Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
$\rho$ and $\omega$ mesons decays As far as I understand, typical decay for $\omega$ meson is into $3\pi$, while for $\rho^0$ is into $2\pi$. In fact they are quite similar particles (same spin, parity, similar masses). Why this difference in their decay?
| The $\rho$ forms an isospin triplet ($I=1$)and the $\omega$ is an isospin singlet ($I=0$). The $g$-parity
$$
g= Ce^{i\pi I_2}
$$ that determines the odd versus number of pions in the decay goes as $(-1)^I$.
| {
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"timestamp": "2023-03-29T00:00:00",
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Does the 4-vector gradient commute with "itself"? If yes, why do they commute? Does $[\partial_{\mu},\partial_{\nu}] = 0$? If yes, why do they commute?
| For a smooth scalar functions $f$ (which are the objects on which the vector fields $\partial_\mu$ are defined to act), we simply have that
$$[\partial_\mu,\partial_\nu]f=\partial_\mu\partial_\nu f -\partial_\nu\partial_\mu f= 0$$
because of the equality of mixed partial derivatives from elementary analysis. Because $f... | {
"language": "en",
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Why is there no temperature difference in the Joule expansion experiment? The whole system is adiabatic, and no heat exchange can take place. If the volume of the gas now doubles, it should actually cool down.
That's why I don't understand $dT=0$
| I like to think about these kinds of thermodynamic problems using kinetic theory and Newtonian mechanics, and not really worry about the ideal gas equation. If we look at problems this way, then temperature changes are really easy to understand. For example, let's consider the classic example where you adiabatically co... | {
"language": "en",
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"source": "stackexchange",
"question_score": "4",
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Fake Perpetual Motion Device using an Electromagnet I was watching a video of one of those fake perpetual motion machines where a ball falls down a hole and then flies off a ramp back onto the starting platform.
As suspected, the large base is hiding an electromagnet. Studying frames of one cycle it seems that the bal... | Another way that this might work is that an electromagnet is turned on when the ball passes through the hole in the platform. This electromagnet would accelerate the ball faster than gravity towards the bottom of the ramp. Before the ball reaches the lowest point in the ramp the electromagnet is switched off allowing t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/708154",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How does the combination of lens create a sharper image? There's a line in a book which states that the combination of lens helps create a sharper image, but I don't understand how. Does more magnification mean sharper image?
| I'd like to try explain this in the context of information. Images that have the highest resolution contain the most accurate information per unit area. In optics, this image information is carried by photons. The more photons collected from an image, the more accurately the image can be reproduced. In an ideal lens sy... | {
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Kinetic energy of quarks and mass of proton I read that:
Most of a proton mass comes from the energy of motion of its three quarks and from the energy carried by the gluons that keeps them confined together.
Does kinetic energy of the three quarks in a proton contribute to the mass of a proton? I assume the energy c... |
I assume the energy carried by the gluons is referring to the binding energy of the three quarks by the strong force.
It is more complicated than this. See how the strong interaction is figuratively modeled in terms of quantum field theory in this article
The invariant mass of the hadron is the sum of the four vecto... | {
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1D bound state for a real potential The prof says: "for 1Dimensional bound states with a real potential, the wave function is real, up to a phase".
The proof goes like this:
1D bound states are never degenerated. So $\Psi_{real}$ and $\Psi_{imaginary}$ are linearly dependent. So $\Psi \equiv \Psi_{real} +i\Psi_{imagin... | No, the wavefunction $\psi(\vec{r})$ is not just 1 complex number: it is infinitely many complex numbers, 1 for each value of position $\vec{r}$. In contrast, the professor is making the non-trivial statement that there exists a global (i.e. $\vec{r}$-independent) complex constant $c$.
For more details, see also this &... | {
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Isometry between Minkowski space and Tangent space In this notes Geometric Wave Equations by Stefan Waldmann at page 70 they have
Having a fixed Lorentz metric $g$ on a spacetime manifold $M$ we can
now transfer the notions of special relativity, see e.g. 50 , to $(M,
g)$. In fact, each tangent space $\left(T_{p}... | Two (metric) manifolds $(M,g_M)$ and $(N,g_N)$ are isometric if there exists a diffeomorphism $\varphi:M\rightarrow N$ such that $g_M = \varphi^*g_N$.
On the other hand, two pre-Hilbert spaces $(V, \langle \cdot,\cdot\rangle_V)$ and $(S,\langle\cdot,\cdot\rangle_S)$ (that is, vector spaces equipped with inner products)... | {
"language": "en",
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Momentum probability density from Wigner distribution I want to prove that $|\hat{\psi}(p)|^2= \frac{1}{2\pi} \int W_\psi \mathrm{d}x $ where $W_\psi $ is the Wigner function.
Starting with the definition I get ($z=-y$ and $u=x+z/2$):
$$\frac{1}{2\pi}\iint \psi^*\left(x-\frac{y}{2}\right)\mathrm{e}^{\mathrm{i}py} \psi\... | Use
$$
\psi\left(x\pm\frac{y}{2}\right)=\int dx e^{ip\left(x\pm\frac{y}{2}\right)}\bar{\psi}(p)
$$
and
$$
\int dxe^{i(p-p')}=2\pi\delta(p-p')
$$
| {
"language": "en",
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"question_score": "2",
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Question about the kinetic energy operator The Kinetic Energy Operator is essentially self-adjoint. Under what circumstances does it have a unique extension?
| The "true" kinetic energy is the self-adjoint extension you are referring to. As you know, the domain of an operator is integral to its definition. The "formula" we want for the kinetic energy operator is (ignoring some constants) given by $-\nabla^2$, but we need to decide which domain it should act on so as to be s... | {
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How to derive Shannon Entropy from Clausius Theorem? I am studying Quantum Information now, and I need to understand the entropy of a quantum system. But before I go there, I need to understand Shannon Entropy which is defined as :
$H(X) = -\sum_{i=1}^{n} {p(x_i) \log_2{p(x_i)}} $
where $X$ is a discrete random variabl... | These are not the same.
Shannon entropy (Information entropy), $H_\alpha=-\sum_i p_i\log_\alpha p_i$ applies to any system with specified probabilities $p_i$.
Boltzmann entropy, defined via the famous $S=k\log\Omega$ implies that the system occupies all the accessible states with equal probability, $p_i=1/\Omega$ (this... | {
"language": "en",
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Does gravitation really exist at the particle level? As I understand, we usually talk about gravity at a macro scale, with "objects" and their "centre(s) of mass". However, since gravity is a property of mass generally (at least under the classical interpretation), it should therefore apply to individual mass-carrying ... | Mass Spectrometer
I don't recall the formal name for the instrument but I was able to tour a lab at Ohio State University that had mass spectrometers that lofted ionized individual molecules a few feet up a column and waited for them to pass a detector as they fell due to gravity. Organic molecules aren't quite point m... | {
"language": "en",
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How much time after will two oppositely charged particles collide for both gravitational force and electrostatic force? Suppose two point objects charged with opposite charges $q_1$ and $q_2$ at a distance $r$ in a vaccum.
