Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why do electrons orbit protons? I was wondering why electrons orbited protons rather than protons orbiting electrons.
My first thought was that it was due to the small amount of gravitational attraction between them that would cause the orbit to be very close to the proton (or nucleus). The only other idea that I would... | Technically the electron and proton are both orbiting the barycenter of the system, both in classical and quantum mechanics, just as in gravitational systems.
You find the same dynamics for the system if you assume the proton and electron are moving independently about the barycenter, or if you convert to a one-body pr... | {
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Would using Cherenkov radiation for lighting be feasible? Could Cherenkov radiation be used for general illumination, for example, to replace LEDs, light bulbs etc? I.e. are there, or could there be, methods to produce substantial amount visible light with Cherenkov radiation:
*
*using devices compact and cheap enou... | Interesting question!
Cherenkov radiation would definitely be inefficient for illumination. You only get Cherenkov radiation from charged particles moving faster than the local speed of light in a medium. If you have a transparent medium with index of refraction $n=2$ and you're sending fast electrons through it, you... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/142132",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Temperature in CFT Non-vanishing Temperature can break conformal symmetry (Can anyone show this point explicitly), my question is that in AdS/CFT the temperature of boundary field theory is non-zero, why the boundary field theory whose conformal symmetry is breaking is still a conformal field theory?
| AdS/CFT correspondence tells you (among other things) the dual geometry for each state of the boundary theory. As @Arnold says (check the link in the comment), a finite temperature state ("spontaneously") breaks Lorentz, and hence, conformal invariance. That's okay because excited states could break many symmetries of ... | {
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"url": "https://physics.stackexchange.com/questions/142191",
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Born's rule and Schrödinger's equation In non-relativistic quantum mechanics, the equation of evolution of the quantum state is given by Schrödinger's equation and measurement of a state of particle is itself a physical process. Thus, should be governed by the Schrödinger's equation.
But we predict probabilities using... | Your question is misconceived. The wavefunction does not collapse. Rather, when you measure a system, each of the possible outcomes of that measurement happens. Each outcome is associated with a different version of the measurement apparatus. Those different versions of the measurement apparatus can't interact with one... | {
"language": "en",
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Is it possible for two holograms to be on the same holographic film? I was thinking if you could use a laser of a specific frequency to write a hologram on a film, and then to try to record over the same film but with a laser of another frequency the the first.
Is it possible for two holograms to be on the same hologra... | From MIT Museum Collections: Mini Kiss II
This hologram was made in 1975 of a person blowing a kiss and is made from multiple exposures (at least 16) on the film so that it appears the person is moving.
| {
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Why aren't classical phase space distribution functions always delta functions? The phase space distribution function (or phase space density) is supposed to be the probability density of finding a particle around a given phase space point. But, classically, through Hamilton's equations, the system's time evolution is ... | Note that various density kernels (like the gaussian kernel used in classical phase-space) have delta functions as a limit. Physicaly, clasicaly delta (dirac) distributions are the correct ones. Mathematicaly more smooth distributions (e.g gaussians) may be used to calculate integrals and take limits (the limits should... | {
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Failure of the Steady State Theory I was reading a journal of astronomy and came to the most famous opponent of Big Bang theory:
The Steady State Theory:
The 20th - century theory was proposed by Hoyle,Gold and Bondie. The theory is based on the Perfect Cosmological Principle which states that universe has no change i... | The main problem for steady state theory now would be bow can steady state theory produce dark matter and baryonic matter?
That is a big problem for the theory.It would be hard to find a conservation law for this process.
| {
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What does it mean that quantum teleportation can be classically simulated? Quoting here from Quantum Computation by Nielsen and Chuang :
(Gottesman–Knill theorem) Suppose a quantum computation is performed which involves
only the following elements: state preparations in the computational basis, Hadamard
gates, p... | I don't really know what answer you expect here.
As you have found out yourself, the Gottesman-Knill theorem tells you that stabilizer circuits can be efficiently simulated by a classical computer. Teleportation can be implemented that way, hence you can efficiently simulate it on a classical computer.
What does that ... | {
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Electric and Magnetic field's phase difference shift in linearly polarized electromagnetic waves I am a high school student and we currently studying the electromagnetic theory. In my textbook i read that the oscillating electric the magnetic fields have phase difference equal to π/2 rad near the source (for example an... | Possibly you are talking about the difference between the "far field" and "near field" solutions for the simple oscillating electric dipole.
Often when dealing with such a system, if we are looking at the field more than a few wavelengths away from the dipole (or more formally, $kr \gg 1$ or $r \gg \lambda/2\pi$) then ... | {
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The influence of the antenna height I am working on a model of a transmitter. The transmitter is attached to the wheel of the vehicle and thus constantly changes it's height. In other words capacitance between antenna and ground is changing.
What happens when the transmitter is in most up and most down position. Is th... | i will give a more general answer unless other information is added (then i can update)
It would depend on type of antenna, the frequency/wavelength of transmission and how this wavelength compares relative to the height of the wheel and rpm (i would say the height mostly).
if the wavelength is comparable to the heigh... | {
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Distribution of current of a rotating cone
If I have a hollow cone (surface with no bottom cover ) as the one in the picture. The cone has surface charged density $\sigma$. It rotates around the symmetry axis with an angular velocity $\omega$. I want to find the distribution of current on the surface of the cone.
W... | Do not open the cone. Think of it in the profile view : You have an isosceles triangle.
Now move along the axis of the cone, say a distance $x$ and take an element $\mathrm{d}x$.
Somewhat like this :
This small element is similar to the rectangle you described. With length as $2\pi r(x)$ and width $\mathrm{d}x$.
You... | {
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Clausius statement of the 2nd Law I'm slightly messed up with the Clausius statement of the 2nd Law.
I've seen at least two versions, which seem to be conceptually different.
a) It is impossible to transfer heat from a colder body to a hotter body without any other effect.
b) It is impossible to transfer heat from a co... | Imagine two systems. A and B. A is in a higher energy state (say is warmer) than B.
Clausius says you cannot transfer energy from B to A without a corresponding change in another system which is neither A nor B (lets say 'C').
But you can transfer energy from A to B without affectng or invoking C.
The 'other affect' bi... | {
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Is this expression for the kinetic energy of a spinning disk revolving about a second axis correct? My question is motivated from a question from another user. You can see the configuration of the rotating system here: https://physics.stackexchange.com/q/143377/.
I am not interested in all the complicated arguments of... | Take the reference frame as centered in the fixed axis. The $R$ that connects the origin to the centre of the spinning disk forms an angle $\phi$ with the horizontal. Now, inside the disk of radius $r$, the angle of a certain point mass is given by the angle it forms inside the spinning circle, which we'll call $\theta... | {
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Tesla Coils - Is there a risk that the discharge can create x-rays? I've built a Tesla coil that stands about 3 ft tall and uses a spark gap as the interrupter for the primary circuit. Judging by the size of the streamers it's reaching at least a million volts.
