Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Asymmetry between space and time in special relativity Consider 2D spacetime with two inertial reference frame S and $S'$, where $S'$ is moving in the $S$ positive spatial direction at velocity $vt$, along with the usual graphical representation with $t$ on the vertical axis and $x$ on the horizontal axis. Use units su... | If you choose to draw the frames so that the $S$ axes are horizontal and vertical on your paper, then they look like this (with the $S$ frame in black and the $S'$ frame in blue):
The marked points are $(1,0)$ and $(0,1)$ in the $S'$ frame.
| {
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"timestamp": "2023-03-29T00:00:00",
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Newtonian vs Lagrangian symmetry Suppose we have a ball of mass $m$ in the Earth's gravitational field ($g=const.$). Equation of motion reads as:
$$
ma = -mg
$$
From here we can conclude that we have translational symmetry of the form $x(t) \to x(t) + const$ (we are working in only 1D). However, we cannot see this sym... | *
*The (infinitesimal) translation $$\delta x~=~\epsilon$$ changes OP's Lagrangian with a total time-derivative
$$\delta L~=~mg \epsilon~=~ \frac{d}{dt}(mg \epsilon t).$$
This is known as a quasi-symmetry. Noether's theorem does also hold for quasi-symmetries.
*Concerning symmetries of action vs. EOM, see also e.g. ... | {
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Contradiction of Units in Polytropic Process A polytropic process is a process that obeys the relation $pV^n=C.$
However, when I try to solve a problem involving this relationship with, for example, $n = 1.5$ my use of units in my equations breaks down. At some point, I find myself having to solve for the constant $C$ ... | The product $pV$ (where $p$ is pressure and $V$ is volume, each with their standard units in your favorite system) has units of energy. As noted in the comments, the product $pV^n$ when $n\neq 1$ does not. Nor should you expect it to. We're no longer dealing with energy but with an invariant in certain adiabatic proces... | {
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Why is $J^P=0$ for all even-even nuclei? I have the following question, for which I have answered fully, but I am questioning the logic behind finding the value of $J^P$ for ${}^{20}_{10}\mathrm{Ne}$:
N.B, when I wrote "Number per level" in the picture above this is really just the degeneracy, $2j+1$.
Now to answer th... | I'll answer by asking you some questions:
For $^7_3$Li, why did you ignore the 4 neutrons? Why did you ignore the two $1p_{3/2}$ neutrons? You mentioned that the third proton was "unpaired."
For $^{29}_{14}$Si, why did you ignore the $14$ protons and their contribution to spin and parity? Again, you mentioned there was... | {
"language": "en",
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Superinsulator infinite voltage Everybody knows about superconductivity, at cryogenic temperatures conductor resistance drops to zero for direct current. There is lesser known related phenomena called superinsulator where material gains infinite resistance.
Does it really block infinite high voltage? That seems to me t... | To quote Wikipedia article on superinsulator:
The superinsulating state is the exact dual to the superconducting state and can be destroyed by increasing the temperature and applying an external magnetic field and voltage.
The reason for calling them superinsulators is then not because it cannot conduct at infinitely... | {
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For capacitors, why does the dielectric need to be inserted at a small constant speed? Likely a very silly question.
I am aware that there is an attractive force from a charged parallel-plate capacitor in an open circuit without battery pulling the dielectric in, and that a decrease in energy will result upon insertion... | If it pulls it on his own, and you disregard friction it will come out on the other side, and so on and oscillate.
| {
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What does the absolute value of an operator mean? In the text, we are given a Hamiltonian for two bodies with a potential energy of interaction that depends on the magnitude of the distance between them as:
$$\hat{H}=\frac{\hat{\mathbf{p}}_{1}^{2}}{2 m_{1}}+\frac{\hat{\mathbf{p}}_{2}^{2}}{2 m_{2}}+V\left(\left|\hat{\ma... | Consider any quantum mechanical observable $\hat O$ so that $$\hat O|\psi⟩=o|\psi⟩$$ with eigenvalue $o$. Then for any function $f$ of the observable $\hat O$ we have, $$f(\hat O) \mid\psi\rangle = f(o) \mid\psi\rangle$$
The same applies for a function of the absolute value operator. So if we consider $V(\mid\hat{\mat... | {
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How long ago was the Universe small enough for interstellar travel? Currently, even the nearest stars are lightyears away, and impossible to reach in our lifetimes. If space is always expanding, and was once infinitely smaller, then at what point in the past was space so much smaller that the average distance between s... | As the universe expands each individual galaxy stays roughly the same size, with stars on orbits of roughly constant diameter, so the stars within any given galaxy were no closer together a long time ago than they are now (at least as far as cosmic expansion effects are concerned).
The distances between galaxy clusters... | {
"language": "en",
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Can an electron near thar the positive terminal of a battery make it all the way to the positive terminal? Following Drude's model of conductivity, can an electron near thar the positive terminal of a battery make it all the way to the positive terminal? The electron is in the wire but near the positive terminal. At le... | This question has no answer as electrons are indistinguishable particles.
| {
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When a person pulls or pushes a cart, why is it advantageous for their body be tilted forward? This is not a homework question. I attempted to draw a free body diagram for a person pulling or pushing a cart.
Based on Newton's third law, the following forces act on the body of the person:
*
*forward reaction force don... | It adds a horizontal component to the vertical force exerted by your legs.
When you're standing straight up, the forces exerted by your legs are straight up and down. Your legs are designed to exert a force to counter your bodyweight and allow you to stand like this, so they're quite strong at countering this force.
Wh... | {
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When a car accelerates relative to earth, why can't we say earth accelerates relative to car? When a car moves away from a standstill, why do we say that the car has accelerated? Isn't it equally correct to say that the earth has accelerated in the reference frame of the car? What breaks the symmetry here? Do the force... | To be pedantically correct, one should perhaps say that the friction of the wheels on the ground serves to both accelerate the car by a macroscopic amount in one direction, and accelerate the combined center of mass of everything else on Earth by a microscopic (or maybe "femtoscopic") amount in the opposite direction. ... | {
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Calculating uncertainty from significant figures of a value A question in Giancoli's Physics for Scientists and Engineers (2. ed) has me confused. Here it is (Ch 1, Problem 3):
What is the area, and its approximate uncertainty, of a circle of radius $2.7 \times 10^4$ cm?
