Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How fast does an electron move? I've been reading this website: www.physics.wayne.edu/~apetrov/PHY2140/Lecture8.pdf to learn how fast an electron moves in a circuit.
On page #8, #9 and #10 It says to take the Cross-sectional Area of the wire, The current, The density, The Charge and the electrons^3
Area- ... | The calculation on page 9 of the PDF is incorrect because of the author's confusion mixing meters and centimeters combined with a numerical error. (Sad!) The correct calculation of the drift velocity for the input values given is
$$v_d=\frac{I}{nqA}=\frac{10.0\,\text{C/s}}{(8.48\times 10^{28}/\text{m}^3)(1.6\times 10^{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/497916",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
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Difference between left- and right-handed, helicity and chirality What is the difference? I know there is the (almost) same question What's the difference between helicity and chirality? but when a particle is given as left-handed. Is it helicity or chirality?
| When we consider spinors of the Lorentz group $SO(3,1)$, recall that the universal covering of $SO(3,1)^+$ (the component of the Lorentz group connected to the identity) is isomorphic to $SL(2,\mathbb C)$.
Two-component spinors are elements of two-dimensional irreducible modules of $SL(2,\mathbb C)$. However, noting th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/498042",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
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Heat reduction based on compression So I was thinking about air conditioner today and how we run air across compressed freon to cool down air but why do we need freon at all why not store just compressed air. My guess is because its inefficient.
My question given a 1 cubic meter tank of air, if the room temperature at... |
Compression brings the molecules closer together thus cooling it down.
This isn't correct. The temperature of a gas isn't related to how close together the molecules are, but their speed.
By compressing the gas, they are closer together, but the work done in compression has sped them up as well. If you wait a while... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/498395",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
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How does phase transition occur in finite sized ising model? I was simulating the square lattice Ising model via Metropolis Algorithm and found that at 0 magnetic field, there is spontaneous magnetisation below some temperature.
I have used Periodic Boundary Condition in a 100x100 lattice.
Is this an instance of a Pha... | In a strict mathematical sense, you will not observe a phase transition in a finite volume, for the reason you mention. If you measure thermodynamic quantities and their derivatives, when you expect a completely sharp transition, you will instead see a smooth curve that approximates the "correct" behavior if the volume... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/498663",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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$SU(2)$ and $SO(3)$ WZW models It seems that the $SU(2)_1$ and $SO(3)_1$ Wess-Zumino-Witten models are quite different despite the Lie algebras being identical. The $SO(3)_1$ model has central charge 3/2 and is equivalent to 3 free Majorana fermions. The $SU(2)_1$ model has central charge 1, and can be expressed in ... | The $G$-WZW model depends not only on the group $G$, but also on a number $k$ called the level. The symmetry algebra is an affine Lie algebra, and it also depends on $k$. Both $SU(2)$ and $SO(3)$ have the same affine Lie algebra, and the central charge is
$$ c = \frac{3k}{k+2}
$$
where $k\in \mathbb{N}$ for $SU(2)$ an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/498756",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Solution to Maxwell-Lorentz equations I am trying, without success, to find an example (preferably simple) of solution for the Maxwell-Lorentz equations, i.e., the coupled system of Maxwell equations + dynamics of a charged particle given by Lorentz force. Say we have a (for simplicity, non-relativistic) particle of ma... | The Maxwell-Lorentz equations for point-like charged particles are meaningless. This is well-known since the beginnig of the 20th century. Older textbooks (like that of Becker) written between the two world wars discuss it in all details. The devil lies in the self-interaction. A hand-made correction, excluding from t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/498892",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Units in general relativity My question is pretty straight-forward: what are the units of the tensors in General Relativity? This should sound easy, but I always studied those in natural units ($c=1$) so I can't figure it out. In particular, what are the units of
*
*$G_{\mu\nu}$
*$g_{\mu\nu}$
*$R^\rho_{\mu\sigma\n... | If you choose coordinates with the units of length, such as $(ct, x, y, z)$, then the metric tensor and its inverse are dimensionless, the Christoffel symbols have the dimensions of inverse length, and the curvature tensors are inverse length squared. In these coordinates the energy-momentum tensor has the dimensions o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/499013",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Bose-Einstein condensation: Bogoliubov Approximation I'm trying to understand the Bogoliubov approximation from "Statistical Mechanics" by Pathria and Beale. First of all they say
Since $a_0^{\dagger}a_0=n_0=O(N)$ and $(a_0a_0^{\dagger}-a_0^{\dagger}a_0)=1<<N$, it follows that $a_0a_0^{\dagger}=(n_0+1)\simeq a_0^{\dag... | The first statement reformulated gives you $[a_0, a^\dagger_0] \simeq 0$ (there is an assumption that operators involving $a^\dagger_0a_0$ are replaced by their expectation values). Then, the approximation is that since the operators commute, they can be replaced by classical objects.
So $a_0$ is a number equal to $n^{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/499144",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Conservation of linear momentum with mass defect Suppose we have an insulating container, like a perfect black body, which absorbs all the radiation coming from a radioactive element placed in the center (or some equivalent process like matter annihilation). Assuming a spherically symmetric emission. It will transform ... | With a simple calculation, it can be shown that there is no acceleration.
Let's assume $dm/dt$ is constant we call $\delta$. We then have
\begin{equation}
\frac{dv}{dt}=-\delta v
\end{equation}
Then:
\begin{equation}
\frac{dv}{v} = -\delta dt
\end{equation}
By integrating:
\begin{equation}
\ln (v) = -\delta t + A
\end{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/499386",
"timestamp": "2023-03-29T00:00:00",
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Why are the left- and right-hand sides of a differential equation with two separated variables equal to a constant? While deriving the Time Independent Schrodinger Equation, my book mentioned this line.
So time and position of a particle are two independent variables. If they are equal to one another for all values of... |
Can't we have other solutions to this other than treating both the
sides as a constant?
No. The TDSE (and many other similar PDEs, like the TISE, the Newtonian wave equation and Fourier's equation) has a numeric separation constant. They are known as eigenvalue problems.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/500067",
"timestamp": "2023-03-29T00:00:00",
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Differences between charge quantity and electric charge As a senior middle school from China mainland, I am teaching physics about electric field. I work with my workmates, and we got a problem now. We cannot get an agreement. There are three viewpoints.