Someone once told me that you have to be careful with Tesl... | Put a cover in front of the spark gap to shield your eyes from direct exposure to the UV light it produces. The risk is similar to arc-welding. You don't want to stare at the spark gap while it's running. The more powerful the Tesla coil the greater the risk. Run the coil for short periods of time somewhere well ventil... | {
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Bosonic Schrödinger field When second quantizating the Schrödinger field
$$\psi(r,t) = \sum_i \phi_i(r)b_i(t),\quad\mbox{and}\quad \psi^{\dagger}(r,t) = \sum_i \phi_{i}(r)^* b_i^{\dagger}(t),$$
we have the commutation relations $[\psi(r,t),\psi^{\dagger}(r',t)]= \delta(r-r')$. Now I want to show that $[b_i,b_j^\dagge... | The $\phi_i(r)$ form an orthonormal basis of (square-integrable) functions on $\mathbb{R}$, i.e. you should have a relation like
$$
\int dr\,\phi_i(r)\phi_j^*(r)=\delta_{ij}.
$$
This is what you need in order to expand $\psi(r,t)$ and $\psi^\dagger(r,t)$ the way you did above. You can use this to write the $b_i(t)$ in ... | {
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Why doesn't a star's core cool down when it expands as a red giant? When a star starts to run out of hydrogen to fuse, it begins to collapse due to gravity until the central core temperature rises to $10^8~\text{K}$
Then due the force generated by the fusion of helium, the star expands again and becomes a red giant.
So... | The simplest answer is that in order to maintain helium fusion, a certain pressure and temperature are necessary. Therefore, given the fact that helium fusion is occurring in the core, and the mass pushing down on the core is X from dynamic concerns, you therefore must conclude that the temperature in the core is Y, i... | {
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Why are permanent magnets permanent? Let me see if I get it right. When an iron bar is attracted by a permanent magnet it becomes a magnet itself because all of its magnetic domains start to point in the same direction. When the iron bar is no longer attracted by the permanent magnet, it is no longer a magnet itself be... | when we apply magnetic field to any ferromagnetic substance and remove it , small fraction of magnetic strength remains. for completely demagnetize it, an opposite magnetic field is needed this magnetic field is called coercivity of the material.this is different for different materials. coercivity is low for iron, so ... | {
"language": "en",
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Kitchen floor dries faster with lights on? My mother used to leave the lights on in the kitchen after washing the floor, saying that it would dry faster.
Does this really happen, or is it just a superstition? If true, how substantial is the effect?
| In principle yes, but the effect is usually marginal. It also depends on how powerful your lights are compared to the size of the kitchen (a 1000 Watt flood light in a home kitchen will probably have a noticeable effect on the speed of drying).
*
*Bascially, the floor dries through evaporation, i.e. the water on the... | {
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Why are the poles of a magnet reversed when a magnet is split into two? This question may be odd, but today i noticed something when my little magnet split into two pieces.
The poles reversed, so they could not get into "one piece" again (because the poles was reversed).
What is the physical explanation of this?
|
This question may be odd, but today i noticed something when my little magnet split into two pieces.
As you clarified in the comments to the question, it was a refrigerator magnet. Those magnets have the poles on the flat sides, so that they stick to the iron metal of the doors. When they break it will be into two fl... | {
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How to find an effective spring constant of a quadratic potential If a potential energy is given like $U(r)=A^3/r^2+2B^3r$, how do I find the effective spring constant using Taylor Expansion?
I compared spring constant $k$ to be equal to second derivative of potential energy with respect to $r$.
Am I going in the cor... | Given the potential $U(r)=A^3/r^2 + 2B^3 r$, the effective spring constant can be defined as the second derivative of $U(r)$ evaluated at the equilibrium point. Hence,
$$U''(r)= \frac{6A^3}{r^4}$$
If $r_0$ is our equilibrium point, then $k_{\mathrm{eff}} = 6A^3/r^4_0$. Another way to perform the calculation is to compu... | {
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Why does Earth behave like Natural Bar Magnet? What is the reason for the Earth to behave like a bar magnet and have poles (North and South poles)?
| When we say that the Earth's field behaves "like a bar magnet", we have in mind a field that is approximately dipolar. So while it is true that a geodynamo powers the field (see this Wikipedia page), we need to say a little more. First, the rotation of the Earth organizes the flow, tending to align it with the rotation... | {
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Do satellites need to have their orbits externally maintained? Is the speed of a satellite self maintained ? Or it needs anything to be done externally ?
Condition : The satellite is in the orbit where it is held in equilibrium by the force of gravity and its centrifugal force.
| All that is needed is gravity. There is absolutely no need to invoke the centrifugal force to explain an orbit. This argument doesn't even make sense because when it is used, the satellite is shown as moving.
A nice simple way to look at orbits is via Newton's cannon. Imagine a cannon atop the only mountain on an airle... | {
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Why do we add the spin angular velocity and orbital anglar velocity when asked to calculate total angular velocity of Gyroscope? Normally when we talk of angular velocity we mean how the angle of a vector changes with time with respect to an origin.Thus the oribital angular velocity of gyroscope makes sense to me.Howev... | Imagine yourself as the center post of the gyro and you lean 15 degrees to the right you have a bucket of water that you spin over your head.(this represents the spin of the gyro) As it spins you will see the angle of the bucket spinning and then have a friend estimate the angle
*
*If you left the bucket at the s... | {
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Have you ever seen in your car a mosquito? it's not capable of going 60 mph. How come it can still keep up with the car as if it weren't trying For instance, a fly is staying at the same spot, then your car suddenly moves forward at a rate of 60 mph. The mosquito IS staying at the same spot but for some reason it moves... | Actually, there are two factors responsible for helping the mosquito keep up with the car:
*
*If we consider the car to be already moving at 60mph, the air inside the car is also moving at 60mph. As the wings of the mosquito are subject to air resistance, its inertia will be resisted by the forward moving air, until... | {
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Newtonian tidal forces and curvature Today in my physics class, my lecturer said something which confused me. He said:
"Newtonian tidal forces are reinterpreted as a manifestation of curvature in General Relativity".
Now I know what tidal forces are (an effect of the force of gravity), a good example is the cause of ... | Have a look at my answer to How to explain centripetal force in terms or relativity because much of the discussion there is relevant.
Consider what we mean by a tidal force. Suppose you're floating around in space and you arrange a number of marbles around you so they lie on the surface of a perfect sphere. Now monitor... | {
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Transverse doppler effect in light In most books to explain transverse Doppler effect the following example is given:
Consider a source that emits flashes at frequency f0 (in its own frame), while moving across your field of vision at speed v. There are two reasonable questions we may ask about the frequency you observ... | There are no the transverse Doppler effect in your two cases. Because there is always a classical Doppler shift when the distance between the source and the observer changes with time.
