Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What happens to circularly polarized light when it hits a linear polarizer? I have seen a lot of examples of what happens when circularly polarized light passes through a circular polarizer composed of a quarter-wave plate and a linear polarizer, but what would happen to the circularly polarized light if it passed thro... | Circularly polarised light can be decomposed into two electromagnetic waves, with their respective electric fields linearly polarised at right angles to each other, of equal amplitude but 90 degrees out of phase. One of the polarisations can be chosen to line up with the polariser and the other at right angles to it. e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/742254",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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The "speed of length contraction" in switching between inertial frames Suppose I want to measure the length of an object in front of me, along the axis separating us (for instance looking headlong at a bus, we could talk about someone standing inside the middle of the bus with a light signal and mirror, but you get the... | If $\rm \ L(t)=L_0/\gamma(t)=L_0 \sqrt{1-v(t)^2/c^2}$
then $\rm \ L'(t)=dL/dt=-L_0 v'(t) \ v(t) \ \gamma(t)/c^2$
see here and here.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/742455",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is it possible to explain radiation of an accelerated charged particle via the Unruh effect? From the point view of a noninertial observer, if a charged particle accelerates then it can catch the Unruh particle and excite. After that, the charged particle emits it and falls back to its ground state.
If we accept radiat... | Indeed, electromagnetic radiation of accelerated charges can be understood in the accelerated reference frame by means of the Unruh effect, as shown by Higuchi, Matsas, and Sudarsky in Phys. Rev. D 45, R3308(R) (1992) and Phys. Rev. D 46, 3450 (1992). The emission of a photon in the inertial frame corresponds to either... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/742608",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why do we choose the Dirac delta function as the eigenstate of position operator? When we try to find the eigenstates of the position operator, we get that the product of (x-y) and the eigenstate must be zero. It is obvious then that for x different than y, the eigenstate must be zero.
Now for x equal to y, how do we k... | This is because the position operator is $x\delta (x-x') $. This may sound like I'm just kicking the can down the road but I'm not.
Naively, you would expect the position operator to be $x \delta _x ^{x'}$, where the $\delta$ is the Kronecker delta. But keep in mind that $x$ is a continuous index. So the action of the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/742750",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 4,
"answer_id": 3
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Open-close string amplitude My question is regarding Polchinski question number 6.12 in which we have to find the amplitude for two open and one close tachyon strings.
I found this solution by Matthew Headrick ("A solution manual for Polchinski's "String Theory""):
Why does the calculation is done in the disk $D_2$ (a... | The calculation done on the disk because in order to be able to have open states we need that our surface will have a boundary.
On the disk we have the boundary that allow us to represent open strings and we also have the interior (bulk) that allow us to represent close strings.
Regarding the vacuum, they do have the s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/743213",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Why $F = m(v_f - v_0)/2$? Force is directly proportional to mass and velocity and inversely proportional to time so why don't we write $F=1/t+m+v-v_0$ where $m$ is mass, $v$ is final velocity, and $v_0$ is initial velocity?
|
Force is directly proportional to mass and velocity and inversely proportional to time so why don't we write $F=1/t+m+v-v_0$
As others mentioned, the units don’t work. However, suppose we modify it to $$F=k_t/t+k_m m+k_v(v-v_0)$$ where the various $k$ are constants with appropriate dimensions that make each term a fo... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How does $\sum_s\left[u_a^s(p)\bar u_b^s(p) + v_a^s(-p)\bar v_b^s(-p)\right] = 2E_p\gamma^0_{ab}$? For Dirac spinors, we have the spin sums for particles,
$$
\sum_{s=1,2}u_a^s(p)\bar u_b^s(p) = (\not\!p+m)_{ab},
$$
and for antiparticles:
$$
\sum_{s=1,2}v_a^s(p)\bar v_b^s(p) = (\not\!p-m)_{ab}.
$$
As $\{u^s(p),v^s(-p)\}... | The correct relation involves inverting only the three-momentum of the spinors,
$$\sum_{s}\left[u^{s}(\mathbf{p})\bar{u}^{s}(\mathbf{p}) + v^{s}(-\mathbf{p})\bar{v}^{s}(-\mathbf{p})\right] = 2E_p\gamma^{0}.$$
This follows straightforwardly from the closure relations, which may be written
$$\sum_{s}u^{s}(\mathbf{p})\bar... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/743615",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How do we maintain polytropic processes? In polytropic processes for an ideal gas,
$$PV^{\alpha}=constant$$ where $\alpha \neq 0,1,\gamma$
And $\gamma$ is adiabatic exponent of gas
So, how these processes are maintained?
What things are done to initiate this process?
| By definition a a polytropic process is one for which $TdS=\mathcal K dT$ and $\mathcal K$ is a constant. Using the $dU=TdS-pdV$ equation it follows that
$$\frac{dp}{p}+\alpha \frac{dV}{V}=0 \tag{1}\label{1}$$
and upon integration you get $$pV^{\alpha}=K_0\tag{2}\label{2}$$
where $\alpha=\frac{C_p-K}{C_V-K}$.
This mean... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why do we Wick rotate before regularizing Feynman diagrams? In Folland's Quantum Field Theory he mentions that we can apply Feynman's formula (Feynman parameterization) to either the Wick rotated integrals or the non-Wick rotated integrals corresponding to Feynman diagrams. However, later in the section he outlines a r... | Well, as long as the singularities of the propagators in Minkowski signature are regularized with a Feynman $i\epsilon$ prescription, Wick rotation is in principle not necessary. However in practice, the loop momentum integrals of the Feynman diagram are simpler to evaluate in Euclidean signature, e.g. because $SO(d)$ ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Understanding this Lagrangian calculation I was trying to understand this section of a Wikipedia article:
$$0 = \delta \int \sqrt{2T} d\tau =
\int \frac{\delta T}{\sqrt{2T}} d\tau =
\frac{1}{c} \delta \int T d\tau$$
For the life of me, I can't figure out how does one get from $\displaystyle \delta \int \sqrt{2T} ... |
I was trying to understand this section of a Wikipedia article:
$$0 = \delta \int \sqrt{2T} d\tau =
\int \frac{\delta T}{\sqrt{2T}} d\tau =
\frac{1}{c} \delta \int T d\tau$$
For the life of me, I can't figure out how does one get from $\displaystyle \delta \int \sqrt{2T} d\tau$ to $\displaystyle \int \frac{\de... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/744328",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
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Why "into screen" and "out of screen" markings in electromagnetism are the way they are? Let's say that you have a bullet going through the metal screen. Into screen. It makes a dot-like hole, like here:
Now, let's say that we have a bullet going out of screen. It makes a jagged, sharp edges, often 3-4 of them, making... | You just need to have the right picture in mind, then it's actually very intuitive and easy to remember. From rfcafe.com:
We anyway draw fields as arrows. Now, imagine someone shot an arrow in the plane and it got stuck, so you either see the pointy end just barely sticking out or the fletching (the feather cross at t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/744431",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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How do atoms emit an electromagnetic wave (infrared radiation)? From what I understand, when an object has a certain temperature, its atoms vibrate and this atomic vibration accelerates the electrically charged particles and this generates infrared radiation.
