Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Is $E^2=(mc^2)^2+(pc)^2$ or is $E=mc^2$ the correct one? I have been having trouble distinguishing these two equations and figuring out which one is correct. I have watched a video that says that $E^2=(mc^2)^2+(pc)^2$ is correct, but I do not know why. It says that $E=mc^2$ is the equation for objects that are not mo... | I agree with answer of ACuriousMind, but I think it might also help to think about it like this....
$E^2=m_0^2c^4+p^2c^2 =m^2c^4$
where $m_0$ is the rest mass and $m$ is the relativistic mass (or inertial mass), defined as $m = \gamma m_0 = m_0 / \sqrt{1 - v^2/c^2}$.
The relatavistic mass increases as the momentum of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/143652",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
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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... |
For a ring:
$Ke = \frac{1}{2}m ( \int_0^{2\pi} (Rw_1-rw_1cos(\theta)+rw_2cos(\theta))² +(rw_2abs(sin(\theta))² d\theta) $
$Ke = \frac{1}{2}m \int_0^{2\pi} R²w_1²+r²w_1²cos²(\theta)+r²w_2²cos²(\theta)-2Rw_1²rcos(\theta)+2Rw_1rw_2cos(\theta)) -2rw1cos(\theta)rw_2cos(\theta)+r²w_2²sin²(\theta) d\theta$
$Ke = \frac{1}{2}m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/143715",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can there be force without motion? I am confused. Can you have a force or tension without motion?
Take for instance two robots with jet packs connected via a cord, each is flying in opposite directions.
The tension of the cord is measured through a sensor of some kind. At some point, the net forces of the robots become... | In a system, the total sum of forces when added together equals mass times acceleration:
$$
\sum F = \frac{\mathrm{d}p}{\mathrm{d}t} = \frac{\mathrm{d}mv}{\mathrm{d}t} = m\frac{\mathrm{d}v}{\mathrm{d}t} = ma
$$
Since the sum of the forces on the robots is zero, there is no acceleration. However, the tension of the stri... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/143822",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why is quasineutrality required for a gas to turn into a plasma? Why is quasineutrality a required condition for a plasma to exist?
Quasineutrality means that no density of electrons and ions should almost be equal but not exactly equal. Can anybody explain this this condition is required?
| If the number of electrons and ions is exactly equal, it is still plasma. You are misunderstanding the quasineutrality requirement.
The term "plasma" was coined by Irving Langmuir with the phrase "We shall use the name plasma to describe this region containing balanced charges of ions and electrons", Oscillations in ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/143918",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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 you cool it the domains so formed align to get minimum energy and that is not the energy in which all are pointing in the same direction.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/144144",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 3,
"answer_id": 2
} |
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 addition to the points mentioned by Andre Holtzner, there is also a non-thermal effect due to photons hitting the water molecules and kicking them out of the water directly. This process plays an important role in the vaporation of water due to irradiation by sunlight. You can think of the photons being at a tempera... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/144221",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Confusion with rotation operator definition in Shankar In Shankar quantum mechanics on page 306-307 it has the following:
12.2. Rotations in Two Dimensions
Classically, the effect of a rotation $\phi_0\mathbf{k}$, i.e., by an angle $\phi_0$ about the $z$ axis (counterclockwise in the $x\ y$ plane) has the following ef... | Shankar is being a little bit sloppy with the term "state," although not that sloppy since he does use the qualifiers "quantum" and "classical" to achieve clarity.
In classical mechanics, the position of a particle is represented by a point $\mathbf r$ in three dimensions $\mathbb R^3$. To rotate the configuration of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/144300",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Is there charge build up before a resistor? I understand that Kirchhoff's current law says that the current, $I$, is constant throughout a resistor, i.e. there is no build up of charge in a resistor. All charge going in to the resistor is the same as all charge coming out. In other words, Coulombs/sec going in = Coulom... | Crudely, electrons repel each other and even out the charge. While the influence of the electrons travels at a good fraction of the speed of light the electrons themselves do not move much. From this link
" The electricity that is conducted through copper wires in your home consists of moving electrons. The protons and... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/144444",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Spectral irradiance units conversion I have a table of data containing irradiance of light at different wavelengths. This is how it looks like for 300.5 nm:
*
*Wavelength, nm: 300.5
*Wavelength, $\mu$m: 0.3005
*W/m$^2$/$\mu$m: 403
*W/m$^2$/nm: 0.403
My question is, how can I convert W/m$^2$/nm or W/m$^2$... | All sources of light have a spread of wavelengths. There is no such thing as a light source that produces light of exactly one wavelength. Let's assume that the power emitted by your light source looks like this:
I just made up this curve, but the shape of the curve doesn't matter for this discussion. The $y$ axis sho... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/144798",
"timestamp": "2023-03-29T00:00:00",
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Choice of the $z$-axis in the Schrödinger equation for the hydrogen atom I am reading about the solution of the Schrödinger equation for the hydrogen atom and have a question about the choice of the $z$-axis. Most websites say that the $z$-axis is arbitrarily chosen. If so, why is the choice of the $z$-axis not part of... | Say we have two different coordinate systems $F=(x,y,z)$ and $F'=(x',y',z')$.