So, the net electrostatic force on both objects $= F_c = \frac {q_1q_2}{4π\epsilon_0r²}$ [$\epsil... | In this video by Flammable Maths, the solution to a similar problem is given.
The only difference is that we just need to include the electrostatic force, besides that the process is exactly the same.
Let's say we have two objects $1$ and $2$ with mass $m_1,m_2$ and charge $q_1,q_2$ respectivey separated by distance $... | {
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What happens to the potential energy when we connect 2 water tanks with different water levels?
Imagine combining 2 water tanks (with equal cross section areas) with different water levels.
I'll call them A (tank with the higher water level) & B.
When water is flowing from A to B, what happens to its potential energy?... | Looking at the following image, it's pretty obvious that the centre of mass will be lower, because the final state will be, just taking a portion of water (blue rectangle) and lowering it.
And obviously, the potential energy also is reduced (lowering mass centre, lowers total potential), in an ideal world the water wou... | {
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Showing that the integration measure is preserved under gauge transformation in the non-Abelian case I am trying to show that the integration measure we use in the Fadeev-Popov method of quantisation of non-Abelian gauge theory is invariant under a gauge transformation.
I am using Peskin & Schroeder chapter 16.2. The g... | What the authors means is this: When you disregard the shift all that's left is
$$ (\delta^{ab} + f^{abc}\alpha^c)\mathrm{d}A^b_\mu,$$
which is the infinitesimal version of a linear transformation generated by the matrix $M^{ab} = f^{abc}\alpha^c$. Since the structure constants are anti-symmetric, $M^{ab}$ is, too, and... | {
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Do supermassive black holes at galactic centers and the galaxies containing them spin with the same axis? If the galactic mass is rotating around a central supermassive black hole, should their spin axis not be the same, just as we would obtain for the rotation of a star and its planets ?
| There is no particular reason they need to. A planet does not necessarily have its axis aligned with the solar system or the galaxy. A star does not necessarily have its axis aligned with its stellar system or the galaxy. Our own star's axis is about 7 degrees out of alignment with the plane of the ecliptic.
If a blac... | {
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"source": "stackexchange",
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How to see that the electromagnetic stress-energy tensor satisfies the null energy condition? I am trying to show that the Maxwell stress-energy tensor,
$$T_{\mu\nu} = \frac{1}{4\pi}\left( F_{\mu\rho} F^{\rho}{}_{\nu} - \frac{1}{4}\eta_{\mu\nu}F_{\rho \sigma} F^{\rho\sigma} \right),$$
satisfies the null energy conditio... | While the answer provided by Nickolas Alves should suffice, here is an alternate proof of NEC satisfied by free Electromagnetic field using the idea of 2-spinor formalism (and hence, this proof is very particular to 3+1 dim space-time, see [1] )
The idea is that a real null vector $k^a$ can be written as tensor product... | {
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Eyes shut, can a passenger tell if they’re facing the front or rear of the train? Suppose you’re a passenger sitting in one of the carriages of a train which is travelling at a high, fairly steady speed. Your eyes are shut and you have no recollection of getting on the train or the direction of the train’s acceleration... | I think you might be able to distinguish the direction of motion by turning sideways and listening for the apparent motion of the clickety-clack sounds and vibrations from the carriage wheels (assuming old fashioned train tracks, on a modern high-speed rail line the sounds may not be perceptible).
At, say 100km/h and 2... | {
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What is the best way of evaluating time-ordered integrals numerically? In time-dependent perturbation theories, one encounters multi-dimensional time-ordered integrals
$$
(-i)^n\int_0^tdt_1\int_0^{t_1} dt_2 \cdots \int_0^{t_{n-1}}dt_n f(t_1,t_2,\cdots,t_n)
$$
What is the best way of numerically evaluating such multi-di... | The time-ordered integral can be transformed to a normal multi-dimensional integral over a rectangular volume by changing variables. Setting $t=\beta$, and using the following change of variables:
$$
\begin{cases}
t_1 = y_1\\
t_2 = y_2\frac{y_1}{\beta}\\
t_3 = y_3\frac{y_2y_1}{\beta^2}\\
\vdots\\
t_n = y_n\frac{y_{n-1}... | {
"language": "en",
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Wavefunction Amplitude Intuition Reading the responses to this question: Contradiction in my understanding of wavefunction in finite potential well
it seems people are pretty confident that, e.g., the wavefunction of a particle in a slanted potential well:
makes physical sense, since the system is non-dissipative, so ... | Having small or large quantum numbers makes the difference.
See also Correspondence principle:
In physics, the correspondence principle states that the behavior
of systems described by the theory of quantum mechanics
(or by the old quantum theory) reproduces classical physics
in the limit of large quantum numbers.
Th... | {
"language": "en",
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Electric potential generated by spherical symmetric charge density I know this question is pretty basic but I found a supposedly wrong formula in my notes and I'm trying to understand where this is coming from. Suppose we have a spherically symmetric charge density $\rho({\boldsymbol{r}})=\rho(r)$, then the formula I w... | The first formula seems to assume that the potential at point r inside the sphere is given only by the charge included in the sphere of radius r. This is true for the electric field but not for the potential, in general. You can see that this is the case taking a constant charge density. According to your formula (1) y... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is sand in a vacuum a good thermal insulator? My reason for thinking that sand in a vacuum would be a good insulator is that heat cannot be conducted in a vacuum, and the area of contact between adjacent grains of sand is very small, which means heat would transfer between grains relatively slowly. Is this correct, or ... | Simply put: If sand in vacuum had a heat conductivity close to that of vacuum, i.e., at least much closer to zero than the heat conductivity of the silicon dioxide (aka glass) it consists of, something similar would have to be true for sand in air.
But: the heat conductivity (all numbers from the German Wikipedia) of d... | {
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"question_score": "4",
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Why is skin depth quoted as when the amplitude has decayed by a factor of $\frac{1}{e}$ The definition of the skin depth is:
"Skin depth defines the distance a wave must travel before its amplitude has decayed by a factor of $1/e$."
My question why is the decay of 37% significant here. The EM wave will still have some ... | The mathematics (exponential decay) would suggest that infinite distance is needed for the amplitude to decay to zero. This would not be helpful, so an arbitrary agreed value is used. The choice of 1/e times the original amplitude gives a simpler form to the decay equation than another value would.
Not that the amplitu... | {
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What is an intuitive explanation for $T = \mathrm{const}$ when $\Omega(E) = e^E$? Temperature is related to number of microstates as follows:
$$
\frac{1}{k_{\mathrm{B}}T} = \frac{\mathrm{d}\ln{\Omega(E)}}{\mathrm{d}E} \ .
$$
Hence, if $\Omega(E) = e^E$, then $T = \mathrm{const}$. This contradicts my intuition. I expect... | The basic intuition here is that temperature is not about number of microstates as such. Rather, it is about how the number of microstates varies with the energy---the standard definition of temperature in terms of entropy and energy.
