Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Fluid velocity in a vertical pipe Consider a pipe with length $L$ and uniform radius $A$ is held vertically. According to the continuity equation, the velocity of water going into the pipe seems to be the same as the velocity of water coming out. But according to Bernoulli's equation:
$$P_{atm}+\frac{1}{2}\rho v_1^2+\r... | Your version of Bernoulli's equation only applies to steady flow -ie. to motion in which the velocity at any point is indepenedent of time. In the case of your pipe open at both ends the fluid will accelerate. In that case you must use the time-dependent version of Bernoulli. For the irrotational flow of in incompressi... | {
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"timestamp": "2023-03-29T00:00:00",
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Calculating reflection of light when the refractive index changes continuously Suppose you have 2 materials, one with refractive index $n_1$ and the other with refractive index $n_2$, and a plane-wave coming from the first material hits the interface with an incident angle of $0^\circ$.
Fresnel tells us that the reflec... | I will outline two approaches. Both involve numerical solution.
Method 1. Use the transmission matrix concept, but for a very large number of small steps through the material. For each small step $\delta z$ find the matrix based on the local change of index, and multiply it onto the matrix you have so far.
Method 2. S... | {
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On the Heisenberg uncertainty relation Are there fundamental limits on the accuracy for measuring both position $q$ at time $t$ and momentum $p$ at time $t+\Delta t$, with tiny $\Delta t$?
If yes, why?
If no, why can't one then measure (in principle) both $q$ and $p$ arbitrarily well at the same time $t$ (which is not ... | Measuring arbitrarily well means observing eigenstates of the observables, so the answer depends on whether the state can evolve from a position eigenstate to a momentum eigenstate in time $\Delta t$.
| {
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Are vectors in integral infinitesimals? There are many equations that deal with the integral, like Gauss' Law and Coloumb's Law. For example, to find the electric field from a continuous distribution requires integrating $d\overrightarrow E = k \frac {dQ}{r^2}\hat r$.
In these situations, it is common to see things l... | In physics, we think of them as ratios. They work like ratios algebraically in that you can divide them and cancel them out.
The Archemedian property thing is not really relevant because we are not saying they are real numbers, just that "$d\vec{E}$ is a symbol for an arbitrarily small change in $\vec{E}$, and $\frac{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/307378",
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Is metric a classical or a quantum field in General Relativity? I am currently reading the article of A Castro about $AdS_3/CFT_2$. I have a confusion in reconciling several definitions. It appears that I've understood them imprecisely or may be wrong. These definitions are:
Einstein gravity, Quantum gravity and Gene... | General Relativity is a classical theory (specifically it is not a quantum theory: people sometimes use 'classical' to mean something like 'newtonian', which it clearly is not). The metric in GR is therefore a classical field.
We do not have a working quantum theory of gravity: if we did, and if it was curvature-based... | {
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The 'right' way to express the line element $ds^2$ Taking Minkowski space as an example, the line element is commonly expressed as,
$$ds^2 = dt^2 - dx^2-dy^2-dz^2.$$
However, when expressing the line element in terms of an orthonormal basis $e^a$ it may be expressed as,
$$ds^2 = e^t \otimes e^t - e^x \otimes e^x - e^y ... | I'm not entirely sure the question but with regards to defining a line element $(ds)^2$ in terms of basis vectors we have the relation $g_{ij}=\mathbf{e}_i \cdot \mathbf{e}_j$ so the line element is given by
$$ (ds)^2 = g_{ij} dx^i dx^j = (\mathbf{e}_i \cdot \mathbf{e}_j )dx^i dx^j$$
| {
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Why is there less information in a written book (which makes me see things) than in a random string of letters and spaces? If I read a book I can see with my inner eye (or ear) see the plot developing. With a random string of letters, with random spacings, this isn't the case. Then why contains the former less informat... | The English language contains about 170 000 words. Some words occur more frequently than others. So if we assign the number 0 to the spaces between words (which doesn't reduce the information) the number 1 to the most frequently used words, the number 2 to the second most frequently used ones, etc. until we arrive at t... | {
"language": "en",
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What are the de Sitter Killing vectors? I'm trying to find the Killing vectors for de Sitter space using global coordinates, i.e. the spherical foliation. In the end, I want to know how to perform a boost on the 1+1 and 3+1 de Sitter manifolds so that I can make two points lie at the same spatial position (the spatia... | To assist with your problem, I will describe the general approach, when we don't necessarily know what we're looking for. As you are aware, finding the Killing vectors $X^\mu$ requires solving,
$$\nabla_\mu X_\nu + \nabla_\nu X_\mu = 0$$
which is an over-determined system of differential equations. As you know, these K... | {
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Can a mirror reflect only one color while allowing all other visible light pass through? Is it possible to construct a mirror such that it only reflects certain wavelengths of visible light while allowing other wavelengths of visible light to pass through? I was reading about microwave ovens and how the doors are desig... | There are mirrors which reflect only particular color wavelengths and not the others. There are mirror which can reflect particular symmetry and not the other. By using proper coating and proper atomic symmetry elements we can develop different kinds of mirrors. In Kurukshetra, India In science panaroma, both these kin... | {
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Is short circuit technically the same as overloading? Taking the simplest circuit: battery and resistors.
If I connect lots of resistors in parallel, wouldn't that increase the current to an extent that it would be technically be very similar to shorting the circuit?
| Yes. The equivalent resistance for $n$ equal resistors of value $R$ connected in parallel is $R(n)=\frac{R}{n}$. As $n \to \infty$ then $R(n) \to 0$, provided that $R$ is finite.
| {
"language": "en",
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"source": "stackexchange",
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Gravitational time dilation and neutron stars How great is the gravitational time dilation close to a neutron star? How would the effects of gravitational time dilation compare with the event horizon of a black hole?
| As it says in the Wikipedia article referred to by Kyle, the relevant formula applicable to clocks situated in the gravitational field of a spherically symmetric object is that an observer at infinity sees a clock in the gravitational field slowed by a factor $(1 - r_s/r)^{-1/2}$, where $r_s$ is the Schwarzschild radiu... | {
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Isn't D'Alembert's wave equation enough to see that Galilean transformations are wrong? The D'Alembert equation for mechanical waves was written in 1750:
$$\frac{\partial^2u}{\partial x^2}=\dfrac{1}{v^2}\dfrac{\partial^2u}{\partial t^2}$$
(in 1D, $v$ being the propagation speed of the wave)
It is not invariant under a ... | There's no problem with the non-invariance of D'Alembert equation for mechanical waves, if I understand what you mean, because mechanical waves do have a preferred inertial frame, an "aether".
For example, a sound wave in a fluid satisfies the wave equation with speed: $$c^2=\left(\frac{\partial p}{\partial \rho}\righ... | {
"language": "en",
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How is it possible for other animals to have better night vision than humans, who can detect individual photons? According to the Wikipedia article on night vision,
Many animals have better night vision than humans do, the result of one or more differences in the morphology and anatomy of their eyes. These include hav... | That research shows that humans can detect single photons, not that we're particularly good at it.
