Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How do we know that one particular solution for the velocities of a two-body elastic collision is the correct one over the other? Assuming there is a 1-D collision between two bodies, having masses $m_1$ and $m_2$, if we conserve energy and momentum, we get two solutions.
$$
v_{1,i} = v_{1,f} \\
v_{2,i} = v_{2,f}
$$
... | I mean the first solution would not change anything in the system at all after the collision right? So the two masses would just pass each other. Since you want to calculate the final state of a fully elastic collision, why would you consider the "not change a thing" solution?
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Explain how scaling of the inverse square law breaks down at a stars surface If the radiation pressure at distance $d>R$ from the center of an isotropic black body star is found to be $$P_{rad}=\large{\frac{4\sigma T^4}{3c}}\left[1-\left(1-\frac{R^2}{d^2}\right)^{\frac{3}{2}}\right],$$
a) How do I show that $P_{rad}$ o... | As about (b):
Why does the inverse square law scaling break down close to the stars surface?
$$ P_{\,d\approx R} = \lim_{d \to R} {\frac{4\sigma T^4}{3c}}\left[1-\left(1-\frac{R^2}{d^2}\right)^{\frac{3}{2}}\right] = {\frac{4\sigma T^4}{3c}} $$
In other words, when you are at the star surface - you get as much radiati... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can a red light photon be different from a blue light photon? How can photons have different energies if they have the same rest mass (zero) and same speed (speed of light)?
| The only difference between the two is the energy they have.
$$
E=\frac{hc}{\lambda}
$$
As you can see from the equation above, different energies means different wavelengths. Different wavelengths means different colors.
It is important to know that even though photons are always massless and always move with the sp... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540485",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "29",
"answer_count": 6,
"answer_id": 4
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Is Stokes' law, for drag force in fluids, accurate? In high school, I was taught that Stokes' law is dependent on assumption that drag force is proportional to velocity, viscosity and radius of the sphere (and the powers/exponents are evaluated using dimensional analysis). Is Stokes' law proven or is it just an assumpt... | Stokes' law only applies when the inertia forces in the fluid (caused by its acceleration or non-uniform motion) are negligible compared with the viscous forces.
The ratio of the two types of forces is described by a non-dimensional number called Reynolds number (usually written as Re). Stokes' law applies when Re is m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540590",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
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Contradiction using amperes law to calculate magnetic field $B$ I am trying to study the influence on the magnetic field B generated by a solenoid in two different cases
*
*the solenoid is wound around an open iron core
*the solenoid is wound around a closed iron core
I am trying to use amperes law to give an est... | Thank you ohneVal for your answer. I still had problems understanding why my approach did't work so I also had a chat with some colleagues about this.
I think I now understand my biggest flaw. Amperes law is actually $$ \oint H\cdot dl=n\cdot I $$
since $ H=\frac{B}{\mu} $ this can be written as $$ \oint \frac{B}{\mu}\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540795",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Finite barrier. Constant including minus or not? For a finite potential barrier of magnitude $V_0$ between $x=-a$ and $x=a$ we know that the time independent schrodinger equation is $\Psi'' +\frac{2m}{\hbar}E\Psi=0$ for $x<-a$. Let $E<V_0.$ Normally we set $k_1^2=\frac{2mE}{\hbar^2}$ and get $\Psi''+k_1^2\Psi=0$ which ... | First, your Shrodinger equation seems to have a some small problems.
From
$$ - \frac{\hbar^2}{2m}\Psi'' +V(x)\Psi = E\Psi$$
one get:
$$ \Psi'' + \frac{\sqrt{2m}}{\hbar} (E-V(x)) \Psi =0.
$$
For your barrier, and for $0<E<V_0$,
One has in the barrier ;
$$ \Psi(x) = A e^{\kappa x} +
B e^{-\kappa x},$$
where $\kappa=\sqr... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do we need Gauss' laws for electricity and magnetism? The source of an electromagnetic field is a distribution of electric charge, $\rho$, and a current, with current density $\mathbf{J}$. Considering only Faraday's law and Ampere-Maxwell's law:
$$
\nabla\times\mathbf{E}=-\frac{\partial\mathbf{B}}{\partial t}\qquad... | This just an explicit example to @vadim's answer: Pick a function $f(\vec x)$, constant in time, such that $\Delta f =5$. Set $\vec B=\vec\nabla f$, $\vec E=\vec J=0$, $\rho=17$. Then Eqns. (1) and (2) are satisfied, buth both equations in (3) are not.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540991",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 3,
"answer_id": 2
} |
Is it possible for a quantum system to evolve out of a determinate state of some observable before measurement is made? On page 96 of his book, Griffiths explains that determinate states of some observable $Q$ are eigenfunctions of that operator. So if a particle starts out in that state it will continue to be in that ... | It is a different application of the word determinate. Griffiths simply means that the result of a measurement is determinate if the state is an eigenfunction. That is not the same as determinism in time evolution.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541063",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Is heat $\delta Q$ an exact differential for an isochoric process (ideal gases)? Generally speaking, heat and work are path-dependent, thus $\delta Q$ and $\delta W$ are not exact differentials. By first law of thermodynamics, we know that $dU=\delta Q - \delta W$
but $\delta W=0$ for an isochoric process, that yields... | Let's assume that the system is in equilibrium throughout the isochoric process and closed. We say the process has to be quasi-static. Under these conditions the work done on the system is
$$\delta W=-pdV+\sum_iy_iX_i
$$
where the $X_i$ represent different work variables, arising from different physical interactions. F... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541220",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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"answer_id": 1
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Why does the range of this integral work out this way? I have a bit of trouble in finding the same limits for the integral in Eq. (17.111) from Peskin & Schroeder. We have something like
$$ \int_0^1 dx' \int_0^1 dz f(x',z) \delta(x-zx').$$
Posing $y=zx'$, I find
$$\begin{align}
\int_0^1 dz \int_0^1 \frac{dy}{z} f\biggl... | The scaling property of the Dirac delta is
$$\delta(\alpha x) = {1\over|\alpha|} \delta(x). $$
So you get
$$
\int_0^1 dx' \int_0^1 dz f(x',z) \delta(x-zx') = \int_0^1 dz \int_0^z \frac{dy}{z} f({y\over z},z) \delta(x-y)
$$
meaning that when you apply the delta function you have $x\leq z$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541381",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
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Fourier Optics - Impulse Response of Free Space from Fresnel Transfer Function I am currently reading the chapter "Fourier Optics" in the book "Fundamentals of Photonics" by Saleh and Teich. However I am not able to follow one specific mathematical derivation.
On page 111 the transfer function of free space is derived ... | I think I was able to solve the problem by applying the same method as mentioned here. However my solution still differs by a constant factor from the solution in the book, so maybe it is still not completely right.
If you look at $h(x, y)$ one can see easily that it can be separated as
$$h(x, y) = K \cdot f(x) \cdot f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541467",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Physics of Project Orion I was reading the book "Project Orion" by George Dyson. For those who are unaware, Project Orion was basically a plan to launch a spaceship by flinging bombs out the rear and detonating them. The plasma from the explosion would contact a "pusher plate", which was attached to shock absorbers, wh... |
I'd like to know where this formula came from...