A hot system does not need to have a lot of microstates. The white-hot pieces of meta... | {
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Energy-momentum tensor for the k-essence theory could anyone please explain or show some simple steps how using matter action:
$S = \int d^4x \sqrt{-g} L(X, \phi)$, where $X = \frac{1}{2} g^{\mu \nu} \nabla_\mu \phi \nabla_\nu \phi$
We can derive energy-momentum tensor:
$T_{\mu \nu} = \frac{2}{\sqrt{-g}} \frac{\delta S... | When making the variations you need to use the following relation
$$\delta L (X, \Phi) = \delta X \frac{\partial L(X,\Phi)}{\partial X} + \delta \Phi \frac{\partial L(X,\Phi)}{\partial \Phi} \ ,$$
which is just a general fact for derivatives/variations of functions.
The variations with respect to the metric will only i... | {
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Invariants of inner product in pseudoreal representation of $SU(2)$ I am reading Peskin's and Schroeder (P&S), "An introduction to Quantum Field Theory", specifically the first paragraph on page 499 in section 15.4 "Basic Facts about Lie Algebras". At some point, the authors claim that the invariant combination of two... | I would like add to Qmechanic's excellent answer a bit of context from the practical point of view.
Apparently the question arises in classical Quantum mechanics not accounting for relativity. So then we can assume that spinors in 3D transform under the effect of rotations like representations of SU(2) which is the uni... | {
"language": "en",
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In order to solve for the states of a spherically symmetric parabolic potential do we need to use cartesian and cylindrical coordinates? In the general case a spherically symmetric potential, the Time Independent Schrodinger Equation is separable in spherical coordinates but not in cartesian, or cylindrical coordinate ... | You don't need to, but you can.
Essentially, what you're doing is choosing between expressing your energy eigenstates as products of functions of spherical, cylindrical, or Cartesian coordinates. Any one of these options is equally good, while in other problems the calculations will get quite cumbersome in, e.g., Carte... | {
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How does current flow in a purely inductive circuit if the net voltage is zero? Considering the equation,
$$E=−L\frac{di}{dt}$$
The negative sign in the above equation indicates that the induced emf opposes the battery's emf.
If we're talking about a purely inductive circuit, the induced emf is equal and opposite to ap... |
If we're talking about a purely inductive circuit, the induced emf is equal and opposite to applied emf. Isn't it just like two identical batteries in opposition?
If that's the case, how does the current flow?
It isn't, because two real batteries of same emfs acting against each other produce equals emfs whether ther... | {
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Why is quantizing the free electromagnetic field in the Lorenz gauge more subtle than in the Coulomb gauge? Quantizing the free electromagnetic field in the Lorenz gauge, $\partial_\mu A^\mu=0$, is subtle. We must add a gauge-fixing term to the action so that $\pi^0$ does not vanish identically. Also, we cannot impose ... | The thing about the Coulomb gauge is that, in vacuum, you get both $A_0 = 0$ and $\nabla \cdot \vec A = 0$, so it eliminates the $(A_0,\pi^0)$ d.o.f. right out of the gate - we just have $A_0 = 0,\pi^0 = 0$ consistently and only need to care about the spatial parts, and due to $\nabla\cdot \vec A= 0$, the whole thing i... | {
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Does electron-proton interaction and electron-electron interaction in an atom gives rise to a microscopic potential energy? When studying thermodynamics we come across a property of a system called internal energy, which is the sum of all energies possessed by the system at the microscopic level. Internal energy has tw... | It depends on your point of view. We say that a spring stores potential energy. In microscopic models, part of that is electrostatic, but part is due to "Pauli force" between electrons. However, in quantum field theory, Pauli force isn't a force and doesn't have a potential. Instead, it's associated with increased elec... | {
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"source": "stackexchange",
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Understanding the definition of a path integral In the Book "Quantum Mechanics and Path Integrals" by Feynman & Hibbs the path integral is approximated (page 32 and following) by
$$
K(b,a)\approx\int...\int\int\phi[x(t)]dx_1dx_2...dx_{N-1}\tag{2.20}
$$
with $b=(x_b,t_b)$ and $a=(x_a,t_a)$ being the start and endpoints ... | For question 2, the bounds should be from $-\infty$ to $\infty$. That is because at each time, we integrate over every possible position through the use of the identity
$1 = \int _{-\infty}^{\infty} |x \rangle \langle x | dx$
In terms of interpretation, at each point in time $t$, the position on the path can be any rea... | {
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Unitary evolution and von Neumann entropy In chapter 5 of the book "Statistical Mechanics" by Pathria it says
Since the density matrix evolves in a unitary manner, the von Neumann entropy is time-independent
Where the von Neumann entropy is defined as the trace
$$S[\rho(t)]=-\mathrm{Tr}\left(\rho(t)\ln \rho(t)\right)... | Hint: Use the spectral decomposition to write
$$\rho(0) := \sum\limits_k \lambda_k \,|k\rangle \langle k| \tag{1} ,$$
and then find an expression for $\rho(t)$ in terms of $\lambda_k$. Especially note that $\rho(t)$ has the same eigenvalues as $\rho(0)$.
Finally, again using the spectral theorem, derive that
$$ S[\rho... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/714098",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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What actually are microscopic and macroscopic viewpoints in thermodynamics? The microscopic viewpoint of studying a system in thermodynamics is the one in which we consider the system on a molecular/atomic/sub-atomic level. (is that even right?)
The macroscopic viewpoint is the one in which we ignore the molecular natu... |
Temperature is the measure of the average KE of the molecules of a system. Clearly, we're talking about molecules when we talk about temperature then why it is a macroscopic concept?
One should distinguish Thermodynamics and Statistical Physics.
*
*Thermodynamics is phenomenological macroscopic theory, describing c... | {
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Can a material be electrically polarized with electromagnetic radiation? Is charge separation possible by bombardnment of electromagnetic radiation?
As conventional dielectric materials can be polarized with a electric field, I am wondering if electromagnetic radiation, which is composed itself of electric fields; coul... |
Can a material be electrically polarised with electromagnetic radiation?
Yes, this always happens when radio waves hit an electrical conductor.
Radio waves are a special case of EM radiation. By synchronously accelerating surface electrons back and forth on an antenna rod, they emit polarised photons.
If a receiving ... | {
"language": "en",
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How can magnetic field lines form non closed loops? I recently came across this paper
"Topology of Steady Current Magnetic Fields", Am.J.Phys (1953)
The author points out the erroneous implications of representing magnetic field lines as closed loops.
He has used the below example to illustrate the problem.
Let us exa... | All the author is saying here is that if we follow the magnetic field line starting at $P$, it will do one of two things:
*
*Eventually return to $P$ after making $n$ circuits of the ring and $m$ circuits of the wire. This is what is meant by "an integral number of linkages": the number of circuits (linkages) made ... | {
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Why we use areal density to measure thickness in different practicals of physics? In many experiments like finding the gamma and beta absorption coefficients we use the thickness of aluminium foils in $gm/cm^{-2}$. Why we do that?, Shouldn't it be possible to only denote thickness in mm?
| First of all, it's not $\rm g/cm^{-2}$. It's $\rm g/cm^{2}$ or $\rm g\cdot cm^{-2}$.
