Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Einstein's relativity of simultaneity - train Einstein's thought experiment has two lightning flashes at either end of a moving train as seen by an observer on the train, and a platform observer. They disagree on the simultaneity of the flashes.. But if we alter the experiment as follows they will agree on simultaneit... | Your interpretation of your modification is correct, and it's also entirely consistent with Special Relativity. What appears to be incorrect here is your assumption that two observers in different frames must disagree on simultaneity of events. This is not actually true (as you have demonstrated), nor does Special Rela... | {
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How does a Galilean telescope form an enlarged image even though it has a diverging lens? I have been reading about Galilean telescope and the picture in the book is something like this:
After rays pass through the converging lens, there is a real image formed which is intercepted by the diverging lens but as I learn... | I think that perhaps the ray diagram in this article
https://thesciencegeek.org/2018/03/13/galileo-and-the-telescope/
is perhaps easier to follow. It shows clearly how the angular magnification is achieved. The article provides useful background
| {
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$SU(2)_L$ Gauge theory and particle-antiparticle annihilation I have a problem understanding how to reconcile the particle antiparticle annihilation vertex with the $SU(2)$ gauge theory, in the context of the weak interaction. Let me explain better :
Invoking $SU(2)$ gauge invariance we deduce there must be three gauge... |
How can this reconciled with the representation of $Z$ as
$\sigma_{z}$?
Don't confuse: the isospin $T$ is not the isospin projection $T_{3}$. The $Z$ and $W^{\pm}$-bosons, as well as fermions, correspond to the definite isospin projections. The difference is that the fermions are in the fundamental 2-dimensional re... | {
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If velocity is relative, how can mass (inertia) be coordinate independent? Would inertia grow differently if we switch the reference frame?
LHC accelerator makes protons x7000 heavier at record speeds and I just wonder if we could change the reference frame (keeping velocity), would its mass be different? (eg. in vacuu... | Your main problem here is that you are mixing ideas from two different ways of formalizing relativity.
If you are using the (old fashioned, unnecessary, and easily misapplied) notion of "relativistic mass" then mass is not invariant.
If you are using the modern nomenclature then 'LHC accelerator makes protons x7000 he... | {
"language": "en",
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How does the sun really produce light in terms of waves? Electromagnetic waves are caused by changing electric and magnetic fields, and these are caused by a charge possible oscillating like an antenna or a varying current etc.
My question is, with the sun, where is this source that causes the electric and magnetic fi... | The visible, UV, and IR radiation which reaches the earth from the sun is due to blackbody radiation from the surface (photosphere and chromosphere) of the sun. You can see more about blackbody radiation here and in the answer by @annav here. Basically, temperature indicates molecular or atomic vibration, which means... | {
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Are all electromagnetic waves transverse in free space? I understand that in vacuum, monochromatic plane waves are transverse. I suppose that a non-monochromatic plane wave would also have this property, as it can be decomposed using the Fourier transform and each of its components would be transverse.
However, what ha... | As discussed in the comments, the plane wave approximation is mostly irrelevant. The only important ingredient is the fact that the homogeneous vacuum Maxwell equations read
$$
\nabla\cdot\boldsymbol E=\nabla\cdot\boldsymbol B= 0
$$
and therefore, after a Fourier transform $\boldsymbol x\to\boldsymbol k$ we get
$$
\bol... | {
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Why are the windows of bridges of ships always inclined?
What is the reason that the windows of ships' bridges are always inclined as shown in the above picture?
| Look at CandiedOrange's answer
This answer was accepted, but CandiedOrange has the right answer. See this document page 21:
The second way in which reflection can interfer e with controller’s vision is light sources within the cab (or direct sunlight that enters the cab), which can cause disturbing refle... | {
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Why does torque produce a force on the axis of rotation? If a door is rotated about its fixed axis in (outer) space, a force parallel to the door on the hinges will arise due to centripetal force on the centre of mass and conservation of momentum (Newton's third law).
But any torque on the door will create a force on ... | "Any" torque will not create a force. Take the simple example of a force $F$ (and the only force in this problem) perpendicular to the door at a distance $r$ from the hinge. The torque's magnitude is $|\tau|=|rF|$ and there is no force on the hinge by the problem statement.
| {
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Does Bayer demosaicing from RGB-filter sensors work *because* the color filters are imprecise? I have an ongoing friendly dispute with another member over on Photo Stack Exchange about the fundamentals of how RAW works, and I'm hoping you can settle it.
My understanding is that Bayer demosaicing works basically entirel... | Most situations, you would probably not notice the difference if there was no overlap. There are a few situations where we see monochromatic light in the real world. Rainbows, lasers, polarized reflections among other things. A rainbow is good example because you have the whole visible spectrum in one shot. If there wa... | {
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Partiton function of lattice gas Suppose I have a single particle on a cubic lattice with lattice site length $a$ and $N$ lattice cells. The particle is feeling a potential $v(\boldsymbol{r})$ which is a continuous spatially dependent potential and a kinetic energy $t(\boldsymbol{p})=-\frac{p^2}{2m}$. One can then form... | You are forgetting a -1, should be subtracted from your exponential and then evaluate the integral
| {
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Wave equation: $y=A \sin(\omega t-kx)$ or $y=A\sin(kx-\omega t)$? What is correct wave equation:
$y=A \sin(\omega t-kx)$ or $y=A\sin(kx-\omega t)$?
How are these wave equations used in the positive $x$-direction
and negative $x$-direction?
| One of the problems of illustrating a wave is that the displacement of the particle $y$ is a function of two variables the equilibrium position of the particle $x$ relative to some origin and time $t$.
So to graph a wave one might draw.
However is is more practical to compare the displacement with time of particles at... | {
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How can a railcar withstand high pressure but fail under a vacuum? A 25,000 gallon (95,000 litre) bulk chemical storage railcar can store products with vapor pressures in excess of 200 psia (1.38 Mpa). The same railcar can not withstand a vacuum when being unloaded. I want to understand why.
A bulk chemical storage ca... | The sealing of a port in a pressure vessel might use the pressure in the
vessel to compress a seal (push an O-ring firmly against a door); such
a seal will not be properly compressed if the vessel is under vacuum.
Many pressure vessels, with thin walls, use pressure-induced tension to hold
the shape (like a balloon); u... | {
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Rewriting the equation for the virial mass of a cluster I have a question that I don't know how to solve, any help is appreciated.
Here it is:
Rewrite the equation for the virial mass of a cluster so that if velocities are entered in km/sec and dimensions in Mpc, the resulting mass is in solar mass
Well the equation is... | This is a very common (and quite subtle) thing done, especially in astrophysics, that is extremely useful to master. It can be a little tricky at first, but it isn't bad. The idea is just to convert standard equations into units that are a little more convenient. The key is to remember that units (like grams, years,... | {
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Why is voltage inversely related to capacitance? $C=\frac{Q}{\Delta V}$ More like charge on each capacitor plate increases $Q$, which increases $C$. However, more like charge on each plate also increases $\Delta V$ right? Because compared to before the capacitor was charged, there was an equal amount of each type of ch... | What you have written about more charge means a larger capacitance is not true.
