Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Estimation of greatest speed in a polyhedron in order to control velocities in a three dimensional volume, I look for a proof or a proof idea for the following assumption:
Given a non-empty solid polyhedron in 3D, all points inside this set have a speed than is lower or equal than the maximum of the speed of the ver... | It seems OP is essentially asking about the speed of a convex combination
$$ {\bf r} ~=~ \sum_{i=1}^N \alpha_i {\bf r}_i,\qquad \sum_{i=1}^N \alpha_i~=~1, \qquad \alpha_i~\geq~0, $$
in a rigid body. The velocity is then
$$ {\bf v} ~=~ \sum_{i=1}^N \alpha_i {\bf v}_i. $$
Finally the speed is given by the 2-norm
$$\begi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why do fans spin backwards slightly after they (should) stop? Today, I've decided to observe my PC fan as I shut the computer down. The fan slowly lost angular momentum over time. What I've found really interesting is the fact that the momentum vector change did not stop at the zero vector, but instead flipped its orie... | I also think the effect is cogging. This torque is position dependent and its periodicity per revolution depends on the number of magnetic poles and the number of teeth on the stator. Cogging torque is an undesirable component for the operation of such a motor. It is especially prominent at lower speeds, with the sympt... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/615003",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "71",
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How do you make more precise instruments while only using less precise instruments? I'm not sure where this question should go, but I think this site is as good as any.
When humankind started out, all we had was sticks and stones. Today we have electron microscopes, gigapixel cameras and atomic clocks. These instrument... | Your intuition that you can only get precision from precision is correct, but your conclusion that you need precise instruments to get precision is incorrect. The trick is always to use precision found in nature to get precision. You should actually look at how people make things to get an idea of where they are gettin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/615177",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is there still an anomalous precession in Mercury's orbit that GR doesn't predict? I was reading through the Wiki pages on tests of relativity and I was curious about this section. Am I interpreting it correctly? Is there still about $1.21''/\text{ cy}$ of precession (Total Predicted: $575.31$ - Total Observed: $574.... | The wikipedia section on the precession of Mercury's orbit is in serious need of an update. The presented observational data is centuries old. Its main reference is the Clemence paper from 1947. Since then the astronomical data have been updated to give a GRT prediction of 42.98"/cy. Clemence gives a slightly higher va... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What does it mean that a free particle has no definite energy in quantum mechanics? In the quantum mechanics case of the infinite square well, the general solution to the Schrodinger equation is a linear combination of solutions with definite energy states. When you measure the particle, it will take one of these energ... | If a particle is somewhere in a very large volume then it is described by wave function normalisation factor that tends to zero. Because it is limited to a finite volume it will have a band width. This bandwidth can be made arbitrarily small. Perhaps Griffiths intends to state this fact.
Plane waves are useful as basis... | {
"language": "en",
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"source": "stackexchange",
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Contraction of Christoffel symbol and metric tensor How can I prove this contraction of Christoffel symbol with metric tensor?
$$
g^{k\ell} \Gamma^i_{\ \ k\ell} = \frac{-1}{\sqrt{|g|}}\frac{\partial\left(\sqrt{|g|}g^{ik}\right)}{\partial x^k}
$$
I know the relation for the Christoffel symbol contracted with itself and ... | The most important point about this computation is to use the formula for the derivative of the metric determinant
$$\frac{\partial_i g}{g} = g^{jk} \partial_i g_{jk} $$
The derivation of this identity can be found in the answer to this question. You can then derive the relationship between $g^{ij}{}_{,k}$ and $g_{ij,k... | {
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Electromagnets' relative strength of attraction & repulsion I have two small 12V electromagnets:
When powered oppositely they attract powerfully so that I cannot pull them apart.
But when they're connected the same way they repel only weakly and I can easily push them into contact.
Why the difference?
Thank-you,
| The difference is the magnetization of the iron core. When the directions are opposite, there is essentially no magnetic flux in the iron cores, almost no magnetization, so the iron does not contribute much to the force.
When the directions are such that the flux through the magnetic circuit is large, the iron is almos... | {
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What does "commuting with the Hamiltonian" mean? In quantum mechanics an observable or an attribute to a particle (like spin) is conserved if and only if it commutes with the Hamiltonian. What does this mean? What observables do not commute with the Hamiltonian?
| Apart from two other answers, consider the Heisenberg picture and the equation of motion where its written as
$$\frac{dA}{dt} = - \frac{i}{\hbar} [A , H]$$
So if an operator commutes with the Hamiltonian, from the above equation its obvious that
$$\frac{dA}{dt} = 0$$
So the quantity attributed to $A$ is conserved.
| {
"language": "en",
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Conditions on $\phi$ and $\boldsymbol{A}$ for when $\boldsymbol{B}$ is uniform I'm reading "Classical Mechanics" (5ed) by Berkshire and Kibble, in the example for uniform magnetic field on pg.243 (Chapter 10 Lagrangian Mechanics) I came across this
A charged particle moves in a uniform static magnetic field B.
Find th... | The authors are just helping you out. It should take only a few moments to verify that those choices for $\phi$ and $\mathbf A$ yield the correct electric and magnetic fields.
Electromagnetism exhibits gauge invariance, so there are an infinity of other choices of $\phi$ and $\mathbf A$ which would also yield the corr... | {
"language": "en",
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Question on Newton's first law In our physics course, Newton's first law was given as a definition of inertial reference frame. Now in order to use it we need to take some object which has zero interaction with other objects. But now in order to check it, we need to know which forces are acting on an object. But how ca... | Very good question. You would do many experiments with many different bodies and you would find that, for all of them, you would have to account for a mysterious force given in terms of a constant vector $\boldsymbol{f}_i=-m_i\boldsymbol{A}$ that must characterize your system kinematically, because it affects all movin... | {
"language": "en",
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Physics experiment with sound I am doing an experiment for a school project which consists of blowing into 6 different bottles to create different notes/harmonics. Each bottle is filled with different volumes of water to create a different sound. I have to calculate the theoretical frequency of each, but I do not know ... | This is called a Helmholtz resonator, a kind of mass-spring oscillator where the mass is the mass of the air in the neck of the bottle, and the spring comes from compression of air in the main volume of the bottle. A formula for the resonant frequency is given here: https://en.m.wikipedia.org/wiki/Helmholtz_resonance
| {
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Why do fireproof safes "capture and hold in moisture"? From The Best Fireproof Document Safe | Reviews by Wirecutter:
Humidity can be an issue with these safes, as they tend to capture and hold in moisture, which can damage their contents.
Someone commented:
Is this really as good as it gets? Is the humidity concern... | Anything that is air-tight will cause trapped moisture to condense as the ambient temperature changes the temperature inside. I don't really see what else could be particularly special about fireproof safes.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "6",
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Doubt in potential energy of sphere on inclined plane This is not a question but a general doubt. So if a sphere is kept on an inclined plane what would be its potential energy.Will it be mgh or mg(h+r).
