Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why don't the electric field vectors cancel each other out in a non-conducting infinite plane sheet? Why do these vectors not cancel each other out in spite of their being in the opposite directions?
| In order to superimpose two or more electric fields, they must be defined in the same region. In other words
$$\mathbf E=\mathbf E_1(x_0,y_0)+\mathbf E_2(x_0,y_0)$$
for some point in space $(x_0,y_0)$
In your case, $\mathbf E_1$ and $\mathbf E_2$ exist in different regions of space. Therefore, you can't superimpose the... | {
"language": "en",
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Different global phase shifts of Pauli-$z$ Matrix eigenstates from rotations around $z$-axis I understand the pauli matrix $\sigma_z = \bigl( \begin{smallmatrix}1 & 0\\ 0 & -1\end{smallmatrix}\bigr)$ rotates a state around $z$-axis by angle $\pi$ in $SO(3)$. We can see it works by thinking about rotating eigenstate of... | The factor you're talking about is a global phase shift, which has no physical meaning.
$$ \sigma_z|-\rangle =\left( \begin{matrix}1 & 0\\ 0 & -1\end{matrix}\right)\left( \begin{matrix} 0 \\ 1 \end{matrix}\right)= \left(\begin{matrix} 0 \\ -1 \end{matrix}\right) = (-1)\cdot|-\rangle $$
Recall that $-1=e^{i\pi}$ is a $\... | {
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Calculate $x+y$ probabilistically from qbits in state of $\frac{1}{\sqrt{2}}(|x\rangle + |y\rangle)$ Assuming we have $N$ qbits, it is placed in a composite state that correspond to integer $x$ and $y$: $\frac{1}{\sqrt{2}}(|x\rangle + |y\rangle)$. The actual integer $x$ and $y$ being unknown.
Is it possible to read out... | *
*It is not possible deterministically, since $|0\rangle+|1\rangle$ and $|0\rangle+2\rangle$ are not orthogonal and thus cannot be distinguished deterministically.
*It is also not possible probabilistically in an unambiguous way, since the Hilbert space is $n=2^N$-dimensional, but there are $2n-3$ possible outcomes.... | {
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Is every open circuit a capacitor? I think that even open-ended wires can let AC current flow through them, just with a low capacitance. I also think an antenna could be a capacitor and open ended. Am I thinking correctly?
| Every object in a circuit has resistance, capacitance, and inductance, but these quantities are often small enough that they can be treated as being zero. When these quantities are large enough that they need to be considered, they are often separated out in circuit diagrams as "separate" objects to make the analysis e... | {
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Why is absorbance calculated as $\log_{10}(1/R)$ and not $1-R$? According to Lambert Beers law, the absorbance ($A$) of a sample at a given wavelength can be described in terms of its transmittance ($T$) according to:
$A = \log_{10}(1/T)$
In near-infrared spectroscopy, when measuring how light is reflected off of opaqu... | These are two different kinds of looking at absorption.
I have a remote sensing background, and we usually look at it from a conservation of energy point of view, stating that the radiation that hits a surface is partly reflected, partly transmitted, and partly absorbed, and that $R+T+A=1$.
These are unitless fractions... | {
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How is the 1D transient heat conduction equation derived? From my book:
$$\frac{\partial T}{\partial t}=\alpha\frac{\partial^2 T}{\partial^2 t}$$
with an initial condition and boundary conditions
$$T(x,0)=T_0$$
$$T(L,t)=T_0$$
$$-k\left.\frac{\partial T}{\partial x}\right|_{x=0}=2A\cos^2\left(\frac{\omega t}{2}\right... | What they have done is focus exclusively on the long-time solution when the system has reached "oscillatory steady state." This solution does not feature any exponentially decaying terms in time.
So their solution for the temperature is taken to be of the form: $$T(x,t)-T_0=\alpha(x)\cos(\omega t-\phi)+\beta(x)\sin... | {
"language": "en",
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Why does a car's steering wheel get lighter with increasing speed I've noticed it is difficult to turn the wheels of a car when the car is stationary, especially cars without power steering, which is why the power steering was invented. However, I've noticed it becomes feather light when traveling at speed (some model... | Even though a car is not a wing, most cars generate some lift as they travel through the air as well as a force moment which tends to torque the car down at the rear wheels and up at the front. In addition, the torque that the engine is applying to the driven wheels results in a countertorque on the body of the car tha... | {
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Conceptual question regarding velocity in projectile motion vs. up a ramp I have a question regarding conservation of energy in regards to two different scenarios:
In the first case I was told that a ball with an initial velocity, V, was launched at an angle, $\theta$ and to solve for the max height in terms of $h$.
S... | Your question wasn't clear, for Q1, there's a "common sense" of where to launch for the highest point, especially when they were teaching energy conservation. For Q2, I think you were suppose to use standard Newtonian and simply integrate it out.
| {
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What's "bimodal" about BEC velocity distributions? I was just reviewing some papers discussing Bose-einstein condensation, specifically "Creation of a Bose-condensed gas of 87Rb by laser cooling" by Hu et al., and I saw repeated references to the emergence of a "bimodal" velocity distribution being a hallmark of the BE... | I am afraid 'bimodal' originates from the fits used to characterise a BEC, like the ones below (from my experiment):
The Bose-condensed atoms and the thermal fraction have different spatial distribution functions, and by fitting both functions at the same time you can compute the numbers of both.
| {
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Why are degenerate states more likely to be filled at a given temperature? Consider if we have a simple two-level toy model, where the ground state has energy $E_0 = 0$ and the excited state has energy $E_1 = \epsilon$ and degeneracy $g$. The partition function for this system is
$$Z = 1 + g e^{-\beta \epsilon}$$
where... | An 'excited state with degeneracy $g$' is actually a set of $g$ different states with the same energy level.
The more excited states there are which a particle can transition to, the more likely the particle is to make a transition to one of the excited states.
| {
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Why are the two outer charge densities on a system of parallel charged plates identical? One of the ways examiners torture students is by asking them to calculate charge distributions and potentials for systems of charged parallel plates like this:
the ellipsis is meant to indicate any number of additional plates coul... | Count the surfaces from left to right: S1,S2,S3...,Sn. Each surface generates a symmetric field (left and right). Hence total field left of S1 (E0) is equal to total field right of Sn. Field between S1 and S2 is zero (within the first plate). Field within the rightmost plate is also zero. So Qext is determined solely ... | {
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Can we define gravity on Calabi-Yau manifolds? I have read about applying Hermitian geometry in general relativity in deriving holomorphic gravity. But if we take it some steps further i.e. allowing Kähler manifolds with the Ricci flatness condition, can we consider general relativistic gravitational force on Calabi-Ya... | The physical point of Calabi-Yau manifolds being Ricci flat is that a string wrapped on it will not spread. The Hamilton equation for Ricci flows
$$
\frac{dg_{ij}}{dt}~+~2R_{ij}~=~0.
$$
If there is a nonzero Ricci curvature then the manifold will change its geometry with time. This will mean that a string wrapped on th... | {
"language": "en",
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Is there a contradiction between isotropy and the Big Bang? Disclaimer: I'm not asking whether the Big Bang happened at a point. I'm asking whether the fact that the universe is isotropic and that the Big Bang happened contradict each other.