I got the correct answer of $2.3 \times 10^9 ... | Most likely, the authors assume Gauss error propagation in which the error on a function $f(x)$ of a variable $x$ is calculated as $$ \Delta f = \frac{\partial f}{\partial x} \Delta x~.$$ In your case, $f(x) = \pi x^2$ and $\frac{\partial f}{\partial x} = 2\pi x$, and $\Delta x = 0.1\times 10^4$cm (this is the worst ca... | {
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Relation between potential energy and conservative force Does potential energy only happen when the work done is by a conservative force? Or does work done by non-conservative forces also create potential energy?
| Forces can be conservative or non-conservative. But conservative forces do work where this work is equal to the change in potential energy. Conservative forces are also characterized by the fact that the work done by the force that moves an object from one point to another is independent of the path taken between these... | {
"language": "en",
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Are galaxies and clusters of galaxies much denser when we observe the 'past' far universe than the 'present' closer part of the universe? Are galaxies and clusters of galaxies much denser when we observe the 'past' far universe?If the universe is expanding, the galaxies should have been much closer in the past so shoul... | Clusters of galaxies generally become denser over time, because they accrete more nearby galaxies as time goes by. In addition, galaxies orbiting within a cluster will tend to lose energy to dynamical friction caused by their interaction with the dark matter in the cluster, so they will gradually sink towards the cente... | {
"language": "en",
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Why do we consider coherent waves interfere as if there is no distribution of energy as the wave progresses? In my textbooks, youtube videos, different websites, I have seen that during calculations regarding interference of waves we derive the equations in such a way as if there is no distribution of energy by waves.,... | Normally we use coherent lasers or collimated beams of coherent atoms in interferometers. The spreading of the waves in the transverse directions relative to the propagation is taken to be negligible over the extent of the wave propagation. Even if this isn't so, the phase of the wave is independent of the amplitude, t... | {
"language": "en",
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Clarification of labeling of Lorentz transformation I read a labeling of Lorentz matrix labeling $\Lambda^\mu_\nu$. To be more specific, it's used as $x^\mu\rightarrow \Lambda^\mu_\nu x^\nu$.
I want to ask:
*
*What does the indices $\mu$, $\nu$ mean in $\Lambda^\mu_\nu$?
*What does $x^\mu\rightarrow \Lambda^\mu_\nu... | *
*Τhe indices $\,\mu,\nu\,$ take the values $\,0,1,2,3$. The value $\,0\,$ corresponds to the time coordinate $x^0=c\,t\,$ while the values $\,1,2,3\,$ correspond to the space coordinates $\:\:x^1=\mathrm x,\:\:\:x^2=\mathrm y\:$ and $x^3=\mathrm z$.
*Equation $\,x^\mu\rightarrow \Lambda^\mu_\nu x^\nu\,$ is better t... | {
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Normal force shift for ball kept in cavity
Adapted from JEE advanced paper-1 of 2020
If you see the left side of the Planck which the ball touches, it seems so that as we vary $\theta$, the contribution of the force from that point of contact drops to zero. I have marked the point of interest in paint:
As we reduce... | To simplify first you can visualize what happens with the cavity when incline has an angle zero. The normal reaction on both the edges is same. Direction of normal reaction is vertical upwards opposite to gravity.
When there is incline the sphere is actually also falling towards the right edge. More the θ, more the sph... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/666231",
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Does Earth's rotation affect the orbital velocity of its satellites? We all know about the spin of black holes. That spin and of course it's gravity determines the minimum distance a star can orbit the black hole with a min orbital velocity.
Do we see similar result? Does spin of earth also effect the orbital velocity ... | The effect of black holes on prograde and retrograde orbits is due to frame dragging, which is a general relativistic effect. Hence the effect is microscopic on Earth satellites.
The LAGEOS satellites tried to detect frame dragging around Earth, but did not succeeded directly. NASA has claimed success with GRACE, thoug... | {
"language": "en",
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How do we know that forces "add" like vectors?
As we all know the basic principle of vector addition. construct a parallelogram as shown, and the diagonal would be the resultant vector. As a mathematical method or formula, it is perfect to define the sum of two vectors in this way, because it is nothing but a binary o... | As far as I see, it is an experimental fact. Applying the forces on an object through springs, it is possible to know the modulus of the forces by the spring displacements. Knowing also the direction of them, the forces can be modelled as vectors.
It happens that adding them using the parallelogram rule works either fo... | {
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Confusion on Normal force and its resolution on inclined plane I had the following doubt regarding normal forces and its resolution on inclined plane. (Also I am quite new to SE, so I have no idea how do we upload diagrams to better represent my arguement).
Consider two cases, in both cases there is a inclined plane wi... | The net force normal to the plane is 0 not $mg cos(\theta)$. The block moving on a one-dimensional plane has only one degree of freedom - along the plane. And the force along the plane is $mg sin(\theta)$
| {
"language": "en",
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Are neutrinos' velocities related to their energies? As they are with other particles? I have read extensively about neutrino energies, including in the popular press, and yet velocities of the neutrinos themselves (not the detectors they 'run into' or the leptons they 'create' after interaction) are rarely mentioned..... | Yes, the speed of neutrinos is related to their energy via the usual formula for relativistic energy:
$E_{\mathrm{kinetic}}=E-E_0=\gamma m_0 c^2 - m_0 c^2$
Now, neutrinos have masses of electronvolts ($eV$) or less - we don't quite know yet. But their (kinetic) energies usually are many orders of magnitude more than th... | {
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Where the reaction force from Newton's third law is acting on this body? In the diagram below I have a fire extinguisher sitting upright on a skateboard. Gas is being expelled out of the fire extinguisher and causing the skateboard to move forward (which is to the right in this picture). This would work in a vacuum as ... | When compressed air is forced to flow through a narrow tube like nozzle it is obvious that it will exert force on the nozzle and that force is marked here as B. Well the force will be torque hence will cast force at the upper part of the extinguisher, now if the extinguisher is attached to the skate board to move forwa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/667168",
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Direction of shear along an oblique plane under a compressive force I think this is a low hanging fruit mechanics question. Here is a picture depicting what I am interested in:
Say I have a compressive force (green arrow) acting perpendicular to the blue block's front surface. As the blue block's oblique surface comes... | Sorry if I overlook the difficulty of your question, but you simply decompose the original force applied (green arrow) into a normal and tangential component. The sum of these components should therefore give you the original force. This doesn't work in your case 1. Case 2 is the correct decomposition.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How seriously can we take the success of the Standard Model when it has so many input parameters? The Standard Model of particle physics is immensely successful. However, it has many experimentally fitted input parameters (e.g. the fermion masses, mixing angles, etc). How seriously can we take the success of the Standa... | The Standard Model may have many parameters, but it also talks about many things, each typically only involving a very limited number of parameters. For example, the muon lifetime$^\dagger$ $$\tau_\mu=\frac{6144\pi^3M_W^4}{g^4m_\mu^5}$$depends on only $M_W,\,g,\,m_\mu$ ($g$ is the weak isospin coupling), and the tauon ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Effective Lorentz Factor in Cold Plasma, Razin Effect I was studying about the synchrotron radiation in plasma medium and got stuck at a point. Usually the Lorentz factor is defined in the following way
$$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$
where $\gamma$ is the Lorentz factor, $v$ is the particle's velocity ... | Let me start by defining $\beta = \tfrac{ v }{ c }$, then we can show that:
$$
\beta^{2} = \frac{ \gamma^{2} - 1 }{ \gamma^{2} } \tag{0}
$$
where $\gamma$ is the Lorentz factor.
We can then show that:
$$
\begin{align}
\gamma^{-2} + \beta^{2} \tilde{\omega}^{-2} & = \gamma^{-2} + \left( \frac{ \gamma^{2} - 1 }{ \gamma... | {
"language": "en",
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How to generalize this hydrostatics problem? Preamble
Consider an ideal, incompressible fluid of density $\rho$ in a uniform gravitational field, in a rigid container and in contact with two massless pistons of differing area $A_1$ and $A_2$. At the same level in the fluid as the pistons is a pressure gauge reading zer... | The force in any given pipe is $PA_{i} = gm_{i} + y_{i}\rho g A_{i}$, intuitively it is carrying the mass and the water difference.
