Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Frames of reference: Inertial and accelerated - and jerked, snapped, crackled and popped? There are inertial frames of reference and the accelerated frames of reference, but are there any frames of references w.r.t. higher order derivatives of velocity? [1] [2]
For example, jerked frames of reference, snapped frames o... | Yes. For simplicity, consider an observer $O'$ moving in one dimension. Suppose that as measured by some other inertial observer $O$, the obsever $O'$ has the following position as a function of time
\begin{align}
x(t) = kt^n
\end{align}
where $n$ is an integer. When $n=2$ or higher, the observer has nonzero accel... | {
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when we rub objects together, what determines which material will pick up electrons? For example We know glass when rubbed by silk will become positively charged while the silk will be charged negative.
What exactly makes glass appropriate for losing electrons in that experiment? (
| The process of transferring charge between two objects by bringing them into contact and/or rubbing them together is known as the triboelectric effect, and is historically, the first recorded observation of an electric phenomenon.
Wiki Page on Triboelectric effect
In general, there are too many competing factors such t... | {
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Is such an orbit possible that allows a satellite on Earth and another on Mars to always be in direct line-of-sight? If not always, how much "most of the time" could it get?
Or would a multi-satellites setup be more suited?
| Yes, but the satellite(s) would be orbiting the sun instead of the earth. You place a satellite at either L4 or L5 Langrangian points on the Earth-Sun two-body system--these are points 60 degrees to either side of earth on her orbital plane around the sun where you can place a satellite. Throughout earth's entire orbit... | {
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Is inflation deterministic? In some theories inflation is supposed to be able to turn quantum fluctuations into macroscopic inhomogeneities.
I don't understand how an isolated system such as the universe can undergo such a random transformation : if at the beginning the universe is in a state $A$, quantum mechanics say... | In quantum mechanics, the state indeed evolves. But when you do an observation, it needs to choose one of the observable states - that's why we talk about superposition of states as long as you don't observe a quantum variable.
For inflation, as long as we were at high energies and short distances, the states could evo... | {
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What is meant when saying "the partial derivative operator $\partial/\partial x^\mu$ is a covariant vector"? Reading Weinberg's Gravitation and Cosmology, I came across the sentence (p.115, above equation (4.11.8))
The partial derivative operator $\partial/\partial x^\mu$ is a covariant vector, or in other words a 1-... | The way I understand it is that he is not referring to the tangent vectors $\frac{\partial}{\partial x^\mu}$, but to a differential operator. Notice that he doesn't use plural, he is talking about a single object. Namely the 1-form valued operator, which maps each function to its gradient. Then you can form the wedge p... | {
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How does humidity affect the path of a bullet? Background
Last night, I was reading the FM 23-10 (The U.S. army official field manual for sniper training), and I've noticed that they're potentially teaching snipers incorrect information.
Generally speaking, when we say "impact goes up" it means that the bullet was eith... | According to several sources, such as http://longrangebpcr.com/accuracy.htm , you are right: higher humidity - higher point of impact. But those sources also point out that humidity effect is small.
| {
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How does a pressure suit work? I recently learnt that a suit called pressure suit is worn by fighter plane pilots to prevent red-outs and black-outs. And it seems to be work by -
"..applying pressure to selective portions of the body."
How do these suits work; i.e. by what means, selective portions of the body are pr... | they provide mechanical constriction to the limbs and torso to prevent swelling in the event of decompression. hands, feet and face are not assisted.
astronauts wear full pressure suits for ascent and re-entry.
the main concern for F1 drivers is fire resistance not low air pressure.
https://airandspace.si.edu/collecti... | {
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What are the implications of the Holographic principle? What are the implications for the Holographic principle? I understand the basics of the principle, the relationship with black holes and string theory but what this is going to tell us? Does it help to explain quantum gravity? Is the model compatible with any mul... | It should be noticed the difference between aplying the Holographic Principle in to a 3D or a 4D world.
First it avoids the idea of infinite dimensions or "reality is unknow (infinite) until you look at it" by allowing fast comunications.
Then if you start with a some sort of +4D world it returns to a 3D world except "... | {
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Dehn twists and topological order I am trying to understand notion of a "Dehn twist" and how it relates to topological order.
In particular refering to http://arxiv.org/abs/1208.4834 it is stated that
Xiao Gang Wen's paper on "Topological Order in Rigid States" (http://dao.mit.edu/~wen/pub/topo.pdf) is supposed to pr... | In my paper, the Dehn twist is referred as modular transformation. See section V of http://arxiv.org/abs/1212.5121 which is available in arXiv. The unitary transformation generated by the Dehn twist is called the non-Abelian geometric phase.
| {
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Determing time to complete known distance with constant acceleration Answer: $a=v^2/d$ is the formula I needed.
This is a problem in a programming assignment, I haven't taken physics.
I have a starting speed (0 m/s), an final speed (208.33m/s) and the distance it took to reach that speed (200km). I need to get the ti... | Converting all units to SI:
$$u=0$$ $$v = 208.33 \text{ m/s}$$ $$d =200000\text{ m}$$So: $$a=\frac{v^2-u^2}{2d}=0.1085\text{ m/s}^2$$
Then, for any distance,$d$ in meters:$$t=\sqrt{\frac{2d}{a}}$$This vehicle maintains a feeble, but constant, $0.01\text{ g}$ for a $200\text{ km}$ trip lasting a little more than 30 min... | {
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How to establish relation between flow rate and height of the water column of the tank? Suppose a water tank has 1" diameter drain at the bottom and is filled with water up to one meter height above the drain. What time it will take the tank to drain out completely. Now say, the tank is filled up to two meter height ab... | Use Bernoulli's equation to derive Torricelli's Law (check any website for this) for the velocity out of the hole; $ v = \sqrt{2 g h(t)} $, where g is gravity and $ h(t) $ is the height of the fluid in the tank at any time.
Write a balance on the mass of the fluid in the tank as:
$$ \text{in - out + gen = accumulation}... | {
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Quantum harmonic Oscillator analytic method I'm using a book from Griffiths, I got really stuck about how he arrived at the approximate solution, is it just by trying( trial solution method?), I really appreciate any help on this.
$$-\frac{\hbar^2}{2m}\frac{\mathrm{d}^2\psi}{\mathrm{d}x^2} + \frac{1}{2}m\omega^2 x^2\ps... | I assume you have no qualms with the "large $\xi$" approximation - it's fairly obvious that $\xi^2-k^2\approx \xi^2$ for large enough $\xi$. After that you're left with the differential equation
$$\frac{d^2\psi}{d\xi^2}\approx-\xi^2\psi.\tag1$$
One way to solve this equation is by the method of divine inspiration: you ... | {
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Do orbitals overlap? Yes, as the title states: Do orbitals overlap ?