See: Investigations on the Theory of the Transverse Doppler effect
blog.sciencenet.cn/blog-267101-748804.html 2013-12-11.
| {
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How to know if a vehicle is moving without any external source of information? The situation is the following:
I'm inside a vehicle (plane or a car, it doesn't matter) and I need to know if the vehicle is moving at a constant speed BUT I cannot perceive any external change like visual changes, vibration, etc.
How can I... | Are you traveling in a vacuum? If not, use a pitot tube
| {
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Why won't a block less dense than water fully submerge? Suppose we have an object of volume $1\: \mathrm{m^3}$. Mass of that object is $500\: \mathrm{kg}$, which means that the density of the object is $500\: \mathrm{kg/m^3}$.
If the object is in water it will float and half of it's volume ($0.5\: \mathrm{m^3}$) will b... |
From the Archimedes principal we know that the object will displace the water of same mass as it. So the object will displace 500kg water and 500kg water = 0.5m3 water.
We also know that the lost weight of an object = weight of water displaced by that object.
The object does not lose any weight. It is pushing down wi... | {
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Atmosphere model Im working on project where I should simulate glider soaring. The goal is to create gliders that will look for regions with hot upwinds using evolution algorithms. That shouldn't be problem.
What I have problem with, is how to simulate the atmosphere with wind and temperature? I've read that meteorolog... | Take a look at wikipedia article on numerical weather simulation and Atmospheric physics
In general the simulations involve complicated models and need fine-tuning and error compensations.
The idea though is simple. Start with simple models of the weather (see for example Lorenz equations)
Some references:
*
*http:/... | {
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What is the entropy of a pure state? Well, zero of course. Because
$S = -\text{tr}(\rho \ln \rho)$ and $\rho$ for a pure state gives zero entropy.
But... all quantum states are really pure states right? A mixed state just describes our ignorance about a particular system. So how can properties like entropy and tempe... |
A mixed state just describes our ignorance about a particular system
I don't think you can call our inability to access a pure state of any system an ignorance about a particular system. Because I think of pure state as a mathematical abstruction that can only be related to reality by application of Born rule - w... | {
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How many more galaxies are out there in the Universe (beyond the observable radius)? Let's say that the number of large galaxies in the observable universe is $n$ (approximated to 350 billion).
If the universe is homogenous and isotropic, what are the estimations for the total number of large galaxies in it?
$5n$, $10n... | Somewhere between zero and infinity, if one believes the eternal inflation scenario. BTW, Max Tegmark covers some of this here
Eternal inflation posits that in the false vacuum from which our own universe inflated there may be any number of others doing the same, beyond our event horizon, all with various combinations ... | {
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Frequency of an open air column Given only the length of an organ pipe to be $2.14 m$, is it possible to find what frequency it vibrates at? If I use the equation $f=\frac{v}{\lambda}$, does the $v$ apply to the speed of sound in the organ pipe or in air?
| The speed of sound should apply to $v$ because the sound waves are travelling through the air after it leaves the organ pipe.
The speed of sound is approximated by the following formula:
$$
v = 331.3 + 0.606T
$$
Where $T$ is the temperature in degrees Celsius, and $v$ is the velocity in meters per second. In your case... | {
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Dirac operator partial integration When you have an action with bosonic $X$ and fermionic $\psi$ (Majorana) fields and perform a SUSY transformation $\epsilon$ (the constant, infinitesimal parameter of transformation, a real, anticommuting spinor) can you do normal partial integration on the Dirac operator just like yo... | In general you cannot, but in your special case it works out.
You should be aware of what the objects in your expression actually are, and how they relate to each other. $X$ is a bosonic field and as such does not feel the presence of gamma matrices at all. Your first line could be rewritten as
$$ S = \int \mathrm d^2 ... | {
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Question on Shockley's equation for FETs I'm currently studying FETs (Field Effect Transistors) in Navy school. What I know so far is that in FETs, $V_{gs}$ is reversed biased, creating a depletion zone. What this means in plain English is that the more negative the gate is with respect to the source, the more narrower... | The exact equations for I-V characteristics of transistors are derived using quantum-mechanics. Several approximations can be used, one of which is based on the shottky barrier analysis
This reference here derives the I-V linear and quadratic approximation (in saturation) for FET transistors.
Another reference here
UPD... | {
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Why would different metals glow red at different temperatures? According to everything I've been taught about incandescence and black-body radiation, and some quick Googling to confirm I'm not crazy, just about everything, regardless of composition, should start glowing red at about the same temperature- 798K, the Drap... | There is no direct relation between melting point and colour of light produced, it's just that some heat energy is used in breaking intermolecular forces and a part of it is transferred to atoms. So for a higher melting point, a bigger part of energy is used in breaking intermolecular attraction and to change its state... | {
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Why does the "counting rule" of band theory fail to predict the conduction properties of some materials? I'm a little confused by the description I commonly hear about the electron counting rule in band theory. The general statement I find is that a "solid with an odd number of electrons per unit cell is a metal, whil... | Are the bands filled for these materials?
Filled bands do not contribute to transport.
If a Band is filled at t=0 it remains filled for all times
(Consequence of Liouville Theorem).
Of course no transport also means the material has to be an insulator.
I hope this helps.
| {
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Usage of Poisson's equation? I revisited electrostatics and I am now wondering what the big fuzz about Poisson's equation
$$\nabla^2 \phi = -\frac{\rho}{\varepsilon_0}$$
is. Wiki says
One of the cornerstones of electrostatics is setting up and solving problems described by the Poisson equation. Solving the Poisson equ... | The integral you wrote integrates $\rho$ over the whole space. This is impossible to calculate if $\rho$ is not known in the whole space.
For example, when the charge $\rho$ is known only inside some finite region enclosed by a metallic shell, the shell is known to have constant potential $\phi$ on its inner surface. T... | {
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What's Optimal About Six Legs According to Physical Laws? In many respects the insects can be regarded as the most successful class of animals in evolutionary terms. And one of the most common features of insects is that they (mostly) all have six legs.
Not discounting other traits, is there something about six legs th... | I can think of two possible reasons: first, you can have half your legs up in the air at one time (as in walking - two on one side and one on the other, then change) and still be perfectly stable (3 legs = most stable, like a tripod); and second, if a predator chews off a leg on either side, you still have two legs (so... | {
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What's the difference between frequency domain and time domain spectra?