The total force is then $P\sum{A_{i}} = g\sum{m_{i}} + \rho g \sum{y_{i}A_{i}}$.
Argue from conservation that $\sum{y_{i}A_{i}} = 0$.
Then $P = \frac{\sum{m_{i}}}{\sum{A_{i}}}g$
In words,... | {
"language": "en",
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Magnetic scalar potential of a straight wire If we have a finite straight wire carrying a current $I$, we can integrate the Biot-Savart Law for the magnetic field along the wire and find the field at every point of the space as:
$$
\mathbf{B} = [0,B_\phi,0]; \quad B_\phi = \frac{\mu_0 I}{4\pi a}(\cos\alpha_1-\cos\alpha... | The two crucial theorems surrounding vector and scalar potentials are
Irrotational Fields Have Scalar Potentials
A vector field $\mathbf{V}$ may be written as $\mathbf{V} = \nabla \Psi$ if and only if $\nabla \times \mathbf{V} = 0$.
Divergence-free Fields Have Vector Potential
A vector field $\mathbf{V}$ may be written... | {
"language": "en",
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If atoms both absorb and emit photons, then why are there still gaps in an absorption line spectrum? In my physics notes there is a section on line spectra, and describing how absorbance line spectra can by used by astronomers to find out what gases are present in a star, should it be emitting white light from its core... | Yes, materials can absorb high energy photons and release it as multiple lower energy photons.
But also important is that the direction of the release is not the same as the absorption. If we have a beam of particular power on an absorptive material that can come to equilibrium, it must radiate that same power. But i... | {
"language": "en",
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Conditions for a planet to become spherical I have a question, from which size/mass will a body in space adopt a spherical shape? Over 500 kilometers wide and/or 1/4 the mass of Pluto?
Something like that, I always had this doubt.
| For a body to become a sphere, it must have sufficient self-gravity to pull itself into the shape of one. However, because the self-gravity of an object depends on its mass rather than size, it means that a body made of a denser material would become spherical at smaller radii than that of less dense material. Addition... | {
"language": "en",
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How much is the inherent quantum-mechanical uncertainty in the definition of the second? Inspired by this other question.
The second is defined such that the electromagnetic radiation whose energy equals the hyperfine splitting of the ground-state of the Cs-133 atom has a frequency of exactly 9,192,631,770 Hz. However,... | This NIST publication is a great source for understanding these errors.
In practice, the clock emits radiation of some frequency to try to excite as many Caesium atoms as possible. The maximum number are excited when the clock's emitted radiation matches the peak resonance frequency of the transition. So, even though t... | {
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"source": "stackexchange",
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Why do rain drops fall with a constant velocity? While reading my physics book. I came across a line that says that:
Rain drop falls with a constant velocity because the weight(which is the force of gravity acting on body) of the drop is balanced by the sum of the buoyant force and force due to friction(or viscosity ... | Here is a slightly different way to think of this. If the net force is zero, the acceleration of the droplet is zero- even though its velocity is not zero. With the acceleration zero, the velocity remains constant as it falls.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/669118",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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"answer_id": 8
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Confusion with Impulse and Work I get Momentum and Impulse as well as Work and energy but struggle when it comes to connecting the two ideas. I understand that an objects KE can change without its momentum changing, Like in a inelastic collision were the KE of the system decreases but the amount of matter moving to lef... | The standard example of a force doing no work is when an object is moving in a circle at constant speed - the force points towards the centre of the circle. Over 180 degrees there is a non-zero impulse; the direction of movement has changed so the momentum vector has changed. However the speed has not changed, so no wo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/669218",
"timestamp": "2023-03-29T00:00:00",
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Finding Average Acceleration with only given angle A car enters a curve in the road with a speed of 32 m/s and emerges from this curve 4 s later with the same speed. However, the direction of the velocity changes by 150 degrees during this time.
What is the magnitude of the average acceleration during this time interva... | We don’t need to know the length of the curve or its radius. We have
$$\displaystyle \text{average acceleration} = \frac{|\Delta \vec v|}{t}$$
We know the change in velocity $\Delta \vec v$ and the time period $t$ so we have everything we need to find the average acceleration.
| {
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Doubt regarding anamolous expansion of water and ice lakes I had a question regarding anomalous expansion of water. So if we have water and we start cooling it up to 4 degrees, water contracts, but after that in the range of 0-4 degree water starts expanding due to hydrogen bonding. The problem was not in this statemen... | The volume of water in ice trays is very small. Hence it has no problem freezing completely as the icy layer doesn't get thick enough to prevent heat loss to the freezer. In a lake or sea, the thickness of the icy layer is a lot more and it provides a lot of thermal resistance. So the lakes do not freeze completely.
| {
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How can the value of charge on an atom be less than that of a proton? The dipole moment of an $\text{HCl}$ molecule is about $3.6×10^{-30} \ \mathrm{Cm}$ and the separation between the atoms of it is about $1.27×10^{-10}\ \mathrm m$. We know that dipole moment, $p=qd$. So substituting the values of $p$ and $d$, we can ... | Whether you believe that this is some sort of time-averaging of point-like electrons moving very quickly, or that the electrons are actually smeared out by the wave function, this is because the electrons in orbit around the atoms are smeared out in orbitals. So, even though we describe the Cl atom as "stealing" the el... | {
"language": "en",
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The relationship between the pressure at the base of a container and the normal reaction on the container This is NOT a homework question. The question here is just an example.
In this question, after both the liquids are mixed and a homogenous mixture is created, I found the effective density of the mixture and found... | To get
the pressure at the base increases by 1/2(rho)gh
presumably you've found that the new density is $\frac{3\rho}{2}$ and done this:
Original pressure is $$2H\rho g + H (2\rho) g = 4H\rho g\tag 1$$
and the new pressure is
$$2H\frac{3\rho}{2} g + H\frac{3\rho}{2} g = \frac{9}{2}H\rho g\tag 2$$
But you should divi... | {
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Clausius inequality leading to absurd result Background: After deriving Clausius inequality, the author of this book derives the following relation:
Consider the cycle shown in the figure in which leg $A \rightarrow B$ is irreversible. In the equation
$$
0>\oint\frac{\mathrm{d}Q}{T}=\int_{A \operatorname{irrev}}^{B} \f... | For the irreversible path between the same two end states, dQ is different than dQ for the reversible path, and in the integral of dQ/T for the irreversible path, you are supposed to use the temperature at the boundary interface between the system and surroundings $T_B$. So for the irreversible path, you should be usi... | {
"language": "en",
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How much longer could Titanic have stayed afloat if it gotten rid of its anchor and chain right after hitting the iceberg? I am wondering how much longer the RMS Titanic could have stayed afloat if the crew had allowed the ship's anchor and anchor chain to fall to the bottom of the ocean immediately after the ship had ... | Titanic weighed 46,000 tons, so removing say 120 tons would have made almost no difference.