The first is that: electric charge is physical attribute and a ph... | Charge is a fundamental and inherent physical property of matter and we know that for sure because we can measure it. It is defined:
*
*by a magnitude, which helps us understand how strongly matter experiences or produces electric, magnetic or electromagnetic fields
*by a unit of measurement, which is a definite ma... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/500189",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Rotational invariance of the conductivity tensor (Classical Hall Effect) In classical Hall effect, the conductivity tensor is given as
$\sigma = \frac{\sigma_{DC}}{1+\omega_B^2 \tau^2} \begin{pmatrix}
1 & -\omega_B \tau \\ \omega_B \tau & 1
\end{pmatrix}$
where the author suggests that since it is rotationally invarian... | A generic $n\times n$ matrix $\sigma$ can be decomposed as
$$\sigma = \sigma_0 + \sigma_H + \sigma_S$$
where $\sigma_0$ is proportional to the identity matrix, $\sigma_H$ is antisymmetric, and $\sigma_S$ is symmetric and trace-free. Explicitly for $2\times 2$ matrices,
$$\pmatrix{a&b\\c&d}=\frac{a+b}{2} \pmatrix{1&0\\... | {
"language": "en",
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Centre of mass of solid hemisphere I am trying to find the centre of mass of a solid hemisphere using theta as a variable. But I am getting the wrong answer. Can you please tell me where I am wrong. My working is shown in the image attached....
| The thickness of the thin disc cannot be $ R \ d \theta $. Otherwise a disc at $ \theta = 0 $ would be counted as having the same thickness as a disc (sweeping the same angle $ d\theta $) at angle $ \theta = \pi / 2 $, when clearly the disc is thicker at $ \theta = 0 $. So your expression for $ dm $ is missing a factor... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/500677",
"timestamp": "2023-03-29T00:00:00",
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As $SL(2,\mathbb{C})$ is a double cover of the Lorentz group, is $SL(2,\mathbb{Z})$ a discrete subgroup of the Lorentz group? The group $SL(2,\mathbb{C})$, the group of $2 \times 2$ complex matrices with determinent $1$, is a double cover of the Lorentz group. (These transformations can be understood as Mobius transfor... | As emphasized in the other answers, $SL(2,\mathbb{Z})$ is a discrete subgroup of the double cover of the Lorentz group (actually of its connected component), so $SL(2,\mathbb{Z})/\{\pm 1\}$ is a discrete subgroup of the Lorentz group itself. The purpose of this new answer is to say something about the geometric signifi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/500808",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Should the 4D normalization constant $8\pi$ in Einstein field equations (EFE) be changed to $(n-2)S_{n-2}$ in other spacetime dimensions? Should the 4D normalization constant $8\pi$ in Einstein field equations (EFE) be changed to $(n-2)S_{n-2}$, where $S_{n-2}$ denotes the area of a $n-2$-sphere, in higher dimensions? ... | It is, indeed, just a matter of convention since Einstein equations in higher dimension are just mathematical, they have no currently known physical application. This means you could even drop any reference to units in them. The typical choice is to place $\kappa$ in front of the stress-energy tensor as a catch-all co... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/502275",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Does light have mass? Why? I've been wondering whether light has mass. Yet given the wave-particle duality of light, the statement seems to be affirmative. With that, how to calculate it?
| I would avoid mass concept of photon at all, because it doesn't have rest mass. Relativistic mass is very slippery thing and is not unambiguously defined. Someone just put Lorentz factor $$ {\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}} $$ besides rest mass (multiply by $m_0$) and has called it "relativistic mass". Now ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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When is total pressure not conserved in a system? I came across a problem that involved two compartments that are separated by a movable, adiabatic wall. As the wall moves, the pressure is not conserved- rather total pressure decreases- assuming this is an ideal gas. How is this possible? Doesn't the second law of ther... | When you talk about conserving pressure it sounds like you think pressures are additive. You might be thinking in terms of adding the pressures before and after the wall moves. The initial pressures were 1 and 4 and you added them to make 5. After the wall moves you add 1.75 and 1.75 and get 3.5 and wonder why they don... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/502501",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do things cool down? What I've heard from books and other materials is that heat is nothing but the sum of the movement of molecules. So, as you all know, one common myth breaker was "Unlike in movies, you don't get frozen right away when you get thrown into space".
But the thing that bugs me is that things in the ... | This can be understood easily: If your temperature is higher than the surrounding temperature heat will flow out to the surrounding. It is analogous to electric current which moves from a higher potential to a lower potential. Similarly heat current flows from high heat potential(high temperature) to a lower heat poten... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/503023",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
"answer_count": 5,
"answer_id": 4
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Is the Earth a gyro? Due to rotation and low friction, can the Earth be considered a gyroscope? If so, any interesting implications to this? Thanks
| The gyroscopic motion of the Earth is the reason we have seasons. For half the year the northern hemisphere is closer to the sun than the southern hemisphere, and for the other half of the year the opposite is true. This is because the axial direction of the Earth stays fixed as it rotates around the sun, a direct resu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/503159",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How exactly is white light a combination of several wavelengths? I have read that light is an electromagnetic wave. Every ray of light has a specific wavelength. The colour perceived by any observer is dependent upon the wavelength of the incident light.
What I don't understand is that how do electromagnetic waves of d... | David White's comment is correct, and I think the existing answers are confusing the point. The poster asks:
How are those wavelengths combined into a single unit which we call
white light?
They aren't. There is no "unit" called white light. Our eyes have receptors for light of three wavelength ranges (graph here),... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/503429",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Will a can filled with vacuum move when we let in air?
This picture is from L.C.Epstein's book Thinking Physics. The upper can is filled with compressed air, and, when an opening is made on the right, the air comes out and the can shoots left. The question is what happens to the lower can, filled with vacuum, when we ... | If the pressure difference between inside and outside is the same (but opposite) then the force on the can in both situations is equal and opposite. If the geometry is the same then the pressure difference evolves in the same way but with opposite sign. The motion of the can, opposite, is only different due to differen... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/503517",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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In de Sitter space, does the cosmic horizon change its shape for fast-moving observer? If an observer moves at a speed close to the speed of light, will the horizon deviate from spherical shape?
If no, will it be the same horizon as for stationary observer (at the same position)?
| No, unless the observer is accelerating. A linearly accelerating observer will perceive a non-spherical Rindler horizon at minimum distance $c^2/a$, where $a$ is proper acceleration. This Rindler horizon will be closer than the cosmic horizon as long as the observer's proper acceleration is greater than $c^2/R_u$, whe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/503639",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Deriving the Heat capacity from Fermi-Dirac statistics I was watching the lectures on Solid state physics by Steve Simon (Oxford). He was explaining how to find Heat capacity of metal due to electrons from Fermi-Dirac statistics. You can write the total number of electrons as $$N =g(E_f) \int_0^\infty \frac{E^\frac{1}{... | There is the handwaving argument that the width of the edge is about $kT$ and that increasing the temperature will cause electrons to occupy states that are something like $kT$ higher in energy.
So the electron energy increases with $T^2$. The electronic heat capacity $c_v$ is the derivative, the cause of the linear te... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/503820",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Measuring acceleration due to gravity in the lab I am measuring the acceleration due to gravity in the lab with an electromagnet apparatus.
My textbook says to take the average time for a number of falls (keeping the height constant of course).
But I recall many moons ago being told to take the shortest value, not the ... | Generally there are two types of errors in an experiment, random errors and systematic errors. In this case there is a random error due to your limited ability to record the time of fall precisely. There may or may not be a systematic error due to the fact the electromagnet does not release the ball the instant you pre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/503968",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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In the Stern-Gerlach experiment, why is there a nonzero force even though the atoms were electrically neutral I know that the magnetic moment of a particle is given by:
$\vec{\mu} = \frac{gq}{2mc}\vec{S}$
I know that in the Stern-Gerlach experiment, neutral silver atoms were used. Additionally, the deflection in this e... | The Stern-Gerlach experiment is famous because it verified quantization of angular momentum in quantum mechanics. However, your question is really a question about classical electromagnetism. For example, you can replace the silver atom with a loop of wire carrying a current, and the question is the same: why does the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/504168",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Motivation for introducing quantum field theory in particle physics Why is it so that because particles can be destroyed and recreated we introduce QFT? I read at the begining of some textbook that this is so. My main problem is not the rest of the book but the first motivation for introducing QFT for modeling.