The answer to your question is "Yes: you can specify thickness in millimeters". Call that thickness $d_{\rm rad}$, the radiation length in "length" units.
The thickness in $\rm g/cm^{2}$ is:
$$ L_{\rm rad} = \rho d_{\rm rad} $$
where $... | {
"language": "en",
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Deflecting a belt under tension I have a belt setup around two pulleys and I want to measure the tension on the belt by depressing it at the middle with a force gauge.
My colleague approaches this problem by taking the perpendicular components of the tension, doing
I don’t think this is the right way to approach this... | I'm voting with your colleague.
Everything comes down the the force it takes to deflect the belt at the point of contact, and since this is for a static situation, action equals reaction. The reaction is the belt pushing back against the defection, and that's going to be $2T\sin\theta$. And this is all about the belt... | {
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Will the potential energy is same in both the cases? Suppose there is a charge $Q$. Now bring in another charge $Q'$ from infinity to a position a distance $r$ from charge $Q$. Then the change in potential energy is equal to $kQQ'/r$.
My question is: will the potential energy will be same if the same charge $Q'$ is bro... | I would think no, it wouldn't be the same.
Having two charges already in position would alter the magnitude of the potential field for all the incoming charges- so it would require more or less work to move subsequent charges to the desired location.
| {
"language": "en",
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Difference between stable manifold and basin of attraction? In 'Nonlinear Dynamics and Chaos' by S. Strogatz, a distinction is made between a stable manifold and basin of attraction of a fixed point in phase space:
Here, the stable manifold of a saddle point is a line, and the basin of attraction of a stable node is a... | Maybe the most straightforward distinction is:
*
*If the set in question is a true manifold, it’s a stable manifold. By true manifold, I mean that it has a dimension that is not equal to that of its embedding space.
*Otherwise it’s the basin of attraction of an attractor. This basin may also be or contain stable man... | {
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How can we experimentally confirm that atoms/molecules in a solid actually "move"? The atoms in a solid are so attracted to each other that they "vibrate" and don't move past each other.
How do scientists "measure" that atomic vibration in a solid (let's say at room temperature)?
As a raw, uneducated person it is easy ... | Another way is to look at the quantum efficiency of photoelectric sensors using indirect band gap materials like silicon. For such materials, a long wavelength photon needs the assistance of a phonon (lattice vibration) to produce an electron-hole pair. A consequence is that the sensor's quantum efficiency varies with ... | {
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Why are fields described as force divided by mass or charge? I have read that application of force on a body from a distance, like gravitational or electrostatic force is a two-step process, first, the field is created by the body, then, the application of force on the second body by the field. I want to know why the e... | Answering my question for anyone who benefits from this.
This is what I understood of everything I read about it . Electric field is simply like a constant of force applied by a particle at a particular point in space, a ratio which is made independent of the test charge by dividing the force formulae by the mass/charg... | {
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Why, in this solution, acceleration is constant even when it depends on distance between two charges? I used integration of $a=dv/dt$ to solve this Why, in this solution is acceleration constant, even when it depends on the distance between two charges? I used integration of $a=dv/dt$ to solve this.
Question
Two partic... | The total change in field energy equals the negative of the total amount of work done on all charges.
For 2 point charges, the total change in field energy is just the change in potential energy between them
$$(U_{2}-U_{1}) = -(\Delta K_{q_{1}} + \Delta K_{q_{2}})$$
$$U_{2} - U_{1} = \frac{1}{4\pi\epsilon_0}\frac{ q_{... | {
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Why do we hear frequencies in the basis of sine waves? When we talk about hearing frequencies and overtones, we almost always mean in the basis of sine waves, according to a standard Fourier decomposition. Couldn't we also decompose a signal into a different basis of orthogonal periodic functions, like square waves? Ac... | We can and do in some cases. Take a look at the Zernike Polynomials for decomposing 2-dimensional frequency distributions, for example.
The short answer is that sine waves are nice and clean, behave well when applying Fourier or other transforms, so why go make things difficult?
| {
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The value of $g$ in free fall motion on earth When we release a heavy body from a height to earth. We get the value of $g=9.8 \ ms^{-2}$. Now, I'm confused about what it means. For example, does it mean that the body's speed increases to $9.8$ every second? Or, does it mean that the speed of the body is $9.8 \ m/s$?
| $$F=-G\frac{Mm}{r^2}$$
$$\frac{F}{m}=-G\frac{M}{r^2}$$
$$a=-G\frac{M}{r^2}$$
Force divided by mass is by definition acceleration. This is denoted as g, as in, the acceleration due to gravity
For the surface of the earth this value is around $-9.81$.
As such the standard definition of acceleration applies. Acceleration... | {
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XKCD Focusing moonlight - Only the component of light perpendicular to a surface heats the surface? Is this XKCD https://what-if.xkcd.com/145/ saying that a surface is only heated by the component of the rays that are perpendicular to the surface?
Conservation of étendue:
| The claim is
... you can't smoosh light beams together without also making them less parallel, which means you can't aim them at a faraway spot.
I don't see where it says "a surface is only heated by the component of the rays that are perpendicular to the surface".
The diagram you show is a counter to the previous on... | {
"language": "en",
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Confusion about the Spinning Top Consider the following symmetric spinning top with a fixed point on the horizontal surface.
I have two questions concerning its motion:
*
*let $\underline{\Omega}$ denote the precession angular velocity, that is, the angular velocity of the reference frame of the spinning top with re... | I think your equation $\Omega\wedge P_c=r_c\wedge Mg$ is not correct. The l.h.s. should be the derivative of the total angular momentum w.r.t. to point of contact with the floor, not w.r.t. the center of mass.
| {
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Did Huygens understand light to be a transverse wave or a longitudinal wave? We have this source that claims Huygens "assumed light to be longitudinal", which contradicts this source which claims "Huygens believed that light was made up of waves vibrating up and down perpendicular to the direction of the wave propagati... | Possibly interesting quote
from the "Note by the translator" section (page ix) of
"Treatise On Light" by Huygens, Christiaan
https://archive.org/details/treatiseonlight031310mbp/page/n10/mode/1up
(bolding mine)
The Treatise on Light of Huygens has, however, withstood the test of time: and
even now the exquisite skill... | {
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Why does the the dielectric constant of a ferroelectric increases with temperature, below $T_C$?
The above figure is taken from C. Kittel.
When a ferroelectric substance (say, BaTi${\rm O}_3$) at room temperature is gradually heated, the dielectric constant $\varepsilon_r$ first increases and then attains a peak at a ... | This reference may help: . "In a crystalline solid, there are only certain orientations permitted by the lattice. To switch between these different orientations, a molecule must overcome a certain energy barrier ΔE", which requires enough thermal energy. With decreasing temperature, "the orientational mode becomes “fro... | {
"language": "en",
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Photon-Atom Interaction: Atomic Spectrum vs Photoelectric Effect Apologize if the question is elementary or already asked (not aware of it).