She had several long tears well below the water line. Flooding was such that there was no means that could have prevented her sinking. It is quoted as about 7 tons per second. It would have taken just 17 seconds to replace al... | {
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From momemtum Hamiltonian to real space Hamiltonian I know how to calculate a bulk momentum space Hamiltonian from a real space one. For example, given a SSH model $$H=v\sum_ic^\dagger_{iB}c_{iA}+w\sum_ic^\dagger_{i+1,A}c_{iB}+h.c.,$$ its bulk momentum-space Hamiltonian is $$H(k)=\left(\begin{matrix}0&v+we^{-ik}\\v+we^... | The momentum space Hamiltonian you have written down is the full Hamiltonian in the sector of the Hilbert space indexed by the quantum number called the (crystal) momentum. It is a 2x2 matrix because, once we specify the momentum $k$, we still need to specify which sublattice $\sigma$ we are in. Therefore, our full Ham... | {
"language": "en",
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Why $E$ is neglected at large and small $r$ of quantum harmonic oscillator? In obtaining radial solution of quantum oscillator why E is neglected?
Radial equation:
Resource: nouredine zettili.
| $E$ is neglected because in both cases (where $r \rightarrow 0$ and when $r \rightarrow \infty$) there is a term multiplying $U(r)$ that gets very large when compared to the constant $E$.
When $r \rightarrow 0$, this is the term which depends on $\frac{1}{r^2}$; when $r \rightarrow \infty$ this is the term which depend... | {
"language": "en",
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What is the physical meaning of "correlation length"? I am studying phase transitions right now and trying to understand the physical meaning of the concept correlation length. I saw the equations but I still couldn't quite wrap my head around the physical meaning of it. Like is it the length of the correlation between... | In a magnet, atoms with positive spin and atoms with negative spin will cluster together and the correlation length $\xi$ measures the typical size of these clusters. When $\xi$ first reaches infinity, you do not have a single infinitely big cluster yet because even though exponentially decaying correlations are gone, ... | {
"language": "en",
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Why proper time is a measure of space? Recently I've been trying to learn General and Special Relativity by myself. There is an specific thing I do not understand perfectly, proper time in the metric of the space-time.
Take the case of an empty space-time:
$$-c^2 \mathrm d \tau^2 = -c^2 \mathrm d t^2 + \mathrm d x^2 +... | $ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2$
If the result is positive, the equation corresponds to a spacelike worldline segment. It is always possible to find a frame, so that $dt = 0$ and two events linked by the segment are simultaneous for this frame, happening at different spatial locations.
If the result is negative, ... | {
"language": "en",
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How does Upthrust/buoyant force act on an object? I came across this question where, In a container there's water at the bottom , kerosene on top and an ice cube floating between them and I was asked to calculate the ratio of height of cube in ice to that in water:
Now till now my intuition for up thrust was that ther... | A buoyant force results when the pressure pushing up from the bottom of an object is greater than the pressure pushing down from above. For your situation, there is an increase in the pressure as you go down from the top of the cube through the kerosene and another increase as you go down to the bottom through the wat... | {
"language": "en",
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Would somebody feel a magnetic field if they are travelling at the same velocity as a charge? I am little bit curious about how magnetic fields are being generated when a charge moves.
I want to check if somebody travelling along with a charged particle, would that person experience a magnetic field?
How are magnetic f... | Magnetic fields are really created by moving charges.
"somebody " would need to describe how to measure or "feel" a magnetic field, anyway she would "feel" the electric field of the charge.
| {
"language": "en",
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A question regarding commutators in quantum mechanics I propose the following thought experiment:
Suppose we have a beam of identically prepared electrons that is splits into two. The first goes through detector A that detects the $x+y$ where $x$ is the coordinate along x direction and $y$ is the coordinate along the $... | You are assuming that the two beams of electrons are two different systems in identical quantum states. The uncertainty principle limits measurement of two non-commuting observables on one system, but says nothing about measurements on separate systems. If I had two identical systems in identical states, I could just m... | {
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Does deceleration require energy? Consider an apple falling from a tree and striking the ground.
The ground decelerates the apple once it hits it, but the force is not applied over any "distance" - it is experiencing the force when it is in contact with the ground - so no work is done, yet there is a change in momentum... |
The ground decelerates the apple once it hits it, but the force is not applied over any "distance" - it is experiencing the force when it is in contact with the ground - so no work is done, yet there is a change in momentum, what is going on with the energy here?
Assuming that the ground is rigid and the earth is muc... | {
"language": "en",
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How to interpret Einstein's Field equations for 1+0 dimension $x$ in General Relativity? The Einstein field equation for our $3+1$ spacetime dimensions is $$
R_{\mu \nu} - {1 \over 2} g_{\mu \nu} R + \Lambda g_{\mu \nu} = \frac{8 \pi G}{c^4} T_{\mu \nu}
$$
I am learning to navigate through this equation and would appr... | In a $1$-dimensional manifold the Riemann tensor's only component is $R_{0000}=0$ by the tensor's symmetries, so $R_{\mu\nu}=0,\,R=0$. The EFE simplifies to $\Lambda g_{00}=\kappa T_{00}$. The two sides are still not scalar-valued, as they depend on the chosen coordinate system viz. $ds^2=g_{00}(dx^0)^2$.
| {
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Does energy conversion always requires Kinetic energy in some manner to be present? Does energy always needs to be converted into Kinetic form in order to convert into another form? What I mean, is Kinetic energy meta form for all energy conversion? As we can see for electricity to light up the bulb the electrons has t... | To put the point another way, energy transfer always requires motion. In an entirely motionless environment, there can be no energy transfer. Given that motion equates to KE, KE is always involved in the transfer of energy.
| {
"language": "en",
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Angular Velocity via Extrinsic Euler Angles I am wondering if the angular velocity of a rotating coordinate system, if expressed through extrinsic Euler angles, is $(\dot{\alpha},\dot{\beta}, \dot{\gamma})$ since extrinsic Euler angles are rotations about fixed axes so the rates should be orthogonal to each other.
| The Rotation matrix is created with those 3 matrices
Rotation about x-axes with the angle $~\alpha~$
$$\mathbf R_x= \left[ \begin {array}{ccc} 1&0&0\\0&\cos \left(
\alpha \right) &-\sin \left( \alpha \right) \\ 0&
\sin \left( \alpha \right) &\cos \left( \alpha \right) \end {array}
\right]
$$
Rotation about y-axes wit... | {
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How to calculate the density of states near a point for the given dispersion relation? The problem's statement is as follows:
Given that
$ E(\vec{k}) = ak_x^2 + bk_y^2 + c|k_z|$,
Calculate the density of states near $(0,0,0)$.
It's easy to do the integration if $E$ is quadratic in all of the components, but in this ... | To give you the main ideas of the resolution without giving it away, you can work in several steps:
First, you can do a change of variable for $k_x$, $k_y$ and $k_z$ in order to absorb the constants a,b and c so that the spectrum in the new coordinates is
$E=q_x^2+q_y^2+|q_z|$
then, you can do
-a polar change of variab... | {
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Fourier Transform in wavefunction of Free particle I was reading Introduction to Quantum Mechanics by David Griffiths and I am at Chapter 2, page 45. He says that
The general solution to the time-dependent Schrodinger equation is still a linear combination of separable solutions (only this time it's an integral over t... |
$$\Psi(x,t) = \frac{1}{\sqrt{2\pi}}\int_{-\infty} ^{\infty}
\phi(k) e^{i(kx-\frac{\hbar k^2}{2m}t)}dk$$
where $\phi(k)$ is eigenfunction of Schrodinger Equation
for free particle.(I think)
No, you misunderstood your text book.
