Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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What's the reason behind the current remaining the same after passing by a resistance? I've been wondering why does this really happen, I mean by intuition if electrons are driven by EMF (ignoring wire's resistance), $n$ coulombs would pass by a point per second, until they encounter something that slows them down thus... | Current us a measure of how much charge is passing a given point (or cross section) of a wire.
If the currents were not equal at all points in a simple circuit, there would have to be charges entering or exiting the circuit. This however does not happen.
Water pipe analogy: current is something like liters per minute ... | {
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Rutherford gold experiment When an alpha particle is nearing the gold atoms nucleus, it is slowing down due to electrostatic repulsion, right?
But then why is the acceleration or velocity not a minimum at that point (the point where the alpha particle reverses its direction)and why is the speed a minimum?
Like isn't... | The electrostatic repulsion force becomes larger as the particles are brought closer together. Since force is proportional to acceleration, this must mean that the acceleration is at a maximum when the particles are at their closest distance.
When something changes direction, the velocity vector changes direction. Ther... | {
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What are some good resources to learn Vector Spaces for Quantum Mechanics? I am currently using Shankar's Principles of Quantum Mechanics. I had no trouble understanding finite dimension vector spaces using it. But I find it difficult to understand infinite dimensional vector spaces using this book. What are some alter... | The first chapter of Shankar's Quantum Mechanics contains a thorough introduction on the linear algebra necessary. I have found out that learning linear algebra from a math textbook can be somewhat counterproductive- but I might be wrong.
| {
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Could a microwave oven be tuned to defrost well? Typical microwave ovens do a lousy job of defrosting because liquid water absorbs their radiation far better than ice. So once a spot melts, it will quickly rise to cooking temperature while the rest of the food remains frozen. Would it be possible to build an oven that ... | In order to “tune” a microwave oven to handle defrosting different from cooking, I think you would need more than one microwave frequency and I don't think that’s going to happen since the FCC sets the frequency range and the frequency of 2450 MHz has become the industry standard. Even if the permitted range by the FCC... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/443693",
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Could quantum fluctuations spawn real matter? Would it be plausible for fluctuations in the QED vacuum to spawn actual matter (such as quarks, electrons the constituents of a hydrgen atom) given enough time and space?
| Also in QED, total Energy is conserved for every time! A difference between QED and classical electrodynamics is that the Expression for total Energy is slightly altered. Classical electrodynamics has kinetic Energy $T$ and a potential Energy $V$ arising from electromagnetic fields. In classical Theory, total Energy is... | {
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Why we consider identical particles for Bose-Einstein condensation? Why we consider identical particles like identical composite bosons for BEC. Why we do not consider non identical particles of differnt masses etc?
| The irreducible representations of the Poincaré group are labelled by mass $m$ and the spin $s$. So as soon you have particles that have different mass, they are intrinsically different and obey their own Bose/Fermi/... statistical distribution.
I assume here that you do not mean idential to be a synonym of indistingu... | {
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Does a rock use up energy to maintain its shape? A rock sitting on land, the ocean floor, or floating in space maintains its shape somehow. Gravity isn't keeping it together because it is too small, so I'm assuming it is chemical or nuclear bonds keeping it together as a solid. If not it would simply crumble apart. So,... | Consider an answer by contradiction:
Imagine the rock is in the vacuum of outer space with no energy able to be added to it.
Suppose it does use energy to maintain shape. Then at some point, it will run out of energy and the shape will change. Now, since it is out of energy and can't change shape, isn't it now maint... | {
"language": "en",
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Can light be compressed? What if we take a cylindrical vessel with an inside surface completely reflecting and attach a piston such that it is also reflecting. What will happen to light if we compress it like this?
| Ideally, this is essentially the same as compressing a quantum gas of any other boson. Macroscopically, there is a pressure exerted by the photon gas on the walls of the chamber, so compressing the piston will take work and thus will increase the internal energy of the photon gas. Microscopically, by compressing the ... | {
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Euler’s Equations of Motion for a Rigid Body and Inertial Forces Euler’s equations of motion for a rigid body can be interpreted as a rewriting of Newton’s second law for rotations in a rotating frame. They basically tell us the sum of the torques equals the rate of change of the body’s angular momentum, In the rotati... |
Do we then not need to take into account inertial forces when computing the torques in rotating coordinates?
No, but there is an inertial torque you have to worry about.
From the perspective of an inertial frame, the rotational analog of Newton's second law for rotation about the center of mass is
$$\frac{d\boldsymbo... | {
"language": "en",
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Wavelength and relativity From de Broglie equation λ=h/p. But p=mv and velocity is a relativistic quantity so also wavelength is relative ? In other words does wavelength depends on the reference frame ?
|
In other words does wavelength depends on the reference frame ?
Yes, but the variation of wavelength we're talking about here is not, as claimed in two other answers, the same as a standard Doppler effect. An electron, in its rest frame, has a wavelength of infinity, i.e., a wavenumber ($k=2\pi/\lambda$) of zero. The... | {
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Relfection and transmission coefficients for wave function in $\delta$-potential Let's assume we have some one-dimensional Delta-potential $V(x)=V_0 \delta(x)$. Then I have found numerous problems where the approach for a wave function is $$\varphi(x)=\begin{cases}e^{ikx}+re^{-ikx},\ & x<0\\te^{ik'x},\ &x>0\end{cases}$... | *
*You have understood this aspect correctly. The bottom line is: $\psi(x)$ is claimed to satisfy the time independent Schrodinger equation, so if in doubt, plug it in and check that it does!
*Transmission here is defined to be the ratio of two physically observable rates, namely $T = R$(transmit) $/ R$(incident) whe... | {
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Is wave function collapse the only source of 'randomness' in QM? What about field fluctuations? Are these two even distinct? Basically I want to know the validity of the statement, "All randomness originates from wave function collapse" or maybe "The only true random event is the collapse of wavefunctions"
This seemed ... | It is important to understand that fields don't fluctuate. This is explored in the question Are vacuum fluctuations really happening all the time? (spoiler: the answer is no).
The randomness you are talking about is due to measuring some quantity when the wavefunction is not an eigenstate of that quantity. For example ... | {
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Examples of central forces on the path of orbit? In solving a problem from Goldstein (3.13), I solved for multiple properties of a circular orbit with the attractive central force where the path of orbit crosses the point of the force (at origin).
The solutions were simple enough to find, but what's been in the back o... | Consider this scenario in which a spring is connected to a bead and the other end of spring is connected to a circular frame and bead is set to contained on that circular frame and end of spring connected to circular frame is glued and take it as origin.
HOPE THIS HELPS.
Note this problem is merely an excersice proble... | {
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Why are protons and neutrons the "right" degrees of freedom of nuclei? This question may sound stupid but why do we visualize nuclei as composed of a bunch of neutrons and protons?
Wouldn't the nucleons be too close together to be viewed as different particles? Isn't the whole nucleus just a complicated low energy stat... | We can measure the form-factors of bound nucleons. For instance by doing quasi-elastic scattering of a proton out of the nucleus $A(e,e'p)$ at low energy loss (my dissertation work involved this reaction for deuterium, helium, carbon and iron).
