Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Boson in Superstring I'm confused about a point. Superstring sigma model is
$$
S=-\frac{T}{2}\int\mathrm{d}^2z \left[\eta^{ab}\partial_aX^\mu\partial_b X_\mu -i\bar\psi^\mu\rho^a\partial_a\psi_\mu \right],
$$
of course, the first term is in common with bosonic string one.
Then in addition to the bosonic string spectrum... | Your confusion comes from thinking that going to superstrings simply means adding fermions in the spectrum. The spectrum is instead different. For bosonic string (let's focus on NN boundary conditions and open strings) you have something like:
$$\alpha' m^2=N-1$$
where N is the number operator of the transverse vibrat... | {
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Energy diagram of a planet with fixed mechanical energy Consider the following energy diagram for the motion of a planet about a star.
The centrifugal potential curve can be represented once I fixed the angular momentum $\vec{L}$ of the planet. To fix the angular momentum vector of a planet in a orbit I have to fix not... | For your second case, you can change the angular momentum, but remember that you have fixed your total energy. You can't make the planet revolve arbitrarily fast or it will have more energy than allowed. By increasing the angular momentum without adding energy, you are circularizing the orbit.
To add, you might tak... | {
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Preference of Chirality I was interested to see that ,
$$
\gamma^5 \psi = \psi_R - \psi_L
$$
By the definition of chirality projection operator and that $\psi = \psi_R + \psi_L$.
since $\gamma^5 \psi$ pops up a lot in QED, I thought it was interesting that $\psi_R$ should necessarily by the positive quantity in this re... | We define positive chirality to be right-handed. Ultimately, this was an arbitrary sign choice (like the choice of which charges are negative versus positive), and (like the choice of charge sign) it was probably not the best choice. However, the choice of chirality, which is really just our choice to use right-hande... | {
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Is there any objective basis for the "south to north" directionality of magnetic fields? While explaining magnets to some students, I just realized a very basic thing I never thought about: We often say that magnetic fields have a "direction", that magnetic field lines "exit" the north pole of the magnet and go back ar... | It is arbitrary. Just as the positive/negative convention for electrons is arbitrary.
The Earth's magnetic pole near the northern geographic pole is of course a south pole - because it attracts the north pole of a magnetic compass needle.
In the past the Earth's magnetic field has reversed, so if compasses had existed ... | {
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Atmospheric Pressure inside a closed room
Even though they’re too tiny to see, all the molecules of air in the atmosphere above your head weigh something. And the combined weight of these molecules causes a pressure pressing down on your body of 10,000 kg per square metre. This means that the mass of the air above the... | This is a duplicate as far as atmospheric pressure goes.
As long as the container is not air tight there will come equalization of pressure. To understand why pressure equalizes one has to see the derivations of the ideal gas law, PV=RT using statistical mechanics, for example here. The attribute "law" is indicative of... | {
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Why is Kinetic Energy = (-) Total Energy and Potential Energy = 2 $\times$ Total Energy? I came across this relation while reading on the Bohr atomic model. Are there any other forces for which these relations hold good?
| You've discovered the virial theorem.
The virial theorem tells us that for a bound system where the potential energy $V$ is given by an equation:
$$ V(r) \propto r^{-n} $$
The average kinetic energy $T$ and average potential energy $U$ are related by:
$$ 2T = -nU $$
For the electrostatic force $V(r) \propto r^{-1}$ so ... | {
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Can $E=mc^2$ be derived from the Minkowski spacetime metric? $s^2=x^2+y^2+z^2-(ct)^2$? Can $E=mc^2$ be derived from the Minkowski spacetime metric? $s^2=x^2+y^2+z^2-(ct)^2$?
If so, how?
Can the equivalence of mass and energy be derived from the Minkowski spacetime metric?
Has someone done this somewhere? Please do sha... | Minkowski spacetime has the symmetries of the Poincaré group, which include the four spacetime translations. Noether's theorem then says that there are four conserved quantities, $p_0, p_1, p_2, p_3$, associated with these four symmetries. Typically $p_0$ is denoted by $E$. The structure of the Poincare group implies t... | {
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Producing gravitational waves in labs Can gravitational waves be created on very small region of vacuum with quadruple movement of atom or subatomic particles?
| A explain this practically, you need to place a spherical mass of 0.5 kilometre diameter at the distance of 10 metre from LIGO sensor to detect its gravitational wave which may read the maximum of 1mm in the reading.
Simple answer would be Yes you can create a gravitational wave with quadruple movement of atom or subat... | {
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How is a mass, suspended vertically by two springs in parallel, kept stable? Consider a mass suspended vertically from above by two springs in parallel with different spring constants. Wouldn't the tension be different in each spring? How is this system kept in equilibrium?
| The thing that the springs must have in common is their length $x$. This comes from the mass which is attached to the springs, having different lengths does not make sense in this setup.
From this you can compute the forces. Say the spring constants are $k_1$ and $k_2$. Then the net force exerted is $k_1 x + k_2 x$. In... | {
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Free Expansion Of and Ideal Gas We know that in free expansion of an ideal gas, no heat enters or leaves the system.
We also know that
$P_\text{initial}V_\text{initial}=P_\text{final}V_\text{final}$
is valid.
If heat exchange is zero, then we can call this process to be adiabatic.
Then why the following is not valid? ... | You can not classify free expansions into any of those categories as free expansion is not a reversible process and hence the intermediate states are not well defined. The equations are not working because they find the area under the p-v graph but here no such graph can be made.
| {
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Kirchhoff's laws in phasor domain While analysing AC circuits, we write voltage, current etc all with complex numbers namely "phasors". While studying the same, I wondered if Kirchhoff's laws held good with current and voltage in their phasor form. And the internet said they did! They argued somewhat as follows:
$I=Re[... | Great observation! The solution lies in the fact that the complex number $\sum I e^{j\phi}$ is rotating with a speed $\omega$ counterclockwise in the complex plane.
Consider what the expression is telling you -
The real part of a complex number that is rotating counterclockwise in the complex plane is always zero or
... | {
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When to consider friction as an impulsive force? Suppose a ball obliquely strikes a rough horizontal surface then it experiences a frictional impulse and conservation of linear momentum cannot be done on the horizontal direction.
Now consider another setup in which one block is resting on a rough horizontal surface an... | We consider friction to an impulsive force, in cases when normal force is impulsive. Here's how:We know that $f=\mu N$(only during slipping motion, for no slipping frictional force is equal to applied force RESISTING friction). Since friction is proportional to normal reaction, it will be impulsive only when normal for... | {
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Why do X-rays go through things? I always heard that the smaller the wavelength, the more interactions take place. The sky is blue because the blue light scatters. So why is this not true for X-rays, which go through objects so readily that we need often use lead to absorb it?
| You have to distinguish, which interactions take place, when electromagnetic radiation passes through a solid and interacts with it.