$\phi(k)$ is a completely arbitrary function.
For any function $\phi(k)$ this $\Psi(x,t)$... | {
"language": "en",
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What do we mean by saying light is a form of energy? "Energy" means "Capability to do work"
We can now write "light is a form of energy" into "light is a form of capability to do work"
Capability can be thought as a Capacity
Whenever we talk about Capability of doing work we have an object that contains the ability to ... | Energy is a physical property of a physical system. There is nothing like pure energy but maybe in Dragon Ball cartoons. Not in our universe.
Therefore, the question if the light is a form of energy is not consistent with known physics.
What can be safely said is that light, either described as electromagnetic waves or... | {
"language": "en",
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Bull in a china shop: Is there a measure of level of organization of energy (flow) to do work? The discussion around the second law of thermodynamics and creation of orderly structures (e.g. life, evolution, etc.) is an old one. Now that creationists learned the difference between open vs. closed/isolated systems, one ... | Yes, it is called exergy, which is the work that can be extracted from a thermodynamic energy flow. It is equal to the amount of energy input times the Carnot efficiency.
For photosynthesis the relevant amount of energy is about $1 \ \text{ kW m}^{-2}$ and the relevant Carnot efficiency is about 0.95 (the Carnot effici... | {
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A Question About the Surface of a Black Hole Singularity In Kip Thorne's book, Black Holes and Time Warps, he states that the mass of the core of a star shrinks until quantum gravity takes over. And then discusses that at this distance, the singularity cannot be distinguished from quantum foam. I am confused. Is he ... | In Thorne's book, on page 477, it says "Because all conceivable curvatures and topologies are permitted in side the singularity, no matter how wild, one says that the singularity is made from a probabilistic foam. John Wheeler, who first argued that this must be the nature of space when the laws of quantum gravity hol... | {
"language": "en",
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Why are photons being identical particles? Recently, I study quantum optics and deal with quantization of EM field in a cavity. We know we can express/quantize vector potential in terms of $\hat{a},\hat{a}^{\dagger}$ to get a quantized EM field in a cavity.
$$
\vec{A}(\vec{r},t)=\sum_{n,\sigma}\sqrt{\frac{\hbar}{2\epsi... | Calling photons indistinguishable particles is an artefact of thinking of them as fermion-like particles, rather than excitation quanta of electromagnetic field - the phrase is used to make the point to those (yet) unfamiliar with second quantization (see also this answer). If you take a specific mode of the field, wit... | {
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How do stars produce energy if fusion reactions are not viable for us? From what I've learned, fusion reactions are not currently economically viable as of right now because the energy required to start the reaction is more than the energy actually released. However, in stars they have immense pressures and temperature... | The problem is not with “creating” fusion: we have H-bombs that will do this. The technical difficulty is with controlling the very exothermic fusion process, so the whole thing doesn’t blow up violently.
| {
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Will Helium any time in the future make up the most part of the Univers? as Stars are using Nuclear Fusion to produce energy, will there theoretically be a time in the future of the universe where helium will take over hydrogens first place as the most common element in the universe?
| It is actually probable that this will happen. It's not easy to work out when in the universes' history this will happen, but some scientists (by looking at the ratio of hydrogen/helium in the universe after 13.7 billion years of universal evolution) estimate that helium, by the fusion of hydrogen, will become more abu... | {
"language": "en",
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Testing Lorentz force on a moving macroscopic charged conductor? Did anyone ever made an experiment with a moving macroscopic charged conductor in a magnetic field testing its deviation due to Lorentz force? I mean: what moves here is the massive charged conductor itself, not only the charges inside it. Would it be fea... | A macroscopic object with charge $q$ will not experience a magnetic force of the form $${\bf F}=q(\bf v\times B)$$ if it were to pass through a magnetic field $\bf B$
And of course if there is an electric field, then we have the full form of the Lorentz (electromagnetic) force $${\bf F}=q(\bf E+ v\times B)$$
and charge... | {
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Why is there a discrepancy between $m_n-m_p$ and $m_d-m_u$? The difference in mass between a neutron and a proton is $1.3\space {\rm MeV}/c^2$, but the mass difference between an up quark and a down quark is $2.5\space{\rm MeV}/c^2$. How come the mass differences aren't the same?
| Some comments mention that calculating the mass of a nucleon is extremely complicated, which is true: see lattice QCD. It does require a supercomputer. But the strong force is insensitive to quark flavor, so I'm not sure that any of that complexity is related to this question.
The quark flavors differ not only in mass ... | {
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How do we measure time? I'm having a little trouble trying to put to words my problem and I apologize in advance for any causation of trouble in trying to interpret it.
We define periodic events as those events that occur over equal intervals of time. But, don't we use periodic events themselves to measure time (like a... | As Marco Ocram describes in the answer above, you will not notice any change in the rate of time inside a closed system. You can only measure a changing rate of time with relation to some other place where time runs at a different rate.
So, for example if we were to take your house, family and all your clocks and put ... | {
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Euclidean propagator expression for massless particle Let $\Delta_F(\tilde{x})$ denote the Feynman propagator in the Euclidean variable $\tilde{x}$, in $D$ dimensions,
$$\Delta_F(\tilde{x}) = \int \frac{\text{d}^D\tilde{p}}{(2\pi)^D}\frac{e^{i\,\tilde{p}\cdot\tilde{x}}}{\tilde{p}^2+m^2}.\tag{1}$$
Since this expression ... | $$
e^{ip\cdot x}= e^{i|p|r \cos \theta}
$$
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How do conservative forces do work on a mechanical system if they conserve mechanical energy? The question arises from my confusion over the two definitions of work (relevant to classical mechanics) I've encountered:
*
*$W= \int \vec F\cdot\mathrm{d}\vec x$
*$W=$ net change in energy of a system
We define the mecha... | Your second definition is incorrect. The total work done on a system by all forces is equal to the change in kinetic energy, not total energy. So, gravity pulling a mass down does work that increases its kinetic energy. Non-conservative forces change total mechanical energy, conservative forces do not. They can both do... | {
"language": "en",
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How can the electron in a hydrogen atom have energy without angular momentum ($n>0$, $\ell=0$)? Been struggling with this concept. Or is this just one of those things in quantum mechanics which attempting to understand is futile? Guess we can see it as the electron just linearly oscillating back and forth but it doesn'... | Classically a particle without angular momentum will have a radial orbit. This is the closest classical picture to an s-orbital. The orbital is spherically symmetric because the orientation of the orbital is undetermined
| {
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Do sunrises and sunsets look the same in a still image? A question that popped into my head: if I see a picture of the sun close to the horizon, in an unknown place, can I know if it was taken at sunset or sunrise?