I am guessing it was an assumption about kinematics where one assumes constant acceleration. If this is valid, then we know:
$$
V_{f}^{2} - V_{o}^{2} = 2 \ a \ \Delta x \tag{0}
$$
where $V_{i}$ is the speed ($i$ = $f$ for final and $o$ for initial), $a$ is the acceler... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542009",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How can a black hole eject plasma? This image from an online Italian newspaper shows photographs of one of the most powerful phenomena in the cosmos.
Nothing, not even at the speed of light $c$, can escape a black hole one it has been caught. So how is it possible mathematically that a black hole, which "swallows" the... | The black hole is defined by its event horizon. This is the point at which the escape velocity reaches $c$. But the accretion disc forms outside the event horizon, so stuff can still escape from it. It is this outer stuff that finds its way into the jets, super-accelerated beyond escape velocity by magnetic fields bein... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542174",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How to build a many-body state starting from single-particle states? Suppose that I have 3 non-degenerate single-partilce energy levels $E_1$, $E_2$, and $E_3$, each one associated to eigenstates $|\psi_1\rangle$, $|\psi_2\rangle$, and $|\psi_3\rangle$.
How do you build the most general many-body state in the case par... | It is easier to do it in terms of wave functions than in the bra-ket notation. The one-particle states are $$|\psi_1\rangle\leftarrow\psi_1(x),|\psi_2\rangle\leftarrow\psi_2(x), |\psi_3\rangle\leftarrow\psi_3(x)$$. The two-particle states are antisymmetrized combinations of the pairwise products, i.e. $$|\psi_1\psi_2\r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542335",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
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Physics of the trikke tricycle I love my trikke, but I still do not understand what propels it forwards.
It is very clear that the energy comes from my legs and not from my arms (I only have to touch the handle bar ever so lightly), but I do not see how my shifting weight from side to side can result in a forward point... | The front wheel provides a friction force perpendicular to the direction it is pointing. Since the wheel turns the trikke one way, the reactive force of the road on the wheel pushes the other way. Since this is perpendicular to the wheel, there is a component of forward force on the bike (or backwards as the case may b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542899",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 3,
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Nicholas Gisin's papers about Time in Physics I recently read the article from QuantaMagazine which says
Over the past year, the Swiss physicist Nicolas Gisin has published four papers that attempt to dispel the fog surrounding time in physics. As Gisin sees it, the problem all along has been mathematical
I tried se... | Here are the papers listed with their preprint links:
*
*Indeterminism in Physics, Classical Chaos and Bohmian Mechanics: Are Real Numbers Really Real? - linked here
*Real numbers are the hidden variables of classical mechanics - linked here
*Physics without Determinism: Alternative Interpretations of Classical Phy... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542992",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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How can a photon collide with an electron? Whenever I study the photoelectric effect and the Compton effect, I have always had a question about how a photon can possibly collide with an electron given their unmeasureably small size. Every textbook I've read says that the photo-electrons are emitted because the photons ... | It is very important to understand that you are asking about the absorption of a photon. Now if you try to imagine this as a classical collision of two balls, that is just not correct. You are confused because you think the photon needs to collide head on with a specific electron to get absorbed.
What is correct to say... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/543056",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "38",
"answer_count": 9,
"answer_id": 6
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Existence conditions for completely positive trace-preserving (CPTP) map Given two separable Hilbert spaces $\mathcal{H}_1$ and $\mathcal{H}_2$, I am wondering: what are the necessary and sufficient conditions for there to be a completely positive trace-preserving (CPTP) map $\Phi:B(\mathcal{H}_1)\to B(\mathcal{H}_2)$?... | The map $\Phi(\rho) = \mathrm{tr}(\rho)\sigma$, for some state $\sigma\in B(\mathcal H_2)$ with $\mathrm{tr}(\sigma)=1$ is CPTP and exists for any pair of separable Hilbert spaces.
(As always for these questions, let me advertise my list of canonical examples for quantum channels.)
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/543468",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Fourier transform of Fermi function As an alternative approach to the Sommerfeld-expansion, my lecturer tries to motivate properties of free fermions, such as temperature dependencies of the chemical potential $\mu(T)$, electron number $N_e(T)$, energy density $U(T)$, etc. by expanding the Fourier transform of the Ferm... | I have in my notes a related Laplace transform:
$$
I=\int_{-\infty}^{\infty} \frac{d\epsilon}{2\pi} e^{\tau\epsilon/2\pi} \left\{ \frac{1}{1+e^{\beta(\epsilon-\mu)}}-\theta(-\epsilon)\right\}= \frac 1{\tau}\left\{ \frac{(\frac{\tau T}{2})}{\sin(\frac{\tau T}{2})} e^{\tau\mu/2\pi}-1\right\}, \quad 0<\tau T/2\pi< 1.
$$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/543917",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is a photon reflected, transmitted or in a superposition? When a photon hits a half-silvered, mirror quantum mechanics says that rather than being reflected OR transmitted it enters into a superposition of transmitted AND reflected (until a measurement takes place). Is there an experiment that demonstrates that this is... | There is a very nice experiment that does this for 2 photons: it is the
Hong-Ou-Mandel experiment:
C. K. Hong; Z. Y. Ou & L. Mandel (1987). "Measurement of subpicosecond time intervals between two photons by interference". Phys. Rev. Lett. 59 (18): 2044–2046.
For simplicity, consider two photons simultaneously ente... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/544061",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Fourier Analysis for Physicists My professor wanted me to master these topics from Fourier Analysis. I need a resource where these topics are discussed in brief. Although i know many of the topics in the list, i prefer a good resource to brush up my rusty knowledge and learn what i don't know. The topics are:
*
*Fou... | *
*If your into solving a lot of examples and gathering some intuition i recommend Schaum's outline series. They have nice solved examples. (https://www.amazon.com/Schaums-Analysis-Applications-Boundary-Problems/dp/0070602190)
*If you are into more technical mathematical stuff, here is a textbook I used. (https://www... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why does a rubber band become a lighter color when stretched? I was stretching a pink colored rubber band, and I noticed that the longer I stretch it, the lighter the pink becomes. I haven't found answers to this question anywhere else. Is there a reason for this phenomenon?
Why does this happen?
| Colour can come from pigment particles embedded in the translucent rubber matrix absorbing light. When you pull the band the particles become separated by a longer distance, but being themselves inelastic remain the same size. Hence the amount of absorption per unit area decreases, and the band become lighter in color.... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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"A spinning top spins much longer because it experiences less frictional torque" is wrong? The above quote was found in my physics textbook, but it struck me as strange because my understanding of friction is that the surface area doesn't matter in calculating the amount of frictional force.
Another question that asked... | There are two types of friction, static and kinetic friction. Imagine trying to push a table across a carpet. Initially you need to generate some force to get the table to move, but once the table starts moving you may feel it's easier to push it further.