My thin... | Quantum Mechanics is about mechanics, and Quantum Field Theory is about fields. Given that all the forces in nature are described by fields, this would mean that QFT is the more fundamental theory. In fact, we can describe QM as a zero dimensional QFT. Zero dimensional as particles are zero dimensional.
It turns out th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/504303",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Standard Model Lagrangian and Euler-Lagrange Equations First off, note that I only know physics through quantum mechanics, so forgive me if this is a foolish question. I've seen the Standard Model's Lagrangian density written out in full. My question is, could one send this through the Euler-Lagrange equations to get a... | That is exactly what you do.
Note that you don't need quantum field theory till the very end.
You've got your nice Lagrangian density $\mathcal{L}$, and apply the classical field theory toolkit of symmetries (global, local), gauge covariant derivatives and Euler-Lagrange equations.
You then get the equation of motion d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/504526",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why do thermal cameras work at infrared radiation and not at visible one? From the Wien's law I have computed the Spectral Irradiance of a black body at 1000°C.
From different thermal cameras manufacturers web sites, a lot of Thermal Cameras work in the range 6-14 $\mu m$. These cameras are able to measure usually fro... | The simple answer is that visible light does not correlate with temperature as well as infra-red light does.
The EM waves received by the camera are a mixture of radiated waves and reflected waves from ambient sources. For example, consider your laptop on your desk in the daylight- it will be emitting black-body radiat... | {
"language": "en",
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How is pressure related to the energy cost Consider the following problem found in this webpage.
Consider a spherical bubble of radius $R$, of a certain fluid of density $\rho$, trapped inside of some other
fluid. The bubble is stabilized by the presence of surface tension. Namely, suppose that the bubble has a
nearly,... | I think one can get the expression for $P$ without that for $E$. Let $p_o$ be the pressure due to the fluid outside and $p_i$ be the pressure due to the fluid in the bubble. Since the bubble is initially spherical,
\begin{equation}\tag{e1}\label{e1}
p_o - p_i = \frac{2\alpha}{R}.
\end{equation}
When the bubble is defo... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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About the pressure of a confined gas According to fluid mechanics, we have Pascal's principle $P_2 = P_1 + \rho gh$. So, the pressure of a confined gas is different depending on the depth.
However, in thermodynamics, we have another formula $PV = nRT$. They use a confined gas to use this formula. Here, what is the $P$... | The ideal gas law assumes constant pressure and temperature throughout the volume of the gas. In case these quantities were vary in the volume, you can use a local form of the law, for instance: $$P=\rho \dfrac{R}{M}T$$
where $P$, $\rho$ and $T$ are the local pressure, density and temperature, respectively, and $M$ is ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is there a way to inspect thin metal weld (2 mm - 3mm) by ultrasonic testing? I am working with an ultrasonic device to inspect welds. So far, I have learned that the minimum thickness of the metal sheet for this inspection is 6mm - 8mm. But the product of mine has 3mm thick welds:
I have basic knowledge working with ... | If the thickness is less than 3-4 of $\lambda$ bulk waves cannot propagate (limits to min. 5-6mm). You need "normal" or so called Lamb waves, you can achieve them with a wedge sensor (inclined angle to the surface, goes definitely below 3 mm) or submerging methods (which is not really very practically).
see e.g. Compar... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/505906",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Differentiability of wave function at boundary in infinite square well I was told in class that a wave function should have the following properties:
*
*Finite and single-valued
*Continuous
*Differentiable
*Square integrable
But if we consider the wave function in an infinite square well, the wave function isn'... | If you consider the differentiability of the wavefunction at the boundary from inside an infinite square well, you find: $\frac{d\Psi(x)}{dx}$ = $\sqrt{\frac{2}{L}}\frac{\pi}{L}$ as $x\rightarrow0^{+}$, and $\frac{d\Psi(x)}{dx}$ = $-\sqrt{\frac{2}{L}}\frac{\pi}{L}$ as $x\rightarrow L^{-}$. Outside the well, you obtain:... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/506007",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Two-coupled oscillator: Doubt in finding normal modes and natural frequency I want to find the natural frequency of a two coupled oscillator system like this-
My book does it this way but I don't really get it.
The equations of motion for the pendula are-
$$I\frac{d^2\theta_1}{dt^2}=−M_\text{eff}\ gL\sin \theta_1− \k... | Consider $\theta_{\rm sum} = \theta_1 + \theta_2$ as one variable, and $\theta_{\rm diff} = \theta_1 - \theta_2$ as a second variable.
The two equations become
$$ \begin{aligned}
I \frac{{\rm d}^2}{{\rm d}t^2} \theta_{\rm sum} & = − \left(M_\text{eff}\ g L\right) \theta_{\rm sum} \\
I \frac{{\rm d}^2}{{\rm d}t^2... | {
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Damped Oscillation and Period In my school experiment, I wanted to measure the gravitational constant ($9.81 \ m/s^2$) by using a pendulum. If we take into account the damped oscillation (i.e. friction forces), does that affect the period?
As far as I know, the position $x$ of a particle undergoing Simple Harmonic Moti... | The free vibration frequency is affected by damping.
If you assume the damping force is proportional to velocity, the math is well known. See http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html for example, particularly the difference between the damped frequency $\omega_1$ and the undamped $\omega_0$ in the last equ... | {
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Does a maximum thermometer assume a room temperature? Consider a liquid-in-gas maximum thermometer. That is usually conventional thermometer designed for measuring body temperature.
Wikipedia says:
One special kind of mercury-in-glass thermometer, called a maximum thermometer, works by having a constriction in the nec... | You are in principle right, that the mercury (or whichever liquid you use) in the "tube" part of the thermometer could expand or constrict independently from the temperature the thermometer bulb is at. However, the expansion/constriction of the mercury is volumetric and the volume of liquid in the bulb is generally muc... | {
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On work done by internal forces which is coming out to be not equal to zero 1) Let us consider a block which explodes due to some internal mechanism into two smaller fragments of equal masses.The system was initially at rest and now is having some finite kinetic energy(due to momentum conservation).We can hence comment... | The answer to your first question is that work done by internal forces only sums to zero in the case of rigid bodies, so the principle does not apply to an exploding body.
The same is true for the two blocks linked by a spring- it is not a rigid body.
The two cases are analogous. In the case of the exploding block, po... | {
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Why doesn't hot charcoal glow blue? I was learning about black body radiation and the explanations given by Max Planck and Albert Einstein when a thought crossed my mind.
When we heat an iron piece, its color changes gradually from red, orange, yellow to bluish white. Yet such a change is not visible in a glowing piec... | Iron is supposed to glow blue-white at around 1600 degrees C. page 7.