I need to use it in derivation (final velocity at bottom when rolling) kindly help me. thanks
| If $h$ is the height of the point of contact P of the sphere with the ramp, and the angle of the ramp is $\theta$, then
$$
V = mgh+ m\,r\cos \theta
$$
as the centre of the mass O of the ball is not directly over $x$ because PO is perpendiculr to the ramp surface.
As @Jonas has said, the $r\cos \theta$ does not change w... | {
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Why do bullets shoot through water but not through sand? There are a few questions only on this site about this but none of them answer my question.
Can cannonballs go through water?
Why does a bullet bounce off water?
I find it hard to understand why bullets shoot through water at longer distances but stop in sand alm... | They can go through sand--just not very much of it.
There's a case from IIRC Desert Storm. A US tank realized an Iraqi tank was hiding behind a dune from the heat of it's exhaust. It successfully engaged the tank through the sand dune.
| {
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"source": "stackexchange",
"question_score": "21",
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Gauss' law from Hamiltonian density of electromagnetic field I am going through David Tong's QFT course, for which lecture notes and exercises are available online at http://www.damtp.cam.ac.uk/user/tong/qft.html.
In Question 1.8 we have the Lagrangian (density)
$$L = -\frac{1}{4} F^{\mu \nu} F_{\mu \nu} + \frac{1}{2} ... | What you found is actually the Hamiltonian Density $\mathcal{H}$. The Hamiltonian is the spatial integral of Hamiltonian Density
\begin{equation}
H=\int_\mathcal{M} d^Nx\,\mathcal{H}(x).
\end{equation}
If you have an spatial divergence in your Hamiltonian Density, its contribution to the Hamiltonian can be converted in... | {
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Why is the radial velocity considered zero? I had recently come across a question which is stated as below:
A disc placed on a large horizontal floor is connected from a vertical cylinder of radius $r$ fixed on the floor with the help of a light inextensible cord of length $l$ as shown in the figure. Coefficient of fr... | Let's say the disk has got a non-zero radial velocity. This then has $2$ possibilities. First, the radial velocity is outward along the string and second, the radial velocity is inward along the string.
The First case cannot happen because of the restriction given in the question, the string is inextensible.
For the Se... | {
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Why does ice fragment vertically? The pool in my back yard froze over, and now that it's warmer it is starting to break up. But I notice that the ice is marred by fractures, and that they all seem to be completely vertical. Handling the ice indeed causes it to fragment into "sticks", for lack of better term.
This link ... | Those are some pretty unusual chunks of ice - as you can see, the boundaries of the 'columns' are visible before he breaks them up. So what you've got is a crystalline solid which clearly is the merging of many "source" crystal starting points, or "seeds" as mentioned in the comments.
I can say with certainty from my ... | {
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If we have a net negative charge in a spherical conductor, why negative charges goes to the surface? So imagine that we have a set of net negative charges, in physics books they said that this set of charges goes to the surface because they repel each other in such a way that this reach to an electrostatics equilibrium... | "negative charges tends to move to higher potential energy position, so why they are still going to the surface?"
The surface is at no lower a potential than the rest of the sphere. We can show from the inverse square law that charges uniformly spread over the surface of a sphere produce zero resultant field at any poi... | {
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How does Inertial force arise? Consider the following scenario$-$
A ball sits on the floor of a bus, which was originally at rest w.r.t the ground. Suddenly it accelerates forward, and we observe the ball moving backwards. Well, originally the ball does not move, it is only the bus that moves forward. Why doesn't the b... | @joseph h
inertia is a natural property of the ball and all material objects
This may be seen from a different perspective. There are confusing uses of mass in which it can be interpreted as an emergent behavior (like temperature) or arguably fundamental, such as its association with the Higgs particle. It is not cle... | {
"language": "en",
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Kepler's laws for circular orbits Kepler's first law states that planets revolve around the sun in an ellipse with the sun at one focus of this ellipse. (a special case would be a circular orbit with the sun at the center).
The second law states that the areal velocity is a constant. Thus we can write ($dA = c dt$). If... | For circular orbits,
$$\frac{dA}{dt}=\frac{L}{2\mu}\Rightarrow \pi R^2=\frac{L}{2\mu}T$$
Further $$E=\frac{\mu C^2}{2L^2}\ \ \ \text{For circular orbits}$$
From now on I'm just going to keep track of proportionality.
$$R^2\propto LT\propto\frac{1}{\sqrt{E}}T$$
But further we known that $R\propto 1/E$
$$R^{3/2}\propto ... | {
"language": "en",
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Relationship between entropy and the number of symmetries
*
*We count symmetries of a system by counting the number of transformations/operations under which a feature of the system remains unchanged.
*Entropy is a measure of the number of microstates that correspond to the observed macroscopic state (which remains ... | @ali I'll take a feeble stab at this.
First, this is my guess at what you mean.
Here is a "system" microstate 00110. Here is another "system" microstate 11000. Distinct microstates and the operation was roughly interchange places 3,4 and 1,2.
A system macrostate property is the sum over "places" for a given microstate.... | {
"language": "en",
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Two boxes, identical other than mass and density, are pushed with a coefficient of kinetic friction $\mu$. Do they slow down at the same rate? Do they slow down at the same rate? And stop simultaneously?
I believe they do because $v_f = v_0 -\mu g t$ for both. But I'm not completely sure why that is.
I've also seen ano... | These two $\mu$s are of different origin. The second $\mu$ depends on the mass.
The first equation
$$ \tag{1}
v_f = v_0 - \mu g t.
$$
The is kinetic friction
$$
f_k = \mu N = \mu m g;\\
a = f_k / m = \mu g.
$$
The accelaration is independent of mass.
But the second equation:
$$ \tag{2}
x=\frac{v_o}{\mu}(1-e^{-\mu... | {
"language": "en",
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Interesting inertia problem Consider the following.
A car is accelerating with acceleration $a$. A string is attached to the roof of the car and to the bottom of the string, an object of mass $m$ is attached. Given $\theta$, the angle between the vertical and the string (which is not $90^\circ$ due to inertia of the o... | In summary, when $\theta$ is constant we have
$T \sin \theta = ma
\\ T \cos \theta =mg
\\ \displaystyle \Rightarrow \tan \theta = \frac a g \text{ ; } T = m \sqrt{a^2+g^2}$
| {
"language": "en",
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"source": "stackexchange",
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What does 3D buckling reconstruction mean? In condensed matter/material science papers, I often encountered phrases like structural reconstruction, 3D reconstruction, 3D buckling reconstruction, etc. What do these phrases mean (especially the last one)?
For example, this paper (and a non-paywalled link).
| In the "structural reconstruction" context it means that the crystal structure has changed -- often at a surface. In particular a "buckling reconstrction" means that the initially flat layer has changed shape -- buckling into the direction normal to the surface --- because of the Moire-modifield electronic structur... | {
"language": "en",
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How to define energy density and pressure for a scalar condensate? Consider a scalar field theory in flat spacetime whose Lagrangian reads
$$\mathcal{L}=\frac{1}{2}\eta^{\mu\nu}(\partial_\mu\varphi)\partial_\nu\varphi-V(\varphi).$$
Then the energy-momentum tensor reads (we use the signature (+,-,-,-))
$$T^{\mu\nu}=(\pa... | There's a mistake in your formulae (2) and (3). You should start from (1) and the following (for an isotropic field, since you want pressure of a perfect isotropic fluid):
\begin{align}\tag{1}
\rho &= T_{00}, &p &= T_{11} = T_{22} = T_{33}.