Do sunrises and sunsets look the same in a still image? Can one tell them apart?
| Yes, the temperature of the air that the sunlight goes through to reach our eyes would be different.
At sunset the air would be warm, at sunrise it's colder and that causes the light to refract differently.
This website shows more about it
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can we make the energy levels of an one-dimensional infinite square well potential equispaced? We know that the energy values for an one-dimensional infinite square well potential is given by $$E_n = \frac{n^2{\pi}^2{\hbar}^2}{2ma^2}$$ where $a$ is the width of the well. Now, as we can see that the difference in en... | the question is not very well defined because it is not clear what we are allowed to change. One thing I can think of is if we make the particle massless, then the energy disperssion becomes linear. We don't have $E_p \propto p^2$ but rather $E_p \propto p$. So if we have $H=\sqrt{c^2p^2 + m^2c^4} + V(x)$ and set $m=0$... | {
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If space is a vacuum, how do stars form? According to what I have read, stars are formed due to the accumulation of gas and dust, which collapses due to gravity and starts to form stars. But then, if space is a vacuum, what is that gas that gets accumulated?
| Basically speaking, the space used to be a gigantic nebula, but most of it collapsed, forming the primordial stars. These stars went supernova, spreading it's material throughout space and making nearby nebula collapse. This process goes on, with the difference that the new stars have heavier elements. This is an overs... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/676131",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
"answer_count": 6,
"answer_id": 2
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Why are time-ordered Greens functions equal to retarded Greens functions at zero temperature? When I calculate a photon polarization diagram:
I get the same answer:
*
*If I calculate it in equilibrium (retarded Greens functions) with finite chemical potential, in the limit of zero temperature, or
*If I calculate i... | assuming you work in perturbation theory, at zero temperature the (unperturbed) state is the vacuum, meaning that $\psi_k(t)|0\rangle = 0$, so the only part of the retarded GF $$g^r(k, t) = \theta(t)\langle 0 | \psi_k^{\dagger}(0)\psi_k(t) + \psi_k(t) \psi_k^{\dagger}(0) | 0 \rangle$$ that survives will give the same r... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Rotating Rod and conservation of energy The question says "A uniform rod of length L and mass M is free to rotate on a frictionless pin passing through one end (Figure is attached below). The rod is released from rest in the horizontal direction"
(a) What is the angular speed of the block when it reaches its lowest pos... |
I assumed the total mass is to be at center of mass which makes I as M(L/2)^2 but am ending with an incorrect solution.
Its very incorrect way of finding moment of inertia. Moment of inertia is found by:
$$I=\int r^2dm$$
So $I$ depends on the distribution of mass from the axis, and not the center of mass.
The standar... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/676518",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Intuition for Spin operator in arbitrary direction I understand why the Spin operators in $x$, $y$ and $z$ direction are given by : $\begin{align*}
S_x = \begin{pmatrix}
0 &\hbar/2\\
\hbar/2 & 0
\end{pmatrix}
S_y = \begin{pmatrix}
0 & -i\hbar/2\\
i\hbar/2 & 0
\end{pmatrix}
S_z = \begin{pmatrix}
\hbar/2 & 0\\
0 & -\hbar... | I'm not sure what reasoning took you to accept that,
$$S_{x}=\boldsymbol{e}_{x}\cdot\boldsymbol{S}$$
is OK, but let's take it from there. There's nothing special about “$x$”, as opposed to “$y$”, or “$z$”. You could have said $\boldsymbol{n}$, instead of $\boldsymbol{e}_{x}$, and you would have,
$$S_{\boldsymbol{n}}=\b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/676836",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Decomposition of product of two antisymmetric Lorentz tensors Suppose I have a tensor $A_{\mu\nu}$ in the $(3,1)\oplus (1,3)$ representation of the Lorentz group where $(a,b) =(2s_a+1,2s_b+1)$. I was wondering on how to decompose explictly in terms of tensors the prouct $A_{\mu\nu}\otimes A_{\rho\sigma}$ (where it is ... | In general dimension, the decomposition is well understood, it follows from basic Young manipulations. In terms of Dynkin labels
$$
(0,1,0,\dots,0)^2=(0,\dots,0)+(2,0,\dots,0)+(0,1,0,\dots,0)+(0,0,0,1,0,\dots,0)+(1,0,1,0,\dots,0)+(0,2,0,\dots,0)
$$
of dimension
$$
\left(\frac12 d(d-1)\right)^2=1+\left(\frac12d(d+1)-1\r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/676939",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 1
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RMS velocity of a gas vs RMS velocity of a gas molecule, which is a more appropriate term? I'm a bit confused by the terminology. Is it the RMS velocity of a gas, or the RMS velocity of the gas molecules or of a gas molecule?
Similarly, is it the mean velocity of a gas, or the mean velocity of the gas molecules or of a... | The RMS velocity of a gas is the square root of the arithmetic mean of the squares (a particular generalised mean) of its molecules' instantaneous velocities.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677050",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Sound proofing: mass-spring-mass or mass-mass-spring? I am trying to improve the sound proofing of a metal box. The box is made of steel of thickness $0.8 \;\mathrm{mm}$. I have additional sheets of steel with $3 \;\mathrm{mm}$ thickness for reinforcement. For vibration reduction, I have access to some bitumen mats (an... | Try sheets of cardboard. They don't transmit sound well.
Consider if you leave an opening for cooling air flow, you have an opening for sound. Open cell foam might help? Pointing the opening away from listeners?
Computer fans are typically noisier than hard drives. But if it is really the drive, you can get a solid sta... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677162",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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There is a way of making a Balloon lighter than Helium/Hydrogen (or vacuum)? I don't know much about physics, but I wonder if there is a way of making something like a Balloon to float more than Hydrogen, Helium or Balloon with Vacuum.
I say "Vacuum Balloon" because, supposedly, if you had a strong and light enough mat... | No, not in air. Helium is good. Hydrogen is better. Warm hydrogen has an even lower density and is thus even better. Vacuum is as low as it gets, but you need a massive hull to avoid crushing.
All that matters for buoyancy is the difference in density between the inside of your balloon and the outside. So, take an air ... | {
"language": "en",
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What allows this tornado to form in a frying pan? I have just seen this video here where a mini tornado has formed in a frying pan:
https://www.youtube.com/watch?v=6CJ-8ze2FjE
Does anyone know how this happens or where I can find an explanation?
| The window on one side is open providing an asymmetric air supply, and you can hear what sounds like a loud overhead extractor fan running. With the hot pan providing a source of rising smokey hot air, these are great conditions for producing an indoor tornado.
The window appears to be cracked open, forming a vertical ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677401",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Polarization of natural light for double slit interference Last week I performed Young's double slit experiment using a laser. As expected, I obtained an interference pattern as predicted by Fraunhofer theory (enveloped by the 1 slit diffraction curve). Then, I added two polarizers with perpendicular axes in front of e... | Unpolarized light has a polarization vector which varies randomly with time, so at any given time, the polarization at the left and right slots will be the same (and thus they will interfere). However, natural light also has low spatial coherence (i.e. the phase varies across the wavefront over a relatively short dista... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What are the magnitudes of the acceleration of the falling balls B and C relative to A? (Need help with binomial approximation) I'm mostly having a problem incorporating the approximation. My trouble is towards the bottom of the post, but I wrote down all of my steps just in case I made an error somewhere.