Averaging across subjects’ responses and ratings from a total of 30,767 trials, 2,420 single-photon events passed post-selection and we found the averaged probability of correct response to be 0.516±0.010 (P=0.0545; Fig.... | {
"language": "en",
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Maximally entangled quantum state - not in hilbert space? I am reading a paper about Gaussian quantum states and the mathematical formalism used to describe them. At one point the authors say
"An important example of a Gaussian state is the maximally entangled state $\Phi$. In their endnotes, they then note that
"Altho... | The maximally entangled state in the Gaussian framework is the state that one gets when taking the limit of infinite energy/photon number of a particular class of state (see equation (4) of the paper you linked). From equation equation (2) it is clear that such a state is not bounded, and thus is not in $\mathcal{H}=L^... | {
"language": "en",
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Synchronized Clocks in Inertial frame Will the synchronized clocks placed in an inertial frame remain synchronized forever?
| Yes.
Assuming, of course, they are mathematical clocks and this is a thought experiment in flat spacetime. Reality introduces too many unquantifiable variables.
They will drift apart under the influence of any acceleration in the direction of their displacement from one another.
If they are held a fixed distance a... | {
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Should Beta Minus decay put an upper limit on the mass of a neutrino? Beta minus decay emits an electron with a range of energies. Within the nucleus, the following is happening: $n\rightarrow p+e^-+\bar{v}_e$. For this reaction to be possible, by lepton number conservation, the neutrino must be present. Since this neu... | Your idea is correct. However, tyical energy releases in a beta decay are of the order of MeV, while neutrino masses are in the range of an eV or so. Current experiments are not sensitive enough to give a definite value of the neutrino mass, but produce upper limits. The best data so far, combining the Minz and Troitsk... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/309019",
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"source": "stackexchange",
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Fourier transforming the wave equation twice The wave equation
$$\nabla^2 u(r,t)-\frac{1}{c^2}\frac{\partial^2 u}{\partial t^2}(r,t)=0$$
can be Fourier transformed with respect to time, using $\frac{\partial}{\partial t}=i\omega$, to obtain the Helmholtz equation:
$$\nabla^2 u(r,\omega)+\frac{\omega^2}{c^2}u(r,\omega)=... | When solving PDE we usually allow solutions to be distributions (aka generalised functions). I'll spare you the details; you'll have to read a book on PDE by a mathematician to understand that there is a deep connection between PDE and distributions. Long story short, the distributional solution of
$$
(k^2-\omega^2)u(k... | {
"language": "en",
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Clashing definition of rays in Weinberg and Sakurai and Born interpretation without normalizability In Sakurai's Modern Quantum Mechanics, it is stated that
One of the physics postulates is that $|\alpha\rangle$ and $c|\alpha\rangle$, with $c\neq 0$, represent the same physical state. In other words, only the "directi... | The quantum state associated to a Hilbert space vector $\psi $ is isomorphic to the orthogonal projector on the subspace spanned by $\psi $. Since $\psi $ and $c\psi $ span the same subspace for any $c\neq 0$, the state associated to either one is the same.
| {
"language": "en",
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Charging by friction Why does charging by friction charges an insulating material even if an insulator does not allow flow of electrons between an object to another? Is it because of the TriboElectric effect but doesn't it violate the law with the material being an insulator?
Does being a conductor or an insulator aff... | Let's consider the following case: an object made of ebonite and some cat fur. Electron's from cat fur will move to the ebonite.
The friction energy $E$ is transferred to the electrons on the outside layer which are in this way freed from their bonds.
Since the material is an insulator they have no where else to go ex... | {
"language": "en",
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Why does a wave not interfere with its secondary wavelets? Huygens principal says that every point wavefront is the source of a secondary wavelet. If this is true, why do those wavelets not interfere with the main wave? Shouldn't waves looks like a circle of interfering circles?
| Huygens principle is taught at the high school level because it was an important historical concept that broke down the old particle only theory of light and showed that a wave model would explain the observed interference pattern. It worked well until in the early to mid 1900s quantum concepts about light as a wave f... | {
"language": "en",
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What constitute the secondary particles beam when a high energy proton beam hits a target material? Basically I want to know what particles emerge along with high energy photons(not sure about it) as the second beam when a specific high energy proton beam is incidented upon a target material such as iridium or gold. Ca... | At the level of complexity suggested by this question, the only reasonable answer is "it depends." Lots of types of particles are produced when hard protons interact with matter, and a clever experimentalist can build an extraction system to focus on any number of them.
The 800 MeV proton accelerator at Los Alamos was ... | {
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Why does a force not do any work if it's perpendicular to the motion? I have a book that says the Moon's orbit is [in this context assumed to be] circular. The Earth does no work on the moon. The gravitational force is perpendicular to the motion. Why is there no work done if support force is perpendicular to the motio... | I think you are right @Shrodingers cat. It would be better to clarify the answer this way.
Work done (w) = F . d
= F d Cos θ
At 90 degrees, θ = 90 and Cos 90 = 0,
W = F x d x Cos 90
= F x d x 0 = 0 Joule.
So, when the force is applied perpendicularly to the surface, the work done will be zer... | {
"language": "en",
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Why are there no stable isotopes with an atomic mass of 5 or 8? One of the things I've encountered in my travels is the mass-5 roadblock. Rod Nave writes about it on his excellent educational hyperphysics website:
The helium-4 nucleus or alpha particle with a mass of 4 is particularly stable. But there are no is stabl... | The extreme stability of He-4.
Look at the decay modes of the the eights and they produce two alphas and if it is necessary convert a neutron/proton to a proton/neutron with an appropriate beta decay.
The production of two alphas is energetically favourable.
Li-6 and Li-7 lack nucleons to form two alphas.
Li-5 kick... | {
"language": "en",
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What is the significance of the phase constant in the Simple Harmonic Motion equation? The displacement of a particle performing simple harmonic motion is given by $x = A \sin(\omega t + \phi)$ , where $A$ is the amplitude, $\omega$ is the frequency, $t$ is the time, and $\phi$ is the phase constant. What is the signif... | All the phase angle does is to give you a facility to decide on the displacement of the particle undergoing shm at time $t=0$ or any other time.
With your phase angle of $\phi$, assuming it to be positive, the graphs of $x_1 = a \sin (\omega t)$ (grey) and $x_2= A \sin (\omega t + \phi)$ (red) are shown below.
In thi... | {
"language": "en",
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Relative velocity with relativistic speeds in 3D I have a question regarding the relative velocities of two objects in $3$D space. If objects $A$ and $B$'s velocities are being observed by stationary observer $C$, what is the velocity vector $A$ will see $B$ with or vice versa. This question also assumes $A$ and $B$ ar... | Let $C$ be rest frame $S$ (or lab frame, earth frame, etc) and $A$ be the moving frame $S'$.
