Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Black hole temperature in an asymptotically de Sitter spacetime I am trying to calculate the Hawking temperature of a Schwarzschild black hole in a spacetime which is asymptotically dS. Ignoring the 2-sphere, the metric is given by
$ds^2=\left(1-\frac{2M}{r}-\frac{r^2}{L^2}\right)d\tau^2+\left(1-\frac{2M}{r}-\frac{r^2}... | See
L. Rodriguez and T. Yildirim, Class. Quantum Grav. 27, 155003 (2010),
arXiv:1003.0026.
Section 2.3 has the Schwarzschild-dS calculation.
Lets define $f(r)=1-\frac{2M}{r}-\frac{r^2}{L^2}$
Radius of the horizon is given by the largest real root of f(r)=0
But of course $L\rightarrow \infty$ is still important.
Once y... | {
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"url": "https://physics.stackexchange.com/questions/104015",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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Sound as a use to separate molecular structures Sound can be a destructive force. However, could it be used to separate say the Hydrogen atom from the Oxygen atoms?
| Molecules are broken apart when they collide with one another with enough force to break the bonds that hold them together. These collisions happen all the time and depend on the density of the gas. This is what defines the mean free path.
The frequency of collisions increases with density. The force involved in the c... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Write down equations for the electric field and magnetic fields components of a linearly polarized plane wave
A linearly polarized plane wave at 100 MHz is propagating in the $z$ direction. The electric field vector makes an angle of 30° with the $x$-axis. Its peaks amplitude is measured to be $2.0\:\mathrm{ V m}^{-1}... | The x component of E(z,t) is |E|cos(30)=2 V/m * (sqrt(3)/2)
The y component of E(z,t) is |E|sin(30)=2 V/m * (1/2)
k=2πf/c = 2*pi/3
ω=2πf = 2*pi*10^8
E(z,t)=2(i(sqrt(3)/2)+j(1/2))cos(2*pi*z/3-2*pi*10^8*t) V/m
B= (kxE)/c = (0i+0j+k)/(3E8) x (i(sqrt(3))+j) [cos(2*pi(z/3-10^8*t))] 10^(-8) T
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/104228",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Size of Universe after inflation I read in some website that during the period of inflation, the expansion of the universe underwent incredibly fast, and its size increased by a factor of $10 ^{50}$, see this link
In this field, I think, there is nothing for sure, but if there was really inflation, what does it mean th... | In the phrase used in the article you link:
inflated the size of the cosmos by a factor of $10^{50}$
the word size is misleading and should be replaced by scale factor. Whether the universe has a size or not isn't clear. The universe may well be infinite, in which case its size isn't defined. However the scale factor... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/104302",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Temperature of gases I can't find any law that states this (maybe the combined gas law does and I'm misinterpreting it?), but Feynman said that if you compress a gas, the temperature increases. This makes sense, for example, a diesel engine (or gas engine with insufficient octane or too high a compression ratio). Also,... | Consider a gas in a container. When the container expands, the gas cools down. The crux is in thinking about why the container expands. The reason the container expands is because there are gas particles hitting the walls, pushing them outward: they do work on the walls!
This work on the walls costs them some energy, s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/104519",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Where is the "event horizon" on a basketball hoop? I'm watching a lot of basketball this month. A common event is the ball going part way into the hoop and then coming out again. Announcers sometimes claim that the ball was "halfway through" when it rims out. Thinking about it, with enough rotation and friction I would... | Theoretically, if you don't limit the rotational speed, The ball going halfway through and coming back out is (probably) possible.
All you gotta do is spin it fast enough in the right direction and launch it at the right angle so that it hits the rim perpendicularly. The normal impulse due to the collision will generat... | {
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"url": "https://physics.stackexchange.com/questions/104595",
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"question_score": "13",
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Help understanding proof in simultaneous diagonalization The proof is from Principles of Quantum Mechanics by Shankar. The theorem is:
If $\Omega$ and $\Lambda$ are two commuting Hermitian operators, there exists (at least) a basis of common eigenvectors that diagonalizes them both.
The proof is:
Consider first the ca... | Since the vector $\Lambda | \omega_i \rangle $ has the same eigenvalue as $| \omega_i \rangle $, it must be in the same invariant subspace as $| \omega_i \rangle $, which Shankar takes to be one dimensional.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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"answer_id": 2
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Proving a step in this field-theoretic derivation of the Bogoliubov de Gennes (BdG) equations In derivation of the BdG mean field Hamiltonian as follows, I have a confusion here in the second step:
$H_{MF-eff} = \int d^{3}r\psi_{\uparrow}^{\dagger}(\mathbf{r})H_{E}(\mathbf{r})\psi_{\uparrow}(\mathbf{r})+\int d^{3}r\psi... | Let's do a fourier transform of the field operator:
$$\Psi_\downarrow(r)=\frac{1}{\sqrt{N}}\sum_p\phi_p a_p$$
Where $\phi_p$ is the plane wave hence the eigenvector of $H_E$.
Now it is easy to show that:
$$\int d^3r\Psi_\downarrow^\dagger(r)H_E\Psi_\downarrow(r)+\int d^3r\Psi_\downarrow(r)H_E^*\Psi_\downarrow^\dagger(r... | {
"language": "en",
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How to show the invariant nature of some value by the group theory representations? Let's have Dirac spinor $\Psi (x)$. It transforms as $\left( \frac{1}{2}, 0 \right) \oplus \left( 0, \frac{1}{2} \right)$ representation of the Lorentz group:
$$
\Psi = \begin{pmatrix} \psi_{a} \\ \kappa^{\dot {a}}\end{pmatrix}, \quad ... | You need to work out the tensor product and will find a direct sum of different contributions
\begin{multline} [(1/2, 0) \oplus (0, 1/2)] \otimes [(1/2, 0) \oplus (0, 1/2)] =\\ \big((1/2, 0) \otimes (1/2, 0)\big) \oplus \big((1/2, 0) \otimes (0, 1/2) \big)\oplus \quad \\\big((0, 1/2) \otimes (1/2, 0)\big) \oplus \big((... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/104822",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Spatial bound on the internal electron structure In 2006 the radius for a possible internal structure of the electron has been pinned down to $10^{-18} m$. This validates the approximation of electrons as point particles at long distances, e.g. in an atom. The upper bound on the internal electron radius has been derive... |
But how do you calculate the g factor of a point particle or an extend particle?
This is done for a point particle, and any experimental deviation from the calculated value for a point particle would suggest structure beyond a point particle.
Dirac theory predicts g=2.
Anomaly from g=2 has QED, hadronic and weak ... | {
"language": "en",
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Correct formula to express the potential generated by a single layer charge distribution Assume that the closed surface $S$ encircles a volume $V$, and that a surface charge with density $\sigma$ ("single layer") is distributed over $S$. My question regards the electrostatic potential $\phi$ generated inside the volume... | Your equation (1) is right.
