Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Mass loss in Red Giants via dusty-winds and chromosphere activity I'm reading some literature on mass loss in the RGB/AGB branches and so far I'm getting a lot of information regarding mass loss via dusty-winds/pulsations but almost no explanation of mass loss by 'chromosphere activity'. I asked my mentor about it and ... | I guess what is meant is mass loss powered by non-radiative heating occurring above the photosphere. i.e The outer atmosphere is heated by magnetic Alfven waves and causes a wind to stream away from the star. The same magnetic field is responsible for heating a chromosphere - a hotter layer above the photosphere.
Here ... | {
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What is the RC time constant in a superconductor? In conventional conductors, the RC time constant is the time required to charge or discharge a capacitor through a resistor by ≈ 63.2 percent of the difference between the initial value and final value:
$$\tau = R \cdot C $$
However, in a superconductor, the resistance ... | The RC constant is not fundamentally related to the speed of signals. It is derived from an equation which already assumes the speed of signals in your circuit is effectively infinite. Therefore there is no relativistic constraint on RC time. To arrive at a formula which takes into account the propagation time you woul... | {
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"source": "stackexchange",
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A water pipe from sea level to beyond the atmosphere If a pipe extended from just above the ocean floor to outside the atmosphere, would water be sucked up it by the vacuum beyond the atmosphere? If a hole was made in the pipe, above sea level, how would that affect the flow of water? Would it stop it completely?
| Ask yourself this: why doesn't the vacuum of space just suck away our atmosphere? The reason is because of the earth's gravity, which pulls on the gas envelope around the planet to keep it in place. The phenomenon we call 'air pressure' is also the result of this.
The tube will only fill until its contents are being... | {
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Are Lagrangians and Hamiltonians used by Engineers? Analytical Mechanics (Lagrangian and Hamiltonian) are useful in Physics (e.g. in Quantum Mechanics) but are they also used in application, by engineers? For example, are they used in designing bridges or buildings?
| I'm not an engineer myself, but as far as I know, Lagrangians and Hamiltonians have their use in complicated but calculable situations. In order to solve the e.o.m. for a bridge or so, most engineers rely on specific programs for exactly such a purpose that calculate the statics using Newtonian mechanics and a finite e... | {
"language": "en",
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Does general relativity fail in conditions with very large gravitational forces? It is said in this wikipedia article (in the 7th paragraph) that where there exists huge masses and very large gravitational forces (like around binary pulsars), general relativistic effects can be observed better:
By cosmic standards, g... | The whystringtheory page is written in a popularized style that makes it impossible to tell what they really have in mind. Their statement doesn't make sense if interpreted according to the standard technical definitions of the terms. GR doesn't describe gravity as a force. In the system of units normally used in GR, w... | {
"language": "en",
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How is energy extracted from fusion? I understand that combining deuterium and tritium will form helium and a neutron. There are three methods to do this (1) tokamak (2) lasers and (3) cold fusion. I would like to know after helium is formed. How is that energy extracted from tokamak and stored?
| As others mentioned it depends on what the product is of the reaction. It's hard enough to get deuterium-tritium reactions to happen efficiently, but if we get the science down it usually gets more efficient as we scale up. If we can get p + B11 -> 3 He4 to work it yields 3 highly energetic He4 ions (alpha particles), ... | {
"language": "en",
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Change of orbit with radial impulse This probably is dumb question, but it has been giving me issues for days.
I was thinking about a point of mass $m$ in a circular orbit around a planet. The question is: giving a radial impulse, what is the change in the shape of the orbit? Will it change in another circular orbit? ... |
Will it change in another circular orbit?
The radial velocity of a circular orbit is zero. Since the radial impulse imparts a radial velocity to the point mass, the new orbit cannot be a circular one.
Or maybe will undergo a spiral motion ?
No, assuming two ideal point masses in the Newtonian context and no drag, ... | {
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Absorption & emission spectra The process of obtaining an absorption spectra involves passing a complete spectrum of light from the material under consideration. The material absorbs the specific wavelength and allows the rest to pass through. But the reason of this absorption is given as the specific quantum gaps betw... | You do not state your question clearly
But the higher energy state is considered to be unstable and thus the electron will fall back immediately and would again give the wavelength preventing any spectra to be formed. The same doubt is in emission spectra when used to describe various flame colours but the same doubts... | {
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Calculating the torque at a point when a motor is stopped? So, I'm trying to solve for the torque $\tau_A$ of a motor. I have attached a strong stick to the motor, like so:
I apply a force $F$ on the stick which stops the motor. The distance from the outside edge of the cylinder to the end of the stick is $L$. The tor... | The first part of your analysis is right. Your hand exerts a torque
$$\tau_{hand} = F(L+r)$$
about the center of the disk. The disk is stationary, so it must have zero net torque on it, so
$$\tau_A = -F(L+r)$$
As long as the system you want to analyze is the disk and rod together, that's the end of the story.
Evidentl... | {
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How can you weigh your own head in an accurate way? I read some methods but they're not accurate. They use the Archimedes principle and they assume uniform body density which of course is far from true. Others are silly like this one:
Take a knife then remove your head.
Place it on some scale
Take the reading
re-attach... | If you can find a way to calculate the density of your head by looking at the amount of the head that is - for example - bone, brain or space, and take the density of each of them, then you could get an average density for the whole head. Then simply measure the volume of the head by possibly submerging it and work out... | {
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Vectors with more than 3 components
*
*I have some confusion over Vectors, Its components and dimensions. Does the number of vector components mean that a vector is in that many dimensions? For e.g. $A$ vector with 4 components has 4 dimensions?
*Also, how can a Vector have a fourth dimension? How can we graphically... | The most basic way to imagine 4 dimensions (or more) is as follows:
Picture four straight lines that are all perpendicular to one another. Imagining 3 mutually perpendicular lines is not a challenge, it's the fourth one that's a challenge. The reason for our three dimensional vision is that our retinas are only a 2 dim... | {
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How does autorefractor work? Autorefractors are being used by eye opticians for eye diagnosis. I searched internet for articles and wiki page as well but I wasn't satisfied. I am interested to know how do they actually work. How the machine is able to focus sharp on retina automatically. How do they figure out spherica... | the autorefractor projects an image into the eye. the light rays pass through the lens and strike the retina. a small amount of the light bounces off the retina, passes through the lens a second time and exits the eye. Imperfections in the shape of the eye's lens distort and defocus the "return" image. the autorefracto... | {
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Are quantum effects significant in lens design? Over on Photography, a question was asked as to why (camera) lenses are always cylindrical. Paraphrasing slightly, one of the answers and follow-up comments asserted that quantum effects are significant and that you need to understand QED in order to understand lens desig... | Your intuition is correct, you don't need quantum electrodynamics to explain/model/engineer camera lenses. When considering the propagation of light, the results of geometric optics can be interpreted in terms of path integrals, as Feynman does in his QED: The Strange Theory of Light and Matter, but this is not necess... | {
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What is physics behind of explosion under Atmospheric pressure? An explosion is a rapid increase in volume and release of energy in an extreme manner.