\end{align}
Then (notice the + sign in front of the squared gradient) $$\tag{2... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Reflection and transmission wave on three joined strings Suppose we have a system of three joined strings, of different linear mass densities and
subjected to a constant tension force, such that the velocity of propagation is $v_1$ in the
string 1 (at $x <0$) and string 3 (at $x> L$), and $v_2$ on string 2 (from $x = 0... | For example, the transmission coefficient $T = |\frac{A_t}{A}|^2$, since
$$ \frac{A_t}{A} =\frac{e^{-ik_1L}}{\cos{k_2L}-i\left( \frac{k_1^2+k_2^2}{2k_1k_2} \right)\sin{k_2L}}$$
Multiply this with its complex conjugate:
$$
T = \frac{A_t}{A} \frac{A^*_t}{A} = \frac{e^{-ik_1L}}{\cos{k_2L}-i\left( \frac{k_1^2+k_2^2}{2k_1... | {
"language": "en",
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Is there a way to measure the amount power of visible light against a surface? If you were to hypothetically shine a single beam of light that is specific in its power source and output efficiency against a wall across a specific measurable distance. Is there a possible way to measure the amount of visible observable l... | I'm assuming you're looking for experimental techniques. You can use a photodiode to measure power. For selecting visible light you could use one or more cut-off filters. There also exists monochromatic filters that select specific wavelengths, if you're interested.
| {
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Flat space limit of the $AdS$ metric: Very basic question Suppose I am given the following global coordinates in empty $AdS_n$:
$$ds^2 = \alpha^2\left(-\cosh^2\rho \, d\tau^2 + \, d\rho^2 + \sinh^2\rho \, d\Omega_{n-2}^2\right)$$
where the length scale $\alpha$ is related to the cosmological constant as $\Lambda = \fra... | Far far away from the boundary, AdS looks flat. We can see this by noting that AdS can be thought of as a spacetime with a "background potential" $V(\rho) \sim \rho^2/\alpha^2$ so the region in the neighborhood of $\rho=0$ is flat. As we move farther away from this point, the potential of AdS becomes stronger and the e... | {
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"source": "stackexchange",
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Jumping into String Theory I am a third year student in physics and mathematics and taking a course in which each student need to prepare and give one lecture about some topic related to physics. As I saw String Theory in the topics list I thought it could be a good opportunity to start learn it.
I have background in q... | It's really wonderful to read a young physicist interested in string theory.
For the matter of the lecture I recommend to follow Witten's essay What Every Physicist Should Know About String Theory.
The following videos are about the enormous impact that string theory has produced for theoretical physics as a whole:
-Wh... | {
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"source": "stackexchange",
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A light problem: What happens when light completely destructively interferes? So here's the setup. We have a spherical source. It emits a pulse of light in all directions with some wavelength $\lambda$. It reflects off of a spherical mirror that is centered around this source.
Now, when the light comes back, it bounces... | Think of an analogous but simpler problem. You have a string attached to a wall in one side and you are handling it on the other side (see this video, your hand is the spherical source of light and the wall is the spherical mirror). If you left your hand without moving when the reflection comes back (as in the video) t... | {
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Why can't a system reach equilibrium with non-interacting particles? I am new to Statistical Mechanics, and have just started reading from this book Tony Genault Statistical Physics
where he writes the following (paraphrased for convenience)-
Consider a system of $N$ weakly interacting particles. If the energy of one ... | Non-interacting in this context means the particles cannot collide and exchange kinetic energy. Without the ability to share energy during collisions, the system of particles has no opportunity to distribute the individual energies of the particles between all those particles and hence cannot eventually achieve a maxwe... | {
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Where from is the distance calculated in Newton's law of universal gravitation? In the equation for universal gravitation $(1)$ between two objects, where from is $r$ calculated? From the surface, from the center? Also, are the objects assumed to be particles in this equation or could the be multiple particles like mol... | Strictly speaking, this equation for the force due to gravity only holds between point-like objects. In the case of a point-like object, the notion of "distance" between them is simply the distance between their positions.
For extended objects, things get a little more complicated. Really, if you had an extended object... | {
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Is conduction band discrete or continuous? My question is very simple. I just want to know that is conduction band discrete or continuous?
|
A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands.
Read on the link.
You ask:
My question is very simple... | {
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Newtonian physics and equivalence principle: a doubt on acceleration and gravity First of all, the famous Einstein's elevator experiment is quite clear in my head, both of versions.
But now, consider the following:
Suppose then you wake up inside a car that is traveling in perfect straight path in a autoban (but you d... | Locally, yes. The geodesic equation of GR and differential geometry contains $\Gamma$. When you move to rotating frame these $\Gamma$s are nonzero. The geodesic equation doesn't care if the terms in $\Gamma$ come from a real gravitational field or a non-inertial reference frame.
| {
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Is it possible to lift an object from rest with constant power? This is inspired by the following question.
Consider some object which I want to lift from rest with a constant power throughout the whole process; the power I apply when lifting the object from rest is the same power I apply to keep lifting it. The force ... | Your discussion is valid till $\displaystyle{F\frac{dv}{dt}=-v\frac{dF}{dt}}$.
I think the only way to reach $F(v-v_o)=v(F-F_o)$, is by assuming $F$ is constant while integrating on the left side and by assuming $v$ as constant while integrating on the right side. This is inconsistent because on the left side $F$ is be... | {
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What is a resonance element? I'm looking at a horn antenna and why its a good addition to a waveguide. I've read that the horn can operate at a wide range of frequencies since it has no resonant element. But I can't find a good description of what a resonant element is in this application.
| In this context, a resonant element would be a chunk of the system that possesses a substantial quantity of impedance (either capacitance or inductance), different from that of the system as a whole. So if the horn had a local swelling or constriction somewhere along its length, the impedance of that segment would not ... | {
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How does the growing up of trees works with respect to energy conservation? We know that the energy (and hence mass) can neither be created nor destroyed. In the light of above statement, I would like to understand views on growing up of fauna and flora on earth.
A small seed is planted in earth. The only visible input... | Of course it is. Mass doesn't magically appear out of nowhere.
In the case of a tree, most of the mass is taken out of the air (the carbon from the carbon dioxide) and water (the oxygen and hydrogen).
| {
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What are so-called opposite colors? Colors are said to be electromagnetic frequencies.
How is this compatible with the notion of color opponency, or opposite colors, since those frequencies form a single dimension?
| The notion of opposite colors has nothing to do with the electromagnetic spectrum. Human eyes have three different photoreceptors, named cones (I won't enter into subtleties such as rod spectrum sensitivity here) with each a certain response curve to the electromagnetic spectrum.
When those receptors are excited by lig... | {
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If electrons can be created and destroyed, then why can't charges be created or destroyed? I read on Wikipedia that electrons can be created through beta decay of radioactive isotopes and in high-energy collisions, for instance when cosmic rays enter the atmosphere. Also, that they can be destroyed using pair annihilat... | Well most of what needs to be said already has been said. But there is something else that I think would interest you.