Transformation of velocity
Velocity of $B$ observed by $A$ is
$$\mathbf{v}'=
\frac{\mathbf{u}+
\left(
\dfrac{\gamma_{v}-1}{v^2}\mathbf{u}\cdot \mathbf{v}-\gamma_{v}
\right)\mathbf{v}}
{\gamma_{v}
... | {
"language": "en",
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Calculating work to move a particle I have this question : There is a negatively charged spherical shell. Within this shell is a positive charge q which is at the center of the shell. How much work is required to move the charge from the middle to a position where the particle is right next to the inside wall of the sh... | The electric field due to the negatively charged shell is zero inside due to symmetry.
There is no field inside ,so force on the particle will be zero and since force is zero you don't need to push the particle against electric field to bring the particle from the middle to a position where the particle is right next t... | {
"language": "en",
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Leading/Lagging terminology for sinusoidal waves Is there a method to identify which wave is leading and which wave is lagging from their equations?
For example, if the two waves are $A\sin(\omega t+\pi/6)$ and $A\sin(\omega t+2\pi)=A\sin(\omega t)$ (by trigonometric relations), is the second wave leading in phase or ... | If you start from $y_1= A\sin(\omega t)$ and compare it with $y_2= A\sin(\omega t+ \phi)$ you find that time $t=0$ motion $1$ has a displacement of $y_1=0$ and motion $2$ has a displacement of $y_1=\sin \phi$.
You will see that whatever motion $2$ does motion $1$ does a little later in time so motion $2$ leads motion... | {
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A question on Collison of macroscopic particles
Hello,
In the above question I could solve for average elastic force by taking velocity with respect to wall and finding change in momentum of the ball after that divided change jn momentum by time interval. Answer comes out to be option b.
But as it is written in the qu... | Alright this is what I got:
sorry for being so slow :(
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Understanding a step in the derivation of the length contraction effect in special relativity I've been trying to figure out how the equation for length contraction is derived in my textbook (Krane, Modern Physics 3e) since a few of the final steps are omitted. The equation in question is:
$$
L = L_0/\gamma = L_0 \sqrt... | It isn't clear which bit is foxing you, so let's go through the argument:
This is viewed from the Earth frame i.e. the frame in which the light clock is moving. In this frame the length iof the clock is $L$. In the outward trip the light moves a distance $L+ut_1$ in a time $t_1$, and since light moves at the speed of ... | {
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Would it be possible to walk up a wall under right circumstances? For example, you are in a box that is connected a distance $R$ from a clockwise spinning centre. If I understand correctly, the spinning box is a result of the resulting centrifugal force $F_{centrifugal}$ = $\frac{mv^2}{R}$. The person then would be pus... | In simple words: Depends on your velocity.
Because if we look from the frame of reference of the box we find the the centrifugal force would provide the normal reaction (assuming cofficient of friction to be constant) and hence the friction force to balance gravitational force acting on the man.
u*(mv^2/r) ≥ m*g(this i... | {
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Short question about moment force I have a question about moment Forces. Let $\mathbf{e_1}$, $\mathbf{e_2}$ be the unit vectors defining a Cartesion coordinate system $Oxy$.
Let $\mathbf{F}$ be the force applied at point $A$.We have:
$$\mathbf{F} = F_x \ \mathbf{e_1} + F_y \ \mathbf{e_2}$$
where
$$\begin{cases} F_x &=... | There is a strict convention for cross product in three space. Your plane $Oe_1e_2$ is viewed as sitting inside the three space $Oe_1e_2e_3$ with orthonormal basis vectors $e_1, e_2, e_3$ and you have the cross product between two vectors $OA = x \, e_1 + y \, e_2$ and $F= a \, e_1 - b \, e_2$. Then the cross product i... | {
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Glasses underwater So I figured the refraction of the cornea is based on the index of air and the vitrous humor to make a perfect image. Underwater this is messed with because water has the same index as the eye. Hence you can't see clearly underwater without making an air pocket with scuba goggles for example.
Would ... | Yes, it’s possible to make glasses that allow you to focus underwater. You could use a high-index material with a concave lens, or a low-index material (such as air) with a convex lens.
| {
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"source": "stackexchange",
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Why doesn't current decrease in series combination? I know that the question is quite stupid but I want to get an insight of this case. consider 3 resistors connected in series with a battery, after the current passes through resistor 1 it loses some of its energy, the kinetic energy of the charge carriers will definit... | You are right - but not for long...
The situation you describe is unstable. This is not steady current. More electrons enter the resistor than what leave it. It will be "filled up" quickly. There will be a pile-up, a queue, of incoming electrons waiting to enter.
When electrons accumulate at a point like that, the ele... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/311558",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Radial motions moment of inertia I'm looking for some references on a specific moment of inertia, for radial motions of a spherical body. In my calculations, I got this integral :
\begin{equation}\tag{1}
\bar{I} = \int r^2 \, dm = \int_{\mathcal{V}} \rho(r) \, r^2 \, d^3 x,
\end{equation}
where $\rho$ is the matter de... | The moment of inertia is the measure of resistance to angular acceleration about an axis. Unless I'm mistaken, what you're after is the modulus of elasticity $E$ (or Poisson's ratio $\nu$) of the object. That dictates the response to radial motion given a uniform pressure field acting on the surface of the sphere.
| {
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Why the generator of $U(1)$ is the particle number operator $N$? When $U(1)$ symmetry is broken, the particle number is not conserved any more. What is the relation between u1 and particle number. Why the generator of $U(1)$ is the particle number operator $N$?
| For a single-particle state, a $U(1)$ rotation operation is simply multiplying a phase factor of the form $e^{-i\theta}$. The same operation on an $N$-particle state multiplies $e^{-i\theta}$ for each particle and hence $e^{-iN\theta}$ on the quantum state in question.
It is easy to see that the operator acting on the ... | {
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"source": "stackexchange",
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Finding Gravitational Force b/w 2 People I just need some clarification. The question is:
What is the gravitational force between two 100 kg people standing 1 m apart, and how does this compare with the gravitational force of either of them relative to Earth?
I'm guessing the formula to use here is Newton's Law of Gr... | $$F = \frac{G m_1 m_2}{ r^2}$$
where $r$ is the distance between the center of gravity of the individuals.
$$
F = \frac{6.67\cdot10^{-11} \text N \cdot { \text m^2/ \text k\text g^2}\times 100~\text k \text g \times 100~\text k\text g}{1~\text m^2}=6.67\cdot10^{-7} \text N
$$
The gravitation force of one of them with... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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If magnetic fields are created by moving charges, how do magnets work? This is probably is stupid question but I think it must clear up some misconception I have. Magnets, presumably have magnetic fields. But where are the moving charges? Don't we need a current?
| Most of the magnetism in a magnet comes from the magnetic dipole moment of the electrons orbiting its atoms. If we think of the electron as a small spinning charged sphere, then it is the spinning chrage that makes the current. Unfortunately this is a not a good model because the surface of the electron (assuming its... | {
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Is the Moon in a "Freefall" Around the Earth?
The force of gravity keeps our Moon in orbit around Earth. Is it correct to say that the Moon is in “free fall” around Earth? Why or why not?
I think the answer is yes. The moon is falling towards the Earth due to gravity; but, it's also orbiting the Earth as fast as it's... | Earth's moon, Luna, is free falling. More particularly, it is in
orbit around the sun, Sol, and is perturbed in its orbit by a nearby
planet, Earth.