Would carbon have that color at that temperature?
Spectral lines of iron
Spectral ines of carbon
Maybe not. Maybe those bright yellow lines would add too much. Carbon might have to be hotter.
Do we have examples of carbon heated very hot? How about... | {
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The potential at a point According to my book, 'The potential at a point is said to be 1 volt when 1 joule of work is done in bringing 1 coulomb charge from infinity to that point.' But I wonder how it is possible. As the charge is being brought from infinity, the work done = force * infinity, thus, the work done would... | Force is dependent of distance $r$, so thing move like this
$$\newcommand{\newln}{\\&\quad\quad{}} \begin{align}&\int^{r_b}_{r_a}\mathbf{\vec{F}}\cdot d\mathbf{\vec{r}}=-(U_a-U_b) \newln \Rightarrow \int^{r}_{\infty}\mathbf{\vec{F}}\cdot d\mathbf{\vec{r}}=-(U_r-U_\infty) \newln \Rightarrow \int^{r}_{\infty}\mathbf{\ve... | {
"language": "en",
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Physical reason for $T^2=a^3$ when $T$ is in years and $a$ is in AU Kepler's third law states $$T^2\propto a^3$$
When $T$ is in years and $a$ is in AU, the proportionality constant becomes $1$. This can't be a coincidence; I would like to know the physical reason for it.
| It's not really a physical reason but you are correct in suspecting that this shouldn't be a coincidence. The fact that the proportionality constant becomes unity follows from the definition of a year and an astronomical unit. A year is defined precisely as the period of time it takes for the Earth to complete a revolu... | {
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Understanding simple LC circuits I'm trying understand the physics of simple inductor-capacitor circuits such that there is just an inductor L and a cacpacitor C and a switch.
Imagine first that the capacitor is fully charged and the switch is then closed.
I do not understand why the current increases from an initial l... | Actually, LC Circuit is cause of LC oscillation,
When you apply kvl you get.
$Q/C=Ldi/dt$, and $dQ/dt$ so after double differentiating we get
$Q/C=Ld^2Q/dt^2$, which look quite same as shm equation $a=-w^2x$,so we get $w=1/(LC)^1/2$, so energy oscillate,
At any instant instant energy will. Be equal. To. Field. ... | {
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Is tension always the same as centripetal force? For example, if a ball is attached to a string and released from a vertical height and then pivots around a point to initiate circular motion, tension is equal to centripetal motion.
If, on the other hand, a ball hands from a string and it’s hit in such a way that it tra... | "Centripetal" is Latin for "towards the center." A centripetal force is not a particular type of force like a frictional force or a magnetic force. It's just a force that makes an object go in a circle. The word "centripetal" describes the direction of the force, not the type of force.
When a car drives around in circl... | {
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Can someone explain what is the force the ball will exert? If a ball is falling under free fall then the force exerted by the ball on the ground would be $mg$. But that's not the case in real life ball would hit with more force. But when i draw free body diagram there is only one force that is acting on it $mg$
Can som... |
the force exerted by the ball on the ground would be $mg$
Why do you say that?
The force that the ball exerts on the ground depends on the modulus of elasticity (stiffness) of the ground and can be very high. The normal reaction of the ground stops the ball over a certain distance. If the modulus of elasticity of the... | {
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Why Don’t We Use Radios for Propulsion? We’ve all heard the idea of laser propulsion before, but why can’t a high powered RF source be used to propel a body? A simple high current coil with an AC signal applied to it to it could produce 100s of watts if not kilowatts of EM power. So why not use these instead of our und... | In principle the thrust-to-radiated-power ratio of all electromagentic radiation drives is identical.1 Frequency doesn't enter directly into the issue.
So it is tempting to say "use the band with the highest ratio of radiated-power-to-supplied-power". Good idea.
But then there is the question of collimation and the inf... | {
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Justification for excluding gravitational energy from the stress-energy tensor I did general relativity years ago at Uni and was just revising with the aid of Dirac''s brilliant book; the beauty of this book is that it is so thin and concise. On reading this book I find that I have a few questions regarding energy.
One... | There are various definitions of the total global mass-energy contained in a spacetime: the ADM mass, Bondi mass, etc. In present understanding, these require specific conditions such as symmetry in time, or asymptotic flatness.
Then there are an awful lot of quasi-local proposals. The idea is that, since you can't def... | {
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Is there a limit of electrons a single hydrogen atom can have? Is there a limit of electrons a single hydrogen atom can have? If so what is it? why? Is the the answer to why scalable to helium?
| By definition, "hydrogen atom" refers to the neutral system with one proton and one electron, so it cannot hold any extra electrons.
However, protons can hold more than one electron, in which case the system is termed a hydrogen anion. This is a stable, bound system, and the reaction
$$
\mathrm{H}+e^- \to \mathrm{H}^-
... | {
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Why impose invariance of the Lagrangian under infinitesimal coordinate transformations? I am reading Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries by Sylvain Marsat.
In section 2B the author imposes the invariance of the Lagrangian under infinitesimal coordinate... | Rather than asking why we should impose this invariance, I think it would make more sense to ask why we should relax it. The Lagrangian is a relativistic scalar, which means that it has to be invariant under any coordinate transformation. An infinitesimal change of coordinates is just one type of coordinate transformat... | {
"language": "en",
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Interpretation of the photon scattering rate? The photon scattering rate $\Gamma$ describes the rate at which photons scatter off an atom$^1$. In a two-level system, the ansatz for the photon scattering rate often is given by
\begin{equation}
\Gamma = \rho_{22}\gamma
\end{equation}
where $\rho_{22}$ is the probability ... | If $\rho_{22}$ is the population of the excited state then for sure $\rho_{22} \gamma$ is the rate at which the atom is emitting photons. I guess the question arises from not realising that $\rho_{22}$ is itself dependent on the conditions the atom is under. For example, if the atom has been left alone for a while then... | {
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Prove equivalence of the definition for coherent states Quote:
The coherent states $|z\rangle$ is defined as $$|z\rangle
=e^{-|z^2|/2}\sum_{n=0}^\infty\frac{z^n}{\sqrt{n!}}|n\rangle
=e^{-|z^2|/2} e^{a^\dagger z}|n\rangle,$$
which was, very understandable and mathematically easy.
However, I encountered an article th... | Note that later in the text on p. 34 the formula (4.54) explains exactly how Zwiebach's coherent states $|\tilde{x}_0\rangle$ are related to the standard coherent states.
The intuition is that actual position-eigenstates does not belong to the Hilbert/Fock space, so instead we roughly speaking consider Gaussian wavepa... | {
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Is this question physically possible? Question: Two smooth vertical walls stand on a smooth horizontal plane and intersect at right angles. A small smooth sphere of mass m is moving with velocity (4i + 3j) m/s when it hits one of the walls. It rebounds from the wall with velocity (i + 3j) m/s and goes on to hit the sec... | Yes the impulse isn't perpendicular to the wall so the restitutive coefficient will be both vertical and horizontal to the wall.