The type of friction that is important for your spinning top exa... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Wavefunction of a photon Does anyone have an explicit closed-form expression for the wavefunction of a single photon from a multipolar source propagating through free space? Any basis is acceptable as long as it is a single photon state.
A reference would also be appreciated, but not essential.
————————
A possible du... | I define the photon wave function in a covariant formulation which has four polarisation states, two of which are not observable. Some authors use only transverse states, but the other two states would appear on Lorentz transformation, and they appear to be necessary to derive the classical correspondence correctly.
Fo... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Inverse of a metric tensor on a Hermitian manifold Let $(M, g)$ be a Hermitian manifold. We have a metric tensor $g^{i \bar j} dz_i \otimes d\bar{z_j}$, where $(g_{i \bar j})$ is a hermitian positive definite matrix. Now we naturally get the inverse of the metric $(g^{i \bar j})$. I have been told being inverse to each... | Metric tensors are usually assumed to be symmetrical, i.e. $g_{\mu\nu} = g_{\nu\mu}$, so
\begin{equation}
g_{\mu\nu}g^{\nu\epsilon} = g_{\nu\mu}g^{\nu\epsilon} = \delta_\mu^{\ \ \epsilon}
\end{equation}
The symmetry is due to the fact that the metric is used to compute the line elements $ds^2$ and the follwing holds
... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545331",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can Higgs potential provide a cosmological constant? Usually, in particle physics, people do not care about a constant term in scalar field potential. Rather, attentions are paid to the local profile at the minimum. But in the context of cosmology, the absolute value of the potential has a physical meaning; it is a cos... | The cosmological constant is part of the mathematical framework of General Relativity.
The Higgs field is part of the mathematical framework of quantum field theory and particle physics .
At the moment there is only effective quantization of gravity, used in cosmological models , and yes, if you google higgs field and... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545509",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Confusion in understanding the Lambertian law Lambertian law states that the luminous intensity of light emitted from a perfectly diffusing surface is proportional to the $cos(\theta)$ between the surface normal and the direction of observation. I understand it in the following way. If we will observe some surface scat... |
each producing a certain constant number of photons per solid angle in all directions.
This would be non-Lambertian emission.
In Lambertian scattering/reflection most rays are emitted along the normal and fewer as we approach large angles.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545741",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Light’s Behavior in a Rotating Reference Frame Let’s say there is a laser on one side of a very large rotating table, and it’s beam is shining onto a target on the other side of this table. The target is equipped with a very sensitive buzzer that will sound if the laser moves off of the target. Here’s what I think will... | As it will take time for the photons to reach the sensor after leaving the emitter, once the sensor starts moving away from where the emitter was originally pointed, the photons will no longer hit the same point on the sensor. So the buzzer will sound until the table stops spinning. This will happen in your spinning ta... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545889",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
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Mach cone geometry from Mach number Given a Mach number, how would I go about determining the geometry of the associated Mach cone? Apologies, I'm not too well versed in physics.
| While @R.W.Bird's answer is absolutely correct,
I will complement it with a more graphical explanation.
Consider an airplane flying with speed $v$,
and the spherical sound waves spreading
from the airplane with the speed of sound $c$.
You see, when $v>c$ (i.e. when the airplane is faster
than sound), then the sound wa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/546413",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What is the term to describe when pressure exerted between two obejcts is balanced? I'm searching for a term here.
All materials compress (some more than others).
Newton's Third law states:
...all forces between two objects exist in equal magnitude and opposite direction: if one object A exerts a force FA on a second... | Newton’s third law does not tell us what the effect of the equal and opposite forces are on each of the bodies. Newton’s second law applied to each of the bodies individually tells us what, if any, acceleration each experiences based on the net external force applied to each. Mechanics of deformable solids helps us to ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/546514",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Decoupled Temperature for photons: why is it 0.25 $\rm eV$ rather than 13.6 $\rm eV$? When calculating the decoupled temperature of photons using Saha' equation for the following process:
\begin{equation}
e^- p\longleftrightarrow H\gamma
\end{equation}
we find that $T_{dec}=3000$ K$=0.25$ eV.
From my understanding, th... | This is because there are hugely many more photons than charge-carriers per unit volume, roughly 10 billion photons for every electron in the universe.
As an example, consider affairs when the universe cooled to a temperature of 1 eV, or around 10,000 K. At this temperature, electrons are no longer relativistic and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/546668",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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A question about conformal time I have a function to calculate the Hubble parameter at a given redshift:
$$H(z)=\sqrt{\Omega_R(1+z)^4+\Omega_m(1+z)^3+\Omega_k(1+z)^2+\Omega_{\Lambda}}$$
And I have another function to calculate the conformal time between two redshifts:
$$\eta(z1,z0)=\int_{z1}^{z0}\frac{1}{H(z]}dz$$
So n... | I am only familiar with your first equation, except my experience is in using
$$a(t)= \frac {1} {1+z(t)}.$$
Your equation seems to have omitted the $H_0$ value as a coefficient of the square-root.
| {
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Classic Man on a Boat problem To be clear I have indeed reviewed the question asked by helios321 (Classic man on boat problem). But i have something else to ask related to man on a boat problem.
The man on a boat problem goes like this:
A man is standing on one side of a boat and the boat is stationary. We ignore fr... | As the man begins to move, the boat begins to move in the opposite direction. So when the man has moved, say forward with respect to the boat the boat meanwhile has drifted backwards. If one would calculate their center of mass it would be at the same place as before. And if one would sum up the momentum vectors of the... | {
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How do electron wavelengths relate to orbitals and probability density? I'm doing a physics research project and I am a bit confused. We haven't learnt much of this on our course so I'm sorry if this is a stupid question, I couldn't seem to find an explaination that I understood online.
I understand stationary waves, a... | Your first sketch (upper left) represents a resonant condition for a 1D wave wrapped around a circle. (Keep in mind that the "waves" in the sketch are a mathematical graph representing the probability density at points on the circle.) An electron orbital is a resonant 3D standing wave, bounded by the electric field of ... | {
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Is the force of gravity always directed towards the center of mass? This is a pretty basic question, but I haven't had to think about orbital mechanics since high school. So just to check - suppose a [classical] system of two massive objects in a vacuum.
If the density of either object is the same at a given distance f... | In order to have gravity to always point to the center of mass, your mass must have a spherical symmetry (be homogenous or at least made of homogenous concentric layers). The approximation can be used (to a certain extent) for bodies that are not symmetrical, but are pretty much apart from each other.
The more the body... | {
"language": "en",
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Can massless particle have effective mass? The effective potential was probably very familiar in many concepts.
However, what about effective mass?
Suppose a massless particle. For simplicity, suppose it's not some superficial particle, i.e. it has observable effect.
Is it possible for such massless particle to gain... | Well if the photon interacts with something and something effectively slows it down. Then the photon will have mass. While the photon does not have any intrinsic mass any interaction will make it to have mass. This is similar to the case with gluons. Gluons can bundle up together. While the gluons themselves are massle... | {
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What is wrong with this calculation of work done by an agent bringing a unit mass from infinity into a gravitational field? Let us assume that a gravitational field is created by a mass $M$. An agent is bringing a unit mass from $\infty$ to distance $r < \infty$, both measured from mass $M$.
