Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What is the point of a voltage divider if you can't drive anything with it? The voltage divider formula is only valid if there is no current drawn across the output voltage, so how could they be used practically? Since using the voltage for anything would require drawing current, that would invalidate the formula. So w... | As an alternative to using a high-input-impedance device like a comparator or op-amp attached to the division point, one can instead use a low-impedance device that draws zero current at its operating point. For example, a Wheatstone Bridge connects a galvanometer (a sensitive low-impedance current detector) between t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567978",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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"answer_id": 5
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Discrete Harmonic Oscillator matrix representation of $x$ for Quantum Simulation (The paper I'm referring to in this question is "Quantum simulations of one dimensional quantum systems")
I've been trying to understand the paper above, specifically on constructing a matrix representation of the position operator, $\hat{... | I think this is it: It seems like we can treat $X$ as the Fourier transform of $p$ to explain the factors.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Relative Velocity of two particles If two particle are neither approaching towards nor receding away from other then their relative velocity is non zero.
How is this possible??
| The answer lies in your question itself. The two particles neither approach each other i.e. their separation isn't decreasing, nor are they moving apart i.e. their separation isn't increasing
In other words with respect to both the particles, the separation between them is not changing. Relative velocity is given as th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Enthalpy during compression of water What happens to the temperature of water when compressed?
Enthalpy $H = U + PV$.
$H$ is conserved in a closed system. By which I mean adiabatic and negligible external work applied.
We compress a litre of water to 10 bar (say). This requires negligible work because water is almost... | For control masses at constant volume it is common to analyse them in terms of the internal energy; the enthalpy is commonly used for reversible isobaric control mass problems (in which the change of enthalpy is equal to the heat flux), and for open systems (such as flowing fluids). The reason for the latter can be see... | {
"language": "en",
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Why didn't heavier elements settle at the core of the solar system? As the solar system formed, why didn't all of the heavier elements such as iron, collect where the sun is leaving the lighter elements in the outer solar system?
| This question is tantamount to asking why do stellar systems, galaxies, and even planet-moon systems have a spatial extent as opposed to forming centralized blobs of decreasing density radially. The answer lies in the fact that all these objects have a rotational motion that spreads the mass outward, with the occasiona... | {
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Derivation for optical path length and the origins of the formula So I've learnt that the formula for optical path length is $OPL = ns$, where $n$ is refractive index of the medium and $s$ is its geometrical length, the problem is i cant really get around this formula like where does it come from? I tried deriving it b... | The quantity $ns$ has a physical meaning. I think that's what you're trying to figure out. If light travels a distance $s$ through a medium with refractive index $n$ in a time $T$, then the distance light would travel in the same time $T$ in a vacuum would be $ns$.
$$T = \frac{s}{v} = \frac{ns}{c}$$
and so the distance... | {
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Different variations of covariant derivative product rule This is a follow-up question to the accepted answer to this question: Leibniz Rule for Covariant derivatives
The standard Leibniz rule for covariant derivatives is $$\nabla(T\otimes S)=\nabla T\otimes S+T\otimes\nabla S$$
so for $T\otimes\omega\otimes Y$ this wo... | Are you just rearraging the backets? If so remember that
the temsor product is defined to be associative: $ (a\otimes b) \otimes c= a\otimes (b \otimes c)$, so we can write eiher form as simply $a\otimes b \otimes c$.
If you are referring to replacing $\nabla$ by $\nabla_X$ remember that $\nabla$ is always $\nabla_X$ f... | {
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What is the maximum deflection angle of a pendulum in a car, when the car, initially at rest, accelerates suddenly? I was doing Kleppner-D.-Kolenkow-R.J. and I came across the following problem:-
A pendulum is tied vertically to a car at rest, the car suddenly accelerates at a rate A. Find the maximum angle of deflect... | Work done by tension in car's frame of reference would be zero. Then we can apply conservation of energy where initial and final kinetic would be zero(since at start it didn't have any energy) then use pseudo force's work equal to work done by gravity. We get answer $$\theta = 2\arctan(\frac{a}{g})$$ (where $\arctan$ i... | {
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Relativity without constancy of light speed Using homogeneity of space, isotropy of space and the principle of relativity (without the constancy of light speed), one can derive:
$$x' = \frac{x-vt}{\sqrt{1+\kappa v^2}}$$
$$t' = \frac{t+\kappa vx}{\sqrt{1+\kappa v^2}}$$
$\kappa = 0$ denotes Galilean and $\kappa < 0$ deno... | As said in the answer of @m4r35n357 it is the case of Euclidean geometry. To see this, look at the transformations, that preserve the distance : $$ds^2 = dx^2 + dt^2$$
Among with the translations there are also rotations:
$$
\begin{pmatrix}
t^{'} \\
x^{'}
\end{pmatrix} =
\begin{pmatrix}
\cos \theta & \sin \theta \\
-\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/571339",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Will objects that go beyond the cosmological event horizon eventually vanish from sight? Suppose a galaxy is headed beyond the cosmological event horizon. Photons it emits now will eventually reach us, but there is a point at which photons will no longer be able to reach us.
Supposing that a finite number of photons ar... | Sources that say that the light is redshifted into the indefinite future are talking about classical cosmology and not considering quantum effects.
Quantum mechanically, as you say, the galaxy emits only finitely many photons before crossing the horizon and so there should be a last photon – although I should qualify t... | {
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Why can't photons cancel each other? The textbook argument against photons canceling each other draws upon the conservation of energy. Does this mean that energy conservation is a "stronger" principle than superposition? Waves in other media than the EM field, e.g., sound or water, do cancel out---presumably by passing... | All waves traveling through a medium don't cancel out. Sound waves, water waves, waves in a rope, etc. pass each other and travel further after they have passed. They don't (or almost not) exchange energy with the medium (like being converted to heat, though there is dampening). Two oppositely traveling waves may seem ... | {
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Screened Coulomb potential in metals One of the reasons why we can neglect electron-electron interactions in metals is the fact that their coulomb interaction is screened. I'm confused about the nature of this screening. In the literature the process is usually described like this:
If we bring an additional charge insi... | Maybe not very useful regarding you question, but other way to see why e-e interactions in a metal can be neglected is by comparing typical kinetic to potential energy.
$ E_F = \hbar^2k_F^2/2m$ and $U_{e-e} = e^2/{4\pi\epsilon_0d}$.
Using the free electron relation $k_F = (3\pi^2n)^{1/3}$ and $d^{-1} \approx n^{1/3}$ y... | {
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Terrell-Penrose effect and surface reflectance All explanations of Terrell-Penrose effect seem imply that the effect makes some of the back-facing walls of a passing-by object visible. You can see some examples of those in many different references. However, from my understanding many of those sources assume that the l... | Concentrate on the nearest top die on the right. The reason you can see the "four" face is that you have already passed the "one" face of the die! It is just that aberration has distorted the image to place it in front of you.
There is nothing more to "Terrell Rotation" than this simple fact.
You can find a more comp... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is the purpose of the roll maneuver on a rocket? I have watched several videos on both rocket launches, ballistic missile launches, even a really cool one by Northrup Grumman on launching a nuclear missile.