The capacitance of a conductor depends on its dimensions and its composition.
For an ideal parallel plate capacitor the capacitance is $\dfrac{\epsilon A}{d}$ where $A$ is the area of the plates, $d$ the separation of the plates and $\epsil... | {
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Symmetry of two-particle system of electrons Consider a two particle system consisting of two electrons. The complete state of the electron includes its position wave function and also a spinor describing the orientation of its spin: $$\psi(r) \otimes \chi(s).$$ Why does it follows that for the the two particle system ... | For fermions, the total wave function, including both the spatial wave function and the spin state, must be antisymmetric under exchange. Since the product of two antisymmetric functions is symmetric (as is the product of two symmetric functions), it is necessary that either the spin is antisymmetric or the spatial wav... | {
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Why is a nonzero VEV for a spinor field said to break Lorentz invariance? Consider a spinor field $\psi(x)$. Its vacuum expectation value is given by $$v=\langle 0|\psi(x)|0\rangle.$$ Using the fact that the vaccum is invariant under Lorentz transformation, we get, $$v=\langle 0|\psi(0)|0\rangle.$$ Why is it that, if $... | To make ACM's argument more explicit, consider
\begin{align}
v&=\langle 0|\psi|0\rangle\\
&=\langle 0|\overbrace{UU^\dagger}^1\psi\overbrace{UU^\dagger}^1|0\rangle\\
&=\overbrace{\langle 0|U}^{\langle 0|}\overbrace{U^\dagger\psi U}^{D_\Lambda \psi}\overbrace{U^\dagger|0\rangle}^{|0\rangle}\\
&=D_\Lambda v
\end{align}
w... | {
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Did inflation stop because of energy density drop or some other reason? If I am understanding big bang correctly... During big bang
Approximately $10^{−37}$ seconds into the expansion, a phase transition caused a cosmic inflation,
Which was 'free lunch' of energy and it continued for some time but then suddenly 'fr... | The standard Big Bang model meets at the singularity proposed by the original Big Bang model, a classical General Relativity model, which was proposed when it was observed that all clusters of galaxies are retreating from each other as if coming from a cosmic explosion.
Diagram of evolution of the (observable part)... | {
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Why are light rays able to cross each other? See the image first:
Why are light rays able to cross each other? Air isn't able to.
| Note: this answer was in response to the original question:
My question is that Why the light rays able to cross each other weather water waves and air could not cross each other
Other waves pass through each other just as with light. This is easy to test. Place four people at the corner of a large room. Have two of th... | {
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Is there any advantage in stacking multiple images vs a single long exposure? Suppose I have a source object that is not time varying, to be concrete let's say it's a galaxy. Is there anything additional that can be learned or done with multiple short exposure images of exactly the same field as compared to a single lo... | A significant increase in dynamic range can be achieved by taking exposures with different exposure settings. Wind,vibration, periodic errors etc. Can be combined with all other techniques. It is used in spectrum analyzers under the name of video averaging. Can also be used in radio astronomy. I wonder if it could ha... | {
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contravariant components of electromagnetic field tensor under lorentz transformation I have to show, how the contravariant components of the electromagnetic field tensor behave under Lorentz transformation.
I guess the answer should look something like this
$$F'^{\mu\nu}=\frac{\partial x'^\alpha}{\partial x^\gamma}\f... | What you're maybe missing is the requirement that the covariant equation should still be valid in the new coordinate system:
$$ \partial'_\mu F^{\mu\nu} = \mu_0 j^{\prime\nu} $$
You can now plug in your three equations and solve for $F'$.
| {
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How can Entropy Distinguish Reversible and Irreversible Process if It is a State Variable? If entropy is a state variable, it means that the change in entropy should not depend on the path between two equilibrium states. But the second law of thermodynamics states that, in an isolated system the entropy change due to i... | A similar question has been asked before, although I cant find it now. In an isolated system, between two given states $A$ and $B$ there can be either a reversible process or an irreversible process, but not both. If entropy of isolated system at $A$ and $B$ are same then the process must be reversible, otherwise not.
| {
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Single photon, double slit question If photons are fired conitnuosly one at a time through the double slits is the statistical outcome going through each slit 50%?
| The key feature of the double slit experiment is that the light passes through both slits at the same time. It does not go through one slit or the other but instead passes through both.
This happens because unlike macroscopic objects like baseballs quantum objects do not have a position. They are fuzzy objects that are... | {
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How are club-style weapons effective? The First Law of Thermodynamics states that I can't swing an object held in one hand with more energy than I can swing my arm, and the Second Law says that the total energy would probably even end up being somewhat less. And yet, a person who might not be afraid of getting punched... | The answer: It's less soft.
It is not as important how much energy is transferred, as how fast. Something more soft makes the impact last longer. The soft material dissipates some energy during its deformation.
You can see this from the momentum version of Newton's 2nd law:
$$\sum F=\frac{dp}{dt}$$
You need to make a... | {
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What is the correct way to estimate the work done by a climber? My teacher gave us a worksheet with word problems and their solutions. It is in German, so I have tried my best to translate it to English:
A 26 year old man climbs Mount Everest (8848 m) in only 8 hours 10 mins from the base camp at 5300 m. Estimate the ... | $W=mgh$ is the potential energy the climber (of mass $m$) gains by changing his altitude by $h=8848~\textrm{m} - 5300~\textrm{m} = 3548~\textrm{m}$.
This will be a lower bound for the work done by the climber. In reality work/energy will be lost in friction and any other activities (e.g. setting up a tent...) the climb... | {
"language": "en",
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What causes a circle of light to appear opposite the sun when looking from an airplane? Today I saw a circle of light outside my plane window on the clouds, as if someone was shining a bright, tightly focused flashlight, or perhaps like the halo that sometimes appears around the sun. I think it was approximately where ... | It is an optical phenomenon called a "glory" caused by a diffraction in very small water drops. In fact, the radius of the glory depends on the size of the drops of water and can change in a dynamic fashion as you fly above different clouds with different size of drops. It is quite different than a rainbow though.
Prof... | {
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Why does each plate receive a charge exactly the same magnitude in parallel plate capacitor? When a parallel plate capacitor is connected through a cell, each plate of the capacitor receives a charge with the same magnitude, but with the opposite sign. Is it because of the battery or the area of the plates?
| The battery creates a potential difference between its terminals. Because, in a steady state situation, the total voltage through a closed circuit is zero, this will create, when the capacitor is charged, the same voltage over this component.
Then, if the charges on the capacitor plates wouldn't be equal in magnitude (... | {
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How to calculate an object breaking point or force require to break it? for example, i have a 10 ft rope that has a strength to hold 2000lbs.
when I attach the rope to an object of 1500lb and pull it toward me, (keep it simple with no friction apply) the rope should not be damaged
Now I wrap the rope around the object ... | You have asked at least two different questions here. I will answer the one in the title of your post.