There is a nice plot on Wikipedia, showing the dielectric response of solids for different wavelengths/frequencies.
Basically, as the frequency gets higher, the wavelength becomes shorte... | {
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Normal force and weight If two books are placed on top of each other on a table, why would it be incorrect to say that the weight on the upper book acts on the lower book? I thought that the weight of the upper book would act on the lower book, but my professor said that the normal force instead of the weight of the up... | Both books are individually attracted by the whole mass of earth. That gives you the force $mg$. In principle also the books attract each other via gravity, but that force is so small that you can safely neglect it.
Let's start with the lower book. It sits on the table, gravity is pulling it downwards. The table then r... | {
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May a point rotate about itself? Suppose we have two equivalent rigid cylinders. Cylinder 1 is moving (translating) with constant velocity of v. Cylinder 2 is rotating without slipping and its center’s velocity is constant and equal to v. So, the motion equations of both centers of cylinders are same (x=vt). If we cons... | Rotations for infinitesimal points are not defined. A rotation is only defined when you have two or more points as a way to describe the fact that their relative distance remains constant.
Also rotational motion is shared for an entire body, meaning that all point on a body rotate the same. The idea of location for rot... | {
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Derivative with respect to a difference of independent variables I am dealing with an equation from nonlinear acoustics (Khokhlova-Zabolotskaya-Kuznetsov equation) where a strange term (for me as a mathematician) is used.
The equation looks like this
$$ \frac{\partial}{\partial\theta} \left( \frac{\partial V}{\partial\... | The problem is that your point view is too "mathematical". No offence, but every acoustician would jump to the ceiling hearing "one can just erase all const, they do not change anything". Oh, they do $-$ very much! Since one of them is the sound speed... But I get it, you solve that as a mathematical problem and we are... | {
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How do we know WHEN to get the result from quantum computers? So I always hear that you can't disturb quantum computers because this will ruin the particles superstate.
Well, how do we know WHEN to retrieve the result from the calculation?
How can we determine when the calculation is finished, without observing it?
| Even if you don't know the outcome of an operation, you know that you've applied that operation. So a quantum computer knows when to measure the same way it knows when to do anything else: it applies the operations it's told to, and measures when it reaches a 'measure' instruction.
Quantum algorithms are made up of ope... | {
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Why current in series circuit is the same? I have read in the internet that the charges do not have any other path to go and they must go through the same in a series circuit,hence the current is same.
It was quite convincing but what confused me was:
"A resistor is a passive two-terminal electrical component that impl... |
Resistors act to reduce current flow...
I will give a counter-example to the claim that resistors "act to reduce current". Consider a $9V$ battery connected across a $100\Omega$ resistor; the battery current is $90mA$.
Now, connect another $100\Omega$ resistor in parallel with the first. The battery current increas... | {
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Time taken for a layer of ice to form The book I have gives the following derivation:
Let the temperature of the atmosphere be $-\theta$ and the temperature of the water be $0$.
Consider unit cross sectional are of ice, if layer of thickness $dx$ forms in time $dt$ with $x$ thickness of ice above it,
heat released due... | A bit late maybe. A few google searches reveal that the speed at which heat propagates is infinite in the thermodynamics I am studying. So, the heat is transferred instantaneously and the time taken for a layer to form is equal to the time in which this heat is transferred.
I had thought that the heat is transferred a... | {
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When only part of the surface an object is in contact with has friction, what is the normal force I should use? I have the following exercise:
A uniform rod of mass $M$ is given a horizontal velocity $v$ on a rough track as shown in the figure. The surface is rough on the right side of the origin $O$ and the surface i... | You are correct : to calculate the friction force, you only need to consider the weight of that part of the rod resting on the rough surface, not the whole of it.
When the block overlaps the rough area by distance $x$, the normal reaction on that portion of the block is $\frac{Wx}L$ and the friction is $F={\frac{\mu W... | {
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Electric field inside a material I was thinking about the polarisation, and how the electric field behaves inside the material of permittivity greater than one.
I think to have understood what happens to D and P, but is not clear what happens to E.
Is the electric field inside the material bigger, remains constant, or ... | I assume you are talking about linear materials with dielectric constant greater than $1$.
Say you have a free charge distribution $\rho$ in vacuum, which produces an E field. Now you introduce linear material. Then the free charges will be "weakened" because they will by partially screened by charges of the dipoles st... | {
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How does electric charge flow in the typical experiment of scuffing your shoes across the carpet? I'm trying to understand the flow of electric charge. I have read about the triboelectric series, but I do not know where the rubber soles of shoes and carpet reside to know whether the shoes acquire a positive or negative... | It looks like I can answer at least one question. The charge imbalance in the carpet will dissipate into the air via ionized moisture, as described in this question: How does an object regains its neutrality after being charged by rubbing?
| {
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Why an impact exerts so much force? If an object of velocity $v$ and mass $m$ moves towards a resting object of mass $M$, then if the object which is hit might break. Why?
What is the reason that a collision has more power than a statical force $F$ acting on this object?
I haven't found any literature where such thing... | To understand this, use the definition of force $\frac{d{\bf p}}{dt} = {\bf F}$, namely the force is equal to the rate of change of momentum. Something like a collision can be very complicated to model, but the average force is approximately given by ${\bf F}_{average} = \frac{\text{change in momentum}}{\text{time take... | {
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Rotation of a vector Is a vector necessarily changed when it is rotated through an angle?
I think a vector always gets changed because its projection will change, and also its inclination with axes will always change. However the direction may remain same. Kindly make things clear to me.
| Rotation of a 3-vector
We'll find an expression for the rotation of a vector $\mathbf{r}=(x_1,x_2,x_3)$ around an axis with unit vector $\mathbf{n}=(n_1,n_2,n_3)$ through an angle $\theta$, as shown in Figure .
The vector $\mathbf{r}$ is analysed in two components
\begin{equation}
\mathbf{r}=\mathbf{r}_\|+\mathbf{... | {
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Intensity fluctuations at the output of a single mode fiber coupled to a He Ne laser I have coupled a Thorlabs HNL050L-EC - HeNe, 632.8 nm, 5 mW, Polarized Laser to a 2 meter long single mode fiber patch chord using a Thorlabs F230-FC-B aspheric lens. While I am certainly able to obtain a pure single mode Gaussian at t... | Some other effects that might be at play:
1. Reflections from the end-faces of the fiber causing interference
2. Brillion Scattering
3. Check to see if in fact the fiber you're using has a cut-off wavelength shorter than the wavelength you're actually using.
| {
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Is it true that $\frac{d}{dt}\int_S \mathbf{B} \cdot d \mathbf{a}$ goes to zero if the amperian loop delimiting $S$ contracts indefinitely? I suppose to have an ordinary magnetic field: in the answer I'm not interested to involve Dirac delta: the integral goes to zero. I want to focus on another point: an infinitesimal... | You're right that a function can be "small" at a point but have a "large" derivative at that point. But maybe the confusion is that you're imagining the surface $S$ shrinking in time, so that it's only "small" at one instant. But the surface doesn't shrink in time - you're taking the limit where it's "small" at all t... | {
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Why is the energy operator special? Only the energy operator controls the time dependence of a quantum system, but not the others, why is that?
| The way I like to understand this is in terms of generators of translation. A well known result from classical mechanics (see Goldstein) is that momentum is a generator of translation in the canonical coordinate conjugate to that momentum. For example, linear momentum generates space translations, and angular momentum ... | {
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If we threw a baseball from the ISS, could we deorbit the ball? Clearly this is a hypothetical question.
