-Savart's law
$$\mathbf{B} = \frac{\mu_0 e\ \mathbf{v} \wedge \mathbf{r}}{4\pi r^3}$$ where $\mathbf{r}$ is the vector f... | $\textrm{curl} \ \mathbf{v} = 0$, since $\mathbf{v}$ is not a function of the position at which the field is measured, i.e., it is not a function of the variable with respect to which we are differentiating.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103226",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Effect of linear terms on a QFT I was told when first learning QFT that linear terms in the Lagrangian are harmless and we can essentially just ignore them. However, I've recently seen in the linear sigma model,
\begin{equation}
{\cal L} = \frac{1}{2} \partial _\mu \phi _i \partial ^\mu \phi _i - \frac{m ^2 }{2} \phi ... | Linear terms are important. But in a Poincare covariant QFT, one can always remove them by shifting the field by a constant computed as a stationary point of the Lagrangian.
If there is only one stationary point, it must be a minimizer (to have the energy bounded below), then this gives a unique normal form without li... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103328",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
"answer_count": 3,
"answer_id": 2
} |
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