Consider the basis spanned by the eigenvectors of the $L_z$ operator for a given $l$, $\{|l \; m\rangle\; ; \;m=-l,\dots,l\}$. Now, one can find the eigenvectors of the $L_{z'}$ on this basis. In general, the eigenvectors of $L_{z'}$ will be... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/144878",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | Choose a point P on the periphery of your gyroscope and paint it with some color. Then, as the gyroscope rotates take photos and if possible, record the time of each picture. Let's name O the origin around which rotates your gyroscope. Now, using the pictures and the times recorded, calculate the change in time of the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/144915",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Tranverse electromagnetic waves TEM waves do not exist in waveguide. Is this the correct explanation- Both curl and divergence of TEM are zero inside the waveguide and because of the boundary conditions (electric field zero at every point of a hollow conductor), the only solution possible is zero i.e. trivial?
| TEM waves do exist in multi-conductor waveguides such as coaxial guides, in fact they exist in any homogeneous waveguide with more than one conductor. There are no propagating TEM, TE or TM modes if the cross section is inhomogeneous but at cutoff frequency the hybrid modes degenerate to the respective transversal mode... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/144987",
"timestamp": "2023-03-29T00:00:00",
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Why is the unitary matrix relating the gamma matrices and their complex conjugates antisymmetical? In Messiah's Quantum Mechanics Vol. II, properties of the Dirac matrices are derived. There is so-called fundamental theorem, which states that,
Let $\gamma^\mu$ and $\gamma^{'\mu}$ be two systems of 4 fourth-order unitar... | Notice that both $B$ and $B^\star$ are unitary matrices and, therefore, $B B^\star$ must be unitary as well, which implies that its determinant must be either $1$ or $-1$. Since you have already determined that $B B^\star = c\,I$, this narrows the possible values of $c$ down to $c = \pm 1$.
About the expression $B^\pri... | {
"language": "en",
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"source": "stackexchange",
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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 ... | curvature produces relative acceleration of geodesics because of equation of geodesic deviation (relation between riemann tensor and relative accleleration of geodesics) and also newtonian theory of gravity predicts tide-producing acceleration which explain two particle with separation x parallel to r ,cause eva... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/145162",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | Transverse Doppler effect
On a plane, parallel lines are drawn. On each,lines, light sources (frequency is the same time) are moving in the opposite direction. Imagine light sources form Japanese letter エ. Transverse Doppler effect will not be.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/145305",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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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... | Acceleration
If your exact need is, as you say, to determine "if the vehicle is moving at a constant speed" then there is a wide range of accelometers available on the market with various degrees of accuracy.
If the accelometer shows 9.8 m/s2 downwards (assuming you install it in a fixed orientation relative to the veh... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/145400",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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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... | In this case you show that the net force acting on the object is zero in this situation, that is, half of the object is within the water and another half on the water. This position of the object is thus equilibrium position. If it would come totally on the water surface or within the water then the equilibrium will be... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/145467",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Tractor wheels -- large vs small This question has stumped me for over a month now:
Why is it that a tractor has large wheels at the back and small wheels in the front?
Current ideas:
*
*small wheel in front --> lower center of mass--> less likely to tip over, moment.
*large wheels in back provides more torque,... | Leverage
Often, a limiting factor in tasks required from a tractor is the amount of pulling force a tractor can apply without tipping over (the front rising up) - the engine is strong enough to do so.
Having the driving axle be high from the ground helps by simple lever action - see the illustration; twice the height m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/145571",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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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... | NASA has created an atmospheric model that should do exactly what you want. It's called EarthGRAM.
It allows you to input a time history of coordinates (latitude, longitude, altitude) and will generate a 3D wind velocity, density, and temperature for each coordinate. The exact values of each output are randomly gener... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/145724",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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How can the linear momentum can be understood physically? Currently reading Classical Mechanics by Herbert Goldstein, and I'm trying to understand every concept physically. Speed can be understood physically, as the distance traveled within a certain amount of time, it makes sense to me. By contrast, I can't attribute ... |
Speed can be understood physically, as the distance traveled within a
certain amount of time, it makes sense to me. By contrast, I can't
attribute a physical explication to linear momentum. How can I
understand it physically? Why do we multiply mass by speed?
'speed' (or velocity) is the measure of 'motion' and... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/145796",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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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... | By definition, anything outside of the observable universe is unobservable. This has the annoying effect (eye twitch) of making it so we have practically no idea what the universe is actually like outside of what we can observe. We can assume that it is homogeneous and isotropic and that there are other large galaxies ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/145893",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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?
| $v$ applies to the speed of sound in the equation $f=\frac{v}{\lambda}$. Assuming air to be an ideal gas we can use the following equation to calculate the speed of sound in air:
\begin{equation}
v=331.3\sqrt{1+\frac{T}{273.15}}
\end{equation}
where $T$ is the air temperature in degrees Celsius.
The wavelength should b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/145988",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Complex Conjugate of Wave Function I've been reading through Griffiths QM book, and the only thing bugging me is they never fully described what $\Psi^* $ should be for any given function. I know it's the complex conjugate at the same time I think I just need concrete examples to solidify it in my head.
What is the cor... | Take the time dependent Schrodinger equation
$$iħ \frac{∂Ψ}{∂t} = HΨ$$
and take the complex conjugate on both sides. The Hamiltonian is real, s.t. we get
$$-iħ \frac{∂Ψ^*}{∂t} = HΨ^*$$
But we can write the last equation otherwise, by inversing the direction of the time,
$$iħ \frac{∂Ψ^*}{∂t'} = HΨ^*$$
where $t' = -t$. I... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/146211",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Can length contraction really be derived from time dilation? Does speed equal speed? I am referring to Wikipedia: "Length contraction can also be derived from time dilation." with the following proof which seems to be the result of a circular reasoning.
The proof uses only one and the same velocity v for the point of v... |
Or am I wrong, and it is evident and without need of further proof that v' = v?
It may not be obvious, and it does require proof, but it is true, and it's not anything terribly deep or mysterious.
Consider two observers, Alice and Bob, moving away from each other. Alice says she's at rest and Bob is moving. Bob says ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/146257",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"answer_id": 0
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How is the scattering length in 2d defined? Scattering length is 3d is well-defined. In the literature, one can also see scattering length in 2d. How is it defined? Can we even generalize it to 1d?
| One has to be careful when extending the concept of scattering length to lower dimensions. A straightforward extension of the 3D methodology to 2D is prone to lead to logarithmic divergences. Reason being that in 2D the radial Schrödinger's equation for the s-wave includes a negative centrifugal potential.
When careful... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/146551",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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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... |
Not discounting other traits, is there something about six legs that has helped insects achieve this success?