Your Neumann boundary value problem is not correct. You actually have a free-space problem (your domain is $\mathbb{R}^3$). In that space some surfaces are charged. You do not have something like ideal conducting surfaces or symmetry conditions which would allow you to reduce the problem to ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/105012",
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Is radioactive decay spontaneous or random? When it comes to radioactive decay, what is the difference between random and spontaneous?
For example, when the count rate of a radioactive isotope is measured, the readings fluctuate. Is this a demonstration of the randomness of the process, or of its spontaneous nature?
| Spontaneous means to me as anything that takes place on its own without any inflience of any external factor e.g
Temperature
Pressure
Magnetic field
Electric field.etc ...........
Radioactivity or radioactive decay is a spontaneous process. It is because the radioactive elements continuously emit radiation from them ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/105107",
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Why is the Gibbs Free Energy $F-HM$? With magnetism, the Gibbs Free Energy is $F-HM$, where $F$ is the Helmholtz Free Energy, $H$ is the auxiliary magnetic field, and $M$ is magnetization.
Why is this? Normally, in thermodynamics, we Legendre Transform the various free energies into each other to maximize the global e... | According to the first law of thermodynamics
\begin{align}U=TS+YX+\sum_j\mu_jN_j.\end{align}
Where $Y$ is the generalized force, $dX$ is the generalized displacement.
Helmholtz Free Energy
\begin{align}F=U-TS=YX+\sum_j\mu_jN_j. \end{align}
Gibbs Free Energy
\begin{align}G=U-TS-YX=\sum_j\mu_jN_j.\end{align}
Therefore th... | {
"language": "en",
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Why is titanium dioxide transparent for visible light but not for UV? I wonder the reason for TiO2 thin films to be transparent for visible light but not for UV. I made a quick search and I found that it is due to the band gap of TiO2. It absorbs UV light but not visible light. I imagine this occurs because of the diff... | The energy per photon of light with wavelegth $\lambda$ is given by:
$$ E = \frac{hc}{\lambda} $$
If the energy per photon is smaller than the band gap the light cannot excite electrons from the valence to conduction band so it will pass through the material without being absorbed. If the energy is larger than the band... | {
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What happens when we bring an electron and a proton together? I have a couple of conceptual questions that I have always been asking myself.
Suppose we have an electron and a proton at very large distance apart, with nothing in their way. They would feel each the other particle's field - however weak - and start accele... | In nuclear fussion electrons and protons can fuse to form neutrons with the release of photons.
| {
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Magnetism due to relativity? So I have been reading in some books that magnetism does not have to be assumed a priori, but can be obtained from the electric field + special relativity.
And I have seen how this leads to the common formula for the magnetic field of a current carrying wire.
Fine.
What about materials that... | Magnetism in ferromagnetic materials (e.g. iron) emerge from the spin alignment of valence electrons. Spin is a purely quantum phenomenon that occurs due to relativity, so without relativity one would not have spin in the first place. The presence of spin causes electrons to possess an intrinsic magnetic moment, equa... | {
"language": "en",
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Viewing glass from an oblique angle When I view most glass from the side it's green which I've found out is due to impurities in the glass specifically from iron oxide.
Why is it when I view the larger face from an oblique angle, it isn't nearly as green? I cannot personally notice any different on the piece I have nex... | As you stated, the degree of green is directly dependent on the thickness of glass you stare at (Beer-Lambert law). It actually comes from the absorption of the other wavelengths by the glass.
Due to refraction, even when you look at the glass from a grazing angle in the air, the light rays bend to a higher angle in th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/105693",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Total Electrical potential energy of two particle system I recently have been studying Electro-statics and I couldn't understand properly how the potential energy of two particle system is found.
Suppose you have two particles with charges $Q_1$ and $Q_2$ respectively. The distance between them is $r$. What is the to... | The potential energy is the energy required (or work done) to pick up one of the charges from infinitely far away, and push it towards the other particle to the distance you want. Since there is a force acting on these particles (either positive or negative, depending on their relative charges) it takes energy to move ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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A question about Hamiltonian phase flow
Show that if a one-parameter group of difeomorphisms of a symplectic manifold preserves the symplectic structure then it is a locally hamiltonian phase flow.
Note that
A locally hamiltonian vector field on a symplectic manifold $(M^{2n}, \omega^2)$ is the vector field $I \omeg... | Hints:
*
*Prove that a one-parameter group $(\Phi_t)_{t\in I}$ of diffeomorphisms $\Phi_t: M \to M$ is generated by a vector field $X\in\Gamma(M)$.
*Prove that if the one-parameter group $(\Phi_t)_{t\in I}$ preserves the a form $\omega$ then ${\cal L}_{X}\omega =0$.
*Prove that ${\cal L}_{X}\omega =0$ together wit... | {
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Why do particles in high pressure air always flow to lower pressure? The title really says it all: Why is this case? A "Feynman type" answer would be really appreciated as I'm more of a layman that a physicist.
| The answer to this question is quite intuitive when you think about what pressure is: a force per unit area. In a high pressure zone, particles experience a high force, and in a low pressure zone, they experience a lower force. The high force "overpowers" the lower force, pushing the particles from the high pressure zo... | {
"language": "en",
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How can point-like particles in an ideal gas reach thermodynamical equilibrium? Having learned that the particles of an ideal gas must be point-like (for the gas to be ideal) I wonder how they can reach thermodynamical equilibrium (by "partially" exchanging momentum and energy). First the probability of two point-like ... | An ideal gas in equilibrium cannot be supposed to have reached its equilibrium from a non-equilibrium state by interaction of its particles, because by definition the particles of an ideal gas do not interact:
*
*Hard spheres of radius $a$ that collide elastically do interact in the time average - even when they int... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is a scaled-up aircraft carrier 'ski-ramp' a viable system to impart enough velocity to significantly assist a spacecraft to orbit? Not a boost straight up to escape velocity, just sufficient added momentum to make a significant economic saving on fuel cost, mass and complexity of a standard launch. It seems ludicrous ... | This concept has gotten consideration from NASA. In the NASA MagLifter concept, a 300-600 miles per hour speed on a superconducting magnetic levitation track appoximately 2.5 miles long and going up a mountain to about 10,000 feet is proposed.
The option of using a helium filled tunnel to reduce drag was also propose... | {
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Can electrons coincidentally flow along a circuit to cause current? My understanding of circuits which are not supplied an e.m.f. is that the electrons randomly just flow about in random directions, and since there's so many of them, probability dictates that any forwards or useful movement is cancelled almost perfectl... | Yes, it is possible.
The simplest qualitative answer to this is that, at the microscopic level, the electrons in a conductor are dictated by quantum mechanics, which is inherently probabilistic. Velocities and positions are rarely ever totally excluded from a given value; it's just insanely unlikely for a single electr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106050",
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"source": "stackexchange",
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Gravity of very distant objects As far as I know stars emit a finite number of photons in all directions in a given period of time and as an observer goes further away he experiences less and less photons to the point where the photon sphere is so spread out that sometimes he will not experience any photons making the ... | According to my limited understanding: gravity isn't part of the Standard Model and gravitons are purely hypothetical. If they exist then I'd say you're right. But if General Relativity is right then gravity doesn't come in quanta and you would always experience a small but non-zero attraction due to the curvature of s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106151",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Size of the Universe: Curved vs flat? Finite vs infinite? I have recently heard the theory that the Universe may be smaller than observed but may be curved to the extent that light rays may have looped past us once already and hence appear to have originated from further away than the source actually is located. If thi... | This is similar to the idea that if the universe was infinite in size and infinitely old, the sky would be as bright as the sun, since every point in the sky would end on a star, somewhere in the infinite universe. Since this is not the case, it led people to conclude that the universe is either finite in size or age.
... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106229",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Centrifugal force when there is no friction Assume that a coin is placed on circular disk and now a disk is rotated with constant angular velocity.
If there is no friction between the surfaces of a disk and coin, according to theory the coin will move away from centre of disk. But I have confusion here that the centrip... | Here, because the coin is placed at the center, the centrifugal forces balance each other. Every point mass in the coin has it's conjugate point at the diameter passing through it and on the same distance from the center on the other side.
Hence the coin is under equilibrium and does not fly off.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106378",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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force on a moving charge in magnetic field Need help in understanding the direction of magnetic force in the magnetic field!Totally confused by directions.
Why is it that magnetic force is perpendicular to the direction of magnetic field and velocity of charged particle.
Why is it(force) not in the same direction as th... | A more comprehensive and deeper explanation of the Lorentz-force is based on relativistic electrodynamics as given in:
http://chip-architect.com/physics/Magnetism_from_ElectroStatics_and_SR.pdf
by Hans De Vries.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106521",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Clarification of multipole expansion for a point charge In Griffith's electrodynamic: 3.4.2 He pointed out that the monopole term is the exact potential for a single point charge.
However I was under the impression that different configuration of a charge distribution can act as a point charge from superposition thus ... | The multipole coefficients associated with a $1/|r|$ distribution $\rho$ depends on the choice of origin. For example, if you have a point charge and you choose the origin to be at that point charge, then it will have a pure monopole character. However, if you choose the origin to be elsewhere, it will have nonzero exp... | {
"language": "en",
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Can a laser be designed to ionize muonic atoms so as to prevent a-sticking? Muon catalyzed fusion is currently little more than a lab curiosity today in part because of how many hydrogen nuclei can be fused before the muon is carried away by an alpha particle. Deuterium+deuterium reactions are ten times more likely tha... | For what it's worth (I cannot verify the claims): http://www.j.sinap.ac.cn/nst/EN/article/downloadArticleFile.do?attachType=PDF&id=448 (NUCLEAR SCIENCE AND TECHNIQUES 25, 020201 (2014) - I guess this is a Chinese journal). Abstract: "Considering the mixture after muon-catalyzed fusion ($\mu$CF) reaction as overdense pl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106644",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Majorara mass and fermion number violation How can it be shown that the Majorana mass violates the fermion number by two units? Can even a Noether charge be defined in presence of Majorana mass term?
| It should be pointed out that there is zero experimental/ observation evidence for Fermion number conservation violation. Fermion number violation is predicted in Grand Unification theories and SUSY but , at least based on current evidence, there is no reason to think nature is fundamentally Super symmetric or that gr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106866",
"timestamp": "2023-03-29T00:00:00",
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Are there any QM effects where charged particles are not intimately involved? Are there any QM effects that have been/could be measured from interactions involving non-charged particles?
Elementary QM is all about the electron energy levels in the atom, photon - atom interactions, etc.
When one looks at the nucleus, ... | Am I missing something here? Photons and the double-slit experiments do the trick. Likewise, you can entangle the polarisation degrees of freedom of photons. This is inherently quantum and photons aren't charged. True, they are the excitations of electromagnetic fields, but they are not charged.
Anyway, I guess the pro... | {
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Calculate the average temperature needed for hydrogen fusion reaction my question is simple. How can we calculate the temperature needed in order to do the nuclear fusion things , and also the temperature after the reaction successful.
If you can describe it, it would be really cool. I just want to know about it
Thank... | Firstly, fusion doesn't happen in the way depicted in the question. Four protons don't participate in a 4-body reaction. Instead there are many intermediate steps:
![enter image description here][1]
Each step has its own reaction rate. The overall reaction rate is determined by the [rate limiting step][2]. The prot... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/107113",
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Why do rocket engines have a throat? Diagrams of rocket engines like this one,
(source)
always seem to show a combustion chamber with a throat, followed by a nozzle.
Why is there a throat? Wouldn't the thrust be the same if the whole engine was a U-shaped combustion chamber with a nozzle?
| Previous answers have focused on the fluid dynamics angle. However, you can also view it from a purely thermodynamic angle, viewing the rocket engine as a heat engine.
In order to get useful work (accelerated exhaust gases), you need some form of thermodynamic cycle with combustion followed by expansion. Due to conserv... | {
"language": "en",
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What happens with a tunneling particle when its momentum is imaginary in QM? In classical mechanics the motion of a particle is bounded if it is trapped in a potential well. In quantum mechanics this is no longer the case and there is a non zero probability of the particle to escape the potential through a process call... | I can give you one example. In a semiconductor reverse-biased p-n junction, a potential barrier exists that prevents electrons from crossing the junction. There is an energetically-forbidden region in the vicinity of the junction. The wave functions of electron states in both the valence and conduction bands are rea... | {
"language": "en",
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How can the tension force be computed to test if a shape is moving or not? Source
Given the coordinates of $n$ 3D joints ($1kg$ each) connected by $m$ rods. Assume rods have zero mass and joints with $z=0$ are fixed to the ground while others are free to move, will the shape be move or not? If not, will it be stable?
T... | This is a partial answer that may get you thinking in the right direction.
Three rods connected in a triangle are rigid. 4 our more rods connected in a square or larger polygon are flexible. This is why high voltage power lines are supported by structures built entirely of triangles.
However, triangles are not enough... | {
"language": "en",
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Sum of acceleration vectors If a point mass has some accelerations $\mathbf{a_1} $ and $\mathbf{a_2} $, why is mathematically true that the "total" acceleration is $\mathbf{a}= \mathbf {a_1}+\mathbf {a_2}$?
| While the other answer are all completely correct, I just want to write a more simplified answer.
It's much the same as distances. I you walk 1 meter North and 1 meter East, you can add the two distance vectors and get $\sqrt2$m North-East:
$$\vec{d}_1=1m[N]=(1,0),~~\vec d_2=1m[E]=(0,1)$$
$$\vec d=\vec d_1+\vec d_2=(1,... | {
"language": "en",
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Why is the periodicity of fields in finite temperature QCD consequence of Trace in the action? In finite temperature QCD, the gauge fields must be periodic in temporal direction. They say this is the consequence of trace in the action for gauge fields. How does trace imply that the fields must be periodic?
| let's say the trace is the expectation value. the action will be invariant so by calculating the expectation value of the action one would expect a minima on the path taken by a particle. This would be independent of time, the same physics will describe the dynamics tomorrow. hence, periodicity in the temporal directio... | {
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What does really mean by- power of a number or an exponential function is dimensionless? Is power of only a number or an exponential function is dimensionless? If power of any other thing can also be dimensionless then please explain with examples.
| To consider an example, take the case of exponential decay
$$N=N_\circ e^{-\lambda t}$$
We can write this as
\begin{eqnarray*}
N & = & \frac{N_{\circ}}{e^{\lambda t}}\\
& = & \frac{N_{\circ}}{\underbrace{e\times e\times e\times e\times\ldots \times e}_{\lambda t\text{ times}}}
\end{eqnarray*}
So $\lambda t$ must be a... | {
"language": "en",
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Electric field in a sphere with a cylindrical hole drilled through it Suppose that you have a sphere of radius $R$ and uniform charge density $\rho$; a cylindrical hole with radius $a$ ($a\ll R$) is drilled through the center of the sphere, leaving it like a "necklace bead".