Far as I understand:
*
*Ground state electrons in atom can only absorb photons of certain (discrete set of) energies to jump to higher energy levels;
*In photoelectric effect t... | you state:
Ground state electrons in atom can only absorb photons of certain (discrete set of) energies to jump to higher energy levels;
The correct statement is "atoms can absorb photons of certain (discrete set of) energies to jump to higher energy levels;"
The electrons with the nucleus are one quantum entity ,the... | {
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Why doesn't $dU=nC_{v}\,dT$ hold for all substances? Consider the following proof for change in internal energy of real gases, liquids and solids(assuming Non-$PV$ work $=0$):
*
*Let X denote real gases, liquids, and solids
*The First law of thermodynamics is $dU=dQ-dW=dQ-PdV$, which also holds for X
*At constant v... | There is a difference between a constant volume (isochoric) process (step 3 in your "proof") and the infinite number of possible paths between two equilibrium states where the initial and final volume is the same.
For a gas where the initial and final volume is the same, it is true that $dq=nC_{v}dt$, even if the volum... | {
"language": "en",
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Gauge-invariant vertex structure for $h\to\gamma\gamma$ via fermion loop I am struggling (a bit) with the following diagram for scalar Higgs to two photons.
$h\to\gamma\gamma$" />
If I put $q_\mu$ on-shell (or at the very least if I put both $q_\mu$ and $q'_\nu$ on-shell),
the vertex function should have the following ... | Ok i made a pretty instructive mistake. Since the diagram is power-counting finite, i assumed it would be fine to take the momentum integral to be 4-dimensional from the start. Then at some point i used
$$
\int\frac{d^4k}{(2\pi)^4} \frac{4k^\mu k^\nu}{[k^2-\Delta]^3} = \int\frac{d^4k}{(2\pi)^4} \frac{k^2 \eta^{\mu\nu}}... | {
"language": "en",
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"source": "stackexchange",
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Heat death of the Universe in LCDM I have often read that the heat deat of the Universe occurs in cosmologies where its age can be arbitarily large, even with a cosmological constant. However the standard LCDM cosmology's conformal age is bounded, even in the arbitarily far future. It seems to me that for the Universe ... | There are TWO LCDM possible assumptions related to what the universe will be like towards the end part of time.
*
*All matter gravitationally bound together in a galaxy, or a collection of galaxies, will ultimately form into a single black hole. All other matter will become so far away from this black hole so that it... | {
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How do resistors work? Why is the current before and after a resistor exactly the same? I understand the same amount of charge that enters the resistor leaves, but current is defined to be charge per time. The way I understand it, resistors slow down the speed of electrons, so even though the same amount of charge that... | Actually the resistor is decreasing the drift velocity because of more collisions and interaction between electrons and the lattice. However, think about what happens if an electron suddenly slows down when entering the resistor. A still faster electron in the wire approaching the resistor will feel the negative charge... | {
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How can the Cosmic Neutrino Background (CνB) have a temperature? How can any neutrino have a 'temperature'? The word temperature usually refers to the average velocity of massive particles, correct?
And the Cosmic Microwave Background (CMB) has a 'temperature' based on the temperature of a 'black body' that would emit ... | A single particle is not assigned a temperature (which is exhibited by a very large ensemble of particles), it is described by its kinetic energy. So a single neutrino can be described as having a certain amount of kinetic energy- but it in and of itself has no "temperature".
Now if we imagine instead a huge burst of n... | {
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Does dusk really remain for a shorter period of time at the equator? It is said that the dusk remains for shorter time at equator than the poles. Because, the equator rotates faster than poles. But it is also true that time is the same in every latitude, and if it's true, then the dusk should remain the same at equator... | The line that separates day and night (illuminated vs dark side of the Earth) is called the shadow terminator. Now, because we don't experience a sudden lights-on/lights-off transition, but a gradual shift towards nighttime (or dawn, at the other end), you can imagine there's a transitional region - a band of sorts - a... | {
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Why doesn't the variation of resistivity with temperature go both ways? I've learnt that the variation of resistivity with temperature for a conductor is:
$\rho=\rho_0(1+\alpha (T−T_0))$
Let's consider resistivity at 0℃ and 100℃.
When heating the conductor from 0℃ to 100℃,
$ρ₁₀₀=\rho_0(1+\alpha (100-0))$
α=$\displaysty... |
I've learnt that the variation of resistivity with temperature for a conductor is:
$\rho=\rho_0(1+\alpha (T−T_0))$
This is not a real physical relationship. It is just a convenient first-order approximation. Suppose we have some arbitrary resistivity $\rho(T)$ as a function of temperature. Then, at any $T=T_0$ we can... | {
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How does an electron move in the $p$ orbital? This is my first time learning about orbitals and I am very confused over how do electrons move around the nucleus in the
$p$ orbital.
Wouldn't it have to move out of the orbital where probability of finding an electron is low in order to complete its revolution? Maybe my u... | While this isn't above criticism, I think that a good starting point to get used to quantum physics is to picture the situation in the following way:
*
*The electron doesn't have to behave like a point-like object that has a trajectory.
*Whether it behaves like a point-like object, a wave, or any hybrid of the two d... | {
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If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it? I have read that water (or any other liquid) cannot be compressed like gases and it is nearly as elastic as solid. So why isn’t the impact of diving into water equivalent to that of diving on hard concrete?
| Adding another perspective to the existing answers:
In your usual diving scenario, water is not confined to the points in space it occupied before, while a slab of ground is – on account of water being liquid and ground being solid.
To construct a scenario where you primarily experience the compressibility when diving ... | {
"language": "en",
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Translating Ashcroft and Mermin's "Second Proof" of Bloch's Theorem to Dirac's Notation At the end of this post I attach Ashcroft and Mermin's proof of Bloch's theorem which is not essential per se (the proof using lattice symmetries is more general), but is key in being used later as a jumping off point for the nearly... | Here's how to do it by inserting an extra complete set of momentum states.
\begin{align*}
\langle \mathbf{r}|H|\psi\rangle
&=\langle \mathbf{r}|
\int \mathrm{d}{\mathbf{k}} \mathrm{d}{\mathbf{k'}}\,|\mathbf{k'}\rangle\langle \mathbf{k'}|
\left(\frac{\mathbf{p}^2}{2m}+U\right)|\mathbf{k}\rangle\langle \mathbf{k}|\psi\ra... | {
"language": "en",
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"source": "stackexchange",
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Are we always allowed to treat an inductor as a battery with the same voltage? When there is an induced emf, Kirchhoff's Loop Rule no longer is true, because electric fields are nonconservative when there is an induced current, as stated by Faraday's Law:
However, I have seen explanations that incorporate inductors an... | It seems I was mistaken in my original answer.