Say we bring a star baseball player into NASA, prep them appropriately for a mission in space, and fly them up to the International Space Station. They go on a spacewalk with a baseball, and at the apoapsis (highest... | On a practical note, there was a space walk a few years back when they replaced a failed ammonia pump that was the size of a refrigerator. The astronaut simply gave it a swift push away from the station knowing that it would soon deorbit fast enough that it wouldn't be a collision hazard.
PS- If you have Kerbal Space ... | {
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Gimbal Lock: why is it a problem? I was watching the video Gimble Lock - Explained, by videodumper, about the gimbal lock problem. I understood that during rotations it could happen that one DOF disappear. Looking at the middle part of the video (min 3.22) can be seen that two planes are stuck in only one plane. For th... | The planes are not deliberately stuck together - they just happen to coincide when one rotation (by 90 degrees) has dragged one plane of rotation to coincide with another. After that, you can no longer distinguish between rotation about the two axes whose planes coincide - so you have gone from three degrees of freedom... | {
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Vertical filaments during Atomic bomb explosion What are those vertical filaments that form in the air whenever an atomic bomb is detonated? They are clearly visible in this movie at 3:08.
|
They are smoke rocket trails. Before each test blast, technicians fired these rockets up in the air, leaving large smoke trails that rose well above the bomb's mushroom.
When the atomic blast's shockwave arrived, they moved the trails. Scientists at observation stations could instantly see the effect of the shockwave,... | {
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Spinning top fixed point I have seen many explanations about the movement of a spinning top. The explanations were in a varied level, from basic newtonian mechanics to Lagrangian formalism. But I do not understand why some people consider different fixed points. In same cases it is the point of contact with the surface... | Spinning of a top about a fixed point is different from spinning in space or about center of mass. When a top lean certain angle it slips like a slanting ladder because of lack of sufficient frictional force. nutation is observed in the case of a top when there is slip at the contact point.
| {
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Is a falling leaf an example of a chaotic system? Let´s assume is a wind still day in autumn. When a little change is made in the initial motion of a leaf at the time it falls off a tree, the resulting path of motion of the leaf is very different from the path that would develop if these changes wouldn´t have been made... | Chaos is typically phrased as a sensitivity to perturbation in initial conditions (amongst other important things things). You can have a statistical distribution describing the final destination of leaves in general, when the path taken by any individual leaf is deemed chaotic.
As an example, consider common strange ... | {
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Find unitary for given rotations on Bloch sphere I want to characterize a unitary by given rotations on the Bloch sphere.
I know, that when I send in the State $|\Psi\rangle =\begin{pmatrix}1\\0 \end{pmatrix}$, I get the state $U|\Psi\rangle=\begin{pmatrix}\cos \theta\\ e^{i\varphi}\sin \theta \end{pmatrix}.$
When I ... | Your 2x2 unitary is mostly determined by its action on the state vector $\left(\begin{array}{c}1 \\0\end{array}\right)$. This is because 1) in a 2-d Hilbert space, for any given vector there is a single other orthogonal vector (up to a phase factor), and 2) a unitary map preserves orthogonality. Once $|u\rangle = U\lef... | {
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AdS boundary global vs Poincare' Is the global boundary of AdS the same of the boundary written in Poincare' coordinates?
| Here's what is written on wikipedia (it may be helpful):
Global coordinate:
$AdS _{n}$ is parametrized in global coordinates by the parameters $ (\tau ,\rho ,\theta ,\varphi _{1},\cdots ,\varphi _{n-3}$) as:
\begin{cases}X_{1}=\alpha \cosh \rho \cos \tau \\X_{2}=\alpha \cosh \rho \sin \tau \\X_{i}=\alpha \sinh \rho \,{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/255086",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
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'Hovering' light rays on the edge of a black hole According to Prof. Hawking, light rays will 'hover' on the edge of a black hole. If this is true, and the light 'stops' on the edge, how can the electric/magnetic fields which, constitute the light, continue their self-perpetuating state?
What does Hawking mean? His qu... | Hawking, I believe, is referring to a more metaphorical 'hovering'. As light, or anything, approaches the event horizon, it becomes more and more redshifted---it's motion appearing to go slower and slower and slower, approaching zero apparent velocity to an outside observer (approximately) infinitely far away. Anythi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/255190",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Does a box containing photons have more inertia than an empty box? A box containing photons gravitates more strongly than an empty box, and thus the equivalence principle dictates that a box containing photons has more inertia than an empty box. The inescapable conclusion seems to be that we can ascribe the property of... | Yes, mass and energy are equivalent. A more competent relativist might be able to give you the complete description, but to first order you can say that the mass of an object is simply the total energy in its volume divided by c^2. That mass is equivalent to the inertial mass by the weak equivalence principle, which is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/255340",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "22",
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Pressure on the sides of a container? Sorry if this is an incredibly basic question for these categories. Basically, I don't understand these types of problems. I'm sure it's something really simple I'm missing.
Let's say there's an open swimming pool with width $w$, length $l$, depth $d$, and density $\rho$ (equal to ... | It can be shown by integration that total force affecting whole pool side wall of width $w$ is :
$$F_{wall} = \frac {\rho gw~d^2}{2}$$
Divide both sides by wall area $A = w\cdot d$, and you'lll get water pressure affecting whole pool side :
$$P_{wall} = \frac {\rho gd}{2}
$$
So average pressure at whole wall will be wa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/255425",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 5,
"answer_id": 4
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Propagating a Gaussian wavepacket backwards in time So, I'm following the MIT OCW lectures on 8.04 quantum mechanics by Prof. Allan Adams. I have the expression for the probability distribution of a gaussian wavepacket for a free particle situation. No initial momentum is imparted. This is a non-relativistic treatment.... | Yes, the gaussian wavepacket can get narrower as the time passes indeed. It's a matter of phases. You know that a gaussian wavepacket is the superposition of plane waves, each one having a precise wavevector. So it really depends on how you "prepare" this superposition, i.e. on how you set the phase of each chromatic c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/255610",
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Why do liquids exert pressure on the sides of a container? What makes a liquid push against the walls of a container if the liquid is completely static?