I mean, if I take a look at this figure...
I see the distribution in different orbitals. So if for example I take the S orbitals, they are all just a sphere. So wont the 2S orbital overlap with the 1S overlap, making the electrons in each orbital "me... | If you mean to ask "do the orbital radial probability distributions overlap?", the answer is yes:
Image Credit
making the electrons in each orbital "meet" at some point
As you can see from the image, the electron orbitals are not position eigentstates. If you're imagining two point-like electrons in different orbit... | {
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Why does voltage remains same over Parallel Circuit Why does voltage remains same over parallel circuit. If a resistor is connected in the circuit some of the charge should be transformed into heat and make a lack of charge after the resistor (in my sense). So, what's the reason in it?
| A single resistor wired in parallel with voltage source like a battery may give confusing reasons for a novice, so a few other things need to be taken into account.
Any battery also has an internal resistance (it is like a resistor in series with the voltage source), and this resistance also varies with the state of ch... | {
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Vanishing of the Ricci tensor in higher spacetime dimensions I understand how, if the Riemann tensor is 0 in all its components, since we construct the Ricci tensor by contracting the Riemann, Ricci tensor would be 0 in all components as well.
I've read that vanishing of the Ricci tensor in 3 spacetime dimensions impli... | The Riemann tensor can be decomposed into a trace part and a trace-free part:
$$R_{abcd}=C_{abcd}+\frac{2}{n-2}(g_{a[c}R_{d]b}-g_{b[c}R_{d]a})-\frac{2}{(n-1)(n-2)}Rg_{a[c}g_{d]b},$$
where the traceless object $C_{abcd}$ is the Weyl (conformal) tensor and the remainder is given by the Ricci tensor and its contraction, ... | {
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Why is moment dependent on the distance from the point of rotation to the force? The formula for moment is:
$$M = Fd$$
Where F is the force applied on the object and d is the perpendicular distance from the point of rotation to the line of action of the force.
Why? Intuitively, it makes sense that moment is dependent o... | The reason why torque (rotational force) depends on the distance $d$ from the pivot of rotation (i.e. why torque is a moment) is the following:
Torque is defined as change in angular momentum; if mass is constant that means change in angular velocity.
To achieve a change in angular velocity using a tangential force $F$... | {
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Accelerated charge inside sphere (again!) Sorry to go on about this scenario again but I think something is going on here.
Imagine a stationary charge $q$, with mass $m$, at the center of a stationary hollow spherical dielectric shell with radius $R$, mass $M$ and total charge $-Q$.
I apply a force $\mathbf{F}$ to char... | There is no obvious inconsistency, whether we use retarded, advanced, or any other field.
If we use only retarded fields, things go as follows. At the time $t=0$, we begin to exert force $\mathbf{F}$ on the charge $q$. It will move with acceleration $\mathbf{F}/m$ for the time interval $R/c$, where $R$ is the radius o... | {
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Energy source for phase transformation-latent heat of vapourisation As per my knowledge, phase transformation require energy gain or loss. If we are changing a liquid to gas we heat it and that is how molecules of liquid gains energy and lattice spacing increases and bonds becomes weaker and thus gets converted to gas.... | In your example of lowering the pressure above water, the water will only boil if you reduce the external pressure to below the vapour pressure of the water i.e. the water is superheated. The energy required to boil off the steam comes from the internal energy of the water, and as a result the water cools down. As the ... | {
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Why does Newton's third law exist even in non-inertial reference frames? While reviewing Newton's laws of motion I came across the statement which says Newton's laws exist only in inertial reference frames except the third one. Why is it like that?
| The cutest way to see this is to restate Newton's third law as "no interaction can change the total momentum of the universe." Then, note that since an accelerating reference frame is accelerating with respect to whatever "base" inertial reference frame you're using, everything else seems to be accelerating away. The... | {
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do lenses with curved focal planes exist I know about spherical, aspherical, cylindrical lenses, but are there lenses that could have a curved focal plane? for example, the retina of the eye is curved, and still we see sharp images of distant objects.
In a recent problem I studied, I wanted to have a lens that would tr... | Surely lenses with curved focal place exist - simplest spherical lens have curved focal plane. Human eye is a bad example here - field curvature of an eye does not match retina curvature. We just used to "see" using central part of retina.
You definitely can design your lens for more-or-less symmetrical field curvatur... | {
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Infinite Wells and Delta Functions In considering a delta potential barrier in an infinite well, I can just enforce continuity at the potential barrier-it doesn't have to go to zero. Why then does it need to go to zero at the walls of the infinite well? These two cases seem to be very similar to be, I even feel like th... | When you consider a potential barrier, you will see that the wave function of a particle with definite energy will decay exponentially at a rate that depends on the difference of the potential and the energy. Precisely, the exponent is proportional to $\sqrt{V - E}$.
In the limit, for $V\to\infty$, it will decay to 0 o... | {
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Expansion of the Universe: Conversion of gravitational potential energy to kinetic energy? Suppose there is an object floating in space which over time begins to fall toward the source of a gravitational field. As it falls, its motion happens to be such that it gets locked in orbit around the source with a greater vel... | There's a blog post that may be of some interest to you here: http://motls.blogspot.com/2013/11/the-expansion-is-accelerating-due-to.html
Basically, the universe is constantly expanding at an accelerated rate due to "negative pressure". This is better understood with the Second Friedmann Equation:
$\frac{\ddot a}{a} =-... | {
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Determining if a semiconductor is n-type, p-type or intrinsic The probability that an energy state in the conduction band is occupied by an electron is 0.001. Would this semiconductor then be n-type, p-type, or intrinsic?
Notation that I use: $E_F$ represents the fermi energy level, $E_C$ represents the energy level of... | Since the Fermi dirstribution is obviously either close to 1 or close to zero except at the fermi level, the answer to you question can be easily answered by looking at the figure below.
Would this semiconductor then be n-type, p-type, or intrinsic?
P-TYPE!
| {
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Intuitive understanding of the entropy equation In thermodynamics, entropy is defined as $ d S = \dfrac{\delta q_{\rm }}{T}$. This definition guarantees that heat will transfer from hot to cold, which is the second law of thermodynamics. But, why do we denote entropy as$\dfrac{\delta q_{\rm }}{T}$ other than $\dfrac{\d... | First off, temperature is an intensive quantity, i.e., not additive. For example, two cups of coffee don't have twice the temperature of one cup. For an extensive (additive) quantity, such as mass, we can't just redefine $m\rightarrow m'=f(m)$, where $f$ is a nonlinear function, because then $m'$ wouldn't be additive. ... | {
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Charged spheres - help with method to work these out? Can anyone demonstrate how to get the answers to these questions? I'm just interested in the method I need to use in order to obtain the correct answer no matter what the values are.