The fact that it says that the coefficient of restitution is the same for each wall implies that it is invariant to incident angle (not in any way realistic, but hey that's what logically mus... | {
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Dimensional regularization of a divergent integral Suppose there is an integral in four dimension Euclidean space
\begin{equation}
I_{d=4}=\int_0^\infty d^4x\frac{1}{|x|^2},~
\end{equation}
which is divergent. $|x|$ is the length of the vector. Can one use dimensional regularization to compute this integral by using $d... | The method of dimensional regularization in QFT comes with a few definitions which are crucial to evaluating integrals of this type. Following Zinn-Justin, they are the properties of these integrals under the following:
*
*Translations:
$$
\int d^d p \, F(p + q) = \int d^d p \, F(p)
$$
*Dilatations:
$$
\int d... | {
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Should the ground state electron density of an atom go to zero at the origin? I have heard from my professor that the particle density of electrons (in the ground state) of an atom should vanish near the nucleus. Hydrogen is an obvious counter-example. So I am trying to work out what he could have meant? Which quantum ... |
Hydrogen is an obvious counter-example.
Indeed it is. The claim as stated is false.
So I am trying to work out what he could have meant?
You'll have to ask him. There's no way for us to read his mind.
| {
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Charm prediction: Required electroweak or just weak? Everywhere I look it up the prediction of the charm quark is predicted by the electroweak interaction, which of course recovers the weak interaction with the spontaneous symmetry break and the Brout-Englert-Higgs mechanism.
My question is, did the new features of the... | You might wish to move or repost your question to HSM where such issues are discussed.
Indeed, the Weinberg-Salam model did not figure at all in the historic GIM paper, 1970, not even as a reference. What is required for the suppression of FCNC is a "conventional mixing" of charged currents, reasonably well understoo... | {
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Does the wavelength of a particle depend on the relative motion of the particle and the observer? The de Broglie wave equation states:
$$\lambda = \frac{h}{p},$$
where $\lambda$ is the wavelength of the “particle”, $h$ is Plank's constant, and $p$ is the momentum of the particle.
Momentum is usually written $\,p=mv$, w... | Yes, the observed wavelength of a particle depends upon the relative motion between the observer and the particle. This is called the Doppler Effect.
| {
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Problem Regarding Buoyancy
A spherical marble of radius $1\,$cm is stuck in a circular hole slightly smaller than its own radius (for calculation purposes , both are equal) at the bottom of a filled bucket of height $10\,$cm. Find the force on the marble due to the water.
I have always been troubled by problems like ... | It all depends on the fluid contact.
Buoyancy comes about due to hydrostatic pressure differences on a submerged or floating object.
For submerged or floating objects, the fluid pressure acts on the submerged volume. Because fluid pressure increases with depth due to hydrostatics; when you submerge an object, the pres... | {
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Where do we see centrifugal acceleration? A body in circular motion always possesses centripetal acceleration which is felt by a person sitting at the center of mass. It will not be felt by a person viewing the motion from the ground frame. Then where do we feel the centrifugal acceleration? We cannot be anywhere on th... | If you are sitting in any kind of vehicle which is moving along a curved path, then you feel the seat exert a centripetal force on you. If you are swinging a mass around in a circle on the end of a rope, then the force which the rope exerts on you might be considered centrifugal.
| {
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Why do we need short wavelength to measure the position of a particle accurately? I am reading "A brief history of time" by Stephen Hawking. It is explaining the uncertainty principle:
... However, one will not be able to determine the position of the particle more accurately than the distance between the wave crest ... | It is analogous to the separation between the physical marks on a measuring tape or ruler. If you have a tape that is only marked to the nearest inch, you will not be able to make as precise a measurement as you might with a tape marked at 1/16th of an inch intervals.
| {
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Why does a chain or rope move the way it does when suspended and rotated on a vertical axis? I have always been interested in why objects like chains, ropes, etc. move the way they do when "rotated" around a vertical axis while being held only where it is suspended. It forms a shape if you will, resemblant of a "C" or ... | If i understand correctly you spin the chain on an vertical axis with angular speed $w$. The 3-dimensional shape of the spinning chain is rather complex, but a 2-dimensional projection of this shape on a vertical plane resembles a standing wave. Where the nodes are the points where the chain is kept in the middle. If y... | {
"language": "en",
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Question about description of Gibbs free energy When introduced to the gibbs free energy, it was derived as follows:
First law: $dU=dq+dw$
Second law: $dS>dq/T$ for a spontaneous change.
Note $dq$ and $dw$ are inexact differentials.
Subsituting $dq=dU-dw$, into the second law gives us:
$TdS>dU-dw$
using $dw=-P_{ext}dV$... | G is not defined by the equations you wrote. For a pure substance or a mixture of constant chemical composition, it is defined by $$G=U+PV-TS$$And this equation applies only to thermodynamic equilibrium states. So, $$dG=dU+PdV+VdP-TdS-SdT$$But since $dU=TdS-PdV$ we are left with $$dG=-SdT+VdP$$
| {
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Would looking out from inside or near a black hole be unimaginably bright? I have the following assumption based on limited knowledge.
A black hole appears dark to us because any light that would be emitted from it, and any light that passes nearby, is caught by the gravity well and either captured or bent from its ori... | The light is not exactly bent from it's original course, the blackhole curves spacetime and the light follows that curvature. The thing is that the time component of "spacetime", as well, is bent near a black hole, so that as the light approaches the event horizon, the time it takes (from an outside perspective) for th... | {
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What is dislocation loop? What is dislocation loop? Is it something different from dislocations? If so can dislocations at higher temperature can combine to form dislocation loop?
| a dislocation loop is a linear dislocation in which its two ends meet together- that is, it's still a dislocation in the crystal lattice but by closing in on itself it has special propagation properties, about which entire chapters of upper-division materials science textbooks have been written.
Years ago, a team of J... | {
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Hermiticity of spin-orbit coupling in real space In the Kane-Mele model, the spin-orbit coupling is defined in real space as
$$\sum_{\langle \langle i j \rangle \rangle \alpha \beta} i t_2 \nu_{ij} s^z_{\alpha \beta} c_{i \alpha}^\dagger c_{j \beta}$$
where the sum is over next-nearest-neighbor sites on a honeycomb lat... | From the first to second expression on the first line, the Conjugation operation should transpose the matrix $v_{ij}$ to $v_{ji}$, giving the missing minus sign.
| {
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Why don't we lose generality when we assume $z^0 > x^0 > y^0$ in the proof of Wick's theorem? In proof's of Wick's theorem it's typically stated (see e.g. page 87 in Coleman's notes) that it's sufficient to consider just one possible time-ordering. For example for the product $T(\phi(z)\phi(x)\phi(y))$ this would mean... | Inside the brackets of the time ordering operator all fields commute. Thus the times are irrelevant as the fields are always ordered so that the assumption is satisfied
| {
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What is the $R$-symmetry group for ${\cal N}=6$ supergravity in $D=4$ dimensions? What is the $R$-symmetry group for ${\cal N}=6$ supergravity in $D=4$ dimensions?
| This is an old post, but I would like to clarify this for others who, like me, stumble upon this question now. As Qmechanic noted, the $R$-symmetry group in $D = 4$ is $U(\mathcal{N})$, which is Table 12.1 on page 240 of Ref. [1]. However, in supergravity theories, the kinetic terms for the scalars are non-trivial and ... | {
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How do I experimentally measure the surface area of a rock? I hope this is the right place to ask this question.