The agent is always forcing... |
The agent is always forcing the unit mass with a continuously changing Force, $\vec{F}$(x) ... = $\frac{GM}{x^2}\hat{x}$
By your force definition, the agent is not the attractive gravitational force but is something which is restricting the motion to constant velocity because the mass M is pulling in the $-\hat{x}$ d... | {
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Approximation of the total number of accessible microstates So, here is a system having two subsystems $\alpha$ and $\beta$ where the two subsystems can exchange energy between them, then the total number of accessible microstates of the whole system is given by, $$\Omega(E)=\sum_{E_{\alpha}}\Omega_{\alpha}(E_{\alpha})... | The approximation is
$$
\Omega_\alpha(\tilde{E}_\alpha) \gg \sum_{E_\alpha \ne \tilde{E}_\alpha} \Omega(E_\alpha)
$$
or in words: the number of microstates of the most occupied macrostate (which is also very close to the one having the mean energy) dominates not just some of the other macrostates, but all of them toget... | {
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Why is the acceleration of the string connected to the cylinder different from which the cylinder is moving forward with?
The following Object 'B' is a cylinder. It is kept mounted horizontally on a massless block, when a tension T is applied by a string passing over the lower end of cylinder, the acceleration of the ... | Firstly, at the point the string contacts the cylinder, their velocity and acceleration are the same (otherwise the string will slip).
Secondly say that the velocity of the center of the cylinder is $v$ and its angular velocity is $\omega$. At that point, its velocity will be $v+\omega\times r$. (why? Hint: Galileo tra... | {
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Does the light pulse broadens in time when passing bandpass filter? What I don't understand about relationship between laser pulse width in time and frequency, is where these rules apply, namely rules of Bandwidth-limited pulses.
Say, I have a femtosecond laser making 100fs pulses with central wavelength 900nm, and FWH... | Usually, femtosecond pulses are produced by a mode-locking. A laser cavity has a certain number of modes at different frequencies, which usually illuminate with a random phase relationship between each other. The mode-locking is a process that results in a certain phase shift between the modes. Imagine that you have a ... | {
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How does cutting a spring increase spring constant? I know that on cutting a spring into n equal pieces, spring constant becomes n times.
But I have no idea why this happens.
Please clarify the reasons
| spring constant is inversely proportional to its length hence when a spring of constant $k$ is cut into $n$ number of pieces, the length becomes $\frac1n$ times initial length so spring constant becomes $k/(1/n)=nk$. therefore $k$ becomes $n$ times on cutting a spring.
| {
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What exactly happens when $\rm NaCl$ water conducts electricity? Assume a DC power source with $2$ electrodes made of Fe. We dip those $2$ electrodes into table salt water. What happens exactly?
*
*Will $H^+$ and $Na^+$ migrate to the negative electrode by electrical field
or diffusion or a combination of both?
*... | To describe the diffusion, migration (under an electric field) and the convection of species we have the Nernst-Planck Equation:
$$ \frac{\partial c}{\partial t} = - \nabla \cdot J \quad | \quad J = -\left[ D \nabla c - u c + \frac{Dze}{k_\mathrm{B} T}c\left(\nabla \phi+\frac{\partial \mathbf A}{\partial t}\right) \rig... | {
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Mathematically prove that a round wheel roll faster than a square wheel Let's say I have these equal size objects (for now thinking in 2D) on a flat surface.
At the center of those objects I add equal positive angular torque (just enough to make the square tire to move forward).
Of course the round tire will move fast... | I think that in perfect conditions, the square and the circle roll AT THE SAME SPEED. The reason for this is that in real life, a circle will roll faster than a square for friction reasons: the kinetic energy of the square will get lost faster than the energy of the circle because of it's shape and go to thermal energy... | {
"language": "en",
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What is the range of Pauli's exclusion principle？ In many introductions to the pauli's exclusion principle, it only said that two identical fermions cannot be in the same quantum state, but it seems that there is no explanation of the range of those two fermions. What is the scope of application of the principle of exc... | It depends on the system to which the fermions belong. The exclusion principle says that no two fermions can have the same quantum state. The quantum state includes the system to which the fermion belongs. If you are looking at electrons in atoms, for example, the atom is the system, and the exclusion principle applies... | {
"language": "en",
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Do things have colors because their electrons are getting excited when photons hit them? Atomic electron transitions can be caused by absorbing a photon with a certain wavelength. An electron jumps to an higher energy level, then it falls back and a photon is emitted. The perceived color of the photon depends on the en... | No, actually what you are talking about is the atomic spectrum of an atom or a system. The colour of a object depends on the crystal structure of the object. As @user12986714 gave the example, copper has crystalline structure which cause the constructive interference of light wave of particular frequency between two cr... | {
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Does an object rotating in place have linear momentum? I understand that an object with linear momentum could have angular momentum. However, can the same be in reverse? For example, will a wheel spinning in place be considered to have both angular and linear momenta? It will have tangential velocity, but the wheel its... | Each particle that the object consists of can carry momentum. And they all except for the particle at the very centre do carry some momentum.
$$p_\text{ non-centre-particle}\neq 0$$
The total momentum (the sum of all particles' momentum) will be zero if the object is spinning about its centre-of-mass (CoM), since all p... | {
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Does the $U(1)$ vector current flip under charge conjugation? The conserved $U(1)$ current of the Dirac Lagrangian is given by $j^\mu = \bar{\psi} \gamma^\mu \psi$, where $\bar{\psi} = \psi^\dagger \gamma^0$. As this is interpreted as electric current I would expect it to flip sign under charge conjugation. Charge conj... | Starting with your third to last line, we begin by rewriting
\begin{equation}
\begin{split}
(\psi^\dagger)^*(\gamma^0)^* (\gamma^\mu)^* \psi^* &= \psi^T \big[(\gamma^0)^\dagger\big]^T \big[(\gamma^\mu)^\dagger\big]^T (\psi^\dagger)^T \\
&= \big[\psi^\dagger (\gamma^\mu)^\dagger (\gamma^0)^\dagger \psi \big]^T\\
&= \psi... | {
"language": "en",
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How do gravitons and photons interact? First of all, I am a noob in physics (I‘m a computer scientist) and started reading Hawking‘s „A brief history of time“. In Chapter 6 he says that “electromagnetic force [...] interacts with electrically charged particles like electrons and quarks, but not with uncharged particles... | Gravitons should couple to almost every particle. It is just a matter of how much it couples with the particle. However in the particle world gravitons are pretty weak compared to the other forces. However on the largest of scales gravitons and gravity wins over. To answer the question gravitons do couple to photons.
| {
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Why is a pump's head usable for any fluid? As far as I investigated, a pump has a specific head in a determined flow rate (relating to its power and rotating speed). Then considering the formula ($\Delta P=\rho g H$), $\Delta P$ is adjusted for any fluid (with a different density) to obtain the same head.