If I have a mechanical oscillator and want to observe the dynamical behavior of the oscillator, is there any additional information to observe it in time domain and frequency domain? Normally, we observe the frequency domain spectra (power spectra... | There are no differences. Frequency domain is used as a mathematics transformation tool (Fourier, Laplace) in order to resolve too complex differential equations in time domain spectra.
| {
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What is the weight of the Philae lander on the Churyumov–Gerasimenko comet compared to earth? We know the payload mass of the Philae lander was 21kg.
We know the mass of the Churyumov–Gerasimenko comet is roughly 1 x 10^13kg.
We know the mass of Earth is roughly 5.9x10^24kg.
I've heard one estimate of the weight of ... | As you rightly pointed out, the fact that 67P is oddly-shaped should alter its gravitational attraction on various parts of the comet.
That said, if we were to go by Wikipedia in a rather off-hand manner, we find that the lander is $100 kg$ (as @fibonatic rightly pointed out) and 67P has an acceleration due to gravity ... | {
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Who plays the role of centrifugal force in an inertial frame of reference? It is noteworthy to quote a sentence from my book,
It is a misconception among the beginners that centrifugal force acts on a particle in order to make the particle go on a circle. Centrifugal force acts only because we describe the particle fr... | In an inertial frame the only force that causes a particle to move in a circular motion is the centripetal force. The reason that a particle does not "fall" into the center is because it has some tangential velocity, so it moves away from the center tangentially as it is falling towards it. The relationship between the... | {
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Is a photon really massless? If a photon travels at a speed of light and its massless then it must have no energy but this is not the case as we see in photo electric effect. Also help me to know what are photons made of, how are they created?.
|
If a photon [is] massless then it must have no energy
This is not the case. One way to think of mass is as nothing more than a convenient name for rest energy. Photons are indeed massless and thus have zero rest energy. This is not an issue because according to special relativity, they do not come with a rest frame.
... | {
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Structure of white light? White light is a mixture of different wavelengths.
If so what will be the structure of a beam of white light ? Is there a separation between different colours ? what does it actually mean ?
Does a beam of white light shows any spacing between different wavelengths ?
| White light is composed of photons of varying energies. The photons themselves do not have to have any perpendicular spatial separation as your picture suggests. Rather, it is possible that the photons of different energies are coming along a single path, one after another.
| {
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Is it possible to create a parachute large enough to stop all velocity? This idea came to me while playing Kerbal Space Program. I noticed that the larger my parachute was, the slower my rocket would fall back down to Kerbin. I would like to know if it is possible to create a parachute so large in the real world that i... | A parachute is a device specifically designed to create viscous friction.
Viscous friction generates a force that:
*
*is oriented opposite to the velocity;
*is proportional to (a certain power of [*]) the velocity.
So the falling velocity will increase until the drag force (pointing upwards) becomes equal to the ... | {
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How two prove the second sound velocity is $1/\sqrt{3}$ times than the first sound From Landau two hydrodynamics model in superfluid, we have the result
$c_1^2=\frac{\partial P}{\partial \rho}|_T$ and $c_2^2=\frac{\rho_s s^2 T}{\rho_n c}$.
In the zero temperature limit, how to relate those two quantities, to get the co... | Let's consider gas of particles which move with constant velocity $V$. In such case we will derive speed of sound. $c_s^2=\frac{\partial P}{\partial \rho}$ where $P$-is a pressure and $\rho$ is a density of gases. Set p is a momentum, then the momentum which gas give the wall from small time $\Delta t$ is $\Delta p=2... | {
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Does the conductivity of a wire in a vacuum decrease over time? Does the conductivity of a wire in a vacuum decrease over time, say over the period of years or decades? In other words: Does current degrade a wire, making it less conductive? If so, by how much, and why does this occur? Does it have something to do with ... | Some corrosion always takes place (pure gold is not used for transmission lines, AFAIK:-) ), so the conductivity decreases with time, although for some materials this effect can be very small (http://books.google.com/books?id=IWn9uuISVIoC&pg=PA109&lpg=PA109&dq=transmission+line+corrosion+conductivity&source=bl&ots=Qt5Z... | {
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Statistical physics and momentum conservation In statistical physics one usually looks at energy as a conserved quantity and e.g. in the canonical ensemble assumes a constant average energy of the ensemble. Now why don't we usually do this for other conserved quantities like momentum? Why not do a 'canonical' ensemble ... | I think it wouldn't be useful. In statistical mechanics you want to model the microscopic behaviour of a thermodynamical system. In the laws of thermodynamics there's no mention to momentum. But I believe nothing forbids you from talking about the average momentum of a statistical mechanical system.
| {
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What does the exponential decay constant depend on? We know the law of radioactivity:
$$N=N_0e^{-\lambda t}$$
where $\lambda$ is the exponential decay constant. My question is: This constant depends of what?
| The constant is a function of the stability of the nucleus, and is experimentally determined for every isotope. In other words - every kind of nucleus has its own value of $\lambda$ and there is no way (that I know) to get an accurate value for it, other than measurement.
But there are some nuclear physicists roaming w... | {
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Why do silicon solar cells only produce ~0.6V when the band gap of silicon is ~1.1V? I've been researching into this and can't quite figure out where that lost voltage is going. When silicon is excited by a photon within its absorption spectrum, it will always have an internal potential of 1.1V as per the band gap. Why... | I'll talk about why silicon diodes usually have threshold voltage of about $0.6V$. For the potential generated by silicon solar cells the argument is much the same.
Built-in potential is what determines threshold voltage. This potential can be calculated using the formula:
$$q\varphi_{in}=kT\ln\frac{n_{n0}p_{p0}}{n_i^2... | {
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Is the world we are living in discretized? I do not know how to use professional words to ask my question, so I will try to use a layman language. Please bear with me for a moment.
A ROUGH GUESS
The world our eyes are seeing every moment is a picture reflected in our eyes. I guess our eyes are like cameras, that are ta... | According to quantum mechanics the time evolution of the universe is described by a path integral that will sum over all histories. If we consider a robot whose processor runs at a clock cycle of $\tau$ to simplify things, then all the possible time evolutions during that period of $\tau$ will contribute to explain the... | {
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What does it mean to say "a paramagnetic material is attracted to an external magnetic field?" I'm just having a hard time wrapping my head around what actually goes on when a paramagnetic material is exposed to an external magnetic field. I understand that the individual dipoles line up so that they point in the direc... | Let me explain the difference using a simple model of an atom - as consisting of electrons revolving in orbits around a heavy nucleus.
When a material is exposed to a magnetic field, the electrons move in such a manner as to oppose it. The material mildly repels the magnetic field.
However, if a material has unpaired ... | {
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Are there eight or four independent solutions of the Dirac equation? I edited the question as a result of the discussion in the comments. Originally my question was how to interpret the four discarded solutions. Now I'm making a step back and hope that someone can clarify in what sense it is sensible to discard four of... | this is not an answer to your question per se but it might be relevant.