Suppose I found a small irregular shaped rock, and I wish to find the surface area of the rock experimentally. Unlike for volume, where I can simply use Archimedes principle, I cannot think of a way to find ... | The task isn't well-defined.
Do you include cracks? If yes, you'll see finer and finer cracks adding to the surface, and in the end you'll be at atomic level and find it hard to even define what's part of the rock and what isn't.
If you don't include cracks: What's your rule for distinguishing a mere unevenness from a ... | {
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When the direction of a movement changes, is the object at rest at some time? The question I asked was disputed amongst XVIIe century physicists (at least before the invention of calculus).
Reference: Spinoza, Principles of Descartes' philosophy ( Part II: Descartes' Physics, Proposition XIX). Here, Spinoza, following... | I assume you are talking about an object that reverses direction through a collision. Take the case of a ball bouncing off the ground. As it hits the ground, the ball deforms and the ground compresses a tiny amount. The resistance of the ball to deformation and the resistance of the ground to compression decelerate the... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 4,
"answer_id": 2
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What determines whether we use a vector or scalar potential? I understand that electrostatic potential is scalar because the curl of the field is zero, and this implies the electrostatic field is the gradient of the scalar potential to satisfy this. Similarly the divergence of a magnetostatic field is zero so a magneto... | From a more general point of view, the scalar potential and the vector potential are parts of the electromagnetic four-potential.
The four-potential is defined up to a gauge transformation. To answer your question, one uses the gauge that is the most convenient for the specific problem. For example, in the case of elec... | {
"language": "en",
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"source": "stackexchange",
"question_score": "2",
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Why coupled oscillators tend to seek integer frequency ratios? In this document, the author writes (page 225)
Coupled oscillators have a tendency to seek frequency ratios which can be expressed
as rational numbers with small numerators and denominators. For example,
Mercury rotates on its axis exactly three times ... | They may in special cases, but this is by no means a rule, and most certainly doesn't hold for all cases. As I'm a firm believer in concrete examples, I'll illustrate this with the following simple case of two blocks, each of mass $m_1=m_2=m$, connected to walls and each other by Hookean springs (which are harmonic osc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/513210",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
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Are the boundary conditions purely a consequence of Maxwell's equations? The boundary conditions, namely
were all these, realized only by looking at Maxwell's equations? Or is there a physical reasoning behind them? For example, Why does the component of the electric field parallel to the surface of interface remain u... | In short: Yes.
Those equations can be understood as boundary conditions, but they can also be understood as being valid between any two points inside the domain. This is because they result from integrating the Maxwell equations over an arbitrary test volume, and hence link the quantities at either end of this test vol... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
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Where does $\pi$ come from in the Heisenberg equation? In class today we were taught about Heisenberg’s equation, $$\Delta x\Delta p\ge\frac{h}{4\pi}. $$
Experience tells me that any time an equation involves pi, circles aren’t far behind. Obviously this is true in geometry, but even pure number theory equations, such ... | There are two different conventions for the constant used in the uncertainty principle, which are written as $h$ and $\hbar$. They are related by
$$\hbar = \frac{h}{2\pi}$$
and the reason for the $2\pi$ is because both appear in the expression for the energy of a photon:
$$E = hf = \hbar \omega$$
and the relation betwe... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
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Mean free path equation derivation I was reading about mean free path equation derivation online and stumbled upon this:
We will derive the equation using the following assumptions: let’s assume that the molecule is spherical, and the collision occurs when one molecule hits another, and only the molecule we are going ... | The cross-sectional area is indeed $A_c = \pi d^2$ but the explanation on this page is not precise in this regard. You basically consider a single particle of diameter $d$ and its collisions with other particle of the same size.
Simple considerations in 2D
The chance for it to collide with another particle is proporti... | {
"language": "en",
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"source": "stackexchange",
"question_score": "4",
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Commutator of $L^{2}$ and $L_{z}$ I'm trying to work through a proof of why $[L^{2},L_{z}]=0$, and am getting lost on this step:
We can use the commutation relation $[\hat{L}_{z},\hat{L}_{x}]=i\hbar\hat{L}_{y}$ to rewrite the term as:
$$
\hat{L}_{x}\hat{L}_{x}\hat{L}_{z} = \hat{L}_{x}\hat{L}_{z}\hat{L}_{x} - i\hbar\hat... | Given
$$
[ L_z, L_x ] = i \hbar L_y
$$
just multiply both sides by $L_x$:
$$
L_x \bigg( L_z L_x - L_x L_z \bigg) = i \hbar L_x L_y
$$
which gives
$$
L_x L_x L_z = L_x L_z L_x - i \hbar L_x L_y
$$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/513963",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How do you tell if a wave is reflected or refracted at an interface? My physics textbook says that a wave traveling through medium $1$ will enter medium $2$ if medium $1$ has a higher index of refraction. Otherwise, the wave will be reflected. This makes absolutely no sense to me, since this would mean all sunlight tr... | It's good that it makes absolutely no sense to you, because that is absolutely wrong, and if your book truly says that then it should be cast into the nearest volcano as soon as possible.
In general, light incident upon an interface will be neither completely reflected nor completely transmitted. The Fresnel equations... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Can the work by kinetic friction on an object be zero? We know that friction is of two types - static and kinetic. Static friction acts when there is no relative motion between the surfaces in contact. Kinetic friction takes place when surfaces rub against each other. I was wondering whether the work done by the kineti... | Hold a piece of wood against a sanding belt. In your frame, the block is not moving, but
*
*kinetic friction is exerting a force: you have to hold the block still
*energy is transferred: the block gets hot, and pieces are pulled off it
| {
"language": "en",
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"source": "stackexchange",
"question_score": "2",
"answer_count": 5,
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Conservation of momentum in photon-atom collision Is this explanation correct:
When a photon with the appropriate energy hits an atom, the electron will make a transition from the ground state to a excited state. This will make the potential energy of the atom higher. Also, momentum is conserved, and the velocity of th... |
I am a bit confused because if that's the case, the atom will gain kinetic energy.
In the way you've set it up (atom is initially at rest in our reference frame), then that is correct.
Doesn’t that violate the conservation of energy?
That depends on the energy inputs and outputs. We haven't described them complet... | {
"language": "en",
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"source": "stackexchange",
"question_score": "5",
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Will August be always summer in the northern hemisphere? Is the Earth orbit precessing, or are there other effects which will create a shift between our calendar (day counting), and the Earth's orbit?
I imagine these effects to be small, but I'm asking for long timescales.
[Edit] To formulate my question better, let me... |
A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. ...
The sidereal year differs from the tropical year, "the period of time required for the ecliptic longitude of the Sun to increase 360 degrees", due to the precession of the equinoxes. The sidereal year is 20 min ... | {
"language": "en",
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"source": "stackexchange",
"question_score": "2",
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Status of Space-Time Many physicists conjecture that space-time is not fundamental.