Solar gravity acceleration at Earth/Luna orbital distance ($1.5\times 10^{11}m$):
($\frac{2\pi R_{orbit}}{3.16 \times 10^7})^2/R_{orbit}$ = $0.0059 ms^{-2}$
Earth gravi... | {
"language": "en",
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"source": "stackexchange",
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Sea quark parton annihilation? Consider the figure below1:
This can be read as follows (please correct me if I am wrong): two particles come in and 'fragment', a parton from each particle $C$ and $D$ annihilate to form the particle $X$. An intuitive guess is that the partons $C$ and $D$ must correspond to valence quar... | Yes, this can really happen. One example is a process called Drell-Yan production (at a hadron collider). A Drell-Yan event is the interaction of a quark and an anti-quark, which annihilate to form a photon or Z-boson (which then at some point decays to a pair of leptons).
At a proton-proton collider this can only happ... | {
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How can we compare the ratio of strenghts fundamental forces? I have read in many books that the ratio of strengths of gravitational force, electromagnetic force, nuclear force is 1:10^36:10^38 (one: 10 raised to thirty six: 10 raised to thirty eight). On what basis are we able to compare this? I mean, there is no conn... | A ratio is produced by comparing the gravitational force $F_g=\dfrac{Gm^2}{r^2}$ between two protons or electrons of mass $m$ and separation $r$ with the electrostatic force $F_e=\dfrac{e^2}{4\pi\epsilon_o r^2}$ with the same separation.
$$\dfrac{F_e}{F_g}=\dfrac{e^2}{4\pi \epsilon_o Gm^2}$$
The exact ratio you get dep... | {
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Why can I assume the force to be constant in this particular interval? If I have force, or any function $f(z)$, I was told that I can assume it to be constant only in the interval $dz$.
However, in this case, I had to calculate the work done by the spring force as a function of $y$
Over here, I assumed the spring forc... | It is, in general, by definition. $dx$ and $dy$ are defined in such a way that the force can be assumed to be constant in such an interval.
That's the general case, the way we use infinitesimals in physical problems mostly. Exceptions to this may occur.
| {
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How does the temperature of an ideal gas exhausting into vacuum vary? Since a gas at a certain pressure exhausting into vacuum has no atmospheric pressure to push against, there shouldn't be any adiabatic cooling taking place.
But looking at the energy conservation:
$TdS=dU+VdP+PdV$
$TdS = 0$ {Adiabatic process}
$PdV =... | The gas in the container does work on the elements of gas that are moving towards the orifice and out. As the the gas remaining in the container expands, it does work and thus cools down.
One can use the dX description for any element in the container, if it does not move too violently. Increase of internal energy of t... | {
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Calculating the (expected) kinetic energy of an electron in the ground state of a Coulomb potential? I've been struggling with this all week to no avail.
I'm asked to calculate the expectation value of kinetic energy for an electron in the ground state of a Coulomb potential. I know that it ought to be $ 13.6 \, \mathr... | The factorization into a radial part plus the angular momentum operator is true, but you don't really need it; instead, you can simply use the Laplacian in spherical coordinates,
$$
\nabla^2
= \frac{1}{r^2}\frac{\partial}{\partial r}r^2\frac{\partial}{\partial r}
+\frac{1}{r^2\sin(\theta)}\frac{\partial}{\partial \the... | {
"language": "en",
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Spherical lens ray-tracing simulation is not focusing rays I am trying to make a very basic ray-tracing simulation of lens.
*
*A single ray origin trigger light photons of a supposed single frequency in all directions. (I do not consider chromatic aberration).
*Some lens emulated as a couple of spherical superficie... | You have found the defect of a perfect spherical lens called spherical aberration which manifests itself when dealing with rays which are far from the principal axis.
It is precisely the fact that the lens is spherical which causes this lens defect.
The simple lens formula is only an approximation for rays which are ... | {
"language": "en",
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Is Lcm really equal to Icm x w? Let's suppose a body is rotating about some axis passing through the centre of mass (cm) with a angular velocity $\vec \omega$.
The angular momentum about the centre of mass axis is given by $L = I_{cm} ||\vec \omega||$, with $I_{cm}$ being moment of inertia about the axis.
Now, does it,... | The angular momentum of a rigid body rotating about some point is given by $\vec L = \mathrm I_\text{cm}\, \vec \omega$, where $\mathrm I_\text{cm}$ is the moment of inertia tensor about the center of mass. It's neither a vector nor a scalar. There are some special cases where the moment of inertia can be treated as if... | {
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Visual interpretation, on the Bloch sphere, when Hadamard gate is applied twice It's known that the Hadamard operation is just a rotation of the sphere about the $\hat{y}$ axis by 90 degrees, followed by a rotation about the $\hat{x}$ axis by 180 degrees.
On the other hand, $H^{2}=I$, where $H$ is the unitary matrix c... | It can be nice to represent things geometrically. We can represent qubits using vectors, as I'm sure you know. So let's start with a qubit in the $|0\rangle$ state, or in the state $\begin{bmatrix}1\\0\end{bmatrix}$. We can graph this as
(That blue there is the vector representing the qubit.) So, now that we have our ... | {
"language": "en",
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Eigenvalues of fermionic field operators Consider the fermionic field operators $\psi_a(x), \psi^{\dagger}_b(y)$ with the canonical anti-commutation relations $$\{\psi_a(x),\psi_b(y)\} = 0 $$ and $$\{\psi^{\dagger}_b(t,\vec{x}),\psi_a(t,\vec{y})\} = \delta_{ab} \delta(\vec{x}-\vec{y}).$$
What can we say about their ei... | *
*An eigenvalue $\lambda$ of an operator $\hat{A}$ (with definite Grassmann-parity $|\hat{A}|$) is a complex supernumber of the same Grassmann-parity. See also this Phys.SE post and links therein.
*Note however that an annihilation operator $\hat{a}$ and a creation operator $\hat{a}^{\dagger}$ of definite Grassmann-... | {
"language": "en",
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Can you power a car by using air pressure In my fluid mechanics class, I've learned that a fluid traveling in a pipe will generate a force when the exit area is smaller then the entrance area. Suppose a pipe is attached to a car that will use the kinetic energy of the air passing over the vehicle. Assuming that the car... | I just learned about air pressure, and to my knowledge you can't really generate enough force form just air pressure to power a full-sized SUV going at a constant velocity. However, if you did create some sort of high and low pressure system using the engine and exhaust pipe, you could make the car move, but the system... | {
"language": "en",
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Universe expansion / contraction ambiguity I've read everywhere that the universe is expanding, and accelerating the expansion. But it is our single point observations of the universe enough to resolve this result?
What gives us 100% conclusion that the universe is expanding, and not contracting, aren't this equivalent... | You are right that objects arrayed radially with respect to a black hole will move apart from each other. This would mean they would appear red shifted according to any observer looking along this radial direction. However, along the plane perpendicular to that radial direction objects would appear blue shifted. They ... | {
"language": "en",
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Finding the vector potential of a spinning spherical shell with uniform surface charge? I have problem solving the following magneto-static problem. I would greatly appreciate help and guidance.