Spiders oftentimes have eight legs, mammals oftentimes have four. But centipedes have lots of legs, and millipedes have lots of legs. The reason mammals have four legs, and millipedes have lots and lots of le... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/146623",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Does zero free current entail zero $\vec H$? There are two kinds of magnetic fields (different authors give them different names), $\vec B $ and $\vec H$ which are related by the equation $$ \vec B = \mu_o (\vec H + \vec M)$$ where $\vec M$ is the magnetization.
Ampere's law for free currents states $$\oint_C \vec H \c... | I think your argument is completely flawed.
Consider a uniform H-field. The closed line integral of this field around any loop is zero - and there must be no free current through the loop. Hence there is no free current, yet the H-field is non-zero.
You might be better off thinking about this in terms of free current d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/146677",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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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... | Let's consider a simple experiment in which a stone tied to a string is moving in a uniform circular motion in a horizontal plane. We can analyze this experiment from inertial and non-inertial frames.
An observer in an inertial frame sees the stone having a radial acceleration and concludes that there must be a radial ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/146823",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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If angular velocity & angular acceleration are vectors, why not angular displacement?
Are angular quantities vector?
... It is not easy to get used to representing angular quantities as vectors. We instinctively expect that something should be moving along the direction of a vector. That is not the case here. Instea... | The wikipedia link does an adequate job of explaining this.
You can find a very mathematical discussion in this partial duplicate question, but here is my simple take on it.
The angular displacement in three dimensions does have a vector nature in the sense of having both a magnitude (the angle through which you turn ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/146897",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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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?.
| No, a photon does not need to have mass to be able to interact with matter. In fact it is its energy which is important in interactions. For the photoelectric effect the incoming photon must contain enough energy to displace the electrons on the metal of the photodiode.
The question of what are photons made of is a pre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/146975",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Velocity of car down an Inclined Plane I was learning to make a car game and came across this situation where my car is on an inclined plane. It's initial velocity is 0. Now, the problem is that my memory serves me this formula to calculate the final velocity
$$v_f^2 - v_i^2 = 2as$$
Since, $v_i = 0$, the equation woul... | You can cast your problem in terms of what is the velocity of the car at any instant of time after it started. The answer is $v = a_{\rm eff} t$ from the first kinematical equation. In the same time, the car would've traveled a distance $s = (1/2)a_{\rm eff} t^2$ from the second kinematical equation.
The other option ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/147195",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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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... | Yes it is possible. The trick is to have a parachute which is large enough that it's Schwarzschild radius extends down to the object it is lifting.
Under such a circumstance, the parachute would stop ALL motion of the object it is lifting.
PS I just watched Interstellar :D
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/147346",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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"answer_id": 7
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Where on Earth does the mass of 1 kg actually produce a 1 kg reading on a digital scale? Gravity on Earth varies by about 0.1% between poles and equator. If someone was buying/selling something mass critical e.g. gold, where is the standard place on Earth where a 1 kg mass produces a 1 kg reading as measured by a devic... | In addition to the good answers already given a couple of points.
1) if you used scales where one mass balances another mass like this one
Then you would not have problems with any variation in $g$.
2) I did a google search to check what people use to measure the mass of gold (and also diamond) and everything came b... | {
"language": "en",
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What do physicists mean by "information"? On the question why certain velocities (i.e. phase velocity) can be greater than the speed of light, people will say something like:
since no matter or "information" is transferred, therefore the law of relativity is not violated.
What does information mean exactly in this c... | In the context of relativity and nonproagation of information at greater than lightspeed between two separated points $A$ and $B$, "information" simply means any particle, feature of in a field (EM, quantum field, curvature in spacetime ...), message or so forth that could allow a causal link between $A$ and $B$, i.e. ... | {
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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 ... | As the previous answers have noted, momentum conservation often isn't useful. However, there are exceptions -- especially in transport problems. Although you're not necessarily directly using the canonical ensemble for these problems, they are decidedly statistical mechanics problems. For example, (quasi)momentum conse... | {
"language": "en",
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"source": "stackexchange",
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What does the exponential decay constant depend on? We know the law of radioactivity:
$$N=N_0e^{-\lambda t}$$
where $\lambda$ is the exponential decay constant. My question is: This constant depends of what?
| The transition probability per unit time of a nucleus from an initial state i to a final state f, representing the decayed system, is modeled by Fermi's Golden Rule:
$$\lambda=T_{i\rightarrow f} = \frac{2\pi}{\hbar}\left|\left\langle i\left|H'\right|f\right\rangle\right|^2\rho$$
Where $T_{i\rightarrow f}$ is the transi... | {
"language": "en",
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What is the point of this type of graph? (Projectile) What is the point of graphing vs range, during kinematic motion?
| Generally speaking, when we graph experimental data it's nice for the graph to be a straight line. This is because it's easy to tell if a graph is a straight line just by putting a ruler on it. If a graph is a curve it's hard to tell whether it's a parabola, ellipse, sine wave or some other curve without diving into so... | {
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What does it mean to say "a paramagnetic material is attracted to an external magnetic field?" I'm just having a hard time wrapping my head around what actually goes on when a paramagnetic material is exposed to an external magnetic field. I understand that the individual dipoles line up so that they point in the direc... | A paramagnetic material is attracted not by the magnetic field but the force on it is towards the direction in which the magnetic field is increasing. In a constant field it would stay in place. This follows from the simple fact that all systems try to obtain a potential energy minimum.
| {
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Are there eight or four independent solutions of the Dirac equation? I edited the question as a result of the discussion in the comments. Originally my question was how to interpret the four discarded solutions. Now I'm making a step back and hope that someone can clarify in what sense it is sensible to discard four of... | There are only 4 independent solutions because:
$$v_{1,2}(+E, +\vec{p}) e^{+i(Et-\vec{p}.\vec{x})} = u_{3,4}(-E, -\vec{p}) e^{-i((-E)t-(-\vec{p}).\vec{x})}$$
(where $u$ and $v$ here don't include the propagating part contrary to your notation). You could choose to work with $u_1,u_2, u_3, u_4$ but it is more convenien... | {
"language": "en",
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Habitable zones around other stars I have a question about measuring the boundaries of habitable zones on other planets.