But my questi... | There are vanes in the impeller of a centrifugal pump, and the tips of those vanes are moving at a tangential speed that is a function of the impeller diameter and impeller revolutions per minute. In SI units, this tip speed is given by $v=r\omega$ m/s. Individual parcels of liquid come off the impeller vane tips at ... | {
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How do metals reflect electromagnetic radiation? Microwaves, for example, can be reflected off metallic surfaces. This seems counter-intuitive, since the metal's electrons could interact with the electric field component of the EM wave and absorb it.
In fact, you can use a metal grid to polarise microwaves, and there t... | You are right that there are ample electronic transitions in a metal that match the frequency of optical and lower frequencies. However these transitions do not satisfy momentum conservation. When you apply a grid then momentum is only conserved up to an inverse lattice vector (of the grating). For a suitably choice of... | {
"language": "en",
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How do electrons in n type (conduction band) fall into holes in p type (valence band with lower energy) in a pn junction? I was studying about the semiconductor physics.I learned about the concepts of holes and all.If the electrons present in n type is in conduction band how can they fall into holes in valence band of... | I'm hoping the diagram at the bottom may help a little, it's one I made when I was writing up to show the basics of what happens in the p-n junction (without any bias). I would highly recommend also the website pveducation.org, which takes you through step-by-step what happens on the formation of a p-n junction and how... | {
"language": "en",
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How can even there be a non-zero BMS vector field with zero asymptotic data? Following the BMS approach, one spacetime $(M,g)$ is asymptotically flat when:
*
*We can find a Bondi gauge set of coordinates $(u,r,x^A)$ characterized by $$g_{rr}=g_{rA}=0,\quad \partial_r\det\left(\dfrac{g_{AB}}{r^2}\right)=0\tag{1}.$$
... | Here is the problem:
It is possible to show that such a vector field is identified by a pair $(f,Y)$ where …
vector field $X$ is not uniquely identified by this pair $(f,Y)$, only its action on the boundary data, while the vector field itself is defined not only near the boundary but everywhere “inside” the manifold.... | {
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Can a very small piece of material be superconducting? The existing theory of superconducting seems to be based on statistical mechanics.
Can an ultrasmall piece of material, like a quantum dot with very few atoms (like a small molecule), be superconducting?
For example, can a cubic of 3 * 3 * 3 = 27 copper atoms be su... | My experience in this field is mostly applied. Here is what i have seen in papers. Superconductors behave as 'macroscopic' only as long as their size is above the coherence length $\xi_0$. For example, in titanium this is nearly 0.5um, in niobium it is 20nm, in YBCO it is at the atomic scale (but anisotropic).
Coheren... | {
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Why is the Force of Gravitational Attraction between two “Extended” bodies proportional to the product of their masses? Newton’s Law of gravitation states that force of attraction between two point masses is proportional to the product of the masses and inversely proportional to the square of the distance between them.... | It is not true in general that the gravitational force of attraction between extended bodies is proportional to their masses. It happens that we usually deal with gravitational attraction between celestial bodies, and that celestial bodies above a certain size are almost invariably close to spherical (in consequence of... | {
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Actual meaning of refraction of light The definition of refraction which I found on wikipedia is
In physics, refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium.
But in the below case, there is no change in direction of light. So, is this also ref... | Refraction describes the change of direction of a light beam in geometrical optics. Since your the light beam does not change it's propagation direction, there is no refraction.
I guess you are somehow mixing the phenomena and its explanation: The change of angle is a phenomena. Its explanation is that the speed of lig... | {
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Can we use quantities other than temperature to describe thermal equilibrium? From the 0th law, Thermal equilibrium is when there is no heat transfer between two objects. So I want to ask is temperature the only "potential"-esque quantity which should be equalized for stop of heat flow? If temperature is the only one t... | In general, thermal equilibrium means maximizing the entropy. The reason we use temperature is that very often, two systems can do this by exchanging energy. Under an exchange of energy $dE$,
$$dS_{\text{tot}} = \frac{dS_1}{dE_1} \, dE + \frac{dS_2}{dE_2} \, (-dE) $$
so the maximum entropy is achieved when this is zer... | {
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Does bending your arm in space require any energy? Since your are weightless in space, your arm has no weight, right? Does this mean that bending it in space requires no energy? Why or why not?
| Well, yes.
Movement of your body parts (hands, legs eyelids, etc.) occurs due to the contraction of muscle fibers. This process requires energy (from cleavage of ATP molecule to form ADP). This is the only way an astronaut can move his arm.
Transforming the internal energy (chemical) into mechanical energy requires the... | {
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Doppler effect of light when it's windy I think I understand the classical doppler effect in sound, where the equation is non-symmetric whether the source of the observer is moving because the speed of medium where sound wave propagates is different according to each of the observers.
I think I also understand why dopp... | I completely agree with Dale, but since the OP talked about both air and water, I decided to generalize the above answer further. The speed of light in any medium is given by $$v = \frac{c}{n}$$ where c is the speed of light in vacuum (the OP denoted this by $c_0$), and $n$ is the absolute refractive index of the mediu... | {
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Should the thermos flask better be half full or half empty? Every evening I am preparing hot water for my two year old son wakes up in the night to get his milk. We use a rather bad isolation can for this. It is a typical metal cylinder shaped can holding half a liter. If I put cooking hot water into it, I know that ab... | It's a metal can so the heat from the water will spread across the whole surface and be lost at approximately the same rate however much water you use.
Now, since a larger volume of water will hold more heat to start with, a full can will keep its temperature better, as the temperature loss will be shared across a grea... | {
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Does the resistance in the secondary circuit of a potentiometer circuit affect the balance length? I just learnt how potentiometer circuits work, and I was taught that the resistance in the secondary circuit does not change the balance length as no current flows through the secondary circuit and thus the only potential... | The bulbs X Y and Z are not part of a normal potentiometer. Normally the battery E is balanced against AC and CB, but now AC is replaced by the combination of AC, X, Y, and Z. The internal resistance of the battery and meter don't matter, but these extra ones certainly do because they are in parallel with the battery i... | {
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Why does light behave like a wave? When discussing a single or double slit experiment, where light is shined through a very small slit, it is often compared to a water wave going through a similar, if larger, slit. It's my understanding that when a ripple hits a wall with a hole in it the reason the ripple "bends" and ... | For the water waves the restoring force is gravity, and there is a circular symmetry for any bump.
For sound, it is a pressure wave, and there is a spherical symmetry for a region with higher or lower pressure and the surroundings.
In both cases, it would be strange if they follow a straight line after the slit, withou... | {
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Is it possible that a series of Feynman diagrams converge? A bit of maybe unnecessary context
I'm reading "Lecture notes on Diagrammatic Monte Carlo for the Frohlich polaron". It says
It is usually unknown whether a series converges or not. The series is guaranteed to diverge at a phase transition, but it may happen ... | The discussion in question deals with resummation of the diagrammatic series for a partition function. If the Hamiltonian and the phase space are properly defined, the partition function is finite. The non-convergence problem here is expanding a function at the point of its non-analiticity (e.g., one cannot expand $\lo... | {
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Amount of electrons in a material? Is there a way to calculate the amount of electrons in a plate of a certain material and certain dimensions?