I would like to find a function for the elec... | I agree with the result, but I would like explain another more general and rapid approach.
Because of the radius of the hole is negligible with respect to the radius of the sphere, and the only posible direction for E compatible with the symmetry is the z axis, and finally having in mind that the tangencial components ... | {
"language": "en",
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In calculating work done by a constant force over a constant distance, why doesn't the subject's initial velocity matter? Assume a point-mass $m$ is travelling in a straight line, and a force $F$ will act on $m$ (in the same direction as $m$'s velocity) over a constant distance $d$; why doesn't $m$'s velocity matter to... | Well, you simply need to accept that work is given by Force time Distance, and it doesn't matter how long it takes.
For example, the work done on a mass $m$ lifted a distance $h$ against gravity with an acceleration $g$ is given by:$$W=F\times h=mgh$$
If you are told that someone is going to drop a $1$ kilogram mass on... | {
"language": "en",
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Galaxies fading away after time Dark energy is constantly pulling all objects away from each other with increasing speed. This in turn causes a red-shift of the light from the most distant object where this effect is most profound. This red-shift will gradually increase as the objects move away faster. Is there going t... | In an acceleratingly expanding universe, there will be an emission time of light from a distant galaxy after which we can never recieve newly emitted light.
Old light will eternally be received, but even more dimmer and red shifted.
See The Long–Term Future of Extragalactic Astronomy for more information.
| {
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Are Verdet Constants Temperature Dependent? The Verdet constant of a magneto-optical material shows up in the calculation of the rotation of polarized light in a medium submerged in a magnetic field. The amount of rotation is given by
$$
\theta=VBd,
$$
where $\theta$ is the angle of rotation of linear polarized light,... | The Verdet constant is a coefficient which sums up the magneto-optical properties of the medium. So, the temperature and wavelength dependence are wrapped up in it. Fundamentals of Photonics by B.E.A. Saleh expresses the Verdet constant in terms of the wavelength as
$$
V\simeq-\frac{\pi\gamma}{\lambda n}
$$
where $\l... | {
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Projection operators and their subspaces (of Hilbert space) I've been watching Susskind's lectures on Quantum Entanglement, and something he said regarding (non-)commuting projection operators confused me.
Consider two subspaces {$|a\rangle$} and {$|b\rangle$} of Hilbert space, with operators $K$ and $L$ for which:
*
... | A complete set of eigenstates spans the whole space, not just the subspace the projection operators project on. In this set of eigenstates you also have a basis of the subspace belonging to the eigenvalue 0.
| {
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Characteristic length for the diffusion equation (temperature) The background: I'm doing some simulation work involving the diffusion equation in 1D. Specifically I have some temperature profile, constant thermal conductivity and fixed temperature at each end of the system.
I know that we can write:
$$
\tau = \frac{L^... | Short answer: $\tau$ is the typical time it takes for heat (energy) to be transported over the distance $L$.
I'll try to elaborate a bit on your analogy to particle diffusion.
For particle diffusion in one dimension, you may think of the particle as jumping around on the x-axis. Some times it jumps to the right, and so... | {
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First Order Correction to wave function in ground state I am looking at a spin 1/2 particle in a magnetic field. This has Hamiltonian
$$H=-\mu s\cdot B_0$$
For simplicity, assume $B_0=B_0\hat z$ so $H=-\mu B_0$. I then apply a perturbative magnetic field such that
$$V'=-\mu B_1 s_x$$
First I wanted to compute $E^{(1... | Spin1/2 particle
Ususally, in this kind of Hamiltonian, people uses $s=s_z$, where
$$s=s_z=\left[ \begin{array}{cc}
1 & 0 \\
0 & -1\end{array} \right].$$
Then, your unperturbed hamiltonian $H_0$ is: $$H_0=-\mu s\cdot B_0 = -\mu \left[ \begin{array}{cc}
1 & 0 \\
0 & -1\end{array} \right]B_{0,z}. $$
Then the eigen vecto... | {
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Shielding RFID with aluminium foil I've been playing around with some contactless bank cards and an RFID reader app on my phone. As expected, if I wrap the card in foil, the reader no longer detects it. But I was surprised to find that if I place a layer of foil on a flat surface, put the card on top of it and the phon... | The metal is detuning both the tag's antenna and depending on how close the phone is, the phone's RFID antenna too. When a piece of metal is placed in the near field area of an antenna it becomes coupled to the antenna and it's resonance frequency drops, the impedance decreases (causing a large signal loss) and the ba... | {
"language": "en",
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How does the frequency of a particle manifest itself? In terms of wave-particle duality for, let's say a photon; how would the frequency practically manifest/demonstrate itself? Like, i understand that the frequency is related to the energy a particle has, but frequency in my mind suggests oscillation about a point. Is... |
Is the photon physically oscillating through space as it travels? I wouldnt imagine so. Which periodic occurrence is referred to when one talks about the frequency of a particle?
No the photon is not oscillating through space. It is an elementary particle of the standard model which is the quantum mechanical descript... | {
"language": "en",
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2D Gauss law vs residue theorem I used to have a vague feeling that the residue theorem is a close analogy to 2D electrostatics in which the residues themselves play a role of point charges. However, the equations don't seem to add up. If we start from 2D electrostatics given by $$\frac{\partial E_x}{\partial x} + \fra... | There is indeed a connection. The holomorphy is easily seen in the electrostatic potential.
In a charge free (two-dimensional) region, the electrostatic potential solves Laplace's equation and hence is a harmonic function. The real and imaginary parts of a holomorphic function are harmonic functions and thus the elect... | {
"language": "en",
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Could Charles-Augustin de Coulomb measure the charge in Coulombs?
*
*Did Charles-Augustin de Coulomb know:
*
*Coulomb's constant
*Coulomb (as a unit)
if not then what was the first time it was measured?
| Coulombs date back to the 1860's, and even predate CGS units. The connection between the volt-ohm-second and mks units were made only in 1904.
Coulomb used e.s.u. based on the french ft lb s system. The coulomb constant is a feature of choice of units, if charge is found from LMT, then the size of the coulomb const... | {
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Why can colors be mixed? We can combine colored light, creating other colors, at least in terms of visual perception.
But how it the result physically "a different color" - if it is at all?
Or is all this not a physical question to begin with - but only about our eye and brain?