This is how the problem is stated:
A spherical shell of radius $R$, carrying a uniform surface charge $\sigma$, is set spin... | The $\phi$ component of $\nabla^2\mathbf A$ is not $\nabla^2 A_\phi$, but
$$ (\nabla^2 \mathbf A)_\phi = \nabla^2A_\phi - \frac{1}{r^2\sin^2\theta} A_\phi + (\text{terms involving $A_r,A_\theta$}) $$
Thus what we need to solve is not a Laplace equation. The solutions are the associated Legendre polynomials $P_l^1(\cos... | {
"language": "en",
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What is the need for angular magnification We've been told that angular magnification is defined as the ratio of the angle subtended by the image to the angle subtended by the object. But why would we need a quantity called angular magnification? Won't the simple magnification formula do?
| Linear magnification is only useable in situations where lenses produce real images such as projection onto a screen. Optical instruments with eyepieces such as microscopes produce virtual images whose linear dimensions cannot be measured. Therefore, with these devices, angular magnification is used.
Read more: https:... | {
"language": "en",
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Is voltage across parallel branches still equal if there's a break?
I was wondering if there is a break in one branch, will the potential difference across it still be equal to that of the branches parallel to it? I know that the top wire would still have to be at the same potential as the other top wires because the ... | The potential across each resistance is the same, that which is established by the battery (it's EMF). This ignores any resistance in the wires. The break in the middle resistor wire in your diagram simply causes that path to act like a resistor with infinite resistance; again, the same as measuring the potential direc... | {
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Conceptually, why is acceleration due to gravity always negative? As the title states, why is acceleration due to gravity always (-). Say you assign "up" as the positive direction. If an projectile is thrown at a 24 degree angle above the horizontal, I get that acceleration due to gravity before the vertex is negative.... | It is about the perspective we are using about the forces. When you put a +Q ball near to another +Q ball you increase the potential energy of the system against the Electrical forces. When you leave the system electrical forces will then push both balls a far from each other. So when we make work against a system we c... | {
"language": "en",
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Can there be really a theory of everything? If quantum theory becomes compatible with Einstein's theory of gravity, we get the theory of everything. But if it can predict anything in the universe (provided boundary equations are given) wouldn't it predict itself. I mean won't the theory tell us when the theory will be ... | There are three flaws in what you're suggesting :
*
*A theory of everything need not be deterministic. Current mainstream thinking would be to expect a non-deterministic theory of everything.
*Even if a deterministic theory was found, you can't use it to deduce when it will be found until after you have it. And t... | {
"language": "en",
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Why are the Xi baryons called "cascade" also? Between the Lambda, Sigma, Xi, and Omega baryons, only the Xi family has an alternate name - cascade. This must be a result of the "particles zoo" and my guess is that the particles cascade in the accelerator is related. Why is this family the only one with this "unconventi... | The first observation paper:
Neutral Cascade Hyperon Event
Luis W. Alvarez, Philippe Eberhard, Myron L. Good, William Graziano, Harold K. Ticho, and Stanley G. Wojcicki
Phys. Rev. Lett. 2, 215 – Published 1 March 1959
Has the world Cascade Hyperon in the title
And in this wiki article
Ξ0 and Ξ− are also known as "c... | {
"language": "en",
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Is weight a scalar or a vector? My professor insists that weight is a scalar. I sent him an email explaining why it's a vector, I even sent him a source from NASA clearly labeling weight as a vector. Every other source also identifies weight as a vector.
I said that weight is a force, with mass times the magnitude of g... | I think your professor is mixing up terms. Mass is scalar, weight is a vector. But many people get into the habit of using the terms interchangeably. Also, don't always believe everything someone in a "superior position" tells you. Sometimes they are wrong, so question everything.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do we invent non-physical concepts (like e.g. point particles) to study physical phenomenons? There is nothing exist like point particles in reality then why did we invented the notion of point particles and how does it relate to real world?
| To be able to understand very physical properties and ideas, simpler theories and concepts have to be developed.
Physics on the whole is not perfect, it is a way to model what is seen around the world. With something like a planet, understanding what happens to the mass if it is considered as a point source simplifies... | {
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Is a tensor which is symmetric in two indices still symmetric after raising/lowering one index? I have had this question for a while. I have yet to find information on this online or use this property in any calculation. I believe myself to have proven that it will still be symmetric but I am somewhat unsure of my proo... | TL;DR: No, it is per definition not symmetric, although OP's eq. (3) indeed holds.
In more detail, if
$$S~:=~S^{ij}~e_i \otimes e_j~\in~ T^2V~=~V\otimes V \tag{A}$$
and
$$g~:=~g_{ij}~e^{\ast i} \otimes e^{\ast j}~\in~ T^2V^{\ast}~=~V^{\ast}\otimes V^{\ast}\tag{B}$$
are symmetric tensors
$$S^{ij}~=~S^{ji}\qquad\te... | {
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Quantum mechanics and gender of unborn baby Having a debate with my other half here, I'm currently pregnant and we have not had any scans or tests to determine gender of the baby.
I'm seeing this as similar to a Schroedinger's cat experiment in that my baby is both male and female until it is determined either way. Ho... | Schroedinger's Cat is a thought experiment and an analogy used to explain superposition and indeterminacy. Instead of a cat you should actually understand a quantum system. This system is under the rules of Quantum Mechanics and in the thought experiment it is in a superposition of two states (live and dead, up and dow... | {
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Why do we not feel weightless at equator but feel in satellite A person living in his house at the equator goes in a circular orbit of radius equal to the radius of the earth. My question is, why does he/she not feel weightless as a satellite passenger does?
If we compare a geostationary satellite with the earth's equa... | The fact that there is a special orbit called "geostationary" should ring a bell. What is so special about this orbit, corresponding to a specific radius? It is the only radius at which the satellite's angular speed is the same as the angular speed of a point on the surface of the Earth (the point has to be on the Equa... | {
"language": "en",
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Green's function for a driven, damped oscillator There's an example given in chapter 4 (Differential Equations) of Mathematical Tools for Physics by James Nearing:
$$m\ddot{x}+kx=F_{ext}(t) \, .$$
Obviously this is a undamped driven oscillator. The exercise is to solve the equation using the method of Green's functions... | When you have damping, the motion will not be a pure sinusoid anymore. You will have an exponential decay as well: $$x(t>t_0) = A \sin (\omega (t-t_0)) \exp(-\gamma (t-t_0)).$$
Try to compute the values of $\omega$ and $\gamma$, and you can use the Green's function technique after that.
| {
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Why electron spin being anti-parallel to the orbital angular momentum gives lower energy than the electron spin being parallel to the angular Take hydrogen atom as example. The 2P orbital will split due to spin-orbit coupling to the $^{2}P_{3/2}$ and $^{2}P_{1/2}$ terms.