To solve for when the rope will break, you need to know three things: 1) the magnitude of the load, 2) the cross-sectional area of the rope, and 3) the yield strength of the rope material.
The yield strength is quote... | {
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Is hermiticity a basis-dependent concept? I have looked in wikipedia:
Hermitian matrix
and
Self-adjoint operator,
but I still am confused about this.
Is the equation:
$$ \langle Ay | x \rangle = \langle y | A x \rangle \text{ for all } x \in \text{Domain of } A.$$
independent of basis?
| There is a definite sense in which self-adjointness is indeed a basis-dependent concept. It really depends on what you start with. If you have a particular inner product in mind, then the truth of your equation is entirely independent of what basis you choose to represent $x, y$, and $A$ with respect to. However, if yo... | {
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Direction of normal force on stick on box
What is the direction of the normal force on the stick in this case, assuming gravity? Is it right angled with the stick? Or is it upwards? Or is it impossible to determine?
| I think the problem is not the stick, it is the edge of the box. For an ideal box the edge changes direction discontinuously : one side is vertical, the other is horizontal. So how can the normal to the surface of the box at an edge be anything other than horizontal or vertical?
For a real box the edges cannot change d... | {
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Do we suspect that any 2 seemingly identical experiments actually change under the passage of time? For example, let's say that I set up 2 consecutive identical experiments where I know that the conditions are exactly the same (go through whatever difficulties you need to). The only thing I can't control is the passage... |
I set up 2 consecutive identical experiments where I know that the
conditions are exactly the same (go through whatever difficulties you
need to). The only thing I can't control is the passage of time.
Totally impossible.
Perhaps the OP was asking as to whether some of the fundamental constants of Physics (spee... | {
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Why don't these two methods of finding the electric potential in a semicircle agree? I was given the following problem:
A wire of finite length that has a uniform linear charge density $λ = 5.51\times 10^{-9}\ \mathrm{C/m}$ is bent into a semi-circle. Find the electric potential from the center of the semi-circle.
A... | Actually you've got that latter formula wrong. It's
$$\Delta V = -\int \vec{E}\cdot\mathrm{d}\vec{s}$$
The $\Delta$ is important. It reflects the fact that you are calculating a change (or difference) in potential between two points, not the potential at a point, as you are being asked for in this problem. So you can't... | {
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Canonical quantization of bosons During my studies on QFT a fundamental question occurred concerning the canonical quantization. In our course, we mentioned that:
"The canonical quantization of a field with values in the complex numbers can lead only commutation relations, as opposed to anticommutation relations."
Ho... | The product of two complex numbers is commutative and that's why you can't have anticommutation relations. If you want to have anticommutative fields you need Grassmann numbers that are numbers whose product is defined to be anticommutative.
This is only a problem for classical fields though. Once you impose the canoni... | {
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Spin of cobalt-60 At many places in beta decay of cobalt-60, the ground state spin of the isotope is given as 5+. However that's not what is predicted by shell model and applying nordheim's strong rule. Is the data given purely experimental in such cases and outside purview of shell-model? Similarly, daughter nucleus N... | Shell Model arguments usually work well for nuclei close to magic neutron and proton numbers, but sometimes fail when that is not the case. Co-60 is just not magic enough. Here is a link to an old paper that might help: http://ist-socrates.berkeley.edu/~schwrtz/PhysicsPapers/01PhysRev_94_95.pdf The data in the nuclid... | {
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Why the electrons below the Fermi level do not conduct electricity? Physically, why is it that the electrons need to excited above the Fermi level to conduct electricity? In other words, why is the current zero when the electrons lie below the Fermi level? Does Pauli exclusion principle play any role here?
| I think of the TV commercial where the escalator stops and all the people are trapped. The steps are energy levels, and there are two people on each step (spin up and spin down). No third person can occupy a step (Pauli exclusion). Only the ones at the top (Fermi surface) are free to move (gain energy). When they do, t... | {
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"url": "https://physics.stackexchange.com/questions/308181",
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"answer_id": 6
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Binding energy per nucleon error I am given that the mass deficit of 114-Cd is -90.01 MeV, and asked to calculate the binding energy, which should simply be 90.01 MeV then, due to the use of natural units (i.e. where $c=1$). I'm then asked to calculate the binding energy per nucleon which should simply be $\frac{90.01}... | The mass deficit is related to, but different from, the binding energy. The bare neutron and bare proton have zero binding energy, while the canonical source for mass deficits defines $\Delta[{}^{12}\rm C] = 0$.
Note also that the NNDC mass deficits are for neutral atoms, and therefore include electron masses.
| {
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Will a contiguous, low-Re, low-Ca, liquid body always become a sphere at zero gravity? Let's assume zero gravity, zero initial speed everywhere, $Re \ll 1$ and $Ca \ll 1$
Will such a liquid body always become a sphere or will it sometimes split?
Formally speaking, I'm talking about
$$
\lim_{viscosity -> \infty} \lim_{t... | If the object is infinitely viscous (and non-volatile, so that it can't evaporate), it will never change shape.
| {
"language": "en",
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"source": "stackexchange",
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Why doesn't Young's modulus change with length and diameter? In this question:
The Young modulus of steel is determined using a length of steel wire and is found to have the value $E$.
Another experiment is carried out using a wire of the same steel, but of half the length and half the diameter.
What value is obtained... | This question was asked about 3 years ago and by now, you might have passed the A Levels too so this answer might seem irrelevant to you now. But as it turns out, I was having the same problem with the exact question and was seeking the same answer as you did.
I finally found it and wanted to share with you and I hope ... | {
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How does $I = \mathrm{d}q/\mathrm{d}t$ work for a capacitor? When the capacitor is charging in a circuit consisting of a resistor, a capacitor and an alternating sinusoidal generator at $t=0$, the charge across the capacitor is 0 and the current is $I =\mathrm{d}q/\mathrm{d}t$. Does this make the current zero too? Whil... | For a capacitor $Q=CV \Rightarrow \dfrac{dQ}{dt} = I = C \dfrac{dV}{dt}$.
When the rate of change of voltage $\dfrac{dV}{dt}$ is a maximum, ie $V=0$ the current $I$ is a maximum.
When the rate of change of voltage $\dfrac{dV}{dt}$ is zero, ie $V= \pm V_{\rm max}$ the current $I$ is zero.
There is a $90^\circ$ ... | {
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What happens to the temperature of the container during phase change of the substance contained inside I know that as the phase of a substance changes the temperature of the substance remains constant. Now, I was wondering what would happen to the temperature of the container (assuming during the phase change of the su... | Elementary thermodynamics tells us that during phase change a system can absorb or release heat without changing its temperature. You have to give to (or take from) the system a certain quantity of energy to have it complete phase transition: this energy must come from (or go to) somewhere.