You can treat (emphasis on the word treat) an inductor as a battery if you took into consideration the emf in the voltage formula and apply Kirchoff's law. But in technical details, since the electromagnetic field is not conservative here, you can't in general apply Kircho... | {
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Application of "real" Grassmann Gaussian integrals In Appendix 2B of the CFT yellow book by Francesco et al, the authors introduced two types of Grassmann Gaussian integrals (the $\theta$'s below are generators of a Grassmann algebra):
*
*The "real" one
$$
I = \int d\theta_1 \cdots d\theta_n \exp(-\frac{1}{2} \theta... | The "real" integral evalautes to the Pfaffian of $A$ where for an $2n$-by$2n$ skew symmetric matrix $A$
$$
{\rm Pf}A= \frac 1{2^n n!} \epsilon_{i_1, \ldots, i_{2n}} A_{i_1,i_2}\ldots A_{2n-1,2n}.
$$
The Pfaffian has the property that $({\rm Pf} A)^2= {\rm det}A$,
and has applications many places in combinatorics. ... | {
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A cylinder rolling down an inclined plane A few questions popped into my mind while studying rotational motion.
Take a cylinder to the top of an inclined plane. Suppose there is friction. Let go of the cylinder. If it is rolling without slipping, is its acceleration constant over the time interval it is rolling down? I... | The acceleration of the center of mass (CM) is the net force divided by the mass; the net force is the component of gravity down the incline minus the force of friction up the incline. You do just apply $\vec F = m \vec a_{CM}$ to determine the acceleration of the CM, $\vec a_{CM}$; however, you need to consider the r... | {
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Does the front of a light wave always propagate at $c$ in media Consider light moving along one dimension at the classical level. I am interested in the situation where a wave front impacts a material with some generic index of refraction $n(\omega)$, and propagates through. My calculations seems to suggest that the ve... | the earliest appearance of the front of an electromagnetic disturbance (the precursor) travels at the front velocity, which is c, no matter what the medium.
| {
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Question about gravitational waves Gravitational waves are measured by interferometers, in particular by the change in length of one of the arms, with respect to the other. In this scenario, the light that has always the same speed, measures a delay by traveling one of the arms. My question is: if an arm pass from leng... | The ruler resists attempts to change its length, due to electrostatic forces between atoms in the ruler (eg see Young's modulus). This means the ruler will not change as length to the same extent as space, when a gravitational wave passes.
| {
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Expression of Klein-Gordon field in Heisenberg picture In Schrodinger picture, the scalar field is
$$
\phi(\vec{x}) = \int \frac{d^3 p}{2E(\vec{p})} \left( a(\vec{p}) e^{i\vec{p}\cdot\vec{x}} + a(\vec{p})^{\dagger} e^{-i\vec{p}\cdot\vec{x}} \right). \tag{1}
$$
We change to the Heisenberg picture, we have
$$
\phi(x) ... | One easy to deal with these difficulties is to just imagine the integral is discretized, then the measure even more clearly is just a c-number multiplying the annihilation and creation operators, $H$ commutes with a c-number (you can put identity with it, to be more clear), then you can move the factor inside.
| {
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Can plasmas be black bodies? I have recently heard the claim that sun can not be composed of plasma because plasma can not be a black body.
I am an uneducated layman, I've seen a lot of people (laymen) deviate from accepted scientific consensus. I am skeptical and I don't have enough knowledge about physics to argue it... | A necessary but not sufficient property that a volume of emitting atoms and molecules needs to have, in order to emit light as a blackbody is that they are in local thermodynamic equilibrium (LTE) with a single well-defined temperature.
In many cases this is just an idealization and even in earth's stratosphere and bey... | {
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Why do ceramics have a yield strength? From what I've learned so far, I look at yield strength as the beginning of plastic deformation in an object.
If ceramics don't (well usually don't) undergo plastic deformation, how can it be said that ceramics have a higher yield strength then metals?
| You can also think of yield strength as the end of the elastic region. For ceramics this is convenient because they do indeed have an elastic region. Alternatively, instead of saying they have "no" plastic region, say that ceramics have zero plastic region, which fits with the fact that the breaking point is at the p... | {
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Why is the slowest point of Earth's rotation in the middle of the year? The following image is taken from Wikipedia's article on the leap second.
Why is the slowest point each year in the middle of the year around July? Does being further from the Sun cause the Earth's rotation to slow down? What's the mechanism in pl... | I don't have access to the paper but the abstract from Carter(1984) suggests that the major cause of rotational variations is due to "the exchange of angular momentum between the atmosphere and the mantle."
This is echoed by Earth Rotation Variations from Hours to Centuries:
Variations with periods of five years or le... | {
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What would happen if you reduced the coupling of $SU(2)$ in the standard model to zero? Ultimately, my goal is to find a free parameter that you could change in order to significantly reduce the strength of, or eliminate, the weak interaction. Would such a modification leave other parts of the Standard Model unchanged?... | It is straightforward to see, even though your ultimate vision should be in trouble. I assume you mean decrease the coupling g of just SU(2), and leave the EM coupling e and the Higgs v.e.v. v alone, which cannot be done.
You then just look at the formulas:
$$\cos \theta_\text{W} = \frac{g}{\,\sqrt{g^2+g'^2\,}\,}, \qqu... | {
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Why flapping rudder produce net thrust if one half-stroke produce thrust and second half-stroke drag? In small sailing boat like optimist is well know technique when there is no wind, rudder pupming which push boat forward.You just need push-pull rudder stick left to right with fast movement.
Rudder works complety unde... | The key point may be that stern of the boat moves laterally. During the first half of the stroke, the force exerted on the rudder by the water is forward and to the side. The sideways component causes the boat to rotate, so that, if you were to release the tiller and allow to rudder to align itself with the flow (which... | {
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Does the force between two magnetic poles ever reach zero? If we hold two magnetic like-poles together and start to move them away, would the repelling force reach absolute zero at certain point?
In that scenario, as a layman, I think that there is something paradoxical :(
We can never reach absolute ZERO in Physics. T... | The magnitude of the force between the two magnets will approach zero as they get further and further apart. It never (in theory) actually reaches zero because they are always a finite distance apart - we say the force approaches a limit of zero as the distance between them approaches (but never reaches) infinity. Of c... | {
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What is the relative acceleration composition law in General relativity? In Euclidean geometry we have the following relative acceleration composition law:
$$ \vec a_{DE} + \vec a_{EF} = \vec a_{DF} $$
Where the relative acceleration between $i$ and $j$ for any $i$ and $j$ is given by:
$$ a_{ij} = a_i - a_j$$
with $a_i... | Precisely this question has been asked and answered in the following paper:
*
*Bini, D., Carini, P., & Jantzen, R. T. (1995). Relative observer kinematics in general relativity. Classical and Quantum Gravity, 12(10), 2549, doi:10.1088/0264-9381/12/10/013, free pdf at archive.org.
Abstract. The straightforward refor... | {
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How do quantum probabilities transform under Lorentz transformations? I think I get how scattering probabilities transform under Lorentz transforms. Once the interaction phase is over, the final probabilities become time independent. Hence, every observer could describe the final state using the same probabilities.
But... | Wavefunctions are not compatible with Special Relativity where the number of particles can be changed over the course of an experiment, perhaps what you mean then is something like the electron field? If so the problem is just not there since all formulations of QFT are manifestly Lorentz invariant (just look at their ... | {
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Mass definition One definition of mass is 'a measure of the quantity of matter in an object at rest relative to the observer'. What do 'at rest' and 'relative to the observer' mean here? I know it has to do with mass resisting motion, but I cannot get what these mean.
| I would guess the confusion arises because of the (widespread but misguided) belief that in special relativity mass increases with velocity. For more on this see Why is there a controversy on whether mass increases with speed?