To generate infrared radiation, it is therefore necessary to... | I would taks H atom as an example. One electron and one proton. There are a number of discrete energy levels (negative energies since the electron is bound to the proton). Normally the electron is in the lowest state of energy called the ground state which is -13.6 eV. If the electron due to collisions with other atoms... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/744698",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Pauli Exclusion Principle with two electrons in box Suppose that I measure the spin of two electrons in the z direction, and that they have the same spin. Then we put both electrons in a box. After a long time, we know nothing about the spatial distribution of the electrons in the box, so their spatial distributions ar... | Why would we know nothing? If you place the electrons in an antisymmetric spatial state, say
$$
\psi_{12}(x_1,x_2)=\frac1{\sqrt{2}}\left(\psi_1(x_1)\psi_2(x_2)-\psi_2(x_1)\psi_1(x_2)\right)
$$
so the full spatial+spin state is antisymmetric as required by Pauli:
$$
\psi_{12}(x_1,x_2)\vert \uparrow\rangle_1\vert\uparro... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/744947",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Can we say that the center-of-momentum frame is the frame in which the center of mass is at rest? Isn't the center-of-momentum frame is same as the frame in which the center-of-mass is at rest? Since the position of the center-of-mass of a system of particles is defined as $\vec R=\sum_i m_i \vec r_i/M\Rightarrow\frac{... | Let's check a simple 1D situation: 2 equal mass particles on a collision course. One (1) at rest at the origin, and another (2) moving in the $+$ direction towards it:
$$ x_1m = 0$$
$$ x_2(t)m = (x_2(0)+\beta t)m$$
Center of mass is clearly:
$$ X_{cm}(t) = \frac 1 2 (x_2(0)+\beta t) $$
Wait. We could do this problem in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/745211",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How to find the corresponding energy given the wave function? So I was struggling doing the following question:
Given the wave function $\psi(x) = A\, \mathrm{e}^{-ax^2} $ with potential $V = \frac12 kx^2$, find the corresponding total energy in terms of $k$ and $m$.
I did the calculation for $\left<x^2\right>$ and $\l... | The energy of a state is the eigenvalues of the Hamiltonian. So calculate the expectation value of it for that state.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/745599",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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In the Lorentz force equations, can the magnetic field be assumed to be singular at one or more points? Consider the relativistic Lorentz force equation (in a simplified form) given by
\begin{equation}\
\left(\frac{u'}{\sqrt{1-|u'|^2}}\right)'= E(t,u)+u'\times B(t,u).
\end{equation}
Here, $E$ and $B$ denote respectiv... | A general solution for the magnetostatic case for the magnetic Vectorpotential (what you call $W$) is given by:
\begin{align}
{\displaystyle {\vec {A}}({\vec {r}})={\frac {\mu _{0}}{4\pi }}\int {\frac {{\vec {j}}({\vec {r}}')}{\left|{\vec {r}}-{\vec {r}}'\right|}}\mathrm {d} ^{3}r'\,}
\end{align}
If your $\vec{j}$ beco... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Nodal circles on spherical harmonics Homework question:
For the spherical harmonic with $l=2$, $m=0$ , at what angle theta relative to the polar axis is the nodal circle in the northern hemisphere?
My attempted answer:
I know that I need to find the values of $\theta$ for which the function is equal to zero. $Y(2,\thet... | Remember the north pole is at $\theta=0°$, the equator is at $\theta=90°$,
and the south pole is at $\theta=180°$.
From this you know which solution to pick for the northern hemisphere.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/745963",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What is so significant about electron spins and can electrons spin any directions? I just want to know what is so significant of with direction electron is spinning. Does it have any effect on the element or on the atom?
Also, does electron must spin up or down or can they also spin sideways or vertically?
| Electron spin is proportional to the magnetic dipole moment produced by an electron that is not traveling. This acts very much like the dipole moment of a current traveling through a circle of wire. The magnitude of the spin vector is set, but it can be in any direction.
When you measure a component, any component, o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/746063",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is it possible to statically generate lift with the difference in pressure like wings? If I understood it correctly, the shape of the wings and/or propellers generates lift/thrust with the difference in pressure in both sides of the wings/propellers; where the lower side has higher pressure airflow and the uper side ha... | If you have a difference in pressure, then fluid will flow to equalise that pressure unless restricted by a barrier. If you have a barrier then that's a balloon, if you don't have a barrier than you don't have a static system.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/746531",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 5,
"answer_id": 2
} |
Metric compatibility and torsion-free condition of GR In an introduction to general relativity, we see the unique connection of a manifold is described by both the conditions, matric compatibility and torsion-free condition. The metric free condition can be physically understood which allows us the parallel transport o... | For knowing why the Torsion tensor is important it is important to know what it is.So,
$$[\nabla_\mu ,\nabla_\nu]f=T^\lambda_{\mu \nu}\nabla_\lambda f$$
Where T is the torsion tensor, so if your covariant derivatives commute you have torsion free manifold. Quickly working out the commutator of the covariant derivative... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/746638",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Thermodynamic work done on a free-falling object By definition the thermodynamic work is the opposite of the mechanical work (engineers'convention).
Consider then an object of mass $m$ falling at constant velocity above the Earth surface (imagine that someone is pushing in order to balance the gravitational pull) for a... | The complete form of the first law is:
$$
\Delta (U + E_K + E_P + \cdots) = Q + W,
$$
where $U$ is internal energy, $E_K$ is kinetic energy and $E_P$ is potential energy. The left-hand side includes all forms of energy in the system; the right-hand side is the net inputs of heat and work. For a stationary system, l... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/746969",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does rate of acceleration change as object gets closer or further to center of a mass? I learnt that newton's law of universal gravitation F = G(m1m2)/R^2, and thought if the R is distance and determined gravitational strength, why do we use 9.81 as default acceleration of earth's gravity when it is not even constant a... | We use 9.81 m/s$^2$ only when dealing with objects close enough to the surface of the earth (heights negligible compared to the radius of the Earth) that the acceleration due to gravity can be considered constant.