Three small spheres are placed at fixed points along the x-axis, whose positive dir... | The spheres are effectively point charges, so the force between any pair of spheres is just given by Coulomb's law. The forces are additive so in (a) the net force on $B$ is just the vector sum of $F_{AB}$ and $F_{BC}$.
The field strength is the force (from Coulomb's law) on a point charge of 1 Coulomb, so in q (b) pro... | {
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Is there a heat transfer equation that takes conduction, convection, radiation and dT/dt into account? I see equations that take 2 or 3 of the listed parameters into account but I haven't been able to find one that is that complete. I'm seeking to solve this equation using matlab for a simulation project to study how t... | The nature of 'complete' heat equation will depend on your domain. If I understand correctly, you want to model the temperature rise/heat dissipation in a microheater (a solid?) when it is electrically powered. The heat transfer inside the heater in this case will be solely due to diffusion. Convection/radiation will n... | {
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Algorithm to simulate impulse response of a solid? There are well-documented methods of calculating the impulse response of a room (ex. image method, ray-tracing method); however, I have not been able to find anything similar for the impulse response of an arbitrary solid given its size, density, etc. Can anyone point ... | The exact answer can easily be computed by solving the elastic wave equation using the finite-difference time-domain method.
You mentioned the image and ray-tracing methods for room acoustics. Theses are geometric methods, which would not be useful for solids since there would need to be separate rays to describe the c... | {
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Have we found a Higgsino? In supersymmetry, for each particle (boson/fermion), there is a symmetric particle which is a fermion/boson.
The MSSM predicts five Higgs bosons: two neutral scalar ones (H and h), a pseudo-scalar (A) and two charged scalars.
Does this mean that there are five higgsinos?
My question arises bec... |
Although I agree with everything that Mitchell Porter wrote in his
nice answer, I would like to add a few remarks.
With supersymmetry, there are equal numbers of bosonic and fermionic degrees of freedom for each type of field.
Prior to electroweak symmetry breaking, in the simplest supersymmetric models (e.g., the... | {
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Determining the spring constant in an oscillation problem
A 130g air-track glider is attached to a spring. The glider is pushed
in 10.4cm and released. A student with a stopwatch finds that 14.0
oscillations take 19.0s
I would like to know why the answer I get is wrong. I set up an equation to represent position ... | Remember that an oscillation can be written as $\cos(\omega t) = \cos(2\pi f t) = \cos(\frac{2 \pi}{T} t)$. You have the period on the top instead of the bottom.
| {
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How does a Tesla Coil exactly work? How does a Tesla Coil exactly work? I am currently making a Tesla Coil in school but before I start, I want to know exactly how does a Tesla Coil work? I understand the various electrical components used in it, but what I don't understand is how do those components together work to m... | A Tesla coil is in many ways the same as a transformer and hence if you know the working of one you can understand the working of the other.
Now in common transformers, the coils are couple tightly, so that a large amount of energy transfers from the primary to secondary. This works well at low voltages, but at high v... | {
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Doppler effect problem with moving mirror This was the given question:
A light beam of intensity $I$ and frequency $f$, directed along the
positive $z$-axis, is reflected perpendicularly from a perfect mirror which
itself is moving along the positive $z$-axis with a constant velocity $v$.
Find the reflected inte... | A real light source moving towards you gets more intense as the inverse square. Why should a virtual light source behave any differently?
| {
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Could velocity be taken as fundamental instead of time? In physics time and length are taken as fundamental in the SI system and, as it seems, in the thinking of physicists. Could one instead take velocity, with c as its unit, together with length as fundamental and then understand time by dimensional analysis in terms... | Personally, I don't see why not. And I too believe it has the potential to open up new lines of inquiry and understanding. I have long thought the concepts of velocity and change have a good chance of in fact being most fundamental. As an example, what if the reality of the fundamental nature of our universe is such th... | {
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Elliptical orbits passing 2 points I would like to find set of possible elliptical orbits which pass 2 points in plane. I was searching for some solutions in orbital mechanics texts but I didn't found any.
There are several possible approaches but I'm not sure which is the best - both looks quite difficult to solve alg... | I am not entirely sure if there is an explicit equation, but I do remember that a by the community made mod for the game Kerbal Space Program, called MechJeb, this is calculated by solving a Lambert's problem. The code they used to calculate this can be found on github.
Someone else also made a web application which ca... | {
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Does antimatter curve spacetime in the opposite direction as matter? According to the Dirac equation, antimatter is the negative energy solution to the following relation:
$$E^2 = p^2 c^2 + m^2 c^4.$$
And according to general relativity, the Einstein tensor (which roughly represents the curvature of spacetime) is linea... | Antimatter is not the negative energy solutions to the energy-momentum relation! Even in the Dirac sea model it isn't. In the Dirac sea model, the negative-energy modes are all filled with electrons, and the absence of one of those electrons is a positron. Just as the absence of a positive-energy particle has (relative... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Will the Hubble parameter reach zero asymptotically in the far future? In the current accelerated expansion universe model will the Hubble parameter $H$ reach zero asymptotically in the far future?
| No, but it will asymptotically approach a particular value. In the Standard Model where dark energy is a cosmological constant, the Hubble parameter is a function of the present-day Hubble constant and the radiation (R), matter (M), curvature (K), and dark energy ($\Lambda$) densities as follows
$$
H(a) = \frac{\dot{a}... | {
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How does energy transfer between B and E in an EM standing wave? I'm trying to understand how an electric field induces a magnetic field and vice versa, its associated energy, as well as relating it to my understanding of waves on a string.
Using a standing wave as an example, I came up with the equations
$\vec{E}=A\si... | The energy conservation is written $\dfrac{\partial u}{\partial t} + div \vec S=0$, where $u$ is the energy density $\vec E^2+\vec B^2$, and $\vec S$ is the Poynting vector $\vec E \wedge \vec B$ (skipping irrelevant constant factors).
If you choose $x,t$ such as $\sin \omega t=0$ and $\cos k x=0$, both $E$, $B$, the ... | {
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Does the moon affect the Earth's climate? So, this morning I was talking to a friend about astronomical observations, and he told me that lately there has only been good weather when there was a full moon in the sky, which was a shame.
I jokingly said: 'maybe there's a correlation!', but then I started thinking: wait,... | It might affect climate, but not on the time scale of a month, and does not significantly affect the weather.