To be honest I am just starting to learn General Relativity and cosmology but ... | Your intuition is faulty because you are imagining universe’s expansion as similar to the expansion of gases from a bomb blast. Something like the “front of the universe” is expanding and occupying some sort of imaginary space, moving away from a central point. A wrong intuition that may come from the name “Big Bang”.
... | {
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Does charge affect space-time? Okay suppose there is an hypothetical particle called Nelectron which has mass = mass of electron but is electrically neutral. It has same spin and other quantum mechanical properties.
Even the same size (I know we don't know electron's size but bear with me)
Would they bend space-time by... | Charge does have an effect on space-time. For example a spherically symmetric charged spacetime metric would be described by Reissner-Nordströrm metric.
The existence of charge unlike mass does not contribute to any intrinsic energy.
Can charge exist without mass ? We know masses without charges
Theoretically, an e... | {
"language": "en",
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Does Graviton bend light? In the weak gravitational regime where the low-energy effective action holds,(linearized) gravity can be quantized, and we can treat graviton as quantum fields on a Minkowski background. One can also couple it to other fields (e.g. Maxwell) to obtain interactions terms.
The classical counterpa... | We know that gravity bends space time and light, and the particles for gravity, which carry it are gravitons, hence we can say that gravitons can bend light, however these particles remain hypothetical and we do not know if they exist or not.
| {
"language": "en",
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How is energy conserved in this case? Consider a permanent magnet introducing a magnetic field at some fixed angle to a loop of wire on a spindle. If a fixed current is allowed to run through the wire, the lorentz force introduces a net torque on the system and causes it to rotate. This will increase the KE of the loop... | In addition to the answer provided by @probably_someone, remember that there is energy associated with constructing the initial state of your thought experiment. One must bring the magnet and loop together from far away, and in doing so must hold the loop in its non-equilibrium position until the experiment begins. The... | {
"language": "en",
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Principle of friction force When two equal and opposite forces act on a body at rest or in motion we say it is rest or in its state of motion. But when a body kept on a table starts moving uniformly due to a force applied, it overcomes force of friction.Does it really overcome the force of friction or is just equal to ... | It overcomes the force of static friction. Which is why it starts moving.
Soon after that, it is set equal to the kinetic friction. Which is why is isn't accelerating. Remember that motion doesn't require force. Only changes in motion do. An object "moving uniformly due to a force applied" has a net force of zero.
| {
"language": "en",
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What is the *DETECTOR* in the double slit experiment and how does it work? Is the detector a passive device or is it just a fictional mathematical probe.
I think the detector is somehow consuming the energy responsible for the wave nature of the photons, electrons or atoms, but I can't find any information about the de... | It's anything that gives you information about where the particle passed by. The problem in measurement in QM is that to measure anything you need to interact with the "thing" you want to measure. If you want to measure temperature in a drop of water with a large thermometer, the heat of the thermometer will affect the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468142",
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Inversion Formula in Conformal Field Theory I was working on my thesis on Conformal Bootstraps. For that, I now have to use the inversion formula to get anomalous dimensions in the $\phi^3$ theory.
Can anyone suggest any good reference(s) to learn how to use Inversion Formula in CFT?
| Probably you are already familiar with the reviews of conformal bootstrap, but this is the standard list
*
*David Simmons Duffin's TASI lectures 1602.07982
*Slava Rychkov's EPFL lectures 1601.05000
*Recent numerical bootstrap review 1805.04405
These links don't discuss the inversion formula (except sec IX of 3. ve... | {
"language": "en",
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If you were to push a block in space in an ideal vacuum scenario with zero friction, what would be the final velocity of that object Say you push an object with 10 N force(just once and let it go) of mass 10kg object in space with zero friction and nothing in the way of its path. What would be the velocity of that obje... | Yes, the time will matter.
To calculate the final velocity of an object v ,with an inital velocity u,which is under a constant acceleration of a
for a time t. We have the relation $$v=u+at$$
The object would continue to move forever with a constant velocity(v) due to Newton's first law , which states that an object con... | {
"language": "en",
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Self-interaction in spin-orbit coupling? In spin orbit coupling, in an atom motion of electrons about nucleus generates magnetic field and we consider this field to interact with magnetic moment of electron. It sound strange as in electrostatics a field is generate by a charge particle but this field does not interact ... | A good picture is to jump on board the electron and ask yourself what is going on in the reference frame in which it is momentarily at rest. In that frame there is a magnetic field whose source is the nucleus of the atom. It can be calculated conveniently by a Lorentz transform from the rest frame of the nucleus. Anywa... | {
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Difference between voltage, electrical potential and potential difference I am having hard time to visualize these two concepts in my mind seriously.
First of this confusion came from two parallel plates that was connected to a power supply, charged then disconnected from power supply and then separated from each othe... | I'll give a simple explanation.
Potential difference is the difference of potential between 2 points (say A and B).
Potential of any point would be the potential difference between that point and another point C, the specialty of C is that its potential is assumed to be 0.Usually we keep C at infinity.
In your question... | {
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Domain of a Hamiltonian In a recent paper (on an exactly solvable toy model and its dynamics), we studied such a toy model:
$$ H = \sum_{n\in \mathbb{Z}} n |n \rangle \langle n | + g \sum_{n_1,n_2 \in \mathbb{Z}} |n_1 \rangle \langle n_2 | . $$
We solved the eigenvalues and eigenstates analytically and in particular, ... | The operator is unbounded. Unbounded densely defined (Hermitian) symmetric operators cannot be extended to the entire Hilbert space (see the comment by DisintegratingByParts ).
The operator in the paper is not properly defined since it does not specify a domain. They do construct vectors which are formally eigenvecto... | {
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Does an electric field penetrate through glass? I was just wondering something ridiculously simple; does an electric field penetrate through glass? Say I have a proton or charged cotton pulp ball inside a Pyrex glass container and apply an electric field on the outside, through the whole thing, do the particles 'feel' ... | The simple answer is "yes": if the container is glass or any other dielectric medium, an electric field goes right through it. You can test this: put some pith balls (little bits of styrofoam will do) inside the glass container, rub a balloon on a wool coat or on the carpet, and bring the balloon close to the glass co... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/469224",
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What objective function is Lagrange's equation of the first kind based on? In Lagrangian mechanics, Lagrange's equation of the first kind states that
$$ \frac{\partial L}{\partial r_k} - \frac{d}{dt}\frac{\partial L}{\partial \dot{r_k}} + \sum_{i=1}^C \lambda_i \frac{\partial f_i}{\partial r_k} = 0. \tag{1}$$
Here the ... | *
*If the constraints $(f_1,\ldots, f_C)$ are holonomic, then OP's Lagrange equations of first kind (1) follows from an extended action principle
$$ S[r,\lambda]~=~~\int \! dt (L + \sum_{i=1}^C\lambda^i f_i). $$
*In case of semi-holonomic constraints or dissipative forces, the situation is more complicated, cf. e.g. ... | {
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Finding the eigenstates of an operator I am currently taking a course in QM and can't see how the eigenstates have been found for examples like this one:
Question
Let $\phi _1$ and $\phi _2$ be two normalised wavefunctions orthogonal onto each other. Let the action of the operator $\hat{A}$ on these states be:
$$\hat{... | Assume $\phi_{1,2}$ form a basis. Consider the eigenvalue equation for $\hat{A}$, i.e. $\hat{A}\psi=\lambda\psi$. If we apply $\hat{A}$ again we get the equation $\hat{A}^2\psi=\lambda^2\psi$. But note from the definition of $\hat{A}$, i.e. its action on the basis, that $\hat{A}^2 =\text{Id}$. Thus the previous equatio... | {
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Perpetual Rotation of Rigid Body Assuming no external torque or forces acting can a rigid body be set in perpetual rotation motion about an axis which is not its principal axis?