Think about a block of ice a... | {
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Covariant Riemann tensor indices Trying to follow a calculation through a paper where, I think, something strange is happening with the indices in the product terms:
How does $\Gamma_{isl}\Gamma^s_{jk}$ in the second line become $-\Gamma_{jks}g^{st}\Gamma_{ilt}$ in the third line? This amounts to setting $\Gamma_{is... | Got it. Had to look at the derivative terms. Use:
$$g_{ij,k}=\Gamma_{kij}+\Gamma_{kji}$$
and
\begin{align}
0&=(\delta_i^{\,j})_{,k}\\
&=(g_{is}g^{sj})_{,k}\\
&=g_{is,k}g^{sj}+g_{is}g^{sj}_{\,\,\,,k}\\
\therefore\,\,&g_{is,k}g^{sj}=-g_{is}g^{sj}_{\,\,\,,k}
\end{align}
Then:
\begin{align}
R_{ijkl}
&=g_{sl}(\partial_i\Gam... | {
"language": "en",
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Why buckets have rims curled outwards? My brother told me that household buckets have rims curled outwards to increase their polar moment of inertia.
But for what? This increased moment of inertia is needed to counteract what?
|
Why have buckets with curved rims?
The polar moment of inertia is used to gauge the capacity of an object to resist twisting, or torsion, (in circular cross sectioned objects). In other words it is a measure of the angular displacement of the bucket when undergoing torque.
So if we filled the bucket with water, and t... | {
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Reconcile three-point function with OPE in CFT Three-point function of primary operators in conformal field theory can be fixed up to a constant by symmetry considerations
$$\left\langle V_{h_1}(z_1)V_{h_2}(z_2)V_{h_3}(z_3)\right\rangle=\frac{C_{h_1h_2h_3}}{(z_1-z_2)^{h_1+h_2-h_3}(z_1-z_3)^{h_1+h_3-h_2}(z_2-z_3)^{h_2+h... | You should sum over all descendents $K$. In general their contributions do not vanish, although they are subleading in the limit $z_1\to z_2$. For example the two-point function
$$
\langle L_{-1}V_{h_3}(z_2)V_{h_3}(z_3) \rangle = \frac{\partial}{\partial z_2}\langle V_{h_3}(z_2)V_{h_3}(z_3) \rangle
$$
is clearly nonze... | {
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Question about simple harmonic motion
A massive bird lands on a taut light horizontal wire. You observe that after landing the bird oscillates up and down with approximately simple harmonic motion with period $T$.
You also notice that during the initial oscillations the maximum height the bird reaches above its positi... | The second line is the clincher in the problem. Once you understand its significance, the problem becomes very easy. When the bird comes to rest permanently on the wire, it reaches the equilibrium position which is the mean position of SHM. If this is A units below landing position, and the maximum height reached is A ... | {
"language": "en",
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Why is a sleeping bag so cold when you first get in? I sometimes put a sweater on when I first get up on a cold morning. The sweater isn't so cold against my skin, but the zipper is. I get this. Even though they are both at the same temperature, the zipper is a better conductor of heat. Heat flows more easily from warm... | i have a potential solution but i'm not sure if it's accurate
say you get up on your cold morning, and your sleeping bag, as rightly stated is a good insulator, but because its been there all night, it will have slowly gotten cold overnight, but because it is such a good insulator, it will prevent a lot of heat getting... | {
"language": "en",
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Why doesn't increasing resistance increase brightness if $P=I^2\cdot R$ Light bulb brightness increases with power, $P$.
So why doesn't increasing $R$ increase $P$ and hence increase brightness as $P=I^2\cdot R$ due to $P=I\cdot V$ and $V=I\cdot R$?
I read increasing $R$ decreases brightness.
| The two equations of relevance are
${\rm power} (P) = \,{\rm voltage} \,(V) \times {\rm current} \,(I)$
${\rm resistance}\, (R) = \dfrac{{\rm voltage}\,(V)}{{\rm current}\,(I)} $
From those two equations you can get $P = I^2R$ and $P = \dfrac {V^2}{R}$
Suppose that it is assumed that the resistance of the light bul... | {
"language": "en",
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Invasive blood pressure measuring and hydrostatics I don't understand why the solution-manometric liquid must be at the catheter level.
I'm studying biophysics, in particular fluid mechanics.
A link to the image
Here is another image
Why A' has to be in the same level of A?
| I'm unable to see your picture but believe I know what you are asking. An arterial line is placed to directly measure arterial blood pressure by accessing an artery with a catheter and measuring the pressure in a continuous manner with a pressure transducer. Access to the artery requires that the catheter remain patent... | {
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Conservative force and its Potential Energy Function We are given that $\vec{F}=k\left<y,x,0\right>$, and asked whether $\vec{F}$ is a conservative force. If yes, we are asked to find $U(x,y,z)$ and then find $\vec{F}$ back from $U$ and show it matches the original form.
Given $\vec{\nabla} \times\vec{F}=\vec{0}$, forc... | Well you integrated it the wrong way.
$$\int ky \, dx + \int kx \, dy = \int k \,d(xy) $$
X and y are not independent.
| {
"language": "en",
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What is the significance of the phase constant in the Simple Harmonic Motion equation? The displacement of a particle performing simple harmonic motion is given by $x = A \sin(\omega t + \phi)$ , where $A$ is the amplitude, $\omega$ is the frequency, $t$ is the time, and $\phi$ is the phase constant. What is the signif... | Based on a point raised by @docscience this answer addresses the phase in terms of "initial conditions" introduced by driving forces. In fact one can think of this as answering how the SHO was set in motion in the first place.
The position of a simple harmonic oscillator at time $t$ that experienced force at time $t'$ ... | {
"language": "en",
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What is the infinity that strikes quantum field theory? I'm confused, on a book I recently read, it talked about renormalization, the creation of renormalization is because of the infinity problem.
Here's is the problem, what is the infinity problem that needs to be eliminated in quantum mechanics? What is the cause?
| It is all about the perturbative expansion for the interaction amplitudes. These are expressed in Feynman diagrams of increasing order.
in calculating loop Feynman diagrams in QED one finds integrals which diverge Such apparent pathologies are dealt with by the process of renormalization. This procedure can be viewed ... | {
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Acceleration of car. One dimensional motion easy problem A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.
My attempt at solving the problem:
$$a(x) = \frac{v - u}{t}$$
where
$v =$ final velocity
$u =$ initial velocity
$$$$
I get... | Yes, I think so. Below is the proper formula for the distance an object accelerating at a constant rate goes over time. I used it to get a formula where you enter distance and time traveled to get the acceleration.
m=0.5at^2
2m/t^2=a
(2*110)/5.21^2=8.10489203915 m/s^2
Hope this helps.
| {
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What causes change in planet's angular velocity? A satellite moving in an elliptical orbit will increase in angular velocity as it nears a planet. I understand that this is consistent with angular momentum. But what causes the increase in angular velocity if there is no torque acting on the satellite?
| Consider an object moving straight past a point that doesn't gravitate at all.