What I want to know is how many electrons are available to remove from a plate when light of appropriate wavelength hits the plate(photoelectric effect).
| Yes. In the free electron model (of a metal), it is possible to define an electron density in the conduction band. See the table in this link for example.
But to a first approximation you can consider the density of atoms in the material (mass density upon molar volume times Avogadro number) times the valency of the m... | {
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Optimize crossbow I'm currently building a crossbow
and was wondering how I might improve the performance of it? I was suggested to fine-tune the rubber band more and maybe change the projectile maybe to a zinc alloy one instead of the plastic ones I use. I do understand this is sort of engineering feat but I think i... | "Performance" is a pretty broad term. For example, it can relate to how fast the bolt (the arrow) is launched, or the repeatability of the bolt's trajectory.
Plastic bolts are not a very good idea: most plastic can deform permanently, which will lead to a wildly variable trajectory. You might do well to buy some fibe... | {
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A uniformly polarized sphere Say there is a polarized sphere with polarization density $\vec{P} = \alpha \hat{r}$. How can I tell if the electric field outside of the sphere will also be radial? I see in many places that it is taken as obvious, but why is it?
*Edit: rephrase
| It's because the whole system (including the polarization density) has spherical symmetry.
Think of it this way, if I rotate the sphere by an arbitrary angle around an axis passing its origin, the sphere, and the associated polarization density $\mathbf{P}(\mathbf{x}) = \alpha \hat{\mathbf{r}}$ are both going to coinc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/551770",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why doesn't Kirchhoff's Law work when a battery is shorted with an ideal wire? Kirchhoff's law states that the sum of voltages around any closed loop sum to zero. The law is true as the electric field is conservative in circuits. Why can we not apply the law here?
Why doesn't the law hold here despite the fact that the... | There are a number of points here.
First if you are saying that there is no resistance in the circuit and nothing else is present then the situation is unphysical and as such you cannot apply Kirchhoff's laws.
However, as drawn the circuit is a loop and therefore has a self inductance $L$.
Once inductance is cons... | {
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What does CERN do with its electrons? So to get a proton beam for the LHC, CERN prob has to make a plasma and siphon off the moving protons with a magnet. Are the electrons stored somewhere? How? I don’t mean to sound stupid but when they turn off the LHC, all those protons are going to be looking for their electrons. ... | The usual thing for a shutdown is to 1) stop injecting fresh particles into the beam tube, and 2) deflect any remaining particles in the main tube and any storage rings into a beam dump which is a very large chunk of metal, a very very large chunk of concrete, or a very very very large pile of earth. Take care not to b... | {
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Angular momentum of the earth We know the tidal waves are decreasing the spin rate of the earth which causes the days to longer, so as the angular momentum of the earth decreases it means it rotational kinetic energy also decreases since energy is always conserved the translational kinetic energy of earth must increase... |
Then that would cause number of days in a year to decrease as we right?
Maybe you should read this article as a lot more goes into the kinematics of the earth around the sun,
Earth rotates faster than the moon orbits it, so the watery tidal bulge travels ahead of the moon's relative position. This displaced mass gr... | {
"language": "en",
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What happens to an inductor if the stored energy does not find a path to discharge? Suppose an inductor is connected to a source and then the source is disconnected. The inductor will have energy stored in the form of magnetic field. But there is no way/path to ground to discharge this energy? What will happen to the s... | If the coil is in a perfect vacuum, then the unduced voltage may become so high that "cold" electron emissions of the coil metallic ends will create an arc for discharge.
| {
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Origins of this interesting optical phenomenon?
Sunlight reflecting off my glasses seem to disperse into these distinct red and blue bands. The glasses are acting as some sort of a prism to split the light. The glasses do have some reflective coating (if that helps).
Any thoughts on what might be causing these?
| An anti-reflective coating would explain it. The coating is a thin film interference filter that is designed to reduce reflections and its performance changes with wavelength and angle of incident of the light. So instead of the glasses strongly reflecting white light, the reflection is reduced. But it is not evenly re... | {
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Why does Flow always occur from Higher Potential to Lower Potential? This is a sort of a generalized question and not just referring to the flow of current. This includes fluids and many other such entities.
But why does this flow occur. For example if I consider current, then the definition of potential at any point i... | To answer in terms of electric circuits, we know that electric field $\bf E$ is related to the electrical potential $V$ by
$${\bf E}=-{\bf \nabla} V$$
That means that a positively charged particle in a region with varying potential will experience a force pointing towards regions of lower potential (and a negatively ch... | {
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Is it necessary that a capacitor stores energy but not charge? Is it necessary that a capacitor stores charge? The definition of capacitor given in books is that it store electric energy. So is it possible that the capacitor does not store charge but stores energy only?
| If you'll take some time to search this site for capacitor related questions, you'll probably find that I and others have often pointed out that capacitors store energy and not electric charge.
A charged capacitor has stored energy due to the work required to separate charge, i.e., the plates of the capacitor are indiv... | {
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Why is surface tension measured in units of milliNewtons per meter? Rather than square meter(s)? Why is liquid surface tension written in units of mN/m, or milliNewtons per meter?
The related concept of surface energy for solids uses units of milliJoules per square meter.
| Notice, the surface tension of a liquid is the force acting per unit length of an imaginary line drawn on the free surface of the liquid (its unit is $N/m$). Furthermore, the surface tension force is small enough hence written in small unit $mN/m$. Example surface tension of water is $72mN/m$
The unit of surface energy... | {
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Determining the state of a system after a measurement I'm confused about the state of a system after a measurement. Say we have a particle $v$ in the state: $ |\psi\rangle= \sqrt{1/4} \ |0\rangle + \sqrt{3/4} \ |1\rangle $.
From my understanding, if one were to measure the state of $v$, one would get the result $|0\ran... | Yes, you have written the state $| \psi \rangle $ in the eigen basis of $Z$ $(|0 \rangle, |1 \rangle) $, that is why $Z$ is diagonal. Since $Z$ and $X$ do not commute with each other they cannot be simultaneously diagonalised in one basis. If the operators commute then they can be simultaneously diagonalised and will h... | {
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How does a water jet hitting a wall move parallel to the wall if momentum is conserved? Classical mechanics says that if I throw a ball with velocity perpendicular to the wall and it collides elastically with the wall with a velocity $v_0$, then it bounces back with the same velocity $v_0$.
However, if I shoot a beam ... | Momentum conservation does not work like that. You can conserve momentum only when there is no external force acting in the direction. Actually, you don't have to take an example as complex as this to understand thhat momentum need not be conserved always.
Imagine that you have a ball in your hand. You leave it at rest... | {
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In the equation: $a = dv/dt$ , is $dt$ the time taken to achieve that instantaneous acceleration? If you solve for $dt$ from $a = \frac{dv}{dt}$ , is it the time taken to to achieved that instantaneous acceleration?
$a$ : acceleration
$v$ : velocity
$t$ : time
| No, it is not.