If no then does the earth continuously change its axis of rotation? as the principal axes of the earth changes changes continuously because o... | The answer to your first question is no, any rotation about a non-principal axis will result in the axis of rotation changing. To see why, lets go into the body frame of the object, where with no torques the angular momentum follows the equation
$$\mathbf{\dot{L}}+\boldsymbol{ \omega} \times \mathbf{L=0}$$
Where $\math... | {
"language": "en",
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Rotational KE vs Translational KE Q. Horizontal electric field E = mg/q exists as shown in the figure and a mass m is attached at the end of a light rod. if mass m is released from the position as shown in the figure. find the angular velocity at the bottom-most position
This is what my teacher did,But I don't see how ... | The ball has no translational kinetic energy. It has only rotational KE about the pivot. ($1/2I\omega^2$) . The work done by Electric field and gravity cause change in rot. KE. The rod has no rotational KE as it is assumed to be massless
| {
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What are equations of state in thermodynamics? So I am having real trouble understanding what equations of state are and how we form them. My issue stems from reading multiple sources. So I understand that an equation of state is used to build a relationship between variables to describe a state of a system.
For exampl... | I think you might be confusing two different concepts.
*
*Thermodynamic potentials (Helmholtz, Gibbs, enthalpy etc.) describe the available energy of a system subject to certain external factors. A system maintained at constant temperature by a heat bath can be described by the Helmholtz potential ($A=E-TS$).
If in a... | {
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How can I calculate the speed at which a gas flows from one volume to another? Suppose that there are two rigid Volumes A and B. Each of these contains a gas with know properties (pressure, temperature, number of moles, volume, composition). Suppose also that there is a pipe with a valve that connects the two Volumes.
... | The ideal gas law is
$\mathbf{S}T = n\mathbf{R}T = dPV + PdV$
and you want to know, the flow rate of one volume to another? The rate of change of a volume is found from a derivative
$\mathbf{S}\dot{T} = n\mathbf{R}\dot{T} = \dot{P}V + P\dot{V}$
But I feel like you need more information, like heat flow, perhaps a geomet... | {
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What is an example of LOCC measurement which is not separable? Could you give me an example of a measurement which is LOCC (Local Operations Classical Communication) but not separable? Or better, one which is separable but not LOCC?
Given an ensable of states $\rho^{N}$, a separable measurement on it is a POVM $\lbrac... | There isn't: Any LOCC measurement is also a separable measurement. This is easy to see: Alice's first measurement has POVM elements $A_{i_1}\otimes I$. Alice then communicates her outcome $i_1$ to Bob. Bob's subsequent measurement has elements $I\otimes A^{i_1}_{i_2}$, where $i_2$ enumerates Bob's outcomes, and $A^{i... | {
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How does cosmological principle imply an expanding space? My understanding of cosmological principle is this:
Space looks same in all directions and is homogeneous. But this principle was under heading of Observational Evidence for expansion of space in this article:
https://en.wikipedia.org/wiki/Expansion_of_the_uni... | The Cosmological Principle doesn't actually imply that the universe is expanding, instead, what this principle implies that the spatial part of the space-time manifold is maximally symmetric. What this actually means that the spatial manifold has a constant curvature everywhere given by Ricci Scalar, $R=-6\kappa$ usin... | {
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Can we know when rolling occurs without slipping? In school we solve a lot of physics problems involving rolling cylinders/hoops/wheels. Often it is specified in the question statement that "rolling can be assumed to occur without slipping". Then we know we can use the relationship between translational acceleration an... | No slipping is when the velocity of rolling object at the point of contact with surface is same as velocity of surface. For ground, the velocity of surface is zero, so we say the velocity of lowermost point of wheel is zero. The same is applicable to rolling on a moving surface, for a belt moving around a wheel, or two... | {
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"url": "https://physics.stackexchange.com/questions/470572",
"timestamp": "2023-03-29T00:00:00",
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Why doesn't Newton's third law mean a person bounces back to where they started when they hit the ground? When we drop a ball, it bounces back to the spot where we dropped it, due to the reaction forces exerted on it by the ground. However, if a person falls down (say, if we push them), why don't they come back to thei... | It's true that on the impact the human body experiences a force upwards equal to the force the body exerts downwards on the Earth: $\vec{F}=\frac{\Delta\vec{p}}{\Delta t}$.
Now $\Delta\vec{p}$ doesn't send the body's momentum in the opposite direction, but instead, the momentum change is used to deform the body (breaki... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470714",
"timestamp": "2023-03-29T00:00:00",
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If atmospheric pressure is 76 cm of $\text{Hg}$ , why won't 76 cm of mercury stay in an open tube when suspended in air? If we keep an hold a tube in air with the closed end up and open end downwards, containing mercury upto a length of 76 cm, why does the mercury not stay in place? Shouldn't atmospheric pressure exert... | If the mercury would stay in an inverted tube depends on the surface tension which is a function of how well mercury wets the tube, the diameter of the tubs, the height of the mercury column, and the density of mercury.
Fill a glass coke bottle with water. Turn it upside down. The water doesn't pour out nicely but glu... | {
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"timestamp": "2023-03-29T00:00:00",
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LSZ reduction derivation Srednicki In the derivation of the LSZ reduction formula equation (5.21) Srednicki claims that in case of an interaction term in the Lagrangian density $a^{\dagger}(\textbf{k})$ will no longer be time dependent. Now does that mean that the only modification to the formula of $\varphi(x)$ will b... | That expression is time independent. Try taking the time derivative, being sure to use the equation of motion for $\varphi(x)$, also notice that the plane wave $e^{ik\cdot x}$ satisfies the same equation of motion.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470971",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do we have to wait half a year to measure stellar parallax To measure distance of astronomical objects, often we may use parallax, the angle it makes with the earth-sun and trigonometry to determine the distance.
The thing I don't get is why do we need to sweep out at least half a circle and then look at the angu... | Astronomical distances are large. So, a 'one parsec' distant object has
one second of parallax for a full Earth-orbit displacement. That's the
equivalent of 5 parts per million of a radian, about the same angle
as a dime seen face-on at a distance of a mile.