A blast wave in fluid dynamics is the pressure and flow resulting from the deposition of a large amount of energy in a small very localised volume.
The equation for a F... | If I understand correctly what you're asking, you are referring to the vacuum created from an explosion. Think about it like this: An explosion is rapidly expanding gas from a central point (the explosive material). As that gas expands, it pushes all of the material (the gas of the atmosphere) away from that central po... | {
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Is there an EMF in a conductor moving at constant speed across the uniform magnetic field If a conductor - a long rod - moves at constant speed across the "lines" of a uniform magnetic field, is there an EMF within this conductor? Or, if a conducting rod rotates at uniform rate, pivoted in the middle or at one of its ... | Faraday's law relates to the amount of energy a charge would gain by going around a loop. This energy per unit charge is called an "EMF". Because there is no change in the flux through any surface in this situation, there is no loop that gives a charge a different energy.
This doesn't mean that there is no path that gi... | {
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1D Ising Model with different boundary conditions The Hamiltonian for one-dimensional Ising model is given by,
\begin{equation}
\mathcal{H} = -J\sum_{<ij>} S_iS_j; \quad i,j=1,2,...,N+1
\end{equation}
where $<ij>$ denotes that there is nearest neighbor approximation. The partition function is given by,
\begin{equation}... | 1.
\begin{equation}
\mathcal{Z}(N+1,+)= \sum_{S_1}...\sum_{S_N} e^{K(S_1S_2+S_2S_3+...+S_{N-1}S_N}e^{KS_N}
\end{equation}
where $K=\beta J$.
We define new variables,
\begin{equation}
\eta_i =S_i S_{i+1}; \quad i=1,2,...,N-1
\end{equation}
The $\eta_i$s take value:
\begin{equation}
\eta_i= \left\{
\begin{array}{l l}
... | {
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What causes a black-body radiation curve to be continuous? The ideal black-body radiation curve (unlike the quantized emission seen from atomic spectra), is continuous over all frequencies. Many objects approximate ideal blackbodies and have radiation curves very similar in shape and continuity to that of an ideal bla... | If the absorptivity of a medium really was discrete, then there would be no way it could emit blackbody radiation. The defining characteristic of a blackbody is that it absorbs light of all frequencies that are incident upon it (and that it is in thermal equilibrium). There is a close relationship (a direct proportiona... | {
"language": "en",
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What is the probability density function over time for a 1-D random walk on a line with boundaries? If a single particle sits on an infinite line and undergoes a 1-D random walk, the probability density of its spatio-temporal evolution is captured by a 1-D gaussian distribution.
\begin{align}
P(x,t)&=\frac{1}{\sqrt{4 \... | This can probably be solved by the method of images, depending on your precise formulation of the problem. The main idea would be to place image particles at the initial time at positions given by treating your impassable boundaries as mirrors; this makes the probability flow at the boundary zero.
To give a more precis... | {
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The stability of D-Brane In "String Theory and M-Theory: a modern introduction" by K.Becker, M. Becker and J.H.Schwarz, they say that BPS D-brane is stable as it preserves half of the Supersymmetry. I really want to understand more about this statement and see detail calculations. What is the mechanism of D-brane stabi... | BPS objects are stable because they're the lightest objects with given values of certain conserved charges. So there exists no potential final state that would be lighter and that the BPS state could decay into, by conserving the energy. The excess energy may be invested to the kinetic energy of the final energy but a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/71720",
"timestamp": "2023-03-29T00:00:00",
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Understanding the different kinds of mass in gravity On this site, the Phys.SE question Is there a fundamental reason why gravitational mass is the same as inertial mass? has been asked. See also this Phys.SE question. The 'answer' provided on this forum has been that the curvature of spacetime explains both. The answe... | Mass universe is constituted of micro / macro mass natural bodies/systems. It is known that the mass (micro / macro) natural bodies is concentrated mainly in neutrons, protons and electrons as entities with a certain stability, fig. 3.
Fig. 3. (Electro)convergence of the electron/neutron /proton, )[4]
1- Neutron matrix... | {
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What caused scientists to study Black Body Radiation? After spending hours understanding what exactly Black Body radiation and Ultraviolet catastrophe is, I cannot help myself asking what was the reason that scientists such as Wilhelm Wien and Max Planck studied Black Body Radiation in the first place? What intrigued t... | In the late 19th century physics seemed more or less complete, in the sense that it explained everything that could be measured. However when applied to a black body the accepted physics of the day predicted that the black body would emit an infinite amount of energy, and this was obviously in conflict with experiment.... | {
"language": "en",
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What is canonical momentum? What does the canonical momentum $\textbf{p}=m\textbf{v}+e\textbf{A}$ mean? Is it just momentum accounting for electromagnetic effects?
| The whole problem starts when you try to do electromagnetism with the Lagrangian because you can't write the magnetic field in terms of a potential. However we CAN write it in terms of a vectorpotential $\vec{A}$:
$\vec{B} = \nabla\times\vec{A}$.
It seems that this is usefull and can be used to derive the appropriate L... | {
"language": "en",
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Lorentz homogeneous group and observables For generators of the Lorentz group we have the following algebra:
$$
[\hat {R}_{i}, \hat {R}_{j} ] = -\varepsilon_{ijk}\hat {R}_{k}, \quad [\hat {R}_{i}, \hat {L}_{j} ] = -\varepsilon_{ijk}\hat {L}_{k}, \quad [\hat {L}_{i}, \hat {L}_{j} ] = \varepsilon_{ijk}\hat {R}_{k}.
$$
F... | Yes, the comination $j_1 + j_2$ determines the spin of the particle. Note however, that this is an addition of angular mementum which may be complicated.
Furthermore, you can count the degrees of freedom:
In $(j_1, j_2)$, each contribute $2j_1 + 1$ states and we construct a tensor product, so $(j_1, j_2)$ gives $(2j_1 ... | {
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Would connecting p-type and n-type semiconductors work as a diode? If we placed p-type and n-type semiconductors close enough to be touching (see fig. 1), would this arrangement work as a diode? Please explain.
Fig. 1 - Connecting p-type and n-type semiconductors
| A pn junction is one piece of a semiconductor that receives n-type doping in one section and p-type doping in an adjacent section. If you simply stick two p-type and n-type semiconductors to each other by hand, it will not behave as a diode.
The main reason that a pn junction can behave as a one-directional device is i... | {
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What is the sign of the work done on the system and by the system? What is the sign of the work done on the system and by the system?
My chemistry book says when work is done on the system, it is positive. When work is done by the system, it is negative.
My physics book says the opposite. It says that when work is done... | It is just a matter of convention. It should be consistent throughout.
Case 1: Work done on the system is positive.