The solutions you've listed are not the general solutions of the Dirac equation. These are only the solutions for a particle at rest. The general solutions have terms dependent on the momentum, energy and mass.
The chirality eigenstates are not de... | {
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Habitable zones around other stars I have a question about measuring the boundaries of habitable zones on other planets.
Is it okay to assume that, if Sun's habitable zone starts at a distance $R_0$ and its luminosity is $L_0$, we can calculate any other star's with luminosity $L$ habitable zone's inner boundary as $$R... | Let me see if I understand the derivation.
$$F=\frac{L}{4 \pi R^2}$$
becomes
$$F_\odot=\frac{L_\odot}{4 \pi R_\odot^2}$$
and
$$F_{\text{ other star}}=\frac{L_{\text{ other star}}}{4 \pi R_{\text{ other star}}^2}$$
and so setting them equal means
$$\frac{L_\odot}{4 \pi R_\odot^2}=\frac{L_{\text{ other star}}}{4 \pi R_{\... | {
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What do we see while watching light? Waves or particles? I'm trying to understand quantum physics. I'm pretty familiar with it but I can't decide what counts as observing to cause particle behave (at least when it's about lights). So the question is what do we see with our eye-balls?
*
*We point a laser (or any kind... | It would be physically impossible to be able to "see" light as anything other than a particle (photon). The only time photons, or any other subatomic particle for that matter, can be described as a wave is when we are NOT looking at them.
| {
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Triple integral $\iiint_{\mathbb{R}^3} d^{3}q ~\delta^{3}(\vec{q})\frac{(\vec{p}\cdot\vec{q})^2}{q^{2}} $ involving Dirac Delta function
I am trying find $$\iiint_{\mathbb{R}^3} d^{3}q ~\delta^{3}(\vec{q})\frac{(\vec{p}\cdot\vec{q})^2}{q^{2}},$$ where $\vec{p}$ is some fixed vector.
The answer should be $\frac{p^2}{... | $$δ^3(q⃗ )=\frac{δ(q)δ(\theta)}{2\pi q^2\sin(\theta)}$$
is wrong. The delta function is spherically symmetric, and thus has no θ dependence. Simply use: $$d^3(q⃗ )=\frac{δ(q)}{2\pi q^2}$$ instead. Use the Jacobian when you switch coordinate systems (from Cartesian to spherical) ($r^2 \sin(\theta)$), and you should get... | {
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Has a body angular momentum and torque only in a circular path? In different contexts, my book(Principles of Physics by Resnick, Halliday ,Walker) , they wrote
For torque, the path need no longer be a circle and we must write the torque as a vector $\vec{\tau}$ that may have any direction. .... Note carefully that to... |
That's what they wrote. But I am really confused why they wrote so. In fact I can't imagine torque & angular momentum without circular motion. Why did they tell so? What is the cause?? Please explain.
A planet in an elliptical orbit has angular momentum alright, there is no problem.
The magnitude of angular momentum ... | {
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What are the definition and examples of topological excitation? I read topological excitation in wiki, while it's too brief. What is the precise definition of topological excitation? And can give me some examples and explain why they are topological excitation? Are there some references which give explainations in deta... | There is no better definition than what Wikipedia offers - in general, a topological excitation is a (field) state, i.e. a localized quantity since fields depend on spacetime, whose integral is a topological invariant.
One prime example are Yang-Mills theories in 4D, where the integral $\int \mathrm{Tr}(F\wedge F)$, as... | {
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All geodesics are inextendable? I think the title is true, because geodesics has a tangent vector with a constant length parametrized by an affine parameter.
Probably, it is easier to think about timelike or spacelike geodesics. In this case, its affine parameter measures the length of the curve. It is difficult to im... | A geodesic $\gamma$ is extendible only if $\gamma$ is incomplete, in the realm of semi-Riemaniann manifolds.
Suppose $\gamma$ is complete and extendible, say $\gamma:(-\infty,\infty)\to M$. Suppose $p$ is a future endpoint without lose of generality. Then, there is $t_0\in\mathbb{R}$, for all $t\ge t_0$, such that $\ga... | {
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Why do the high frequency waves have the most number of modes? While reading the Wikipedia page of Ultraviolet Catastrophe, I came across how Rayleigh and Jeans applied the equipartition theorem. They told that each mode must have same energy. Now as the number of modes are greatest in small wavelengths or large freque... | Edited and simplified on behalf of the crowd (useless at this point of other very good answers):
Consider a cube of edge length L in which radiation is being reflected and re-reflected off its walls. Standing waves occur for radiation of a wavelength λ only if an integral number of half-wave cycles fit into an interval... | {
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Ball lightning: How are they formed? Ball lightning: How are they formed?
According to some Chinese researchers:
These strange balls of electricity are seen during intense thunderstorms as glowing orbs. They can be yellow, white, red, orange, purple or green and accounts report them passing through glass windows with... | Ball lightning appears as glowing orbs that seem to occur during thunderstorms, usually following a lightning strike.They can be white, yellow, orange, red or blue in color.
There's no scientific explanation for balls of lightning, although there are several proposed theories.
The most popular current theory, proposed ... | {
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Strong CP Problem So, as far as I know, the Strong CP Problem in QCD results from the theta angle term in the action: $i\theta\int_X F_\nabla\wedge F_\nabla$ where $\nabla$ is the gauge connection and $X$ is a manifold on which the theory is defined. This term obviously breaks CP symmetry with non-zero choice of theta ... | "Would making experiment and theory consistent warrant a Nobel Prize? Or is it simply an irritating discrepancy that is not fundamentally important to our understanding of the Standard Model?"
As far as I can tell:
It depends on what the experimental results will be :) If strong CP is found to be broken it is quite i... | {
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Best way to heat something in aluminum foil? Let's say we have a wet piece of paper, wrapped in aluminum foil, that we need to heat up in the fastest and most energy efficient way possible (no flamethrower).
What would that be?
Details regarding the methods would be highly appreciated.
| Not sure how hot you want it, but a hairdryer or heat gun would be quick, but not very energy efficient while it was blowing - but it turns on and off quickly so might be efficient by not having to be on for long.
edit - ok for 250 degrees C - heat gun probably not hot enough.
I would put an oven on at close to max tem... | {
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Why does the light reflecting off of ocean water sometimes appear 'smoother'? Looking out the window at some water in the Harbour - I noticed that some parts of the water appear 'smoother' than others.