The fact that the moon exists may significantly stabilise the inclination of the Earth relative to the Sun. This, in turn, affects climate in the long run. The debate is ongoing. For example, see long term a... | {
"language": "en",
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Thin lens formula Can someone help me or guide me how the thin lens formula:
$$\frac{1}{s_1}+\frac{1}{s_0}=\frac{1}{f}$$
can be proven?
I was trying to prove it on my own using similar triangles, only to fail.
| Another high school proof of the general lens equation:
Let's suppose you have a lens of refractive index $n_2$ seperating two media of refractive index $n_1$ and $n_3$, then by the equation of curved surface refraction, we can write image as refracted by first surface of lens:
$$ \frac{n_2}{v} - \frac{n_1}{u} = \frac{... | {
"language": "en",
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Classical Wave Equation - Approximations I don't understand the derivation of the wave equation given below -
$$T \sin (\theta _1) - T \sin (\theta ) = T\tan (\theta _1 )-T\tan (\theta ) = T \left. \left(\frac{\partial f}{\partial z} \right|_{z + \Delta z} - \left. \frac{\partial f}{\partial z}\right| _z \right) = T \f... | I just realized that the reason we're using $\tan \theta = \partial _z f$ is because $\tan \theta = \frac{df}{dz}$, which makes sense if we consider this a right triangle.
| {
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Chinook Helicopter Torque The Chinook Helicopter has 2 rotors to counteract the torque generated by spinning the blade.
Theoretically, could you use a smaller "back" rotor that is farther away from the main rotor to achieve the same result, ie no twisting?
| Assuming a mass moment of inertia of $I_1$ for the main rotor and $I_2$ for the secondary rotor, and a coefficient of drag of $\beta_1$ and $\beta_2$ respectively then the torque on the rotor shafts are
$$ T_1 = I_1 \dot \Omega + \beta_1 \Omega^2
\\ T_2 = I_2 (\gamma \dot \Omega) + \beta_2 (\gamma \Omega)^2 $$
where $... | {
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Proper name for a thermodynamic process with constant internal energy $U$ Back in the day I learned that a few special thermodynamical processes have special names.
For example, if one keeps $P$ constant, the process is called isobaric, if one keeps $T, V$ or $S$ constant, one gets, correspondingly, isothermic, isocho... | A process where the energy is kept constant is called isoenergetic (or, if you prefer, iso-energetic).
It also seems from the literature that a flow where the energy is constant when following a fluid particle is usually called an isoenergetic flow.
Similarly, when the enthalpy is kept constant, the process (or the fl... | {
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One way insulation? I know from basic physics lessons that a box painted black will absorb heat better than a box covered in tin foil. However a box covered in tin foil will lose heat slower than a black box.
So what is the best way to conserve the temperature of a box? (aiming for 0 degrees Celsius inside the box whe... | A perfectly one way insulator would violate the law of conservation of energy. You could place it in a fluid filled box and let a temperature gradient develop. You could then use it to drive machinery. Bam! Energy for nothing. Therefore by the conservation of energy (and second law of thermodynamics: the entropy would ... | {
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What spacetimes satisfy this identity?
*
*What spacetimes satisfy $R^{\mu\nu} R_{\mu\nu} =\alpha R^2$, where $R = g^{\mu\nu}R_{\mu\nu}$ is the Ricci scalar, and $\alpha$ is some constant?
*A follow-up question: in what spacetimes does $R^{\mu\nu\sigma\rho} R_{\mu\nu\sigma\rho} =\beta R^2$, for some constant $\beta$... | I can give you some particular solutions, but not the most general solution.
*
*Any metric in 2 dimensions satisfies
$$
R_{\mu\nu\alpha\beta} = \frac{R}{2} \left( g_{\mu\alpha} g_{\nu\beta} - g_{\mu\beta} g_{\nu\alpha} \right) \implies R_{\mu\nu} = \frac{1}{2} g_{\mu\nu} R
$$
This implies
$$
R_{\mu\nu\alpha\beta} R^... | {
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What is fundamental difference between wave and its 180 flip phase? I'm studying property of sound wave and I was wondering what is difference between two waves (one is original and one is 180 flip phase of original) ?
Amplitude and frequency remains same and also wavelength is same, so are they same?? I could not dete... | The difference is that at each instant in time, the 180-degree delayed wave has exactly the opposite value of the original wave.
If $y_1(t) = \sin(2\pi{}ft)$ and $y_2(t) = \sin(2\pi{}ft + 180^\circ)$, then $y_1(t)=-y_2(t)$ for all t.
If you are talking about a sound wave, then whenever one wave has a minimum of pressu... | {
"language": "en",
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Question about the quantization of lattice vibration (phonons) In my syllabus about solid state physics they state that lattice vibration is quantized, analogous to the harmonic oscillator:
$$E = (n+\frac{1}{2})\hbar\omega$$
So the lattice vibration has zero-point energy $\frac{1}{2}\hbar\omega$.
I wonder what this act... | In classical mechanics, you can describe a crystal (in some approximation) by a Hamiltonian that is a quadratic form in coordinates and momenta of atoms. After you diagonalize this quadratic form, you obtain a Hamiltonian of a set of independent, rather than coupled, oscillators (modes). Then you can quantize this syst... | {
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Slow light and gravitational lensing It has been proposed that the Sun's gravitational lens be used to observe distant objects, but according to relativity a spacecraft would need to be 550 AU away in order to take advantage of the effect.
Would it be possible to instead slow down the light while it is being deflected ... | The limiting factor in optical observations isn't usually the magnification but rather how much light can be collected. The advantage of using the Sun as a lens isn't that it's especially powerful, but that it's exceptionally big!
So you could sit on an asteroid to make your observations, but there would be no benefit ... | {
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Why are high voltage lines “high voltage?” If I have two spheres of the same size and one sphere has a small amount of charge compared to the other that has a lot more charge, then clearly the sphere with the larger charge has a larger voltage (relative to the ground). My question is do high voltage power lines have a ... | They do carry a bit of extra charge, but it's sort of a side effect. Every conductor (such as a high voltage wire) has some capacitance. The capacitance of an object can be defined as the amount of charge added, per unit change in voltage on that object (keeping all other voltages constant). When we energize the high v... | {
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Why don't metals bond when touched together? It is my understanding that metals are a crystal lattice of ions, held together by delocalized electrons, which move freely through the lattice (and conduct electricity, heat, etc.).
If two pieces of the same metal are touched together, why don't they bond?