The value of $g$ near the surface of the Earth can be computed when you substitute the radius of the eart... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/747083",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Linear Harmonic motion (simple oscillator) We know that for a simple harmonic linear oscillator, the displacement is given by $x(t)=A\sin(\omega t + \phi)$, where $\phi$ denotes the phase angle. Now as per my understanding this $\phi$ is only significant when considering SHM in form of a sinusoidal wave. Is there any p... | SHM has this differential equation
$$\ddot x(t)+\omega^2\,x(t)=0\tag 1$$
to solve this differential equation you need two initial conditions.
$$x(0)=x_0~,\dot x(0)=v_0$$
with your Ansatz $~x(t)=A\,\sin(\omega\,t+\phi)~$ in equation (1) you obtain $~0=~0~$ thus $~x(t)~$ is the solution of the SHM. to obtain the constant... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How did we get the formula $d U = nCvdT$? Our teacher taught us that for any thermodynamic process, dU=nCvdT where Cv is molar specific heat capacity at constant volume and dU is change in internal energy. How did we get this formula and why is it valid for all processes
| The general relation for all materials is $$dU=C_V\,dT+(\alpha TK-P)\,dV,$$
with internal energy $U$, constant-volume heat capacity $C_V\equiv T\left(\frac{\partial S}{\partial T}\right)_V$, temperature $T$, constant-pressure thermal expansion coefficient $\alpha\equiv\frac{1}{V}\left(\frac{\partial V}{\partial T}\righ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/747357",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why is the acceleration vector the spatial gradient of the lapse function? If we have a Lorentzian manifold $(M, g)$ with a foliation by spacelike surfaces $\Sigma_t$ with unit-normal vector field $n$, we can define the lapse function $N$ by
$$
\partial_t = N n + X
$$
where $X$ is the shift vector. I have seen several ... | Write
\begin{align*}
\langle \nabla_n n, Y\rangle &= -\langle n, \nabla_Y n\rangle-\langle n, [n,Y]\rangle
\\
&=-\frac 12 Y \langle n,n\rangle - \langle n, N^{-1} Y(N)\rangle
\\
&=N^{-1} Y(N).
\end{align*}
You can get the formula for $[n,Y]$ by writing $n=\frac 1N(\partial_t-X)$ and using the coordinate expression for ... | {
"language": "en",
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Can red and blue light interfere to make fringes in young’s double split experiment? Supposing in young’s double split experiment, I cover one slit with red filter and the other slit with blue filter. The light coming out from the first slit would be red and the second slit would be blue. Would there be any interferenc... | So the concept of double slit "interference" is historical dating back to Young and Fresnel (early 1800s)... and is still the basis for the typical high school/university textbook. When quantum mechanics came about in the early 1900s some of the most famous scientists (Dirac and others) pointed out that "each photon i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/747560",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Coefficient of restitution bouncing ball I was researching for my physics investigatory project and I have very big confusion.
The ratio between the initial height of the ball (the independent variable) and the height the ball bounces (the dependent variable)
$$\mathrm{COR} = e =\sqrt{\dfrac{\text{final height}}{\text{... | The COR is technically only defined for collisions. In this case the ball collides with the floor so we use the COR. The COR is more precisely defined as
$$e=\frac{v_f}{v_i}$$
where $v_i$ is the (relative) velocity before the collision and $v_f$ is the (relative) velocity after the collision. With relative I mean the r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/747702",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do non-periodically varying currents produce electromagnetic waves? Electromagnetic radiation is created by the varying/accelerating of a system of charges and currents. Suppose that the time dependence of the charges and currents are $\rho(x,t)$ and $J(x,t)$. Then the subsequent radiation will have the same time d... | Fourier analysis does not require periodicity. This was one of the things about Fourier's work that shocked mathematicians. Essentially, any function you can graph may be decomposed into sinusoidal waves.
Imagine electric field lines converging at a charge in a particular position. Now, move that charge to a new positi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Wavefunction of distinguishable spin 1/2 fermions Does the total wave function for distinguishable (i.e. not identical) spin 1/2 fermions need to be anti-symmetric under particle exchange? Or does the Pauli exclusion only hold for indistinguishable fermions?
| No. Particles may be indentical but may or may not be indistinguishable. Indistinguishable particles will be described by a quantum state fully symmetric or fully antisymmetric under permutation.
It is perfectly possible to have partially distinguishable particles: two photons with non-orthogonal polarization made to... | {
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Why can you hear loud TV in the next room despite the wall and door? In a house, when two rooms are next to each other, why can you hear the loud TV on the next room, despite the wall between them and despite that their two doors are closed. (I don't know a lot on physics, but isn't there something like sound travellin... | Their are two main transmission mechanism: The first one is air gaps: residential doors are not airtight and even a small gap will transmit a fair bit of sound.
The second is structure borne: The TV or loudspeaker will vibrate quite a bit and mechanically excite the surface they are resting on: the shelf, cabinet, floo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/748664",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 2,
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How to justify this small angle approximation $\dot{\theta}^2=0$? Suppose the equation of motion for some oscillating system takes the following form:
$$\ddot{\theta}+\dot{\theta}^2\sin\theta+k^2\theta\cos\theta=0$$
Applying small angle approximation to $\theta$ gives $\sin\theta\approx\theta$ and $\cos\theta\approx1$,... | There is no mathematical justification for setting $\dot \theta^2$ to $0$. If this equation represents some specific physical system and if it is known for physical reasons that $\dot \theta^2 \approx 0$ then it could be justified. But that will require a specific physical argument for the specific system in question, ... | {
"language": "en",
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Is relativity of simultaneity an "observer issue"? There are some threads about this, but some answers seem to disagree.
First, this is what Einstein said on this matter:
The light rays emitted by the flashes of lightning A and B would reach him simultaneously", and again: " the observer will see the beam of light emi... |
do the observers disagree on the simultaneity of the events after the "post-processing" (tracing back the actual events in spacetime)?
Yes. The relativity of simultaneity specifically refers to the disagreement about simultaneity that remains after the observers have accounted for the finite speed of light.
In other ... | {
"language": "en",
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Does the spin have to be of opposite sign for fermions to form cooper pairs in bcs theory? I recently started exploring superconductivity and here's what I've understood wrt to bcs theory of superconductivity:
Two electrons can have a close association as there is low agitation of the lattice below the critical tempera... | While $^3He$ is superfluid, rather than superconductive, Cooper pairs in $^3He$ have two fermion atoms/quasiparticles with the same spin.
While $^4He$ is a boson, $^3He$ with three rather than four nucleons
is a fermion, and superfluid $^3He$ is formed by condensation of
Cooper pairs of $^3He$ atoms (or more precisely... | {
"language": "en",
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How to move from AdS to dS space? I studied different black holes in different spacetime and I also checked their differences, for example, the difference that exists in dS and AdS spaces. The question that has been created for me is whether it is possible to change the space of black holes from dS to AdS or vice versa... | Simply changing the sign of cosmological constant in an expression for a metric should give a solution of Einstein equations for the new value of cosmological constant (and in particular, the Plebanski–Demianski family, to which accelerating black holes belong, exists for all values of cosmological constant). However, ... | {
"language": "en",
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Diode $I$-$V$ characteristic for inverse region This is the Shockley equation for the current of the diode:
$$I_D = I_S \left( e^{\frac{V_D}{nV_T}} - 1 \right)$$
It is also valid for $V_D < 0$, when this equation tends to be
$$I_D = - I_S$$
Wikipedia specifies that the equation fits for a "moderate" reverse bias.