So in this ... | When you have an expression of the form $(a + b)^n$, where $|a| \gg |b|$, you can rewrite it as $$(a + b)^n = \left(a\left(1+\frac ba\right)\right)^n = a^n \left(1+\frac ba\right)^n$$ and then, given that $\left|\frac{nb}a\right| \ll 1$ (and $a + b > 0$), apply the binomial approximation to obtain $$a^n \left(1+\frac b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677735",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Time evolution of $\pi/2$ pulses This is the topic Ramsey interferometry. I want to do this without referencing the Bloch sphere, just with the Hamiltonian (given on Wikipedia and below) and Time-Dependent Schrodinger Equation.
A $\pi/2$ pulse in a two-level system is defined as a pulse that sends the excited and groun... |
My question is mainly: what time evolution operators do you apply and when, and when do you apply the unitary operator of the /2
π
/
2
pulse?
You apply the unitary time evolution operator in between the $\pi/2$-pulses. This is in the order that they physically happen during a Ramsey sequence. The evolution of the sta... | {
"language": "en",
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How fast can manned spacecraft slingshot from Black Holes? I've read of Black Holes launching particles at over 99% the speed of light. Could manned spacecraft use Black Holes to slingshot ourselves at this speed, or would the G forces kill us?
Intuitively, I worry the inertia of turning the curve would kill the crew.
| This won't work unless the black hole is orbiting something else. It doesn't make a lot of difference to this whether we use a black hole or any other type of body - it's just gravity and conservation fo momentum and energy at work.
If you just had an isolated body and approached it, a slingshot won't happen. All tha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/678120",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is there any sensor that creates a visual image of magnetic fields? I am working on a project where I am trying to create a magnetic tag that can be detected from $20 - 50$ cm away. Is there any sensor on the market capable of this?
| You maybe interested in looking here:
Magnetic field gel based viewing film
or for more advanced applications the ferrolens (commercial product named Ferrocell).
However these optical magnetic sensors need more likely to be in physical contact with the magnetized matter and have a sensitivity at about 400 Gauss (i.e. 4... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/678210",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
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The effect of gravitational lensing during the lunar eclipse During the lunar eclipse, the Moon turns into bloody colour while the shadow of the Earth is casting over the lunar surface. The red hue can be explained by means of the refraction of light and Thomson scattering. Besides these two, will the gravitational len... | Earth's gravity is far to weak to make much difference. But the Sun's gravity makes a solar lens that could be used as a telescope, if we devoted enough resources and ingenuity to it. We could literally map the surface of an exoplanet $100$ light years away at $25$ km/pixel. See The Solar Gravitational Lens will Map Ex... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/678331",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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If a person drops a briefcase in an elevator and it does not fall to the floor, what is the elevator's aceleration? I read this question on my Physics book and I'm still wondering whether my answer is right. My first thought is that the elevator is accelerating downwards. If it were accelerating upwards the briefcase w... | If the briefcase remains in equilibrium with the elevator, then the elevator is accelerating downwards. This means that $a=-g$, where the minus sign means the motion is downwards.
If the briefcase rises to the elevator's ceiling, then $a \geq -g$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/678492",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
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Question about indices and matrix This is essentially a trivial question, which can be answer probably immediately, but i have this doubt anyway.
If, say, $$\Lambda^{a}_{b} = \begin{pmatrix}
f & -fc\\
-fc & f
\end{pmatrix}$$
$$\Lambda^{b}_{a} = \begin{pmatrix}
f & -fc\\
-fc & f
\end{pmatrix}^T or \begin{pmatrix}
f & ... | The tensor indices can represent matrix elements, but to do so you have to give them an order! Placing them one on top of each other is ambiguous. For example:
$
\Lambda_a \,^b
$
has as rows $\Lambda_0 \,^b$.
Then there is another issue. Transposing a matrix means interchanging its indices only if they are both contrav... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Deriving Hartree from fundamental atomic units leads to error? I am trying to find how many newton meters are in a Hartree by using the following definition in terms of other physical constants:
$$E_h = \frac{\hbar^2}{m_ea_0^2} $$
The values of the other physical constants in SI units (according to Wikipedia and the NI... | You are comparing
\begin{align}
E_h &= 4.359\ 744\ 722\ 2071(85)\times10^{−18}\ \mathrm J \\
\\
\frac{\hbar^2}{m_e a_0^2} &= 4.359\ 744\ 722\ 2232\ 755 \times 10^{-18}\ \mathrm J
\end{align}
Your final digits $\cdots 755$ are superfluous, smaller than the uncertainty. Your disagreement is
$$
\frac{(\cdots 2232) - (\cd... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/679193",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why doesn't a parallel circuit violate conservation of energy? Let's imagine a hypothetical circuit where there are a large number of wires placed in parallel to each other, hooked up to a simple power source.
We know that voltage at each wire would be equal $V_{total}=V_1=V_2=...=V_n$ where $n$ approaches a large numb... | It does not violate the conservation of energy rule. If you add more parallel wires instead of a single wire, the charge will get distributed between multiple wires but the total charge $Q$, which in second case will be the sum of all the smaller charges pushed through multiple wires, will stay the same. Attempting to ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Vector operator formulation I showed that the ladder operators: $ \hat{\overrightarrow{a}}=(a_x, a_y , a_z)$ and $\hat{\overrightarrow{a}}^{\dagger} = (a_x^{\dagger}, a_y^{\dagger} , a_z^{\dagger})$ can form a vector operator by proving:
$$ [J_k, a_l] = i \hbar \varepsilon_{klm} a_m \hspace{1,5cm} [J_k, a_l^{\dagger}]... | You would first find a linear combination of your operators so that
$$
[\hat J_+,\hat{T}^\ell_m]=0\, ,
$$
and once you have that you can ladder down using
$$
[\hat J_-,\hat T^\ell_m]=\sqrt{(\ell+m)(\ell-m+1)}\,\hat{T}^{\ell}_{m-1}\, .
$$
This does not fix the “norm” of the operator, i.e. $A\hat T^{\ell}_m$ also has the... | {
"language": "en",
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Solve the stationary Schrödinger equation with the finite difference method I am trying to solve the stationary Schrödinger equation for a double-level well potential through the finite difference method.
Here is the shape of the potential I would like to solve it for
where the second walls are infinite.
The Schröding... | First of all, I suspect one can solve this problem analytically.
As for scipy.linalg.eigh() (https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.eigh.html), you just include V in matrix a.
| {
"language": "en",
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"source": "stackexchange",
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Interpretation of $\oint PdV\neq0$ I hope you are excellent. I'd like you to help me make sense of the integral $ \oint PdV \neq 0 $ for some thermodynamic process. What can it mean for the integral to be nonzero? I can only interpret it as if there is work, however my deep understanding is very limited. I apprecia... | Given integral repersent the work done to a closed path . Which is non zero means think as a non conservative force you will get intuition. Since force is directly related to pressure and then work done work done. hope this answer might help you to why work done through a closed path is non zero.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/679868",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If I lift a body with a force greater than its weight, what will happen to the excess energy provided to the body I will give an example to explain my question.