(https://www.youtube.com/watch?v=HWZXinRwCaE)
I understand why missiles have a pitch maneuver. I have watch... | When I was teaching physics, one of my students was an intern at NASA. I asked him the specific question of why the space shuttle performed the roll maneuver. He talked to NASA personnel, and reported to me that the maneuver was performed in order to turn the shuttle antenna towards the ground so the astronauts could... | {
"language": "en",
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Why is maximal kinetic energy lost in a perfectly inelastic collision? A perfectly inelastic collision is one where both of the colliding objects stick together and move as one.
My question is, why, of all possible combinations of final velocities that conserve momentum, does this one lead to the greatest loss in kinet... | If you don't want calculus and need a physical interpretation, here's one:-
Meaning of inelastic collision is some energy of collision transforms into potential energy, either by changing shape or heat or sound etc.
So, in a perfect inelastic collision, the maximum amount of energy is converted into potential energy. A... | {
"language": "en",
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What is the difference between the specific heat capacities of water under isobaric and isochoric conditions Can the difference of specific heat capacity of water under isochoric and isobaric conditions be explained in terms of the internal energy of the system? Most of the videos I have watched base their explanation ... | In general it is the same idea as with ideal gases. This here is not what is formal answer, because specific heat is generally defined with entalpy and internal energy. This is rather the explanation, why there is a difference.
In order to change volume $V$ when the pressure is constant, some work $A$ has to be provide... | {
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Confusion in definition of emf The emf of a cell is defined as the work done per unit positive charge in taking it around the complete circuit of the cell (i.e. in the wire outside the cell and the electrolyte within the cell). But Kirchoff's Second Rule states that the work done in moving a charge around a closed loop... |
Electromotive force is the electrical work done to move a unit positive charge from the positive electrode to the negative electrode. It is not about moving the charge through the whole circuit. It is basically the potential difference between the electrodes when no current is flowing.
But according to Kirchoff’s Seco... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/573032",
"timestamp": "2023-03-29T00:00:00",
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Black Hole Formation If you plot a space-time diagram of an object falling through the event horizon of a black hole, and draw the past and future "light cones" of the object at every point, wouldn't the point infinitely to the event horizon have a light cone which allows light being radiated by the object to reach an ... | You are not wrong. If we could live forever, and if we could observe indefinitely small light energies, we would observe the light from material falling into to a forming black hole forever. Because time appears to stop at the Schwarzschild radius, an issue is raised as to whether a singularity can actually form. In 19... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is the electromotive force (EMF) highest in the loop when $\theta$ = $90$? My question is in regard of the following snippet provided by my textbook.
So why is the electromotive force (EMF) highest in the loop when $\theta$ = $90$ or $270$?
So the magnitude of the induced EMF will be determined by the rate at whic... | *
*The level magnets are exherting their normal N - pole and S - pole magnetic fields.
*As the loop wire moves into 90*, the electric current going through the loop is also generating a secondary electro-magnetic field.
*The interaction and clash between the 2 magnetic fields is the highest as the loop wire electr... | {
"language": "en",
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How is melting time affected by flow rate and temperature of surroundings? Suppose you have a solid sphere of m, where m is an element with freezing point of 0 degrees Celsius.
In one scenario, you place your sphere in a (“static”) 25 degree Celsius environment and measure time, t, until melting. The sphere is fixed an... | For the first case the differential equation for evolution of temperature of the sphere
$$
m * C_p * \frac{dT_m}{dt} = h_{nat} (T_{amb} - T_s) \\
$$
$$
\begin{array}
\text{where} \\
m & \text{mass of of the sphere} \\
C_p & \text{Specific heat of the solid} \\
T_m & \text{Mean tempera... | {
"language": "en",
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Can a single-slit experiment demonstrate the particle nature of light? Young's two-slit experiment is generally credited for demonstrating the wave nature of light. But what about a similar experiment with just one slit? My understanding is that this will create an interference pattern. Shouldn't that be enough to demo... | Actually it proves the wave theory. If the slit is narrow enough, then the light would diffract, which cannot be explained using particle nature, rather wave nature has to be used to explain diffraction, so it would actually prove the wave nature of light.
| {
"language": "en",
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Why does energy come in the form of packets? Photons are the packets of energy released by continuous oscillation of charges.
But I have some questions about this.
Since the electrons oscillate regularly while transitioning between orbitals then why is the energy released in the form of packets and not continuously in... | The straight answer is that nobody knows why. We only know how.
By how I mean that we have accurate methods to predict experimental numbers. We can solve wave equations with advanced methods, as in quantum chemistry, and add on QED radiative corrections, for example.
So we know how but not why wave equations account, a... | {
"language": "en",
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Why is QED renormalizable? My understanding of renormalizability is that a theory is renormalizable if it the divergences in its amplitudes can be cancelled out by finitely many terms. I see that by adding counterterm (in the MS-bar scheme)
$$L_{ct}=-\frac{g^2}{12\pi^2}\left(\frac{2}{\epsilon}-\gamma+\ln4\pi\right),$$
... | QED has only a finite number of irreducible divergent diagrams. The main notion of divergence of a diagram is power-counting: The term every diagram represents has the form of a fraction like
$$ \frac{\int\mathrm{d}^n p_1\dots\int\mathrm{d}^n p_m}{p_1^{i_1}\dots p_k^{i_k}}$$
and you can compute the difference between t... | {
"language": "en",
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When did the Big Bang happen? Did the Big Bang happen at a point? goes through the fact that the Big Bang happened everywhere at the same time. John Rennie's answer explains this as being a consequence of all points in space beings squished into a single point, so technically the Big Bang happened everywhere. But, when... | No, the Big Bang did not happen at all points in time. It happened at one point in time, approximately 13.8 billion years ago. As you already know, the Big Bang was not an explosion in space, it was an explosion of space. However, the same is not true of time. (But if you're interested in the idea of an explosion encom... | {
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Why does the spring constant not depend on the mass of the object attached? It is said that:
$$ F = -m\omega^2 x = -kx, $$
so $k=m\omega^2$. Since $k$ is the spring constant it doesn't depend on the mass of the object attached to it, but here $m$ signifies the mass of the object. Then how is $k$ independent of the mass... | $\omega$ isn't a constant of the spring, but it actually depends on the mass you attach to the spring. $\omega$ refers to the frequency of oscillation of the attached mass. The formula for $\omega$ for an attached mass $m$ is $\sqrt{\frac{k}{m}}$, where $k$ is the spring constant. If you use $\omega=\sqrt{\frac{k}{m}}$... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Phase velocity in monatomic chain When considering a one-dimensional monatomic chain of atoms (identical masses $m$ & spring constant $\kappa$), one finds the following dispersion:
$$ \omega(k) = \sqrt\frac{\kappa}{m}\cdot\left|\sin\left(\frac{ka}{2}\right)\right|\, ,$$
which is $\frac{2\mathrm{\pi}}{a}$-periodic. So w... | The phase velocity is kind of meaningless outside the first Brillouin zone. The phase velocity is the speed that the "crest" of a wave travels, but outside the first Brillouin zone, the wavelength is less than the spacing between atoms, so there aren't really crests; most "crests" occur in the gaps between the atoms wh... | {
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Why do electrons flow in the opposite direction to current? I'm 15 and just had a question about physics and electric fields.