Is it okay to assume that, if Sun's habitable zone starts at a distance $R_0$ and its luminosity is $L_0$, we can calculate any other star's with luminosity $L$ habitable zone's inner boundary as $$R... | This looks fine, BUT, indeed have a good read of the wikipedia pages on the topic of habitable zones to see all the complications there are in deducing where around a star the conditions may be "habitable". In addition I recommend, if you are serious about this calculation, reading the short article by Kane & Gelino (2... | {
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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... | You are seeing particles. However there's more to this than meets the eye so I need to explain exactly what I mean by this.
Light is neither a particle nor a wave. Instead it is a quantum field. As a general rule while light is travelling it appears as a wave, but when the light quantum field is exchanging energy with ... | {
"language": "en",
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Capacitance of two non parallel plates What is the formula for capacitance of two non parallel plates at an angle with each other?If the plates were parallel then the value can be calculated as
(PermittivityX area of one plate)/distance between them.But what happens in case the plates are tilted at an angle?The questio... | Let's do some calculus.
Suppose you have two plates, almost parallel (off by an angle $\alpha$). The plates lie in the XY plane, from $(0, 0)$ to $(x_1, y_1)$. At $x = 0$, the plates are separated by a distance $z_0$, and at $x = x_1$, the plates are separated by a distance $z_1$.
We'll now consider an infinitesimally... | {
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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... | Actually, your book is correct. Even if the most usual uses of angular momentum involve circular or rotating motion, this is not the general case. An object moving in a straight line has angular momentum in a reference frame in which the origin does not fall on the the line.
To see this simply remember the definition ... | {
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Is it possible to make laser beams visible midair without smoke? My question is: Is it possible to make laser beams viable midair without smoke? I thought it would be a great idea to have a (second) smartphone or pc screen without having a solid screen. The reason why it has to be without smoke is that smoke would be t... | Not really; you need to have the laser light pass through particles in a medium. Laser light is made of photons; in order to see the laser, photons must be reflected off of a something to your eyes. You cannot otherwise "see" a photon because photons don't interact via the electromagnetic force - in other words, photon... | {
"language": "en",
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Restrictions on Bell-type inequalities While deriving and proving Bell-type inequalities of the form
$|E(a,b)-E(a,b')|+|E(a',b)+E(a',b')|\leq 2$
I know that the conditions on the operators $O_a$ and $O_b$ are that they must be bounded by $\pm 1$.
Joint operator $O_{ab}\equiv O_a O_b$ is consequently bounded by $\pm 1... | The CHSH inequality was not proved for any state, but for the spin singlet or for the photon singlet, s.t. to your question
"is there any such bound on the correlation E(a,b) given by operating by O_{ab} on whatever state you're studying? Does E(a,b) necessarily NEED to be bounded by ±1 as per the definition?
As I sa... | {
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How can the Andromeda Galaxy alone have more mass than the Local Group? I was reading about the Local Group, and it is stated that the total mass of the group is $1.29±0.14 × 10^{12}$ Solar masses.
The number actually felt a bit low to me because I know the Milky Way galaxy alone is close to a trillion solar masses, so... | It is difficult to estimate the masses of either galaxies or clusters of galaxies, and it depends on what source you consult. You can get different values from different sources, for instance in this reference: the local group is estimated to have $5.27\times 10^{12} M_\odot$ (which does include dark matter). I didn'... | {
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Disturbing a line of infinite alternating charges Consider a line of infinite number of alternating charges. All are point charges having charge of same magnitude and are placed in a line. Neglect the effect of gravity here. Consider one of the positively charged particle. I disturb it a little upwards.
What will happ... | The original system as described in inherently unstable (or at best metastable).
According to Earnshaw's Theorem, "a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges"
So the introduction of the slightest disturbance ... | {
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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.
| Put it in a microwave at the right power, and it will quickly heat up withouth burning (and heat whatever is inside). But do not try this at home. Too much power and you will get the microwave oven on flames.
| {
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Proper way to write the units to indicate that they include an offset? Past a certain point of complexity, I get rather confused with physical units, so I am asking a physicist for help.
I have a code that represents temperature, with a resolution of [0.5 °C], whose value ranges from 0 to 255 as the temperature goes fr... | While it is not a general answer, there is an engineering standard that holds that thermometer readings in non-absolute scales and temperature differences in the same scales have both different written notation and different spoken reading.
The prescribed convention is:
*
*Thermometer readings get the degree symbol ... | {
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What would Earth have been without the Moon? Would Earth rotation have been more slowed down because of the tidal effect from the Sun, as seems to be the case with Mercury and Venus? Due to the giant impact hypothesis the angular momentum from the impact was increased and split.
If Earth not would have been a two part ... | Tidal forces drop rapidly with distance - the derivative of $1/t^2$ is $-2/r^3$. Further, the difference in radius of the orbits of Earth and Mercury is a little more than a factor 3x and radius of mercury is about 2.5x smaller than that of earth.
From the orbits we gather the tidal effect is 27x smaller - from the rad... | {
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Where do ultra-high-energy cosmic rays come from? Physicists have detected an amazing variety of energetic phenomena in the universe, including beams of particles of unexpectedly high energy but of unknown origin. In laboratory accelerators, we can produce beams of energetic particles, but the energy of these cosmic ra... | Here is a topical proposal (from arxiv.org/abs/1602.06961):
The recent detection of the gravitational wave source GW150914 by the
LIGO collaboration motivates a speculative source for the origin of
ultrahigh energy cosmic rays as a possible byproduct of the immense
energies achieved in black hole mergers, provid... | {
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Can the relative position of two masses connected by a spring become negative?