It seems to me ... | I think that mere touching does not bring the surfaces close enough. The surface of a metal is not perfect usually. Maybe it has an oxide layer that resists any kind of reaction. If the metal is extremely pure and if you bring two pieces of it extremely close together, then they will join together. It's also called col... | {
"language": "en",
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Could there have been two "Big Bangs"? A couple of years ago, I remember seeing a documentary on the big bang theory. The theory presented was that to explain the cosmic microwave background radiation, there needed to have been two big bangs. Is this theory legitimate? I've tried searching for details without success.
... | The term Big Bang does not have rigorous physical definition. And if you mean specifically inflation, then the modern inflationary models (chaotic inflation with various scalar field potentials) predict that inflation is always present at certain regions of space.
Inflation is driven by a scalar field, the value of wh... | {
"language": "en",
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Infinitesimal Lorentz transformation is antisymmetric The Minkowski metric transforms under Lorentz transformations as
\begin{align*}\eta_{\rho\sigma} = \eta_{\mu\nu}\Lambda^\mu_{\ \ \ \rho} \Lambda^\nu_{\ \ \ \sigma} \end{align*}
I want to show that under a infinitesimal transformation $\Lambda^\mu_{\ \ \ \nu}=\delta... | Since the Lorentz transformation is valid for any $x\in M_{4}$, it can be rewritten as $\Lambda_{\rho}^{\mu}\eta_{\mu\nu}\Lambda_{\sigma}^{\nu}=\eta_{\rho\sigma}$. Substituting the infinitesimal form of the Lorentz transformation into the previous formula we get
$$(\delta_{\rho}^{\mu}+\omega_{\rho}^{\mu})\eta_{\mu\nu}... | {
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What is negative Energy/Exotic Energy? So I have been researching around a little as I am highly interested in Astrophysics and I came across an energy I have never heard of before; negative energy also commonly known as exotic energy. Now I started to research this however I found the concept rather hard to grasp due ... | Negative energy is a quite different than Anti-matter. If you collide Anti-matter with regular matter you get a result with positive energy (Gamma rays). If you were to collide Negative energy and matter you would get nothing. It has negative mass (Anti-matter has a positive mass.) It is a hot topic in physics as it al... | {
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Difference between primitive unit cell and the associated basis? As I understand it, the basis is the group of atoms whilst the primitive unit cell is the unit space that fits the total space without any gaps, and only containing one lattice point? How do the two relate to each other? Thanks.
| They don't relate.
The primitive unitcell is a property of the lattice. The lattice has nothing to do with the basis. You can have a single atomic basis or a thousand atomic basis but both have the same lattice, and therefore the same primitive unit cell.
One of the most important facts you have to wrap your head aroun... | {
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Importance of MHV amplitudes Why are MHV amplitudes so important? How/where are they used and why do people keep trying to rederive them in many different ways?
| MHV amplitudes are not really any more important than next-to maximal helicity violating amplitudes ($NMHV$) or $N^kMHV$ amplitudes. You need all of them to compute a general scattering amplitude.
Basically, scattering amplitudes for non-Abelian Yang Mills theories are very complicated to compute for more than 4 partic... | {
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Is there some special cutoff density after which spacetime "collapses" and forms a black hole? With crude calculations following densities can be approximated:
Given that radius of proton is $1.75×10^{−15} m$ and it's mass is $1.67 × 10^{-27}kg$, this gives density of proton to be $\dfrac {1.67 × 10^{-27}kg} {\frac{4}{... | I think you're asking if there is some special cutoff density after which spacetime "collapses" and forms a black hole. If this is your question then the answer is no, there is no specific cutoff.
Density unites are $\frac{\mathrm{mass}}{\mathrm{volume}}$ but the size of black holes is dependent on the mass and the si... | {
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Detecting a photon without changing it: Does it break conservation laws? This is about an article published on ScienceMag: Nondestructive Detection of an Optical Photon. I don't have access to full text, but you can see a brief transcription in this link.
Basically, it says that a photon causes a phase shift in another... | the simple answer is that a quantum state has several variables (degrees of freedom), so if you measure only one of them and leave the others unchanged, then you detect the photon , change its state but do not destroy it completely. this is what they say in introduction
Second, nondestructive detection can serve as a... | {
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Photons from stars--how do they fill in such large angular distances? It would seem that far-away stars are at such a distance that I should be able to take a step to the side and not have the star's photons hit my eye. How do stars release so many photons to fill in such great angular distances?
| Allow me to channel something akin to the anthropic principle here. You can only see the stars that have a lot of photons reaching your eye. If a star were so far away that photons were reaching your eyes only occasionally then the star would be too dim for you to see in in the first place. Even if you could see the... | {
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Nokia PureView microscope: fluorescent Imaging I've come across this article: Fluorescent Imaging of Single Nanoparticles and Viruses on a Smart Phone.
And what is the theoretical limit for such smartphone extension? And how that limit can be computed (same as for microscope $\sim 1.22\,\lambda / D$)?
| The imaging is not being done by focusing transmitted light as would be done in an optical microscope. Instead it's detecting light emitted by the nanoparticles as they fluoresce. This means there is no lower limit to the size of the particle detected, except that when the particles get very small they emit too little ... | {
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How do they draw collision pictures in Atlas? Is the picture below a simulation? How to they draw these pictures? The picture is from here.
| This picture is not a simulation, it is an actual collision event. But it could have been either: both real and simulated events can be visualized in this way. Everything is done mainly by using the GEANT4 software package.
(As partially mentioned in the comments, the small boxes are deposits of energy in detectors; d... | {
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Archimedes' principle for two liquid layers
Problem: I have a cylindrical vessel of height $H$ and radius $R$. There are two liquid layers in the vessel. The first has density $D_1$ and height $h_1$, the second has density $D_2$ and height $h_2$. The second liquid is floating on the first liquid (thus $D_2 < D_1$) and... | You do no say what information you know and do not know. For example if the cube sinks and $h_1$ is big enough, it is possible that $s_2=0$. But if you know $s_1$ and $s_2$ then it is easy.
The volume of liquid displaced is $(s_1+s_2)n^2$ so the extra height (ignoring overflows) is $\dfrac{(s_1+s_2)n^2}{\pi R^2 }.$ S... | {
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Electromagnetism: Conductors Even though the thermal velocity of electron in a conductor is comparatively high, the thermal velocity is not responsible for current flow? Why is this the case?
| that's because thermal motion is random in nature, you'll find almost same number of electrons moving in any direction at some specific time, so on average the net motion of charges(i.e., current) in any direction is zero, so no current due to thermal motion,
now, if you apply external field to the metal the overall ra... | {
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The velocity of a cloud? I noticed an unusually fast moving cloud this morning.
My questions:
*
*What is the average velocity of a cloud on Earth?
*What is the greatest ever recorded cloud velocity?