Here the first law is written as
$$ \mathrm{d}U = \mathrm{d}Q + \mathrm{d}W \,.\tag{1}$$
If your frame of reference is "system", then the work done on the system ($W$) is positive and the heat that is ... | {
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Steering forces on a bicycle I always notice this weird thing and try to overcome it but cant.
As shown in the image when I ride the bike by just one hand and pull the handle back say from the right side so as commonly the handle should rotate towards right and the bike should turn to right. But that doesn't happen. No... | Pulling the right handlebar rotates the front wheel clockwise. This causes the bottom of the bike to move to the right. If you haven't leaned to the right as part of this maneuver then you are now out of balance and leaning to the left (your body hasn't moved, but since the bottom of the bike moved right you are now le... | {
"language": "en",
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Would a small puddle of water evaporate faster if you spread a dry towel over it? Let's say you spill 10ml of water on the kitchen counter. It forms a small puddle that would evaporate after a while (assuming room temperature and sane humidity).
Would spreading a large, dry towel over the puddle cause the water to evap... | I think it would evaporate quicker for anything we normally call a "towel". The evaporation of the plain puddle is limited by the surface area of the water. A towel provides many capillary pathways for the water to diffuse thru the fabric, eventually presenting a much larger surface are for evaporation. Other fabric... | {
"language": "en",
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Reflection, transmission, absorption...how to calculate them? I was wondering whether there is an equation that enables me to calculate the reflection, transmission, absorption and polarization, when the electric field everywhere is given?
Consider this: You have solved the full Mie scattering process, so incident fiel... | For example, you can calculate absorption through integration of the Poynting vector over the surface of the sphere. I am not sure there are any standard general definitions of transmission and reflection for diffraction on a sphere.
| {
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How to prove that we are living in a 3+1D world? Is there any scientific experiment that can lead us to conclude we live in 3 spatial dimensions without the premise of the conception of limited dimensions?
Thank you all who helped in the improvement of this question (which was not clear at first).
EDIT:
I know that th... | First , human brain would not be able to benefit from the great amount of information that electromagnetic force provide about the natural world . Human beings will then resort to mechanical means to interact with the environments .They would develop more sophisticated mechanisms that can sense chemical and mechanical... | {
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Opening the fridge door to cool a room I'm well aware that the default answer to this textbook default question is "it doesn't work", but still, I believe it does.
To cool the insides of the fridge, the compressor must do work, and since the efficiency isn't 100% you are constantly warming the whole room to cool it's i... | NO. What allows a fridge maintain cool inside is the fact that the walls of the CLOSE fridge prevents heat from outside (the room heat) flows to the inside of the fridge WHILE the rate the fridge's compressor is drawing heat out (from the back or lower grills of the fridge). But if you open the door, the same amount o... | {
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About an upside down cup of water against atmosphere pressure There is an experiment we learned from high school that demonstrated how atmosphere pressure worked.
Fill a cup of water and put a cardboard on top of it, then turn it upside-down, the water will not fall out. The explanation said this was because the atmosp... | Atmospheric pressure is caused by air gravity and air molecules movement, air pressure in the half filled upside-down cup is lower than the air pressure outside due to less gravity, so the air pressure can still hold the water in half filled cup.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/73201",
"timestamp": "2023-03-29T00:00:00",
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Why does the guy moving on spaceship look younger in twin paradox? If there is no particular absolute choice of frame of reference, the guy who sits on Earth is also moving away from the guy on spaceship perspective and hence time on Earth should also dilate when viewed from the guy on spaceship perspective. But why do... | I assume the inertial twin is A ,while the one in the spacecraft is B
The relative velocity between A and B is v.
The distance B has to travel is from x0 to x1 as seen by A observer= x1-x0.
The same distance is k*(x1-x0) as seen by B observer,where k =(1-(v^2/c^2))^0.5 because of length contraction.
So from the point ... | {
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What do you call the period after sunrise when the sky is bright? At sunrise, the sky isn't actually up in the sky yet. Twilight occurs before sunrise, then at sunrise the leading part of the sun crosses the horizon. But, the sky isn't bright yet. It takes some time for the sky to be blue again.
Then, at the closing of... | The time after the Sunrise is known as Morn.
| {
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} |
Fukushima vs Thorium This is not a question about traditional nuclear power plants vs the thorium based. But about the Fukushima plant itself and the very negative environmental effects from its meltdown of reactors 1 and 3 vs a Thorium based design under similar natural stressors.
Fukushima leaking radioactive water ... | This is not so much a question of nuclear fuel (uranium fuel cycle versus thorium fuel cycle) as the question of reactor design such as choice of liquid vs solid nuclear fuel, choice of coolant / moderator containment vessel design.
For instance molten salt reactors have freeze plug safety feature allowing evacuation... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/73548",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How to block neutrons What is a good way to block neutrons and what is the mechanism that allows this? It's my understanding that polyethylene is somewhat effective. Why?
| To expand on dmckee's answer, water is an excellent way to both slow and block neutrons. If you are doing any home experiments with any type of radiation, remember that the human body is mostly water and radiation will happily dump energy into YOU. Be very very careful and protect yourself. Better yet, seek the help of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/73596",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Is the symmetrisation postulate unnecessary according to Landau Lifshitz? The symmetrisation postulate is known for stating that, in nature, particles have either completely symmetric or completely antisymmetric wave functions. According to these postulate, these states are thought to be sufficient do describe all poss... | Check out the section about Chapter 17 Identical particles in Ballentines, he not only points out why looking at the Permutation operators of two particles in a multi particle setting is misleading but also discusses some errors in previous claims.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "7",
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Why does the thickness of a wire affect resistance? For small thicknesses of wire, it's pretty obvious why resistance affects thickness. (The electronics squeeze to get through). But after a certain thickness shouldn't the thickness become irrelevant?
For example if your trying to pour a bucket of water through a straw... | All (non-superconductor) metals have electrical resistance, no matter how thick a wire made of them is, as the conducting electrons are always "bumping into" the atoms in the lattice of the metal, slowing them down. Therefore there is always a resistance that can be reduced by increasing the cross sectional area of th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/73781",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Electric potential due to circular disk Relevant diagram is available here.
The circular disk of radius $a$ lies in the $xy$ plane and carries surface charge density of
$\sigma (s, \phi) = s^{2}cos\phi $,
where $(s,\phi)$ are in cylindrical co-ordinates.
The problem is to find potential at a point which is slightly dis... | The problem is that you're ignoring the angular dependence of your probe point $\mathbf r$, and that is messing with your integral. If your probe point has cylindrical coordinates $(s,\phi,z)$ and your integration variables are $(s',\phi')$, then the distance between the two is
$$\frac 1 {|\mathbf r-\mathbf r'|}=\frac{... | {
"language": "en",
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How do we know photons have spin 1? Electrons have spin 1/2, and as they are charged, they also have an associated magnetic moment, which can be measured by an electron beam splitting up in an inhomogeneous magnetic field or through the interaction of the electrons's magnetic moment with an external magnetic field in s... | I would say this is an empirical fact. In atomic physics you
don't observe optical transitions (e.g. induced by a laser)
without angular momentum transfer. The change in angular
momentum is always $\pm$ 1, that's what the photon can transmit.