My question is: Why does the light reflecting off of ocean water sometimes appear 'smoother'?
| Most likely what you are seeing is a thin film of oil floating on the surface of the water that comes either from natural underwater sources, runoff from the shore, or from ships. The oil breaks the surface tension of the water and reduces traction forces from the wind - thus ripple amplitudes are reduced or entirely d... | {
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Must Matter Particles Have A Hard Edge? It's my understanding that electrons are particles, and it's also my understanding that their location while orbiting an atom cannot be determined precisely and must be determined by statistics and probability, almost like electrons can be in multiple places at the same time. Tha... | A particle does not need to have a hard edge. It can for example, be a density function, which sort of fades to zero.
One might note that waves can intersect each other and come out as if the other wave was not there.
Particles with hard edges are more an artefact of our minds rather than 'what's really there', unti... | {
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Cooling a satellite Satellites are isolated systems, the only way for it to transfer body heat to outer space is thermal radiation. There are solar panels, so there is continuous energy flow to inner system. No airflow to transfer the accumulated heat outer space easily. What kind of cooling system are being used in sa... | Typically, satellites use radiative cooling to maintain thermal equilibrium at a desired temperature.
How they do this depends greatly on the specifics of the satellite's orbit around Earth. For instance, sun-synchronous satellites typically always have one side in sunlight and one side in darkness. These are particula... | {
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Width of the decay of Higgs boson into dimuon According to Standard model, the partial width of the decay of Higgs into dimuon (up to tree level) is:
$$\Gamma\approx\frac{m_H}{8\pi} \left(\frac{m_{\mu}}{\nu}\right)^2$$
with the Higgs mass $m_H=125 GeV$, muon mass $m_{\mu}=0.106 GeV$, and the vacuum expectation value of... | It is mainly measurement and detector errors that make up the width in the plots you show. The Monte Carlo simulates the detector resolution and folds in the theoretical values when it says that the width agrees. The real width is expected to be much smaller.
In this we see that the real width is only given as a bound ... | {
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Klein-Gordon propagator integral in the light-like case In Kerson Huang's Quantum Field Theory From Operators to Path Integrals (Amazon link), pages 28 and 29, he calculates the propagator in the following case: time-like, space-like and light-like. First he integrates the time-component of $k$, and arrive this express... | I'll only consider the case $s \leq 0$. Consider your original integral;
$$
\Delta_{F}(s) \ = \ \frac{i}{4 \pi^2 r} \int_0^\infty dk \frac{k\ e^{i |t|\sqrt{k^2 + m^2}}}{\sqrt{k^2 + m^2 }} \sin(rk)
$$
If we're careful, we notice that this integral is quite naughty; it doesn't converge for $\mathrm{Im}(|t|)=0$. To see w... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Does the CMB signal get weaker over time? If the universe is infinite or flat, then this isn't true (I guess).
But if the universe is finite, then as it expands wouldn't the CMB signal weaker at any given point over time?
| If we define a scale factor $a$ for the universe (could be the distance between two galaxies), then this scale factor will change with time. This is also true in flat or infinite universes, so long as the Hubble parameter is $>0$ (i.e. the universe is expanding).
The energy density contained in the cosmic microwave bac... | {
"language": "en",
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What is the difference between electromagnet and solenoid? What is the difference between electromagnet and solenoid? Both these terms seem as the same thing to me. The only difference that I can find seems to be that an electromagnet contains a soft iron core. I'm sure there must be some other difference between the t... | An electromagnet is an electromagnet. i.e.: A (insulated) wire that is wrapped around an iron core that produces an electromagnetic field when current is passed through it. A solenoid uses an electromagnet to perform a mechanical function.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/150570",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Non-geodesic circular orbit? From N. Straumann, General Relativity
Exercise 4.9: Calculate the radial acceleration for a non-geodesic circular orbit in the Schwarzschild spacetime. Show that this becomes positive for $r>3GM$. This counter-intuitive result has led to lots of discussions.
This is one of those problems ... | The equivalence principle tells us that we can evaluate $\nabla_u u$ in a co-moving reference frame and that for geodesics we should find no acceleration (to the occoupants of an elevator in free-fall, the contents seem to be experiencing no acceleration). Therefore, if we evaluate this when we are not along a geodesic... | {
"language": "en",
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"source": "stackexchange",
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What limits the doping concentration in a semiconductor? Si and Ge can be blended in any ratio, $\mathrm{Si}_x\mathrm{Ge}_{1-x},\ 0\le x\le 1$. So do
InxGa1-x.
So what exactly causes doping impurities inside Si/Ge/etc. to saturate at $\sim 10^{-19}\ \mathrm{cm^{-3}}$?
| These are actually two questions in one. On one hand, certain materials are miscible like for $$ Si_{1-x}Ge{x} $$ or likewise for $$ In_xGa_{1-x}As $$. Depending on the phase diagram, some materials can be mixed, while some are not soluble and would segregate, like Steve B mentioned before. Some materials can be mixed ... | {
"language": "en",
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Why is Graphene So Strong? There has been a lot of news about Graphene since its discovery in 2004. And as we are all told it is a revolutionary material which is very strong, conductive and transparent.
But what is it about the structure of Graphene which makes it so strong?
| What makes Graphene so strong is its electrostatic forces resulting from delocalized electrons flowing through positively charged carbon atoms. This diffrence in charge creates a strong electrostatic attraction that holds Graphene together. This phenomenon also explains why it is such a strong conductor.
| {
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Doesn't a box holding a vacuum weigh the same as a box full of air? This was recently brought up, and I haven't been able to conclude a solid answer.
Let's say we have two identical boxes (A and B) on Earth, both capable of holding a vacuum and withstanding 1 atm outside acting upon them.
A is holding a vacuum, while B... | The way I would think about this just for a quick answer:
A balloon filled with air gradually sinks. Now if you took the same balloon and made it rigid, sucked all the air out of it but it still had the same volume, it would float straight up. So I would say that the balloon filled with air weighs more.
Same would go f... | {
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"source": "stackexchange",
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What is the origin of CMB fluctuations? I have read somewhere that CMB (cosmic microwave background radiation) fluctuations in temperature are linked to mass distribution fluctuations in the early universe (at ~350000 years after Big Bang, which is of course when the cosmic radiation was emitted), and that is used to e... | The CMB is a snapshot of the state of the universe at the moment when the universe cooled enough to allow protons to capture electrons to form atoms, thereby allowing light to travel unimpeded for the first time - prior to this the universe was a remarkably uniform distribution of plasma. But there -were- minute varia... | {
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Induced EMF of a rectangular loop should be zero? Considering the shape of a rectangular loop in a changing magnetic field:
The induced $\epsilon$ would be zero? Since a rectangular loop is a combination of wires in series to create such a shape. Each wire in this loop induces $\epsilon$ opposes the other, and they sh... | I think your problem comes from the fact that a 'wire' is an idealized conductor with zero resistance. A loop formed by such wires does inded not allow for any voltage drops to appear.