Consider the following diagram. Two masses of 1 kilogram each are attached by a spring of 1 N/m. The $x$-axis is chosen such that $x_1(0)=0$ and $x_2(0)=L$ where $L$ is the length of the spring in relaxation (no restoring force acting on th... | I haven't combed through your math, but I suspect that you made some mistakes along the way. For instance, in your first set of equations $\ddot{x}_1(t)=-(x_1-x_2)$ should actually be $\ddot{x}_1(t)=(x_2-x_1-L)$. You can check yourself on this fact because the force ought to be $0$ when $d=L$. Furthermore, you need to ... | {
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Kirchhoff's current law with a nonlinear resistor It is said that by Kirchhoff's current law
$$
\frac{e - v_c}{R_1} = c\frac{dv}{dt} + f(v_c) + i\tag{1}
$$
and from Kirchhoff's voltage law
$$
v_c(t) = iR_2 + L\frac{di}{dt}\tag{2}
$$
from the following diagram:
It is easy to see equation (2) but I dont see how equatio... | Kirchhoff's current law says that the current entering any junction is equal to the current leaving that junction.
The current through $R_1$ must therefore add up to the current through the three legs of the circuit.
$$ I_{\mathrm{R}_1} = I_{\mathrm{cap}} + I_{\mathrm{nonlinear\ R}} + I_{\mathrm{R}_2} $$
Using the term... | {
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How do microwaves heat moisture-free items? Today I learnt that microwaves heat food by blasting electromagnetic waves through the water molecules found in the food.
Does that mean food with 0% moisture (if such a thing exists - dried spices?) will never receive heat from a microwave oven? And how in that case is a mic... | This Isn't About Water
Microwave heating actually has nothing to do with the moisture content of items. It has everything to do with the amount of electric dipoles (polar molecules) in the item of concern. Water molecules (with many other organic molecules) happen to be electric dipoles. (That is, one side of the molec... | {
"language": "en",
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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... | The decay width of a particle is antiproportional to its lifetime. Looking at the partial width of the $H \rightarrow \mu \mu$ decay, one could expect that the lifetime of the Higgs is large. This would be correct, if the Higgs could only decay to muons. In other words: The Higgs decaying to muons has a low probability... | {
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How do you define a "universe" (in the context of multiverse)? How do you define a universe (in the context of multiverse)?
The traditional definition of universe is something like
"The Universe is all of spacetime and everything that exists therein".
But in multiverse theory one talks about "universes" and this raises... | As far as I know, "a" Universe is caracterised by fundemental constants such as the speed of light, Newton's gravitationnal constant, the Planck constant and so on.
You could distinguish between two different universe from the variation of these values I think.
| {
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How does An Electric Field Create a Dipole Moment of a Rydberg Atom? I know that an Rydberg Atom will not usually have a Dipole Moment - as the positive nucleus are surrounded by a negative electron cloud, so there is no uneven charge distribution.
However, I also know that a Rydberg Atom with experience an Electric Di... | The Rydberg electron - the electron in the high n level - is highly polarizable and very weakly held. The binding energy of the electron is very small.
A small electric field will distort the wavefunction of the Rydberg electron so that it spends more time on one side of the atom than the other. The result is the form... | {
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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... | Electromagnets can be of various types ranging from simple solenoids to superconducting electromagnets, bitter electromagnets to explosively pumped flux compression generator. Thus, electromagnet can be considered as a universal set and solenoid is one of its subsets.
| {
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Coulomb's Law in the presence of a strong gravitational field I was under the impression that the $1/r^2$ falloff of various forces were because of the way the area of a expanding sphere scales. But that strict $1/r^2$ falloff would only be globally true in a strictly Euclidean geometry, yes? So, if you had an electron... | Yes. Strictly speaking you can't apply Coulomb's law, or in general any law about the falloff of something with distance, in curved space.
Instead you have to shift to a field-based formalism. You can calculate the way the electromagnetic field propagates through a curved background—basically you take Maxwell's equat... | {
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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 $\sim 10^{-19}\ \mathrm{cm^{-3}}$?
| If you dope the semiconductor too much it becomes what is called degenerate.
At normal levels of doping, the dopant atoms generate localized states in the material that can donate electrons or holes by either thermal excitation or optical excitation (e.g., a photon hitting a solar panel). The more you increase the dop... | {
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Why is Graphene Transparent? Graphene is always in the news now a days and its key features are that it is; very strong, conductive and transparent. It is so transparent that each layer of graphene will only absorb 2% of Light passing through it.
But what is it about the structure of Graphene which makes it (almost) tr... | I assume the biggest factor is the thickness. Graphene is a layer of carbon one atom thick. Light is absorbed/reflected by the top layers of a material and if you make any material into a layer one atom thick you'll find it increases transparency a lot.
The thing that is special about graphene is that it forms bonds i... | {
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What is the procedure (matrix) for change of basis to go from Cartesian to polar coordinates and vice versa? I'm following along with these notes, and at a certain point it talks about change of basis to go from polar to Cartesian coordinates and vice versa. It gives the following relations:
$$\begin{pmatrix}
A_r \\
A_... | This properly belongs on math.se, but to properly derive these you need to remember that we can write a vector in terms of basis vectors. The vector $\vec{A}$ is unchanged, but it is just expressed as a different linear combination:
$$\vec{A} = A_x \hat {x} + A_y \hat{y} = A_r \hat{r} + A_\theta\hat{\theta} $$.
Because... | {
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How introduce sound wave in molecular dynamics or dissipative dynamic particles? How could I introduce sound wave in molecular dynamics or dissipative dynamic particles?
What do specify which is applicable between molecular dynamics and dissipative particle dynamics? problem is simulating a 50 nm bubble in a MHz sound... | DPD doesn't have attractive forces so I don't see how it's possible to simulate a bubble with it. And a 50 nm bubble with MD? I hope you have a lot of computing power!
Assuming you use MD: I think the most elegant solution would be to use NVT with periodic boundary conditions, and modify the MD code you're using so tha... | {
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Does constant velocity of center of mass imply linear momentum is conserved? I know that if momentum is conserved for a system, you can derive that the velocity of the center of mass of that system is constant. I was wondering if the second condition also implies the first: if I can demonstrate that the velocity of the... | The linear momentum of a system is given by $\vec{p} = m \vec{v}$.