To have an example, we
*
*have an i... | The cells in our retina that detect by frequency (read: colour) detect most strongly in three slightly different bands we know as Red, Green and Blue.
To make a slight correction I would say an incadescent bulb is quite far from white, so I would rather proceed talking about sunlight on a clear day. The reason why sun... | {
"language": "en",
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Reconciling total internal reflection and the evanescent Wave I understand that light is guided in a dielectric waveguide via total internal reflection. My question is regarding the origin of power contained in the evanescent field traveling along the direction of propagation.
From Fresnel equation we get that the ref... | It's a "tunneling" behavior. In effect, all the light is "pulled back" into the medium unless there's another body of high-index (well higher than the $n_1 = 1$ ) material within the distance covered by the evanescent wave. If that material is close enough, then that part of the evanescent wave, which you can view as... | {
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Electric Field inside a regular polygon with corner charges If we have equal charges located at the corners of a regular polygon, then the electric field at its center is zero. Are there other points inside a polygon where the field vanishes?
The simplest case would be an equilateral triangle of equal charges. I thou... | In addition to Ali's answer, here are some pictures which may be helpful in convincing people that the origin is not the only point inside the polygon where $\mathbf{E}=\mathbf{0}$. Letting the charges be located at $(\cos(2\pi k/N),\sin(2\pi k/N))$ for $k\in\{1,2,...,N\}$, we can generate plots of $|\mathbf{E}|^{-1}$ ... | {
"language": "en",
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Studying Quantum Electrodynamics? As an electrical/computer engineer, I already have a relatively thorough understanding of classical electromagnetism.
From what I understand though, classical EM is only an approximation to quantum electrodynamics. I'm very curious about how it all really works though.
So as an ECE en... | What is an ECE engineer, an electronic-computer-engineering engineer?
Indeed Classical Electrodynamics is only an approximation to Quantum Electrodynamics.
If you just want to get a taste, I would suggest reading Feynman's QED: The Strange Theory of Light and Matter. It describes the theory quite nicely without too mu... | {
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What determines the speed required to pull a table cloth? I was watching this show "Street Genius" on National Geographic and the host Tim Shaw demonstrated an experiment about Inertia, What he did was, He tied one end of a table cloth to a car through a long rope and started driving the car, when the rope was taut, th... | Not sure anyone will look back at this, but I'd like to give an answer anyway!
How do you not disturb the dishes when pulling a tablecloth out from under them? You're exactly right: this is about the inertia of the dishes and the forces on the dishes from the table cloth while the cloth is being pulled.
Remember from ... | {
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How do I simulate this simple quantum circuit in MATLAB? I want to simulate a circuit similar to the one below in MATLAB. If you have a state matrix describing the state of 3 qubits, I understand that you could apply a CNOT matrix tensored with and identity matrix to $\psi_{0} $ get $\psi_{1}$, but if you want to apply... | The answer is $|\psi_{FINAL}\rangle = CNOT_{12} \cdot CNOT_{13} \cdot |\psi_{INITIAL}\rangle$
;
where $|\psi_{INITIAL}\rangle = |\psi\rangle \otimes |00\rangle$.
So this operation goes as follows:
*
*1st) if $|\psi\rangle$ is in state $|1\rangle$, then perform NOT on the 3rd qubit ($|0\rangle$ goes to $|1\rangle$ in... | {
"language": "en",
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Why are there interference patterns inside a diffraction envelope? When double-slit diffraction occurs, there are interference patterns inside, say, the central diffraction maxima (or envelope). I am trying to understand how these interference fringes are created.
Here is what I know: each individual slit in the doubl... | In a simplistic model, you can view destructive interference for a two-slit situation as arising from one of two possible events: Either light from a single slit is destructively interfering (and hence light from the other slit will as well, since the off-set is usually ignored), or light leaving both slits interfere w... | {
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Is the molecule of hot water heavier than that of cold water? We know that the molecule of hot water($H_2O$) has more energy than that of cold water (temperature = energy)
and according to Einstein relation $E=mc^2$ ,this extra energy of the hot molecule has a mass.
Does that make the hot molecule heavier?
| $E^2 = m^2c^4 + p^2c^2$, where $m$ is rest mass and $p$ is momentum. If a molecule is moving faster it would have more momentum and more energy, but the same rest mass.
Some have defined "relativistic mass" as opposed to "rest mass" as $E=m_rc^2$, so yes the faster moving molecule would have a greater so-called rela... | {
"language": "en",
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What is the energy of a black hole? This might be a stupid question but given Einstein's general theory of relativity $E = m c^{2} $ what is the energy of a black hole? Isn't the mass of a black hole infinite? Wouldn't that be infinity multiplied by the speed of light squared?
| Black holes are just objects which have very large mass (not infinity) and they are concentrated in very small region of space, Which is called Schwarzschild radius $$r=\frac{2GM}{c^2}$$
it means escape velocity from orbit equals the speed of light (thats why black hole is black, light can't escape it) but black hole ... | {
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What provides the centripetal force for a glider? Whenever any object follows a circular path, there is always a centripetal force which is provided by something.
However, in the case of a glider making a loop in air, what provides the centripetal force?
This is the picture that made me think of this question:
| There is indeed a centripetal force acting on the glider as it moves through its loop. The size of the force depends on the mass of the glider, the speed of the glider and the radius of the circle the glider is following at the moment.
There are two sources for this force:
*
*The component of the force of gravity a... | {
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Moment of inertia of a hollow sphere wrt the centre? I've been trying to compute the moment of inertia of a uniform hollow sphere (thin walled) wrt the centre, but I'm not quite sure what was wrong with my initial attempt (I've come to the correct answer now with a different method). Ok, here was my first method:
Consi... | The mass of the ring is wrong. The ring ends up at an angle, so its total width is not $dx$ but $\frac{dx}{sin\theta}$
You made what I believe was a typo when you wrote
$$\text{d}m = \frac{M}{4\pi R^2}\cdot 2\pi \left(R^2 - x^2 \right)\text{d}x$$
because based on what you wrote further down, you intended to write
$$\te... | {
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wave-particle duality and entanglement By fundamental definition of a entangled system we can say that if we know the quantum state of one subsystem then we can describe the state of another subsystem.
A particle possess wave-particle duality. If one experiment verify the wave nature of particle then we can not see its... | To see the quantum states of Gigi10012's answer.
1. The state of the electrons is
$|\psi >=\frac{|+-\rangle+|-+\rangle}{\sqrt{2}}$, when you measure one electron$|\psi\rangle$ will collapse into $|+-\rangle$ or $|-+\rangle$ then if you know the spin of the first electron you can know the second one. Before measuremen... | {
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Does electricity flow on the surface of a wire or in the interior? I was having a conversation with my father and father-in-law, both of whom are in electric related work, and we came to a point where none of us knew how to proceed. I was under the impression that electricity travels on the surface while they thought ... | Both in the interior (bulk) and at the surface, depending on the source voltage and frequencies. Surface charge is always required on a conducting wire, in order to establish powerflow over the wire. There are two types of current density $\boldsymbol J$: $\operatorname{div}\boldsymbol J = 0$ or $\operatorname{div... | {
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Fourier transformation I have recently studied Fourier and Laplace transformation in maths. I wanted to understand the utility in physics with some examples that requires this change in dimension and the reason why.
| Just to give 3 simple examples:
Someone is playing piano. Every key he hits, will produce not only the desired tone but also a full range of resonants and higher harmonics. Those will show up in fourier space.