It isn't easy to accurately measure those small angles,
s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/471076",
"timestamp": "2023-03-29T00:00:00",
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Geometrical Optics: Infinite Rays Normally in ray optics, we draw a parallel line from the top of the image to the lens and stop when this line intersects an angled line (drawn from the height of the real object) and intersects. However, why do we stop? We can draw infinite rays from this object and they should be able... | (I wanted to put this as a comment, but I don't have enough reputation)
The different rays have to intersect at a point for an image to be formed there, as you said. What happens is that when you look at the rays, they seem to be coming from that point where they intersect, which is the location of the image.
If you pu... | {
"language": "en",
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Why is normal force at the bottom dependent on normal force on top?
Why does the normal force on bottom of the track have anything to do with the normal force on top of the track? Why isn't the normal force at the bottom simply $mg$?
| Normal force is a special force. According to the situation, it can be greater or lesser than $mg$. More precisely, if an object $A$ has mass $m$, and it's exerting $F$ force on the surface normal on it, then $F$ is also the normal force experienced by the object (Newton's III Law)
So, if the object is freely falling i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/471561",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Pair creation and annihilation and Wheeler's one electron universe I stumbled upon Wheeler's idea that there could be only one electron. If I understood correctly, basically the idea is that one electron moves forward and backward in time such that it appears as if there are many electrons and positrons. Of course ther... |
I wondered whether it is possible to interpret
a pair creation of electron and positron followed by pair annihilation
as one electron moving in a timeloop continuously absorbing and emitting photons.
This phenomenon actually exists and is called vacuum polarization.
You can imagine it as one electron moving in a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/472028",
"timestamp": "2023-03-29T00:00:00",
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How to make an object stay under water? How to make an object submerged under water? Neutrally buoyant?
| You can calculate the amount of water to put in the submarine.
The buoyant force on the submarine will be
$$ F_b = V \rho _w g $$
Where V is the volume of submarine submerged in the water and $\rho _w$ is the density of water.
This buoyant force must balance all the weight of the submarine ( ie weight of submarine plu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/472652",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Do we need dark matter and dark energy, if the behaviour of the universe in its initial stages was similar to that of the Sun? According to CMBR the universe was a cloud of plasma and was a perfect black body, $380,\!000$ years after big bang.
But the Sun in our solar system also is in the state of plasma, thus making ... |
But the Sun in our solar system also is in the state of plasma and yet doesn't act like a blackbody
Wrong, the sun radiation is approximately fitted as a black body. The word "black body" does not describe the frequencies, but the assumption that it absorbs all radiation falling on it and re-emits it.
Here is the s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/472803",
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"source": "stackexchange",
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Role of AdS/CFT correspondence in the context of integrability I was wondering how the AdS/CFT correspondence fits in the context of integrability. As I understand, the AdS/CFT correspondence postulates a duality between gravity theories and CFT's. If one theory has a strong coupling, the other has weak coupling. AdS/C... | I would recommend the review
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99, 3 (2012), arXiv:1012.3982.
For example, here is an excerpt from p.10:
Methods of integrability provide us with reliable data over the complete range of couplings. We can investigate in practice a gauge... | {
"language": "en",
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Does putting an aperture in a laser beam make the smallest point it can be focused to larger or smaller? If you put an aperture in a laser beam to block some of it, I would imagine that the spot it can be focused to becomes larger due to diffraction. The numerical aperture of the system is limited by that truncation of... | If you had a perfect laser (which is impossible) all beams are parallel and with an aspheric lens the spot is very small, limited by Airy disk of lens. Adding any aperture increases diffraction at the aperture, thus spot size increases because the rays are no longer parallel, there is no perfect focus any more. The a... | {
"language": "en",
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"source": "stackexchange",
"question_score": "4",
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What causes the direction of lightning flashes? During a lightning strike, the flashes appear as cloud to ground or cloud to cloud. Why is this the only manner of propagation? Why do the flashes not go upwards from the clouds into the sky?
| The lightning has a visible direction of propagation, from top to down, that is normally the same as the electrons it is carrying: free electrons get accelerated (downward) by the electric field and ionize other molecules, thus progressively creating the lightning plasma pathway.
Another reason why lightnings start fro... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/473283",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is the magnitude of friction acting on the rear wheels greater than the magnitude of friction acting on the front wheels? When a car is accelerating on a horizontal road , friction acts in the forward direction on the rear wheel and in the backward direction on the front wheel .
But I am not able to understand why... |
Let's look a the case of rear wheel drive and designate all the forces acting during acceleration (air drag, ball bearings friction and other non-conservative forces are ignored)
In the $y$-direction where there's no acceleration we get:
$$N_F+N_B-mg=0\tag{1}$$
In the $x$-direction:
$$ma=F_B-F_F$$
This the Equation of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/473418",
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Why do pipe organ tubes need to have different thicknesses? In a pipe organ, there are many tubes—long and short, thick and narrow. Each tube presumably resonates at a specific frequency based on its length and produces a distinct note. Why do they have to be different thicknesses? I'm aware that amplitude determines t... |
Each tube presumably resonates at a specific frequency based on its
length and produces a distinct note. Why do they have to be different
thicknesses?
Because they have different timbres.
So you have one bank of pipes that are different notes in one timbre, and another bank that's the same notes in the different ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/473555",
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Why hasn't QCD fed back to nuclear engineering? A recent commenter on one of my questions noted that Fermi could take a tour of a modern nuclear powerplant and not be suprised by anything, and I believe that. I also think this shouldn't be the case, there have been many advances in high energy physics, with enormous le... | As pointed out by Jon Custer, everything that physicists needed to know in order to initiate a fission chain reaction was known long before QCD was invented, and the basic physics behind reactor design and operation haven't changed since then. Detailed knowledge of what's inside a proton isn't needed when you're extrac... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/473643",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is Lorentz and Galilean invariance mutually exclusive? I know that the classical mechanics stays valid under Galilean transformation. The same argument applies to relativistic equations and Lorentz transformation. My question is, can a set of equations dependent on both spatial coordinates and time be valid under both ... | If we consider an infinitesimal displacement in space, $(dx, dy, dz)$, and and infinitesimal displacement in time, $dt$, then in Galilean transformations the quantities:
$$ dx^2 + dy^2 + dz^2 \\
dt $$
are both invariants. In special relativity neither of these are invariants. Instead the invariant is the proper distanc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/473831",
"timestamp": "2023-03-29T00:00:00",
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If a satellite speeds up, does that make it move farther away or closer? If a satellite is in a stable circular orbit and goes about 41% faster (escape velocity) then it leaves its host forever. I get that. However, what if it speeds up by less than 41%?