If we define the relativistic mass as:
$$ m_r = \gamma m = \frac{m}{\sqrt{1 - v^2/c^2}} $$
th... | {
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Shape of fastest spinning rod A one-meter steel rod of variable thickness is attached at one end to a spinning hub. The cross-sectional area of the rod is a function $f(x)$ of the distance $x$ in meters from the hub, x ranging from 0 to 1. My question is: how can I choose the function $f(x)$ to maximize the speed at wh... | Assume that you know the primitive F(x) of the integrand.$$ \frac{dF(x)}{dx}= \rho. x.f(x). \omega ^{2}$$ Then your equation reads:$$ F_{tu} f(c)=F(1)-F(c)$$ Differentiate both sides relative to c to get:$$F_{tu} \frac{df(c)}{dc} =- \frac{dF(c)}{dc}=-\rho. c.f(c). \omega ^{2}$$ From which you get:$$ f(c)=k. e^{- \frac... | {
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Boundary conditions of the Casimir's effect on Sakurai On 3rd edition of Sakurai's modern relativistic quantum mechanics, section 7.8.3 when discussing the Casimir effect, we want to write down an expression for the vacuum energy for two metal plates separated by distance $d$:
$$\tag{7.183}E_0(d)=\hbar\sum_{k_x,k_y,n}\... | Regarding the former issue, the book simply integrates twice from $0$ to $+\infty$ both in $k_x$ and $k_y$ and multiplies the result by a factor $2\times 2$, because the integrated function is symmetric under $k_j\to -k_j$.
Notice that, in fact, a factor $1/4$ which arises from $$dn_x dn_y = \frac{L}{2\pi}\frac{L}{2\p... | {
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Does the intermolecular forces change during phase transition? When water is heated but not yet boiling, I understand that the intermolecular attraction does not change, but the molecules vibrate more.
But when water boils to gas, does the forces of attraction between the molecules change, or are the intermolecular for... | Interactions between molecules of water are always the same, regardless of the temperature and the phase. What happens when you heat water is that the increase in temperature causes the water molecules to have higher average velocity, so they can overcome the attractive interactions and a gas forms.
The reason why this... | {
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If angle random walk (ARW) is the integration of white noise [°/s], why is its unit [°/sqrt(hr)] and not [°]?
How can ARW have the unit [°/sqrt(hr)], if it's the integration of white noise which has the unit [°/s]? Shouldn't ARW be given in [°]?
I don't understand the correlation between these two. Besides, how can I ... | The angular random walk is a Wiener process in the angular dimensions, which means that the increments of the process are independent (uncorrelated) and that the differences follow a Normal Distribution (ND) with 0 mean and variance $t-s$ (with $t>s$),
$$W_{t}-W_{s}\sim\mathcal{N}(0,t-s)$$
Since every ND can be express... | {
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What percentage of sunlight isn't scattered by the atmosphere? What percentage of sunlight isn't scattered by the atmosphere and instead will arrive at your eyes directly from the sun.
It's been aksed here before but a proper answer hasn't been given.
I was thinking about the effects looking directly at the sun would h... | A good approach to the question is the Air Mass Coefficient, widely used in solar/photovoltaic context.
It deals with the scattering and extinction of the solar radiation in visible and near-visible spectrum.
This may or may not be a good measure for you, depending on what use you have for your sunlight. E.g. human eye... | {
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Brightness of bulbs in Parallel When adding bulbs in parallel, the brightness is brighter than that of series. But does that mean adding bulbs in parallel will increase the brightness of the other bulbs?
My intuition is as follows: When adding a bulb in parallel the current doubles, but that current splits between the ... | You have it correct except that the parallel bulbs aren't in a branch and the current doesn't double. The power generator produces a constant voltage. Both are part of the same system so both have full voltage through that system and will always have full voltage.
The difference with the other bulbs comes because you a... | {
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Why does the opposing force differ in when falling on concrete vs on water in spite of Newton's third law? If a person jumps from the first floor of a building and lands on a concrete surface, they will suffer serious injury because of Newton's third law.
If the same person jumps the same distance and lands in swimming... | We should calculate the Force required to break the concrete. I don’t think that the force which is generated from falling certain height is enough to break the concrete since it’s Mechanical properties are strong enough to withstand, that’s what we say resistance by the solid body when you apply force on it on some pa... | {
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Why does this fan with one blade missing rotates counterclockwise while running? Video: Fan with one blade missing rotates while running.
The fan worked just fine until my friend tried to stop the spinning blades with her finger and knocked one off. Now it always rotates counterclockwise when running. Can someone expl... |
the red points are the blades center of mass . the rotation about the y-axes ,cause a wind force $~F_w~$ towards the y-axes. the torque about the z-axes ,$~\tau_z~$ cause the ventilator to rotate .
with
\begin{align*}
\begin{bmatrix}
\tau_{xi} \\
\tau_{yi} \\
\tau_{zi} \\
\end{bmatrix}
=\begin{bmatrix}
... | {
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Why is it easier to raise AC current to high voltage than DC? In my country (and maybe all around the world I don't know) once electricity has been generated, it is then raised to 200k Volts for transportation.
I know this is to reduce the loss. Given $P=U.I$ and $P=I^2.R$, raising U will lower I and so limit the loss ... | Because voltage is induced by the rate of change in the magnetic field.
If we tried to build a DC transformer, then to maintain the rate of change in the magnetic field the magnetic field would have to increase without bound, this is clearly impossible for two reasons.
*
*It would imply the input current increasing f... | {
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Nature of tangential friction force When a ball rolls down a ruff slope the frictional force acts tangent to the ball and causes the angular acceleration of the ball but at the same time the frictional force is acting to reduce the translational acceleration of the ball. How is this possible when the frictional force i... |
How is this possible when the frictional force is acting only
tangentially and not through the centre of mass of the ball?
It is possible because the static friction force that enables rolling (without slipping) gives the ball both rotational kinetic energy and translational kinetic energy of its center of mass (COM)... | {
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Question Regarding The Movement of Charges We know that two electrons repel each other since they have like charges, which means they move in opposite directions. But how can they move if they exert equal and opposite charges, aren't the forces balanced which means there is no movement?
| Let $-q_1$ be placed at x = 0. Let $-q_2$ be placed at x = 1.
Charge 1 exerts a force on charge 2 via Coulomb’s law. The only force exerted on charge 2 comes from the electric field of charge 1. I.e. the only force on charge 2 is a repelling force due to charge 1. Because the repelling force is the only charge exerted ... | {
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Illuminance Formula This page says illuminance is
$$E=\frac{I}{L^2} cos \space \alpha$$
This page does something similar, but it ignores the $cos \space \alpha$ factor. Which is the correct formula?