*What factors affect the velocity of a cloud? (e.g. do they experience inertia?)
| Clouds move with the wind, so the cloud velocity is just the wind velocity. The recent storm in the Philipines reached wind velocities of 200 mph, though the higest speed reported is apparently 253 mph.
The fastest moving clouds known are on Neptune, where the winds reach 1340 mph.
| {
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Steps involved in photon emission What are the detailed steps involved in the emissions of a photon, for example, when an electron drops to a lower energy level? How well do we understand the production of the photon in this example? Any good reference material I can study?
| The best account for photon emission when an electron drops to a lower eigenstate is the Wigner-Weisskopf Model for spontaneous emission, see this paper from the Photonics group at ETH Zürich and the co-efficients for this model can be calculated by standard quantum electrodynamics. I explain this model further and gi... | {
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Why is the decay of a neutral rho meson into two neutral pions forbidden? Why is the decay of a neutral rho meson into two neutral pions forbidden? (Other modes of decay are possible though.)
Is it something with conservation of isospin symmetry or something else? Please explain in a bit more detail.
| If we look at isospin, $\rho = |1,0\rangle$ and $\pi^0= |1,0\rangle$.
Since SU(2) isospin is a really good symmetry in strong interactions, it must be conserved. Looking at the isospin of the final state:
\begin{equation}
|1,0\rangle \otimes |1,0\rangle = \sqrt{\frac{2}{3}} |2,0\rangle + 0 |1,0\rangle - \sqrt{\frac{1}... | {
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Physics of the inverted bottle dispenser
When you invert a water-bottle in a container, the water rises and then stops at a particular level --- as soon as it touches the hole of the inverted bottle. This will happen no matter how long your water-bottle is. I understand this happens, because once the water level touch... | Water stops draining from the jar into the dispenser once it forms an interface as draining of more water would result into the formation of a vacuum in the jar because no air can rush into the jar to displace the water as it has an interfacial-lock.
Consider the water level above interface $= h$, water level below in... | {
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How to exchange light and matter? A while ago an experiment demonstrated that it is possible to stop a light pulse in a supercooled sodium cloud, store the data contained within it, and totally extinguish it, only to reincarnate the pulse in another cloud two-tenths of a
millimeter away.
Most of the papers discussing ... | Never worked with BEC but for ordinary matter it works like this: The incoming field makes the electrons oscillate with the same phase and frequency as the driving field (superposition state). If this state emits radiation before any kind of dephasing (usually takes femto/picoseconds) the outgoing field will be a copy ... | {
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If a spaceship was pulled toward a sun, would it spin? I was watching a movie. A spaceship was forced into "warp speed". The co-ordinates could not be set. The spaceships trajectory was that of a nearby sun. Forcing the spaceship to power down was the solution. Now out of "warp speed" and with no computer aid (steering... | The angular momentum of a massive sun may cause the freely falling spaceship to start spinning in the direction of the sun's angular momentum for an effect of frame dragging. You can take a look at the Kerr metric which describes the behaviour of the spacetime near a massive spinning object. If you're not familiar with... | {
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Physical intuition for independence of components of velocity in derivation of Maxwell–Boltzmann distribution Maxwell derived the shape of the probability distribution of velocity of gas particles by starting with just two assumptions.
These are:
*
*The probability distribution is rotation invariant.
*The component... | If I have a velocity which has some component $v_x$ in the $x$-direction, then is there any reason for you to assume you know anything anything about the component of my velocity which might be in a perpendicular direction, $v_y$?
No. So you can see that it is reasonable to assume that, if you know my $v_x$, my $v_y$ ... | {
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Calculate average speed with unknown variable accelaration I am in the middle of a vehicle tracking project where I have to calculate the distance traveled by the vehicle in a given amount of time.
Data I am getting:
Speed : 30.2 km/hr 12.7 km/hr 15 km/hr 21.8 km/hr
Time : 11:00:00 11:00:22 11:00:45... | From this data, you don't actually know how the speed varies between steps. If you have more information about the acceleration then you could change the model from this but I would propose the following...
Assume a linear change in the speed between steps, you could take a simple graphical approach. Plot the speed (in... | {
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Are coherent states of light 'classical' or 'quantum'? Coherent states of light, defined as
$$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle
$$
for a given complex number $\alpha$ and where $|n\rangle$ is a Fock state with $n$ photons, are usually referred to as the most c... | If coherent state are indeed the most classical states (which means that the mean value of the EM fields obeys the classical Maxwell equations), the state used in the paper you mentioned are not coherent state (at least in the arXiv paper), but cat states !
The state $|\alpha\rangle+|-\alpha\rangle$ is not a coherent s... | {
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Is a particular force different in different frames Can a particular real force have different magnitude in different frames?
| Well, take the electromagnetic force...it has been shown that the induced magnetic field around moving charges is a relativistic reference frame effect. See this post How Special Relativity causes magnetism
Therefore a static electric force in one frame becomes a magnetic force in another.
However, from a Newtownian vi... | {
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Dimension of the space of solutions in an electric circuit Consider an electric circuit with dc sources ( voltage and current) and resistors. Write down the equations. In the most general case, the solution of the system is not unique. The set of solutions can be empty or positive dimensional (simple example: 2 points ... | This may not be a direct answer, but it can be shown by an elementary method that the relation between the number of nodes, branches and loops in a well-posed problem corresponds to Euler's polyhedron formula.
| {
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Momentum conservation problem Lets a plastic ball of mass m which is collided with steel. After collision the ball is coming back with the half initial speed. If the steel doesn't move then how can I interpretate this ?
Let the initial speed of the ball is $u_1$ and mass $m_1$ and mass of steel $m_2$ speed of stee... | If "the steel" that you're referring to is a fixed object or has a large mass, then the energy lost in the collision goes into increasing the internal thermal energy of the plastic ball and "the steel". This is an inelastic collision and kinetic energy is never conserved in inelastic collisions. Momentum, on the other ... | {
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Question on energy mass conversion I have a question regarding the energy-mass conversion. Well, when a particle starts moving with a speed comparable to that of light, its (relativistic) mass increases that means some matter is created and that too of the same particle...energy being converted to mass is ok but how do... |
"how does energy perceive what atoms it has to form"
May i correct you here energy will not create new matter(or new atoms as you mentioned) in the case you mentioned. It will just increase the mass of the existing matter. For if you accelerates an electron from rest to a speed comparable to speed of light what you w... | {
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Why are roofs blown away by wind? Whenever there are high winds, such as in storms, thin metal roofs on sheds as well as concave roofs on huts are sometimes blown away.