Any attempt to induce a voltage (such as changing the magnetic flux) would immediately create an induced current, which in turn would c... | {
"language": "en",
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Is Parity really violated? (Even though neutrinos are massive) The weak force couples only to left-chiral fields, which is expressed mathematically by a chiral projection operator $P_L = \frac{1-\gamma_5}{2}$ in the corresponding coupling terms in the Lagrangian.
This curious fact of nature is commonly called parity v... | I guess it is because you first of all change sign of $\vec x$ to $- \vec x$ in physical space(this is parity transformation in a nutshell). All this peculiar algebra concerning left and right chirality fields comes from $J = 1/2$ Lorenz group representation, so transformation rules are defined as representatives of pa... | {
"language": "en",
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Is time travel impossible because it implies total energy in the universe is non-constant over time? I have always argued with my friends regarding Time Travel that it is impossible. My argument has been that it will destroy the theory that all the energy in the universe is constant since when one travels to a differen... | Time travel is not impossible because of conservation of energy, time travel is not impossible at all. Entropy does not allow you to go backwards in time, but forwards does not present any problems.
| {
"language": "en",
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"source": "stackexchange",
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What is the cause for the validity of Newton's third law? What, specifically, causes newton's third law? For instance, if I push on a wall, why is it that I experience a force in the opposite direction?
I seem to vaguely understand that is has something to do with electronic repulsion or molecular compression (maybe... | We start by noting that force is the rate of change of momentum. Let's suppose you and I are floating in space (so we are the only two interacting bodies) and you're pushing me so I feel a force $F_{me}$, then:
$$ F_{me} = \frac{dp_{me}}{dt} $$
where $p_{me}$ is my momentum.
But we know that momentum is conserved, so s... | {
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Does gravity affect water permeability? Suppose I have an approximately rectangular prism composed entirely of folded paper. If I place 600 lbs (250 kg) on top of these rectangular sheets of paper, the paper should compress. How does this affect water permeability across the sheet? Is the rate across which the fluid fl... | You elaborate in a comment:
We assume capillary action of flow of fluid, as any type of pressure may alter composition of the paper. The paper is similar to paper towels, except the sheets are folded.
The height $h$ of a column in a capillary with radius $r$ is given by
$$
h = \frac{2\gamma \cos\theta}{\rho g r}
$$
w... | {
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What will happen to a permanent magnet if we keep the same magnetic poles of two magnets close together for a long time? What will happen to permanent magnet's magnetic field or magnetic ability if we keep same magnetic poles of two permanent magnet for long time?
Will any magnetic loss happen over the long period of ... | In my experience (with ferroxcube materials) nothing happens. In fact, to change the magnetic properties the magnetic domains inside must be reoriented. But the force excerted by the second magnet is not strong enough to do so. But one can magnetize a non-magnetic piece of iron (for instance the tip of a screwdriver) b... | {
"language": "en",
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Why does room temperature water and metal feel almost as cool as each other? From what I've read about heat, temperature and conductivity, I understand that the reason water at room temperature feels colder than most other things at the same temperature (like wood, air, cotton) is because of its higher thermal conducti... | The parts of your body that generate heat and that can sense temperature and the loss of heat are insulated from the environment by a layer of dead skin cells. The total thermal conductivity to the environment is the thermal conductivity of the materials that you touch in series with the thermal conductivity of this la... | {
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Simple example showing why measurement & interaction are different Does someone know of a clear (pedagogical) example where one can really see(with the math) where interaction and measurement are not synonymous in quantum mechanics?
*
*I know that every measurement involves a certain interaction with the outside wo... | QM says that interactions are not always measurements. The canonical example is Schrödinger's cat. We have countless trillions of interactions per microsecond for hours - the state of the system is a very complex huge wave function which lives in a hilbert space one can only describe as awesome. Then the box is opened,... | {
"language": "en",
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"source": "stackexchange",
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Solar spectrum units Why is intensity $I$ on a graph of the solar spectrum always showed in units of $[\mathrm{W/m^2/nm}]$ instead of simply $[\mathrm{W/m^2}]$? (The y-axis on the graph.)
It is apparently shown as intensity per wavelength, but why add this extra specification? For me it just complicates matters (it is ... | $W/m^2$ would be the total energy emitted, regardless of wavelength. When you use $W/m^2/nm$ you are explicitly saying that it corresponds to a specific part of the spectrum (nm is a unit of wavelength). Which is what the graph you posted is showing. The first one is called "irradiance", the one plotted here is called ... | {
"language": "en",
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How are momentum and position operators dependent on the chosen inertial frame? How are momentum and position operators in quantum mechanics dependent on the chosen inertial frame of reference?
| The are defined just once you have fixed an inertial reference frame and a Cartesian orthonormal coordinate system co-moving with it. Changing inertial reference frame, the new operators are related with the initial ones by means of a strongly continuous projective-unitary representation of (connected) Galileo group $G... | {
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Length contraction in cyclic space Consider a flat universe with at least one finite cyclic spatial dimension: travel x meters in one direction, and you will end up back where you started.
For an object that is of small size relative to the scale of the cyclic dimension, relativistic length contraction ought to work ou... | There is no length contraction in circular movements! Length contraction is only in the direction of movement.
A cyclic universe would be e.g. a 3-dimensional universe curved in a fourth dimension, or if a cyclic dimension is curved in a second dimension Thus length contraction could happen only locally, where the curv... | {
"language": "en",
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QFT and violation of Heisenberg uncertainty principle In some QFT books is said that a free electron can emit a virtual photon as long as it reabsorbs the photon and returns to its original state within a time:
$$\Delta t<\dfrac{\hbar}{2\Delta E}$$
That inequality DOES VIOLATE the Heisenberg Uncertainty Principle. Why ... | The first relation you give is simply wrong (typo in the textbook?). Because for on-shell stable particle $\Delta E=0$, it leads to $\Delta t< \infty$, meaning that any value from 0 to infinity could be possible. It's a non sense, a stable particle cannot live 0 s. The second formula is the good one: the greater the ma... | {
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How are these types of time dilation related? How are these two phenomena related (if at all):
1. Gravitation slowing down time
2. High speed slowing down time
| I believe the answer you are looking for is in the link below.
If you take how many Schwarzschild Radii you are from the center of a mass (or how deep you are in a gravitational field) it is equal to how many times faster light is going squared.
x=y^2
so if you are 4 (x) Schwarzschild radii from the center of a mass th... | {
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For creating beats how small the difference should be between the two frequencies It is said that to create beats we need two "slightly" different frequencies, and subtract it.
1- My question is why do we need slightly different frequencies? Why not large difference?