But w... | The Shockley equation assumes that the breakdown wasn't produced yet. If you are in the breakdown region things get complicated. You need the ionization rates because the impact ionization generation is what predominates. Read chapter 7.4 from Donald Neamen's - Semiconductor Physics and Devices, but the formula you wou... | {
"language": "en",
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Mass-Energy Equivalence and First Law of Thermodynamics Einstein showed mass can be converted into energy and vice versa.
$E=mc^2$
However, in school we are taught that according to the First Law of Thermodynamics, energy can neither be created nor destroyed.
Are they not contradicting each other? I already tried findi... | I think the best way to resolve this question is to forget about more colloquial descriptions of $E=mc^2$ and just take a look at special relativity. SR imposes that the famous mass-energy relation (in natural units): $$ p_{\mu} p^{\mu} = E^2 - \vec{p}^2 = m^2$$ holds for all particles in all reference frames since $p_... | {
"language": "en",
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Experimental searches for magnetic quadrupole moment My professor mentioned that a particle with an intrinsic magnetic quadrupole moment would be CP violating in an analogous manner to how a particle with an electric dipole would be evidence for new sources of CP violation. Are then any active or past experiments whic... | A spin-half particle cannot have an intrinsic quadrupole moment, because the two-state system does not have enough degrees of freedom. See this answer for a hand-waving explanation, which is related to the Wigner-Eckart theorem.
In a comment, you link to this preprint, which discusses magnetic quadrupole moments in a ... | {
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Why does the double slit experiment not prove that the wave function is ontological? To me, it seems that the interference pattern is the evidence that the wave function is a physical aspect of reality, but people still seem to be trying to decide whether or not it's ontological or just a mathematical construct.
Why is... | Even classical physics predicts a wave pattern on the screen when you do the double-slit experiment with light. Not all waves are wave functions. In fact, any wave that you can see isn't a wave function. The wave function encodes the probabilities of various measurement outcomes before measurement happens. To say that ... | {
"language": "en",
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Is the attractive Fermi-Hubbard model solvable by Bethe Ansatz? I know that the one-dimension Fermi-Hubbard model is solvable by using the Bethe Ansatz method. The results I have seen, however, seem only to treat the repulsive case, i.e. $U > 0$, and I have not come across any discussion of the attractive case ($U < 0$... | In brief, yes. The attractive case is addressed in chapter 16 (and references therein) of the Hubbard chain "bible": Essler, F. H., Frahm, H., Göhmann, F., Klümper, A., & Korepin, V. E. (2005). The one-dimensional Hubbard model (Cambridge). A draft of the book is available here, on Korepin's website. As the chapter des... | {
"language": "en",
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Can eigenvalues of the density matrix in the Lindblad equation be negative? Can the density matrix in the Lindblad equation for an open mixed quantum system have (real part) negative eigenvalues?
| The density matrix by definition is a positive semi-definite matrix. It therefore has real positive eigenvalues.
Physically, these eigenvalues correspond to the probability $p_i$ of being in one of the pure eigenstates $|\phi_i\rangle$ according to
$$\rho = \sum_i p_i |\phi_i\rangle\langle \phi_i|.$$
Clarification in r... | {
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Why does magnetic force only act on moving charges? I don't understand why the magnetic force only acts on moving charges. When I have a permanent magnet and place another magnet inside its field, they clearly act as forces onto one another with them both being stationary. Also, I am clearly misunderstanding something.... | This is basically just a matter of definition. The magnetic force is not something independent or complete on its own. Instead, it is the electromagnetic force that is the underlying concept. The electromagnetic force can be split into a portion that acts on stationary charges and a portion that acts on moving charges.... | {
"language": "en",
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Kepler third law for circular orbits This question may be uber trivial, but it has been stuck in my head for a while.
Kepler's third law states that the period of the orbit $T$ is related to the semi-major axis $a$ though
\begin{equation}
T^2 = 4\pi^2\frac{a^3}{G(m_1+m_2)}.\tag1
\end{equation}
where $m_1$ and $m_2$ ar... | You are trying to apply Kepler's third law in the form
$\displaystyle \omega^2 = \frac {G(m_1+m_2)} {r^3}$
where $r$ is the radius of a planetary orbit, $m_1$ is the mass of the primary and $m_2$ is the mass of the secondary. However, this form only applies when $m_1 >> m_2$. If $m_1$ and $m_2$ have similar values then... | {
"language": "en",
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Maxwell stress tensor on two steady current carrying wires I am having trouble thinking about the force on a wire via maxwell stress tensor. The problem is as follows; given two parallel infinite wires separated by a distance of 2a with steady currents in the same direction, find the force per unit length on the two w... | In a suitably chosen Cartesian coordinate system, the current density (assuming equal currents $I$ in both wires) is given by $$\vec{j}(x,y,z)= I \delta(y)[\delta(x+a)+\delta(x-a)]\vec{e}_z,$$ generating the magnetic field $$\vec{B}(x,y,z)= \frac{\mu_0 I}{2 \pi} \left[\frac{-y \, \vec{e}_x +(x+a) \, \vec{e}_y}{(x+a)^2 ... | {
"language": "en",
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Why is electromotive force in magnetohydrodynamics a vector quantity? In the mean-field dynamo theory in magnetohydrodynamics, I frequently came across a quantity;
$\langle v'\times B' \rangle$, which is termed as the mean electromotive force. I want to know that why is it termed as electromotive force, if it is a vect... | The usual EMF in circuits refers to a closed oriented path: it is the integral of net motional force per unit charge acting on current. Physical unit of this EMF is Volt. Sometimes EMF for a non-closed path is discussed, which is based on the same idea, only the integration path is not closed but has starting point and... | {
"language": "en",
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Uncertainty Calculation: Applying Product Rule instead of Power Rule I use $\delta$ to represent absolute uncertainty. The power rule for the calculation of relative uncertainty in $t^2$ is
$$\frac{\delta (t^2)}{(t^2)}=2\left(\frac{\delta t}{t}\right).$$
But if I treat the power as a product and apply the product rule,... | As was pointed out by Sandejo's answer, uncertainties only add in quadrature if the two quantities being measured are uncorrelated. The formulas for propagation of uncertainty have additional terms that must be included if the variables' uncertainties are correlated.
Specifically, suppose we have two quantities $A$ an... | {
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Projective representations of the Lorentz group can't occur in QFT! What's wrong with my argument? In flat-space QFT, consider a spinor operator $\phi_i$, taken to lie at the origin. Given a Lorentz transformation $g$, we have
$$\tag{1} U(g)^\dagger \phi_i U(g) = D_{ij}(g)\phi_j$$
where $D_{ij}$ is some spinor projecti... | Your observation is correct, which is why careful statements of the Wightman axiom eq. (1) (see e.g. Wiki, nLab) stipulate that $D$ is a representation of $\mathrm{SL}(2,\mathbb{C})$, the universal cover of the Lorentz group, not a representation of the Lorentz group itself.