I've read that electrons flow in the opposite direction to current. Isn't current the flow of negative charge and therefore the flow of electrons?
Or are they referring to conventional current?... | By 'current' we normally mean electrical (also called conventional) current, i.e. the amount of electrical charge that is passing a given point in the circuit at any given time.
If a positive charge carrier (say, a 'hole' in a semiconductor) passes from left to right, then that counts the charge $q$ to the current, ove... | {
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Continuity equation in quantum mechanics - Verification Sakurai 2.7.30 I am trying to verify Equation 2.7.30 from Sakurai's "Modern Quantum Mechanics" 2ed. The bottom line of my question is:
$?? \psi^{*}\vec{A}\cdot\nabla\psi+\psi\vec{A}\cdot\nabla\psi^{*}=0 ?? $
And here is how I arrived at it. Below, all equations st... | There should be a factor of 2 in the equation $d\rho /dt=...$ since $ \nabla (\bar{A} \psi) + \bar{A} \nabla\psi = 2 \bar{A} \nabla \psi $ since we can impose $\nabla \bar{A}=0$. Hope it can be helpful :)
| {
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Is my understanding of how a force is applied through a string correct? Let there be a situation where a force 'F' is acting on one end of an in extensible string which is connected to a box named 'A' resting on a friction less horizontal surface through the other end.
The Force F is transmitted through the string and... | There is a mistake in modeling the system. Indeed, the string is not a rigid body and you can't use the rigid body equations of motion and to be expecting that they will work. You consider, for example, in place of the string, a rigid thin (metallic) rod. In this case, you can consider the box and the rod as a unique r... | {
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Reason for peaks in graph of binding energy per nucleon A similar question was asked before, but it asked for a different thing. My question here is: What is the reason for spikes in this graph? The graph initially has spikes and then shows a constant decrease. Is it related to something called magic numbers as it is s... | It has to be with the pairing term. Nature likes even-even pairs of nucleons. I mean, an even number of protons and an even number of protons. The reason is ultimately related to spin couplings.
So, odd-even pairs are more or less over the curve. Even-even isotopes, like $C^6$, or $O^18$, are especially stable. On the ... | {
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Energy Conservation in Rolling without Slipping Scenario
A solid ball with mass $M$ and radius $R$ is placed on a table and given a sharp impulse so that its center of mass initially moves with velocity $v_o$, with no rolling. The ball has a friction coefficient (both kinetic and static) $μ$ with the table. How far do... | *
*since it's rolling without slipping the friction (static) won't affect the energy , so yes energy is conserved.
*here is a good demonstration https://www.youtube.com/watch?v=hxa6jAYA980 about similar case , after applying delta k= w ( transltaion )the forces you have are( only weight because again the friction yo... | {
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Young Modulus in Finn's Thermal Physics In Finn's Thermal Physics (equation 2.4), the Young modulus $Y$ of a stretched wire with tension $F$ is given to be
$$Y = \frac{L}{A} \left( \frac{\partial F}{\partial L}\right)_T$$
However, usually the Young modulus is defined to be the ratio of stress and strain, specifically
$... | When assuming infinitesimal strains, one can use either $Y=\frac{L}{A}\left(\frac{\partial F}{\partial L}\right)_T$ or $Y=\frac{L_0}{A}\left(\frac{\partial F}{\partial L}\right)_T$, depending on what's convenient; the difference is negligible. The former is related to the definition of the true strain $e$ from $de=dL/L... | {
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Does Energy & Momentum also Dilate & Contract respectively? Does energy and momentum also dilate and contract as time and length do respectively, since energy and time and momentum and length are complementary quantities both in relativity & QM?
| Energy and momentum together form a "four vector" just like time and space do. So we find that $(E/c,p_x,p_y,p_z)$ transforms the same way that $(c t, x, y, z)$ transforms. However, time dilation and length contraction are more specific.
Time dilation is the time in a "moving" frame for a clock which is not moving in t... | {
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Why do fluids not accelerate? A fluid flowing in a horizontal pipe must be flowing at a constant velocity because of the conservation of mass.
However, considering how there would be a pressure and hence force acting behind the fluid, for it to have a constant velocity, there must be an equal force slowing it down (dep... | Once into the pipe, there is no net acceleration (before it leaves the pipe), $ma=0$. But you have significant viscous sheering. This creates resistance to flow. Similar to drag. Viscous friction.
The only force driving flow from point A in the pipe to nearby point B in the pipe is the pressure gradient.
$$F= A ~\Delta... | {
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Artificial Muscle | Is Electromagnetic Attraction Better then Maxwell Stress? I was watching a TED-talk on artificial muscle, HASEL, where the inventor demos that an insulated oil in the presence of electric potential field gets displaced due to induced Maxwell stress. In other words, electric potential gets converted ... | Short answer "No" HASEL is not more efficient then electromagnetic actuaturs.
The following is taken from their paper:
Peak specific power during contraction of the two-unit actuator was 614 W/kg; specific work during contraction was 70 J/kg (fig. S12) (24). The measured peak specific power is double that of natural m... | {
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Can rolling without slipping occur without friction? If a body is rolling without slipping is it necessary that there is friction acting on it ? I encountered a question in which there is a spherical body and a force is being applied on its top point ...so if there is only force then it should do translation motion on... | If there is no frictional force between an object and the surface it is moving on, then there will be no relationship (or connection) between the rate (or direction) of rotation and the translational velocity. If a horizontal force is applied to the top of a sphere on a friction-less surface, it will cause (independen... | {
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Energy transfer between oscillators Suppose I have two mechanical oscillators $a(t), b(t)$, coupled through the interaction $V_\text{int} = \mu^2 a(t) b(t)$. Is there a simple way to express the rate of energy transfer from $a$ to $b$ using only $V_\text{int}$? Something like $\partial_t V_\text{int}$ would have the co... | The answer is actually extremely simple. The power transfer between oscillators is just the time derivative of the work done on $a$ by $b$, minus the work done by $b$ on $a$
\begin{align}
P &= \frac{dW_{a\to b} - dW_{b\to a}}{d t}\,,\\
W_{a\to b}-W_{b\to a}&=\int{\rm d}a \partial_b V_\text{int} - \int{\rm d}b \partial_... | {
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Do elementary particles last forever? I have heard that not even black holes last forever, because of Hawking radiation. But what about elementary particles? Will an electron, for example, exist for all time?
| The electron, an elementary particle, is the least massive carrier of negative EM charge currently known. If it would decay, it would involve the production of lower mass particles (such as the neutrino), but all known particles with lower rest mass have no EM charge.
https://en.wikipedia.org/wiki/Electron
Thus, during... | {
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Probability of measuring state $|+\rangle$ and state $|-\rangle$ given a state and a basis I am given a basis $|+\rangle = \frac{1}{\sqrt 2}(|0\rangle + |1\rangle)$ and $|-\rangle = \frac{1}{\sqrt 2}(|0\rangle - |1\rangle)$ and i am given a three qubit state $|\phi\rangle = \frac{1}{\sqrt 3}|1\rangle |0\rangle |1\rangl... | Step 1: Notice that $\vert 0\rangle = \frac{1}{\sqrt{2}}(\vert +\rangle + \vert - \rangle)$ and $\vert 1\rangle = \frac{1}{\sqrt{2}}(\vert +\rangle - \vert - \rangle)$.