2- Also how slightly different? what is the limit... | By superposition principle we will arrive at,
$$y_{total} = {[ 2Acos(2\pi \Delta f/2) ]cos(2\pi f_{av})} $$
(source: unsw.edu.au)
The term inside the [] brackets can be considered as the slowly varying function that modulates the carrier wave with frequency $f_{av}$. (It is indeed an example of amplitude modulation or... | {
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Why does the tongue stick to a metal pole in the winter? since the Christmas season is here, I would like to ask a question about the movie, "A Christmas Story." In one of the subplots of the movie, Ralphie's friends were betting each other that their tongue would stick to to a frozen pole. Finally, the kid did it and ... | The reason is the same as why a metal pipe feels colder than wooden plank at the same temperature: thermal conduction.
The heat from your tongue (including the moisture) is absorbed faster than your body can replenish it. This has the effect of freezing your saliva in the tongue's pores to the metal surface (which its... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/153668",
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Temperature of electroweak phase transition How does one estimate the temperature at which electroweak phase transition (EWPT) occurred? Somewhere I have read it is around 100GeV but the reason was not explained.
| We calculate the free energy (density) for the Higgs field $\phi$ at finite temperature. In the Standard Model, this looks like
$\mathcal{F}_{SM}(\phi,T) = -\frac{\pi^2}{90}g_* T^4+V_{SM}(\phi, T) \ ,$
where $g_*$ is the number of degrees of freedom in the SM ($g_*=106.75$).
The potential has the form
$V_{SM}(\phi,T) =... | {
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Why do floating water drops form spheres? Consider a drop of water floating in an inertial frame in STP air (e.g., the ISS). Intuitively, the equilibrium shape of the drop is a sphere.
How would one prove that? Is it equivalent to showing that the minimal surface area for a simply connected volume in $\mathbb{R}^3$ wit... | The droplet wants to minimise its surface energy. This energy is proportional to its surface area. So the equilibrium shape is that which minimises the surface area for fixed volume (the bulk density is fixed by the temperature and pressure).
| {
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Minimum spread of frequency and wavelength in neodymium laser What is the equation linking the minimum spread in wavelength and frequency of a pulsed laser, in relation to the lasers pulse time and operational wavelength.
For example:
If a Neodymium laser operates at a wavelength of 1×10–6 m and the laser is operated i... | Obtain the frequency spread from the Energy-time uncertainty relation. Then you argue that from Energy-frequency relation and wavelength spread by extension can be calculated..... Just a trial. Thank you.
| {
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Force of a Train Imagine that there are two trains and the first train is twice as long as the second train. They have the same mass per unit length and they are traveling at exactly the same speed.
If the first train hit me, would it hit me with twice as much force as the second train? These are two distinct situati... | First of all you should note that Newton's law says when $F$ acts on a mass $m$, then that mass will move with acceleration $a$.
Here, we should apply the laws of collision and by using the conservation of momentum, find out what your velocity will be after the collision. Before collision we have: $p_{tot}=mv$ and afte... | {
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Does lunar module need the same amount of fuel for landing and take off? Let's assume there is no atmosphere and let's assume there is no change in weight due to fuel consumption, will reactive rocket need the same amount of fuel for landing on a planet as for take off?
In theory - I think - you need the same escape ve... | Landing is gravity-assisted, so requires less energy. A spacecraft on the moon has used up fuel resulting in its mass being less. If it is significantly less, then it takes less energy to lift a less massive craft back into orbit, than landing a heavier craft.
Escape velocity applies only to non-powered projectiles, su... | {
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How would gravitons couple to the Stress-Energy tensor? How would gravitons couple to the Stress-Energy tensor $T^{\mu\nu}$? How did physicists arrive at this result? I've read that it follows from the analysis of irreducible representations of the 4-dimensional Poincaré group, but is this accurate?
| The stress-energy tensor, is up to multiplicative factors, can be defined by $\frac{\delta S}{\delta g^{\mu\nu}}$, where $S$ is the action and $g_{\mu\nu}$ is the metric. When people talk about the graviton, they talk about quantizing the metric around it's classical solution, so we consider field values $g_{\mu\nu} = ... | {
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How to reconstruct the dependence of the potential from a coordinate? An ion moves along the x-axis of a black box with a speed $V$ and returns in a time
$$T=a V^b$$
where $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of a field potential $U(x)$ of this box?
So far I have managed to... | No, I don't think that you proceed correctly. You need the relationship between force and distance, and this is what you should integrate.
So, please follow my formulas. So, I understand that $V$ is the velocity of the ion (not of the box).
From your formula $T=aV^b$, I deduce the acceleration $A$ acquired at the end o... | {
"language": "en",
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The work-energy theorem Well here's the question.
From some previous excercises we know that from
\begin{align}
A&=\int F\;ds,\\
&=\int ma\;ds, &&(F=ma)\\
&=\int m \frac{dv}{dt}\;ds, &&(a=dv/dt)\\
&=m \int_{v_1}^{v_2}v\; dv,\\
&=m \frac{v_2^2}{2}-m \frac{v_1^2}{2},\\
&=W_2-W_1, &&(W_i=\frac12mv_i^2)\\
&=\D... | The height $h$ is probably the vertical displacement pointing downwards. Therefore:
$$
h = \left(-\mathbf{\hat j}\right)\cdot\mathbf s = -|\mathbf{\hat j}||\mathbf s|\cos\alpha = -s\cos\alpha
$$
Now we can derive:
$$
\frac{dh}{ds} = -\frac{d}{ds}\left(s\cos\alpha\right) = -\cos\alpha
\quad\Longrightarrow\quad \frac{dh... | {
"language": "en",
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Why are position and velocity enough for prediction and acceleration is unnecessary? In classical mechanics, if you take a snapshot and get the momentary positions and velocities of all particles in a system, you can derive all past and future paths of the particles. It doesn't seem obvious why the position and its fir... | The reason that you only need to specify initial position and velocity to exactly solve the equations of motion for a system is simply because Newton's Second Law (which is the equation governing motion in Classical Mechanics) is a second-order differential equation. The upshot is that to solve a 2nd-order ODE, you bas... | {
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Does wave interference happen only to same frequency waves? As the title says, from books and results from internet, I find that examples of wave interference always have the same frequency, only different in phase constant.
So, I'd like to know if wave interference happens only to same frequency waves
| Usually examples in textbooks, the internet, and others will use two waves of the same frequency for experiments such as the Double Slit experiment, or else to show complete constructive or destructive interference. All EM waves will interfere with one another to varying degrees. Usually if we are considering frequenci... | {
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In what order will the magnetic quantum number be filled For example, the electron configuration for Cu(II) ion is [Ar]3d9. So only the 3d shell matters to the total orbital angular momentum of the ion. For 3d shell there are 5 possible values of $m_l : 0,\pm 1,\pm 2$. So how will the 9 electrons fill the 10 slots? Wha... | Sorry, never mind. Hund's rule answers this directly.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/154628",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
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