Note that classical fields - the things on w... | {
"language": "en",
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Horizon related question I'm a student taking an undergrad course in physics and we were discussing light and how it works in relation to vision. This question stumped us. What altitude would you need to reach on the globe before the horizon vanished from your view provided you maintained a line of vision parallel to t... | If I understand the question correctly, to be fully defined you would need to specify the field of view. The horizon would disappear from a viewpoint "parallel to the surface of the earth" right at the earth unless you have a nonzero angle for your field of view. If your field of view is 180 degrees, you could technica... | {
"language": "en",
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What is sound and how is it produced? I've been using the term "sound" all my life, but I really have no clue as to what sound exactly is or how it is created. What is sound? How is it produced? Can it be measured?
| Sound is a form of energy. And what does sound do? It provides the sensation of hearing. But that's just what the definition tells us. Sound is a mechanical wave. Now just by seeing that you must realise it needs a medium to propagate and must also ask yourself how does a wave propagate in a medium. Well; whenever ther... | {
"language": "en",
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Does leaning (banking) help cause turning on a bicycle? I think it's clear enough that if you turn your bicycle's steering wheel left, while moving, and you don't lean left, the bike will fall over (to the right) as you turn. I figure this is because the bike's momentum keeps it moving in the direction you were going, ... | Yes. A lean induces a side force that makes the bike follow a circular path.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "20",
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Mnemonics to remember various properties of materials I'm trying to figure out how to remember that
*
*hardness: how resistant it is to deformation
*toughness: how resistant it is to brittle failures
*stress: force on a surface area
*strength: ability to withstand stress without failure
*strain: measurement of d... | For Shiny, Malleable, Ductile, Conductors of heat and electricity and forming Ionic compounds, there is a mnemonic which goes like
Silver
Made
Desert i.e
Cupcakes and
Ice-creams for after dinner
| {
"language": "en",
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Is it possible that all neutron stars are actually pulsars? I'm assuming that what I've been told is true:
We can only detect pulsars if their beams of electromagnetic radiation is directed towards Earth.
That pulsars are the same as neutron stars, only that they emit beams of EM radiation out of their magnetic poles.
... |
Do there exist neutron stars without relativistic jets? Also, could jets be locked in alignment with the spin axis, resulting in a beam that does not pulse for any line of sight? For some reason discussion has been focused on Earthbound detectability of these jets. Instead, I'm looking for an answer using astrophysics... | {
"language": "en",
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Book about classical mechanics I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical consideration related to these to formalism (like tangent bundle, cotangent bundle, 1-for... | This isn't explicitly about just mechanics as it tries to hit a lot of different areas in physics but it covers the material you are asking for:
http://www.amazon.com/Differential-Forms-Applications-Physical-Sciences/dp/0486661695
It will absolutely provide you with a firm basis in the geometrical considerations you me... | {
"language": "en",
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Law for tap water temperature I was wondering if anyone put together a law to describe the rising temperature of the water coming out of a tap.
The setup is fairly simple: there's a water tank at temperature T, a metal tube of length L connected to it and a tap at the end where temperature is measured. The water flows ... | The answer is going to depend on the heat transfer coefficient between the tube and the surrounding room (unless you specify that the tube is held at constant temperature), the heat transfer coefficient between the tube and water, the outside & inside diameter of the tube, and the length of the tube. This is a moderate... | {
"language": "en",
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Is acceleration an absolute quantity? I would like to know if acceleration is an absolute quantity, and if so why?
| I've finally figured it out.
First, let's define precisely what it means for some quantity to be absolute or relative. In the context in question, it has to do with whether a quantity is absolute (that is, has the same value) or relative (that is, has different values) when measured by two inertial observers moving wi... | {
"language": "en",
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Why can you "suck in" cooked spaghetti? We all know that there is no "sucking", only pushing. So how are cooked spaghetti pushed into your mouth? The air pressure applies orthogonal on the spaghetti surface. Where does the component directed into your mouth come from?
| When you perform the sucking action, a pressure difference is clearly created and maintained by your lungs between the surrounding air and the air inside your mouth. An important point to notice here is that the mouth must not too far open (a bit lets it work still), else the pressure gradient between inside and outsid... | {
"language": "en",
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What property of objects allow them to float? I used to think that the shape of an object determines its ability to float (boat-shaped objects are more likely to float, and spheres tend to sink). But my friend, who is fond of making me look stupid, took me to the local lake showed me a sphere that floated and a boat-s... | Actually, the answer is a bit more subtle than just density. The principle that is behind floating objects is Archimedes' principle:
A fluid (liquid or gas) exerts a buoyant force, opposite apparent gravity (i.e. gravity + acceleration of fluid) on an immersed object that is equal to the weight of the displaced fluid.... | {
"language": "en",
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Why don't spinning tops fall over? One topic which was covered in university, but which I never understood, is how a spinning top "magically" resists the force of gravity. The conservation of energy explanations make sense, but I don't believe that they provide as much insight as a mechanical explanation would.
The hyp... | From your linked article:
Spin a top on a flat surface, and you will see its top end slowly
revolve about the vertical direction, a process called precession. As
the spin of the top slows, you will see this precession get faster and
faster. It then begins to bob up and down as it precesses, and finally
falls o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/271",
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Why does water make a sound when it is disturbed? When I disturb a body of water, what causes the familiar "water moving" sound?
| If you throw a stone in a large body of water, this is what you should hear:
*
*a high pitched slapping sound when the stone makes contact with the water. This is due to the air between the stone and the water being pushed out, as well as the surface ripples
*a low pitched sound growing in pitch (like "Doo-eeeee" ;... | {
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Planet orbits: what's the difference between gravity and centripetal force? My physics teacher says that centripetal force is caused by gravity. I'm not entirely sure how this works? How can force cause another in space (ie where there's nothing).
My astronomy teacher says that gravity is (note: not like) a 3D blanket... | Gravity is a force.
Gravity is directed towards the center of the orbit i.e. the sun.
That makes gravity the centripetal force.
Imagine a ball attached to a string and you are holding the other end of the string and moving your hand in such a way that the ball is in circular motion. Then tension in the string is cent... | {
"language": "en",
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Home experiments to derive the speed of light? Are there any experiments I can do to derive the speed of light with only common household tools?
| There is a trick I have heard about before but never tried. The basic idea is to put a mars bar in a microwave oven for a short amount of time. First you remove the turntable, so the chocolate bar stays stationary. Then you turn the microwave on just long enough for the chocolate to start to melt. It should melt at the... | {
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Positrons versus holes as positive charge carriers From Wikipedia: [The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the Dirac ... | Holes in semi-conductors are considered to be quasiparticles. A quasiparticle is a group of particles that end up acting and having many of the properties of a single particle for a period of time. They are normally considered to have a lifetime tau and decay exponentially.