Step 2: Expand $\vert\phi\rangle = \frac{1}{\sqrt 3}\vert 1\rangle \vert0\rangle \vert1\rangle + \frac{\sqrt{2}}{\sqrt 3}\vert0\rangle \vert1\rangle \v... | {
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Why are voltage and volt both are denoted by $V$? Why are voltage and volt both are denoted by $V$? Won't it cause confusion?
| Volt is the unit of measurement of Voltage. There's no possible confusion. The voltage is the physical quantity that we measure, using a multimeter for example, and the result of that measurement is given in Volts.
If you have a 9V battery you're implicitly saying that if you measure the voltage across the leads of the... | {
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Transformers: How does current in primary coil change? I was doing a question on transformers and found this really confusing question:
A 100% efficient transformer converts a 240V input voltage to a 12V
output voltage. The output power of the transformer can be a maximum
of 20W. The output is connected to two 0.30A b... | The 20 W is a maximum rating for the transformer and is of no concern unless it is exceeded. At 100% efficiency the power in equals the power out. In this case the power out (7.2 W) gets cut in half, so the current in (0.03 A) will also be cut in half.
| {
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The Cause of lightning and charge distribution in clouds I was going through this video about lightning and I couldn't understand some points .
1: What caused the water molecules in ice crystals to be arranged in that specific pattern i.e. having positive charges at its boundary and negative in the inner region ?
2: ... | Assuming that the lightning occurs at the boundary or near boundary between the region of sky experiencing cold weather and the region of sky experiencing warm or hot weather, winds from the warmer side tends to move to the cold side. I'm the same manner, wind from the cold side moves towards the warmer side. When thes... | {
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Are distributions of position and momentum assumed to be independent in quantum mechanics? Given a wave-function of a single particle we can calculate probability density for positions. We can also calculate probability density for momenta. Are these probability densities assumed to be always independent?
Or, in other ... | Any real world position measurement result also implicitly includes a momentum measurement. Why? Any measurement of x results in some psi(x), its Fourier transform is psi(p), both are measurement results and quantum states, they are simply represented in different bases and have inversely related widths, neither width ... | {
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Why does metal change its color under polarized light? I've taken two photos of a metal in an experimental setup.
The first image shows the metal illuminated by a halogen-lamp from above. The second image shows the same metal illuminated by the same lamp but there are two additions: There is a linear-polarizing filte... | Let's look at the frequency distribution of a halogen lamp:
You can see that all frequencies are present (hence the white color). The temperature of the burning lamp is about $800$ Kelvin. If you polarize the beam nothing, in particular, should happen because the photons have a random distribution of polarization. The... | {
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Maximizing entropy with Lagrange multipliers This is a problem I saw in a stat mech textbook, and I think it is a fairly common problem.
Given the entropy function: $$S = - \sum_{i=1}^N p_i \log p_i$$
Maximize $S$ subject to constraints:
$$ \sum_{i=1}^N p_i = 1 \\ \sum_{i=1}^N p_i e_i = c$$
It was suggested to solve th... | You cannot solve for $\mu$ unless you know the $e_i$'s. But that shouldn't bother you, because in the context of the canonical ensemble, $\mu$ is defined to be the (inverse) temperature, and all quantities are written in terms of it. $c$ is the expected energy for a given $\mu$.
| {
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What is the centripetal force when instead of a mass point we have a physical rotating body? I was wondering what is the centripetal force of a body rotating in a circular motion. I know that the centripetal force of a point mass is $mv^2/r$. I only have done an introductory physics class so I can not find the answer.
| Centripetal force is the force which keeps a body on a circular path. It is not a new force.
Any force that acts towards the center of that circular path is your centripetal force. For example in case of earth and sun , the gravitational force is the centripetal force on the earth and it is just
$ mg = \frac{mv^2}{r} $... | {
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Application of Noether Theorem I attempt to understand one of the examples of the application of Noether theorem given in Peskin & Schroeder's An Introduction to Quantum Field Theory (Page no. 18, Student Economy Edition). The relevant portion of the text is given below.
If I understand the derivation and the correspo... | For what it's worth, it is very important at which stage one uses Euler-Lagrange (EL) equations in an application of Noether's (first) theorem. Noether's first theorem has 2 sides:
*
*Input: A global off-shell$^1$ (quasi)symmetry. Here one should not use EOM. (An on-shell symmetry is a vacuous notion, because wheneve... | {
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Why do electric field lines curve at the edges of a uniform electric field? I see a lot of images, including one in my textbook, like this one, where at the ends of a uniform field, field lines curve.
However, I know that field lines are perpendicular to the surface. The only case I see them curving is when drawing fi... | I have taken your image and created a few additional field lines at one end of the plates in the first diagram below.
When you come to the ends of the plates, the field starts to resemble that associated with two point charges instead of a sheet of charge. The second diagram below shows the field lines between two poin... | {
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Would an atomic bomb detonate a uranium stockpile? If a uranium atomic bomb directly hit a stockpile of weapons grade uranium, would the chain reaction also detonate the stockpile?
what about a stockpile of nuclear reactor fuel rods?
what about a stockpile of various nuclear weapons?
what about a plutonium bomb or a hy... | If the chunk of fissile material that the atomic bomb explodes close to is subcritical then the neutron flux from the bomb will trigger fissions and energy release in that material but as soon as the neutron burst is over, those fissions will die out and stop; no chain reaction will result. The material may melt down a... | {
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"source": "stackexchange",
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Particle as wave, stable? I've started reading about the wave-particle duality but, after a few steps, reached a dead end:
*
*Schrodinger equation solutions for a free particle is a sum of terms of the form:
$$\psi(\mathbf{r}, t) = Ae^{i(\mathbf{k}\cdot\mathbf{r}-\omega t)}$$
however, a single element of this form c... | The solutions of the Schroedinger equation (SE) are not "particles." They are wave functions. (More precisely, a wave function can be written as a normalizable superposition of the solutions of the SE.) The modulus square of a wave function gives a probability distribution to observe a particle at a specific point. Thi... | {
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A photon scatters an electron at an angle... Does it imply electron having an area greater then the photon's? Even we don't know much about scattering areas of photons and electrons does the fact that a photon scattering an electron at an angle mean that the photon cross-section area hits only a small lateral area of t... | I think the question is based on a very mechanistic idea of scattering. IN reality what is important is energy and momentum conservation. Assuming for simplicity a non-relativistic electron, this means
$$
\frac{p_i^2}{2m} + \hbar ck_i = \frac{p_f^2}{2m} + \hbar ck_f,\\
\mathbf{p}_i + \hbar\mathbf{k}_i = \mathbf{p}_f + ... | {
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Kinematics: rest and motion A ball is dropped from a height of 19.6 m above the ground. It rebounds from the ground and raises itself up to the same height. Take the starting point is the origin and vertically downward as the positie X-axis. Draw approximate plots of a versus t graph. Neglect the small interval during ... | The acceleration points downwards when the object is moving freely, no matter if rising or falling (its gravity what accelerates it, and gravity points to the ground, doesn't it?) The only time when acceleration is not $g$ is when the object is not falling/rising freely, this is when it is in contact with the ground.
| {
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Will a plastic feel less heavy when I put it in a bucket of water and carry it? If I'm carrying a bucket of water in one hand and a piece of plastic in the other, and then I decide to keep the plastic in the bucket of water (it floats). Will it feel less heavy in the second case?