Case 1:
An elevator lifts body a with force equal to its weight for a distance $d$
*
*Energy given to the body (work done)$=$ Weight $×$ $d$
*Amount o... | Elevators go through a phase of acceleration, constant speed and then deceleration.
It is only during the acceleration phase that the force is greater than the weight of the elevator and contents. The 'excess' force is converted into kinetic energy.
During constant speed (by definition) the force is EQUAL to the weight... | {
"language": "en",
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Why does a body accelerate when there is a force applied to it? Why does a body accelerate or changes velocity when a force is applied on it?
How force acts upon things to make them accelerate?
| Frame challenge: Your question doesn't make sense; nor can it be readily answered in words
cause i am from another world and i don't know about these things
One thing that we assume for physics is that the laws of physics (such as we understand them) apply everywhere. Time and space may behave differently around mas... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Microstates of the canonical ensemble In the micro canonical ensemble the microstates of a system in an arbitrary macrostate, are also eigenstates of the Hamiltonian. Does the same apply to the microstates of the canonical ensemble? Are they eigenstates of the the Hamiltonian? I would expect them not to be, since here ... | When talking about the canonical ensemble, one has to distinguish
*
*the Hamiltonian of the system of interest, $H_S$
*the Hamiltonian of the system of interest + bath/thermostat/reservoir, $H_{tot} = H_S + H_B + V_{SB}$
$H_{tot}$ is treated in a microcanonical ensemble framework, and hence we are discussing its eig... | {
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What is the relationship between a boost transformation and a high energy limit? S-matrix element is calculated by a following formula,
$$S_{\beta \alpha}=\langle \beta_{in}|U(+\infty,-\infty)|\alpha_{in}\rangle.$$
The time-evolution operator $U(+\infty,-\infty)$ is
$$U(+\infty,-\infty)=T\exp\Big(i\int^\infty_{-\infty}... | Start at the classical level. Say that in frame 1, a point particle is moving slowly in the $x$ direction. Frame 2, is related to frame 1 by a big boost in the $z$ direction. What is the particle doing in frame 2? It is still moving slowly in the $x$ direction, but it also has a huge momentum in the $z$ direction. So a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/681248",
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Physical reasons for why systems are chaotic? Are there any reasons why a system would exhibit chaotic behavior? Or is this something only found through numerical modelling or experimental testing?
For example, the simple forced, damped pendulum or the duffing oscillator. Were these experimented on and it was found tha... | In a chaotic system, if you start with two initial states that are nearly identical, they will diverge from each other exponentially. Soon they will be in completely different states.
Note that this implies the system will have no stable repetitive paths through its state space.
Consider the example of the frictionless... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Will electric field cause electrons to move in disconnected wire? Imagine a straight piece of wire, not connected to anything. Parallel to one of it's ends is a section of circuit with direct current in it. They're placed in such a way, that only about 1/4 (or less) of disconnected wire is near a powered circuit. Quest... | If you had an electric field, charge separation would build up in the disconnected conductor such that the electric field inside the conductor was zero. This movement of charges would constitute a current that very rapidly decayed to zero.
However, neither of the diagrams you show appear have a changing magnetic field ... | {
"language": "en",
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Finding the resonance frequency for forced damped oscillations I have a problem regarding a forced, damped harmonic oscillator, where I'm trying to find the resonance frequency. I have calculated the frequency for free oscillations as $$\omega_{free}=\sqrt{\frac{\kappa}{I}-\left(\frac{b}{2I}\right)^2},$$ where $b$ is t... | Resonant frequency which people define as $\omega_0$ is not the frequency with maximum osccilation, https://youtu.be/Y_DmzZcQR7A Walter lewin explains this at 20:00
$\omega_{max}$ is.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/682059",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why there is no reaction Deuterium + Deuterium $=\rm {}^{4}He$? Why there is no reaction like
$D+D={}^{4}He$
specified here and in other places like this?
Apparently
$2\times2.0141-4.0026=0.0256$
is positive. What is the problem with this reaction?
| According to Krane's Introduction to Nuclear Physics (Chapter 14), the reaction
$$
D + D \to {}^4\mathrm{He} + \gamma
$$
is possible but rare. The gamma ray is necessary because (as you note) there is energy released in the reaction, and it has to go somewhere. However, the $Q$-value for this reaction (23.8 MeV) is g... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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What would happen if a teaspoon of neutronium crashed through Earth's atmosphere? Pretty self explanatory hypothetical. I realize this is probably an impossibility and maybe it'd be more likely to be hit by a small black hole or primordial black hole. I'm just curious, because we always talk about how much a teaspoon ... | The teaspoon of neutronium would have a mass of about $10^{12}$ kg.
Due to it's small size (and area), the pressure caused by the impact would be very high, so it's likely to plough straight through the earth and out the other side.
It depends on the velocity, but things coming from space are usually moving fast.
As th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/682568",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Simple oscillator displacement, speed, and acceleration diagram I'm currently studying the textbook Fundamentals of Acoustics (2000) by Kinsler et al. Chapter 1.2 The Simple Oscillator says the following:
$$\dfrac{d^2 x}{dt^2} + \omega_0^2 x = 0 \tag{1.2.5}$$
This is an important linear differential equation whose gen... | Express displacement $x$, speed $u$, and acceleration $a$ via the same trigonometric function with positive amplitude:
$$x(t) = A \cos (\omega_0 t + \phi) = A \sin (\omega_0 t + \phi + \frac{\pi}{2})$$
$$u(t) = - \omega_0 A \sin(\omega_0 t + \phi) = \omega_0 A \sin(\omega_0 t + \phi + \pi)$$
$$a(t) = -\omega_0^2 A \cos... | {
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"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
Observing relativistic motion from afar If I were to look at a clock from a very far distance ( let's say 10 light-years away ), and the clock starts to move on a direction perpendicular to my line of sight, with a speed approaching c (e.g. 0.999c), will I see the clock ticking at a different rate (slower/faster) than ... | Yes, you would see the clock running slowly- the result of the transverse relativistic Doppler effect. See https://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Transverse_Doppler_effect
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/684076",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Mathematical background required for Lagrangian Field Theory? I want to start teaching myself Lagrangian Field Theory. I can do multivariable calc, tensor calc, Lagrangian mechanics, and some calculus of variations. Are there other math fields I should study before diving in to field theories? I’m hoping to work my way... | I am no expert on the field, but when I was in college I was taught many concepts in Lagrangian and Hamiltonian mechanics that required group theory. It would be nice to have it on your maths background, apart from the ones you already have.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/684465",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How does spontaneous symmetry breaking (SSB) happen? I've just finished studying for an exam on the Standard Model (so electroweak theory and symmetry breaking) and I can't figure out how this question never crossed my mind. I'm now studying the QCD chiral symmetry breaking, but I think my question applies to any (phys... | I'm just sketching the trail map of where your question might wish to go... it is a subject of limitless complexity.
The universe cools down, and thermal QFT dictates mutation of the Higgs potential with temperature, section 3.
This mutation of the effective Higgs potential from the form favoring the symmetric phase to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/684630",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
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