The term $^{2}P_{1/2}$ has anti-parallel orienta... | The magnetic potential energy of two magnetic dipoles is minimal when the magnetic dipoles are anti-parallel. You can easily check this with two bar magnets.This also explains why anti-parallel electron spin and orbital angular momentum (and thus anti-parallel magnetic dipole moment) gives, in general, lower energies t... | {
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Does the system of a spherical and massless mirror, at rest in our reference frame, with photons moving around in it, has a rest mass? Can we say that if a big number of photons is travelling in a perfect, massless spherical mirror which is at rest in our reference frame, the combined system of the massless mirror and ... | Yes. Imagine that there are only two photons, one with 4-momentum $(p,p,0,0)$ and the other with $(q,q cos(\theta),q sin(\theta),0)$, the sum of their 4-momentum will be $(p+q,p+q cos(\theta), q sin(\theta), 0)$, and because we take the mirror as massles (I will asume that it doesn't have a 4-momentum asociated with n... | {
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What determines the direction of a path on a line integral (vector case)? Line integrals are very important to use in Physics. For example, we calculate work by: W=∫<F,dr>. But I just got confused about something. What determines the direction of motion? The integral limits, or the vector dr?
Well, when we do the inter... | The correct form of an integral over a path takes the form $\int_{\overrightarrow{r_i}}^{\overrightarrow{r_f}}d\overrightarrow{r}$. The direction of motion was determined when you chose the path and the limits were determined when you chose the path.
If you know the velocity, the direction of the path is obvious becau... | {
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Why do we regard $W^\pm$ as physical fields but not $W^1$ and $W^2$? When expanding the electroweak Lagrangian, we obtain terms like
$$
\mathcal L = \frac{g}{2}(\bar e_L (W^1_\mu + iW^2_\mu)\gamma^\mu \nu_L + \bar \nu_L (W^1_\mu -iW^2_\mu )\gamma^\mu e_L)+ \dots
$$
and then redefine the fields as $W^\pm =W^1_\mu \mp iW... | It's not that we don't want two different gauge fields interacting with the same fermions, it's that you can clearly see from this Lagrangian that if an antineutrino interacts with an electron, they can produce a particle given by $W^- =W^1_\mu + iW^2_\mu$. The two gauge bosons that are produced are coherent, so they ... | {
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What does it mean if an intertwiner respects a group action? This is more of A maths question however it cropped up when I was researching isospin so I think it belongs here. I am wondering what exactly is meant by 'respects' and how it works in the context of isospin and hilbert spaces. The link to the source I have b... | There are some details in [this paper][1], On the page 95 it says"...an orthonormal basis of the
invariant subspace of a tensor product of vector spaces, are usually known as
intertwiner operators or simply intertwiners.
"
[1][Daniele Regoli]-The relation between Geometry and Matter in classical and quantum Gravity and... | {
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How does voltage affect boiling ability of a kettle? I was reading an article about the lack of electric kettles in the USA - the claim at the end states one reason is the lower voltage at the socket. Personally, I think that the main reason is that morning tea is not as big in the US as it is in the UK or Australia, b... | The boiling time is a function of power, not voltage. However, to get the same power at a lower voltage requires a proportionally higher current. Yes, a 110 V kettle could draw more current to get to the same power as a 220 V kettle, but there are limits and downsides to drawing more current:
*
*The cord needs to be... | {
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How Do I Increase The Range Of An Home Made Electromagnet? Please forgive me, I am new to this forum and I am not a physics guy but any help would be appreciated. I would like to know how to I increase the range or reach of my electromagnet. By range, I mean the distance from my magnet to a metal object (paper Clip). C... | *
*Increase the current
*Increase the number of turns of wire
*Place an iron core inside the coils of wire
*Bend the electromagnet into a horse-shoe shape
| {
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Is the magnetic quantum number dependent on my choice of coordinate system? I'm reading on wikipedia: https://en.wikipedia.org/wiki/Magnetic_quantum_number
that
"The axis used for the polar coordinates in this analysis is chosen arbitrarily. The quantum number $m$ refers to the projection of the angular momentum in thi... | If we denote $\hat{L}^2$ as the total angular momentum (squared) and $l_i$ its projection onto the i-axis than:
$$[\hat{L}^2, l_i] = 0 \phantom{text}\text{but}\phantom{text}[l_i,l_j] \neq 0$$
This means that, given some state $\psi$ we cannot measure its total angular momentum and all projections. The "best" thing that... | {
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Why is potential difference in ECG considered a vector? In the electrocardiogram, there are leads placed on the limbs and an "electrical vector" is calculated as the difference in potentials measured I the two leads. The direction is given by the line joining the position (or representation of) of the two leads.
I don... | In an anisotropic material (like the human body) the Ohm's law is written as
$$E_i=\rho_{ij}J_j$$
Where $\rho_{ij}$ is the resistivity tensor, $J_j$ the current density and $E_i$ the electric field.
The voltage between two points is defined as
$$ \Delta V=-\int_{\ell}\mathbf E\cdot d\mathbf l $$
where $\ell$ is the lin... | {
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Why doesn't saturation current in the photoelectric effect depend on the frequency of light absorbed by the metal emitter? If current $I$ is given by $I = nAev$, where $n$ is the number of electrons per unit volume, $A$ is the area, $e$ is the charge of an electron and $v$ is the velocity of the electron, it must mean ... | In the relation, $I=neV_dA$, the velocity is the drift velocity of the electrons inside the conducting material.
The saturation current depends on the intensity of the light,for a given frequency. More photons correspond to more electrons. One photon knock out one electron and if you increase the number of photons (or ... | {
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Probability of finding the oscillator in some position in $[x,x + \mathrm d x]$ Given that the position of a one-dimensional harmonic oscillator is given by
$$x(t) = Acos(\omega t + \phi)$$
where $A,\phi,\omega \geq 0$ are constants of real numbers I'm trying in some sense
find the $p(x)\mathrm dx$ probability of ... | This can also be solved using the standard microcanonical method given in statistical mechanics textbooks. Start with the Hamiltonian:
$$ H = \frac{p^2}{2m} + \frac{1}{2} k x^2 $$
It gives us an ellipse in phase space as the phase trajectory. Calculate the total number of microstates ($\Sigma_{tot}$) with energy less t... | {
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Hypercharge and Isospin as additive quantum numbers in $SU(3)$ flavour symmetry I am studying the $SU(3)$ flavour symmetry and I'm reading that we use the fact that hypercharge and isospin are additive quantum numbers in order to decompose the tensor products of the fundamental representations $3\otimes3\otimes3$ and $... | The (strong) hypercharge operator $Y$ and the (strong) isospin operators $(I_1,I_2,I_3)$ are generators of a $u(1)\oplus su(2)$ Lie subalgebra of the Lie algebra $su(3)$ of flavor symmetry. A Lie algebra is a vector space, and hence has a linear structure. Representations can be decomposed in eigenspaces for $Y$ and $I... | {
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Musical notes and colors of a rainbow I have wondered that in an octave in piano there are seven primary notes, and also we observe mostly seven primary colors of a rainbow. I know we perceive logarithmically, that means we only care about relative differences.