I think it will feel the same because i... | Fluids, like all objects, obey Newton's Third Law. This means that any upward buoyant force exerted on the plastic by the fluid has a counterpart downward force exerted on the fluid by the plastic. The force you must exert on the bucket & the fluid to keep it from falling is therefore increased by the amount of the b... | {
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Force exerted by blocks on an angled rail I'm trying to figure out the force exerted on blocks positioned on an angled rail due to gravity. This is the scenario I have (apologies for the poor graphic):
where each block (red square) is equipped with a wheel (black circle) which is fitted on a rail (black lines). The to... | I think the force exerted on the bottom wheel is just the vertical component of your force diagram i.e. $2mg + mg \sin^2 (50^o)$.
The top block exerts a force $mg \sin (50^o)$ on the middle block along the line of the upper part of the track, but the horizontal component of this is opposed by an equal and opposite hori... | {
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How do forces 'know' they need to move when a system is in motion? I am curious as to how forces move when a system is in motion. This was never fully explained in my physics classes at university. Let me explain:
I understand the Newtonian (classical) physics that there are equal and opposite forces in play. So when ... | Assumptions
Energy is conserved
Static forces are all relative potential energy.
Zero motion (macro) is a system in equilibrium.
Change in position required human energy, but net forces (due to F=mg) never changed.
Only the % of total force shared by each foot changed.
Mass did not change
gravity, g did not change.
Hum... | {
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Properties of conductors If there is a cavity inside a conductor and a charge is placed within it then what exactly happens?
I've read in one book that the charge in the cavity induces a charge (the induced charge is opposite in nature obviously) on the outer surface surface of the cavity. Here is the exact picture. (I... |
So which diagram and explanation is correct?
Both of them are correct. They just are drawn in different ways.
Figure 1 shows how the positive charge in the middle attracts electrons in the conductor around it. The minuses, representing a negative charge (electrons), are drawn onto the conductor. It leaves out the fac... | {
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What does $\hat{\phi}$ mean in cylindrical coordinates? When talking about the unit vectors in cylindrical coordinates, $\hat{\phi}$ often comes up. However, I cannot find a straightforward meaning for it. However, I do know that it is perpendicular to $\hat{\rho}$. How is that significant?
| If you're giving a thumbs-up with your right hand with your fingers loosely curled, and your thumb is pointing along $\hat{z}$, then your other fingers are curled along $\hat{\phi}$.
| {
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Is it possible to bend light without changing its color? It seems to me that whenever you change the direction of a wave it also affects frequency. Would this not also be true of light waves bending from, for example, gravity?
| No, it doesn't, as the comments point out.
You might possibly be confusing the change in wavelength when the light is inside the "bending material" such as a glass lens. However, upon exiting the lens -- or the localized gravitational field -- the light, now moving in a new direction, retains its vacuum wavelength. T... | {
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Charge on the plate of the capacitor I was reading parallel plate capacitors in my book today and there I saw that the battery provides +Q charge to positive plate and -Q charge to negative plate? But we know that only electrons can flow so the battery should provide only -Q charge right?
Is it that, the electrons flow... | You have got the right idea. When a circuit consisting of a battery and capacitor is switched on, the electrons from the negative terminal start accumulating on the capacitor plate. The negative capacitor plate induces an equal and opposite charge on the other capacitor plate. Together, an electric field is created and... | {
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Electric field inside charged non-conducting spherical shell In class we had an exercise, where for a non-conductiong spherical shell given a potential inside and out we had to find a charge distribution and E field inside and out, with a charge distribution $\sigma =Q\cos\theta$, so the sphere is kind of like a charge... | For any closed surface, Gauss's law states
$$ \oint \textbf{E} \cdot d\textbf{a} = Q_{enc} / \epsilon_0 $$
Applying the divergence theorem to the left side of the above leads to
$$ \int_{volume} ( \nabla \cdot E ) \ dV = \oint \textbf{E} \cdot d\textbf{a} $$
and rewriting the right hand term in terms of the charge dens... | {
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Why are the capacitors in this circuit in parallel but not in series?
In the circuit, the capacitors are said to be connected in parallel. Why is that so?
Edit: The switch will be closed and C2 is fully charged by C1 and no more current will flow between C1 and C2. The question asks for the voltages and charges hold b... | I assume that this is an example where one charged capacitor charges another after the switch ic closed.
The main use of assigning the labels series or parallel to capacitors (and other circuit elements) is to decide which combination rule to use to find the effective capacitance of a number of capacitors.
The derivati... | {
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Expansion in flat spacetime I have been studying Raychaudhuri equation and focusing theorem related to it. Focusing theorem says that if the strong energy condition is satisfied and rotation tensor vanishes $\omega_{ab}$=0 then rate of expansion is negative. Frobenius theorem for timelike vector says that timelike geod... | In flat spacetime, let $(t,x,y,z)$ be a global inertial cartesian coordinate system. Then the lines with $x,y,z$ fixed are orthogonal to the hypersurfaces of constant $t$.
This is the simplest case possible: trajectories of infinitely many inertial observers in rest relative to each other.
If you apply Raychaudhuri to ... | {
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What is the polarization of an EM wave after it suffers scattering? If a linearly polarized classical monochromatic electromagnetic radiation undergoes a scattering, does the scattered electric field have the same polarization as the incident electric field? I am looking for an answer (or deduce the conclusion mathemat... | This is a huge subject in radar and it has a vast literature but there are no simple answers besides that depolarization (i.e., the generation of the orthogonal polarized reflected/scattered wave) is dependent on frequency, incident angle, statistics of the reflecting surface, etc. I only mention here one application, ... | {
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Earth doesn't have seafloor craters. Does it mean water has been on Earth since long time before in the past? Is it true that Earth didn't get its water by cometes impacts as there are no subocean craters so it seems water acted as a comete bumper long before in the past?
| Because the sea floor is continually being renewed through spreading and subduction, most of the sea floor is no older than something like ~250 million years. Also note that meteor impacts were much more common longer ago than that than they are today, which means that almost all of the marine impact craters have been ... | {
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Why is the mean density the same for all nuclei? Tell me if this is a correct theory? So the radius $R$ of the nucleus is directly proportional to $A^{1/3}$ (the nucleon number).