One explanation provided to me said that the higher velocity of the air outside causes the air pressure above the roof to decrease and when it has decr... | Refer Bernoulli's Theorem. Watch this video for demonstration http://dornsife.usc.edu/labs/lecture-support-lab/wind-storm/.
Brief explanation: When the velocity of the wind is great enough, the air pressure above the surface is lower compared to that underneath. This cause the roof to blow off. The aeroplane work in th... | {
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Question about heat engine efficiency I would like to know how much thermal energy is converted to kinetic energy in a steam engine, or a more efficient means if available.
I have done some research and found out that Carnot made some equations to determine efficiency. It is also mentioned that as part of the Carnot cy... | Look up something called the Carnot efficiency. That is the theoretical limit of how effecient any heat engine can be at converting heat power to some other form. This maximum possible efficiency is
Carnot efficiency = Tdiff / Thot = (Thot - Tcold) / Thot
By simple 8th grade algebra, you can see that you get a hi... | {
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How would I explain Ohm's Law in terms of Electrical Fields and Force? In terms of current, resistance, and voltage, it's easy: Ohm's Law is the relationship between current, voltage, and resistance of a circuit. Boom, simple as that. How could I put this in terms of $E$ and $F$? I can sort of see a way to do it by rel... | There are a number of ways you can examine the law in a microscopic view. One of them is this:
An applied voltage creates an electric field, which superimposes a small drift velocity on the free electrons in a metal conductor. This drift velocity is way smaller than the speed of transmission in a conductor.
Now, the ba... | {
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Why does $\ell=0$ correspond to spherically symmetric solutions for the spherical harmonics? In quantum mechanics why do states with $\ell=0$ in the Hydrogen atom correspond to spherically symmetric spherical harmonics?
| Suppose that there existed a spherically symmetrical wavefunction $\psi({\bf r})=f(r)$ for which $l\neq0$. This cannot be, for if we calculate $\langle \psi | L^2 | \psi \rangle$ we will always get zero, as each term in $L^2$ has derivatives with respect to $\theta$ and $\phi$.
Conceptually speaking, a spherically symm... | {
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Braiding statistics of anyons from a Non-Abelian Chern-Simon theory Given a 2+1D Abelian K matrix Chern-Simon theory (with multiplet of internal gauge field $a_I$) partition function:
$$
Z=\exp\left[i\int\big( \frac{1}{4\pi} K_{IJ} a_I \wedge d a_J + a \wedge * j(\ell_m)+ a \wedge * j(\ell_n)\big)\right]
$$
with anyons... | The (unitary) "phase" factor for non-Abelian anyons satisfies the
(non-Abelian) Knizhnik-Zamolodchikov equation:
$$\big (\frac{\partial}{\partial z_{\alpha}} + \frac{1}{2\pi k} \sum_{\beta \neq \alpha} \frac{Q^a_{\alpha}Q^a_{\beta}}{z_{\alpha} - z_{\beta}}\big )U(z_1, ....,z_N) = 0 $$
Where $z_{\alpha}$ is the complex... | {
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Experimental evidence for non-abelian anyons? Since non-abelian anyons have become quite fashionable from the point of view of theory. I would like to know, whether there has actually been experimental confirmation of such objects.
If you could cite original literature, that would be great!
| Try http://arxiv.org/abs/1301.2639 (Phys. Rev. Lett. 111, 186401 (2013)): "Magnetic field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at v=5/2" , although I am not sure this is a definite evidence.
"We show that the resistance of the v=5/2 quantum Hall state, confined to an interferometer, osci... | {
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When is quasiparticle same as elementary excitation, and when is not? Can anyone shed light on the comparison between these two concepts?
| In the context of condensed matter physics:
To make it short, and with the caveat that it is not a universally accepted definition, an elementary excitation may be called a quasiparticle if it is fermionic (e.g. dressed electron), and collective excitation if it is bosonic in nature (e.g. phonon, magnon).
But there is ... | {
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Which surface to use in Ampere's law? In calculating the current enclosed by an Amperian loop, one must, in general evaluate an integral of the form
$$I_\text{encl} = \int \mathbf{J}\cdot\mathrm{d}\mathbf{a}$$
The trouble is, there are infinitely many surfaces that share the same boundary line. Which one are we suppose... | The identity is correct for all of the infinitely many surfaces (isn't math amazing?).
In general you either have a surface you care about in the first place or are in a position to choose the easiest surface.
| {
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Why is a vacuum cleaner not as good heater as an electric radiator? I've read this question and answer: How efficient is an electric heater?
, but still don't understand.
If I have an electric radiator it heats the room with 1000 Watts of power. And I feel the room's getting warmer.
In contrast, if I turn on a vacuum c... | It is because you wouldn't hide in the corners like your kitty does!
A electric radiator is designed to be directional and therefore it doesn't heat the unnecessary part of your room. It makes you feel warming in front of it, but some part of the room don't get heated like those corner and the ceiling. In comparison, a... | {
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What gives an object its colour? My understanding of colour is that atoms in a particular object will absorb certain wavelengths of electromagnetic radiation, and the scattered wavelengths give the object its colour. The absorbed wavelengths contribute to lattice vibrations, increasing the kinetic energy and raising th... | Your coloured object is absorbing light, i.e. light is changing into mechanical energy, while the atoms in the Bunsen burner are emitting light, i.e. mechanical energy is changing into light.
If you have, for example, sodium atoms in a flame those atoms are continuously colliding with air molecules. The velocities of t... | {
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Observations in the cathode ray tube experiement
1.One of the observations I learned was that the glass tube begins to glow with a brilliant green light. Many websites I read through refer to a fluorescent material. However, as shown in the above diagram there was no fluorescent material in the experiment carried out ... | Notice the "Air at very low pressure"? That thin air is what glows. And it has to be very thin or it disrupts the "ray" nature of the phenomena. I'm not sure what exactly was glowing in the earliest experiments, but it might well be the $\mathrm{N}_2$.
Later it was normal to put some mercury in the tubes because it wo... | {
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Derivation of Lagrangian density for an infinite classical dielectric in interaction with the EM field I am tasked with reading and reproducing all the steps in J.J. Hopfield's 1958 paper "Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals". Embarrassingly I am stuck on equation (3). ... | I will set constants like $c$ equal to one.
Then he starts with the normal relativisitc lagrangian, $\mathcal{L} = -\frac{1}{4}F^{\alpha \beta} F_{\alpha \beta} - A^\alpha J_\alpha$. Translating this into non-relativistic language, we get $\mathcal{L} = \frac{1}{2}(E^2 - B^2) - \phi \rho + \mathbf{A} \cdot \mathbf{J} ... | {
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A question about Fermi-Dirac Distribution function It seems more like a mathematical question, about the property of Fermi-Dirac Distribution function $$f=\frac{1}{e^{(E-\mu)/k_BT}+1}$$
where $\mu$ is the chemical potential and $k_B$ is the Boltzmann constant.