Is this the orthodox view in physics these days?
Follow ups - If a philosopher argues that space-time is reducible, are any physicists likely to argue? Are there many or any theories (for instance versions of string theory) that actua... | It is the prevailing view among high-energy physicists that spacetime should be emergent from some more basic structure because of the following basic argument: if you want to probe regions of spacetime that are arbitrarily small then according to the principles of quantum mechanics (and special relativity), it corresp... | {
"language": "en",
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"source": "stackexchange",
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Unitarity/Hermiticity condition for $osp(m,n|\mathbb{C})$ superalgebra According to Dictionary on Lie Superalgebras (page 82), the compact form of $OSP(m,n|\mathbb C)$ Lie superalgebra must satisfy $M^{\text st}H\,M=1$ and $M^{\ddagger}M=1$ (is this the unitarity condition?), this means that the conditions for the corr... | Apparently $E^{\#}\equiv E^{\ddagger}$ and $*\equiv\dagger$, so the condition $$E^{\#}=-E\tag{1}$$
for unitarity, is the same as $$E^{\ddagger}=-E \tag{2}$$
That's why you have a transpose in the definition of $E^{\#}$! SO, actually $C=-iB^{\dagger}$. And, with $E^{\text{st}}H+HE=0$, you get the generators of $uosp(m,n... | {
"language": "en",
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Interacting lagrangian with multiple terms We know that for a $\phi^4$ interacting theory with $$
\mathcal{L}_{int} = -\frac{\lambda}{4!}\phi^4
$$
the interaction $\phi \phi \rightarrow \phi \phi$ gives a vertex with a factor $-\frac{i\lambda}{4!}$ which stems from Wicks theorem.
If we now use the same procedure for an... | Your second Lagrangian would generate of two vertices:
A cubic self interaction for $\phi$ (in your notation $\phi \phi \rightarrow \phi$, say) and an inter-field interaction between $\Phi$ and $\phi$ (in your notation $\Phi^{*}\Phi \rightarrow \phi$).
Both vertices have three legs; in the first they're all $\phi$ fie... | {
"language": "en",
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How can the mechanism of electrons in an atom be explained? I am a high school student who takes both Physics and Chemistry.
Recently I learnt about the quantum mechanical point of view of looking at electrons or nuclei. I also learnt that the wave functions can be obtained by solving the Schrodinger's equation with va... | curios,
It is important to make a clear distinction between what is known or knowable and what it exists.
Quantum mechanics does not say that the electrons do not have precise positions or precise momenta. It tells you that:
*
*You cannot prepare a state where both the position and momentum of an electron are known ... | {
"language": "en",
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"source": "stackexchange",
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Hamiltonian for 2-qubit system What is the general form of a Hamiltonian for a 2 qubit system?
The Hamiltonian for D-Wave system is:
$H = K_1\sigma_x^1 + K_2\sigma_x^2 + H_1\sigma_z^1 + H_2\sigma_z^2 + J_{12}\sigma_z^1\sigma_z^2 $
https://arxiv.org/abs/1512.01141
Is this true for all superconducting qubit system? If n... | The hamiltonian of a two qubit system can be any $4\times4$ hermitian matrix. In general, we can write this
\begin{align}
H = \sum_{i,j=0}^3 h_{ij} \,\sigma^1_i\sigma^2_j
\end{align}
where the coefficients $h_{ij}$ are real, and the $\sigma_i$ are Pauli matrices, with $\sigma_0$ the identity.
What the hamiltonian of a ... | {
"language": "en",
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Why is torque a cross product? If I'm not wrong, torque is perpendicular to both the radius and force i. e. It is along the axis of rotation. Questions that arise are- why do we consider the length between the axis/point of rotation while calculating torque? More importantly why is torque a cross product?
| (a) "why do we consider the length between the axis/point of rotation while calculating torque?"
We can calculate torque about any point, O, that we choose; it doesn't have to be a physical axis of rotation. But it's often more useful to calculate torque about a possible physical rotation axis, for example when thinkin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/516011",
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"source": "stackexchange",
"question_score": "8",
"answer_count": 7,
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How do physicists compare the relative strengths of the four forces? Since the four forces are different, with different force carriers, how are they (seemingly) directly compared? I often read that the weak force, for example, is many orders of magnitude stronger than gravity, and that electromagnetism is several ord... | In particle physics, the strength of fundamental forces is specified by either masses of force-carrier particles (e.g. masses of $Z$, $W^{\pm}$ bosons for weak interaction) and/or by a numerical "coupling" coefficient (e.g. electron charge in electromagnetic interaction).
One of the ways to measure the relative strengt... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/516169",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Could approaching an unknown object in space electrocute you? Say you're out for a spacewalk on the ISS one day, and you see an unknown object floating next to you (ignoring the probability that it somehow matched your orbit perfectly and didn't just plunge straight into Earth's atmosphere). Let's say a bowling-ball si... | Putting your hands on opposite terminals of a large, high voltage capacitor will do it. They are dangerous.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Different apparent brightness of a distant star from a moving frame - an apparent paradox Consider a stationary star at a distance $L$ from the Earth.
A spaceship at Earth moving with velocity $v$ towards the star will find the star to be at a distance of $\dfrac{L}\gamma$ in its own frame.
But it won't actually see th... | The star will look dimmer because to the moving observer the star is aging slower, so to this observer, the star emits less energy per unit of time. Also, the total number of photons each observe between two events will be the same, but they will disagree on how much time has passed between the two events and about the... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Might a cast iron pan set on top of a microwave oven affect the operation? Our microwave seems to take longer to get the job done these days. I notice that someone is storing a large, heavy cast iron pan on the top of the microwave. Is there any way at all that it is possible that the iron pan is interfering with the m... | Elaborating a bit on terri's answer... If (big, hypothetical if), some object like the cast iron pan were reducing the energy going into the food, then it should be heating up. But, a big hunk of metal in firm contact with the Faraday cage that is your oven's enclosure should at most act as part of the cage.
Metal obje... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Misconception in partial derivatives of Lorentz transformation Let us consider a Lorentz transformation of four vectors from frame S to S' where S' is moving with relative velocity $\textbf{v}$ with respect to S. The boost is given by
$$t'=\gamma(t-vx), \quad x'=\gamma(x-vt), \quad y'=y, \quad z'=z.$$
The inverse trans... | You forgot that $x'$ is not only function of $x$, but also of $t$: $x' = x'(x, t)$. Similarly, $x=x(x', t')$. Hence:
$$ \frac{\partial}{\partial x'} = \frac{\partial x}{\partial x'} \frac{\partial}{\partial x} + \frac{\partial t}{\partial x'} \frac{\partial}{\partial t}$$
and
$$ \frac{\partial}{\partial x} = \frac{\par... | {
"language": "en",
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Phase transition on magnetic materials Is ferromagnetic to paramagnetic phase transition a reversible process?