I was thinking a comparable situation would be a bin full of baseballs. Unless the balls were perfectly stacked they would be rolling off one another and the walls of... | In a liquid (or any fluid), the molecules are in random motion (best to say is vibration). So each molecule is vibrating and hence collides with each other. Likewise the molecules in contact with the container also collides with the container walls. Assuming perfect elastic collision, the collided molecules are pushed ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does the interference pattern change with given relation when the source slit changes? Why should the dependence relation be like $${\frac{s}{S}}<{\frac{\lambda}{d}}$$ for the interference condition to be seen?
Where $s$ is the width of the source slit and $S$ is the distance between the source slit and the double ... | Let $L$ be the distance from the double slit to a screen, $S$ be the distance from a source slit to a double slit, and $s$ be the width of the source slit.
The interference pattern produced by a source point is like the cross section of a Fresnel diffraction pattern: the fringes get closer together as the distance from... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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"answer_id": 1
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Vertical circular motion/How can tension be negative?
This is a rock tied to a string spinning vertically.
Here,
$T+mgsin\theta = mv_1^2/r => T = mv_1^2/r-mgsin\theta$
Suppose I give it a velocity $v$ at the bottom.
1) At what angle $\theta$ will the tension become zero?
2) If the velocity ends up $=0$ at $\theta = ... |
[...] which would end up giving tension a negative value. How is this possible?
It isn't. If you set zero speed $v=0$, then you will no longer have circular motion, and the object will accelerate downwards. A non-zero speed $v$ is a requirement for circular motion to happen, because a radial acceleration towards the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/256163",
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"source": "stackexchange",
"question_score": "1",
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Wave speed derivation
The wave speed derivation approximates the wave as a circle. It uses that to know that $$a=\frac{v^2}{R}$$However, numerous functions can approximate the wave. A straight line, $x^2$, $x^3$, etc. If I used those I would get a different equation for a. So why is a circle the correct approximation ... | The wave can be any shape $f(x)$. But when you focus in on a sufficiently small element of the curve, you can do a Taylor expansion about the point $x_0$:
$$f(x) = f(x_0) + (x-x_0)f' + \frac{(x-x_0)^2}{2!}f'' + ...$$
As the distance $(x-x_0)$ gets smaller, higher order terms can be neglected. If you consider a point wi... | {
"language": "en",
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"source": "stackexchange",
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Covariant derivative of a covariant derivative I'm trying to find the covariant derivative of a covariant derivative, i.e. $\nabla_a (\nabla_b V_c)$.
This is something I've taken for granted a lot in calculations, namely I though that by the Leibniz rule we just have:
$$\nabla_a (\nabla_b V_c) = \partial_a(\nabla_b V_... | Easy way
Let me first state the straight-forward way to do this computation.
$$
\langle \nabla_a \nabla_b V, \partial_c\rangle =
\partial_a \langle \nabla_b V, \partial_c \rangle - \langle \nabla_aV, \nabla_a \partial_c\rangle = \partial_a (\nabla_bV)_c - (\nabla_bV)_d \Gamma_{ac}^d
$$
First equality follows from compa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/256393",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can light be a spinor? A recent discovery suggests that photons can have half-integer spins. This seems to contradict the well understood notion that photons are vector (1-form) fields
What does this mean for the fundamental picture of electromagnetic propagation?
| It probably does not mean anything. That paper concerns the quantization of electromagnetic waves in less than three spatial dimensions. In fact, there are a number of decades-old results showing that it is often possible to evade the spin-statistics relationship in lower-dimensional systems. While these kinds of re... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Flat space Solution of Einstein Field Equation Does a trace-free energy-momentum tensor $T_{\mu}^{\mu} = 0$ ensure that the Einstein's field equations have a flat space solution?
| The Einstein field equations
$$
R_{\mu\nu}~-~\frac{1}{2}Rg_{\mu\nu}~=~8\pi GT_{\mu\nu}
$$
for zero stress energy means that the Ricci Curvature $R_{\mu\nu}$ is proportional to the metric with $R_{\mu\nu}~=~\frac{1}{2}Rg_{\mu\nu}$. This is called an Einstein spacetime, and for a constant Ricci scalar $R~=~R_{\mu\nu}g^{\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/256955",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What does it mean that the laws of physics are time reversible?
The Universe, as far as we can tell, only operates according to laws
of physics. And just about all of the laws of physics that we know are
completely time-reversible, meaning that the things they cause look
exactly the same whether time runs forwar... | This is not a useful answer!
1. The statement: "There is no force/law that makes the cup rise" is completely misleading because it deals in likelihood (probability) not law.
2. The statement, "Even though, the mathematical formulas may allow the backward flow of events, there are no such forces that would cause it" i... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 3
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What does a voltmeter actually measure? For time varying fields (even quasistatic ones) the electric field is given by
$${\bf E} = - \nabla \Phi - \frac{\partial {\bf A}}{\partial t}$$
So what does a voltmeter measure? Does it measure a difference in $\Phi$ between two points $a$ and $b$, or does it measure $\int_a^b ... | Although both answers above have valid correct facts, they are both missing the original point in the question. The op tried to ask what happens in the electrodynamic case when the line integral of the electric field is path dependant.
In this case the line integral would give a different value for each trajectory of t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Analysis of a system consisting of a leaking tank of water The departure point is this problem:
A water tank on wheels is moving over an horizontal trail with negligible friction. There is a small opening in one of the walls, at a depth of $h$ below the tank's water level. The cross-section area of the opening is $A$. ... | Using Torricelli's law (https://en.wikipedia.org/wiki/Torricelli%27s_law) you get $v=\sqrt{2gh}$ irregardless of how big the opening is. Now you can calculate how much mass is leaving the tank at any time by multiplying the volume that is leaving the tank by its density: $$\Delta m=A\Delta s\cdot\rho$$ with $\Delta m$ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/257576",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Where does $\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$ come from? It's a very basic question, where does the relation $$\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$$ for any square integrable $\psi(x)$ come into existence? Some texts I found states that the above relation comes as a consequence of momentum being defi... | Ab initio the momentum operators can be constructed using de Broglie Plane waves
In one dimension, using the plane wave solution of the Schrodinger equation,the wave function
Psi = exp. i (kx -wt) ,
if one takes the partial derivative w.r. to x of the wave function
delta/delta x (Psi) = ik. Psi
and using de-B... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/257670",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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"answer_id": 4
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Determination of the electric field of charged object using Gauss's law when we determine the electric field of a charged rod of infinite length,we consider a circular cylinder to be the gaussian surface for convenience.In the case of a charged sheet we choose the gaussian surface to be a cylinder going through the she... | When you choose an arbitrary gaussian the flux is still given by the charge inside the surface. However it would be useless in calculating the electric field unless you are able to write
$$\int\vec E\cdot d\vec A=\int EdA=E\int dA.$$
That is, Gauss law is useful when the surfaces elements are always parallel, antiparal... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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A Formula for the Phase Difference Between the Electric and Magnetic Wave Oscillations? A) Is there a formula for the phase difference between the electric and magnetic field oscillations, in vacuum, in an electromagnetic wave emitted from an antenna, as a function of the frequency the distance from the antenna?