In uniform linear motion, the angular velocity with respect to this point starts out very small, then grows to a finite value, and then decreases towards 0 again -- all without any force at all acting on the moving object.
Change in angular ... | {
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An appropriate way to store neodymium magnets Okay so I've bought a few small neodymium magnets to play around with, they're very powerful and I really like them, but I was wondering what's the actual best way of storing those magnets in a way that doesn't affect their magnetic fields or degrades them in any way.
I'm c... | I just purchased a large-ish neodymium magnet. It is 2.75 inches in diameter, disk-shaped. It also came with a thin disk of steel sheet metal the same diameter that is called a "striker plate." It can be used in non-metal applications to get the magnet to attach. (e.g. if you want to use the magnet to hold a wooden c... | {
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The equilibrium concentration of vacancies In the derivation of the equilibrium concentration of vacancies by statistical mechanics method, I was stumped by this procedure (marked by "?").
$\textbf{Physical Model}:$
1.Solid viewed as a collection of $N$ atomic sites;
2.Each site may or may not be occupied, and assume n... | Calculate the ratio of the number of vacancies in equilibrium at 27 C in aluminum to that produced at 527 C. The energy of the formation of vacancies in aluminum is 68 kJ/mol
| {
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Magnetic behaviour of magnet A very direct question regarding behaviour of a magnet-
When a magnet is heated such that it melts, why does it lose its magnetism?
This is what I was wondering -
When a solid magnet is heated, the heat is able to provide potential energy to the constituent atoms and thus the magnet turn... | Ferromagnetism is a quantum mechanical effect that relies on the ability of atoms to achieve "long range ordering". This ordering results in a coupling of the angular momentum of electrons in neighboring atoms, which leads to magnetic domains. When enough domains align, you get net magnetism.
Heating a material above t... | {
"language": "en",
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What is a "thermal" particle? I have seen various uses of the word "thermal" recently (e.g. in black hole physics) that make me wonder what is the exact meaning of "thermal" in particle physics. There are also "thermal neutrons", for example, so my initial understanding of "thermal" as related "thermal radiation", i.e.... | Thermal means a type radiation (i.e photons) which is given out by a body to reduce the temperature of itself. It is generally in microwave range.
| {
"language": "en",
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Is it possible for light to fall into a geo-synchronous orbit around a sufficiently massive planet? Is it possible for (visible) light to fall into a geo-synchronous orbit around a sufficiently massive planet?
Can a planet or heavenly body be massive enough for it to happen?
What will that suspended light look like t... | *
*No, light cannot fall into Geo-synchronous orbit. Because light is emitted from on point and travels in straight line and terminates due to scattering or absorption. Considering the massive Celestial objects where it is seen that light bends are near the black holes.
*It is impossible for any planet to be as mass... | {
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Do physicists use particle "energy" to refer to kinetic energy? In 1963, this paper was written about the effects of radiation on solar panels. The paper states that:
When electrons at energies greater than 145 KeV and protons at energies
greater than 98eV bombard a silicon crystal, they can displace an atom from t... | Yes, in this case what's meant by "energy" is the kinetic energy $K = (\gamma-1)mc^2$ that the incident particle can transfer to the target system. As you point out, it wouldn't make sense to talk about an electron, which has rest energy $E_0=mc^2=511\rm\,keV$, to have a total energy $E=\gamma mc^2 = mc^2 + K$ of only... | {
"language": "en",
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Translation of Vectors I am a bit confused about translation of vectors. In the first class in physics itself we are told that we can translate vectors as we like to the desired position to do whatever that we are trying to do. For example, if someone draws two random vectors then to get the sum, we translate them, ma... | The definition of a vector as having magnitude and direction is typically used in physics, so the exact location of the vector is not included in the definition. This is also called a "free" vector. As you say the effect of the vector depends on its location. For example, a force (vector) cannot act upon a point mas... | {
"language": "en",
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Is the concept of in-compressible fluid valid in special theory of relativity? Is the concept of incompressible fluid valid in special theory of relativity?
Can anybody answer this question without going into speed of sound and fluid dynamics ?
| In an incompressible fluid the density does not change in response to changes in the pressure. This means that the speed of sound is infinite,
$$
c_s^2= c^2\left.\frac{\partial P}{\partial \rho}\right|_s=\infty .
$$
Here, $P$ is the pressure and $\rho$ is is the energy density. In the non-relativistic limit $\rho=mnc^2... | {
"language": "en",
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How does one show that the curl of magnetic field is equal to $\mu_0\mathbf J+\mu_0\epsilon_0\frac{\partial \mathbf E}{\partial t}$? Normally, the curl is supposed to be equal to $\mu_0\mathbf J$. However, when checking for invariance for Maxwell's equations under duality transformations, the term $\mu_0\epsilon_0\frac... | I do not see what you mean by "normally, the curl is supposed to be equal to $\mu_0\vec J$". I will assume that you mean: experiments show that $${\rm curl}\ \!\vec B=\mu_0\vec J,$$ i.e. an electric current generates a magnetic field turning around the wire. However, this equation cannot be true: taking the divergence,... | {
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Can you build a compass that is attracted to the South Pole? Was just curious, since all compasses point to the North Pole.
South is just the opposite polarity of of North, so it seems very likely, but I've never seen an example of this. Is there any videos demonstrating this?
Could a South attractor be added to a stan... | Another approach is to remagnetize the needle in the opposite direction using a strong magnetic field. Then the painted end will point south.
| {
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Breit-Wigner Peak - Not quite a Lorentzian? The non-relativistic Breit-Wigner peak is given by:
$$\sigma_{fi}=\frac{\pi\hbar^2}{q^2} \frac{2j+1}{(2S_1+1)(2S_2+1)} \frac{\Gamma_i \Gamma_f}{(E-Mc^2)^2+\Gamma^2/4}$$
where $q$ is the center of mass momentum of one of the particles and $E$ is the center of mass energy. From... | You are right that the relativistic Breit-Wigner distribution isn't functionally quite the same as the Lorenzian distribution. However, the approximation that you described and which compares the relativistic distribution to the non-relativistic, Lorentzian one may be extremely accurate.
Well, it is extremely accurate ... | {
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Can relative velocity be found? Can you find the relative velocity between two cars with constant velocity of U1 and U2=-U1. In other words is there any kind of experiment you can do to understand that you are moving also and not just seeing the other car with 2U1?
| "Can relative velocity be found?"
Yes. More on that in a moment.
"is there any kind of experiment you can do to understand that you are moving also"
Theoretically, no. However, in actual practice, an accelerometer will give you a pretty good idea of whether or not you are "moving" in the sense that you're thinking. ... | {
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Does a purely tangential force create centripetal force? Suppose there's a circular disc pivoted at is center and a purely tangential force is applied to change the angular speed of the disc. So as the disc's rotation speed changes constantly, the particles get accelerated towards the center too. Has the tangential for... | The tangential force somewhat creates the centripetal force.