Intuitively, it would seem to make the satellite move farther awa... | The parameters of stationary orbits depend on the energy and orbital momentum. For circular orbits, we have a simple relationship for orbital velocity and orbit radius $v^2 =\frac {GM}{r}$. It follows that Venus moves faster than Earth, and Mercury moves faster than Venus. However, for elliptical orbits, the speed does... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/473934",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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How to find drag of a cylinder? How can I find a drag on the cylinder placed in uniform water flow, if I know a velocity field around it?
| In the case of a potential flow, the resistance is zero (d'Alembert paradox). In the case of viscous flow, it is necessary to calculate the pressure distribution and the derivative of velocity along the normal. Calculate the integral
$$F_D=\int _S{\left( \mu \frac {\partial u_t}{\partial n}n_y-pn_x\right)\mathrm dS}$$
... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Scale factor at surface of last scattering Is there an exact theoretical scale factor associated with the CMB? More specifically, since the CMB is associated with a temperature of around 3000K (as I understand), is there an exact thermodynamic relationship that says what the scale factor must be for the Universe to hav... | In terms of temperature and scale factor then
$$T_0 = (1+z)^{-1} T_{rec},$$
where $T_{rec}$ is the recombination temperature and $T_0$ is the temperature of the CMB now. To put this interms of scale factor, we note that $a = (1+z)^{-1}$. So
$$ a_{rec} = \frac{T_0}{T_{rec}}$$
The universe is "matter-dominated" at the ep... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/474155",
"timestamp": "2023-03-29T00:00:00",
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Why there are 3 significant figures in 86400 but 5 in 86400 s ( because of Unit) My book states one rule for determining the number of significant figures as under:
All zeroes to the right of a non zero digit but to the left of an understood decimal point are not significant . Eg. 86400 has 3 significant figures.
But... | I have never encountered this usage and I would be skeptical about a source that used it. You are invited to name-and-shame your text.
Your first example is a little unusual, because $86\,400 = 24\times60\times60$ is exactly the number of seconds in a twenty-four hour day. So in many contexts you might find yourself... | {
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Resistors parallel to short circuit I have a trouble solving this problem.
(Actually, each resistor is not parallel with the bottom wire since the voltage across each of them is different with that of wire.)
In the manual, the bottom wire(which is red circled) is simply ignored and thus can be easily solved.
I don't un... | Listen brother....if its looked in one perspective the point made by you is the ignored wire... actually its not ignored if it is a perfect conductor then the whole resistance R would be equal to zero this is one of the point which strikes my mind after looking into this question....
Hope you have got your answer
| {
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Vector calculus notation, maybe? I just got a new book on turbomachinery that uses some notation I'm not familiar with.
$$ \nabla \lor \vec{W} = -2\vec{\Omega} $$
The del-(something)-vector format makes me think its vector calculus. From context (rotating equipment), maybe its vector calculus in a cylindrical coordinat... | There are several notations in use for
the curl of a vector field $\vec{W}$:
*
*$\vec{\nabla} \lor \vec{W}$
*$\vec{\nabla} \times \vec{W}$
*$\text{curl } \vec{W}$
And they all mean the same thing.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/475775",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Doing addition and subtraction with tensor diagrams? Tensor diagrams are a beautiful and useful tool for making calculations with tensors, up until you need to contract with the sum or difference of two tensors, at which point it seems to become awful. Is there an standard or elegant way to diagrammatically notate the ... | There is a way to notate the sum or difference of two tensors. You draw one diagram, and then you write a plus or a minus sign, and then you draw the second diagram. This is fairly standard, but definitely not elegant. As far as I know there is no elegant way to write the sum.
One trick that is sometimes elegant is to ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/475917",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Symplectic group $Sp(2N)$ in Srednicki's book There is a question in Mark Srednicki's Book (Problem 24.4, p.160) about $Sp(2N)$, but I am not sure I understand the significance (application?) of this group. In that chapter, he talks about $SO(N)$ and $SU(N)$, which are part of the Standard Model and from accepted answe... | It is true that symplectic geometry plays a pivotal role in the Hamiltonian formulation, but this aspect is not really explored in Srednicki's book in any depth. Non-abelian Lie groups are mostly discussed in the context of Yang-Mills gauge theory. Unitarity imposes conditions on the gauge group, cf. e.g. this & this P... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/476147",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What does matrices act on different spaces mean in QFT? I have a Dirac kinetic term in a Lagrangian.
$$ i\bar{\psi}\gamma^\mu D_\mu\psi
= i\bar{\psi}\gamma^\mu\partial_\mu\psi
+ g\bar{\psi}\gamma^\mu\psi A^a_\mu T^a,$$
However, I usually heard that people say that:
$\gamma_{\mu}$ and $T^a$
are both matrices, but ... | A simple example of how operators act in different spaces and then commute is a quantum mechanical two-particle system, A and B. A (non-entangled) state will be the following:
$$\left | \psi \right > = \left | A \right > \times \left | B \right >$$
A operator $O_1$ acting on the first particle is actually $O^A_1 \times... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/476458",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is thermodynamics only applicable to systems in equilibrium? So I was going through callen's thermodynamics book and their he says that thermodynamics is only applicable to systems which are in equilibrium and that naturally raised a few questions in my mind
Is thermodynamics really never applicable to systems which ar... | It entirely depends on what you think "thermodynamics" is.
The traditional idea of thermodynamics dealing with systems whose macrostate can be fully described by e.g. temperature, pressure and volume indeed only applies to systems in equilibrium. Of course, as an approximation it also applies to systems "not far" from ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/476554",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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The Electromagetic Tensor and Minkowski Metric Sign Convention I am trying to figure out how to switch between Minkowski metric tensor sign conventions of (+, -, -, -) to (-, +, +, +) for the electromagnetic tensor $F^{\alpha \beta}$.
For the convention of (+, -, -, -) I know the contravariant and covarient forms of t... | I use this way:
\begin{equation}\tag{1}
F_{ab} = \partial_a \, A_b - \partial_b \, A_a,
\end{equation}
where
\begin{equation}\tag{2}
A^a = (\phi, \, A_x, \, A_y, \, A_z), \qquad\qquad A_a = (\phi, - A_x, - A_y, - A_z).
\end{equation}
Then, we have:
\begin{align}
E_i &= \Big( -\, \vec{\nabla} \, \phi - \frac{\partial \... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/476673",
"timestamp": "2023-03-29T00:00:00",
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What is the radiation density in a spherical oven? Does this pertain to the universe? Imagine a spherical oven with radius R. The inside of the spherical wall is at temperature T (everywhere) and is assumed emit perfect black body radiation (everywhere).
(1) What is the energy density in the interior of the oven?
(2)... | The answer to (1) is that the energy density is $4\sigma T^4/c$, where $\sigma$ is the Stefan-Boltzmann constant, $T$ is the absolute temperature, and $c$ is the speed of light. A derivation can be found here. Note that the oven radius $R$ is irrelevant as far as the energy density is concerned.