Charge in a system is only conserved when a very specific symmetry in the system in not broken. Noether's theorem links symmetry to conservation laws. If you can find a way to break the symmetry that g... | {
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The definition of Quasi-static process? A quasi-static process is often defined as a process "that occurs infinitely slowly such that equilibrium holds at all times."(Harvard, Matthew Schwartz, statistical mechanics Spring 2019). My question is a simple but possibly subtle one which I haven't seen mentioned anywhere.
S... | I would consider the process you described as quasi static. In fact, in that particular process, both the system and the surroundings experience reversible changes. However, for the low thermal conductivity medium in-between, the process is not reversible, and entropy is generated within this medium. This generated e... | {
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How do I find the approximate surface area of a chicken? I'm working on building a chicken army and I'm trying to find out how much metal or kevlar (still deciding) I need to make armor for the chickens. this measurement does not need to be exact I'm just trying to get an estimate for how much I will need. You will be ... | Archimedes' principle can also be used to measure rate of change of volume as the chicken is lowered into liquid. Sedate the chicken before doing this. Plot a curve of volume vs depth. This tells you the area of a cross section of the chicken at the surface of the liquid at each depth. Each cross-sectional part of th... | {
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Assumption while deriving Time Independent Schrödinger equation While deriving the Time Independent Schrödinger equation we assume that the wave function is composed of the two separate functions of time and space. And since we do not have any information regarding the wave function, then how is it correct to assume th... | The Time Dependent Schrödinger Equation (TDE) is a linear, second order partial differential equation (PDE) with variables time $t$ and position $\mathbf{r}$.
When trying to obtain the Time Independent Schrödinger Equation (TISE) we apply a well-known method known as separation of variables (SoV). This method is not in... | {
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Is no acceleration a cause or consequence of no net force? If a body is moving with constant velocity, or is at rest, then the net force on it must be $0$. If the net force on a body is $0$, then it must be moving with constant velocity or must be at rest.
Is $0$ net force a consequence of being at rest or moving with ... | This is a question about philosophy not physics. Here is the answer. If I kick a ball it accelerates. It is not because of the ball accelerating that I kick it, for what would be the point of football (EU English) if it was the other way around?
| {
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Forces and point of application Let us consider a rod and two forces acting on it that are not concurrent, that is, to say that their points of application are not identical, but they intersect somewhere outside the rod. Now, if we theoretically find the direction of the resultant $P$ from the point where both the line... | Yes. You can slide any force along its line of action (parallel line through the point of application) and it does not change the system.
In your case $R$ is going to be along the line of action where it intersects the rod. As shown below:
Note that $F$ and $R$ must have the same magnitude and direction.
| {
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Raising a canal's water level using anchored tug boats? You've all read about the enormous container ship stuck in the Suez Canal:
source
They're planning to attempt to unstick it today when the tide is high, as the 50cm rise in the water level should help significantly.
That, plus all the tugboats running around the ... | If there was only one tugboat, then the effect would be to pump water along the canal. But the opposing tug prevents that; the force of the pushed water from one balances against the push of the water from the other.
Since the tugs are isolated, we can treat the push of each tug as a generalized push against the water.... | {
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What is the significance of the sign of the velocity for a particle executing SHM? So while deriving equation for the velocity of particle executing SHM at any point, I noticed a difference in the result depending on what wave (sine or cosine) you chose.
For $x=A\cos\omega t$:
$\quad \ \,v=-\omega\sqrt{A^2-x^2}$
For $... | It is just related to two different initial conditions for the system.
Assume the system is a mass attached to a spring.
If $$x=A\cos(\omega t)$$ then this represents holding the mass with the spring extended in the +x direction at t=0. When you let go, the velocity is in the negative x direction.
This agrees with the... | {
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Distribution of charge when 2 metallic spheres are connected It is given in my textbook that when 2 charged conducting sphere of different radius are connected by finite wire the redistribution of charges takes place such that the potential just outside of both spheres become equal.
But why potential is the necessary c... | When you touch two spheres, you can consider them as one system, in other words, one big conductor. Now, if a conductor has different potentials on either side, then current (charges) flows through it from higher potential to lower potential.
This happens as a system always wants to be in the lowest energy state, hence... | {
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Derivation of the radial Hartree-Fock equations Can anyone help deriving the radial Hartree-Fock equations of atoms from the Hartree-Fock equations
$$(h_i + J_i - K_i) \psi_i = E_i \psi_i$$
where each orbital $\psi_i$ involves three space coordinates? I'm interested in the restricted Hartree-Fock formulation.
| If found the following formula
$$
\frac{1}{\vert \mathbf{x}-\mathbf{x}'\vert} =
\sum_{k,q} \frac{r_<^k}{r_>^{k+1}} \frac{4\pi}{2k+1} Y_{kq}(\Omega) Y_{kq}^*(\Omega')
$$
in this page. That's all what I need for helium.
| {
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How to know if the error is in a law or in uncertainty of the measurement? I read these words in a (great) answer to this question:
There are errors that come from measuring the quantities and errors that come from the inaccuracy of the laws themselves
But how do we know that the errors are in the measuring or in the... | Measurement errors or experimental errors can be reduced by, for example, using more accurate and more sensitive equipment; making multiple measurements and taking an average; thinking about possible sources of noise and trying to compensate for or reduce these. If you do all these things and there is still a differenc... | {
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What is the physical importance of topological quantum field theory? Apart from the fascinating mathematics of TQFTs, is there any reason that can convince a theoretical physicist to invest time and energy in it?
What are/would be the implications of TQFTs?
I mean is there at least any philosophical attitude behind it?... | In condensed matter physics, topological quantum field theories provide an effective description of (many, but not all) gapped phases of matter at low energies and long distances. A phase of matter is gapped if it costs a finite amount of energy to create any excitation above the ground state.
Examples of gapped phases... | {
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Will the cosmic microwave background radiation eventually not be microwaves? I was reading through this answer about the cosmic microwave background radiation, which implied that we receive it as microwaves because it's been shifted to that wavelength by the expanding universe. Did I understand that correctly?
If so, w... | Yes you read the other answer correctly. The expansion does change the wavelength and not just the perceived wavelength. Each individual photon gets stretched as its traveling through a stretching spacetime. The CMB was released back when the entire universe was filled with a hot opaque plasma which emitted light as a... | {
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In a solar cell when an electron is freed due to light in the depletion layer, why does it move to N-type layer even though it is negatively charged? Even though in a solar cell the N-type layer is negatively charged why do the electrons from the depletion layer get attracted to it?
| I think the main misunderstanding is that the n-layer is neutrally charged overall so it does not attract anything.
Only in the depletion region is there an electric field. The electric fields acts to sweep electrons towards the n-layer and holes toward the p-layer.