As $$V = \frac 43 \pi r^3,$$ this makes $V$ directly proportional to $R^2$. Also, as the nucleon number increases, the mass also increases an... | Yes, the nuclear density is approximately constant with nucleon number. Expanding on Vadim's answer, perhaps I can explain why this is somewhat intuitive.
Nucleons are held together by the residual strong force, which is attractive between nucleons and mediated by massive pions. As as result, it has limited range such ... | {
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How is it possible for the same force to do different amounts of work in two different inertial frames? Consider an object which has been given a speed $v$ on a rough horizontal surface. As time passes, the object covers a distance $l$ until it stops because of friction. Now,
Initial kinetic energy = $\frac{1}2mv^2$
A... | The coefficient of friction is the same in both cases. You have assumed the distance traveled to be the same in both cases, which is why you are getting different values for $\alpha$. Your other questions have been cleared in many answers above, so I just wanted to mention this point.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/580579",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "29",
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When is a quantum state pure and when mixed? Every definition of the two is always very abstract to me. Like, A pure state is located on the surface of the bloch sphere while the mixed state is somewhere within.
First of all, what is an intuitively definition?
And second of all, how do you practically recognize whether... | A pure state is a ket in Hilbert space. A mixed state is a probabilistic mixture, which cannot be described by a single ket. The importance of the concept is illustrated in Bell tests, which show that quantum mechanics (i.e. the result of calculation using Hilbert space) cannot be replicated by classical probability th... | {
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Why are there fewer lines on the absorption spectrum than on the emission spectrum for some gases? I don't know if this is right, but I think that it is because:
*
*when the gas is heated, the electrons get 'excited' and move up to an energy level (lets say an electron moves up 4 energy levels).
*Then as they move ... | I found the answer!
So the continuous spectrum is formed is usually formed from a heated body (i.e a heated filament or a star) and when the continuous spectrum passes through a cooler gas, the electrons in the gas absorb the energy of a photon with a specific wavelength (which is why is shows black lines against a con... | {
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Magnetic, geographic and geomagnetic poles
Can someone explain me in simple terms where and what are the magnetic, geographic and geomagnetic poles?
Some sites say that magnetic north pole is in the south and thus it attracts the south pole of the magnetic needle while some say the north pole of the needle points sou... | Although an answer has been accepted, there are lots of errors and ambiguities in the above answers. First of all, when you talk about getting a local angle between the magnetic and geographic axis, that is the magnetic declination. At most points on Earth, your compass does not point to any of the North geographic pol... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Understand the total angular momentum in 2 cases I'm a little bit confused with how to understand the relationships between spin angular momentum $S$, orbital angular momentum $L$, and the total angular momentum $J$ by visualizing those quantities. Classically, if we consider the motion of the Earth, I think $S$ is its... | In this picture, both orbital and angular momenta are treated as vector. As the third case illustrates, it is perfectly possible for the sum of two vectors to be smaller in length than the length of both constituents in the sum.
This third figure would correspond roughly to the case where the rotation of the Earth abo... | {
"language": "en",
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Will energy in an LC circuit become 0 if its is disconnected when the capacitor is fully discharged? In a recent test I had a question in which there was an LC circuit with an inductor a capacitor and a switch. According to the answer key
If switch is opened when capacitor is fully charged energy of LC system remains ... |
If switch is opened when capacitor is fully charged energy of LC
system remains same.
If it's a series LC circuit, then the energy will be $E=\frac{CV^2}{2}$ all residing in the electric field of the capacitor. If it is a parallel LC circuit of an ideal inductor and capacitor, the energy will remain the same but it w... | {
"language": "en",
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Difficulty with Kallen-Lehmann spectral functions The following is for $D=4$. The correlators at a fixed point are power laws of the form $x^{-2\Delta}$, where $\Delta$ is the scaling dimension. Suppose I wish to find the nature of the spectrum at the fixed point, for which I calculate the spectral function $\rho(p^... | I answered that in
For which values of lambda the euclidean two-point function $(p^2 +m^2)^{-\lambda}$ is reflection positive
In the notations of that other question, take $m=0$ and $\lambda=\frac{D}{2}-\Delta$ where
$D=4$ is the dimension of spacetime. Note that the condition $\lambda\le 1$ amounts to the unitary boun... | {
"language": "en",
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Why is uranium's atomic weight listed as 238.02891, higher than almost all known isotopes? The vast majority of uranium is U-238, and most of the rest is U-235, U-232, U-234, etc....
So how can the averaged atomic weight be a little over 238?
| The isotope mass of uranium-238 is 238.05078826 amu, which is greater than 238. So it's not surprising that the standard atomic mass (averaged over relative abundances of all isotopes) is greater than 238 amu as well.
In fact, the masses of most heavy nuclei are greater than 1 amu per nucleon. This is because the bin... | {
"language": "en",
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Ordering ambiguity in the Feynman propagators obtained using Wick's theorem Applying Wick's theorem to a string of four field operators, $\phi_a\equiv\phi(x_a)$:
$$T(\phi_1\phi_2\phi_3\phi_4)=\{...\}, \tag{1}$$
we obtain several terms, three of which are fully contracted fields: $$\phi_1^{\bullet}\phi_2^{\bullet}\phi_3... | Mmm... For bosonic fields isn't the propagator symmetric? If so there is no ordering issue.
For fermionic fields you get a determinant or a Pfaffian instead of a hafnian or a permanent, just start with things in their original order and count the number of interchanges as you move them into adjacent pairs: a minus sign... | {
"language": "en",
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Will back emf supports flux change? In an inductor, back emf is induced as there comes flux change. It is said that back emf decreases as time passes (when inductor is just connected to DC source).
When back emf decreases current increases in inductor. Current increases flux associated with inductor.
Back emf comes ob... |
Then why and how back emf reduces?
The back emf reduces as the current increases, only because the inductor also has some parasitic resistance, and/or you've connected it in series with a resistor, so that some of the applied voltage is required to maintain the current through the resistance and isn't available to dr... | {
"language": "en",
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Proof of a uniqueness theorem in electrostatics I am trying to understand problem 3.4 in Griffiths' Introduction to Electrodynamics:
Prove that the field is uniquely determined when the charge density is given and the potential $V$ is specified on each boundary surface. Do not assume the boundaries are conductors, or ... | I think that you are assuming that $\nabla^2\phi=0$, $x\in \Omega$, and with $\phi=0$ on the boundary $\nabla\Omega$ then $\phi$ must vansish everywhere. This is kind of begging the question because it assumes that solutions to Laplace are unique. One can prove this, though, by
$$
\int_\Omega |\nabla \phi|^2... | {
"language": "en",
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Trouble solving partial differential equation with Laplacian squared I am working in extensions of General Relativity Theory and at the moment of taking the Newtonian limit of this extension theory (essentialy, mathematically speaking, this is just linearizing the field equations obtained via the variational principle,... | Take the Fourier transform of each side with
$$
h(x) = \int \tilde h(k) e^{-ikx} \frac{d^3k}{(2\pi)^3}
$$
so that
$$
\nabla^2 h(x)= \int \left\{-|k^2|\tilde h(k)\right\} e^{-ikx} \frac{d^3k}{(2\pi)^3}, \quad etc.
$$
Here $|k^2| = k_x^2+k_y^2+k_z^2$.