Are positrons and electrons that we obverse q... | {
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Why is it thought that normal physics doesn't exist inside the event horizon of a black hole? A black hole is so dense that a sphere around it called the event horizon has a greater escape velocity than the speed of light, making it black. So why do astronomers think that there is anything weird (or lack of anything In... | If you are inside the event horizon of a spinning black hole, there are closed timelike curves--paths through spacetime which, when you progress them into the future, they end up in their past. These curves clearly violate the principle of causality, and thus, the region inside the black hole can be considered unphysi... | {
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Notation of plane waves Consider a monochromatic plane wave (I am using bold to represent vectors)
$$ \mathbf{E}(\mathbf{r},t) = \mathbf{E}_0(\mathbf{r})e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t)}, $$
$$ \mathbf{B}(\mathbf{r},t) = \mathbf{B}_0(\mathbf{r})e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t)}. $$
There are a f... | "Space-dependent phasor" makes some sense. Electrical engineers will often just say that's the "complex amplitude of the time-harmonic field" or "time-harmonic phasor".
| {
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What is the temperature of the surface and core of a neutron star formed 12 billion years ago now equal to? In what part of the spectrum is it radiating? In the infrared, in the microwave? Or is not radiating anymore at all?
In russian:
Чему сейчас равна температура поверхности и ядра нейтронной звезды, которая образо... | You'll have to wait for a real physicist to jump in for a numerical answer. As far as I know, it doesn't burn but is simply radiating the energy it started out with. I suspect the
thermal conductivity is quite high. If you assume the thermal conductivity is so high that there is essentially no temperature difference be... | {
"language": "en",
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Why does kinetic energy increase quadratically, not linearly, with speed? As Wikipedia says:
[...] the kinetic energy of a non-rotating object of mass $m$ traveling at a speed $v$ is $\frac{1}{2}mv^2$.
Why does this not increase linearly with speed? Why does it take so much more energy to go from $1\ \mathrm{m/s}$ to... | One way to look at this question of yours is as follows:
$$ E(v) = \frac{m v^2}{2} \; . $$
So, if we multiply the velocity by a certain quantity, i.e., if we scale the velocity, we get the following,
$$ E(\lambda v) = \frac{m (\lambda v)^2}{2} = \lambda^2 \frac{m v^2}{2} = \lambda^2 E(v)\; . $$
That is, if you scale y... | {
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How do neutron stars burn? Is it decay or fusion or something else?
*
*What makes a neutron star burn, and what kind of fusion/decay is happening there?
*What is supposed to happen with a neutron star in the long run? What if it cools, then what do the degenerated matter looks like after it cools? Will
the gravitat... | I think this is a good almost-popular introduction to neutron stars, the processes expected to occur therein and their evolution.
| {
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Equilibrium and movement of a cylinder with asymmetric mass centre on an inclined plane A cylinder whose cross section is represented below is placed on an inclined plane. I would like to determine the maximum slope of the inclined plane so that the cylinder does not roll. The mass centre (CM) of the cylinder is at a d... | The centre of mass (CM) is at distance $r=\frac{m_2 d}{m_1+m_2}$ from the geometrical centre of the cylinder.
In diagram (a), if the centre of mass lies within the red circle then it will be always on the downhill side of the point of contact P. It will always exert a clockwise torque about P, causing the cylinder to... | {
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logarithmic wind speed profile Under some atmospheric stability condition, over flat terrain, it has been observed for a while that the ratio between wind speed at height $h_1$ above the earth and the wind speed at height $h_0$ is $\log\frac{h_1}{h^*}/\log\frac{h_0}{h^*}$ where $h^*$ is related to the terrain (called r... | Logarithmic profile for wind speed regards the bottom part of atmospheric boundary layer (say, about the bottom 100 m, on a boundary layer about 1000 m high). It can be deducted doing some non obvious but reasonable assumptions.
A) Vertical flux of horizontal momentum due to turbulence must be uniform in the lowest par... | {
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Learning physics online? I'm thinking of following some kind of education in physics online. I have a master degree in Computer Science and have reasonable good knowledge in physics. I would like a program of 1-2 years and I'm more interested in particle physics.
Is there any good online program that offer something s... | Stanford has posted a bunch of theoretical physics courses by top physicist Leonard Susskind:
Classical Mechanics
Quantum Mechanics
Special Relativity
General Relativity
Cosmology
Statistical Mechanics
I'm a physicist but I still watched all these, just because Susskind is such a great teacher of physics. This is as go... | {
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How many atoms per light year does light encounter when traversing interstellar space? Interstellar space is pretty empty but there a small number of of atoms (mostly hydrogen?) floating around. How many atoms per light year would a photon encounter while traversing interstellar space?
| The number of scattering events ("encounters") per unit path length is equal to the density of scatterers times the scattering cross section (summed over all species of scatterers).
The density of particles (mostly hydrogen atoms) in the interstellar medium (ISM) is on the order of 1/cm^3. If we assume that the photon ... | {
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Books that every physicist should read Inspired by How should a physics student study mathematics? and in the same vein as Best books for mathematical background?, although in a more general fashion, I'd like to know if anyone is interested in doing a list of the books 'par excellence' for a physicist.
In spite of the ... | "Récoltes et Semailles" by Alexander Grothendieck, however it's not for a physicist, but for a scientist in general. I've read it at roughly the same time as "Surely, you are joking Mr. Feynman" and I appreciate RS much more.
I think that book is just invaluable. It is translated in English somewhere and around 25% in ... | {
"language": "en",
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Lightning strikes the Ocean I'm swimming in - what happens? I'm swimming in the ocean and there's a thunderstorm. Lightning bolts hit ships around me. Should I get out of the water?
| My girlfriend and I were swimming in the ocean about 30 feet from a beach in Costa Rica as a storm was approaching. We saw occasional flashes of lightning, and I was counting the time it took to hear the thunder, which was at least 7-8 seconds at the fastest, and often 10 or more seconds. I figured as it was at least a... | {
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"source": "stackexchange",
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Explanation: Simple Harmonic Motion I am a Math Grad student with a little bit of interest in physics. Recently I looked into the Wikipedia page for Simple Harmonic Motion.
Guess, I am too bad at physics to understand it. Considering me as a layman how would one explain:
*
*What a Simple Harmonic motion is? And why... | Simple harmonic motion (SMH) describes the behavior of systems characterized by a equilibrium point and a restoring "force" (in some generalized sense) proportional to the displacement from the equilibrium.
Example system
A simple mechanical system with this behavior is a mass on a spring (which we will consider in one... | {
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Common false beliefs in Physics Well, in Mathematics there are somethings, which appear true but they aren't true. Naive students often get fooled by these results.
Let me consider a very simple example. As a child one learns this formula $$(a+b)^{2} =a^{2}+ 2 \cdot a \cdot b + b^{2}$$ But as one mature's he applies t... | I would say that for most people, the quadratic scaling of kinetic energy with speed is somewhat of a mystery.