The result are quite similar to (but measurably not identical to) the equi... | {
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How are the coefficients determined in the high temperature expansion of the 2D Ising model? I have been studying the 2D Ising model lately and have been looking at high and low temperatures. But I'm having problems when trying to understand the high temperature one. The final expansion looks like this:
$$Z =(\cosh K)^... | I am certainly not the person on Physics SE with most expertise concerning lattice models, but since nobody has offered an answer yet, here is mine.
As you have indicated, the partition function can be expressed as a high-temperature expansion involving closed loops or polygons (of nearest-neighbour interaction terms) ... | {
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The minimum diameter of a sphere such that a cone may balance on it There is a solid sphere of diameter D, with a right circular cone placed on top of it. The cone has a height h and the diameter of the cone base is d, and d=h. Explain why the minimum value of D (diameter of sphere) must be d=h in order that the cone m... | HINT: Think about the potential energy $U(\theta)$ of the cone when the contact point is at the top of the sphere ($\theta = 0$) vs. when the contact point is at an angle $\theta$ from the vertical. If the cone is stable when $\theta = 0$, what can you say about the potential energy function $U(\theta)$ at that point... | {
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Primary field in CFT and path integral I should feel ashamed to ask such a naive question, but anyway let me start with the $\phi^4$ theory in the Minkowski spacetime, which has a Lagrangian of the form
$$\frac{1}{2}(\partial\phi)^2-\frac{1}{4!}g\,\phi^4$$
One say that it is scale invariant if under the transformation... | To be brief, no you integrate over all field configurations. Field configurations are not operators they are ordinary functions that are summed over in the path integral. Primary fields are operators. They appear in correlation functions which involve an expectation value over all field configurations. The conformal in... | {
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Metric for 2D de Sitter? What is the correct metric to use for two dimensional de Sitter? If one starts with the following metric, which looks similar to de Sitter in 4 dimensions:
$$ds^2 = -dt^2 + e^{2H t} dx^2,$$
one can calculate $R = 2H^2$, and $R_{00} = -H^2$, which gives the $\Lambda = 0$, which is not the solut... | In two-dimensional spacetime, the Einstein tensor $R_{ab}-\frac{1}{2}g_{ab}R$ is identically zero , which explains why you get $\Lambda=0$.
In any number $D$ of spacetime dimensions, including $D=2$, de Sitter spacetime can be constructed like this. Start with the $D+1$ dimensional Minkowski metric
$$
-(\mathrm dX^0... | {
"language": "en",
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How did Coulomb arrive at value of electron charge? Charge of one electron is known to be as $1.6$ x $10^{-19}$ C or alternative 1 Coulomb contains charge of $6.24$ x $10^{18}$ electrons. I am just wondering if these numbers are arbitrarily chosen or were derived through some calculations?
| 1 Coulomb is defined as 1 As, where the Ampere is defined as a current producing a given amount of force between two ideal conductors, and the second is defined in multiples of the period of a transition in Cs. Since both definitions of Ampere and second are somewhat arbitrary, them combining to the numbers you have gi... | {
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Can we ever "measure" a quantum field at a given point? In quantum field theory, all particles are "excitations" of their corresponding fields. Is it possible to somehow "measure" the "value" of such quantum fields at any point in the space (like what is possible for an electrical field), or the only thing we can obser... | Quantum Fields can't be physical, you can see this from the Equivalence Theorem which states that if I have a quantum field $\Phi(x)$, I can perform a field redefinition in my action $\Phi(x)\rightarrow \Phi'(x) = f(\Phi(x))$, so that as long as $f(\Phi(x))$ satisfies some simple properties, all S-matrix elements (basi... | {
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Transformation of a Lagrangian $$L(\lambda,\mu,\dot{\lambda},\dot{\mu})=\frac{m}{2}(\lambda^2+\mu^2)(\dot{\lambda}^2+\dot{\mu}^2)-\alpha \lambda^2\mu^2,$$
I'm supposed to express this Lagrangian through
$x=\lambda^2-\mu^2$
$y=2\lambda\mu$
My first thought was to use
$x+\mu^2=\lambda^2$
by putting it into the second e... | This is the answer that physshyp had in mind but felt like not writing down. Define the complex variables $\zeta = \lambda + i\, \mu$ and $z = x + i\, y$. Then
\begin{align}\zeta^2 =& (\lambda + i\, \mu)^2= (\lambda + i\, \mu)(\lambda + i\, \mu) \\
=& \lambda^2 + i\, \lambda\, \mu + i \, \mu \, \lambda + (i\, \mu)^2 =... | {
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Are the Fermi-Dirac, Bose-Einstein and Boltzmann distributions all probabilities, or are they ways to get to probabilities? Hyper physics has a page for the energy distribution functions (here), they say that each of the distributions are the probabilites that a particle has a certain energy state E, but other websites... | Start with the grand canonical partition function $Y$ and the microstate $r=(n_{p_1},n_{p_2},...)=\{n_p\}$:
\begin{align}
Y&=\sum_r\exp\left(-\beta\left(E_r\left(V_rN_r\right)-\mu N_r\right)\right)\\
&=\sum_{n_{p1}=0}^\infty\exp\left(-\beta\left(\epsilon_{p_1}-\mu\right)n_{p_1}\right)\cdot\sum_{n_{p2}=0}^\infty\exp\lef... | {
"language": "en",
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Having trouble making sense of Einstein's thought experiment So I was reading about Einstein's thought experiment where he tries to show that simultaneous events in one frame may not be simultaneous in another frame.
So, in the given pic, light from B' reaches Mavis before light from A' and I get that because she is m... | Stanley doesn't know about A' and B'. In his world, there is A and B. What does it mean for Stanley to "see the strike occur at A' and B' simultaneously?" If it mean he can read Mavis's clocks and he sees that they read the same time (let's say $t=0$) when they are struck, then he sees the following:
When the clock at ... | {
"language": "en",
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Does a particle with infinite energy escape an infinite well? Currently, my modern physics class is going over particles in finite and infinite wells, general quantum formalism, and tunneling.
What happens to a particle as it gains an infinite amount of energy? Does it stay inside of the infinite well? Does it escape? ... | Particle and potential wells are in the framework of quantum mechanics. In this framework one cannot be talking of potential wells arbitrarily changing the particle's energy, because the energy is strictly defined by the solution of the quantum mechanical equation for the given potential.
What happens to a particle as... | {
"language": "en",
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Can a battleship float in a tiny amount of water? Given a battleship, suppose we construct a tub with exactly the same shape as the hull of the battleship, but 3 cm larger. We fill the tub with just enough water to equal the volume of space between the hull and the tub. Now, we very carefully lower the battleship into ... | The issue is just in your "definition" of displaced. When we say "the buoyant force is equal to the weight of the displaced fluid" (which is more true than it seems people are saying it is), displaced does not mean "how much fluid overflows out of our container" (unless we started with a full container).