See http://en.wikipedia.org/wiki/Selection_rule
The atomic states with differ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/73942",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does electricity need wires to flow? If you drop a really heavy ball the ball's gravitational potential energy will turn into kinetic energy.
If you place the same ball in the pool, the ball will still fall. A lot of kinetic energy will turn into thermal energy because of friction, but the gravitational potential e... | Electrons do flow without a wire. This is exactly what is happening in a cathode ray tube. So why don't electrons flow from one conductor to another through vacuum or air if there is a potential difference? There is a minimum energy of a few eV required for an electron to exit a metal known as the work function. In a c... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do electrons not bump into impurities in a superconductor? Just a simple question. Why is it, that when a material becomes superconducting, and by that gets zero resistivity, the electrons don't hit impurities in the material?
For the material to have zero resistivity, that means that the electrons can just flow wi... | When the electrons pair up this opens an energy gap between the energy of the Cooper pairs and the energy of the lowest quasiparticle excitation. There is a nice article discussing this effect here (NB it's a PDF).
The gap means that you cannot scatter a Cooper pair by an arbitrarily small energy. If the energy is less... | {
"language": "en",
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Why was the conversion factor of the metric unit bar chosen the way it was? The unit bar for pressure is clearly a metric unit, but its order of magnitude is a bit strange. In the centimeter–gram–second system of units we have:
1 bar = 1 000 000 baryes = 1 000 000 dyn/cm²
so the bar is not "coherent" with this system ... | The $\text{pascal}$ seems of a much later date than the $\text{bar}$. In fact, it seems that, at some time, the $\text{bar}$ was adjusted a bit away from the average air pressure on earth (its originally intended definition), to get it "in line" with the SI units, and therefore also with the new or later $1~\text{Pa}=1... | {
"language": "en",
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Why is there a factor of $4\pi$ in certain force equations? I mean to ask why there is $4\pi$ present in force equations governing electricity? Though all objects in universe are not spherical and circular, the constant of proportionality in both equations contain $4\pi$. Why?
| For example, if you mean $k_e=\frac1{4\pi\epsilon_0}$, it comes from a natural "Gauss's law" understanding of Coulomb's law, where the electric field is distributed over the surface of a sphere of area $4\pi r^2$.
$$F= \frac1{\epsilon_0}\frac1{4\pi r^2}q_1q_2 $$
This is also the explanation for the $1/r^2$ term (and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/74254",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
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What are correlated magnetic moments? My book has the following sentence and I don't understand what correlation or lack of correlation means:
At high temperature the magnetic moments of adjacent
atoms are uncorrelated (to maximize the entropy) so the crystal has no net magnetic moment.
The book is touching on sec... | It means that the directions of the magnetic moment of neighboring atoms is statistically independent. At high temperature the thermal energy is greater than the magnetic energy; the resulting thermal fluctuations cause any material to become paramagnetic. As you lower the temperature these thermal fluctuations are r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/74377",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How far can you scatter light using a prism? If I were to scatter light how far do you think it would disperse? What prism most effectively scatters light?
| A prism refracts light, it doesn't scatter it. I'm confused about what you're asking.
If you're asking about the dispersion that occurs when (for example) white light passes through a prism, that depends on the material of the prism, and it's a fairly involved topic. But the Wikipedia article points out some of the phy... | {
"language": "en",
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"source": "stackexchange",
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Walking along a moving train, we make 18 steps. Opposite: 11. How long is the train?
A man walks in the same direction as a slowly moving train ($v_{man} > v_{train}$). He counts the train to be 18 steps long. Then he turns around and counts the train to be 11 steps long.
(Suppose both man and train are moving at a co... | Key is to notice that your steps provide you with a unit length as well as a unit time. So, let's measure distance in $steps$ and time in $ticks$, with your speed being $1 \ step/tick$.
The length of the train is $x$ steps, and its speed is $v \ steps/tick$ ($v<1$).
It follows that
$$x \ + \ 18 \ v \ = \ 18 $$
$$x \ -... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/74533",
"timestamp": "2023-03-29T00:00:00",
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Does alternating current (AC) require a complete circuit? This popular question about "whether an AC circuit with one end grounded to Earth and the other end grounded to Mars would work (ignoring resistance/inductance of the wire)" was recently asked on the Electronics SE.
(Picture edited from the one in the above lin... | For me, AC is a closed circut all together within the same unique wire
As the + and - are chasing eachother in the same line. As for DC, the - chase the + around the other end of the loop
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/74625",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "47",
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Study of Black-body Radiation Why did scientists study black body radiations from something as complicated as a hollow container rather than the radiation from something simple like a thin solid cylinder?
| Since a black body is an exact absorber and during practice it's demanding to make things that is really exactly a good absorber so to make black body we choose a material that is as good an absorber as we can obtain it into a hollow Sphere with a small hole in it. The black body is then the hole not the sphere. It is ... | {
"language": "en",
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When is temperature not a measure of the average kinetic energy of the particles in a substance? I had always thought that temperature of a substance was a measure of the average kinetic energy of the particles in that substance:
$E_k = (3/2) k_bT $
where $E_k$ is the average kinetic energy of a molecule, $k_b$ Boltzm... |
temperature of a substance was a measure of the average kinetic energy of the particles in that substance
This is only true for a monatomic gas. Even without quantum mechanics, a classical diatomic gas has three more degress of freedom than a monatomic gas—two rotational and one vibrational—for a total of 6. The equi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/74836",
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"source": "stackexchange",
"question_score": "9",
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Strings and their masses How do strings present in particles give mass to them? Is it only by vibrating? I have been trying to find the answer but could not find it anywhere, can this question be answered?
| I presume that you are asking about the mass spectrum of string theories.
The mass spectrum of a Classical string theory, or the mass of a string is (due to Special Relativity) given, by:
$$m=\sqrt{-p^\mu p_\mu}=\sqrt N $$
In natural units $c_0=\ell_s=\hbar=1$. Where $N$ is an operator, called the "... | {
"language": "en",
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Can Deuterium undergo a nuclear fusion without the presence of Tritium? I've been reading about fusion fuels for a while now, and I understand that in Lithium-Deuterium fuel, the neutrons from the fission reaction bombard the Lithium to produce Tritium and the D-T reaction occurs and we get the energy.
So what about De... | All three isotopes of Hydrogen can undergo fusion under the right conditions. The main reason to use D or T is that they fuse more easily than H. For example, H-H fusion is primarily what drives our sun, but in the lab D-D or D-T reactions are much easier to initiate.
The D-T reaction gives off 17.6 MeV of energy, D-D... | {
"language": "en",
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Where does gravity get its energy from? I would like to know where gravity gets its energy to attract physical bodies?