People don't understand how if you go twice as fast, a car accident actually four times as energetic, hence the high number of reckless drivers and deadly accidents.
| {
"language": "en",
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How do contact lenses work? I understand how telescope, microscope and glasses work.
But how do contact lenses work?
| The thing that confused me at first about contact lenses was that they didn't look like "normal" lenses, in which each side of them curved in the opposite direction to each other.
As I understand them, contact lenses are Meniscus lenses - wherein the sides are curved in the same direction as each other, but more curved... | {
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Home experiment to estimate Avogadro's number? How to get an approximation of Avogadro or Boltzmann constant through experimental means accessible by an hobbyist ?
| Well, addressing only $N_A$, and allowing that it only gets you halfway there: Carl Sagan did a bit on Cosmos for estimating the size of a oil molecule. Put a known amount (both volume and mass) of cooking oil on a calm body of water and wait for the slick to diffuse to it's maximum contiguous area. Estimate the area.{... | {
"language": "en",
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"source": "stackexchange",
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What's the difference between helicity and chirality? When a particle spins in the same direction as its momentum, it has right helicity, and left helicity otherwise. Neutrinos, however, have some kind of inherent helicity called chirality. But they can have either helicity. How is chirality different from helicity?
| Chirality and helicity are exactly the same thing in the massless limit. By this, I mean that either term can be used interchangeably in the massless limit (recall that a condition for massless particles, is that they necessarily move at velocity c). And yes you are correct in that there is no frame of reference where ... | {
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What is the difference between "kinematics" and "dynamics"? I have noticed that authors in the literature sometimes divide characteristics of some phenomenon into "kinematics" and "dynamics".
I first encountered this in Jackson's E&M book, where, in section 7.3 of the third edition, he writes, on the reflection and r... | You should think of it in terms of programming a computer to simulate the physical system. Kinematics is the data structure you need to simulate the general situation, what variables with what range of values. Dynamics is the actual algorithm that simulates the motion.
| {
"language": "en",
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Doppler's effect use While i was in high-school i learn't the Doppler's Effect which if i remember correctly is:
*
*The Apparent change in the frequency of sound caused due the relative motion between the sound and the observer.
This phenomenon seems obvious, but what i would like to know is, what use does Doppler... | To my knowledge,following are some uses of Doppler effect:
*
*Measurement of the speed of approaching automobiles.
*Ships are equipped with an instrument called SONAR which works on the principle of Doppler effect. It detects the pressence of under water rocks and submarines...
| {
"language": "en",
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What sustains the rotation of earth's core (faster than surface)? I recently read that the earth's core rotates faster than the surface.
Well, firstly, it's easier to digest the concept of planetary bodies, stars, galaxies in rotation and/or orbital motion.
But, what makes a planet's core rotate? And in the earth's cas... | According to our current understanding of the formation of planets, they are created from dust which originates in a previous supernova (or other large) explosion. This is called a nebula.
http://en.wikipedia.org/wiki/Nebular_hypothesis
As this nebula contracts into planets, there are generally two possible cases: that... | {
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Best example of energy-entropy competition? What are the best examples in practical life
of an energy-entropy competition which favors entropy over energy?
My initial thought is a clogged drain -- too unlikely for the
hair/spaghetti to align itself along the pipe -- but this is probably
far from an optimal example. Cu... | Well, as a physicist working mainly in the field of statistical physics, I obviously have to mention Ising model. In this case the model is actually tractable (at least in two dimensions) and can tell us a whole lot about (not just) energy-entropy battle. It's obvious that the ground state (for ferromagnetic case) is a... | {
"language": "en",
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Is it possible to separate the poles of a magnet? It might seem common sense that when we split a magnet we get 2 magnets with their own N-S poles. But somehow, I find it hard to accept this fact. (Which I now know is stated by the magnetic Gauss's Law $\vec{\nabla}\cdot \vec{B} =0.$)
I have had this doubt ever since r... | Magnetic monopoles certainly exist. This does not require a GUT, they exist in any theory where the electromagnetic U(1) is compact (i.e. where charge is quantized). This follows only from the semiclassical behavior of black hole decay, and so does not require unknown physics.
The reason is essentially the one you stat... | {
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Can I parameterize the state of a quantum system given reduced density matrices describing its subparts? As the simplest example, consider a set of two qubits where the reduced density matrix of each qubit is known. If the two qubits are not entangled, the overall state would be given by the tensor product of the one q... | Given an n-partite system and observables $\hat{T}_i$ with exspectation values $<\hat{T}_i> = t_i$, you can write your state as a maximum entropy state:
$$\rho = \frac{1}{Z}exp\left(\sum_i \theta_i \hat{T}_i\right)$$
see Theorem 2 in http://arxiv.org/abs/quant-ph/0603012
| {
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Is it possible to obtain gold through nuclear decay? Is there a series of transmutations through nuclear decay that will result in the stable gold isotope ${}^{197}\mathrm{Au}$ ? How long will the process take?
| Natural gold exists, so the answer to the first part of your question is unambiguously "Yes". 'Cause all those heavy elements get made by transmutation in supernovae.
I can't answer the time scale thing because I haven't a table of the isotopes in front of me right now.
Checking with http://ie.lbl.gov/education/isotop... | {
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Which experiments prove atomic theory? Which experiments prove atomic theory?
Sub-atomic theories:
*
*atoms have: nuclei; electrons; protons; and neutrons.
*That the number of electrons atoms have determines their relationship with other atoms.
*That the atom is the smallest elemental unit of matter - that we ca... | I would say that one experiment that demonstrates the atomic nature of things is the observation of Brownian motion. But it is not the experiment itself that convinces that things are made of atoms, rather its theoretical explanation given by Einstein in one of his 1905 papers (actually Einsteins work for his PhD was o... | {
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Spectral Line Width and Uncertainty principle so I've been at this for about 3 - 4 hours now. It is an homework assignment (well part of a question which i've already completed). We did not learn this in class. All work is shown below.
An atom in an excited state of $4.9 eV$ emits a photon and ends up in the ground st... | Hint: Your problem is in the "take $\Delta f$ an convert it to wavelength using $\lambda f = c$" part. The equation $\lambda f = c$ does not imply $\Delta \lambda \Delta f = c$.
Answer: Rather it implies,
$\lambda f = c$
$\lambda = \frac{c}{f} $
Now differentiate:
$d\lambda = -c\frac{df}{f^2}$
$df \ll f$ so treatin... | {
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What's the difference between running up a hill and running up an inclined treadmill? Clearly there will be differences like air resistance; I'm not interested in that. It seems like you're working against gravity when you're actually running in a way that you're not if you're on a treadmill, but on the other hand it s... | What if the runner gets on her bicycle on the treadmill? Does she have to bike harder on an inclined treadmill than a horizontal one, both running at the same speed?
(In this case, biking on a horizontal treadmill is almost effortless because on a bike, the real effort is the wind resistance, which would be non-existe... | {
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Why does the (relativistic) mass of an object increase when its speed approaches that of light? I'm reading Nano: The Essentials by T. Pradeep and I came upon this statement in the section explaining the basics of scanning electron microscopy.