The depletion region partially overlaps both n and p ... | {
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Friction force on a rotating car I can't understand how the frictional force is the reason for both the tangential and the centripetal acceleration in a car that is rotating. I found some useful answers on how it provide one of them, but I can't visualize how it provides both at the same time.
| a) Tangential acceleration:
By definition, frictional force opposes the direction of motion. For the part of the car's tire that is in contact with the ground, the friction acting is static friction unless the car is skidding (in the case of skidding, the point in contact with the ground moves along the surface). Becau... | {
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Series combination of springs When a spring mass system is connected vertically with two massless springs in series whose spring constants are $k_1$ and $k_2$ to a block of mass $m$ we know that equal forces act on both the springs. Let that force during oscillations be $F$.
When we calculate effective spring constant ... | ok so the first condition for the series spring system is :
The spring force in the entire system is the same i.e the tension in the springs is the same
therefore
$k_1x_1=k_2x_2$
$k_e(x_1+x_2)=k_1x_1$
where $k_e$ is the equivalent spring constant
so if the system is vertical let gravitation force, mg, be $F$
hence
$x_1... | {
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Angular momentum commutation relations The operator $L^2$ commutes with each of the operators $L_x$, $L_y$ and $L_z$, yet $L_x$, $L_y$ and $L_z$ do not commute with each other.
From linear algebra, we know that if two hermitian operators commute, they admit complete sets of common/simultaneous eigenfunctions. The way I... | This is possible precisely because $L^2$ is degenerate: for an eigenvalue $l(l + 1)$, it has an eigenspace of dimension $2l + 1$ (i.e., it has this many linearly independent eigenstates). The choice of basis in a degenerate eigenspace is not unique -- thus explaining how it can be that the eigenstates $L^2$ shares with... | {
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What is light, a wave or a particle or A wave-particle? What is light?
And how do we know that light is an electromagnetic wave?
I asked my teacher and he said that when you place a compass in light's path, the needle of the compass rotates. Which I think is not a valid answer and thats not what actually happens when w... | Light is a range of frequency of electromagnetic waves which our eyes can detect.
Light consists of photons, which is a weightless particle. Light is a medium through which energy can be released.
| {
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Reconstructing wavefunction from the density matrix Say I have a state, $$| \Psi \rangle = \frac{1}{\sqrt 2} \left( | 0 \rangle + \exp( \text{i} \phi ) | 1 \rangle \right) = c_{0} | 0 \rangle + c_{1} | 1 \rangle.$$
Now I construct the density matrix (DM), $$\hat \rho = | \Psi \rangle \langle \Psi | = \frac{1}{2} \left(... | On solving, we find:
$$\frac{1}{2}\begin{pmatrix}
1 & e^{-i\phi}\\
e^{i\phi} & 1
\end{pmatrix}= \begin{pmatrix}
|c_0|^2 & c_0c^*_1\\
c_1c_0^* & |c_1|^2
\end{pmatrix} $$
$$\Rightarrow |c_0|=|c_1|=\frac{1}{\sqrt{2}}$$
$$c_0c^*_1=\frac{1}{2}e^{-i\phi}\Rightarrow c_0=e^{-i\phi}c_1$$
$$|\psi\rangle =c_0|0\rangle +c_1|1\rang... | {
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Is dark energy (like) normal energy? I know that the term 'dark' is used because a) dark matter does not interact with light b) we know so little about them. Dark matter I guess could be just an unexplained type of particle we don't know about. But what about dark energy?
When we say 'dark energy', are we saying that i... | What we know is that the mass-energy density of the universe must be much higher than expected from baryonic matter/dark matter in order to fit the accelerated expansion observed. It could be a particle. It could some gravitational feature we don't understand... The thing is, what we currently think is that the density... | {
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What is the exponential (or geometric) rule (or law) for uranium enrichment? Uranium ore starts at about .72% U-235...
At ~20% U-235, it is considered to be about '90% of the way' to weapons-grade uranium, which is about ~90% U-235...
Because uranium enrichment in centrifuges follows a geometric (or exponential) law...... | The exponential law for enrichment is that doubling the percentage of U-235 requires the same amount of effort regardless how much there already is. Getting from 20% to 40% is just as hard as getting from 1% to 2%.
Though obviously, this only works well when the percentage is below half. Getting from 95% to 99% is a lo... | {
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What is granularity in particle physics? What is granularity in particle physics? It is used throughout "The ATLAS Experiment at the CERN Large Hadron Collider" http://nordberg.web.cern.ch/PAPERS/JINST08.pdf without being defined anywhere.
An example use: "high detector granularity is needed to handle the particle flux... | In this instrumentation review:
Next follow the detectors, whose key parameters are efficiency, speed, granularity and resolution.
The term is used and not defined further because it is descriptive of the "number of sensitive to measurement ΔV(ΔxΔyΔz) per unit volume : how many "grains" and what a "grain" is will ... | {
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According to general relativity planets and Sun bend the spacetime (explaining gravity), but does this hold true for smaller objects? According to general relativity planets and the sun bend spacetime, and that is the explanation of gravity. However, does this hold true for smaller objects, like toys, pens, etc.? Do t... | Yes, small objects such as pens, paper, tennis balls etc, all bend spacetime.
Not only does spacetime bend, warp, and stretch, but it also flows. You can see that idea in this video which is a really good visualization of gravity.
Another way to think about gravity is that gravity is a difference in proper time. When a... | {
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Muon $g-2$ experiment: is there any theory to explain the results? The nature of the experiment has been discussed here, but my main question is this: is there any theory that has predicted the results of this experiment or are we completely clueless about what's happening? In other words, have we come up with a new hy... | Yes there is a theory that explains the results ... the Standard Model. In other words, the claim is that the Standard Model already is consistent with the experimental data, and the original "prediction" was calculated wrong.
Check out the paper published in Nature together with the muon g-2 results, or the writeup at... | {
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Why do images not appear inverted when looking directly through a pinhole camera? I understand that the way light takes through a pinhole creates an inverted image on a surface behind the pinhole. I remember this effect from school experiments, it's also described in this wikipedia article. I punctured a piece of paper... | I assume that what you are describing is peering through a pinhole such that the field-of-view you get is smaller than normal. That is, I assume you describe a looking through the pinhole that comes with "tunnel-vision".
So, I assume that what you are describing is peering through a pinhole such that for the light to t... | {
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Why is $ \text{div}(\vec{r}/r^3) = 0 $? Let's begin with some context. I was reading Griffiths's introduction to electrodynamics.
This makes sense given all the content one can find online in order to understand visually the divergence.
for example: https://youtu.be/rB83DpBJQsE or https://en.khanacademy.org/math/multi... | As @Uyttendaele comments(1)
\begin{equation}
\boxed{\:\:
\boldsymbol{\nabla}\boldsymbol{\cdot}\left(\dfrac{\mathbf{r}\boldsymbol{-}\mathbf{r}_{0}}{\:\,\Vert\mathbf{r}\boldsymbol{-}\mathbf{r}_{0}\Vert^{\bf 3}}\right)\boldsymbol{=}4\pi\delta\left(\mathbf{r}\boldsymbol{-}\mathbf{r}_{0}\right)\:\:\:\vphantom{\dfrac{\tfrac{... | {
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What is momentum? Momentum tells you the mass of the object and how fast it is going right? So if I have a 2 kg ball moving at 2 m/s, then the ball has 4 kg⋅m/s of momentum. My question is why do we multiply mass and velocity to get momentum. (From the example above) Why cant we just say the ball is 2 kg moving at a sp... | In the context of classical mechanics, and especially rigid body motions momentum can have the following interpretation. The statements below might seems a bit circular, but they work.