I know that the law of conservation states that total energy of an isolated system cannot change. So gravity has to be getting its energy from somewhere, or else things like hydropower plants wouldn't ... | The universe is composed of over $90$% dark matter and dark energy. Dark energy comprises about $70$% of this. So far, dark matter and energy remain undetectable and until there are the mechanism that produces gravity, will probably remain a puzzle. If you want to know more in detail you will need to research quantum m... | {
"language": "en",
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"source": "stackexchange",
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How does electron know when to change into a wave? It is known that electron behaves as a wave also.
How does electron know that it has to change into a wave?
Are there any factors that influence the behavior of electron changing into wave?
| The electron is always a wave.
The electron is wave, as experiments of diffraction and interference showed.
Waves come in an infinity of "shapes". Some kinds of shapes have some properties, and others have other properties. Examples of properties are position and momentum. The two shapes of the electron's wave having t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/75328",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Frequency of small oscillation of particle under gravity constrained to move in curve $y=ax^4$ How to find the frequency of small oscillation of a particle under gravity that moves along curve $y = a x^4$ where $y$ is vertical height and $(a>0)$ is constant?
I tried comparing $V(x) = \frac 1 2 V''(0) x^2 + \mathscr O(... | Is it fine if I solve it using Newton's laws? You can then maybe convert it to a Lagrangian. I will assume the path on which it oscillates is almost flat for small oscillations
At a displacement of $x$($\lim_{x\to0}$), the gravitational force on it will be
$$F_{mg}=-mg\sin\theta$$
where $$\tan\theta=\frac{dy}{dx}=4ax^... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/75411",
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Why does boiling water in the microwave make a cup of tea go weird? When I boil water in the kettle, it makes a nice cup of tea. Sometimes I need to use a microwave because a kettle isn't available. I boil the water in the mug and it looks pretty normal, but when I drop in the teabag the water froths up and looks foa... | http://en.wikipedia.org/wiki/Superheating
I think you are superheating the water and you provide nucleation sites (by means of the tea bag) so it starts to boil.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/75465",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "32",
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Why can't we destroy energy? From a wikipedia article:
In physics, the law of conservation of energy states that the total energy of an isolated system cannot change—it is said to be conserved over time. Energy can be neither created nor destroyed, but can change form; for instance, chemical energy can be converted to ... | It is much more appropriate to call it a law than a theory. A theory is an explanation, whereas a law is based on repeated observation and/or experimentation. If you are concerned that it isn't or can't be proven then you could call it a hypothesis, assumption, or postulate of conservation of energy. Of those three, po... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/75616",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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View from a helicopter rotor: why is the horizon distorted? This video ("rotor panorama") was captured by a camera attached to the rotor head of a radio-controlled helicopter, with the frame rate set to the rotor's frequency. During a long segment of the video, the horizon looks distorted:
What causes this distortion?... | The frame rate and the rotor frequency do not exactly match.the picture seems to be clear some times when the rotor reaches its set rpm. But after that the vibration starts with a different noise.the wobble increases and the distortion too.as Emilio pisanty said there is a vertical displacement due to vibration.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/75709",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Why does electric field intensity $E$ can be uniquely determined by its divergence and curl? My question is, the number of following equations
$$\nabla\cdot E=\frac{\rho}{\varepsilon}$$
$$\nabla\times E=-\frac{\partial B}{\partial t}$$
is 4 while the number of unknown variables $E=(E_1,E_2,E_3)$ is 3. Intuitively, the ... | The divergence and curl do not uniquely determine a vector field. For example, if all the derivatives are zero, any constant field is a solution. In order to determine the field, we must include boundary conditions.
As far as your question, you are not looking at equations for the three components of $E$. You are looki... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/75782",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can the same car with 100HP and 500HP produce the same acceleration on first gear? My friend and I are debating about the acceleration of cars in first gear. He said that the same car (weight, tires, etc) produces the same acceleration with both 100HP and 500HP. I imagine that the moment when the tires catch the surfac... | I am his friend :). This argument came up when we were discussing the G forces felt by our bodies in a smaller powered car (let's 90 hp) and a larger power one (400 hp). I said that the G forces are dependent on the amount of grip you can catch with your tires and assuming both cars are exactly the same in (body mass, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/75955",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Why do meteors explode? A report on the Chelyabinsk meteor event earlier this year states
Russian meteor blast injures at least 1,000 people, authorities say
My question is
*
*Why do meteors explode?
*Do all meteors explode?
| I suspect that there are multiple phenomenologies involved, but for a gravitationally bound pile of aggregate, there is not a lot of cohesion. Thus it is possible that entry dynamic pressure might be high enough to cause the "pancake" behavior described above.
But I suspect that there is another way for more cohesive ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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Double Slit Experiment: How do scientists ensure that there's only one photon? Many documentaries regarding the double slit experiment state that they only send a single photon through the slit. How is that achieved and can it really be ensured that it is a single photon?
| In the double slit experiment, if you decrease the amplitude of the output light gradually, you will see a transition from continuous bright and dark fringe on the screen to a single dots at a time. If you can measure the dots very accurately, you always see there is one and only one dots there. It is the proof of the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/76162",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "41",
"answer_count": 4,
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CMBR temperature over time? How has CMBR temperature dropped as function of time? A graph would be nice, but I'd be happy with times (age of universe) when it cooled enough to not be visible to human eye, became room temperature equivalent, or reached some interesting temperatures regarding matter in the universe.
If t... | The exact formula in the Standard ΛCDM-model is
$$
T(t) = T_0\big(1+z(t)\big) = \frac{T_0}{a(t)},
$$
where $a(t)$ is the cosmological scale factor, which can be calculated by numerically inverting the formula
$$
t(a) = \frac{1}{H_0}\int_0^a\frac{a'\,\text{d}a'}{\sqrt{\Omega_{R,0} + \Omega_{M,0}\,a' + \Omega_{K,0}\,a'^... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How are the Weyl & Riemann curvature tensors related to the stress energy tensor in GR? Einstein's vacuum equations, that is without matter, allows the possibility of curvature without matter. For instance, we may consider gravitational waves.
The question is: Is there some link between the Riemann curvature tensor, a... |
Is there some link between the Riemann curvature tensor [...] and some gravitational "physical" quantities*
Maybe you could clarify what you want that would qualify as "physical." Curvature is observable, and IMO is physical. Projects like LIGO are designed to detect gravitational waves. Gravity Probe B was a project... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/76473",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Pulley problem - unable to understand the concept Given:
*
*The pulley is moving towards the right.
*All blocks have different masses. (The pulley and the strings are massless.)
What I don't understand:
*
*Is the tension the same for both A and B?
*If the tension is the same, then both blocks should have di... |
Is the tension the same for both A and B?
Yes. A massless string needs to have constant tension, otherwise it would feel a net force and have infinite acceleration.