Is there any relation between $7$ musical notes (in an oct... | As requested in comments:
There is a connection in the sense that Isaac Newton regarded both musical harmony and optical physics as branches of mathematics (Kepler did the same with harmony and astronomy, and this kind of thing was not original to them), and deliberately chose 7 rainbow colours to match the common West... | {
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How is entropy a state function? Is there only one reversible way to move from one state to another?
If we consider two states $A$ and $B$ on an isotherm and we move from $A$ to $B$ by first reversible isochoric process and then reversible isobaric process. Now the path followed should be reversible since both the ... | There are generally many reversible paths between different states. As an example consider a Carnot cycle. If I start at the beginning of the cycle at the point where the working medium is fully contracted I can, since every step is reversible, get to the point half way through, where the working medium is fully expand... | {
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Difference between note and tone: which one has only one frequency? What is note and tone both in physics and musical terms? Are the two used in different ways in the different fields or are they the same thing. Moreover, which one has only one frequency?
Well this one got me really confused: https://music.stackexchang... | Both note and tone are terms used in music rather than physics. Both refer to the pitch of the sound but in music they include other information also. As far as physics is concerned all 3 terms mean essentially the same thing : a sound of a particular frequency.
In music, notes are usually identified by letter - eg mid... | {
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Field inside a plate capacitor with a dielectric material Suppose I have two plate electodes with a dielectric material between them with a permitivity of $\epsilon=10$. I now put a voltage V between them. What is the electric field in the dielectric region?
Well since the electrodes are plates we have simply:
$E = V/... | In general, a dielectric will decrease the $\vec E_{in}$-field inside the plates as this dielectric will become polarized.
You are correct in pointing out that $V=E_{in}\times d$. Here,
$\vec E_{in}$ is the net electric field, which is the sum of the external electric field and the polarization, so that the magnitu... | {
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How does inflation get rid of initial Baryon asymmetry (if any)? Why is it said that even if the baryon asymmetry existed as an initial condition, the asymmetry would have been destroyed by inflation. How does inflation get rid of initial Baryon asymmetry (if any)?
EDIT: For reference see the section 1.1 (last line of ... | There can be a relation with inflation and leptogeneis which also can lead to asymmetric baryogenesis. The inflation will indeed smooth out everything, but there were no baryons then, as @Anna correctly states. Could not be, temperature was too high for baryons, though if there had been they would have been smoothed ou... | {
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On the derivation of the canonical distribution in deriving the canonical distribution $\rho_c$ for a sistem (labeled by 1) of N identical particles in thermal equilibrium with a heat bath (labeled by 2), at one point I get into the Taylor expansion of the entropy of the reservoir . It is justified with the assumption ... | Here, $\rho_{c}(E_{1})$ is just the probability of the system $1$ being found at the given energy $E_{1}$, and so the constant pre-factor factors out of expression.
$Z$ is just the sum of all the $\Gamma(E_{2})$ as $E_{2}$ is varied over all possible discrete values (or we need an integral if the number of admissible ... | {
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Relationship between orbital radius, mass, and orbital velocity I have a question regarding the relationship between a body's orbital radius, mass, and orbital velocity.
I understand that there is the equation $V = \sqrt{\frac{GM}{R}}$, where $V$ is the orbital velocity, $G$ is the gravitational constant, and $R$ is th... | The article states:
To account for this, the mass of the galaxy within the orbit of the
stars must increase linearly with the distance of the stars from the
galaxy’s centre.
So the mass inside the orbit of radius $R$ is $M = M_oR$ where $M_o$ is a constant.
$\Rightarrow V = \sqrt{\dfrac{GM}{R}}= \sqrt{\dfrac{GM_o... | {
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Incorporation of adiabatic phase into quantum effective action Suppose we have a system (or a subsystem) in the quantum state $|\text{in}\rangle$ and the same system in the state $|\text{out}\rangle$, which differs from $|\text{in}\rangle$ only by a phase:
$$
\tag 1 \langle \text{in}|\text{out}\rangle = e^{i\theta},
$$... | You might find the paper "Effective Action for Adiabatic Process" (Prog. Theo. Phys. 74 (3), 439 (1985)).
https://academic.oup.com/ptp/article/74/3/439/1894676/Effective-Action-for-Adiabatic-ProcessDynamical
There in authors discuss about a correction coming from berry phase term (under adiabatic conditions for some i... | {
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Quark explanation of reaction I've got an issue. There's a reaction in cosmic rays which I need to discuss on 'subatomic' level. I do not need calculations or anything, it has to remain very basic. Could you please explain to me how does this reaction happen on quark level?
$$K^{-} + p^{+} \rightarrow K^{0} + K^{+} + \... | This is a famous reaction, that led to the discovery of the $\Omega^-$ baryon.
The quark-line diagram is shown below. The important features are:
*
*It's all quarks and gluons, no weak bosons or photons, so it's a purely strong-interaction process.
That means the reaction rate will be relatively large. (Whereas the ... | {
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What is the force that pushes a car upwards when moving on a banked road? On banked roads, if the road is frictionless, we can drive a car in circular motion only at a particular velocity called safe velocity. Now if the velocity is less than the safe velocity, then the car would slide down the road(so that radius is d... | What makes the car go up and down the slope is the centrifugal "force". I have put the word force in quotes, because it is not a real force, but rather an apparent one.
What causes the centrifugal force is inertia. The car wants to go in a straight line, but it is prevented from doing so by the friction of the tyres a... | {
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How to calculate the vacuum expectation value of a scalar field? Let's consider a complex scalar field $\phi$ with potential $\frac{\lambda }{4!}(|\phi|^2-v^2)^2$ (Goldstone model).
Applying the Schwinger-Dyson equations, I obtain $\langle \phi \rangle=0$. This result is intuitive because if we have an interaction inv... | You have to rewrite the Lagrangian in terms of the field $\varphi = \phi - v$. Then quantize perturbatively around $\varphi = 0$. This will give you (by Schwinger-Dyson eq) $\left< \varphi \right> = 0$, which in turn means that $\left< \phi \right> = v$.
Or are you asking something completely different?
P.S. Exploring ... | {
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Why as distance decreases capacitance increases? I understand mathematically that as the distance between the capacitor plates decreases, capacitance increases, but I find there is a small contradiction that I want to understand. If the capacitance equals the charge on the capacitor divided by the voltage, isn't the ch... | By definition, capacitance measures the ability of a system to hold charge. Mathematically, it can be stated as the amount of charge the system can hold per unit potential difference across it.
$$CV = q \tag{1}$$
where $V$ is the potential difference (or potential) of the system, $C$ is the capacitance of the system an... | {
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What causes like electric charges to repel and opposite electric charges to attract at the smallest level? When talking about charged particles, the law of charge dictates that two particles with opposite charge will attract each other and two particles with the same charge will repel each other.
However, I have never... | Electric charge is fundamental to the structure of matter.
The atomic nucleus contains protons, which attract electrons that occupy different levels of energy, or electron shells around the nucleus. Atoms can become electrically charged ions by gaining or losing electrons from their outer shells, unbalancing electrica... | {
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Have quarks been observed in free states? I had been reading a book in particle physics very recently. The book has probably been written in the late 90's, (and obviously before 2000), and states that quarks, the underlying particles in all baryons and mesons, has not yet been detected in free state.