B) Doe... | The electric and magnetic fields are always in-phase if the wave can be treated as a plane wave (which simply means it cannot be too close to the source), and in vacuum or any medium with linear response, such as air.
Boundary conditions of wave guides change this relationship, and must be solved for each specific case... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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The relation between anomalous dimensions and renormalization constants I am trying to understand the general strategy and technical details of calculating $\beta$-function at higher orders. $\beta$-function is the anomalous dimension of the coupling constant and there is a complete set of anomalous dimensions correspo... | In $\overline{MS}$ the $\beta$ function does not depend on the gauge parameter. This means that the dependence on $\mu$ in $Z$ only comes from the coupling constant $a \propto \mu^{-2 \epsilon}$.
For general $Z(a_s,\xi)$, the relation is as follows (eq. 21 in the Chetyrkin paper):
$$-\gamma =\left(-\epsilon + \beta(a_s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/258641",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Tractrix - velocity pointing to pulling point It is said the tractrix is the curve described by a mass being pulled by a string, where the end of the string being pulled moves with constant speed, and the mass suffers a friction force. What is the physics explanation for why in the tractrix the velocity is always align... | You can imagine it as you pulling your dog (object) with a rope (string), while walking on a straight line, but the dog don't want to follow where you are pulling him and just want to stay in place. As you move, the tension of the rope felt by the dog is always directed toward you, making the dog move slightly (but unw... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/258767",
"timestamp": "2023-03-29T00:00:00",
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Why does Bernoulli's equation only apply to flow along a streamline that is in viscid, incompressible, steady, irrotational? I am learning about hydrofoil on this website.
In a later video I watched, I learned that in the process of deriving Bernoulli's equation, $$constant=P/d+gh+1/2v^2$$ has to multiplied through by ... | It can also be derived from Euler's equation of motion of a fluid element $dm$ moving (translating but NOT rotating) along a flow line through a conduit:
That equation (a balance of forces acting on the fluid element) is:
$$\frac{dp}{\rho g}+\frac{vdv}{g}+dh+\frac{d\sigma_w}{\rho g}=0$$
The fourth term is the shear st... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/258876",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Muon lifetime determination My colleagues and I performed several experiments to determine the lifetime of the muon (from secondary cosmic rays) using scintillator detectors coupled to multi-channel analysers. The results invariably showed a muon lifetime lower than the standard 2.2 microseconds. Apart from poor statis... | I know that you are explicitly asked about not equipment related answers.
But when I learned something from experimental physics then that you should always consider equipment flaws.
I could imagine a scenario where the events on which you trigger to start/stop the clock have different rise times depending on where the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/258961",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Coherence length of a single photon If I pass individual photons through a M-Z interferometer with equal arms I will observe interference (eg only one detector will respond). As I increase the path length of one arm I will observe the two detectors responding alternately as I pass through each phase cycle. Eventually I... | By length maybe you mean wavelength. A single photon traveling at the speed of light and oscillating at a certain frequency will oscillate through one cycle every wavelength or say 500 nm. As you increase the length of one arm of the experiment the interference will go in and out of phase every one half cycle or every ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/259116",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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Relativity paradox with mirrors and light pulses
Consider two very short light pulses emitted from the centre (C) of two mirrors A and B (as shown in the diagram).
From the point of view of the lab frame, the apparatus is all moving to the left at velocity v.
Imagine there is also an electron near the centre of the ap... | In the lab frame both pulses arrive at C at the same time. The reason is that the distances traveled are the same (they do not reach A and B simultaneously). The distances of paths CA and BC are equal, the same happens with the paths AC and CB. The distance CAAC is equal to CBBC.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/259199",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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"answer_id": 0
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Meaning of the phase space in statistical physics I have a silly question about the phase space. I am confused with the meaning of points in phase space. Does the each point in phase space represent concrete particle of the system, or does it represent the whole state of the system? Our teacher told us, that we use the... | The quickest way to understand phase space is to read a phase diagram. It may be a PV diagram, or mixture fraction-temperature diagram. So read carefully what x axis represents and what y axis represents. Take PV diagram for example. each particle on the diagram is a pair of pressure (P) and volume (V). It describes th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/259412",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why are usually 4x4 gamma matrices used? As far as I understand gamma matrices are a representation of the Dirac algebra and there is a representation of the Lorentz group that can be expressed as
$$S^{\mu \nu} = \frac{1}{4} \left[ \gamma^\mu, \gamma^\nu \right]$$
Usually the representations used for them are the Dirac... | Thats a nice question. To answer this lets start with clifford algebra generated by $\gamma$ matrices.
\begin{equation} \gamma_{\mu}\gamma_{\nu}+ \gamma_{\mu}\gamma_{\nu}=2\eta_{\mu\nu} \end{equation}
with $\mu,\nu=0,1,2,\cdots N$
with the metric signature $\eta_{\mu\nu =}\text{diag}(+,-,-,-,\cdots,-)$. Using $I$ and $... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/259514",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is a spacetime of constant positive curvature just a 4-hypersphere? In discussions of basic cosmological models, I don't see "spacetime of constant positive curvature" described more simply as a "4-hypersphere". What am I missing?
| There are different descriptions of Spacetime according to General Relativity.
Look at the De-Sitter-Space. It is a mathematical concept of Spacetime with a positive curvature. It is a submanifold of Minkowski-Space.
there is also an Anti-De-Sitter-Space, which has a negative curvature. It plays a role in some cosmo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/259592",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Can we write the wave function of the living things? If yes then how? In quantum mechanics we studied that everything has a wave function associated with it.My question is can we write down the wave functions of things. Then how we can write down the wave functions of the things like animals, human eye, motion of snake... | There are 37.2 trillion cells in a typical human body, (probably a good few more in mine ;), then in each cell there are 20 trillion atoms, then you have to obtain the wave function for each of the electrons.......
Actually, it may well be that you cannot describe a wavefunction for a macroscopic object, like a human ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Birefringent filter, optical path length difference? In 'The Light Fantastic' by Kenyon, I.R. (p424), it is said that for a birefringent material inclined at Brewster's angle and who's optical axis lies in the plane of the plate, we have an optical path length difference between the ordinary and extraordinary waves of:... | Note I am the OP.
The first and foremost thing to note about this equation is that it is not exact and is based on approximations.