If the tension is the same, then both blocks should have different
accelerations
Yes.
but this is not true?
Why do you think the boxes should have ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/76532",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What does imaginary number maps to physically? I am taking undergraduate quantum mechanics currently, and the concept of an imaginary number had always troubled me. I always feel that complex numbers are more of a mathematical convenience, but apparently this is not true, it has occurred in way too many of my classes, ... | A rotation by a right angle. So complex numbers come up whenever you have periodicity/oscillations/phases etc.
For a simple example, consider the physical intuition for Euler's formula -- if you push something with force $F=kx$, you get exponential motion, but $F=-kx$ is periodic motion. The latter, where you have peri... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/76595",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Similarity Transformation How can I find the similarity transformation $S$ between gamma matrices in the Dirac representation $\gamma_D$ and Majorana representation $\gamma_M$ in 4 dimensions theory?
The relation is $\gamma_M = S \gamma_D S^{-1}$
Actually, my question is about the general method of finding the similari... | If you know the change of the (vector) basis, the answer is straightforward.
If you don't know the change of the (vector) basis, but only want some particular representation for the gamma matrices (for instance you want only real matrices, or only imaginary matrices), you may try for $S$ :
$$S=\frac{1}{\sqrt{2}} \be... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/76719",
"timestamp": "2023-03-29T00:00:00",
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What is the definition of a quantum integrable model? What is the definition of a quantum integrable model?
To be specific: given a quantum Hamiltonian, what makes it integrable?
| Quantum integrability basically means that the model is Bethe Ansatz solvable. This means that we can, using the Yang-Baxter relation, get a so-called "transfer matrix" which can be used to generate an infinite set of conserved quantities, including the Hamiltonian of the system, which, in turn, commute with the Hamilt... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do I find the amount of atoms in a pure gas in a confined area? Say I have Argon gas in an area such as a cube with pressure around pressure between 10-5 and 10-3 Torr (pressure) at 25 degrees at 320 Kelvins . How do I find the amount of atoms in that cube? Any formulas?
| If you assume it is an ideal gas and you know the volume of the cube, the temperature of the gas, and the pressure, you can calculate the number of atoms using the ideal gas law:
$PV=nRT$
Where P is pressure, V is volume, n is the nuber of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
| {
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Where to place my second image charge? (Spherical ungrounded conductor) I am trying to find the potential $V$ inside a sphere using the method of image charges.
I have a conducting spherical shell. The charge $q$ is inside the sphere. The sphere is ungrounded and is an equipotential because it is a conductor.
If I pla... | Your first image charge made the spherical shell an equipotential (@ V=0). So, by superposition, you can now add a uniform surface charge density to the shell, and it will stay an equipotential, but no longer at zero...
| {
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Deriving the Lorentz force from velocity dependent potential We can achieve a simplified version of the Lorentz force by
$$F=q\bigg[-\nabla(\phi-\mathbf{A}\cdot\mathbf{v})-\frac{d\mathbf{A}}{dt}\bigg],$$
where $\mathbf{A}$ is the magnetic vector potential and the scalar $\phi$ the electrostatic potential.
How is this d... | Hints: Use
$$\frac{\partial U}{\partial {\bf v}}= -q{\bf A}, $$
and the defining property of a velocity-dependent potential:
$${\bf F}~=~\frac{d}{dt} \frac{\partial U}{\partial {\bf v}} - \frac{\partial U}{\partial {\bf r}}.$$
See e.g. Herbert Goldstein, Classical Mechanics and Wikipedia for more details.
| {
"language": "en",
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Why should nature of light(or any quantum object) depend on observation? We know that, in the double slit experiment, observation changes the behavior of a quantum object, that it behaves like a particle when observed and a wave when not observed. But why should its nature depend on observation? What if we didn't exist... | Your confusion is perfectly justified. Congrats, you just discovered what is called the measurement problem. There have been several attempts to resolve this problem, most of them based on introducing interpretations of quantum mechanics other than the Copenhagen interpretation (or more concisely standard or orthodox i... | {
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Surface gravity of Kerr black hole I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand.
Firstly, the metric is given by
$$\mathrm{d}s^2=\left(\frac{\Sigma}{\rho^2}\sin^2\theta\omega^2-\frac{\rho^2\Delta}{\Sigma}\right)\ma... | Ok, every book I looked has this solved by looking at four velocity and four acceleration of a free particle at the horizon, so that must be it :\ Altho I'm sure there's a way to do it via Killing vector $\chi^\mu=\partial_t+\Omega_H\partial_r$.
So I'll just go through this derivation with acceleration...
| {
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"source": "stackexchange",
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Riemann tensor in 2d and 3d Ok so I seem to be missing something here.
I know that the number of independent coefficients of the Riemann tensor is $\frac{1}{12} n^2 (n^2-1)$, which means in 2d it's 1 (i.e. Riemann tensor given by Ricci Scalar) and in 3d it's 6 (i.e. Riemann Tensor given by Ricci tensor).
But why does t... | The simplicity of geometry in lower dimensions is because the Riemann curvature tensor could be expressed in terms of simpler tensor object: scalar curvature and metric (in 2d) or Ricci tensor and metric (in 3d). That fact, of course, does not alter the possibility to write Riemann tensor (as well as Ricci tensor and s... | {
"language": "en",
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Small oscillations of the double pendulum From the Lagrangian I've got the following equations of motion for the double pendulum in 2D. (The masses are different but the lengths of the two pendula are equal.) Let $m_2$ be the lowest-hanging mass.
$$(m_1+m_2)\ddot{\theta_1}+2m_2\ddot\theta_2\cos(\theta_2-\theta_1)=\\ -... | I think the issue here is that you need to keep a consistent level of approximation in your "small angle approximation." By small angles, we typically mean $\theta_1$ and $\theta_2$ are both of order $\epsilon$, where $\epsilon \ll 1$. Then the question is - to what order in $\epsilon$ do you want to write down the e... | {
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Quantum entanglement as practical method of superluminal communication As I understand it (from a lay physics perspective), quantum entanglement has been experimentally demonstrated - it is a reality. As I understand it, you can measure something like the spin of an electron and know that its entangled pair will, in th... | This 'spooky action at a distance' will not and can not lead to communications technologies. The point is that the correlation between the two states cannot be used for information transmission. The two observers can influence each others' observations, but they can never communicate their own observations to the other... | {
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Is there an easy way to get water at roughly 70°C in our kitchen? Some green tea requires to pour water at 70°C. I have no thermal sensor or kettle with adjustable temperature with me.