The centripetal force is a reaction of the object or system to the tangential force. In the case of a disk, when you apply the tangential force somewhere, if the disk is being held so it can only rotate, then the tangential motion won't be able to accelerate... | {
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Experimentally measure velocity/momentum of a particle in quantum mechanics In the context of quantum mechanics one cannot measure the velocity of a particle by measuring its position at two quick instants of time and dividing by the time interval. That is,
$$ v = \frac{x_2 - x_1}{t_2 - t_1} $$ does not hold as just af... | In condensed matter physics community, one can use the ARPES apparatus. ARPES gives information on the direction, speed and scattering process of valence electrons in the sample being studied (usually a solid). This means that information can be gained on both the energy and momentum of an electron, resulting in detail... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/312834",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Interaction terms in the Standard model which cause Higgs decay to electroweak bosons The coupling of the Higgs boson to the electroweak gauge bosons in the Standard model is given by
$$\mathcal{L}_{\text{H-g}} = - \left( \frac{H}{v} + \frac{H^{2}}{2v^{2}} \right) \left(2M_{W}^{2}W_{\mu}^{+}W^{-\mu} + M_{Z}^{2}Z_{\mu}Z... | The reason is very simple -- term of the form $H A_\mu A^\mu$ corresponds to the vertex with one Higgs and two bosons -- directly the Feynman diagram giving the decay. The term $H^2 A_\mu A^\mu$ is the vertex with two Higgs bosons and two gauge bosons. At tree level this is some scattering process (say, $2H\to 2Z$), ... | {
"language": "en",
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Orbitals and electron jumping Bohr model (tries to) explain how electron goes to higher state(orbit) from lower state(orbit) on photon absorption.But in quantum mechanics, we have orbitals which can at most accommodate 2electrons.
Let's consider an electron that has absorbed a photon sufficient to make it jump from Orb... | If the excited electrons can't be stimulated, then the photon simply won't interact with the lower-level electron as the electron's transition is forbidden.
| {
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Calculate which composite will give the lightest beam for a given force and deflection. A uniform rectangular-section beam of fixed width, W, unspecified depth, d, and fixed length,L, rests horizontally on two simple supports at either end of the beam. A concentrated force, F,acts vertically downwards through the centr... | The mass of the beam, $M$, is equal to $$M = \rho L W d,$$ where $L$ and $W$ are the same for every beam. For a given force $F$, we can calculate the minimal width of the beam $d$ so that the deflection would not exceed $\delta$: $$d = L\left(\frac{F}{4E_cW\delta}\right)^\frac13.$$
The mass of the beam is then $$M = \r... | {
"language": "en",
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Current as the time derivative of the charge I have been told that the current $i$ can be defined as
$ i = \displaystyle\frac{dq}{dt} $,
where $q$ is the charge and $t$ is the time.
I do not understand this definition because, if the charges are moving so that the net charge remains constant in an infinitesimally thin... | Current is not related to the charge "in an infinitesimally thin cross-section of a wire". Electrical current is the amount of charge that passes across that cross-section per unit of time.
If the current is constant, the last expression you show works:
$ I = \displaystyle\frac{q}{t} $,
If the current varies, your fir... | {
"language": "en",
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Heat shields and the atmosphere Space capsules and the Shuttles were equipped with heat shields to protect the spacecraft and those on board from the tremendous heat generated from friction as they reentered earth's atmosphere at thousands of miles per hour. Why weren't heat shields installed on the vehicles to protect... | The answer is simple. During launch, much of the acceleration occurs above the bulk of the atmosphere. During entry, almost all of the acceleration (deceleration) occurs within the atmosphere. Launching vehicles carefully balance the need for horizontal velocity versus losses due to drag. Reentering vehicles rely very ... | {
"language": "en",
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How can the free charges of a conductor redistribute to the surface? I have studied that if I put a conductor (perfect or non-perfect) at rest in a place where there is an electrostatic field, the charges of the conductor will distribute so that negative charges will be in the surface near the source of the electric fi... | Think of it a different way.
The electrons from only the atoms on the surface of the metal redistribute themselves.
Part of the surface layer becomes positive net, and part of the surface layer becomes negative net.
The net charge of the entire surface remains zero.
| {
"language": "en",
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Can an object falling in vacuum generate electricity by itself? When an object falls through vacuum, gravitational potential energy is converted to kinetic energy. Is there some way to get electrical energy out of the equation by itself (i.e. somehow convert the gravitational potential energy to electrical energy)? I... | If by 'electrical energy' you mean 'an electric current', then no, that won't work. The stationary coil you are excluding is there to provide the supply of electrons to be moved by the magnet - no electrons, no current.
And no, nothing can be generated within the falling object. Current is generated by the relative m... | {
"language": "en",
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"source": "stackexchange",
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Can Zener Breakdown be converted to Avalanche breakdown? Wikipedia says:
The Zener effect is distinct from avalanche breakdown. Avalanche breakdown involves minority carrier electrons in the transition region being accelerated, by the electric field, to energies sufficient for freeing electron-hole pairs via collision... | Zener breakdown (the breakdown mechanism described by Clarence Zener) occurs
in practical semiconductor devices at low voltages. Avalanche breakdown
dominates at high voltages and includes amplification by carrier-generating
processes similar to a small rockfall initiating an avalanche.
Zener breakdown has a negative ... | {
"language": "en",
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Why Newton's equation of motion is time reversally invariant (TRI)? I am really perplexed by the fact that Newton's equation is time reversal?
Newton's equation of motion is time reversally invariant, evident from the equation itself:
$$m\dfrac{d^2x}{dt^2} = F(x).$$
My question is why?
Is there some deep reason they co... | I'm not sure if this helps or even if it addresses your question, but one way to think about this is that Newton's law says that accelerations (not, say, velocities) are proportional to forces. If you accept that as a "non-perplexing" given, then the resulting differential equation can be interpreted as an expression o... | {
"language": "en",
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About effects of torque off center of mass I am trying to deepen my intuition: If in outer space is a rod of length 2 meters standing still. At the both ends it has some heavy wheels of equal mass and the associated motors. If a motor starts spinning one of the wheels ... will the center of mass of the rod stand still ... | Farcher has already given a good explanation : the centre of mass of the system does not move; the total angular momentum of the system remains zero unless ther is an external torque.
If the centre of the rod coincides with the centre of mass of the sytem, the centre of the rod will not move. If the centre of the rod d... | {
"language": "en",
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More light reflected off of double pane windows? In glass windows, you get light passing through and light reflecting off the front and back surfaces. Would you get more light reflecting off of triple or double pane windows? Because you have double or triple the amount of surfaces for the light to reflect off of.
| You hit on half of the idea of optical thin film coatings. The other half is that light is a wave. Multiple reflections can interfere constructively or destructively. This can be used to make either an antireflection coating, or a mirror, or something more complex.