For the situation described above, once the light has entered the filter it splits into two, one that experiences the ordinary refractive index $n_0$ and the other that experiences the refr... | {
"language": "en",
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Merging black holes makes them less dense, so According to What is exactly the density of a black hole and how can it be calculated? (more specifically, John's answer here made me think: if you merge a whole load of chunks of an element heavier than iron (to prevent them from fusing), the resulting object would either ... | If I understand you correctly you are concerned that a black hole somehow manages to become less dense than the matter that made it, as if it somehow expands against its own gravity to increase its volume.
However a black hole event horizon is not an object - it is just a place in spacetime. Although we can calculate a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/260927",
"timestamp": "2023-03-29T00:00:00",
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Check dimensions of the integral of a function I and a colleague are arguing about the dimensions of:
$$\int_0^x f(x) dx $$
in this particular case $[f(x)]=m^2/s^3$ and $[x]=m$.
Does it follow that $[\int_0^x f(x) dx]=m^2/s^3$ or $[\int_0^x f(x) dx]=m^2/s^3m$?
| The dimensions of the integral are simply those of $f(x)dx$, so in this case they would be $m^2/s^3 \times m = m^3/s^3$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/261166",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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What's the minimum time scale for a candle to be lit in order for it to establish a steady state? My Understanding
When a candle is lit initially, it goes through a few stages (see, e.g. this explanation from the National Candle Association):
*
*Wick burns.
*Crusted wax on wick melts, evaporates and burns.
*Base... | Factors affect the time (i.e. from start to the time of equilibrium state where the following processes are sustainable: flame heat up wax, liquefied wax being pulled up, evaporated, wax vapor mixes with air, burn and produce heat) are followings,
- size of wick (the larger, the more heat it can produce)
- size of wick... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/261275",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to pour water from a bottle as fast as possible? When one pours water out of a bottle, it first flows smoothly but then a pressure 'blockage' develops and the pouring becomes interrupted and turbulent, so that the water comes out in splashes. This seems to slow down the flow of water from the bottle.
What is the op... | I assume you are not worried about the few drops that are always left in the bottle after pouring out the water. The reason I make this assumption is that without "evaporating lasers" being allowed every method suggested would need to wait hours for the drops to naturally evaporate. Even then, there would still technic... | {
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Friction-free rolling/sliding on an inclined plane Suppose a sphere is rolling down an inclined plane. There is no friction. The body will not roll and undergo just a translation. But why is this so?
If we consider the axis to be along the point of contact, then there would be a torque which will cause it to rotate bu... | In such a hypothetical situation in which there is no friction between the sphere and plane, there can be no tangential force acting on the sphere, and hence no torque. The only force acting on the sphere would therefore be its weight, and the component of that force acting perpendicularly to the plane would be respons... | {
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If the speed of light is constant, why can't it escape a black hole? When speed is the path traveled in a given time and the path is constant, as it is for $c$, why can't light escape a black hole?
It may take a long time to happen but shouldn't there be some light escaping every so often?
I'm guessing that because tim... | The picture I always liked is for an observer free-falling into the black hole, when they're just outside of the event horizon, it looks like the event horizon is propagating outward at nearly the speed of light. After the observer falls just inside, the event horizon now looks like it's propagating outward at greater ... | {
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Problem with magnetic field due to relative motion We know that, moving charge produces magnetic field in the surrounding space.
Consider this scenario :
A charge 'q' is moving with a constant speed 'v' in the direction of positive x axis of a coordinate frame 'A'.
As a result, there exists magnetic field everywhere in... | Electric and magnetic fields are not relativistically invariant. What you measure will depend on the frame of reference you are in.
In your example, the moving charge in frame A will be responsible for both an electric field and a magnetic field.
In frame B where the charge is stationary, then an observer would only se... | {
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Definition of anomalous symmetry in Hamiltonian formalism In the Lagrangian path-integral formulation of QFT, an anomalous symmetry is defined to be a symmetry of the action which is not a symmetry of the measure of the path integral, and therefore not a symmetry of the partition function. How do we define an anomalou... | According to this paper, the Hamiltonian interpretation of anomalies is that one cannot formulate any Gauss-like law to constrain the physical states in the anomalous theories.
*
*Luis Alvarez-Gaumé and Philip Nelson, Hamiltonian Interpretation of Anomalies, Comm. Math. Phys. Volume 99, Number 1 (1985), 103-114.... | {
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Vlasov equation, Maxwell distribution I have the Maxwellian distribution:
$$f(v)=n\left(\frac{m}{2\pi kT}\right)^{\frac{3}{2}}\exp\left(-\frac{mv^2}{2kT}\right)$$
I have to show that it is a solution to the Vlasov equation:
$$\frac{\partial f}{\partial t}+\vec{v}
\cdot \text{grad}(f)+\frac{q\vec{E}}{m}\cdot \text{grad}... | when you put the Maxwell equation in the vlasov equation, you calculate the averages and that is how the terms
$\left\langle \frac{\partial f}{\partial t}\right\rangle =0 $ since the distribution is not dependent on time and
$\left\langle v.\nabla f\right\rangle =0$ because distribution is uniform on an average.
simil... | {
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What is the angular velocity of the electron? An electron has angular momentum. Shouldn't it also have angular velocity?
Ignoring the g-factor (just for the order of magnitude approximation) and the fact that an electron is not a sphere the electron's angular velocity should be around:
$$ \omega \approx \frac{\mu}{er^2... | the spin is assumed to be an intrinsic property unrelated to rotation, as it is assumed usually that the electron is truly elementary and does not have any size. The same happens with the expansion of space into... the nothingness, not necessarily into another spatial dimension. If you can accept that you are a long wa... | {
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Relationship Between Magnetic Dipole Moment and Spin Angular Momentum I am reading Introduction to Quantum Mechanics 1st edition by David J. Griffiths and I have a couple questions about this section on page 160.
A spinning charged particle constitutes a magnetic dipole. Its magnetic dipole moment $\mu$ is proportion... | $\mathbf{S}$ is the spin operator. It is a vector operator that acts on spinors. It will have three components $(S_x, S_y, S_z)$ and for example if you take the $z$ axis as your spin measurement axis, you define spin up and down as the two eigenstates of $S_z$.
It can be shown that in matrix form $S_i$ is proportional ... | {
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Can I recirculate water from an open reservoir to the bottom of a bigger, closed one, without a pump? A fountain head pumps water out of the main tank into a 'pond' reservoir. Can the water recirculate back into the main tank without the help of another pump?
I'm sorry if this a dumb question. I'm guessing it would not... | The water level in the pond must be the same as in the tank, so:
:-)
| {
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System rigidity What is the meaning of system rigidity in mechanics? I can't understand how to classify the system as rigid or not, and what is the effect of rigidity on the whole system.
If you know anything about system rigidity... Please let me know
| In the materials science context, rigid means hard, resisting deformation. It is the opposite of elastic.
If two material bodies are forced sideways against each other and one or both are elastic like rubber, it/they will deform, allowing them to squeeze past each other without much damage being done.