The Stefan-Boltzmann co... | {
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Renormalisation group flow of the $\phi^4$ theory I am reading Peskin & Schroeder about the renormalisation group flow of the $\phi^4$ theory:
$${\cal L} = \frac{1}{2}(\partial_\mu\phi)^2 +\frac{1}{2}m^2\phi^2 + \frac{\lambda}{4!}\phi^4 $$
P & S writes on the topic (p. 403-404):
"In general, the criterion that the sc... | Peskin is making a much simpler point than you think. Imagine, for example,
$$\mathcal{L} = \frac12 (\partial_\mu \phi)^2 + 10^{-10} \Lambda^2 \phi^2 + 10^{-2} \frac{\phi^6}{\Lambda^2}.$$
The RG flow from this Lagrangian gets closer to the fixed point as the irrelevant term decays, then gets further away from the fixed... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/477162",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Wigner-Eckart theorem and vectors Let's consider a system in state $^3$D$_1$:
$$\vec{L}^2=L(L+1)=6 $$
$$\vec{S}^2=S(S+1)=2$$
$$\vec{J}^2=J(J+1)=2$$
According to Wigner-Eckart theorem, if this is an irreducible representation, all vectors are proportional, so for example $\vec{S}=a\vec{J}$.
$$\vec{S}\cdot\vec{J}=a\vec{J... | You are misinterpreting W-E theorem. Let me review it for your
example. You are given two irreps, the one for $\vec S$, of dimension 3, and the one for $\vec L$, of dimension 5. Then you build up their direct product, which is of dimension 15 and reducible. Reduction is effected via $\vec J$ and gives three irreps, of ... | {
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Does a particle exert force on itself? We all have elaborative discussion in physics about classical mechanics as well as interaction of particles through forces and certain laws which all particles obey.
I want to ask,Does a particle exert a force on itself?
EDIT
Thanks for the respectful answers and comments.I edited... | Well a point particle is just an idealization that has spherical symmetry, and we can imagine that in reality we have some finite volume associated with the "point", in which the total charge is distributed. The argument, at least in electromagnetism, is that the spherical symmetry of the charge together with its own s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/478060",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can’t you see at the start of the Big Bang? I’m quite confused with regards to photon emission throughout the creation of the universe.
From what I’ve heard, there was no light (of any frequency) in the universe until 300,000 years after the Big Bang. This because then the universe cooled down enough to allow for a... | You heard wrong. There were photons, electrons, protons, and neutrons before 300,000 years. And before 3 minutes! (And before there were protons and neutrons, there were quarks.)
Before 300,000 years, the photons could not propagate freely; they were being constantly scattered by the charged plasma of protons and elect... | {
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"timestamp": "2023-03-29T00:00:00",
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Does the hypothesis in an experiement need to mention the independent and dependent variables? My current understanding of a hypothesis is just that it is 'an educated guess to explain a phenomenon'. Which follows that in an experiment, any guessing statement can be correct as long as it can be proved by said experimen... | Yes, relationships between measured quantities should be made explicit in any physics model. I think most physicists would think of independent vs. dependent in terms of controlled (varied) vs. response, at least for simple experiments. For example, a common physics experiment in an introductory course will measure the... | {
"language": "en",
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Examples of non-sine waves? What would be a non-sine wave? AFAIK, all sound is a sine wave, equally to waves on the sea. What would be a common example of something in nature that's a wave but not a sine wave? Or, would we have to look at man made regularities like bus timetables or stock prices to find non-sine waves?... | Waves can take all sorts of funny shapes. This is especially true if the differential equation generating them is nonlinear. This makes fluid mechanics a wonderful source of complicated waves. My personal favourite example is the solutions $\phi(x,\,t)=-\frac{c}{2}\operatorname{sech}^2\left[\frac{\sqrt{c}}{2}(x-ct-a)\r... | {
"language": "en",
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Adiabatic Approximation, Solving the Schrödinger equation In the adiabatic approximation one looks at the Hamiltonian
$$ H_0 = \sum_{i = 1}^{N_e} \frac{\vec{p}_i^2}{2m_e} + \sum_{i < j} \frac{e^2}{|\vec{r}_i - \vec{r}_j|} + \sum_{k < l} \frac{Z_k Z_l e^2}{|\vec{R}_k - \vec{R}_l|} + \sum_{i, k} \frac{- Z_k e^2}{|\vec... | Perhaps the answer may lie in properties of Hermitian operators. (The Hamiltonian is Hermitian). For example, the solutions (eigenfunctions) of a Hermitian operator form a complete orthogonal set. Another property of Hermitian matrices is that an $nxn$ Hermitian operator (matrix) has $n$ eigenvalues. So perhaps that an... | {
"language": "en",
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Sintering of Yttrium barium copper oxide I will do an experiment on superconductors, specifically $\text{YBa}_2\text{Cu}_3\text{O}_7$, and I am curios about some steps in the preparation. The starting materials are $\text{Y}_2\text{O}_3$, $\text{BaCO}_3$ and $\text{CuO}$.
First, all three starting materials will be cr... | For the first question: Crushing the precursors in a mortar does not create YBCO. It only creates tiny particles of each precursor. Heating to high temperatures allows the tiny particles to chemically react into YBCO. Tiny particles are much more reactive that large chunks as the surface to volume ratio is much higher.... | {
"language": "en",
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Momentum matrix elements in a crystal I am trying to follow along a derivation (E. I. Blount, Solid State Phys. 13, 305 (1962)) in which he derives the matrix elements of the true momentum $p_{n,n'}(k,k')$ (not the crystal momentum). He arrives at the following expression:
$p_{n,n'}(k,k') = \delta(k-k')(\hbar k\delta_{... | I will use atomic units throughout. The Bloch states are formed by the product of a plane wave times a periodic part $|u_{n\mathbf{k}}\rangle$,
\begin{equation}
\langle \mathbf{r} |\psi_{n\mathbf{k}} \rangle = \frac{1}{\sqrt{V}} e^{i \mathbf{k}\cdot \mathbf{r}} \langle \mathbf{r} | u_{n\mathbf{k}} \rangle
\end{equation... | {
"language": "en",
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Why is it that magnetic fields(or any field)not move in space? When I imagine a magnetic field produced by a magnet, or the electric field produced by a charge, I've learned that the fields are stationary, however, their value(across space) changes.
If I placed the magnet at a point $P$($0,0,0$), and then moved the m... | Fields permeate infinite space and always have a value at each point. The only sense in which they can move is that those values can change with time. For example, a field can become strong in a place where it was previously weak. So you could talk about, say, the maximum of the field moving, but the field itself isn’t... | {
"language": "en",
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Calculating acceleration of end point of rod Suppose I have a rod hinged at its end, of length $\ell$ free to rotate about an horizontal axis; initially in the horizontal position and I have to calculate the acceleration of its other end point. I know the derivation using torque but what if I consider the free body dia... |
Two forces, gravity and tension act on it but since tension can only act in the horizontal direction only gravitational force acts in the vertical direction and hence its acceleration is g
You are missing a major force called the hinge reaction . I've drawn it
*
*you can yourself check that your fbd must be wrong b... | {
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Can energy increase during neuron dynamics? Consider a system of Ising spins, with Hamiltonian:
$$H(\mathbf{S})=-\sum_{i, j} J_{i j} S_{i} S_{j} \qquad (1)$$
where $J_{ij}$ are symmetric real couplings ($J_{ij}=J_{ji}$) and $S_i=\pm1$.
Consider a time dynamics with the following parallel update rule:
$$S_{i}(t+1)=\oper... | The bias term $\theta_i$ should be represented in the Hamiltonian: $$H(S)=-\frac{1}{2}\sum_{i,j}J_{ij}S_iS_j + \sum_i \theta_i S_i$$
(The half factor is standard in the neural network literature, not sure if it is needed here). This is the form used for Hopfield networks.