As (I think!)
$$
\frac{e^{-m|x|}}{4\pi r}= \int e^{ikx}\frac 1 {|k^2|... | {
"language": "en",
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Is string theory the boundary theory of M-Theory? Looking at various AdS/CFT correspondences, we find that some (n-1) dimensional field theories on the boundary of $AdS_n$ with $N=\frac{8}{n-3}$ supersymmetries are equivalent to M-Theory in $AdS_n \times S_{11-n}$.
(e.g. for $n=7$ we get 6D $N=(2,0)$ superconformal CFT... | No, AdS/CFT relates a theory of quantum gravity in d dimensions to a QFT without gravity in d-1 dimensions. M theory and string theory are both quantum gravity theories.
The holographic dual to M theory is a type of CFT called ABJM theory.
However, there is a case unrelated to holography where your suggestion is valid ... | {
"language": "en",
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Doubt on net acceleration during non-uniform circular motion During non-uniform circular motion, the direction of net acceleration is not in the direction of the centripetal acceleration, then why does a particle still move in a circular path, please explain.
|
During non uniform circular motion,the direction of net acceleration
is not in the direction of the centripetal acceleration, then why does
a particle still move in a circular path,please explain..
Assuming by "non uniform circular motion" you mean a change in speed of the particle moving in a circle, then it is beca... | {
"language": "en",
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How does information of the parent neutron star get encoded on the event horizon of a black hole? I was watching a video on a typical black hole formation from a neutron star and it suggested that the event horizon appears instantaneously at the surface of the star even as the stellar matter inside starts to converge i... | The event horizon is by definition the boundary between the black hole interior and exterior in spacetime. Any matter that starts outside the hole and ends inside it must cross the horizon at some point by definition, whether it's "founding" matter or matter that falls in later.
The horizon doesn't appear instantaneous... | {
"language": "en",
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Why does homogeneity imply $d P^{\mu} / dX^{i} = 0$ along geodesic? I'm reading the Cosmology lecture notes Daniel Baumann and there they describe the path of a freely-falling particle along a geodesic, which is denoted by the curve $X^{\mu}(\tau)$, $\tau$ being proper time and $\mu$ denoting a spacetime coordinate. Th... | First, $\frac{d}{dX^{i}}= 0$ can be considered as "generator" of displacement in $X^i$ direction so the statement $d P^{\mu}/dX^{i} = 0$ implies the velocity/momentum is independent of displacement along the $X^i$ axis, which is just the definition of homogeneity. I used quote when saying generator since Hamiltonian fo... | {
"language": "en",
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In what case can we describe forces by potential? Let's consider a particle in an $N$-dimensional space and let's assume that acceleration of this particle depends on its position. So, one can say that we have an $N$-dimensional vector field in an $N$-dimensional space (a mapping from position to acceleration)
What all... | If the force at $\vec r$, $\vec F(\vec r)$, is the gradient of a potential i.e. $\vec F = - \nabla \phi$ then $\nabla \times \vec F=0$. And vice versa, if the curl of $\vec F$ is zero everywhere then there is a potential field $\phi( \vec r)$ such that $F= -\nabla \phi$. See this Wikipedia article for more details.
| {
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Does light have a mass? Could you please argue with work and gravity? Or however you like. I just don't get it. Thanks.
A physics professor talked about if light had a mass, it should do work ($W=N\cdot m = \frac{kg\cdot m}{s^2}\cdot m$) to get out of the gravitational field. But because we somehow can see it doesn't, ... | Does light have a rest mass? No, the rest mass of a photon is zero. Is light affected by gravitational fields? Yes, because it has energy. In particular, light moving against a gravitation field does work and loses energy - we can see this because the light is red-shifted.
| {
"language": "en",
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Sand leaking out of bag and skater "A person skating on a frictionless icy surface is holding a sandbag. The sandbag has a small hole at the bottom, from which the sand starts to leak. As the sand leaks from the sandbag, the speed of the skater..."
The answer was that the speed of the skater stays the same. I thought t... | The problem is that you have to consider the full $p_{system}$ when you look at $p_{system} (t_f)$.
The full momentum of the system has to consider every part of the system for it to remain conserved, and that includes the falling sand. So really you have:
$$p_{system} (t_f) = (m_{skater} + m_{sandbag} + m_{sand}) v_f... | {
"language": "en",
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Does the oscillating electric and magnetic field of a photon generate gravitational waves? From my understanding, little as it may be, because photons have energy they warp spacetime. The energy is expressed as an oscillating electric and magnetic field. Would this mean that the energy is also oscillating and would gen... | You are correct, photons do have stress-energy and they do create their own gravitational effects, like bending spacetime.
So the idea that photons bend spacetime is part of mainstream cosmology, such as the standard Lambda-CDM model.
Do photons bend spacetime or not?
Now you are saying that the oscillating EM field ... | {
"language": "en",
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Perpetual motion: Conditions for rolling a wheel sliding on a bar This is a basic question about energy conservation and classical mechanics:
Question: Under what situations can this motion be perpetual?
*
*Without gravity and without frictions.
*Without gravity and with frictions.
*With gravity and without fri... | Look , the object in question is undergoing accelerated motion so it will create ripple in spacetime fabric . The energy will be released in the form of gravitational waves which will ultimately make it slow down .
Had there been friction the ceasing of motion would be clearly apparent. But in case of energy released d... | {
"language": "en",
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"source": "stackexchange",
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Is there any physical interpretation of the constant which is seen in the constraint curve of an adiabatic process? What is the $C$ in $ PV^{\gamma} = C$? I always saw it as a result out of the mathematical calculations that we do but I recently saw this video which made me think that the constant may have more meaning... | An adiabatic reversible process keeps the entropy the same. So adiabats are lines of constant entropy, i.e. the entropy depends on $P$ and $V$ only through the combination $PV^\gamma$.
Of course, that doesn't mean the entropy is literally $PV^\gamma$. It's a more complicated function given by the Sackur-Tetrode equatio... | {
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If objects in motion experience time differently, how does my body stay synced when I move my legs or arms? If I move my swing my arm really fast, the matter in my arm should experience time slower than the matter in my body.
So how does my body still sync with each other?
And a more general question that derives from ... | Forgive me for answering a question with a question, but what makes you think that your limbs do stay "in sync" as you put it?
Let's examine one particular molecule in your wrist. As you swing your arm, the atom of this molecule that's closer to your arm probably experiences one or two more Planck Times, and thus has a... | {
"language": "en",
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"source": "stackexchange",
"question_score": "17",
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Density of States of 1D (ideal) Fermi Gas discrepency - Missing factor? I wanted to find the density of states of a 1D ideal, noninteracting Fermi gas. My workings are below:
$$D(\epsilon) = \frac{1}{2\pi}\int_{0}^{\infty}\delta(\epsilon-\epsilon_k)dk \times2$$
$$\epsilon_k=\frac{\hbar^2k^2}{2m} \rightarrow dk=\frac{\s... | It looks to me like you're only integrating over positive values of $k$. If you want to take account of electrons going the other way, you'll need an additional factor of $2$ (which is taken care of by the polar coordinate angular integral in $>1$ dimensions).
| {
"language": "en",
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"source": "stackexchange",
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Symmetry for dipole conservation in field theory In article The Fracton Gauge Principle complex scalar field is considered.