The displaced... | {
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When is it more efficient to blow air over a wet laundry in order to dry it - when it's wetter or when it's drier? If I want to speed the drying of laundry and allocate for it one hour of fanning - should I use it just after I hang it to dry or several hours later?
When we want to cool hot tea it's better to add the co... | This case is quite similar to the heating case in some ways, but not others.
Thermal gradients behave quite similarly to evaporation concentrations. That is, the rate of evaporation is greater if the difference in concentration is greater. The rate is also increased by convection, the same as with heating.
A big diff... | {
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Can very very few photons form the EMWs? One maybe interesting question please!
In quantum point of view, the electromagnetic waves (EMWs) consist of photons. However, if there are only very very few photons, can they form a wave-like macro EM field?
OR
If a spherical monochromatic EMW (frequency is $\nu$) propagates ... | The smallest EM wave is generated by single electrons in atoms and has discrete energy levels, which we can call a photon. This small EM wave tends to propagate in one direction where its E and M fields are strongest, the solution to Maxwell's equation says the E and M fields are well confined to sinusoids in a certain... | {
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Light through a cylindrical fiber-cable which has decreasing radius; one in shape of a helix
I thought of the idea during breakfast this morning, and it has been nagging me all day - so hopefully (probably) I will find some good answers here. I'm not a physics student (economics), so please be gentle!
Suppose that you... | The great advantage of fiber cables is that they are almost perfect waveguides, they turn corners, so a helical or whatever geometry for the cable does not affect the light within,and that is why they are useful in communications.
Only if the diameter of the cable would change to become smaller there would be an int... | {
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Why can't a particle penetrate an infinite potential barrier? I am studying basic quantum theory. My question is:
Why can't a particle penetrate an infinite potential barrier?
The reasoning that I have applied is that particles under consideration have finite energy. So, to cross an infinite potential barrier the parti... | The relation between the particle's wave function $\psi(x)$, potential $V(x)$ and energy is
$$
E = \int dx\ \psi^*(x)\left(-\frac{\hbar^2}{2m}\psi''(x) + V(x)\psi(x)\right) \quad
\label((*)
$$
Suppose $V(x)$ is bounded from below and is equal to $+\infty$ on some interval $[x_1,x_2]$. If $\psi(x)\neq 0$ for $x\in[x_1,x... | {
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How can two electrons repel if it's impossible for free electrons to absorb or emit energy? There is no acceptable/viable mechanism for a free electron to absorb or emit energy, without violating energy or momentum conservation. So its wavefunction cannot collapse into becoming a particle, right? How do 2 free electron... | It is true that the reactions
$$e + \gamma \to e, \quad e \to e + \gamma$$
cannot occur without violating energy or momentum conservation. But that doesn't mean that electrons can't interact with anything! For example, scattering
$$e + \gamma \to e + \gamma$$
is perfectly allowed. And a classical electromagnetic field ... | {
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Would a charge imbalance act like dark energy? I realize that there are theoretical reasons to reject the idea that the charges on electrons and protons may not be exactly equal and opposite; and I am not suggesting that they're not.
Edited 12/20/18: However, I would like to know: if there were a very, very tiny imbala... | I don't think this idea works, for the simple reason that the electromagnetic and gravitational forces scale the exact same way: they are both proportional to their respective 'charge' and inverse square.
Since your idea implies most apparently neutral objects would have roughly the same charge to mass ratio (since it... | {
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Violating Newtons First Law! Suppose you are inside a very large empty box in deep space , floating ( i.e not touching the box from anywhere initially).The box is at complete rest.
Now you push the box forward from inside.
Now you would go backwards but the box will move forward to conserve momentum.
However since you... | If you say that pushing against the box (and the box pushing against you) is an internal force, then that means that you and the box are considered to be two internal parts of a single object. The center of mass of this object does not move when you push against the box, since all forces are internal. So you will move ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/449699",
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Is the period a physical observable in General Relativity? I am currently seeing the classical tests of GR. To justify the introduction of a test based on the Doppler effect, the professor says that the previous test ( Shapiro and echo-radar test ) is based on non-physical parameters as the radius of Earth's orbit sinc... | As Elio and others have written, the comment by your professor is not really very meaningful. I would rather like to write about the title of your question. Of course the period of Revolution of Earth is a physical observable, after all you can measure it! Obviously different observers might measure different periods, ... | {
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From where electrons flow to make a bulb light? Suppose we have the "basic" stuff like a battery 2 piece of wire and a bulb. Battery has a potential difference. But from where electrons flow to make the bulb light? from wire or from battery or from both? also if electrons flow from battery and they go through the wire ... | Electrons from the material in the entire circuit flow. Conductors are different to insulators because their atomic structure is made of a “sea of electrons” around the positive nuclei. These electrons are free to move from atom to atom in the conductors and not in the insulators. This may be better explained why by a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/450081",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can the pion decay into two photons? The neutral pion belongs to the pseudoscalar meson octet, so it has, in the ground state ($L=0$):
\begin{align}
P_{\pi^0}&=-1 \\
C_{\pi^0}&=+1.
\end{align}
And the photon has
\begin{align}
P_\gamma = -1 \\
C_\gamma=-1.
\end{align}
Therefore, since electromagnetic interactions co... | The photons have intrinsic spin (or, better, helicity) one, so the pair can have odd orbital angular momentum, still conserving total angular momentum (which has to be zero, as the pion is spinless).
Specifically, the spins of the two photon can combine to give total spin $S=1$. This, conmbined with an angular momentu... | {
"language": "en",
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"source": "stackexchange",
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How to understand the two-point correlation function in momentum space? Let's take the Ising model as an example and study the
two point spin spin correlation function:
$$\langle s_0 s_r\rangle = \frac{\sum_{\{s_i\}}e^{K\sum_{\langle i ,j\rangle}s_i s_j} s_0 s_r}{\sum_{\{s_i\}}e^{K\sum_{\langle i ,j\rangle}s_i s_j} }.... | If the spins are at positions $\bf R$, it is possible to define a $\bf k$-dependent collective variable $s_{\bf k}$ (Fourier component of the spin vector configuration) as:
$$
s_{\bf k}=\sum_{\bf R} e^{i\bf k \cdot R}s_{\bf R}
$$
(maybe with a normalization factor depending on the exact choice of definition).
The k-s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/450582",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Angular momentum in different points I have a question about angular momentum:
Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?
| Angular momentum relative to an origin ${\mathcal O_1}$
$$ \mathbf{L_{\mathcal O_1}} = \mathbf{r_{\mathcal O_1} \times p_{\mathcal O_1}}$$
where $\mathbf r_{\mathcal O_1}$ is the position vector to the particle relative to some origin ${\mathcal O_1}$.
Now suppose that angular momentum is conserved in ${\mathcal O_1}$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/450722",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is there a useful way to visualize the symmetries of the relativistic Riemann curvature tensor? I find it useful to see diagrams such as trees, colored 2D and 3D arrays, etc., which illustrate how terms combine in composite expressions. For example, the following is my visualization of the genesis of multinomial coeffi... | In Geroch's Differential Geometry notes (1972, ISBN 978-1927763063) page 60,
he uses an octahedron to describe the symmetries of the Riemann Curvature Tensor.