However, if bo... | {
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How to find entropy production of opening the windows in the winter? Every time you open the windows in the winter (to bring in healthy and fresh air), room's warm air goes outside into the atmosphere.
How to find entropy production of opening the windows in the winter?
The room's volume is denoted by $V_r$ and its tem... | Step 1) Find a model for the gas in the room. We might as well take an ideal gas for this demonstration; I think this is generally an alright model for the air since it's mostly inert nitrogen.
Step 2) Apply the first law of thermodynamics, ignore the work done in opening the window. The first law now states
$$ \Delta... | {
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Is anisotropic radioactivity really impossible? What if the nucleus has a magnetic moment, and also the electron shell has one? I suspect, in this case, the orientation of the nucleus could be "fixed" by the electron shell.
Maybe a mono-crystal of such a material would have an anisotropic radioactivity. Thus, its radio... | The idea that you propose is possible. In fact, there is a very famous example of your setting: the Wu experiment.
Chien-Shiung Wu at the US National Bureau of Standards prepared a thin surface of ${}^{60}Co$. This isotope decays by beta decay, producing one electron and one antineutrino. Due to the small magnetic mome... | {
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Ball spontaneously rolling down hill I'm trying to remember a problem in classical mechanics involving a special surface that allows a ball to roll to the top and lose all it's momentum in finite time.
This leads to some interesting problems with time reversibility, as it implies the ball will spontaneously roll down ... | I believe the analysis of the Norton Dome is flawed (as many philosophers thought experiments). The ball does not stay at rest and start to move spontaneously in the absence of any force. If there were no forces it will stay there forever. The reason it starts to move is some small perturbations. They could be either e... | {
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Why do we believe baryon asymmetry? The question is that how can we make sure that our universe is baryon asymmetric? I mean, is it possible that there are antimatter domains beyond some very large scale. Yes, if that kind of domains exist, the scale must be very large. But does such constraint bring any problems such ... | So, there are several possible ways the universe could be baryon symmetric:
*
*A region of the universe where antimatter dominates. There is a problem with this theory, though - 30 years' worth of scientific research has calculated just how far away this type of region would have to be, and from these calculations i... | {
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The analytical result for free massless fermion propagator For massless fermion, the free propagator in quantum field theory
is
\begin{eqnarray*}
& & \langle0|T\psi(x)\bar{\psi}(y)|0\rangle=\int\frac{d^{4}k}{(2\pi)^{4}}\frac{i\gamma\cdot k}{k^{2}+i\epsilon}e^{-ik\cdot(x-y)}.
\end{eqnarray*}
In Peskin & Schroeder's bo... | In the following, I will carefully deal with Wick rotation. In the
end, I have found that I was confused.
The integration is
\begin{eqnarray*}
& & \int\frac{d^{4}k}{(2\pi)^{4}}\frac{1}{k^{2}+i\epsilon}e^{-ik\cdot x}\\
& = & \frac{1}{(2\pi)^{4}}\int d^{3}ke^{i\mathbf{k}\cdot\mathbf{x}}\int_{-\infty}^{\infty}dk_{0}\fr... | {
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Accessibility by reversible processes and the Second Law of Thermodynamics One common way of motivating the existence of Entropy as a state function is the following. Let us take the Clausius/Kelvin-Planck statement of the second law, from which we can deduce Clausius' theorem
$$\oint \frac{\delta Q}{T} \le 0,$$
where ... |
Is this taken to be an additional (and apparently implicit) assumption?
You are correct.
Take two arbitrary points $A,B$ on the $PV$ (or any other) plane, and draw an arbitrary curve connecting them: you have just defined a reversible transformation connecting $A$ and $B$.
This is because every point in the $PV$ (or... | {
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How to choose proper measurement operator? Let's assume I have two states inside the Bloch sphere, at radial vectors $r_1$ and $r_2$ respectively $(r_1<r_2<1)$. Their angular location is same. These are like:
\begin{equation}
\rho =
\begin{pmatrix}
\frac{1+r_1 \cos\theta}{2} &\frac{r_1 \exp(-i\phi)\sin\theta}{2} \\
\... | When don't you condition on the result, measurement of a qubit can only decrease its purity (you end up with less information than you started with).
When you do condition on the result, measurement of a qubit will make it 100% pure but there are two possible results. One possible result is along the measurement axis y... | {
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Out-of-plane electronic band structure for 2D materials? There's been much recent interest in 2D materials since they can form monolayer-thick films. Since their crystal structure is periodic along the in-plane directions, the electronic band structure along these directions is quite well understood and can be formulat... | You're right, the usual language of band theory doesn't apply in the out-of-plane direction. The system really becomes a quantum well in that direction, so you will have a discrete spectrum of energy levels and there won't be any dispersion with $k_z$ ($dE/dk_z = 0$) if $z$ is out of the plane.
The relevant tunnelin... | {
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Is there any effect on mechanical waves by electromagnetic waves (and vise versa)? Do electromagnetic waves like light and gravitational waves (due to moon for instance) affect on mechanical waves like sound?
Can sound change the path of light?
| Yes, sound waves in a gas, liquid or solid can affect the light passing through it, as the motion of the atoms due to sound waves changes the atomic spacing, and this changes the index of refraction slightly. So the light would be diffracted and some amount of the light would experience a frequency shift up and a frequ... | {
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Force of water hitting a wall If you had a 8" pipe with 500psi stream of water exiting it and hitting a wall at 90 degrees 8 feet away, what would the force of the water on the wall be?
Thank you all.
Non-mathematician.
| Actually. the velocity can be determined as follows.
V = sq. root of 2gh where: V = velocity in ft./sec. g = acceleration const. 32.2 ft per sec per sec. And h = head in feet of liquid.
h = P * 2.31/SG where: P = pressure in psi. SG = liquid specific gravity.
With the above information you can now calculate F.
| {
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Torque on electric dipole placed in non uniform electric field When electric dipole placed in non uniform electric field, what is the approach to calculate torque acting on it? Can it be zero?
| If the dipole is small enough, then the force on dipole would be:
$$\vec{F}=\nabla(\vec{p}.\vec{E})$$
and consequently the torque would be:
$$\vec{F} \times \vec{r}=\nabla(\vec{p}.\vec{E}) \times \vec{r}$$
where r is the length of the dipole
| {
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Relation between entropy and internal energy I am confused as to what is the relation between entropy and internal energy. Entropy is always presented as a measure of the randomness in a system. So when we supply heat to a well insulated system say ideal gas in a container with fixed boundary, the internal energy and t... | The chaos comes from by changing of volume or pressure of the system. The average kinetic energy doesn't change, but number of collisions increases (if pressure increase) or length of paths increases (if volume increases).
| {
"language": "en",
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What is the significance of the Inverse-square law? Considering its occurrences in various fields like Electrostatics, Gravitation, Acoustics etc. how does the law bind these topics together?
| For point sources of a field or energy source, such as a charged particle, a gravitational body (which acts like a point source), or a loudspeaker on top of a tall column, the geometry of the problem controls how energy and fields distribute themselves in space. At all points that are an equal distance from a point so... | {
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Prove that an electron in a hydrogen atom doesn't emit radiation According to electrodynamics, accelerating charged particles emit electromagnetic radiation.