Suppose, a body is moving at a uniform velocity $v$, now there is no restriction on how much time it wants to remain with that same velocity. And after sometime it can accelerate if there is a net force on it. Now, acceleration means a rate of change in velocity and obviously it will take some time to in... | {
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C, P and T transformations of $\phi$ that preserves symmetry I have a series of exercises regarding C, P and T symmetry but I am not really sure how to start with the problems. If anyone could help me with one of the problems, or show me a few example problems with full solutions, I would be very grateful. Then I can h... | You must inspect how the last piece of the Lagrangian transforms, the rest of them are invariant. For example, let's do P.
Dirac fields transform as:
$$\psi \xrightarrow{\mathcal{P}} \gamma^0 \psi,$$
$$\overline{\psi} \xrightarrow{\mathcal{P}} \overline{\psi}\gamma^0.$$
So the quatity $\overline{\psi}\gamma_5\psi$ tr... | {
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Problem in Translational invariance In Shankar's QM (second edition, p-282), There are some equations are given, They are following as,
$$T(\epsilon)|x\rangle = |x + \epsilon \rangle$$
where $T(\epsilon)$ is Translation operator.
I understood equation given above, but Shankar says, "X is basis is not unique" then gener... | Note that $|x+\epsilon\rangle$ and $e^{i\epsilon g(x)/\hbar}|x+\epsilon\rangle$ represent the same state (both kets belong to the same ray).
Here what is g(x) ?
From Shankar (2nd edition), exercise 7.4.8
This exercise teaches us that the "X basis" is not unique, given a
basis $|x\rangle$, we can get another $|\ti... | {
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How is it physically possible that the electric field of some charge distributions does not attenuate with the distance? Let's consider for instance an infinite plane sheet of charge: you know that its E-field is vertical and its Absolute value is $\sigma / 2 \epsilon _0$, which is not dependent on the observer positio... |
An observer may put himself at an infinite distance from all charges
and he will receive the same E-field.
I'm compelled to address this misconception just in case it is at the root of your question.
When we solve this problem for the electrostatic field, the result is independent of the distance $r$ from the plane... | {
"language": "en",
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Is my friend right about omitting $c^2$ in world famous tiny equation? I know $E = mc^2$ says that inertial mass of a system is equal to the total energy content of a system in its rest frame. My friend told me the $c^2$ can be omitted from this equation because that's just an `artifact' when measuring inertia and ener... | In the Natural Units, the speed of light in vacuum i.e. $c$ is taken to be the fundamental speed of the universe. Under this system, all the fundamental physical constants are defined in such a way that their value is just 1 (e.g. $\hbar=k_B=1$).
However, in the end one has to include the numerical values when switchi... | {
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Two solutions for a 4-velocity component given 3 other components? The Setup
Suppose I know, in some particular coordinate system, three components of the four-velocity vector $u^{\alpha}$ with $\alpha = \{0, 1, 2, 3\}$. For this question I'm going to assume the known components are the spatial components $u^{i}$ with ... | *
*That's correct.
*That's incorrect. In your example above you also get different signs for the two solutions, which is obvious from the $-2g_{i0} u^i \pm \sqrt{(2g_{i0} u^i)^2-{...}}$ so you have to chose the positive solution.
*Only if you chose unphysical values for the other components, for example if the local... | {
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What is really meant by the area of black hole? The area of a black hole is an important parameter in the thermodynamic description of a black hole. In particular, reading popular literature, everyone knows that the entropy of a black hole is proportional to its area as discovered by Stephen Hawking. Can someone explai... | The area of the event horizon is simply $4\pi r_s{}^2$ where $r_s$ is the Schwarzschild radius. However this is because that's how the radial coordinate $r$ is defined.
$r$ is not the distance to the centre of the black hole (in fact the radial distance to the singularity is undefined). For any point $r$ is defined as ... | {
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Does the number of accessible microstates decrease overall when heat is transferred? We have two systems of ideal gas with different temperatures. $N$ & $V$ are being kept constant. The number of accessible microstates of each gas is thereby only influenced by a change in $E$.
The number of accessible microstates is:
... | The formula is valid for units of energy
The multiplicity $Ω$ for q units of energy among N equally probable states is given by the expression
This is sometimes called the number of microstates for the system.
Organic life exists because it exchanges energy and diminishes entropy by using the environment it fin... | {
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Does tangential acceleration change with radius? Do tangential velocity and tangential acceleration change with radius (change of radius on the same object)?
For example consider a spinning disk. Does the equation $$a_t = \alpha R$$ (where $a_t$ is the tangential acceleration, $\alpha$ is the angular acceleration and ... | Firstly defining circular motion
Circular motion is when a body moves in circle or as they say have a fixed distance from a point (moving or stationary)
Now when we consider rotating rigid bodies.We usually take torques ,angular momentum, moment of interia about the point which is stationary with respect to ground. As... | {
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Why X-ray and radio waves can penetrate walls but light can not? Why can visible light, which lies in the middle between X-ray and radio waves in terms of frequency/energy, not penetrate walls?
| X rays penetrate matter because their energy is much higher that of any matter excitations. The electrons in matter are to slow and too heavy to react and compensate the field, as they do for optical frequencies. Fort radio wave the opposite applies. They reflect off matter, especially off metals, unless you apply very... | {
"language": "en",
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Velocity of undamped pendulum On this page, under the heading "Orbit Calculations": http://underactuated.mit.edu/pend.html or here.
The author says,
"This equation has a real solution when $\cos{\theta} > \cos{\theta_{\rm max}}$"
and then they give a piecewise function for $\theta_{\rm max}$.
I have no idea how th... | If the pendulum has enough energy to go all the way around, then any value for $\theta$ is possible between 0 (hanging down) and $\pi$ (standing straight up). For simplicity, take $\theta$ to be the absolute value of the angle between the pendulum and $-\hat{y}$ since the situation is invariant under $\theta\to -\theta... | {
"language": "en",
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Does the angular velocity of a spinning disk increase if it has a completely inelastic collision with a object with a greater tangential velocity?
A roller of radius 10cm is spinning with a angular velocity of 15 rad/s. It has a completely inelastic collision with a hunk of clay, with mass m moving at 3m/s at it's ver... | By using conservation of momentum the angular velocity increases because the clay apply a torque about centre which moves the spinning disk fastly
| {
"language": "en",
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Space Time Diagram - world line of a wave My understanding so far:
*
*A wave is a vector field defined on the space-time. i.e. mathematically wave is just a mapping which for every point in the space-time maps it to a vector.
*A world-line is function which maps an event (or a particle) on the space-time. In case t... | Normally an EM plane wave is taken as sinusoidal vector field in space time. But it is not required to have this form to solve the wave equation.
An electric field $E_y = e^{-u^2}$ where $u = k(x+/-ct+a)$ also solves the wave equation:
$$\frac {\partial^2 E_y }{\partial t^2} = c^2k^2(4u^2 - 2)e^{-u^2}$$
$$\frac {\parti... | {
"language": "en",
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What's the debate about Newton's bucket argument? I visited some other QA threads about this topic, and I don't understand why people think it's mysterious that the bucket knows about its rotation.