If one neuron flips as $S_i'=\text{sgn}\left(\s... | {
"language": "en",
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Why is the orbit of the Earth around the Sun very intricate? The movement of the earth around the sun is very Goldilocky. Did it happen over the years as the orbit of earth averaged out into how it is now? Is there any chance of it (orbit) changing by itself in the future without the interference of external factors?
... | First, the sun has a large amount of protons on the plasma, so it has a positive charge.Next, the ionosphere of the earth is positive and the surface is negative.The charge of the sun and the earth has been confirmed in mainstream science.
As the Earth approaches the perihelion, the effect of the solar wind increases t... | {
"language": "en",
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Why aren't satellites disintegrated even though they orbit earth within earth's Roche Limits? I was wondering about the Roche limit and its effects on satellites.
Why aren't artificial satellites ripped apart by gravitational tidal forces of the earth?
I think it's due to the satellites being stronger than rocks?
Is th... | The Roche limit applies only to bodies which are held together purely by internal gravitational attraction. Compact objects such as artificial satellites are held together by the much stronger inter-molecular electromagnetic forces (this is another demonstration of just how weak gravity is compared to electromagnetism)... | {
"language": "en",
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Convergence Property of Path-Integral Let the action be $$S= \int \bigg\{ \frac{1}{2} \big(\frac{dX}{dt}\big)^2 - V(X) \bigg\} d\tau$$
and the corresponding Path-Integral
$$Z= \int DX(t) e^{iS}.$$
Since the convergence is not clear we Euclideanize the time coordinate $t$ by the Wick rotation
$$ t \rightarrow -i \tau$$
... | In a nutshell, the Euclidean Boltzmann factor is exponentially suppressed because the Euclidean action is bounded from below (assuming the potential $V$ is bounded from below), while the Minkowskian Boltzmann factor has modulus 1 and is oscillatory.
| {
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Siphon/Pump Hybrid For Getting Water From a River Forgive me if this answer is already up on here, but I couldn't find anything particular to what I am trying to do. I need to lift water approximately 50 feet vertically and 200 feet horizontally from a river to the top of our property. I plan to have one hose for water... | Water cannot be 'sucked' higher than atmospheric pressure would push into
a vacuum; depending on
your altitude, that's maybe 30 feet. So, regardless of 'priming', it won't
suffice to use a high-located pump.
One easy solution is to dig a pit (sump) next to the water stream, and install a well pump there (where it ... | {
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Does the ideal gas law apply to a moving vehicle? If for example you have a car travelling along a road. There is obviously a high pressure region in front of the car, where the air is forced around the vehicle. Likewise, I understand that cars will leave a region of low pressure air directly behind them.
Air is descri... | You can model a gas as incompressible. But, that does not mean that it is incompressible.
The difference between compressible and incompressible arises in how you treat a kinetic energy term in the Bernoulli equation. With incompressible fluids, the term can be determined directly because conservation of mass flow also... | {
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Why does the potential difference across a type of parallel circuit not act like a potential divider?
Image credit (Q3)
In this attached circuit, when $R_1=0\Omega$, I am failing to understand how the two cells affect the potential difference across the central resistor R3. I understand that potential difference is co... | So this is how I've solved it generally, where the resistance for R1 is equal to k volts:
P.D. across R3 from V1: Equal to the P.D. across the parallel resistors of R3 and R2, as P.D. is identical across parallel components. Resistance of R3 and R2 branch equal to $\frac{1}{\frac{1}{30} + \frac{1}{10}}$, or 7.5. Theref... | {
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Why is there no current between two capacitors connected in series? I want to ask a question about the figure below.
Why the current does not flow from $-Q$ term to $+Q$ term or from a to b since there is a voltage?
| Short answer: Potential is defined depending on the choice of a origin (e.g. ground). The positive plate of a capacitor has potential $Q/C$ greater than negative plate of the same capacitor. We do not know its potential compared to anything else, unless we know how they are connected in a circuit. Here the points a and... | {
"language": "en",
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Are quasi-particles really particles? In my understanding, quasi-particles were just some real world particle (like electrons) but in different environment i.e. an electron in a crystal.
But
Recently, I have started studying Spintronics/Magnetism and I see words like "quasi-particle", "excitations" and "elementary exci... | They have kinetic energy and momentum, some have rest energy. They only live in a medium but some would argue that space-time itself is a medium. Let me reverse the question: why not ?
| {
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Why do my books introduce the equation $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$ without showing partial derivatives of $\mathbf{E}$ exist? In electromagnetism (electrostatics), we often come across the equation $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$.
In order for this equation to be meaningful, $\ma... | The equation is a condition that an electric field $\mathbf{E}$ must meet to be a "valid" field for the situation in question, which is specified (at least in part, though this is tagged "electrostatics") by the charge distribution, $\rho$.
The fact that a differential equation must be satisfied logically implies that ... | {
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Apart from the sine wave, are there any other waveshapes that could be thought of as commonly appearing "in nature"? I'm familiar with the sine wave being something that can be used to model many types of oscillation in nature (and the way that multiple sine waves can be seen as sum to produce complex repeating wavesha... | stick-slip friction cycling gives rise to a sawtooth waveform, which is nonsinusoidal- although it can be built up out of a series of sine waves by superposition.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Radio Waves / Light: Atmospheric Refraction The following image differentiates between a visual horizon and a radar horizon.
Sidenote: I'm not too familiar with primary surveillance radar
technology, but this image refers to secondary surveillance radar,
where the aircraft emits a radio signal at 1090MHz. So this... | The refractive index of air is frequency dependent, so just as different colours of light are deflected by different amounts in a prism, radio waves and light waves can be deflected by different amounts by the air.
| {
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Diameter to prevent water flow into a closed-end tube? Imagine I drill three holes of different diameter into a large block of plastic but the holes don't go all the way through. (They form three close-ended tubes, see the image.) I then submerge the block into a bucket and fill it with water. I want to know which hole... | Water will flow down into that tube which supports something called two-phase flow, in which the water can enter the tube at the same time the air already there is leaving the tube.
Two-phase flow can occur when the surface tension of the liquid is low and the diameter of the tube is large. In this case, the fluid and... | {
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Energy inside cyclobutadiene, a 2D infinite well I have a question about a question in the book Introduction à la théorie quantique by Michèle Desouter, Yves Justum and Xavier Chapuisat (ISBN 9782340-016675).
In this book, the exercise IV page 63 presents the modelisation of pi-electrons inside a 2D infinite well of po... | Assuming that $\alpha>1$, the state shown in the answer is the lowest-energy state. Since $\frac{1}{\alpha}<\alpha$ in this case, this means that increasing $n_x$ raises the energy less than increasing $n_y$. Therefore, the state with two electrons with increased $n_x$ is lower in energy than any other possibility.
If ... | {
"language": "en",
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Is the derivative with respect to a fermion field Grassmann-odd? Fermion fields anticommute because they are Grassmann numbers, that is,
\begin{equation}
\psi \chi = - \chi \psi.