This shows the idea of an antireflection coating. Att... | {
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Looking for a good casual book on quantum physics I'm looking for something that is going to blow my mind without any scientistic ideas (e.g. something that sounds like science, but doesn't have anything in common with science), written by a professional physicist who spent a lot of time considering "what it all means... | I would like to recommend this book, the theoretic minimum: quantum mechanics written by Leonard Susskind. It is very nice to talk about many important points in quantum mechanics.
Here is course website for this course.
| {
"language": "en",
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"source": "stackexchange",
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What does one second after big bang mean? Consider the following statement:
Hadron Epoch, from $10^{-6}$ seconds to $1$ second: The temperature of the
universe cools to about a trillion degrees, cool enough to allow
quarks to combine to form hadrons (like protons and neutrons).
What does it mean to say "from $10^... | Adding a little more argument about co-moving, we know that momentum is conserved, even in relativity, so we can talk about the center of mass frame, the frame where the total momentum is zero. This is the preferred frame.
| {
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Method of image charges for a point charge and a non-grounded conducting plane I know how to solve Laplace's equation for a point charge in front of a grounded conducting infinite plane. But I want to know what happens (both physics and math) when the infinite conducting plane isn't grounded, or is connected to a poten... | I also think that there would be a difference between the two situations. Lets take a non-grounded PEC plane and say a positive charge lies above it. The field created by the charge will induce negative charges to be stacked on the top (towards the positive charge) of the PEC, and since there is no creation nor destruc... | {
"language": "en",
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Density of states of Bogoliubov quasiparticles For a simple fermionic system the formula for calculating the density of states (DOS) is $N(E) = \sum_{n}\delta(E-E_{n})$ where $\{E_{n}\}$ is the set of eigenvalues obtained after diagonalizing the hamiltonian. Now to diagonaloize a hamiltonian with pair correlation terms... | Write BCS ground state (reference) $|\Psi_{BCS}\rangle$:
$$|\Psi_{BCS}\rangle=\prod\limits_{\bf k}(u_{\bf k}+v_{\bf k}c_{\bf k\uparrow}^\dagger c_{\bf -k\downarrow}^\dagger)|0\rangle$$
and calculate the number density expectation:
$$\langle \hat n_{\bf k}\rangle=\langle c^\dagger_{\bf k}c_{\bf k}\rangle$$
| {
"language": "en",
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Centrifugal force in inertial systems My textbook gives an example:
There are two systems, $O$ is inertial and $O'$ non inertial. $O'$ is rotating whit $\omega=\mathrm{constant}$ and $O=O'$.
We assume that a disc is rotating whit the same $\omega$ of $O'$, and we put an object on the disc. There isn't friction between ... | You are correct in suposing centrifugal forces are not the explanation because they do not appear in inertial frames of reference.
In $O$ the object is performing a circular motion, and this motion does not appear when there is no force on the object (it would perform a straight motion).
What the rope does in $O$ is to... | {
"language": "en",
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Would a gas "weigh" less than a liquid if they have the same mass? Thought experiment: I acquired two boxes of the same dimensions and same weight. One box contains $1\ \mathrm{kg}$ of water at room temperature while the other box has $1\ \mathrm{kg}$ of water, but in steam form, because the temperature of the box is a... | Weight is proportional to mass, end of story, the two boxes will weigh the same. However to contain the mass of 1kg of steam in a ten litre box will require an enormous pressure. The volume of an ideal gas (which steam is not but neglect that for a moment) is 22.4 litres per mole at STP. One mole of water weighs 18g, s... | {
"language": "en",
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Schrödinger equation and non-Hermitian Hamiltonians Is the Schrödinger equation still valid if we use a non-Hermitian Hamiltonian with it? By this I mean does:
$$\hat{H}\psi(t) = i\hbar\frac{\partial}{\partial t}\psi(t)$$
if $\hat{H}$ is not Hermitian?
| Let's suppose that we have an operator $\hat{\mathcal{O}}$ such that $i \hat{\mathcal{O}} |\psi\rangle = \partial_t |\psi\rangle$. The question is then: What is $\partial_t (\langle \psi | \psi \rangle)$? Well, by definition of the adjoint we have $\partial_t \langle \psi | = \langle \psi| (i \hat{\mathcal{O}})^\dag... | {
"language": "en",
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Conceptually, why is acceleration due to gravity always negative? As the title states, why is acceleration due to gravity always (-). Say you assign "up" as the positive direction. If an projectile is thrown at a 24 degree angle above the horizontal, I get that acceleration due to gravity before the vertex is negative.... | Acceleration due to gravity in itself is not negative but it is directed toward center of earth (downward) and we take
Downward direction as negative by convention.
And as force of gravity is pointing to same direction at every point on the trajectory hence acceleration due to gravity is same for before or after the v... | {
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Expectation value of $p^2 (1/r) + (1/r) p^2$ I'm trying to derive $\langle kl | \lbrace 1/r , p^2 \rbrace | nl \rangle$, where the states satisfy the equation of motion (I omit factors of $1/2m$ etc.):
$$(p^2 + V)| n,l \rangle = E_n | n,l \rangle$$
and $\lbrace A,B \rbrace = AB + BA$ is the anticommutator.
I have two s... | A paradigm is worth a hundred puffs of bloviation.
Exploit your spherical symmetry, $\hat{r}\cdot \vec{\nabla}=\partial_r$, and $\vec{\nabla} f(r) =\hat{r} \partial_r f(r)$; and, since the challenge you are concerned with is the singularity at the origin, r =0, we might as well drop all l>0, which are softer than s-wav... | {
"language": "en",
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Liquid vs. gas cooling I have an aluminum can that needs cooled. I put it in the refrigerator, where it is cooled by the cold air surrounding the can.
If I were to place the same can in water that had been cooled to the same temperature as the refrigerated air, would the can cool down faster?
I'm inclined to assume th... | The two different methods of cooling the can are completely different and governed by different properties and have different heat transfer coefficients.
Because the can is warmer the direction of heat transfer is from the can.
In the refrigerator the method of heat transfer is radiation. The heat transfer is govern... | {
"language": "en",
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How to remove gravity component from accelerometer $X$, $Y$ readings? So I have an accelerometer which I am wanting to use in an IMU.
When the device is tilted but stationary I want the x, y values to be 0, so effectively negate the effect of gravity along the x and y axes of the accelerometer.
I have found lots of con... | well as i experienced, you could compute rotation matrix from Azimuth(yaw), pitch & roll. computationally it is simple as mentioned by formulas for kinematics everywhere.
then simple by multiplying 3*3 rotation matrix with 3*1 accelerometer data to convert the readings and compute new values corresponding to fixed glob... | {
"language": "en",
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Ball inside an accelerating frame Why does a ball inside a moving bus at rest start moving backwards when the bus suddenly accelerates? Also does the moving ball have some acceleration?