If a non-rotating bucket is all there is in the universe, then, initially, all the parts of the bucket are at rest wrt to ... | Suppose that instead of talking about the bucket's angular velocity, you talked about its linear velocity. Then it would have indeed been the case that you can't speak of an absolute linear velocity in an empty universe. The paradox is why the same logic doesn't apply to angular velocity, since they're both "velocities... | {
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What does the Problem 14 from Goldstein's book on classical mechanics chapter-7 (special relativity) really mean? I am having difficulty in understanding problem number 14 in Goldstein's Classical Mechanics, 3rd edition, chapter 7 on special relativity. Here is the problem ---
A rocket of length $l_0$ in its rest syst... | The difference between measurement and observation is crucial in relativity.
When we observe the rocket, the finite speed of light affects our observation. In general, light from the head and the tail of the rocket will take a different amount of time to travel to the observer.
When we measure the rocket, we compensat... | {
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Does the potential of a charged ring diverge on the ring? I know that the density and potential (in spherycals) of a charged ring is, respectively,:
$$
\rho(\textbf{r})
=
\frac{\lambda}{a}
\delta(r-a)\delta(\theta-\tfrac{\pi}{2})
$$
$$
\varphi(\textbf{r})=
\frac{2\pi a \lambda}{r_>}
\left[
1+ \sum_{n=1}^\infty (-1)... | This is actually a fun question, I learnt something new about double factorials while trying to answer it!
I don't see why that term diverges. Using the identities on Wikipedia for the "double factorial", we have that for even integers $k$,
$$\int_0^{\pi/2} \sin^{k}(x)\text{d}x = \frac{(k-1)!!}{(k)!!}\frac{\pi}{2}.$$
... | {
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Question about Faddeev-Popov gauge-fixing in Schwartz textbook I am trying to understand equation (25.91) from Schwartz's Quantum Field Theory textbook. The goal is to gauge-fix the path integral for Quantum chromodynamics using the Faddeev-Popov trick. Briefly, the argument boils down to multiplying the integral by:
$... | OP has a point. Ref. 1 transforms the integration variables$^1$
$$ A^b_{\nu}\quad\longrightarrow\quad A^{\prime a}_{\mu}~=~A^a_{\mu} - \partial_{\mu}\pi^a - gf^{abc} A^b_{\mu}\pi^c~=~A^a_{\mu} - D_{\mu}^{ab}(A)\pi^b$$
upstairs in the exponential function of eq. (25.91) but forgets to also transform the factor $\frac{1}... | {
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Question about fluid flow through a funnel or cone I am an MD, I am studying the fluid flow of the tears through the tears duct system of the eye. The newer view suggests that the first part of the system is a funnel or a cone. I cant seem to understand (without equations), what are the main advantages of fluid flow th... | The primary characteristic of flow through a funnel is that the ratio of the velocities of flow in one end and out the other is scaled by the ratio of the cross-sectional areas of the two ends. Slow flow in the big end is transformed into fast flow at the small end. A funnel is also called a bernoulli transformer for t... | {
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Hydrogen atom and scale transformation for radial variable While solving Schrödinger equation for Hydrogen atom we make a scale transformation for radial variable ($r=\frac{ax}{Z}$; where $a=$ Bohr radius, $x=$ dimensionless variable and $Z=$ atomic number), this turns out to be a very good scale transformation. But my... |
this turns out to be a very good scale transformation.
We don't really care that it's a good or bad choice. We start by choosing a scale factor with just a symbol to move to dimensionless coordinates and follow the math through using it. The physical problem is solved no matter what we choose (as long as it's not s... | {
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What is the torque produced by 2 rotating bodies with a clutch I am trying to simulate a car engine etc, but I have failed to find any equations governing the torque created by $2$ different constant velocity shafts of different angular momenta joining together with some given slip or friction factor. I know $I_1w1 + I... |
I can see the Torque transferred to the engine from the wheels could be limited by torque clutch, but I dont know the Torque and I dont know the clutch join time!
Correct. You need to make assumptions. If you have an inexperienced driver that releases the clutch instantly, the maximum torque that can be applied may... | {
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"Boiling is to evaporation as melting is to... ?" Or, why aren't 31 degree ice cubes wet? Well before a liquid reaches boiling point, it gradually looses molecules with exceptionally high kinetic energies to its surroundings, which is called evaporation. Does this phenomenon occur to some solids as well, where before ... | They do, although its very thin.
The three phases of matter are merely approximations which let us treat a whole bunch of molecules as if they were a bulk object.
However, when a liquid molecule gains enough energy to act gas-like, it tends to get away from the liquid body. When a molecule of a solid gets enough energ... | {
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Why do we describe probability amplitude rather than probability itself in quantum mechanics? In the quantum mechanics, the dynamics of quantum system are described in terms of probability amplitude. However, we want to calculate the probability in the end which can be measured. Why don't we develop quantum mechanics d... | You are right. In proper treatments of the mathematical foundations of quantum mechanics, following von Neumann, the probability amplitude is simply defined from the probability using the Born rule and satisfying Hilbert space. This does indeed make quantum mechanics much easier to understand, and being rigorous, it ac... | {
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Does it make sense to say that something is almost infinite? If yes, then why? I remember hearing someone say "almost infinite" in this YouTube video. At 1:23, he says that "almost infinite" pieces of vertical lines are placed along $X$ length.
As someone who hasn't studied very much math, "almost infinite" sounds like... | "Almost infinite" is a sloppy term that might be used to mean "effectively infinite", in a given context. For example, if a large value of $x$ in $y = 1/x$ produces a value smaller than the accuracy of measurement of $y$, then it's often reasonable to set the value of $y$ to zero, which is equivalent to setting the va... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/558491",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
"answer_count": 11,
"answer_id": 3
} |
Capacitance of a single straight wire What is the capacitance of a single straight wire?
calculating the electric field using Gauss's law, I get a constant divided by the distance from the wire (r). Integrating 1/r gives me ln(r). evaluating r at the radius of the wire and infinity gives me infinity. On the one hand, I... | Using Gauss's law, you should have found that the field strength (radial) at distance $r$ from the central axis of a long straight wire of length $\ell$ and radius $r_1$ carrying charge $Q$ is of magnitude
$$E= \frac{Q}{4 \pi \epsilon_0 \ell r}$$
So the pd between the surface of the wire (of radius $r_1$) and a surroun... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/558905",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
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How does one determine the $R$-symmetry group? As far as I understand it, the $R$-symmetry group is just the largest subgroup of the automorphism group of the supersymmetry (SUSY) algebra which commutes with the Lorentz group. I know for $\mathcal{N}=1$ SUSY, the $R$-symmetry is $U(1)$, mainly due to there being only o... | Properties of R-symmetry group depends on spinor structure:
Here M means Maiorana spinors, MW - Maiorana-Weyl, S- symplectic.
Spinor structure depends on dimension and signature of space. For more details one can consult Tools for supersymmetry.
Put supersymmetric theory on curved space is not simple task. To do such ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/559047",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
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