If you differentiate this with respect to time in an inertial frame, you have:
$$
{d\vec{p} \over dt} = m {d\vec{v} \over dt} + {dm\over dt} \vec{v}
$$
If $\vec{v}$ is constant with time, this becomes
$$
{d\vec{p} \over dt} = {dm\over dt} \vec{v}
$$
Wh... | {
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Physical significance of temperature Some books say when heat flows into a monatomic gas at constant volume, all of the added
energy goes into an increase in random translational molecular kinetic energy. But when the temperature is increased by the same amount in a diatomic or polyatomic gas, additional heat is needed... | Absolute temperature relates only to translational degrees of freedom (connection to pressure via momentum exchange with a supposed exterior membrane).
Since energy is constantly being randomly reshuffled between translational and non-translational degrees of freedom, the molar heat capacity is greater.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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 ... | They will repel each other and slowly they will lose their magnetic property which is also called demagnetization
| {
"language": "en",
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"source": "stackexchange",
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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... | Several things are happening here that may make the sensations of touching metal and touching water similar when they are at room temperature (~ 25 C), although the thermal conductivities are a couple of orders of magnitude different. The sensation of coldness comes from the loss of heat from the part of your body cont... | {
"language": "en",
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Formula for the magnetic field due to a current loop I need expressions for the $\mathbf B$ field generated by a circular current loop at a point off-axis from the ring's axis of symmetry.
The ones I came across on the internet aren't very convincing. I verified them with Mathematica, and none seems to be correct ─ I'm... | As mentioned in the accepted answer, the second link in the original question (now hijacked) does have the correct exact expression for the magnetic field, which is essentially given by direct line integration of the vector potential into
\begin{align}
\mathbf A
&=
\frac{\mu_0 I}{4\pi}
\oint_C \frac{\mathrm d\mathbf l}... | {
"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}$$
That inequality DOES VIOLATE the Heisenberg Uncertainty Principle. Why ... | I have been thinking about this question. Tell me what you think:
1) The relation
$$\Delta \tau \Delta \Gamma \geq \dfrac{\hbar}{2}$$
is RIGHT, applied to the timelife AND width of RESONANT states in QFT. A completely stable particule would have "zero width" and infinite timelife.
2) The equation
$$\Delta t\Delta E<\... | {
"language": "en",
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Physical examples where changing the order of limits yields wrong result In mathematics it is generally not allowed to change order of limits. For example it is not always true for a sequence of functions $f_n$, that $\int_a^b \left(\sum_{n=0}^\infty f_n(x) \right) dx = \sum_{n=0}^\infty \left(\int_a^b f_n(x) dx\right)... | The low-frequency ($\omega\rightarrow 0$), long-wavelength ($q\rightarrow 0$) conductivity of an electron gas in the random phase approximation depends on the order in which those two limits are taken.
Intuitively, if you take the $\omega\rightarrow 0$ limit first, you're talking about a static, long-wavelength potent... | {
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Half-integer eigenvalues of orbital angular momentum Why do we exclude half-integer values of the orbital angular momentum?
It's clear for me that an angular momentum operator can only have integer values or half-integer values. However, it's not clear why the orbital angular momentum only has integer eigenvalues.
Of ... | From $\mathbf{L}=\mathbf{Q}\times \mathbf{P}$ we have $L_z=Q_xP_y-Q_yP_x$. Then, introduce the following new operators (assuming units of $\hbar=1$):
\begin{align}
q_1=\frac{Q_x+P_y}{\sqrt{2}},\\
q_2=\frac{Q_x-P_y}{\sqrt{2}},\\
p_1=\frac{P_x-Q_y}{\sqrt{2}},\\
p_2=\frac{P_x+Q_y}{\sqrt{2}}.
\end{align}
It is immediate to... | {
"language": "en",
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Conformal Killing fields on Schwarzschild I am trying to understand which are the conformal Killing Fields on the Schwarzschild spacetime.
I say that $X$ is a conformal Killing field on $S$ ($S$ is Schwarzschild) if there exists a function $f: S \to \mathbb{R}$ such that
\begin{equation}
\mathcal{L}_X g = fg,
\end{equa... | In the Schwarzschild geometry, the Schwarzschild radius breaks naive dilation symmetry. In the simple case of a radial dilation $r \to \lambda r$, the geometry is only preserved by $R_S \to \lambda R_S$. So, it naively seems like it would be difficult to find a working dilation, even just a radial dilation.
I went to s... | {
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Electric field inside a diode When a voltage is applied to a diode (forward or reversed bias) the depletion zone is changed due to charges change in this region. My question is in both case (forward or reversed bias), how the electric field that is responsible of moving the charges in the P and N region is established ... | I don't think any of the current answers address your question as I understand it.
My understanding is that your question is effectively: What spatial distribution of charge gives rise to the electric field in a diode?
In the case of a uniform dielectric, the internal field is created by surface charges on the two sur... | {
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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... | The beat frequency is very simply:
$$f_{beat}=|f_1-f_2|$$
So there is no limit on how far apart they can be. In demonstrating the beat frequency one frequently uses frequencies that are slightly apart because it produces the typical "beating."
If for example you were using the frequencies $561.6$ Hz and $300$ Hz you wo... | {
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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.
| higgs field causing electroweak transition. before higgs field w,z boson photon all are massless. but higgs field gives masses to them and symmetry spontaneously break. because if particles having masses then su(2)u(1) symmetry break. all gauge symmetry break if we give mass to the particles.so transition must have to ... | {
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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... | A Community Wiki answer to make some other people's comments permanent and tie some loose ends up.