Note: I don't have a physics background. I was looking at optimization problems in Calculus (which is why I came across t... | I believe the first formula is the correct illuminance. It takes into account the angle of the table's surface. The second definition seems to be for luminance or something similar. See this page, for example.
| {
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What is the analogy of cross section for particle decays? So if two particles are fired at each other the chance they interact is the cross section of the interaction. What is the equivalent term for the chance that a particle decays into certain particles? If it is the branching ratio, then what does the decay width m... | Here is how the cross section has been used in particle physics.
Early collision experiments were intended to measure the size of particles from their collision rate. Rutherford’s experiment, which collided alpha particles and gold nuclei in 1911, revealed that nuclei are much smaller than previously supposed. But soo... | {
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Is turbulence more likely to form with the Euler equation as opposed to Navier-Stokes? The Euler equation models perfectly inviscid fluids. Under this assumption, with $\nu = 0$, the Reynolds number should be infinite. I would guess that this implies the Euler equation is always turbulent, but this is not the case as i... | Wiki states on turbulence:
Turbulence is the time-dependent chaotic behaviour seen in many fluid flows. It is generally believed that it is due to the inertia of the fluid as a whole: the culmination of time-dependent and convective acceleration;
So every continuum equation which includes material derivative of flow ... | {
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Can I really see what is on the opposite side of a black hole? This question is only about objects outside the event horizon. Both the observer and the object are just outside the event horizon.
I have read this question:
An observer can see the back side of the neutron star to some extent and can actually see the who... | There is this new video showing the effect on Messier 87 black hole.
| {
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Methods in Numerical Relativity I have been reading the book of Masaru Shibata Numerical Relativity to grasp some ideas on the methods used. I see that at the heart of the method the system of differential equations is "converted" in a set of algebraic equations, by the means of finite difference method and this works ... | One reason is inertia. FDM has worked (and continues to work) for over 50 years, and a lot of development has been done in that time to optimize and build on the early codes. Is there any indication FEM will be better than what we already have? Not that I'm aware, so it would be a huge task to get back to the cutting e... | {
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How is Newton per meter Cubed related to Newton per meter squared (=Pascal)? Is there a way to relate $\frac{N}{m^3}$ to $\frac{N}{m^2}$?
| I have used force density ($N/m^3$) in calculations of optical forces. That is, when light interacts with a three-dimensional object, how is the optical force distributed in space? A total force ($N$) is applied to the whole object, and then that force is distributed through the object as a density. If there is a direc... | {
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Questions about Maxwell's demon I've been reading about Maxwell's demon and the current accepted solution for it (deleting information results in an increase in entropy), but there are two things I don't understand about the solution.
*
*Suppose the demon has a large enough memory to store all the information about t... | The Demon's memory store acts like an entropy reservoir. In the process of measuring the speed of each molecule, the Demon reproduces the random pattern of fast and slow gas molecules on either side of the barrier in the memory store, so the entropy for the entire system is exactly the same. When the Demon deletes the ... | {
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Destroying a black hole Is there any (known? theoretical?) way to destroy a black-hole?
*
*"Destroy" means forcing it to disappear - before it evaporates through Hawking radiation.
*"Disappear" means that it stops being a black-hole: no more event horizon, no more impossibility for light to escape it, etc - it becom... | The standard definition of a black hole in classical GR is that it has an event horizon. By that definition, there is no way to convert the stuff that has fallen into the hole to other stuff that can then be observed from infinity. That would just mean that the spacetime never met the definition of being a black hole s... | {
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Why is current finite for point charges? If an electron passes through a flat plane, then there will only be a single point in its entire path which lies on the plane,i.e the entire charge of an electron passes through in an instant (as it is a point charge), then why isn’t the current infinite at that instant and zer... | Yes, single point particle with finite charge crossing a control plane means infinite current on that plane, in that instant of time. However, this infinite current does not last for any finite amount of time; it is there only for that instant, i.e. zero time interval.
If there are more such particles, we have current ... | {
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Circular motion of two bodies: how to determine when they meet up again?
Let's say that there are two satellites, one of them moves in the red orbit and the other one in black one. At the time t0 they start together on the green point. How can I set equations to deduce when are they going to meet each other again? Mas... | If you use Keplers third law $T^2/a^3=\textrm{const},$ you will know the relative orbital periods by knowing the relative size of the major axes of the two orbits. You can calculate $nT_1=mT_2.$ If there are not whole numbers $n$ and $m$ that make the equation true, they will never meet exactly again.
| {
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How do you visualize the electric field exciting this vibration in a molecule? This image is very common in chemistry, where most people don't really visualize the electric field that produces molecular excitation.
What would be a good first picture to think about? Maybe it could be classically reduced to a dipole int... | On the picture the wave is monochromatic end describes by formula
$$E(x,t)=sin(\omega t-kx)$$
So if we put there coordinate of dipole $x_d$ we'll obtain
$$E(t)=sin(\omega t+kx_d)=sin(\omega t + \Delta\varphi)$$
I think the best way to visualize it is to draw vectors of field, that point to the direction where dipole wi... | {
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If resistance in an electric current is 0 (ideally) then would there even be current flow? From my understanding batteries are used to charge electrons with electric potential which they then use to do work on resistors in a circuit. After doing work the electrons return to the opposite terminal with less potential ene... | No, in fact it would be quite the opposite. The current would be so high that all of the voltage would be dropped over the internal resistance of the battery. Thus the terminals would be at the same voltage even with the large current.
| {
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"answer_id": 0
} |
Why Is Capacitance Not Measured in Coulombs? I understand that the simplest equation used to describe capacitance is $C = \frac{Q}{V}$. While I understand this doesn't provide a very intuitive explanation, and a more apt equation would be one that relates charge to area of the plates and distance between them, I'm havi... | Capacitance, as you describe it, is capacity to store charge - it's not charge itself. So why you expect it to be measured in unit of charge?
For SI Units, it has been decided to measure every physical quantity in terms of only 7 base units, namely, second, meter, kilogram, ampere, kelvin, mole and candela. All other u... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/728239",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "20",
"answer_count": 7,
"answer_id": 3
} |
Partial derivative of momentum with respect to position in Poisson bracket representation The representation of a Poisson bracket is given by the following equation:
$$\tag{1} \{f,g\} = \sum_{s=1}^n \sum_{i=1}^{d=3}\left ( \frac{\partial f}{\partial x_i^{(s)}} \frac{\partial g}{\partial p_i^{(s)}} - \frac{\partial f}{\... | Variables $x_i$ and $p_i$ are independent variables used as arguments for the Hamiltonian $H(x_i, p_i)$. Since they're independent variables, the partial derivative of one w.r.t. the other is identically zero.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/728359",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Varying energy density of photons? I know photon energy density is proportional to the fourth power of the scale factor, because it dilutes and redshifts.
I want to take into account the added photon energy density from astrophysical sources along the scale factor to the CMB energy density from the beginning of the age... | For self-consistency, we need the energy to come from somewhere. For astrophysical sources, it of course comes from matter. In that case you can assume that there is some energy exchange rate $\Gamma$ such that
$$
\frac{d}{dt}\rho_m + 3H\rho_m = -\Gamma\rho_m,
\\
\frac{d}{dt}\rho_r + 4H\rho_r = \Gamma\rho_m,
$$
where $... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/728750",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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