Do you know a way to get water at roughly 70°C like “boil water and wait for x minutes” or “mix x part of boiling water with 1-x part ... | You can start with water at $0^{\circ} C$, as suggested in Vibert's answer, measure the height of water in the container, and start heating the water. The density of water at $0^{\circ} C$ is $1 g \cdot cm^{-3}$, at $65^{\circ} C$ it is $0.981 g \cdot cm^{-3}$, at $70^{\circ} C$ it is $0.978 g \cdot cm^{-3}$. So if at ... | {
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What are the assumptions of the Navier-Stokes equations? I wanted to model a real life problem using the Navier-Stokes equations and was wondering what the assumptions made by the same are so that I could better relate my entities with a 'fluid' and make or set assumptions on them likewise. For example one of the assum... | The Navier-Stokes equations assume (assuming we are looking at a vector conservative form):
*
*The continuum hypothesis, which is applicable for Knudsen numbers of much less than unity.
The Navier-Stokes equations must specify a form for the diffusive fluxes (e.g. otherwise you would have the Cauchy momentum equat... | {
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Confusion With How Dimensions Work Form what I understand if you have an equation such as:
$$v = v_0 + at$$
then the dimensions must match on both sides i.e. $L/T = L/T$ (which is true in this case), but I have seen equations such as 'position as a function of time' $x(t) = 1 + t^2$, and obviously time is in $T$, but a... | Units must always be consistent, that is correct. So using your example of:
$$ x(t) = 1 + t^2 $$
where the left hand side has units of $L$ (distance). This means the constant $1$ on the right side has implied units of $L$ while the coefficient in front of $t^2$ (which has the value of $1$) has implied units of $L/T^2$.... | {
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Distribution of point charges on a line of finite length How will $N$ freely moving charges confined to a line with length $L$ be distributed? What are their equilibrium positions?
| Aside from the special cases of $N = 1,2, 3$, in general the solution will be a quite involved system of simultaneous equations. I don't know if there's any way to not do the algebra at all and simply rely on physical arguments... but the full solution is:
Let $q = 1, \epsilon_0 = 1, L =1$ i.e. set all constants $=1$ f... | {
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How is relativity equation approximated What is the technique with which I can approximate the equation
$$\frac{mc^2}{\sqrt{1-(\frac{v}{c})^2}}-mc^2$$
when $v\ll c$?
Any hint would be much appreciated
| When $v\ll c$, the ratio $\beta = v/c$ is small, so we perform a Taylor expansion about $\beta = 0$;
\begin{align}
\frac{1}{\sqrt{1-\beta^2}} = (1-\beta^2)^{-1/2} = 1+\frac{1}{2}\beta^2+\frac{3}{8}\beta^4+\cdots
\end{align}
Now plug this into your expression and simplify.
| {
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Lightcone singularity of a 3 point function in CFT I had a quick question regarding the title of the question. In e.g. 2D CFT (for simplicity), the three point function of three operators with conformal dimension $a$, $b$ and $c$ are given as
$$
\langle\mathcal{O}_1(x_1)\mathcal{O}_2(x_2)\mathcal{O}_3(x_3)\rangle~=~\fr... | You need to refine your intuition a little bit. If you bring two operators together, you indeed get singular behaviour, which is taken into account by the OPE. The unit operator is the most singular, and the higher the scaling dimension of an operator $\phi$ in the $O_1 \times O_2$ OPE, the less singular its contributi... | {
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What happens if an already excited electron gets hit by another photon (lasers)? Slightly vague title but it is the best I can do. My question stems from some interest in how 3 stage lasers function. A photon from the pumping source comes in and strikes a atom in the active medium. The photon is absorbed, an electr... | The answer is yes. If there would be a state available so that an electron in an excited state could be further excited (by the laser wavelength), this would also happen and reduce the efficiency of stimulated emission.
Hence, active media are chosen in such a way that this can not happen, or is at least at reduced pro... | {
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How do you determine the value of the degeneracy factor in the partition function? In the partition function, expressed as $$Z = \sum_j g_je^{-\beta E_j}$$ I'm wondering what determines the $g_j$ factor. I've been trying to look around the internet for an explanation of it but I can't find one. I guess it is the number... | Consider a quantum system with state (Hilbert) space $\mathcal H$. For simplicity, let the Hamiltonian $H$ of the system have discrete spectrum so that there exists a basis $|n\rangle$ with $n=0,1,2,\dots$ for the state space consisting of eigenvectors of the Hamiltonian. Let $\epsilon_n$ denote the energy correspond... | {
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How does humidity affect the path of a bullet? Background
Last night, I was reading the FM 23-10 (The U.S. army official field manual for sniper training), and I've noticed that they're potentially teaching snipers incorrect information.
Generally speaking, when we say "impact goes up" it means that the bullet was eith... | Could be that the expanding gasses behind the projectile diminish faster as the outside air influenced the outcome ,herefore decreasing ramp time(bullet arc)wich lead to bullet drop on its intended path!pesonal experience in sub tempreatures using a 45acp had the same outcome at 15metres.2seprate 1911 pistols were fire... | {
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Entropy inequality Assume that you have two bipartite systems $\rho_1^{AB},\rho_2^{AB}$ then I would like to prove the following:
$$S(\frac{1}{2}( \rho_1^{AB}+I^A\otimes\rho_2^B))+S(\frac{1}{2}(\rho_2^{AB}+I^A\otimes\rho_1^B)) \geq S(\frac{1}{2}(\rho_1^{AB}+I^A\otimes\rho_1^B))+S(\frac{1}{2}(\rho_2^{AB}+I^A\otimes\rho_... | (very) partial answer:
In a very particular case, this is true.
Let's have $\rho_1^{AB} = I^A \otimes \rho_1^{B}$ and $\rho_2^{AB} = I^A \otimes \rho_2^{B}$
The left hand side is $L = 2 S( \frac{1}{2}(\rho_1^{AB}+\rho_2^{AB})) $
The right hand side is $R = S(\rho_1^{AB}) + S(\rho_2^{AB})$
By the concavity of the Von Ne... | {
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Quantum tunneling effect in a potential of the kind $V(x)=A\frac{x^2}{1+x^4}$ Given a potential: $$V(x)=A\frac{x^2}{1+x^4}$$ with $A\gt 1$ and a quantum particle inside the well around the point $x=0$. I'm stuck on the calculation of the transmission and reflection coefficients for this particle vs. its energy.
| In order to compute the transmission coefficient, we can use the first correction in the WKB approximation. Ignoring constants that we can pull outside the integral, we essentially are faced with the integration problem,
$$I(x) = \int \mathrm dx \, \sqrt{V(x)-E}.$$
In the case of your potential, we thus have,
$$I(x) = ... | {
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Gravitational acceleration on the Moon and Mars There are plenty of formulas that use gravity acceleration of Earth. This is represented with the symbol $g$. In my school work (I am a high school student) we usually take it as $g= 9,8 \,\text m/\text s^2$.
This thing is obviously a number that is only usable on Earth.... | Let's see how the acceleration due to gravity is obtained for any planet, and then we can apply this to Earth or the Moon or whatever we want.
Newton's Law of gravitation tells us that the magnitude of the gravitational force between to objects of masses $m_1$ and $m_2$ is given by
\begin{align}
F = G\frac{m_1m_2}{r^... | {
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If I am travelling on a car at around 60 km/h, and I shine a light, does that mean that the light is travelling faster than the speed of light? The title says it all.