Momentum is the quantity needed to completely remove all movement from a rigid body or a point mass.
Specifically, momentum is a vect... | {
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} |
Is the distance between all points on the event horizon zero? These are the Kruskal-Szekeres coordinates of Schwarzschild spacetime:
It is isomorphic to the split-complex plane. But on the split-complex plane the distance between all points on the null diagonals, as measured by the norm of the difference between two s... | If this were a 1+1 dimensional spacetime then you'd be correct, but there are two other spatial dimensions not shown on the chart. Each point on the chart is really a sphere whose radius is a function of $X^2-T^2$.
The event horizon is a 3-cylinder (direct product of a 2-sphere and a line), but with a degenerate metric... | {
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Why does there being no finite dimensional unitary representations of the Lorentz group lead to QFT? In Schwarz's Introduction to QFT and the standard model they say that because there are no finite-dimensional unitary representations of the Lorentz group we must have fields and not particles.
However, for a single par... | There are a number of reasons why the single particle theory of QM can't be extended into a quantum theory of fields and this is another one. Generally speaking we have to move into a picture where particles can be created and annihilated. This is the multi-particle picture.
Freeman Dyson discusses some of the reasons ... | {
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How to inject the maximum acoustic power into a block of granite? I know that we can use transducers that are glued to a surface to achieve this. If I want, for example, to have 200 watts of actual acoustic power in the audible range in the granite, is a transducer the easiest cheapest way? Are there other methods?
| *
*Use an industrial size vibrator motor bolted to the granite. The motor shaft has an eccentric mass on it which will vibrate at the rotational frequency of the motor. Not enough power? Use more than one.
*Use a plate compactor if the process can be conducted outdoors.
*Use a jackhammer, or its smaller cousin, an... | {
"language": "en",
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Trouble showing from first principles the equation describing the motion of a water drop through a cloud If we had a water drop, initially of mass $m_0$ and speed $v_0$, falling through a cloud for a time
T and during this time its mass increases at a constant rate $\alpha m_0$, through accretion of
water vapour initia... | Starting with the second law of dynamics:
$$ \frac{dp}{dt} = mg$$
We have to consider that here the mass is variable.
$$p(t) = m(t)v(t) = m_0(1 + \alpha t)v $$
Then:
$$ \frac{dm}{dt}v + \frac{dv}{dt}m = mg$$
Since the rate of change of the mass is $\frac{dm}{dt} = m_0\alpha$
$$ m_0 \alpha v + m_0(1 + \alpha t)\frac{dv... | {
"language": "en",
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Perception of simultaneous events I have a two-fold question about the light-cone structure of spacetime, specifically about space-like separated events.
As far as I understand it, any two events that happen at the same time in a given reference frame are space-like separated. If so, any two simultaneous events occurri... | You are correct to think that all the events we perceive are in our past light cone.
We perceive, more or less simultaneous events, since for all intents and purposes, for us, light is more or less instantaneous.
To actually see how Einstein goes about constructing a synchronisation of clocks - that is simultaneity - ... | {
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Which types of strain tensor are positive definite? I am taking a look at different types of strain tensor. Specifically, I am thinking about if the infinitesimal strain tensor
\begin{align*}
\epsilon_{ij} = \frac{1}{2} (\frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i})
\end{align*}
is positive-def... | I think the material you found is just wrong. A trivial counter example is zero displacement = zero strain, which is not positive definite.
Nor do I see where such a property would be particularly useful when calculating anything.
It's a different story when talking about the other tensors we deal with (such as the ela... | {
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Euler Equation in General Relativity For a perfect fluid the stress-energy tensor is $T^{\mu \nu} = (\rho + p)u^{\mu}u^{\nu} + pg^{\mu \nu}$, thus the equations of motion read:
$$0 = T^{\mu \nu}_{\; \; \; ;\nu} = (\rho + p)_{;\nu}u^{\mu}u^{\nu} + (\rho + p)(u^{\mu}_{\; ;\nu}u^{\nu} + u^{\mu}u^{\nu}_{\; ;\nu} ) + p_{;... | Just, to make it more clear (as mentioned in the comment), first prove this
$${P_{\alpha \mu }}{u^\mu } = ({u_\alpha }{u_\mu } + {g_{\alpha \mu }}){u^\mu } = {u_\alpha }\underbrace {{u_\mu }{u^\mu }}_{ = - 1} + \underbrace {{g_{\alpha \mu }}{u^\mu }}_{ = {u_\alpha }} = 0,$$
and hence, you get this
$${P_{\alpha \mu}}(\... | {
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Derivation of proper time with respect to time I’m confused on how the author got this answer.
He started with this:
$$\frac{d(\text{proper time})}{dt}=\frac{\sqrt{dt^2-dx^2}}{dt}
=\sqrt{1-v^2}$$
I don’t get how this is solved, specifically where the $1$ came from in $1-v^2$.
| The author is doing typical "physics mathematics", so it may be considered to be a little sloppy to a pure mathematician. ;)
The $1$ comes from $\frac{dt}{dt} = 1$. Perhaps it will make more sense if we do the derivation in a more formal way.
It's common to denote proper time using, $\tau$, the Greek letter tau. Note t... | {
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Isotopy class of spacetime We know that spacetime is an orientable manifold:
Can spacetime be non-orientable?
But supposing that spacetime is an orientable closed 2D surface, one might envision a variety of non-equivalent solutions in the following sense:
Given a 2D strip, by one rotation(twist), one can create a Moebi... |
Is there any way to determine which spacetime relates to ours(2D)
No: all these spaces are (globally) homeomorphic. They are not isotopic, but that is a property of embedded manifolds, not of all of spacetime, and general relativity depends only on the intrinsic geometry of spacetime.
Can I find any physical observa... | {
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Covariant derivative of the spin connection I wish to compute $$[\nabla_{\mu}, \nabla_{\nu}]e^{\lambda}_{~~a}. $$
To do so, I make use of $\nabla_{\nu}e^{\lambda}_{~~a} = \omega_{a~~~\nu}^{~~b}e^{\lambda}_{~~b}$, so that I may write
$$\nabla_{\mu}\nabla_{\nu}e^{\lambda}_{~~~a} = \nabla_{\mu}(\omega_{a~~~\nu}^{~~~b})e^{... | Note that from the relation $e^\lambda{}_{a;\nu} = \omega_a{}^b{}_\nu e^\lambda{}_b$ you give you can deduce by contracting with $e_{\lambda c}$
$$e^\lambda{}_{a;\nu}e_{\lambda c} = \omega_{ac\nu}$$
Note, however, that I am using the definition of the covariant derivative that takes tetrad indices $a,b,c$ as mere label... | {
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Why does silver paper work as Faraday cage for x-rays and does not shield just a simple phone call? I believe the topic of the present question fully explains the issue I would you to talk with me.