However, the equation breaks down when the electron velocity approaches the... | The mass (the true mass which physicists actually deal with when they calculate something concerning relativistic particles) does not change with velocity. The mass (the true mass!) is an intrinsic property of a body, and it does not depends on the observer's frame of reference. I strongly suggest to read this popular ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/1686",
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Ice skating, how does it really work? Some textbooks I came across, and a homework assignment I had to do several years ago, suggested that the reason we can skate on ice is the peculiar $p(T)$-curve of the ice-water boundary. The reasoning is that due to the high pressure the skates put on the ice, it will melt at tem... | Yup, this is true that the pressure is too small, but the true explanation is not justified yet. Nevertheless the common sense is that there is a lubricating film of water or at least anomalous ice.
For an overview, see: http://lptms.u-psud.fr/membres/trizac/Ens/L3FIP/Ice.pdf
| {
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Hawking radiation and quark confinement The simple picture of Hawking radiation is that a pair-antiparticle pair is produced near the event horizon, then one falls into the black hole while the other escapes. Suppose the particles are quarks-antiquarks, which experience quark confinement thanks to QCD. If one of them i... | I think your reasoning should be correct.
However, as I understand the Hawking radiation (i.e. not much) the effect is derived independently of the microscopic theory. You just assume that particle (which is to escape from around the horizon) needs to accelerate (a lot) in order to overcome black hole's gravity and the... | {
"language": "en",
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What is terminal velocity? What is terminal velocity? I've heard the term especially when the Discovery Channel is covering something about sky diving. Also, it is commonly known that HALO (Hi-Altitude, Lo-Opening) infantry reaches terminal velocity before their chutes open.
Can the terminal velocity be different for... | Terminal velocity is the (asymptotic) maximum velocity that you can reach during free-fall. If you imagine yourself falling in gravity, and ignore air resistance, you would fall with acceleration $g$, and your velocity would grow unbounded (well, until special relativity takes over). This effect is independent of your ... | {
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Can I levitate an object without using an electromagnet? I know that it's possible to make an object levitate using an electromagnet to hold it up.
But is it also possible to do this with regular magnets? Is there a special kind of magnet I need in order to have one powerful enough to hold an object up?
I'm asking bec... | yes, you can. Not easily though.
My favorite is the Meisner effect. It would require a superconductor for B, which would most likely require liquid nitrogen. Basically, the levitating magnet (A) would create an current in the superconductor (which has "zero" resistance). The current would then go for as long as the... | {
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"source": "stackexchange",
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How can one find the energy eigenfunctions of a particle in a finite square well via the Klein-Gordon equation? It is said that Klein-Gordon equation is a relativistic version of the Schrodinger equation. In Schrodinger equation, it is straightforward to include potential energy. But for K-G eqn things seem to be more ... | K-G is a relativistic equation. So if you want to couple it to external fields you have to use a vector potential $A_\mu$ which will modify the partial-derivative, so that the Klein-Gordon equation:
$$ \left( \partial^\mu \partial_\mu + m^2 \right)\phi = 0 $$
becomes:
$$ \left ( D^\mu D_\mu + m^2 \right) \phi = 0 $$
... | {
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"timestamp": "2023-03-29T00:00:00",
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How long a straw could Superman use? To suck water through a straw, you create a partial vacuum in your lungs. Water rises through the straw until the pressure in the straw at the water level equals atmospheric pressure. This corresponds to drinking water through a straw about ten meters long at maximum.
By taping se... | I have an argument that the water in the straw will rise to twice the equilibrium height.
David and Martin's answers consider the system of water in the straw. I will consider the system of the water in the straw plus the water in the reservoir.
As water goes into the straw, the water level in the reservoir drops, and... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/2111",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why did this glass start popping? I remember a while ago my father dropped a glass lid and it smashed. It looked something like this. When that happened, for about 5 minutes afterwards, the glass parts were splitting, kind of like popcorn, and you could hear the sound. I was just wondering why this happened, and the pa... | Here is an idea. You could have cracking (fracture) behaving as a critical process. From the dropping of the glass you could have micro-fractures forming. In time and because of the amount of tension (and energy) concentrated in the glass from the fall, these micro-fractures slowly could organize to form big fractures,... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is it possible for information to be transmitted faster than light by using a rigid pole? Is it possible for information (like 1 and 0s) to be transmitted faster than light?
For instance, take a rigid pole of several AU in length. Now say you have a person on each end, and one of them starts pulling and pushing on hi... | The answer is no. The pole would bend/wobble and the effect at the other end would still be delayed.
The reason is that the force which binds the atoms of the pole together - the Electro-Magnetic force - needs to be transmitted from one end of the pole to the other. The transmitter of the EM-force is light, and thus th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/2175",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Anti-gravity in an infinite lattice of point masses Another interesting infinite lattice problem I found while watching a physics documentary.
Imagine an infinite square lattice of point masses, subject to gravity. The masses involved are all $m$ and the length of each square of the lattice is $l$.
Due to the symmetrie... | I think that your initial intutiion is right--before the point particle is removed, you had (an infinite set of) two $\frac{G\,m\,m}{r^{2}}$ forces balancing each other, and then you remove one of them in one element of the set. So initially, every point particle will feel a force of $\frac{G\,m\,m}{r^{2}}$ away from ... | {
"language": "en",
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"source": "stackexchange",
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What is the definition of colour (the quantum state)? I heard somewhere that quarks have a property called 'colour' - what does this mean?
| Let me give a straightforward and basic answer here; perhaps someone else can elaborate.
The best way to think of colour is something analogous to charge in electromagnetism. (Indeed, colour is often called colour charge). It is the fundamental property of particles relating to the strong force, and like electric charg... | {
"language": "en",
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Why are materials that are better at conducting electricity also proportionately better at conducting heat? It seems like among the electrical conductors there's a relationship between the ability to conduct heat as well as electricity. Eg: Copper is better than aluminum at conducting both electricity and heat, and sil... | What links the two conductivities is that they both depend on how transparent the material is to electrons traveling around the Fermi energy.
Thermal conductivity also has a contribution from lattice vibrations, but for metals the contribution from electrons dominate.
In an analogy, imagine two recevoirs of water conne... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/2245",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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Polar vs non-polar fluid In the book "Vectors, Tensors, and the Basic Equations of Fluid Mechanics" by Rutherford Aris I read the following:
If the fluid is such that the torques
within it arise only as the moments of
direct forces we shall call it
nonpolar. A polar fluid is one that is
capable of transmitting... | A polar fluid is just a fluid where the constituent molecules have a polarization -- it could be a fluid of molecules that have a magnetic spin moment, or something like H2O where each individual molecule has a nonzero electric dipole -- and at the macroscopic level, as you average over all of the microscopic moments, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/2364",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 6,
"answer_id": 0
} |
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