If I was on a bus at 60 km/h, and I started walking on the bus at a steady pace of 5 km/h, then I'd technically be moving at 65 km/h, right?
So my son po... |
If I was on a bus at 60 km/h, and I started walking on the bus at a
steady pace of 5 km/h, then I'd technically be moving at 65 km/h,
right?
Not exactly right. You would be correct if the Galilean transformation correctly described the relationship between moving frames of reference but, it doesn't.
Instead, the... | {
"language": "en",
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What is the importance of state functions in physics? I'm currently reading about the Carnot cycle and its significance on the formulation of entropy (because I want to try to understand the concept better), but I can't seem to answer the following question:
*
*Why are state functions important in physics? What does... | state functions are important because you can analyse the system at a specific moment of time if you know its configuration at that moment, it doesn't matter how the system got to the state it is in now, they also describe the equilibrium state of the system. its similar to the importance of conservative forces in clas... | {
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How to establish relation between flow rate and height of the water column of the tank? Suppose a water tank has 1" diameter drain at the bottom and is filled with water up to one meter height above the drain. What time it will take the tank to drain out completely. Now say, the tank is filled up to two meter height ab... | This is a very simple problem. The relation is given by using
$$A \frac{dh}{dt} = \frac{-\pi D^2}{4}v;$$
where $D$, $h$, $A$ are the diameter, height and area of the tank and v is velocity.
I will leave the derivation up to you
| {
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Nature of frictional force I was thinking about a situation where a person in standing on the ground with some friction. The frictional force is directly proportional to the normal reaction acting on him by the ground. Assume that he leaned forward i.e his center of mass is not vertically up the point of contact of him... | It's not correct that runners lean forward to begin a race in order to increase friction. They lean forward because otherwise, they would experience no propulsion whatsoever because static friction is zero when the runner is completely upright.
When the runner leans forward and flexes his leg muscles, he exerts a hori... | {
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Is it possible for the entropy in an isolated system to decrease? As far as I can tell, the concept of entropy is a purely statistical one. In my engineering thermodynamics course we were told that the second law of Thermodynamics states that "the entropy of an isolated system never decreases". However, this doesn't ma... | As you said, entropy is a statistical phenomenon. As with everything statistical, the parameters of your sampling effect the quality of your conclusions.
In your given example - a random molecular gas spontaneously forming a pressure gradient - you examine a brief timescale during which the entropy of the system is les... | {
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Do orbitals overlap? Yes, as the title states: Do orbitals overlap ?
I mean, if I take a look at this figure...
I see the distribution in different orbitals. So if for example I take the S orbitals, they are all just a sphere. So wont the 2S orbital overlap with the 1S overlap, making the electrons in each orbital "me... | Yes, orbitals do overlap. However, these orbitals do not necessarily mean that is where the electron is. The orbitals are only the probable locations that an electron would be. In fact, electrons are not even necessarily in those orbitals; they could be anywhere. This is able to be shown mathematically, but it is relat... | {
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How to understand wavefunction in quantum mechanics in math I am reading some introduction on quantum mechanics. I don't understand all but I get the point that the wavefunction tells some probability aspects. In one book, they show one example of the wavefunction $f(x)$ in position space as a complex function, so they... | "$| f(x) \rangle$" does not mean anything and is not proper bra-ket notation. For translating back and forth beteween wavefunction and bra-ket notation, here is the #1 thing to keep in mind:
$$
f(x) = \langle x \mid f \rangle
$$
So, the probability density to find the particle at $x$ is
$$
\left|f(x)\right|^2 = \left| ... | {
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Why are we not affected by the radiation of the radioactive decay going inside the Earth? I was reading the question Why has Earth's core not become solid?, and one of the answers says that
The core is heated by radioactive decays of Uranium-238, Uranium-235, Thorium-232, and Potassium-40
Why are we not affected by ... | You are always subjected to a low background of ionizing radiation from a number of natural and artificial sources, which include cosmic rays, trace amounts of radioactive nuclei in the air and in food, and indeed from the ground. A good place to read up on this is the corresponding Wikipedia article.
The radiation fro... | {
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Why can't Iron fusion occur in stars? It is said that iron fusion is endothermic and star can't sustain this kind of fusion (not until it goes supernova). However star is constantly releasing energy from fusion of elements like Hydrogen and Helium. So, can't that energy be used for fusion of Iron nuclei?
| As you correctly stated in normal situation the star cannot sustain the process. This doesn't mean that there are no such reactions going on in the core. The difference is that during the pre-supernova phase of the star the production of iron is negligible compared to the star. When it goes supernova, it produces a com... | {
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Myopia / Hypermetropia eye glasses inverting image on retina As far as I'm aware, the eye acts like a pinhole camera in that it inverts the image on the rentina. This makes sense as the rays converge and form a focal point that is upside down.
Myopia (shortsightedness) is described as the rays focusing before the retin... | The eye does not act as a pinhole camera. It is a multi element optical system with the cornea and inter-ocular lens doing most of the work. An image is inverted because the light entering the eye from above is headed DOWN, below the optical axis and will therefore image on the lower half of the retina. The light comin... | {
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Any quadrupole approximation? Any example? In atomic and molecular physics we quite often encounter with electric dipole approximation. The dipole approximation we do when the wave-length of the type of electromagnetic radiation which induces, or is emitted during, transitions between different atomic energy levels is ... |
The tides are essentially caused by the quadrupole component of the moon's gravitational field, as shown in this picture.
If you think about it, the classic Stern-Gerlach experiment also depends on a quadrupole field. It's a basic fact of magnetostatics that you can't have a field gradient in the x direction without a... | {
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Why is moment dependent on the distance from the point of rotation to the force? The formula for moment is:
$$M = Fd$$
Where F is the force applied on the object and d is the perpendicular distance from the point of rotation to the line of action of the force.
Why? Intuitively, it makes sense that moment is dependent o... | Understand that there is a tradeoff. You can apply a smaller force with a larger wrench, but you have to move it through a larger distance (arc length) to accomplish the same amount of work (force x distance).
| {
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"question_score": "3",
"answer_count": 10,
"answer_id": 4
} |
Can I make a rod in the vertical plane move with its one end on the ground in a slanting position? Consider a rod kept vertically on the ground. I keeps the rod in a slanting position making some angle with the horizontal. Can I now move this rod along the horizontal plane by applying a force at its bottom? The torque ... | The situation in your question is not clear. Without a sketch, all I can offer is the following. The governing equations of a sliding, slanted rod driven by a force $F$ at the bottom are:
$$ \ddot{\theta} = \frac{ \frac{\ell}{2} \left( m \cos\theta \left( g - \frac{\ell}{2} \cos\theta\,\dot{\theta}^2\right) + F\,\sin\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/80603",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 0
} |
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