In his example, using the upper back triangular face,
the sum of the terms at the vertices is
$$R_{bdca}+R_{cdab}+R_{dacb} \stackrel{{}_{[ab][cd]}}{=}R_{dbac}+R_... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/450889",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Gauss theorem and inverse square law I know that the gauss law states that the Flux of the electric field through a closed surface is Q/ε , but does the gauss theorem works also for non inverse square law Fields?
| I'd like to draw a distinction:
Gauss's Theorem (Also called Divergence Theorem):
$$\iint_{\partial V} \mathbf{E} \cdot d\mathbf{A} = \iiint_V \nabla \cdot \mathbf{E}\ dV $$
This is a purely mathematical statement and holds for all differentiable vector fields $\mathbf{E}$.
Gauss's Law: $$\nabla \cdot \mathbf{E} = \... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/451119",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does the half-life of an element mean it will never decay completely? Example:
Half life of Polonium-194 is 0.7 seconds. If we supposedly take 50g of Polonium, there will surely be a time when no more of this Polonium will be left because if we consider the decay discretely, in the form of individual atoms, won't there... | No, not really. For example, suppose you have a sample of $2^{1000}$ atoms with half-life $t$. (Note: there are only about $10^{80}$ protons in the Universe.)
*
*If you wait for a time $t$, then half of them have decayed, and you have on average $2^{999}$ remaining.
*If you wait $1000t$, then you will have on av... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/451240",
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Explicit computation of singular part of two-loop sunrise diagram For $\phi^4$, there is two-loop self-energy contribution from sunrise (sunset) diagram.
The integration is
$$
I(p)=\int\frac{d^D p_1}{(2\pi)^D}\frac{d^Dp_2}{(2\pi)^D}\frac{1}{(p_1^2+m^2)(p_2+m^2)[(p-p_1-p_2)^2+m^2]}.
$$
I try to use trick like Feyn... | If you can be satsfied with the $m=0$ case, the integral is easy provided you work in configuaration space rather that momentum space. The $x$-space propagator in $n$ dimensions is
$$
g(x,x') = \frac{1}{ (n-2)S_{n-1}} \left(\frac {1}{|x-x'|}\right)^{n-2}
$$
where $S_{n-1} = 2\pi^{n/2}/\Gamma(n/2)$ is the surface are... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/451474",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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A drone, or any lifting vehicle, enclosed in a container. Will it lift along with the container? Consider a drone, or any lifting vehicle, enclosed in a container. Will it lift along with the container? Suppose I place a small drone in a large container of negligible weight and place them in space. Will drone move forw... | The reason why it will not work is because the air that the drone is pushing down will push the bottom of the container down too.
Imagine yourself in a box half your height. Will you be able to get up straight? No, because you will be pushing the bottom of the box down with the same force that you are using to push y... | {
"language": "en",
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Different predictions from differential vs integral form of the Maxwell–Faraday equation? Assume a toroidal solenoid with a variable magnetic field inside (and zero outside) and a circular wire around one of the sides.
Because there is no magnetic field outside the solenoid, we have
$$\nabla \times E = - \frac{\partial... | You are re-discovering the Aharonov-Bohm effect. it is not a problem of differential vs integral form of Maxwell equations, but the issue is that in order to prove equivalence between the local condition on vanishing curl and the global of vanishing of the line integral of the field is required a simply connected dom... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/451919",
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"source": "stackexchange",
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Poynting theorem in Landau and Lifshitz’ field theory book In Landau & Lifshitz’s The Classical Theory of Fields, in section 31, they have proved the Poynting theorem (equation 31.6) in its integral form. In the footnote on page 76, they mention
We assume that at the given moment there are no charges on the
surface... | I think the answer should be such: that charge on the surface of the volume creates an electric field is equal $\vec E=4\pi \sigma \vec n$, where $\sigma$ is the surface charge and then the energy flux is $\oint c \sigma [\vec n,\vec H]df$
The charges of the electric field are formed on the surface of the dielectric, ... | {
"language": "en",
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Why acceleration comes to be different when using $F=ma$ and when using $\tau = I \alpha $? Consider a Disc of mass $M$ and radius $R$, I applied force $F$ tangentially on it. Now using $F=Ma$ , acceleration comes up to $$a=F/M$$
Now, let's use the torque equation: Here, the moment of inertia $I$ is $\frac12MR^2$ , and... | For translations, it doesn't matter how the mass of a body is distributed, the acceleration will be $a=F/m$.
For rotations, the distribution of the mass is important. A ring whith large radius is harder to get into rotation than a small ring with the same mass. This is captured by moment of inertia.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Noether's theorem for scale invariance When we have the Lagrangian
$$\mathcal{L} = \frac{1}{2} \partial _\mu \phi\partial^\mu \phi \tag{1} $$
We have a symmetry given by $$x^\mu\mapsto e^\alpha x^\mu, \qquad\phi\mapsto e^{-\alpha} \phi.\tag{2}$$ I'm struggling to find the Noether charge for this symmetry. The formula ... | If u want to compute the Noether currents, u can do as follows:
$$x'^u=x^u+\delta x^u \quad \delta x^u=e^aE_a^u$$
$$\phi'=\phi+\delta\phi \quad \delta\phi=e^aX_a$$
$$J_a^u=[\eta_p^uL-\frac{dL}{dd_u\phi}d_p\phi]E_a^p+\frac{dL}{dd_u\phi}X_a$$
So in your case results:
$$E^u=x^u \quad X=-\phi$$
$$J^u=\frac{1}{2}d_p\phi d^p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/452414",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Gravitational redshift discrepancy? I want to compute the redshift of a signal emitted by a static observer in $r=R_1$, $\phi=\phi_1$and recieved by another static observ at $r=R_2$, $\phi=\phi_2$ with $R_2>R_1$, in Schwarzschild metric.
So i determined it in two different manners obtaing different results.
First i con... | The expression
$$\left( 1 - \frac{r_s}{r}\right)\frac{dt}{d\tau} = \frac{E}{mc^2} = {\rm constant}$$
would apply to an inertial observer in the Schwarzschild metric. i.e. The $\tau$ here corresponds to the proper time experienced by an inertial (free-falling) observer.
Your first expression
$$ \left( 1-\frac{r_s}{r}\ri... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Action of rotation operator on spin 1/2 system In Sakurai book on QM in chapter 3, he states the following relation $$e^{\frac{iS_z\phi}{\hbar}}[(\rvert+\rangle\langle-\rvert)+(\rvert-\rangle\langle+\rvert)]e^{\frac{-iS_z\phi}{\hbar}}$$
$$=e^{\frac{i\phi}{2}}\rvert+\rangle\langle-\rvert e^{\frac{i\phi}{2}}+e^{\frac{-i\... | The operator $S_z$ the operator representing the $z$-component of angular momentum, which also generates rotations about the $z$ axis. Assuming that $|\pm\rangle$ are the eigenstates of $S_z$ for a spin-$1/2$ object, the first interpretation gives
$$
S_z|\pm\rangle=\pm\frac{\hbar}{2}|\pm\rangle,
$$
which then implies
... | {
"language": "en",
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Double slit experiment record but not look at it I am having a tough tough stressful week trying to write an article about quantum mechanics. I know there was a question asked the same thing before, but I didn't understand nor I did not want to wake up an old thread.