Is this still true... | The quark-gluon plasma is a hot dense soup of (mostly) free quarks and gluons. It is created in heavy ion experiments like ALICE, and ATLAS Heavy Ion at the LHC or STAR at RHIC, among others, via two large (typically gold or lead) nuclei smashing together at close to the speed of light. However, this "free" quark state... | {
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Why do gases have higher internal energy than solids and liquids, when at the same pressure? I was given the following question:
Three containers filled with $1 kg$ of each: water, ice, and water vapor at the same temperature $T = 0C$.
Now apparently, the vapour has the highest internal energy, the water has the next h... | I figured out the answer to my own question.
Internal energy is higher when there is more degrees of freedom.
The formula U=3/2nRT only works for monotomic substances.
Every time that more degrees of freedom are added, the 3/2 constant increases.
So in fact, the potential energy formula should yield correct results had... | {
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Why does the Earth accelerate upward, according to Einstein? I recently watched a video on the YouTube channel PBS Space Time which was called "Is Gravity an Illusion?". In this video, the host explains that Einstein claimed that it is not the apple that accelerates towards Earth but the other way around. In Newton's t... | It depends upon the frame of reference.
If one adopts the frame of reference of the apple then the Earth accelerates towards it.
If one adopts the Earth's frame of reference then it is the apple that accelerates towards it.
In GR, there is an equivalence to frame of references and so either scenario is correct.
An o... | {
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The water in the tank are pressurized to 50- 100 PSI? but water cannot be compressed I was looking up about how domestic water heater (DHW) works, and couldn't understand the following:
considering the fact that water (and all other liquids) cannot be compressed (practically), how can they state that the tank is a " he... | They mean that if you were measuring the pressure on the walls of the tank (without opening up the tank or anything like that), it would read 50-100 PSI.
You can pressurize a liquid by applying force on it while it is constrained. Since that force cannot go towards compression very well, it just pushes out in every di... | {
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Why do power lines use high voltage? I have just read that using high voltage results in low current, which limits the energy losses caused by the resistance of the wires.
What I don't understand is why it works this way. Does it have anythnig to do with electromagnetic induction in the wire which resists the current?... | From the formula $P=VI $, $I=\frac {P}{V} $. So, if the voltage is high, current becomes low for same power. Now, $H=I^2RT $, so lower the current, lower is the heat production. Mainly to reduce heat production, the voltage is increased.
| {
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Where does the reaction force act? Does it act on the centre of mass? I know that the reaction force acts perpendicular to the surface in contact with the body. But where exactly (on the body) does it act?
When we deal with the forces on bodies of finite size, we usually refer to the force on the centre of mass. What... | A reaction force is basically an electromagnetic force. When we push on a rigid surface, what we are doing is that we are decreasing the distance between two surfaces. This results in increase of the unbalanced electromagnetic forces on the two surfaces since they are not perfectly neutral thus the reaction force acts ... | {
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Doubt on precession So we are studying rotation of rigid body. Our teacher talked about precession but not in much detail
It got me thinking so if we have axis of axis of rotation then
*
*how many such axis of axis of .......of body can be there
*if the answer is many can't we ultimately represent any motion as sum... | Refer to the bible of physics :http://www.feynmanlectures.caltech.edu/I_11.html
| {
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What is intuitive or physical meaning of wave functional and field configuration and field eigenfunction? what is the physical meaning of field configuration in quantum field theory. I have come across such terminologies in Schrodinger field theory and path integral field theory. What is the actual difference between q... | The field operators $\psi^{\dagger}$ and $\psi$ are creation and annihilation operators for particles in the position eigenstate $\left|x\right>$. A wavefunctional is the analogue of a wavefunction in ordinary QM, it gives you the probability amplitude when applied to an entire classical field configuration, just like ... | {
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What makes the number of neutrons the number of proton similar? In basic chemistry, we are taught that an atom has roughly the same number of neutrons and number of protons, this doesn't seems to hold for larger atoms, but it is always roughly proportional (i.e. you seldom find an atom with 100 protons but 1 neutron, t... | This is my first answer, be nice please.
A different approach (previous answers are already very good) that might give you a better intuition:
Back in the day, Weizsäcker proposed a parametrization of the binding energy of nuclei by analogy with a liquid drop such as
$BE(A,Z) = a_VA - a_SA^{2/3} - a_CZ^2A^{-1/3} - a_A(... | {
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Why is Maxwell's theory insufficient to explain the photoelectric effect? You can argue that electromagnetic waves from a UV light source travel towards a metallic plate, and by the time they reach where a loose electron is located, they affect it with a electromagnetic field (force), so the energy might be enough to ... | Maxwell Equation do not take into account the quantum nature that comes after introducing the Planks constant. The energy of a photon is Planck constant X frequency. There is no Planck constant in Maxwell equations in this sense they are termed classical. To explain photoelectric effect the quantum nature of light has ... | {
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Problem of the ideal in the GNS construction I read this in the wikipedia's article about the GNS construction:
"the degenerate elements, a in A satisfying ρ(a* a)= 0, form a vector subspace I of A. By a C*-algebraic argument, one can show that I is a left ideal of A (known as the left kernel of ρ)."
Is there a full ... | I had the answer in one of my own books. $\|$
I did not find the answer online but in Haag's book: Local Quantum Physics.
He defines a state over a C* algebra $\mathcal{A}$ as a
normalized positive linear complex form.
Positive means that $f(A^*A) \ge 0$
Having defined the set $\mathcal{I}$ of the X with $f(X^*X) = 0$
... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/323753",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
A rod is moving in space and an insect is on it. How many degrees of freedom does the insect have? Is the answer 7? The number of degrees of freedom of a system can be viewed as the minimum number of coordinates required to specify a configuration. Applying this definition, we have:
*
*For a single particle in a pl... | 3 for rod and 1 for insect, total 4
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/323891",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
Do particle and antiparticle annihilate when they meet? Do particle and antiparticle annihilate when they meet? As we know, an electron and a positron will annihilate when they meet. However, many quarks and antiquarks do not annihilate, but coexist as mesons. For example, a neutral pion $\pi^{0}$ is made up of $u, \ov... | Mesons are unstable and decay , either through the weak decay of a quark in the charged cases, or because quark + antiquark annihilate in the neutral through the strong interaction. The strong interaction allows also for other decays, with no annihilations by the ability of gluons to generate a quark antiquark pair an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/324025",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
"answer_id": 0
} |
Conservation of angular momentum in a glass of wine? I've been pondering about something i experienced the other day, hope you smart people might help :)
I was holding a glass of wine, filled half way more or less. And at some point i was swirling the wine, by holding the glass at its neck and making circular clock-wis... | As you move the full glass, this tosses the contents around the inside (swirling).
Even if you're not attempting to tip the glass, the force of the liquid on the vessel is going to (slightly) tip it. You can imagine that as the liquid is farthest from you, the glass is also slightly tipped away from you. This means t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/324111",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
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