To add to Mark Mitchison's Answer, the reason that the prevailing shape is the one that minimises surface energy as he states is that, in the case of water, the liquid's total energy is an (almost) constant offset (the po... | {
"language": "en",
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How do we find the accuracy of atomic clocks? We say that atomic clocks are the most accurate clocks ever made, they may lose or gain $x$ seconds in $y$ years. How do we find this uncertainty because we do not have an ideal clock to compare with the clock that we made?
| The nearest we have to a standard is International Atomic Time. This is:
TAI as a time scale is a weighted average of the time kept by over 200 atomic clocks in over 50 national laboratories worldwide.
The errors in individual clocks can be assessed by comparing them to the weighted average.
Re the mention of pulsars... | {
"language": "en",
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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... | The difference in force to stop the trains you are talking about here is the difference in force is needed to bring the train to a stop within a particular distance Let me tell you what I mean.
When you try to stop the train, you'll obviously be dragged in front of the train. Say the dragging causes an uniform force (d... | {
"language": "en",
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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... | Now it occurred to me that the escape velocity/breaking may be symmetrical - that means you need the same amount of energy to counter the gravity on the way up as you need on the way down - but what also matters is how long you stay "hoovering" in the gravitation filed. This is what consumes fuel no matter what way you... | {
"language": "en",
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"source": "stackexchange",
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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?
| It is not known yet.
Gravitons are from quantum mechanics model, while stress-energy tensor is from General relativity (GR) model.
Two models are not connected until quantum gravity created.
Also, gravitons were never observed, so they are pretty hypothetical.
Simultaneously, it is known, that metric tensor is "gener... | {
"language": "en",
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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... | As it follows from the Mechanics by Landau-Lifshitz (which can be found here — page 28), the desired dependence can be found in the form of
$$x(U)=\frac{1}{2\pi \sqrt{2m}}\int_{0}^{U} \frac{T(E)dE}{\sqrt{U-E}}$$
Where $T(E)$ from the law of conservation of energy and the initial statement $T_{½}=\alpha V^\beta$
$$T(E)... | {
"language": "en",
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Electromagnetic radiation bending on Earth Most articles say that a radiowave is able to propagate itself beyond the horizon because it is reflected off by the ionosphere (and the Earth itself).
But do radio waves also get bent according to the Earth's curvature due to gravity thus transmitting beyond the horizon with... | Calculating the path that a light ray takes in a gravitational field is a complicated business, but for the special case of a light ray coming from infinity and escaping to infinity there is a convenient approximate formula for the angle, $\theta$, the light ray is deflected:
$$ \theta \approx \frac{4GM}{r_0 c^2} $$
W... | {
"language": "en",
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Exploring beyond event horizons In the expanding universe the velocity of separation between galaxies depends upon how far they are. If they are much far away will they have relative velocity of separation greater than speed of light and if so how can we even detect such galaxies.
There are things like Quantum informat... |
If they are much far away will they have relative velocity of separation greater than speed of light and if so how can we even detect such galaxies.
We can't detect such galaxies. Redshift goes to infinity at the cosmic horizon, and we cannot see beyond. Note that the cosmic horizon is different from the Hubble spher... | {
"language": "en",
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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
| No; wave interference takes place whenever two waves of any frequency, same, nearly the same or widely different interact. An air molecule next to your ear, for example, can only respond to the sum of all the different sound waves reaching it at any moment.
The results are simpler when the two waves are closely relate... | {
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The subtle differences between angular momentum and centrifugal force I am a mathematician wanting to understand the differences between the concepts of angular momentum and centrifugal force.
The following two ideas are clear to me from a physical point of view, but I have a difficult time discerning the difference be... | Angular momentum is around, centrifugal force is out (from the axis). Subtle in the sense that they are related, but distinct?
| {
"language": "en",
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What makes Sun's light travel as parallel beams towards earth?
Sun's light appear to travel as parallel beams towards earth $_1$. Sun produces electromagnetic radiations through pp chain and other reactions in Photosphere $_2$.
I don't see whether these reactions send photons in that neatly arranged parallel rays,... | Light from the sun actually converges on the earth - the sun is about 220 Earths across, so light from one edge and light from the other edge must converge to reach the same point on Earth. The angle is small enough (about 0.5 degrees) that for most practical purposes we can consider the sun to be either a point source... | {
"language": "en",
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Is there a commonly used unit of measure (other than temperature units) that is not absolute? I live in a country where we use Degree-Celsius(°C) to measure the temperature.
Sometimes from one day to the other, the temperature rises from 10°C to 20°C and I hear people say, "Wow! Today is twice as hot as yesterday!".
I ... | Best one I can think of is shoe (or clothing or ring) sizes. Another common measure might be wire gauge.
There are many others, but almost all are less common and I doubt they'd be effective.
| {
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Is Boltzmann distribution contradicting with the fundamental assumption of statistical thermodynamics? In equilibrium statistical physics the fundamental assumption of statistical thermodynamics states that the occupation of any microstate is equally probable (i.e. $p_i=1/\Omega, S=-k_B\sum p_i\,{\rm ln}\,p_i=k_B{\rm l... | The equal probabilities are meant for states of an isolated system with constant total energy. Each state with this energy is then equally probable.
The Boltzmann probabilities are meant for systems in thermal contact and equilibrium with reservoir of definite temperature - in that case the energy of the system may cha... | {
"language": "en",
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Cosmic Background Radiation and redshift vs. temperature I get that the CMB has gone from high energy photons, to low microwave photons today. And that is probably due to the redshift from the expanding Universe. But, since CMB is a black body it is temperature dependent, i.e. it has a high peak at high temperatures, b... | Red-shifted black-body radiation is just like black-body radiation at a lower temperature, that is why you might think the two effects are mixed. The CMB comes from the time when the universe was about 379,000 years old, the time at which (as the universe expanded) adiabatic cooling caused the energy density of the pla... | {
"language": "en",
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General question about the potential barrier problem: Why does $\exp( kx)$ diverge when $x>0$ in the case when $E < V(x)$? For the two images below, the first potential barrier has particles approaching it where $E > V_o$ & the second has a particle that has $E < V_o$, where $E$ is the energy of the particles and $V_o$... | Complex and real exponentials are fundamentally different mathematical objects. Recall Euler's Formula:
$e^{i z} = \cos{z} + i \sin{z}.$
So, for a real value of $k$, we have
$e^{i k x} = \cos{k x} + i \sin{k x}.$
This is a sum of sinusoidal functions - and we know that sinusoidal functions have no limit as $x \rightarr... | {
"language": "en",
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Why does a pitcher with lemon juice have foam, while one with pure water does not? Whenever I pour water into lemon juice (pouring directly from the tap into the pitcher, not quietly along its edge) I get a foam on top:
The same pitcher with water (same water tap, pitcher, time between the water poured and the picture... | I too have seen this effect with pure, unsweetened lemon juice.