If I start with a ferromagnetic material with a spontaneous magnetization below the Curie temperature, and then I start to heat it, it will become paramagnetic above the critical temperature. If I then start t... | Spontaneous symmetry breaking
Unless there is a preferred direction for magnetization, specified, e.g., by the external magnetic field or crystal symmetries, there is no reason for the magnetization to point in the same direction as before. The direction chosen by the magnetization when entering the ferromagnetic phase... | {
"language": "en",
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If a basis set is complete, are the elements in it mutually orthonormal? If a basis set is complete, are the elements in it mutually orthonormal? For example, we can express the field operator in the basis of the creation and annihilation operators.This basis is complete, are the elements in it mutually orthonormal?
| The answer is NO
Given any complete basis, one can construct another by taking independent combinations.
Assuming the original basis is complete and orthogonal, and contains $V_1$ and $V_2$, (which are thus orthogonal).
Replacing $V_2$ by $V_2'=V_1+V_2$ does not change the completude of the basis. But now two vectors ... | {
"language": "en",
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Is time slower on the far galaxies? Since far galaxies move away faster, what would be the speed of their time relative to us?
If there is a difference:
*
*What determines whose time would be faster?
*(If I haven't understood it wrong) To resolve the twin paradox, acceleration is required. Is the expansion of the... | When you talk about farther galaxies moving faster relative to us, you are presumably talking about the effects of the expansion of the Universe. When you refer to the twin paradox, you are presumably talking about the special relativistic effects of relative motion. These are not the same thing. To see this, note t... | {
"language": "en",
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"source": "stackexchange",
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Acoustic Standing Wave and Shape of Pipe Does the shape of the container matter when constructing an acoustic standing wave? Is there an advantage of using a cylindrical container over a rectangular prism?
| The shape effect on fundamental pitch is slight, but the effect on the overtone series is significant. Most wind instruments have cylindrical shapes for this reason, and also because square cross-section pipes with bends in them are more difficult to fabricate. This is a topic about which a lot has been written in the ... | {
"language": "en",
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How come Goldstone boson, PQWQ axion, be able to have mass at all? Quote:
Goldstone's theorem: For every spontaneously broken continuous symmetry, there is a massless particle created by the symmetry current.
However, under $U(1)_{PQ}$ symmetry, I read that PQWW axion can obtain mass from $G\tilde{G}$.
Both these s... | Two conditions for pseudo goldstone boson:
*
*The broken symmetry is not gauged, otherwise the (pseudo)
goldstone boson will be eaten by the gauge field.
*Something else (chiral anomaly in this case) breaks the symmetry
even before the spontaneous symmetry breaking is taking place.
To visualize, think about a ... | {
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Observed speed of a receding light source Let’s say there’s a planet 4 light years away from Earth and we send a rocket ship towards that planet at 99.9% light speed. We stay behind on Earth and watch the rocket ship travel towards the other planet.
Eventually we should be able to see our rocket ship reach it’s destina... | It takes the spaceship 4 years to get there, and then it takes light from the spaceship getting there 4 years to get back, i.e. 8 years for an observer on Earth to see it land on the planet.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/518147",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What exactly causes particles to drift toward the bottom of a tube in a centrifuge? As I understand, centrifuges can effectively create gravitational fields that are a thousand times stronger than the Earth's. And it is this pseudo-gravitational force that causes particles to sink toward the bottom of a test tube, but ... | Rotating reference frame
In the rotating reference frame the centrifugal force explains the sinking of dense particles, just as gravity does on the surface of earth. Unfortunately, the terminology “fictitious” makes it seem as though it cannot do anything. For that reason I prefer the term “inertial force” instead of “... | {
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Why do we use cross products in physics? We can define cross products mathematically like if we take two vectors, we can find another vector with certain properties but why do we use it in physics, if we consider a hypothetical physical quantity like force which is equal to cross product of certain vectors?
For exampl... | It's really much simpler than the other answers so far have made it out to be. We use the cross and dot products (and all the other math) because they allow us to create fairly simple mathematical models (that is, the laws of physics) that accurately represent what the universe actually does.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "55",
"answer_count": 8,
"answer_id": 1
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Light beam vs sound beam Why is it that it's very common to have beams of light but not beams of sound? Laser beams are widely available, and I am aware that it is also possible to direct sound, however, we rarely see examples of it.
Is it more difficult to direct due to longer wavelength or is it more dispersive in a... | Like very well the rest of the contributors commented "wave-beams" (apologies for the slight abuse of the term) are not uncommon at all. Medical imaging is just one field where they are used. Sonars is another possible application (both transmission, and reception).
In general, in acoustics (whether it is ultrasound, u... | {
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What is meant by "information" with regard to general relativity and/or black holes? In The Universe in a Nutshell chapter 4, Hawking explains the warping of spacetime according to general relativity and introduces the basics of black holes.
It surprised me to read about "information" that fell into the black hole, and... | Consider a vibrating violin string. To predict its motion, it suffices if I know two functions. One function, $y(x)$, specifies its shape, and the other, $v(x)$, gives its initial velocity at each point. If I know the functions $y$ and $v$ at some time $t$, then I can find them at any other time $t'$ using Newton's law... | {
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Physical interpretation for wave function in infinite square well If you look at the wave function of a particle in infinite square problem for some specific energy level, say for n =1, then the probability of particle to be found in middle of the well is higher than at any other point. Similarly for higher energy lev... | I am going to focus on the last sentence of your question, which sums it up: "why are some points more probable than others?"
The answer is that the waves have to satisfy Schrodinger's equation, and that equation includes that higher kinetic energy goes with higher $d^2 \psi/dx^2$. Meanwhile the boundaries of the box e... | {
"language": "en",
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Is the weight of a projectile launched from earth and while still flying in the atmospheric sky transferred to the ground? Raised by this question.
Q1. Is the weight of a projectile like a bullet or a ballistic missile (atmospheric flight trajectory) transferred to the ground?
Of course i know that if the projectile wa... | Any object in the atmosphere, that is not in freefall, is ultimately transferring it's weight to the ground. A normal bullet fired from a gun is essentially in freefall once it leaves the gun. After leaving the gun, it has no lift, it starts falling. It may have upward momentum which it will immediately start losing. I... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/519793",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Fermi energy definition Ok, so I'm having a hard time understanding the definition of Fermi Energy. Several sites basically repeat each other, saying that it is the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero 1, and ot... | From the Schrödinger equation, energy for a bound electron is quantized, such that only certain energy levels are allowed. Because electrons are fermions, they obey the Pauli exclusion principle, which states that no two electrons can have all their quantum numbers (such as energy level, orbital, spin) equal.
This mea... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/520184",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Justification for Loop de Loop minimum speed I was trying to figure out the minimum speed an object would have to travel on a loop not to lose contact with the loop. Setting the centripetal force equal to gravity $m\frac{v^2}{r} = mg$ gives $v = \sqrt{gr}$ that explanation is valid and makes sense to me but I was wonde... | First case :- In the first case(where you used centripetal force), the velocity $v=\sqrt{gr}$ is, in fact, the velocity of the object at the top of the loop. To find the velocity of the object at the bottom of the loop, you will need to use energy conservation.
$$\frac{1}{2}m((\sqrt{gr})^2-v_{bottom}^2)=-2mgr \Rightarr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/520382",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 0
} |
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