It is well known that the higher the electromagnetic frequency, the more difficult is its shielding.
I have seen many x-ra... | I personnally wrapped my phone with silver paper (aluminium foil to be precise) and the phone was shielded. However, the phone has to be completely covered in foil for it to work, a few mm hole will leak enough for the experiement to fail.
| {
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What are the weaknesses, if any, of the relational interpretation of quantum mechanics? Carlo Rovelli's 1996 relational interpretation of quantum mechanics (RQM) seems to solve many of the quandaries of traditional theories, including the Copenhagen interpretation (what privileges the observer? Why does he/she instigat... | It's fair to say that the discussion about RQM has begun to gain momentum in recent years. I have the impression that it has increased in popularity among physicists and philosophers of physics.
But to make contact with the title of your question, there certainly are substantial open problems. Inter alia, some critics ... | {
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How does a copper ring levitates above a AC supply primary coil? Doesn't AC current gives decreasing current and so decreasing magnetic fields or flux. This should then attract the copper ring above primary coil. When magnitude of current increases in AC then due to Lentz law as we know ring will get repelled. But what... | I was wrong in my first answer. It is slightly more subtle than I thought.
Perhaps it has to do with the shape of the exciting field and its oscillation frequency.
If the field diminishes quickly (spatially) with the distance to the exciting coil (e.g. if the field diverges strongly), the second coil could be in the ai... | {
"language": "en",
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How can parallel rays meet at infinity? I found that in every book (till my 12th) it is written that, in concave mirror, when object is at focus, then reflected rays will be parallel and they meet at infinity to form a real image.
But, as we know, parallel rays never meet. Then, does this mean that all books are wrong ... | When physicists say something "goes to infinity", what they mean is "as you take the limit, this value gets bigger and bigger without any bound, and will eventually exceed any number you choose".
In the standard system of real numbers (which is used for most things in classical physics), infinity isn't actually a numbe... | {
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Phase difference approximation I'm sitting and trying to solve the equation of the phase difference given by:
$\Delta \phi = k (\sqrt{a^2+d^2} -d) \approx \frac{ka^2}{2d}$
Where $a$ is the size of an aperture and $b$ is the distance of the point at the aperture's center as shown in the figure below.
I'm not a math exp... | After fixing the typo in your equation you can use the binomial theorem
$$
\sqrt{1+x}= 1+\frac 12 x+\ldots
$$
to get
$$
k(\sqrt{a^2+d^2}-d)= k\left(d\left(1+\frac{a^2}{d^2}\right)^{1/2}-d\right)\\
= k\left(d\left(1+\frac 12 \frac{a^2}{d^2}+\ldots\right)-d\right)\\
=k\frac{a^2}{2d}+\ldots
$$
| {
"language": "en",
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"source": "stackexchange",
"question_score": "1",
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Energy of Hydrogen Atom (Electron vs Proton) In many textbooks, energy changes of the hydrogen atom are attributed to the electron transitioning between energy levels. However, the energy itself is that of the whole system (proton+electron) so how can we attribute its changes to the electron? what's preventing us from ... | THe protons are reside inside the nucleus . Hence they arent the ones who can transitions between different orbits . The thought of protons leaving the nucleus is just a vague thought . That would just mean that we can make ions by loss and gain of protons too which we all know is not possible
| {
"language": "en",
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"source": "stackexchange",
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In the theory of special relativity speed is relative so who decides which observer’s time moves slower? If for example we have 2 people one moving in speed v relative to the other, according to special relativity the time passing for the moving person is slower than for the stationary person. However from the moving p... | They are both right.
But, then, what happens if they meet? Well, in order to meet, you have to accelerate. And if one is accelerating and the other is not, the symmetry is broken.
If they both accelerate equally, they'll end up agreeing anyhow.
Under relativity, events can be separated by spacelike or timelike curves... | {
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Cosmology - Confusion About Visualising the Universe as the Surface of a 3-Sphere Consider the FRW metric for the Universe in the form found in many standard cosmology textbooks:
$$ds^2 = -dt^2 + a(t)^2\left(\frac{dr^2}{1-Kr^2}+r^2(d\theta^2 + \sin^2\theta d\phi^2)\right)$$
I am confused as to what $r$, $\theta$ and $\... | A common elementary coordinatization of the $2$-sphere of radius $R$ uses two angles $(\theta,\phi)$ as (co)latitude and longitude. If we embed the sphere into $\mathbb R^3$, then the points $(x,y,z)$ on the surface take the form
$$\pmatrix{x\\y\\z} = \pmatrix{R \sin(\theta)\cos(\phi)\\R\sin(\theta)\sin(\phi)\\ R\cos(... | {
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Calculating the Wigner transform of operators Recently I started to study the formulation of quantum mechanics in the phase space. So I was introduced to the concept of Wigner function and Weyl transform.
I learned that if F is an operator, then I can represent it by an integral as follows:
\begin{equation}
F = \int_{-... | Pauli matrices are mere constant matrices acting on 2d spinors, not functions of x or p, so you may be barking up the wrong tree.
I assume you or your text have evaluated the free particle hamiltonian,
$$
h(p,q) = \frac{1}{2m}\int_{-\infty}^{+\infty}e^{\frac{i}{\hslash}qu}\langle p+\frac{u}{2}|\hat p^2|p-\frac{u}{2}\ra... | {
"language": "en",
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Are there any known or theoretical substances that don't experience creep? Creep is very slow elasticity that most materials have, that cause pipes to sag over decades. Are there any materials, in theory or in practice, that are creepless?
| Creep in many engineering materials requires dislocation travel. Since dislocation travel is assisted by diffusion, and since diffusion processes in metals kick in exponentially at temperatures above about ~1/2 the melt temperature (in degrees absolute), creep can be prevented by choosing alloys with the highest possib... | {
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Kinetic Energy and Moment of Inertia In this video, at around 12:00, it is said that spinning about the axis with the smallest moment of inertia gives the most kinetic energy. But, isn’t rotational kinetic energy equal to $(1/2)(I)(ω)^2$ . Thus, shouldn’t kinetic energy increase with increase in moment of inertia?
| It is because the angular momentum is conserved while the kinetic energy is not.
So: $$I_1\omega_1=I_2\omega_2$$
When $I_2$ decreases, $\omega_2$ increases. $\omega$ is squared in the expression of kinetic energy and hence the net kinetic energy increases.
| {
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Why are the lenses of a Keplerian Telescope positioned the sum of their focal points apart? I am currently designing an extremely simple Keplerian telescope and am confused as to why many explanations say that the objective lens and eyepiece lens are positioned a distance of the sum of their focal points away (fobjecti... | Parallel rays entering a relaxed eye with normal vision will be focused by the cornea and lens of the eye to form an image on the retina. As far as the eye is concerned, the parallel rays coming from a Keplerian telescope are entirely equivalent to the (nearly) parallel rays coming from a distant object. If one relax... | {
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Why 2nd Shell can have 8 electrons? I recently watched this video:https://youtu.be/INYZy6_HaQE
and understood why 1st orbital can have only 2 electrons: According to Pauli's exclusion principle, two electrons cannot have the same quantum states.In the first energy level,all other quantum states are same except for the ... | There is no such thing as a "second orbital". There is a second shell which is "made of" four orbitals which each can hold 2 electrons – this is where the 8 comes from.