This is my theory:
Initially the bus and the ball are at rest. When the bus starts accelerating, due to inertia of rest, the ball resi... | Take it like this imagine yourself as an by stander watching the bus then you would notice the ball goes in the direction opposite to bus but when we only take the ball the direction of pseudo force is opposite to the motion of the bus when we consider the floor to have friction then this $μN$ force to opposethis pesud... | {
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How do I find the time evolution of a ket? I have a question which reads:
Let \begin{bmatrix}
{E_0} & 0 & A \\
0 & E_1 & 0 \\
A & 0 & E_0
\end{bmatrix}
be the matrix representation of the Hamiltonian for a three-state system with basis states $|1>, |2> \mbox{and } |3>$.
a. If the state ... | Actually I believe both answers are correct. I can't seem to find anything wrong with either. Certainly a. is correct since the hamiltonian in the time operator should just be replaced by the eigenvalue, seen simply if we expand the matrix exponential.
For b, there is nothing wrong with expressing our time dependent ... | {
"language": "en",
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Michelson interferometer beam splitter phase shift In a Michelson interferometer (image from Optics by E. Hecht ) .
To quote from the same book:
As the figure shows, the optical path difference for these rays is
nearly $2d \cos 0$. There is an additional phase term arising from
the fact that the wave traversing th... | There is an automatic change in the phase when the wave goes ..... bounces off the mirror. Then after all that you start to play with the path lengths to introduce more phase changes.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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What is the difference between mean free path and intermolecular distance? Why is the mean free path not be equal to the intermolecular distance?
A particle moving in a particular direction should strike the object in that direction after the traveling the same distance as the distance between them initially.
| There's a few things to point out. @lemon already pointed out one of them in the comment -- it is possible for a molecule to move and end up going between other molecules and missing them. So even though they start out, say, equally spaced (think like an equilateral triangle), it's possible for a molecule to move betwe... | {
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Proper volume in different frames of reference (and tetrads) I am interested in the behavior of the proper volume when we switch the frame of reference. For example, I know that the proper volume element for the Schwarzschild and Kerr black holes may be extracted easily from the formulae:
$V=\sqrt{g}dr d\theta d\phi = ... | Well, to calculate volumes, you need a hypersurface.
Let $\Sigma$ be such a hypersurface, locally described as $$ x^\mu=\Phi^\mu(\xi), $$ where $\xi=(\xi^1,\xi^2,\xi^3)$ are local coordinates on the hypersurface. Let us assume $\Sigma$ is spacelike, since that's what you seem to be going for.
The induced metric is then... | {
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When can one omit a total time derivative in the Lagrangian formulation? I am studying Lagrangian and Hamiltonian mechanics and i am using Landau & Lifshitz and Goldstein books. Both of them state that a modified lagrangian $$L'=L+\frac{df}{dt}$$ gives the same solutions than $L$ wich i kind of understand but its not t... | To understand this f you need to be aware that f can only be a function of q and t, not of q dot.
I got tripped up by the same question a long time ago as an undergrad. When you get $a^2 \omega^2 sin^2(\omega t)$ then this is a function of t only (a and omega are not dynamical variables, right?) We know any function of... | {
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Spinor decomposition I just read in the book "Covariant loop quantum gravity" of Rovelli about spinors (section 1.7.1) I'm confused about the decomposition of an spinor of two indices that it is done:
$$z^{AB}= z_0 \epsilon^{AB} + z^{(AB)} $$
where $z^{(AB)}$ is the symmetric part, $\epsilon$ is the antisymmetric matr... | \begin{eqnarray}
z_0 \epsilon^{AB} &=& \frac 1 2 \epsilon _{CD}\,z^{CD} \times \epsilon^{AB}\;,\\
&=& \frac 1 2 \delta^{AB}_{CD} \,z^{CD} \;,\\
&=& \frac 1 2 \big( z^{AB}-z^{BA} \big)\;,
\end{eqnarray}
where
$$
\epsilon _{CD}\,\epsilon^{AB}= \delta^{AB}_{CD} \equiv \det \begin{bmatrix} \delta^A_C & \delta^A_D \\... | {
"language": "en",
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LIGO Gravitational wave discovery - how did they know the cause of spike? I understand how unbelievably lucky the discoverers were to catch the wave produced billions of years ago by an event that happens so rarely one hour into a test run of their equipment. But one thing is still not clear to me – how did they know w... | People ran computer simulations that told them what wave pattern would be observed for various cosmological events.
Each even has its own "fingerprint" than can be used to distinguish the various events.
As far as I know there were no additional astronomical observations that gave definite results on the origin of the... | {
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Conservation of momentum in refraction Light, when passing through a boundary refracts. How is momentum conserved here? There can't be an impulse, the energy doesn't change.
| In your question, you are assuming that you cannot have a change in momentum without a change in energy. Consider, however, what happens if a force is applied perpendicularly to the trajectory of an object: no work is done but the direction of the momentum is changed. An example of that is a planet in orbit of its star... | {
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If two particles are entangled and you collapse the wave function of one of the particles. Does the other particle collapse as well? Let's suppose you entangled two photons, you separate the photons, and then you measure the polarization of one the photons collapsing its wave function. The wave function of the other ph... | If you have two spins in an entangled state they define a wave function
$$
|\psi\rangle~=~\frac{1}{\sqrt{2}}\left(|+\rangle|-\rangle~+~e^{-i\phi}|-\rangle|+\rangle\right)
$$
in a singlet state of entanglement. What exists is the entangled state. In effect the individual spin states do not exist. A measurement of one sp... | {
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If free quarks can't exist, how did the universe form? As I understand, the Big Bang started with a photon gas that then created the other particles. Thus obviously there would be some free quarks in the early Universe unless quarks are always created in pairs for some reason. How does physics resolve this?
| "Free quarks can't exist" is simply an oversimplification of the actual situation in quantum chromodynamics (QCD). A better statement is "free quarks cannot exist at low energies", where "low energy" means below the deconfinement scale.
Confinement is precisely the phenomenon that says that the force between two quarks... | {
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Elasticity of solid A rod $1m$ long is $10cm^2$ in area for a portion of its length and $5cm^2$ in area for the remaining. The strain energy of this stepped bar is $40$% of that a bar $10cm^2$ in area and $1m$ long under the same maximum stress. What is the length of the portion $10cm^2$ in area.
My attempt:
$$strain-e... | The tension is same same all along the length of the composite bar, as it is in the uniform bar. So the stress will be higher where the cross-section is lower.
The question is saying that the stress in the narrow section of the composite bar is the same as in the uniform bar with which it is being compared.
| {
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"answer_id": 0
} |
Low power loss in electricity transmission lines To reduce the heat lost during transmission of electricity, we say we increase the voltage of transmission, taking the formula $I^2R$ in consideration. Couldn't I consider $V^2/R$? If I consider the second form, increasing voltage will increase the power dissipated. No?
| No, I believe you are misinterpreting something.
For same power to be transmitted in simple terms,
$$VI=constant$$
$V$ = voltage between source and sink.
So higher the votage drop, lesser would be the current.
The tricky part is that when we talk about current, it's passing through the transmission line and being a lo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/318230",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 3,
"answer_id": 1
} |
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