The double slit experiment we all know, if we put an... | The interference pattern will be destroyed even before the wavefunction-collapse.
Let's say your particle is described by the wavefunction $|\text{p}>$. When passing the double slit (I call those the up and down slits), it becomes entangled with the sensor, and your wavefunction becomes :
$|\psi> \equiv|\text{sensor}_{... | {
"language": "en",
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Intuition behind dual vectors ('Bongs of a bell' does not help) Similar to the post here (How to visualize the gradient as a one-form?), I'm wondering about an intuition behind dual vectors and differential forms (and the link in that answer to Thorne's notes is broken now). I'm not as familiar with level sets (as ment... | Since no one has explicitly mentioned Schutz's explanation in A First Course in General Relativity I will outline it, as it is particularly intuitive:
As others have mentioned, dual vectors/one-forms/covectors can be seen as a map from a vector to a scalar (and in general, covariant n-th order tensors map contravariant... | {
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Does the eigenbasis associated with an observable changes after measuring a different observable? Suppose a system is initially in a superposition:
$$\psi(x) = \sum\limits_{i}|c_i\phi_i(x)\rangle$$
After a position measurement, the wave function collapses to one of the position eigenfunctions,$\phi_i(x).$
Geometrically... | The state, your initial state collapses on, is always one of the eigenstates of the observable you are measuring.
these eigenstates are defined a priori, and don't change as long as the observable doesn't change.
So, the formal answer to your question depends on the picture you are working in:
*
*if you are in Schro... | {
"language": "en",
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What if humans doubled size... and everything else... could we notice? After the big bang, everything expanded from a small mass. That expansion is said to be still happening.
Imagine if everything observable constantly grew in size. EG. Everything slowly doubled in size over a decade? Would we notice difference? Wo... | We always measure size with relative to a known size. When we see in a microscope ,until we don't know that they are small ,they will look very much large.This is the first sense that is by seeing. The second sense is by touching.and the third thing is by a known speed of an object and it's known size.Usually we measur... | {
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Is there anything special about ebonite and fur? I'm from Czech Republic, born 1980. From elementary school, we all remember this mantra:
When ebonite rod is rubbed with fox fur, electrostatic charge is created.
Electrostatic charge is created by rubbing ebonite rod with fox fur.
Rubbing ebonite fur with fox fur ... | Static electricity is observed with a plastic comb after you comb dry hair.
So there is nothing special about ebonite except ancient report which led to the name electricity.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/453656",
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Why a rope grabbed by a single end seems to follow the hand that grabs it? Context
I am thinking about the physics of the movement of a rope in the context of a person running and grabbing a rope in one hand (the other end is "free", there is nothing attached).
When the person is just standing, the rope simply falls d... | The rope can be modeled as an elastic system consisting of individual massive elements connected by springs. Each massive element moves under the action of elastic forces, gravity and air resistance. Let's consider the task: at the initial moment of time, the rope hangs vertically, in the next 1 second the upper end of... | {
"language": "en",
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Fire -Thermodynamics Could a steel box lined with Rockwool (interior only) be an adequate shelter during a fire? How can I determine the temperature inside of the box at peak fire temp? How long could someone withstand the peak internal temperature? How could I cool the interior? Would a fire extinguisher explode at pe... | Imagine a box of area $A$, volume $V$, density $\rho$, temperature $T$ and interior heat capacity $C$ surrounded by a fire at temperature $T_f$. It has a thickness $d$ thermal insulation of thermal conductivity $k$. Let's ignore the thermal capacity of the insulator. The heat flow across the area will be $kA(T_f-T)/d$ ... | {
"language": "en",
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Is the Higgs boson an elementary particle? If so, why does it decay? The Higgs boson is an excitation of the Higgs field and is very massive and short lived. It also interacts with the Higgs field and thus is able to experience mass.
Why does it decay if it is supposed to be an elementary particle according to the sta... | All fundamental or elementary particles decay after being born. Take, for example, electron. While being created in some process, it "decays" into "another electron" and many soft photons. As it is unlikely that "another electron" may stay without further interactions with its environment, it continues to interact, i.e... | {
"language": "en",
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Why can blue LEDs be used for generating white light, but red LEDs cannot LEDs consist of pn-junctions, so why can blue LEDs be used for generating white light, but red LEDs cannot
| The blue led has wavelength of about 450nm and has more energy than red photons at about 600nm wavelength. To create white light phosphors were discovered a long time ago, phosphors are used in fluorescent bulbs (convert UV to blue, green, red) and in old CRT TVs that converted electrons into colours of light. The ph... | {
"language": "en",
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Is it possible to have a planet entirely made out of liquid water? Earth is mostly covered in oceans, but they only go a few kilometres deep. It's obviously not possible to have a planet the size of the earth to be made entirely out of water, because of the kind of pressures reached in the interior.
a. But say that we ... | The related question points out that water would become ice at a depth of around sixty km. This answers the first question. And this suggests we should expect a body of water a 120km in diameter to remain water all the way through. This is far smaller than a dwarf planet and more the size of a large asteroid.
| {
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"source": "stackexchange",
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Conservation of momentum if kinetic energy is converted to mass There is a moving object. Through an unspecified (science fiction) mechanism its kinetic energy is converted to mass and the object comes to rest.
The mechanism is fictional but in good scifi it is good to adhere to the laws of nature. Does the convers... |
Through an unspecified (science fiction) mechanism its kinetic energy is converted to mass and the object comes to rest.
That part is fine. Einstein gives us the equivalence between mass and energy. So converting the kinetic energy to mass is quite doable. Any form of energy storage will do this.
Does the convers... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/455764",
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What is the meaning of effective density in porous media? Is the density of air inside the pore space not same as density of free air? I am trying to understand the physical meaning of using effective density in porous media. Is it a fictitious value? Can't I use the density of solid and fluid as it is while modeling p... | The density inside a porous medium cannot be the same, in general, as the density outside. The simplest way to understand why, is to look at the system (pourous medium + air inside and air outside) as a two component system. Interactions inside the porous medium modify the chemical potential of air inside. Condition of... | {
"language": "en",
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Is it possible to use visible light to transmit "radio" like AM/FM? When I see a big radio antenna, I like to imagine it's a giant incandescent light bulb filament in the vertical, but of a invisible light. So that it "glows" the radio, performing oscillations which contains all the music/voice information.
But at the ... |
But at the reverse, is it possible to create a practical experiment which modulates (or something) an analog audio signal and transmits it by glowing some sort of light, then have a antenna or sensor to pick it up and reproduce the signal to a speaker?
Yes, in principle.