So there is no contradiction: Each atomic orbital can hold two electrons with opposite spin (according to the Pauli exclusion principle), but there are... | {
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Does the albedo of a photovoltaic cell correlate with its load? Exactly what the title says. Since solar panels convert (to my understanding) visible light into electricity, will a solar panel under load appear visually darker compared to a solar panel under no load?
Better phrasing: Does the albedo of a photovoltaic c... | For "regular" (silicon-based) solar panels, I believe the answer is no. Silicon is an indirect band gap material. Recombination rarely releases photons, so an increase in conduction band electrons does not make the material glow. Likewise, an increase in valence band electrons does not make the material darker.
Now ... | {
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Why electric field is scaled by gamma? Two opposite charges are in a spaceship and are attracted by the electric field $E_s$
But for an observer on earth the Electric force is $$E_e=\gamma E_s$$
Normally the forces are scaled down by $\gamma$ in the earth frame and here also the total force is scaled down.
But why the ... |
Normally the forces are scaled down by γ in the earth frame and here
also the total force is scaled down. But why the Electric component of
force is scaled up?
The actual derivation is based on Lorentz transformation equations but one intuitive way to visualise this is to visulalise the electric field lines. In a cha... | {
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Nonlinear extension of Lorentz Group The Lorentz group is defined to be the set of linear transformations that leave $ds^2 = -dt^2 + |d\vec{x}|^2$ invariant. The Poincaré group contains the Lorentz group, but now we allow transformations of the form $t' = t+a$ where $a$ is some constant.
Is there a name for the group o... | NOTE ADDED IN PROOF The linearity for Minkowski metric preserving diffeomorphisms is treated here:
Interval preserving transformations are linear in special relativity
However, one may go a step further and ask a better "foundation of SR question": what are the linear/non-linear transformations that preserve wave-front... | {
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What does it mean for the gravitational force to be "between" two bodies? What is the meaning of the word "between" in the law that the force between two masses at separation $r$ is given by $\frac{GM_1M_2}{r^2}$? I am confused about how can a force be in-between, either it is on body A or on body B, or on both.
Suppos... | The meaning of the word "between" in this case is the same as the meaning of between in the sentence:
The love between two people
Of course it is understood that love does not exist in air. One person loves another. Air has no brain and thus has neither emotions nor feelings.
The word between in the sentence above me... | {
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In this ray diagram, a plane mirror seems to form a real image In this ray diagram the image formed seems to be real with the given position of the eye. I have learnt that plane mirrors cannot form real images at any circumstance. But at this one it does. Please explain the answer like I'm 5 and how you deduced what y... | Some diverging rays have been left out as shown below!
A cone of diverging rays which appear to come from $B_1$ are reflected off the mirror and the eye focuses those rays onto the retina to form a real image of the bottom of the feet.
| {
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Which force came first in Newtonian gravity? Force A on B or force B on A? Can a body $X$ apply a gravitational force on a body $Y$ without itself being acted on by a gravitational force from $Y$? Just per intuition, we deduce from Newton's third law that if $A$ applies force on $B$ then $B$ applies force on $A$. But i... | Both forces appear at the same time.
No, a force cannot be applied by one body on another body without the first body feeling a reaction force. This is due to Newton's third law, as you mention.
For the action/reaction force pair we can't say that one "came first". Both forces of the pair must be present simultaneously... | {
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Velocity is relative, which means acceleration is relative, which further implies that forces are relative as well So how would we know whether a force truly exists or not. I can be accelerating a car my 5 meters per second squared but another car accelerating with the same acceleration would think that my car is at re... | In Galilean relativity, physics is unchanged for frames that are related to uniform boost. That is, we introduce an equivalence relation $\sim$ among frames and define $\mathcal{A} \sim \mathcal{B}$ if frame $\mathcal{B}$ moves with constant velocity vector as seen by the frame $\mathcal{A}$. Then Newton's first law sa... | {
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Is Weyl transformation part of diffeomorphism? Does a gravitational anomaly capture also the anomaly due to Weyl transformation?
*
*Weyl transformation is a local rescaling of the metric tensor
$$
g_{ab}\rightarrow e^{-2\omega(x)}g_{ab}
$$
*Diffeomorphism maps to a theory under arbitrary differentiable coordinate t... | No to both. A Weyl transformation will send a metric to another metric that will not be the image of the first under diffeomorphism. Some diffeomorphisms have the effect of a Weyl transformation on the metric; those are called conformal maps and are quite special (finite in number outside of dimension 2 and 1).
| {
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Does the Oort cloud act as a kind of shield for the Solar System? Does the Oort cloud act as a kind of shield for the Solar System? When an interstellar object impacts the cloud, does its momentum get absorbed substantially?
| The Oort cloud is extremely diffuse, and while there are numerous small bodies, they're spread out over a very large region of space. Assuming that the outer Oort Cloud ranges from 20,000 AU to 50,000 AU and contains $\sim10^{12}$ bodies on the scale of a kilometer or greater, I find an average number density $n$ of 0.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/634722",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Do partial derivatives of different coordinate systems commute? Consider an arbitrary set of coordinates $x^\mu$ and another set of coordinates $y^{\mu}$, which is a (lorentzian) transformation from $x^\mu$ given by $y^\mu = f(x^\mu)$.
So I want to know whether $\frac{\partial}{\partial x^\alpha}\frac{\partial}{\partia... | It depends on the transformation at hand, but in general the answer is no. It boils down to whether $x^\alpha$ can change while $y^\beta$ is kept constant.
Denote by $J_{\nu}^\mu(x) = \frac{\partial y^\mu}{\partial x^\nu} $ the Jacobian of the change of coordinates.
By the chain rule
$$ \frac{\partial}{\partial x^\alph... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/634888",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
"answer_id": 0
} |
Why do I feel electric shock even in the presence of wood? I feel mild electric shock when my laptop with aluminum body is kept on a wooden desk is charging, while both my leg rests on the the leg of the table . Why is that ? Why isn't wood behaving like an insulator here ?
| If the chassis of your laptop is "hot,*" then you would feel a tingle when you touch it even if your body was perfectly insulated from the Earth. That's because the "hot" wire in home electricity supply is an alternating voltage with respect to Earth, and your body and the Earth act like the plates of a capacitor. Each... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/635214",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Why doesn't $v_T = \omega r$ involve the direction of its variables? We derived $v_T = \omega r$ by the following procedure, and it's said that $v_T = \omega r$ "is a relation between the magnitudes of the tangential linear velocity and the angular velocity". Why doesn't the formula involve the direction of its variabl... | Suppose we have a rigid object rotating at some angular velocity $\vec{\omega}$ about some fixed axis. It can be shown that in general, $\vec{v} = \vec{\omega} \times \vec{r}$, where $\vec{r}$ is the instantaneous position of the object. This more general equation does take the directions of the quantities into accou... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/635299",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
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