\end{equation}
I was wondering whether derivatives with respect to Grassmann numbers also anticommute, as in
\begin{equation}
\frac{\partial}... | In a Grassmann algebra (or more pedantic, a $\mathbb{Z}_2$-graded algebra), the expression with two equality signs you wrote is ill-defined. One either has a left-derivative, or a right-derivative, which are different operators in terms of results. More precisely,
$$ \frac{\partial^L}{\partial \psi} \left(\bar{\psi}\ps... | {
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Illusion that $v > c$? I am currently studying length contraction in special relativity (and having the hardest time getting the harder exercises in my book right) and there is the following exercise in my book is driving me crazy (I apologize if the translation I am making isn’t the best, the book is in French):
A h... | Essentially, special relativity states that any body's speed with respect to you cannot exceed $c$. There are no restrictions on the relative velocities of 2 bodies from your frame of reference.
If we observed the photon from the frame of the sensor, it would still be $c$ - then, their relative velocities would not be ... | {
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Is there a sharp distinction between particles and fields? The quantisation of the electromagnetic field, proposed originally by Planck, blurs the distinction between particles and fields. 'Point' particles become fuzzy and subject to a wave equation. Also, the field takes on a particle-like nature (photon) which is ot... |
'Point' particles become fuzzy and subject to a wave equation
One must not confuse the wave equations of classical mechanics with the wave equations of quantum mechanics. Mathematically they have sinusoidal solutions, but it is the variable assignments on the mathematics that describe measurable physical quantities... | {
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Why the work done by system not stored as potential energy? Now choose a spring mass system now work done by external agent in slowly moving from equilibrium position is stored as potential energy but where is work done by spring force gone.For genralization work done on system is stored as potential energy but where i... | After the spring is extended by x (until this, work is done on the spring, i.e. not by the spring), this spring then returns back to its natural length for which it does some work that is $(1/2)kx^2$. This also applies for the case when the spring is compressed.
| {
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Do any quantum interpretations not include nonlocality? Are there any interpretations of quantum theory that have a mechanism such that there is no need to invoke nonlocality?
| There's no necessity for the nonlocality in the quantum theory. In fact all experiments to this day can be explained by the local interactions.
The myth about the "quantum nonlocality" comes from the impossibility to explain the experiments with help of the local hidden variables. I.e. if you think that the quantum the... | {
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Winding number in 4D & $SU(2)$ group In the book Quantum field theory by Mark Srednicki (chapter 93, pages 575-576) in order to compute winding number, $n$, in a 4-dimensional space with coordinates $x = (x_1, x_2, x_3, x_4)$ and such that
$$\hat{x} = (\sin\chi \sin\psi \cos\phi, \sin\chi \sin\psi \sin\phi, \sin\chi \... | I don't have Sredniki to hand, but it seems to be that your "four dimensional" space of the $x^\mu$ at the beginning of the question is really the three dimensional space forming the surface of a three sphere and the integral is over this three-dimensional space. Your $U\in {\rm SU}(2)$ is also parametrized by a three... | {
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Why does a helium balloon rise? This may be silly question, but why does a helium ballon rise? I know it rises because helium is less dense than air. But what about the material of the ballon. It is made up of rubber/latex which is quite denser than air. An empty ballon with no air in it falls, so why does a helium fil... | A too heavy balloon would never rise.
If you fill helium slowly into a light balloon, there are three different phases. At first the balloon will not rise because the weight of the balloon itself plus the filled helium is higher than the weight of the displaced air.
At a certain point both weights are equal and the bal... | {
"language": "en",
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What is it that drives the electrons from one plate to another through a battery in a capacitor? The situation is as follows:
You have a parallel plate capacitor, disconnected from a battery on both ends.
We know the battery tries to maintain a constant potential difference between its two ends. The capacitor is unchar... | The battery acts like a 'pump' which creates a potential difference across its terminals. The potential difference causes electrons to accumulate on one place of capacitor. This repels electrons from the other plate into the battery hence completing the circuit. A battery acts jump of potential. You can consider it to ... | {
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Is it there any relation between an action functional and entropy? I've found papers that seem to suggest that these concepts are the same, like this one: https://arxiv.org/abs/1005.3854
But I've found answers in Physics Stack Exchange that say that both are incompatible. Although other answers say they are related: En... | We have shown that entropy is a logarithmic function of the action ratio (@/hbar) and the entropy of atmospheric gases is easily calculated using this approach (Kennedy et al. Entropy, 21, 45, 2019). Entropy indicates the scale of energy needed to sustain the action of a molecular system. This approach provides a new w... | {
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Possible to weaken single-slit diffraction? Without changing the source of the waves or width of the slit, is it possible to make the electromagnetic waves passing a small slit spread less by changing some other aspects of the slit such as surface material or border geometry?
| One possible thing you can do is place another single-slit after the first single-slit to block the peripheral fringes and let only the middle fringe through.
The single-slit creates its own diffraction pattern as seen here and here. The trick I'm suggesting here is to block the bright spots/fringes to the sides using... | {
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Does a moving charge interact with the magnetic field it produces? So the title cuts my question a bit short.
If a moving point charge produces a magnetic field, does the magnetic field it produces affect it?
And let's suppose a moving charge is moving in a region with an externally provided magnetic field, how does th... | Yes. Like most things in Physics there is a reciprocal relation. The reverse phenomenon can most readily be seen in eddy currents that a magnetic field induces in a conductor. For a current that creates the magnetic field, there will be a damping effect from the magnetic field called reverse emf. It acts to oppose the ... | {
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"answer_id": 2
} |
Why do atoms interact differently? We live in a 3-dimensional Universe, so why don't atoms (electrons) follow the same rules as humans, planets and other 3-dimensional objects? So does that mean electrons and other quantum objects pop into existence from another universe or dimension?
| The pursuit of knowledge is the asking of many questions. The question you have asked here is a complex one, about which whole books have been written, but I will try to give you a brief answer.
The quantum rules that govern the behavior of objects as small or smaller than individual atoms are quite different from the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/484158",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Intuition of 2D Velocity Vectors I understand 2D vectors in terms of displacement. For example, Bob moves 3m to the east and 4m to the north, the total change in position (displacement) equals 5m to the north east.
But I don't understand how 2D velocity vectors can be broken down into their horizontal and vertical comp... | We need to be very careful, in some cases, not to try to combine a horizontal and vertical vector into a single diagonal vector especially when they are incompatible like apples and oranges. Take, for example, a tiny vector pointing and moving vertically. When it is moving simultaneously horizontally it is still poin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/484479",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 3
} |
Why don't we use Ampere's law to find the magnetic field due to a wire of finite length at its perpendicular bisector? I know that finite length doesn't have symmetry and thus it's hard to apply maths here but take the case of magnetic field of a wire of finite length at a distance $r$ from axis of the wire exactly at ... | Ampere's law always applies everywhere (in static conditions); it is one of the Maxwell equations. The only thing is that you have to apply it correctly. It only ever tells you about one component of $\bf B$ at a time, so you have to look at the components one by one, and make sure you do the integral correctly. The ca... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/484567",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 0
} |
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