Analog modulation of optical signals is not su... | {
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If I leave a glass of water out, why do only the surface molecules vaporize? If I leave a glass of water out on the counter, some of the water turns into vapor. I've read that this is because the water molecules crash into each other like billiard balls and eventually some of the molecules at the surface acquire enough... | The water molecules in the liquid attract each other. Their thermal velocity distribution allows some molecules to be fast enough to overcome this attraction. If it happens to a molecule at the surface to be kicked by such a fast molecule, it may be kicked with an impulse stronger than the attractive forces, and theref... | {
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Collision of rotating sticks Q: Two identical uniform sticks are rotating about their stationary centers with equal angular speeds. The vertical stick is slowly raised until its top end collides with the center of the horizontal stick. The sticks join together to make a rigid object in the shape of a T. Assume that the... | After thinking about it some more, we need to calculate the velocity of the t-joint where the two pieces connect. For now, consider the rotation of the vertical rod. Its angular momentum is:
$L=\frac{m\ l^2}{12}\omega$
When they attach, angular momentum in the x direction is conserved. The center of mass of the comb... | {
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Einstein's Elevator - Constant acceleration eventually reaches $c$. Can't that be used to detect gravity vs acceleration? Objects with mass that continuously accelerate will eventually approach $c$, but cannot exceed it. So if I find myself in an elevator, unable to determine if I'm in a uniform gravitational field or ... | In your idea, the at rest observer sees the accelerating rocket (or elevator) acquire a velocity $\Delta v_1=a \Delta t_1$ then an additional $\Delta v_2=a \Delta t_2$ in the next interval of time $\Delta t_2$. You assumed all the $\Delta v_i$ will eventually add up to c or greater. Unfortunately, according to special ... | {
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What's the difference in a $P$-$V$ diagram that is curved versus one that is straight?
So what would the difference be between the graph above versus one that has the same initial and final points but the path is curved. I'm sure it has something to do with temperature, so does it mean temperature is constant? Or is t... | You have $PV=NkT$, and along the path, $P=-aV+b$, where I assume you know how to compute $a$ and $b$. Replacing the second into the first results in:
$T=\frac{V(b-aV)}{Nk}$
which means that, along the path, the temperature varies quadratically with the change in volume.
| {
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Central Forces: Newtonian/Coulomb force vs. Hooke's law We know that a body under the action of a Newtonian/Coulomb potential $1/r$ can describe an elliptic orbit. On the other hand, we also know that a body under the action of two perpendicular Simple Harmonic Motions can also have an elliptic orbit. Hence I was wonde... |
I was wondering if we can differentiate between a body under the
influence of a central potential 1/r and a body under the action of
two perpendicular SHM's just by observing the orbits without prior
knowledge of the potential they are under.
As a first note, you have described the two motions in different ways... | {
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In particle colliders, according to QM, how are two particles able to "collide"? According to QM, we know that
The act of measurement forces a particle to acquire a definite (up to
experimental errors) position,
so in a particle collider, like the one in CERN, by which means do we force particles to acquire a defin... | To get particles to actually collide in a collider, many, many particles are formed into a high-speed beam which is separated into clumps that circulate one way around the collider, while other particles are similarly circulating around in the opposite direction. When both beams have been given the right amount of ener... | {
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Rabi flopping vs. rate equation approach? In Chapter 7 of C. J. Foot's Atomic Physics, Foot discusses the interaction of a two-level atom with radiation. He derives the phenomenon of Rabi flopping from the Schrodinger equation, using perturbation theory and the rotating wave approximation as is standard to do. Then he ... | The distinction is precisely given by the balance between the 'coherent dynamics' (ie., the Rabi flopping), and the rate of decoherence. In particular, the coherent dynamics of Rabi oscillations only holds when there is no dissipation, so the system remains in a pure quantum state.
The rate equations governing the syst... | {
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Transparency and visibility of light in tyndall effect Oil and water are both transparent however, they lose their transparency once they are mixed together. What is the reason for this? The size of the molecules are still the same so why does the substance become cloudy?
| Although the size of the molecules are still the same, the oil (nonpolar) cannot dissolve into the water (polar), so the oil drops form inside water, which is much larger than the molecule itself. Those drops (emulsion) reflects light and causes tyndall effect.
| {
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Hydrodynamic interaction between two spheres in $Re\ll 1$ flow I am studying the interaction between two spherical particles of radius $a$ in a low Reynolds number flow. Because of linearity, I know that their respective velocities will be linear in the forces applied to them. Similarly, the force $\boldsymbol{F}_j$ ap... | When distance between spheres is large compared to their size, the velocity of each sphere is predominantly determined by the balance between drag force and external force acting on it, and the inter-sphere interaction force is negligible. That's why the external force term is "blowing up" in relation to interaction fo... | {
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Does the existence of electrons validate the integral form of electric fields? For an arbitrary charged object, it seems to be the case that we express it as a continuous sum (sum on the reals/integral) of point charges $dq$ that have a canonical Coulomb's law force.
That is to say, for an arbitrary charged object, we ... | If I understand the question correctly it is about the impact on the field of the difference between a continuous and a discrete charge dustribution. This difference manifests itself as shot noise.
| {
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What is energy in quantum mechanics? Is it wrong to say energy is the expectation value of Hamiltonian?
Or should I say energy is the eigenvalue of Hamiltonian?
| You must be a bit more explicit in your language than in the classical case. Either could be correct but I lean towards the eigenvalue description and I'll explain why.
First of all, the Hamiltonian $\hat{H}$ is something which "belongs" to system. Energy is something which belongs to a state. So for example if a state... | {
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Why do we neglect higher order terms in Cauchy's Equation? Cauchy's Equation for finding the refractive index for a light of given wavelength is:
$$n(\lambda)=A+\dfrac{B}{\lambda^2}+\dfrac{C}{\lambda^4}.....$$
This formula however is simplified to
$n(\lambda)=A+\dfrac{B}{\lambda^2}$
by neglecting higher order terms.
... | The Cauchy equation is empirical relationship.
However, the refractive index can be obtained from the classical Lorentz model where a light wave creates oscillatory motion of the electrons and the electron displacements form dipole moments. This polarizes the medium , and the refractive index can be estimated theoreti... | {
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Hooke's full unapproximated law It is known that the Hooke's law relating the restoring force of a spring to the distance of retraction from the equilibrium position, is only an approximation.
That is, the equation $F=-kx$ is only the linear term that approximates the relationship, but gets less accurate the more the s... | The answer isn't well defined, since the full behaviour is different for different materials. It is not that the function is some mysterious transcendental function, but rather some function typically described by a series of powers of x with coefficients dependent on the material.
| {
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What is the electromagnetic 4-vector potential in Reissner-Nordström coordinates? If you have the usual Reissner-Nordström metric of a charged black hole, is the electromagnetic potential of the black hole still:
$$A_0(r,\theta,\phi) = \frac{Q}{r}$$
in these units?
| A Schwarzschild black hole has no charge and no electrostatic potential. This is the potential of a Reissner-Nordström black hole, in Gaussian units.