In image analysis, sometimes you have periodic patterns overlaying your image (e.g. Moiré fringes) that distur... | {
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Obtain the eigenfunction of Jz for the wave function of an electron in a hydrogen atom?
The wave function of an electron in a hydrogen atom is given by
*
*Is this wave function an eigenfunction of Jz , the z-component of the electron’s total angular momentum? If yes, find the eigenvalue. (Hint: For this, you ... | The last spin state is wrong.
It should be $\frac{|\uparrow\downarrow\rangle+ |\downarrow\uparrow\rangle}{\sqrt{2}}$, to be the $S_z=0$, $S=1$ spin state.
*
*The state would then be an eigenstate of $J_z$, with eigenvalue $+1$.
*Measurements of $S_z$ could be $S_z=0$ ($P=1/3$) and $S_z=+1(P=2/3)$.
*$J^2=2*3=6$, wi... | {
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Higgs boson production via positron-electron collision One of the suggested diagrams for the Higgs production is the following:
so basically an electron-positron pair annihilates and forms an (excited?) Z boson, which then decays into another (less excited?) Z boson and a Higgs boson.
Why can't the electron-positron pa... | The $^*$ notation does not mean excited in this case, it means "off shell" (i.e. virtual or having the "wrong" mass).
At the second vertex the $Z^0$ is put "on-shell" by the emission of a Higgs (note, however, that it will decay very quickly in any case).
The lepton pair can annihilate directly to the Higgs, but the ev... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/110241",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Diver view of refraction I'm studying the refraction in optics.
If a red light monocromatic beam of red light (700 nm) passes from air to water it becomes with a wavelenght of aprox 526 nm.
So, my question is: How is going to see this beam a diver? Red (700 nm) or something more like green (526 nm)? (Let's suppose tha... | You will see it the same, regardless of the refraction index of your medium. The reason is as simple as that, when the light hits your retina, it will be travelling through the interior of your eye, so the only refractive index that matters is that of the eye.
What is what we actually detect, wavelength of frequency? F... | {
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Is frequency quantized in the black body spectrum? I'm aware that there're some questions posted here with respect to this subject on this site, but I still want to make sure, is frequency quantized? Do very fine discontinuities exist in a continuous spectrum like the black body spectrum?
The quantization of photon ene... | "Yes", but the quantisation depends on the size of the box. In practice the 'box' is large and of variable shape, so all sizes are available, so all frequencies are available.
Ultimately, it is somewhat of a philosophical question who's answer depends on which axioms and base concepts you (they) are using at the vario... | {
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Why does squeezing a water bottle make the water come out? This seems natural, but I can't wrap my head around it when I think about it.
When I squeeze an open bottle filled with water, the water will spill out. When I squeeze a bottle, the material collapses where I squeeze it, but expands in other areas, resulting in... | Squeezing the bottle does decrease its volume. Rather than a bottle, it may be more helpful to think of a full toothpaste tube; the mechanics will be the same.
If you squeeze the middle of the tube, the middle will collapse, the back will expand, and the front will expand and squirt out some toothpaste. Treating the t... | {
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Why electrons have less energy than photons with the same wavelength? I am studying quantum physics and I have a question: what is the physical explanation for electrons having less energy than photons with the same wavelength?
Energy of a photon : $E = h ... | For the photon we have $$E_\gamma = \frac{hc}{\lambda}$$
and for the electron $$E_e = \frac{h^2}{2m\lambda^2} =\frac{hc}{\lambda} \frac{h}{2mc\lambda} = E_\gamma \frac{h}{2mc\lambda}. $$
You can check that the proportionality factor is dimensionless. So what you are asking is why this quantity is less than unity. But r... | {
"language": "en",
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Do I need to take weight of the rocket into account when calculating escape velocity? Here there is the old problem.
I know from the old problem that the work $W_v$ that I need to make a rocket fast enough to reach the escape velocity is
$$W_v= G \frac{mM}{r}$$
therefore because $$W_v=F\cdot S = G \frac{mM}{r} \right... |
Do I also have to count the weight of the rocket?
You already have! This is the $m$ in $G\frac{m M}{r}$.
I don't understand the line of reasoning for your second equation, and you made a subtraction/multiplication error as DavePHD pointed out. The value $F_g+F_v$ would be the total acceleration experienced by astrona... | {
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Magdeburg Hemispheres The Magdeburg Hemisphere experiment was the experiment that showed the effect of pressure differences on a vacuumed sphere.
We know that the Force caused by pressure is $\Delta p A$ and so you can calculate the force by using the area of the base of one of the hemispheres of the the vacuumed ball... | At all points on the sphere the pressure points normal to the surface (because that it what pressure does...).
That said this system has a preferred direction: the line between the hoops where we hook the harness on for the horse to pull. And we have built the device such that the joint between the two halves lies at ... | {
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Why fermions have a first order (Dirac) equation and bosons a second order one? Is there a deep reason for a fermion to have a first order equation in the derivative while the bosons have a second order one? Does this imply deep theoretical differences (like space phase dimesion etc)?
I understand that for a fermion, w... | Fermions obey the Fermi-Dirac statistics, while Bosons the Bose-Einstein statistics. This is an experimental fact and we can't do anything about it. You find its first and most famous evidence in the Pauli principle. To mention some more, Bose condensation and Fermi blocking are a fact of everyday science, and we have ... | {
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Differences between strong, weak, and micro lensing distinct or subtle? In gravitational lensing, there are three categories of lensing: strong, weak, and micro. As I understand it, strong lensing (just as the name implies) occurs when a source and a gravitational lens are relatively close by and the lens is strong, p... | They are all the same phenomenon and they are basically just arbitrary distinctions. However they are useful ones.
Strong lensing normally means we see a clear image. We can then use the shape of the image to precisely calculate the mass distribution in whatever is doing the lensing. For strong lensing we need two thin... | {
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Equations of motion for the Yang-Mills $SU(2)$ theory I have an exercise for Yang-Mills theory. I can't find answer anywhere.
Derive equations of motion for the Yang-Mills theory with the gauge group $SU(2)$ interacting with $SU(2)$ doublet of scalar fields.