There's statement, that for conservation of charge one needs usual U(1) global symmetry:
$$
\phi \to e^{i\alpha}\phi \Rightarrow Q =\int d^Dx \rho
$$
For conservation of dipole moment:
$$
\phi \to... | For a symmetry
$$ \phi \rightarrow \mathrm{e}^{\mathrm{i}\lambda(x)}\phi, $$
Noether's theorem gives you a conserved four-current:
$$ J^\mu = \mathrm{\lambda}\frac{\partial \mathcal L}{\partial\frac{\partial \phi}{\partial x_\mu}}\phi $$
which satisfies the continuity equation:
$$ \partial_\mu J^\mu = 0 \Leftrightarrow... | {
"language": "en",
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Why is kinetic friction present when two objects are slipping across each other my mechanics sir was telling us the other day that when the relative velocity is zero between the surface and the object then the object starts sliding, eg in rolling motion without slipping, the v rel is zero at the bottom most point .how ... | When a wheel is rolling without slipping or sliding, it has static friction with the ground not kinetic friction. When a wheel is slipping or sliding, such as on ice or mud, it has kinetic friction not static friction. The words slipping and sliding are fairly synonymous, but we might be more inclined to say that when ... | {
"language": "en",
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Proof Rényi entropy is non negative The Rényi entropy is defined as:
\begin{equation}
S_\alpha = \dfrac{1}{1-\alpha}\log(\text{Tr}(\rho^\alpha))
\end{equation}
for $\alpha \geq 0$. This can be rewrited in terms of $\rho$ eigenvalues, $\rho_k$, which verify $0 \leq \rho_k \leq 1$, as:
\begin{equation}
S_\alpha = \dfrac{... | Consider 3 cases : ($\alpha > 1$, $\alpha < 1$, $\alpha = 1$)
*
*$\alpha > 1$
$$
\sum p_k^{\alpha} \leq \sum p_k = 1 \Rightarrow \log (\text{Tr}(\rho^\alpha)) \leq 0\Rightarrow S_\alpha \geq 0
$$
*$\alpha < 1$
$$
\sum p_k^{\alpha} \geq \sum p_k = 1 \Rightarrow \log (\text{Tr}(\rho^\alpha)) \geq 0\Rightarrow S_\alpha... | {
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Why do the Dirac-Maxwell Lagrangian and the QED Lagrangian look the same? I know that QED is some kind of second quantized version of the Maxwell-Dirac theory. But why is it that this modification to a second quantized version is just to replace the scalar function $\Psi$ by a field operator $\hat{\Psi}$?
| When going to second quantisation, the fields once denoted by $\phi$ and $\psi$ are replaced by field operators $\hat \Psi$ and $\hat \Phi$ which are essentially operators which create/annihilate particles at points in space represented by the fields.
| {
"language": "en",
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Can the universe ever contract? I am currently going through this answer related to the Big Bang theory and from there a question arose in my mind:
*
*Can the universe ever contract?
*Can it ever contract to singularity?
I wonder, if it is possible, how it would happen? Is there any chance at all?
I am unaware abou... | Nobody knows for sure how the universe will evolve. It's accepted by almost all cosmologists that the universe is expanding at an increasingly accelerated rate.
Almost all. There are indeed convincing experimental facts (type IA supernovae, the CMBR), but there is also counter-evidence. I think this is not taken too se... | {
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Why doesn't planet Earth expand if I accelerate upwards when standing on its surface? According to General Relativity I am being accelerated upwards by planet earth while writing this question. But a curious person on the the other side of the planet relative to me would have the same experience. That means we are acce... | What is asserted is that gravity isn't a force at all; rather, it's acceleration such that if I sit on a chair here in California, the acceleration is upward by Earth against me and my chair. What about my friend in China sitting on his chair? What about everyone else, Earth-wide, sitting on their chairs. I don't know ... | {
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"source": "stackexchange",
"question_score": "10",
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Why is there a need for the concept of energy if we have the concept of momentum? We have two concepts that are energy and momentum. To me, momentum is more fundamental than energy and I think that momentum was the thing which we wanted to discover as energy.
Now momentum can describe several things that that energy do... | Your impression that "momentum can describe several things that that energy does and if it is not able to describe it then it can be somehow extended to describe that thing" is a reflection of something real and deep.
When you move to the framework of general relativity, in which space and time are combined to form the... | {
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What does it mean for particles to "be" the irreducible unitary representations of the Poincare group? I am studying QFT. My question is as the title says. I have read Weinberg and Schwartz about this topic and I am still confused. I do understand the meanings of the words "Poincaré group", "representation", "unitary",... | This is really a deep question.
I am still learning, so any feedback is more than welcome
My key takeaways and interpretations are:
*
*Particles are interpreted as field excitations
*The complexified (thanks ZeroTheHero, for clarifying) full Poincaré ISO(3,1) when studied, e.g. through the Little Group (Wigner metho... | {
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Computing a quality factor of multiple measurements Suppose I measure the same quantity twice with two methods, first I get 0 with 0.001 uncertainty, then I get 1 with 0.000001 uncertainty. We can see from this most likely there is something wrong with the uncertainties or measurements. I am faced with such a problem, ... | If you assume the uncertainties are Gaussian distributed, then 1 is 1000 sigma away from 0 +/- 0.001. To a first approximation, you can ignore the much smaller uncertainty on 1.
You can use the complementary error function to determine the probability of finding a value at $n$ sigma away from the mean value (for Gaussi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/585565",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Why two orbitals having same phase is not a random phenomenon? I have been reading about Molecular Orbital Theory for Chemistry.
*
*I tend to believe that when two Hydrogen atoms approach each other, whether the $1s$ orbitals are in-phase or out-phase is a random phenomenon. However I know that this is not so. Please... | The total wavefunction is a function of both electron positions. There is no phase between them. The wave function is also a function of the electron spins. The total wave function (both spin and spacial part) must be anti-symmetric. Although a clever experimenter could prepare a pair of hydrogen atoms which had sp... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/585648",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Is spin necessary for electromagnetism? I know that spin is needed for defining the magnetic moment of any particle, and I have also read that the spin actually is the reason why some materials are magnetic. What I want to know is whether spin is necessary for the some interactions in the electromagnetic field.
Let me ... | The charged pions, for example, $\pi^+$ and $\pi^-$, have zero spin but interact with a magnetic field, as can be seen from the curved tracks they leave in a bubble chamber with a magnetic field. So, to answer your question, spin is not theoretically necessary for electromagnetism. You could have a perfectly good and c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/586741",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 6,
"answer_id": 1
} |
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