If you are talking about the potential of a point charge at rest outside a Schwarzschild black hole, with $r$ being some measure of distance from the charge rather than t... | {
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Spot welding technique I am trying to make electrical contacts by the spot welding technique. For Hall effect measurements, the contact size should be as small as possible and the sample is very very thin (0.025mm). But while spot welding, i am somehow able to make contacts, but it creates a hole in my sample. How to ... | Yes, there are several, as follows.
First there is thermosonic bonding, in which a heated tool applies local pressure to the two pieces being bonded, and then a burst of ultrasound is used to vibrate that tool. This technique is used to make contact between a silicon chip and a kapton/gold flexible leadframe (or "flex... | {
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Why is the internal energy the expected value of energies of individual particles? In this Wikipedia page: https://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics)
.. the total sum of energy in an ideal gas is given as:
$$\langle E \rangle = \sum_s E_s P_s $$
where $s$ runs over all states.
But isn't th... | Reading carefully the Wikipedia page, one finds that the internal energy is the "ensemble average energy, which is the sum of the microstate energies weighted by their probabilities". Therefore, $E_s$ is the energy of the s-th microstate, where a microstate is the microscopic state of $N$ particles. Once the equilibriu... | {
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Radial term in the spin-orbit coupling The spin-orbit interaction for the hydrogen atom is of the form
$\hat{H_1} = A\frac{1}{r^3}\pmb{\hat{L}}\cdot \pmb{\hat{S}}$
Now in my course, we treated this interaction by working in the basis of total angular momentum $\pmb{J} $and from there calculated the energy eigenvalues o... | You have uncovered one of the pitfalls of trying to treat spin non relativistically. If you had used the Dirac Hamiltonian rather than the Schrodinger Hamiltonian you would not encounter this problem. Frequently these $1/r^3$ singularities can be avoided in non relativistic treatments by using the fact that the nucleus... | {
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How come planets with different masses can orbit at the same velocity at the same altitudes? Angular momentum is equal to r × p and angular momentum is also what gives planets with lower orbits a higher speed (because angular momentum is conserved). So as r decreases either m or v (p=mv) has to increase and as the mass... | That the velocity of an orbiting body is independent of the orbiting body's mass is independent of mass is a consequence of Kepler's laws. Kepler's laws however are only approximately correct. Newtonian mechanics says otherwise: It says that ignoring the influences of other planets, the angular velocity of a planet orb... | {
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Why aren't particles constantly "measured" by the whole universe? Let's say we are doing the double slit experiment with electrons. We get an interference pattern, and if we put detectors at slits, then we get two piles pattern because we measure electrons' positions when going through slits. But an electron interacts ... | There are time-scales related to interactions, or, equivalently, interaction rates. These interaction rates are often calculated in lowest order based on Fermi’s Golden Rule. An experiment that measures electron interference needs to make sure that the time-of-flight of the electrons from the electron source to the obs... | {
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Parity transformation and mirror reflection I have some trouble understanding what exactly is parity transformation.
The definition of parity transformation is a flip in the sign of all three spatial coordinates, ie
$$(x,y,z) \rightarrow (-x,-y,-z).$$
Consider a stationary particle at a position $(a,b,c)$ in space des... | These are more general properties of the parity which I think, they give a better explanation of what this symmetry is really about.
The general definition of parity is an operator $\mathcal{P}$ with the properties $\mathcal{P} = \mathcal{P}^*$ and $\mathcal{P}^n=\mathbb{1}$, $*$ denotes complex conjugation. Most of t... | {
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Do topological transitions only occur at Dirac points? Topological phase transitions happen when the band gap closes. It is not true that all band crossings are topological.
There are Dirac (linear) band crossings, quadratic band crossings, Dirac-like triply degenerate band crossings, double Dirac cone crossings, semi-... | I'll leave the aspect of classifying band closings at topological transitions to others, and focus on this statement:
Topological phase transitions happen when the band gap closes.
Although that's the standard story, there's a growing understanding that you can actually have topological transitions without gap closin... | {
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Why friction causes energy to be lost in terms of heat when it appears to be an energy transfer mechanicsm? For example, when we move/walk, we apply a force (via friction) on earth, and the earth in turn on us. So essentially I see it as an energy transfer as follows:
Suppose I move in same direction as earths rotation... | You are describing static friction. Static friction is not dissipative. It's only when your foot skids on the surface that the friction force becomes sliding or kinetic friction. It is only sliding or kinetic friction that dissipates energy in the form of heat.
Hope this helps.
| {
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Muon decay in muons frame of reference, time muon expects us to record I have already asked a question regarding this concept but it was flagged as a duplicate. I know this misconception is very common for special relativity but I haven't found a question that talks about the misconception I'm having. Or atleast I have... | Indeed, the muon will think that our clock is not only running slow, but running ahead, by the usual relativistic $dv/c^2$ delay. The final reading we take down, according to the muon, is
$$\frac{t}{\gamma} + \frac{dv}{c^2} = \frac{t}{\gamma} + \frac{v^2}{c^2} \frac{t}{\gamma} = \frac{t}{\gamma} \gamma^2 = \gamma t$$
w... | {
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How do ion thrusters create a force against the spacecraft? I recently saw an old thread, How do reaction engines create a force against the rocket?, get bumped up, and it asks a good question: in a chemical rocket, the fact that the rocket exhaust gets propelled away means that Newton's Third Law requires that there b... | The principle is very simple, though of course actually constructing the things is a lot more complicated.
A propellant gas is ionised between two charged plates. The cations are attracted to the negative plate and repelled by the positive plate and acquire an energy $E = qV$ and a momentum $p = \sqrt{2mE}$.
The plat... | {
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How can we derive from $\{G,H\}=0$ that $G$ generates a transformations which leaves the form of Hamilton's equations unchanged? In the Hamiltonian formalism, a symmetry is defined as transformation generated by a function $G$ is a symmetry if
$$\{G,H\}=0 ,$$
where $H$ denotes the Hamiltonian.
On the other hand, a sym... | Express your equations of motion as
$$
\dot q= [H,q]\\\\\dot p=[H,p]
$$
Note that, on the mass shell, any function $f(q,p)$ obeys $\dot f(q,p)=[H,f]$. Now just hit the commutator $[G, ]$ on both sides in the equations of motion. Since $[G, H]=0$ then $G$ commute with the time derivative, i.e. $\dot G=0$. Using the Jac... | {
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Density $\rho$ in the Friedmann equations In the Friedmann equations:
$$\ddot{a}=-\frac{4}{3}\pi G(\rho+\frac{3p}{c^2})$$
$$\dot a^2+Kc^2=\frac{8}{3}\pi G\rho a^2$$
I didn't understand if $\rho$ is the mass density deriving from $m_0$ (the rest mass) or from $\gamma m_0$. In other words $\rho c^2$ is the energy density... | The $\rho$ comes from the component $T^{tt}$ of the stress-energy tensor, which is the density of mass-energy $E$, not the density of mass. We never have any way of knowing or defining the density of mass. For example, I could say that a proton in my body has some mass which contributes to my mass, but its mass may act... | {
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Why do electrons move towards a vacant position (hole) in a crystal lattice? Why do electrons in a crystal lattice move towards the vacant position? Aren't electrons stable in their current position?
| Consider first an intrinsic semiconductor crystal at zero temperature. The crystal will be charge neutral. All states in the valence bands (and at lower energies) are occupied with electrons, all higher energy states above the band gap are unoccupied.