I don't even know how to derive EOM for Lagrangian here. An... | The Lagrangian of Yang-Mills theory coupled to scalars/fermions, etc. takes the form
$$
{\cal L}_{YM} = - \frac{1}{2} \text{Tr} F_{\mu\nu} F^{\mu\nu} + (D_\mu \phi) (D^\mu \phi)^* + i {\bar \psi} \gamma^\mu D_\mu \psi + \cdots
$$
where the $\cdots$ represents other interactions terms that might be present. Let me expla... | {
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Global Properties of Spacetime Manifolds When solving the Einstein field equations,
$$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi GT_{\mu\nu}$$
for a particular stress-energy tensor, we obtain the metric of the spacetime manifold, $g_{\mu\nu}$ which endows the manifold with some geometric structure. However, how can we de... | The initial value boundary problem in general relativity only gives you the metric on a patch of the spacetime. Other methods must be used to find the true global extension of that spacetime. Therefore, Einstein's equation alone cannot tell you the topology of the spacetime.
| {
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Why doesn't this model plane fly? I have been designing a model plane for Design Technology for the past month or so, and today I laser cut my final design and assembled, it then tested it. Upon testing the plane does not get any lift, whereas the previous testing model which was virtually the same did.
The plane is bu... | The shape of the wings does not appear right to produce lift. More convex on top, less on the bottom, would be better
And planes often have dihedral, wingtips raised, for stability.
EDIT - This answer was too hasty. The comments below are much better.
| {
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Adiabatic expansion in the atmosphere When an air parcel rises and cools adiabatically, it is said that there is no heat transfer as work is done on the surrounding atmosphere as the parcel expands. The parcel loses internal energy and condensation occurs. I do understand this concept, but why is it that work is done o... | The work being done on the surroundings is because the air parcel expands as the pressure decreases.
There would be some heat transfer if the parcel of interest has a different temperature than the surrounding air. This effect is smaller because gases are poor conductors of heat, as mentioned by @gerrit. We take adva... | {
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Estimating the weight of a vehicle moving in a highway I need to know the estimated weight of a truck in a highway without using scales.
What do I have?
*
*Speed of the car at time X
*RPM at time X
*horse power
*Estimated distance from a point A to B (calculated from GPS data)
*And everything I can get from th... | My previous answer seems to be misleading as I found a way to calculate what you asked by the measurements you said you can take!
Assuming that the weight is equally distributed on each tyre, we can equate the torque due to friction with angular acceleration of tyre multiplies by moment of inertia of tyre. The equation... | {
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Description of the heat equation with an additional term I have the following equation:
$$\frac{\partial U}{\partial t}=k\frac{\partial^2 U}{\partial x^2}-v_{0}\frac{\partial U}{\partial x}, x>0$$
with initial conditions:
$$U(0,t)=0$$
$$U(x,0)=f(x)$$
In the problem is requested to give an interpretation of each of the ... | If you re-write the equation to take the form
$$
\frac{\partial\psi}{\partial t}+v\frac{\partial\psi}{\partial x}=k\frac{\partial^2\psi}{\partial x^2}
$$
Then we can note that the first term is the one-dimensional form of the material derivative:
$$
\left(\frac{\partial}{\partial t}+\mathbf v\cdot\nabla\right)\equiv\fr... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How come this paper clip is " floating" on the subway floor? What's the physics behind the paper clip floating? Technically this was filmed on a subway floor in motion. So I'm guessing it has some Newtonian mechanics involved here, and maybe some other stuff I don't know? Please explain. Thank you.
http://www.youtube.c... | To give a real explanation one would have to repeat the experiment under controlled conditions, which is not simple with a moving metro cab.
Steel objects will move and be attached to magnetic fields: think of the magnetized scissors picking up fallen pins.
If it is an electric train, which a metro would be, there are... | {
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What is the symbol Å? I saw this symbol like:
$$\lambda=3000\overset{\circ}{\text{A}}$$
and I don't know what this means. Is it a frequency? (since $\lambda$ is usually used for frequency)
| It is an ångström, a unit of length commonly used in chemistry to measure things like atomic radii and bond lengths. Although not an official SI unit, it has a simple relationship to the metric units of length:
$$1\:\mathrm{ångström} = 1\:\mathrm{Å} = 10^{−10}\:\mathrm{m} = 0.1\:\mathrm{nm} = 100\:\mathrm{pm}.$$
| {
"language": "en",
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"source": "stackexchange",
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Will glass always break in the same way? This question has had me thinking for a while. If I have two large panes of glass and a rock or similar item is thrown in exactly the same place on the glass, would the two panes break in the same way. Does the shattering of glass follow any rules or is it always random and subj... | The answer is sort of yes and no.
YES: If you have two perfectly identical panes of glass and two perfectly identical projectiles, and you throw the two projectiles in a perfectly identical way, then the two panes will shatter in a perfectly similar fashion. This is really just by construction, you did the same thing t... | {
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Calculating $\mathrm{Tr}[\log \Delta_F]$ I am stuck with this problem for quite sometime. I have a propagator in the momentum representation (from this Phys.SE question), which looks like
$$ \widetilde\Delta_F(p) = \frac{1}{(p^0)^2-\left(\left(n\pi/L\right)^2+m^2\right)+i\epsilon} $$
I wish to know how do go about calc... | Since you want to extract the Casimir force, just take (minus) the derivative wrt to L of your expression in momentum space, the result is finite.
This is actually a general mechanism to regularize the theory by taking derivatives of some parameters that lower the divergence degree. You can integrate back after you ha... | {
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If I'm floating in space and I turn on a flashlight, will I accelerate? Photons have no mass but they can push things, as evidenced by laser propulsion.
Can photons push the source which is emitting them? If yes, will a more intense flashlight accelerate me more? Does the wavelength of the light matter? Is this practi... |
Can photons push the source which is emitting them?
Yes, photons have momentum and momentum must be conserved. The source is pushed in the opposite direction of the photons.
If yes, will a more intense flashlight accelerate me more?
Yes, more photons means greater momentum.
Does the wavelength of the light matte... | {
"language": "en",
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Motion of a car rounding a bank When a car is traveling round a banked track as fast as possible, it has a tendency to slip up the slope.
Opposite in the case when the car travels slowly and has a tendency to slip down.
Can someone please give me an intuitive reason as to why this "tendency to slip up or down" occurs.
| If you need just an intuitive reason here it is- the primary forces that pushes the car up and down the track is the balance force of centripetal force and tyre friction force. If the friction between the tyre and road is more than the centripetal force (which in turn depends on velocity of vehicle) due to the banking ... | {
"language": "en",
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What would we see in the sky if it weren't blue What would we see during the day when we look into the sky (other than clouds), if it weren't for Rayleigh scattering making the sky blue? Would the sky be dark, like at night?
| Consider this picture of earth from the moon:
Most other photographs taken from the moon would do. From how earth is illuminated, or the shadows of objects on other photographs, it is clear that we are in broad daylight. The sky it pitch black however.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Wrapping plastic in aluminium foil to protect it from heat Does it make any sense to wrap the plastic handle of a pan in aluminium foil to protect it from overheating when placing it to the hot oven?
| No. If your saucepan can take the heat of an oven, the handle needs no protection. If it can't take the heat of an oven, there's really nothing you can do to provide any practical protection to the handle.
Not only will there be heat transfer from the surrounding air (and radiant heat from the heating element/burner an... | {
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Is it possible to produce gamma radiaton using radio emitter? As in the title, I'm wondering is it possible.
I think it is possible, because we have powerful enough radiotechniques and gamma radiation are just EM waves, not particles. However I think is useless, because it costs too much.