To form a foam, (1) a surfactant is needed to lower the host liquid's surface tension (2) one needs to do mechanical work on the liquid to swell the surface area of the bubbles/foam and (3) the foam needs to be made faster than it breaks down. The Foam Wik... | {
"language": "en",
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Opacity/transparency of conductive meshes to charged particles (electrons/ions) When using a conductive (metal) mesh, effectively a metallic woven fabric, in vacuum applications as a "grid" for charged particle optics, how does one calculate (or at least estimate) the opacity or transparency of this grid?
$$
\begin{arr... | Generally, people simply look at the fraction of area covered and assume that the transparency to ions and electrons will be the same as the transparency calculated by open area/total area.
For most applications for ions and electrons woven grids are not used - grids can be used which are are formed by electrochemistry... | {
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What is going on in a rotating magnet in a quantum scale? If there is a rotating magnet in an empty space and there is no outer field acting on it. Rotating in such a way that after half rotation magnet's N pole will be in the place where magnet's S pole was. I imagine that spin of the electrons inside magnet are follo... | A rotating magnet can be handled as an "orbital" angular momentum problem, no spins needed, but nothing stops you from using the usual spin-orbital coupling to calculate the total magnetic moment of a realistic solid state system. What matters for the interaction of the magnet is its total magnetic moment. Since angula... | {
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Drift velocity of charges in current In an electric curcuit, charges (electrons e.g.) move randomly around very, very fast. When a current is set in a curcuit, the charges still move randomly, but have a drift velocity around the curcuit. This is only in the order of about 0.1 mm/s.
The question is short and simple, an... | The collision frequency of electrons in a metal at room temperature is given by the thermal distribution of the electron velocities (please note that this is already a somewhat questionable approximation, metals really require a quantum mechanical treatment). I do not believe that this collision frequency increases muc... | {
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Given a wave function $\psi(x)$, is there always a potential $V(x)$ such that $\psi(x)$ is an eigenstate? Given any unit norm wave function $\psi(x)$ which is in the Hilbert space, can we always find a $V(x)$ such that the $\psi(x)e^{-i\omega t}$ is a solution of the corresponding Schrödinger equation? (I mean the Hami... | I'm not quite sure where OP is going with this, but from a mathematical perspective, assuming that the wave function $\psi:\mathbb{R}\to \mathbb{C}$ is twice differentiable and different from zero, consider the (possibly complex) potential
$$ V(x)~:=~\hbar\omega+\frac{\hbar^2}{2m} \frac{\psi^{\prime\prime}(x)}{\psi(x)}... | {
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Why do things here on Earth fall down? I want to have an answer with that question above for my physics lesson. I really don't have an idea about it, so, I ask help from you guys and hope that someone can help me with it.
| In 1600 Newton discovered a formula that could explain why things fall down on earth
things fall due to the gravitational force of the Earth. The formula for the intensity of the force is: $$F = G \dfrac{m_1 \cdot m_2}{r^2}$$
where $m_1$ and $m_2$ are the 2 masses of the object, $r$ is the distance between them and G ... | {
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Can we test QFT on a curved spacetime? It is possible to extend a quantum field theory to a curved spacetime. But does this lead to predictions that can be tested and measured? Had it been confirmed?
The underlying reason I am asking this is: curved spacetime means emergence of gravity and therefore General Relativity ... | Cosmology and inflation provide a hugely important test of quantum field theory in curved spacetime. During inflation, there is a scalar field (the inflaton) that is providing the vacuum energy that drives inflation. This scalar field is subject to the rules of quantum field theory in curved spacetime. The quantum f... | {
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How is mass reduced in a normal chemical reaction which releases energy like heat, sound or light? I was reading this link.
Just above the paragraph titled "OTHER CONSERVATION LAWS", it says that
"This conversion of mass to energy happens well below the speed of light, in a very small way, when a stick of dynamite exp... | As a matter of fact, chemical reactions can reduce mass just like nuclear reactions. I find it hard to accept, but it's true.
When the molecules in the dynamite explode, bonds between atoms are broken and reformed in different configurations. The result of this is that the net electrical potential energy in the resul... | {
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"answer_id": 0
} |
Are there new physics scenarios that predict low lying hadrons? There is a significant ongoing experimental effort to search for new hadrons with masses in the GeV range. This is used to find the spectra of QCD bound states, with a particular emphasis on finding exotic resonances such as the tetraquark. To my knowledge... | If you mention about exotic state hadrons which are composite of two anti quarks and two quarks, yes there are some new observations. The recent and approved one is Z(4430) which observed by LHCb group from CERN http://home.web.cern.ch/about/updates/2014/04/lhcb-confirms-existence-exotic-hadrons It consists $c^-cdu^-$ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/156921",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
Two superimposed sounds traveling through low- and high-density matter: is separation possible? Two superimposed sounds (at source: $s(t) = s_1(t) + s_2(t)$; the two sound components overlap completely in time, partially in spectra) travel through low- and high-density matter and are recorded from two different positio... | I don't see how this can be done, given the problem as-stated. What defines it as being 2 superimposed sounds, rather than just 1 sound, other than just an arbitrary definition? What stops me coming along and saying: "No, it's actually 4 superimposed sounds, or 27!"? If both sounds are coming from the same source then ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/156999",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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