Suppose now that we remove one electron from the valence band, there... | {
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Classification of 2D time dependent diffusion equation I was trying to classify the following PDE:
$$\frac{\partial{u}}{\partial{t}}=\frac{\partial^2{u}}{\partial{x^2}}+\frac{\partial^2{u}}{\partial{y^2}}$$
where $u = u(x,y,t)$. I was originally using the definition of $B^2-4AC$ and found this equation to be elliptic, ... | homogenous, linear and parabolic.
In a generalization of the 2-dimensional equation, any equation of the form
$$
\partial_t y = -L u
$$
where $L$ is positive elliptic (such as $-\nabla^2$) is said to be parabolic. It shares with the 2d case the fact that it has well defined solutions with inital value data an a line wi... | {
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Why do objects rebound after hitting the ground? When an object, say a shoe, falls from a height (under the influence of gravity), it rebounds after hitting the ground. For an object to move upwards, it requires a force to overcome its weight. When the shoe hits the ground some of its energy is lost and the ground push... | There are also many objects that do not rebound when they got the ground but rather they get deformed . So the total potential energy stored in the body at a height is used to deform the body and some energy is lost in the form of heat or sound energy. The objects which are elastic in nature have a tendency to rebound ... | {
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Is internal resistance of cell part of the equivalent resistance of the network of resistors? Do we include the internal resistance of cell while calculating equivalent resistance of network? Take, for instance, the question given. Do we include the 1 ohm internal resistance while calculating equivalent resistance of t... | From the wording "A network [...] to a battery with internal resistance" I would say the network is everything except the battery, where the battery consists of the ideal voltage source and the $1\,\Omega$ resistor. It is impossible to know for sure though what the author really meant.
| {
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Do orbiting planets have infinite energy? I know that planets can't have infinite energy, due to the law of conservation of energy.
However, I'm confused because I see a contradiction and it would be great if someone could explain it.
Energy is defined as the capacity to do work. Work is defined as Force x Distance. Fo... | Remember that work is force times displacement, not distance. Displacement is a vector, which means when a planet moves a full circle, its overall displacement is zero, resulting in a work of zero.
| {
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Confusion over units in force equation? While discussing Newton's laws, our book says
Force is proportional to rate of change of momentum
so they say
F is proportional to mass * acceleration if mass is constant
So $F=kma$ where $k$ is a constant.
They then say we choose a unit of force such that it produces accele... | I'm breaking your question into parts to identify what confuses you:
so $F=kma$ where $k$ is a constant
OK until there.
They say we choose unit of force such that it produces acceleration of 1ms-2 in 1 kg mass so 1N=k*1kg*1ms-2
So they "define" $1N$ such that $F=1 [N] = k \times 1[kg] \times 1[m.s^{-2}]$. If $k$ wh... | {
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How does Hamilton's Principle give us the path taken? We defined the action as:
$$\mathcal{S}(t)=\int_{t_1}^{t_2}\mathcal{L}(q_i,\dot{q_i},t) dt$$
where $q_i(t_1)$ and $q_i(t_2)$ are known and fixed.
Hamilton's principle states that the path that is followed has minimum action. Suppose we know just the initial coordin... | OP is correct: The stationary action principle (SAP)/Hamilton's principle(HP) needs$^1$ boundary conditions (BCs), i.e. both initial and final conditions. This is because we need the
$$\text{boundary-terms}~=~\left[\sum_{j=1}^np_j\delta q^j \right]_{t=t_i}^{t=t_f}~=~0\tag{1}$$
to vanish when we vary the action $\delta ... | {
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Why does a sonar or radar's frequency correlate with its resolution? A sonar's (or radar's) frequency determines its limit on the smallest size that it can detect and its resolution.
I've heard that it's due to aliasing, if so, please explain the reason behind it a little more.
EDIT: My own understading:
Lower frequenc... | I’ll confine my answer to pulsed radars. Longer wavelengths reflect just fine from large targets, unless the targets have been specially shaped to minimize back-scatter by diverting reflections, as in the design of stealthy aircraft.
The range resolution is roughly $c/2B$, where B denotes signal bandwidth, which is ... | {
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Why Neutrino is a ghost particle? why neutrinos are called ghost particle.why it is not affected by strong magnetic field. why it does not interact with matter. why it does not interact with gravitational field? I am unable to understand it
| This is a misleading way of talking in popularized versions about neutrinos, not recommended for physics vocabulary, since in the theories for particle physics "ghost" has a different mathematical meaning.
The everyday version of "ghost" is a moving impression that can pass walls and appear randomly, and popularizers ... | {
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How much time does it take for a broken magnet to recover its poles? I understand that when you cut a magnet you end up with 2 magnets but I wonder how much time does it take to the magnetic domains to rearange and form the new pole. I know the answer may vary depending on the size of the magnet, the material, and some... | The molecules that make up the magnet have a magnetic dipolar moment. You can think of them as small magnets aligned so that the total magnetic field is the sum of all the small magnets. If you cut a magnet in two, the two magnets are still made of aligned dipolar moments, so there is no rearrangement of poles. The two... | {
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Schrodinger's Equation in three dimensions Consider Schrödinger's Equation,
$$H=\sum^3_{i=1} \frac{p^2_i}{2m_i}+V(x_1,x_2,x_3).$$
In one dimensional case, we can analyse the shape of the potential, i.e
$$V(x)=\frac{1}{2}m_1 \omega^2_1 x^2$$
is the potential for quantum oscillator. The ground state of quantum oscillato... | The graphical representation of the probability density distributed over the three-dimensional space would be a four-dimensional plot--just like the plot of a probability density distribution over one dimension is two-dimensional and that of a probability density distribution over two dimensions is three-dimensional. T... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/464729",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 0
} |
What are the Basic Properties of a Photon? I want to grasp the idea of a photon.
While researching, I have come upon many different ways of describing a photon, but have found "quantum of the electromagnetic field" to be most satisfying. However, I still have a few questions about this description.
I. What does 'quantu... | I. A photon is the quantum, or the basic building block, of the electromagnetic field. For example, visible light, which is an electromagnetic field, is a large collection of photons.
Photons exhibit wave-particle duality. This means that they have some properties that exhibit their wave-like properties manifestly, whi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465083",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
If sound is a longitudinal wave, why can we hear it if our ears aren't aligned with the propagation direction? If a sound wave travels to the right, then the air molecules inside only vibrate left and right, because sound is a longitudinal wave. This is only a one-dimensional motion. If our ears are oriented perpendic... | The revised question, as I understand it, amounts to asking how it is possible for a sound wave propagating along (instead of towards) a wall with a small hole in it to generate any sound waves on the other side of the hole. What happens in this case is easiest to explain with a diagram:
Whenever the air pressure on t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465203",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "17",
"answer_count": 9,
"answer_id": 2
} |
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