Can anyone say something more ... |
Is it possible to produce gamma radiaton using radio emitter?
Unlikely. A 'radio emitter' consists of, at least, some type of antenna and a transmitter to drive that antenna.
The size of the antenna is related to the wavelength of the transmitted radio wave, e.g., half-wave dipole, quarter-wave monopole.
But the wav... | {
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Gravitational force from spherical shell Say we have a point mass $\mu$ located at $(0,0,R)$ and a spherical shell (not considering it's volume!) of radius $R$ located in the origin. So we have a particle standing right on top of the sphere and we want to determine the total gravitational force exerted on the particle ... | The factor of two is correct as far as the integral goes; it comes from the unphysical situation of having your test mass exactly on the thin shell. Intuitively, you get the average of the "just outside" result (as if mass is concentrated at the centre) and the "just inside" result of zero.
A more physical thing to do ... | {
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Apparent dimensional mismatch after taking derivative Suppose I have a variable $x$ and a constant $a$, each having the dimension of length. That is $[x]=[a]=[L]$ where square brackets denote the dimension of the physical quantity contained within them.
Now, we wish to take the derivative of $u = log (\frac{x^2}{a^2})... | You are doing nothing wrong except failing to take the second derivative correctly. Remember, derivative is "the speed of change" of a function. Now, you take a dimensionless number and want to find how fast it changes in respect to x. Of course the resulting dimension will be ~ [1/m], where m is the thing you measure... | {
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What is Jacobian about the "Jacobian Edge" in $E_\mathrm{T}$ distributions? Particle physicists often talk of a "Jacobian Edge" in distributions, i.e. when looking at the $E_\mathrm{T}$ distribution of $W \to e \nu$ decays at rest. How is this related to the Jacobian determinant we all know about?
| Imagine you have a $W^+$ decaying (at rest) in the electron channel, so $W^+\rightarrow e^+ \nu$ . The transverse momentum of the electron is given by (neglecting electron mass, which is very small compared to $M_W$):
$$p_t=\frac{M_W}{2}*\sin{\theta}$$
Now you want to have the differential cross section versus $p_t$ so... | {
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Deriving Bernoulli's equation via conservation of E So I'm not OK with how some people derive this equation.
These people consider a pipe whose endings have cross-sectional areas and heights which are different. They then use the conservation of energy principle by saying $dW = dK + dU$ (Where $W$ is work, $K$ is kin... | You cannot derive the classic Bernoulli Equation from conservation of energy, because, contrary to popular opinion, it is actually not an expression of conservation of energy at all. It is more accurately construed as an integrated expression of the conservation of linear momentum, $F=ma$.
| {
"language": "en",
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Is evaporative cooling more efficient with dry or moist air? I live in India, and in the summer season, the temperature can reach up to $45 \sideset{^\circ}{}{\mathrm{C}} .$ We use Split 1.5 Ton AC in our small office. The idea is to put an evaporative cooler on the inlet side of the heat exchanger of AC to give it mor... | I think it will increase efficiency,
Compared to a normal AC there will be a significant change.
I dont know the exact change.
But you will probably feel a difference.
| {
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"url": "https://physics.stackexchange.com/questions/114156",
"timestamp": "2023-03-29T00:00:00",
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How would one compute the angle of deflection, in a relativistic collision - underspecified system? Consider the simplistic case of two identical mass particles colliding elastically with the second particle initially stationary and the first particle travelling with energy $E$. By conservation of 4-momentum we have:
$... | Yes, it's underspecified. In real experiments with beams elastically scattering from fixed targets you have scattered particles coming out at all angles; usually the cross section as a function of angle tells you about the energy levels involved.
| {
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Feynman's $i \epsilon$ prescription in loop expansion I have some questions about the $i\epsilon$ factor in Feynman diagrams. First, what is the physical meaning of $i\epsilon$ in loop amplitudes. Second, how does it ensures unitarity?
And third, Dyson series assume that incoming and outgoing particles are free, this c... | At first, the $i \epsilon$ prescription: In Feynman diagrams we have a lot of Green's functions connected by some rules, the Feynman rules. Actually, the $i \epsilon$ prescription is more related to the Green's function. The prescription is responsible for a choice in the boundary conditions (asymptotic behaviour). We ... | {
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Why Does Change of Magnetic Flux Induce an emf? Why does change in magnetic flux with time through a coil induce an emf across it? Please explain what happens to the charges in the coil when magnetic flux changes?
Also, why does a constant magnetic flux not induce an emf?
| To produce EMF we need to drive electrons or we need to produce a net charge difference at the ends of conductor. As we all know that a moving charged particle will experience force by a magnetic field, so, if we are talking about dc machines, the magnetic field produced by the fieldcoil remains constant, that is, no f... | {
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Is Newton's third law always correct? Newton's third law states that every force has an equal and opposite reaction. But this doesn't seem like the case in the following scenario:
For example, a person punches a wall and the wall breaks. The wall wasn't able to withstand the force, nor provide equal force in opposite ... | Almost off-topic, it's worth mentioning that Newton's laws only apply in a Galilean reference frame, which is rather utopic (making Newton's law an approximation of the reality… but what else is Physics anyway?)
In any case, other answers were right: the wall has a reaction from you (and it may break) and also applies ... | {
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Does the Earth gets closer to the Sun? We know that the sun loses an amount of it's mass equivalent to the amount of energy it produces, according to the $E=mc^2$ equation.
so the sun is losing mass every second. Does this affect the space-time curvature it creates. Or does this affect the distance between the Sun and ... | The answer is here
There exists the effect of the loss of mass and therefore gravitational attraction between the earth and the sun but it is small:
If we assume that the Sun's rate of nuclear fusion today is the same as the average rate over those 10 billion years (a bold assumption, but it should give us a rough ide... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114735",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Starting a nuclear reaction In Chemistry, an amount of energy has to be supplied for a reaction to occur. This energy, known as the "activation energy", breaks up the bonds between molecues in the substance. It is equivalent to the total bond energy of the reactants.
However, in high school I learnt that the energy req... | For nuclear reactions we commonly talk about the Q of the reaction. for the reaction A(a,b)B where "A" and "a" are reacts (A is generally the target, "a" is the projectile) and "b" and "B" are the products,
$Q = \left(m(\mathrm{A})+m(\mathrm{a})-m(\mathrm{B})-m(\mathrm{b})\right)c^2.$ Here, $m(A)$ is the ${nuclear}$ ma... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114823",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why is the ratio of velocity to the speed of light squared in the Lorentz factor? Why is the ratio of velocity to the speed of light squared in the Lorentz factor?
$${\left( {{v \over c}} \right)^2}$$
My only guess is the value must be positive.
| It derives from the special relativistic version of the Pythagorean theorem.
The hypotenuse of a Euclidean triangle is given by
$$h^2 = a^2 + b^2$$
In Minkowski space (special relativity) you get a minus sign instead of a plus sign, but you still have to square everything:
$$\Delta s^2 = \Delta t^2 - \Delta x^2$$
(and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114913",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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