I'm asking myself if the electron in an hydrogen atom emits such radiation. In How can one describe electron motion around hydrogen atom?, Murod Abdukhakimov says... | You have your "prove" in the wrong place. The way to prove that ground-state electrons in hydrogen atoms don't emit radiation is the following:
*
*Construct a sample of ground-state neutral hydrogen atoms.
*Place this sample near a detector which is sensitive to the sort of EM radiation you expect.
*Die of old ag... | {
"language": "en",
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Physical meaning of enthalpy I've been reading about thermodynamics and reached the topic about enthalpy . I've understood its derivation but I don't understand its physical meaning ... Also I don't understand why they have divided by the mass of gas to get to the specific enthalpy equation . what's the use of it? I kn... | Enthalpy, H, is H = U + PV where U is internal energy, P is pressure, and V is volume. Specific enthalpy, h (enthalpy per unit mass), is h = u + pv where u is internal energy per unit mass, P is pressure, and v is specific volume (inverse of density). Physically, enthalpy represents energy associated with mass flowi... | {
"language": "en",
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Why don't the magnetic dipole moments in a neutron cancel out? This may be a silly question. I thought magnetic dipoles were dependent on electric charge, so why in a neutron do the dipole moments not just cancel each other out?
| The magnetic moment of the neutron is not due to circulating charge. Instead it is due to the combined magnetic moments of the partons inside it.
The inside of a hadron is a ferociously complicated place, but let's take the simple model of a hadron as made up of three quarks. The quarks have a magnetic moment due to th... | {
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Quantum master equation and off-diagonal terms I have a couple of related questions
*
*What is exactly the difference between the quantum master equation and the regular master equation? My understanding is that the normal master equation is used to find a "vector" of state probabilities (like in a regular Markov ch... | For the first question on master equation, it turns out that there are loads of equations from different fields that are respectively being called master equations, but they are not related in any certain ways. The Markov Chain master equation and the quantum master equation are one example of this. It seems like you u... | {
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Running Constant Values At Very Low Temperatures From Wikipedia Coupling Constants, using QED as an example. I realise that the one-loop beta function in quantum chromodynamics is negative.
If a beta function is positive, the corresponding coupling increases with increasing energy. An example is quantum electrodynamic... | The fine structure constant $\alpha\approx\frac1{137}$ appears in the Coulomb force between fundamental charges:
$$
\alpha\hbar c = e^2/4\pi\epsilon_0,
\quad\text{so}\quad |E_\text{Coulomb}| = \frac{e^2}{4\pi\epsilon_0} \frac1r = \frac{\alpha\hbar c}{r}
$$
Quantum electrodynamics is pretty well tested down into the rad... | {
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Electric field dependence on distance How can it be proved that for a point charge, $E$ is proportional to $$1/r^2$$ using the concept of Electric field lines (or lines of force)? I tried to show that if field lines are close, then magnitude of Electric field is higher. But, I couldn't show the given dependence.
| This is a much more deeper question then it looks in first glance. The simple logic given by @Anthony B is not enough for proving the inverse square law. There are numerous experiments that have been done to verify this law. There is a collection of the experimental works in this review.
In earlier days Cavendish and ... | {
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Is measure relative velocity the same for both observer n particle A particle is moving at velocity v. A stationary observer tries to measure its velocity. From the observer reference frame, he will measure a shorter distance travel as compared to what the particle will measure due to length contraction. The observer w... |
In Figure 1 the system $\bbox[#99FFFF,2px]{S'\equiv O'x'y'z'}$ is moving with velocity $\mathbf{b}=(b,0,0)$ relatively to $\bbox[#E0E0E0,2px]{S\equiv Oxyz}$.
In Figure 2 we build two systems $\bbox[#E0E0E0,2px]{\Sigma\equiv K\rm{uvw}}$ and $\bbox[#99FFFF,2px]{\Sigma'\equiv K'\rm{u'v'w'}}$ as shown therein.
The sy... | {
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If a electrical current can induce a magnetic field, can the reverse be true? From my GCSE studies, near to the end of a module, I was told that when an electrical current flows through a conductor, a magnetic field will be induced. Can a magnetic field create an electrical current?
I ask this because I hear about "fre... | A stationary magnet will not induce a current, but a magnet that is moving will induce a current
Currents are induced by the time derivative of the magnetic field (see faradays law) EM induction
Now there is the fun idea of relativity in that everything is in relative motion so viewed from a moving frame you will see a... | {
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Measuring different components of spin simultaneously I'm reading Griffiths Introduction to QM and I'm having trouble understanding why you can't simultaneously measure the x,y and z components of spin. I know that the uncertainty principle prevents this but I still don't see why.
Griffiths' example is that if we have ... | Mutually non-commuting operators cannot have simultaneous eigenstates, namely the eigenstates of the former must by all means be expressed as a linear combinations of (all) the eigenstates of the latter. In the case at hand, given ${|+\rangle}_z$ as eigenstate of the operator $S_z$, the following must hold:
$$
{|+\rang... | {
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Can an inhabitant of a spacetime region measure its curvature tensor? So, lets say that I am an ant living on a 2-D spherical surface that is stretching to the equator...like half a sphere. I can not describe this surface in terms of the outside coordinates only someone living in the outside world can do this. So, can ... | So as I was going through smart stuff of general relativity, still confused with this problem of detecting the curvature I realised how not very smart I was. In my question I am confused because I think that the stick shoul shrink as unit distance of a coordinate shrinks but of course it wont....sphere does not care if... | {
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Why can we see the moon when it is between the Earth and the Sun? A rather stupid question, why can we see the moon when it is between the Earth and the Sun?
| The moon circles around the earth, so half the time it is between the earth and the sun and half the time the earth is between the sun and the moon.
Therefore also the moon rises and sets, the same way the sun rises and sets.
If it's midnight (your are on the opposite site of the earth than the sun) and the moon is bet... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "17",
"answer_count": 6,
"answer_id": 5
} |
Extension of Schrödinger's cat thought experiment My question is quite simple. In the thought experiment of Schroedinger's cat: When the scientist measures the state of the cat, its wavefunction collapses into either the alive or dead state. But wouldn't then the scientist in turn be in a superposition of measuring dea... | This is an excellent question and stresses one of the weird features of quantum mechanics.
Indeed, the scientist would in turn be in a superposition. And we could even measure this if we'd be able to maintain coherence of such large systems.
Ultimately, your question is asking for the solution of the Measurement probl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/266606",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "46",
"answer_count": 9,
"answer_id": 1
} |
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