I find that $\frac{\partial^nf}{\partial T^n}|_{T\to0}=0$,... |
Are there any physical meaning or application of this property? Why nature gives this property to the widely used Fermi-Dirac Function?
The property you've found (Taylor expansion $\neq$ original function on any interval around the point) has nothing to do with physics or nature, and is not particularly connected onl... | {
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How to calculate velocities after collision? I'm currently writing a program for a particle simulator. One of the requirements is that the particles collide in a realistic way. However, I don't know how to calculate the final velocities.
For each collision, I have the $x$-component and $y$-component of each velocity, a... | Note: The simplest method of calculating collisions use some method of applying impulses to objects that collide at some point in time. The simplest algorithm is to test if two objects are intersecting at some point in time, and if they are you fix it so that they stop intersecting each other, and then apply the calcul... | {
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Increase in velocity by loss of mass?
A trolley of mass 300kg carrying a sand bag of 25kg is moving uniformly with speed of 27km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05 kg/s.
What is the speed of the trolley after the entire sand bag i... | The answer is... 27 km/h.
It is a trick question, the net force on the trolley is always zero.
People might be tricked into blindly applying momentum conservation to find an increase in velocity but this would be incorrect. As the sandbag decreases in weight the momentum carried by the trolley-sandbag system decrease... | {
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Quantum eraser double slit experiment In the quantum eraser double slit experiment, does the photon (or wavefunction) pass through one slit or both slits when different polarizers are placed over the slits?
| According to quantum physics, when certain different polarizers are placed over the slits in the double-slit experiment (for instance, one vertical and one horizontal polarizer, or one circular clockwise and one circular counter-clockwise), thus "marking" each photon with which-way information, the photon indeed passes... | {
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Stacking Shelves with Overhang I want to stack some boxes which are 14" x 10" with some 12" records inside. This means that there will be a 2" overhang outside of each box.
I know that to have an item to balance on a edge 50% of an item needs to be supported. So I think I'm safe to load the boxes in this way.
If I w... | While the standard answer to this problem is usually given in terms of harmonic series,
(see for instance this page at MathWorld) which results in stack looking like this:
I would like to share the nonstandard answer I found following one of the MathWorld links.
A whole new class of solutions was found in the paper by... | {
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Transforming a lagrangian to hamiltonian and vice versa I am not refering to Legendre transform, but to something more simple.
In analytical mechanics, the Lagrangian can be described as $L=T-V$, and the Hamiltonian is if the Lagrangian doesn't explicitly depend on time, then $H=T+V$.
There a simple change of functions... |
$U=i \sqrt{V}$, the the lagrangian becomes: $L=T+U^2$, and the hamiltonian becomes $H=T-U^2$.
Many Lagrangians/Hamiltonians are not of the $T\pm V$ form. If there are velocity dependent potential terms or similar, this breaks down and you have to use a Legendre transform to switch between the two.
For more complicate... | {
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Is it possible to "cook" pasta at room temperature with low enough pressure? It is known fact, that boiling point of water decreases by decreasing of pressure. So there is a pressure at which water boils at room temperature.
Would it be possible to cook e.g. pasta at room temperature in vacuum chamber with low enough p... | If you hydrate pasta by keeping it in cold water, it won't be 'cooked' from a technical standpoint. Cooking requires heat (or the chemical equivalent, as in ceviche). It will taste like wet, raw flour.
| {
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Realistic calculation of heat loss for pipe Good day everyone,
I am new on this site and I hope to find here help, since I am not going anywhere with the literature I have found.
I try to calculate realistically the heat loss of a hot, uninsulated pipe. Let's say,
it is $170\,\,C$, 1 meter long, $8" (=0,203\,\,m)$ of d... | According to http://www.engineeringtoolbox.com/steel-pipes-heat-loss-d_53.html , the heat losses are close to what you get. I'd note that the convective coefficient of air is rather tricky: it depends even on the orientation of the pipe (horisontal/vertical).
| {
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General relativity in terms of differential forms Is there a formulation of general relativity in terms of differential forms instead of tensors with indices and sub-indices? If yes, where can I find it and what are the advantages of each method? If not, why is it not possible?
| differential forms. It's not 100% clear how to read the question so I'll fire in all directions.
In general relativity, the field of interest is the symmetric metric tensor $g$ which you see written $g_{\mu\nu}$ or e.g. $g_{ab}$. The latter often implies abstract index notation.
The base vectors on the cotangential sp... | {
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Is it possible to estimate the speed of wind by the sound emitted by a cable of an overhead power line? I was near ($\approx40m$) an overhead power line and I heard a sound coming from the cables of the power line; I think the sound was made by the vibrations of the power cables due to the wind but I am not sure. The w... | The sound by the cable is produced because of the Kármán vortex shedding.
This empirical formula from the wikipedia page relates the frequency of the vortex shedding with the Reynolds number:
$$
\frac{fd}{V}=0.198\left (1-\frac{19.7}{\mathrm{Re}}\right),
$$
where $f$ is the frequency, $d$ cable diameter and $V$ is the... | {
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How can space and time arise from nothing? Lawrence Krauss said this on an Australian Q&A programme.
"...when you apply quantum mechanics to gravity, space itself can arise from nothing as can time..."
Can you elaborate on this please?
It's hard to search for!
| This is not so much an answer as a comment and caution: ex nihilo nihil fit (from nothing nothing is produced).
From Wikipedia:
It is important, however, to recognize what a physicist may mean by
the word nothing. Some physicists, such as Lawrence Krauss, define
nothing as an unstable quantum vacuum that contains... | {
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What exactly is a bound state and why does it have negative energy? Could you give me an idea of what bound states mean and what is their importance in quantum-mechanics problems with a potential (e.g. a potential described by a delta function)?
Why, when a stable bound state exists, the energies of the related station... | If you have a copy of Griffiths, he has a nice discussion of this in the delta function potential section. In summary, if the energy is less than the potential at $-\infty$ and $+\infty$, then it is a bound state, and the spectrum will be discrete:
$$
\Psi\left(x,t\right) = \sum_n c_n \Psi_n\left(x,t\right).
$$
Otherwi... | {
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Meaning of the chemical potential for a boson gas My lecturer told me that $\mu$, the Chemical potential, is zero or negative, and in the following example, mathematically it acts as a normalization constant. But is there any physical insight about why boson gas can be zero or negative?
I think it is due to the fact th... | To be a little more precise: the chemical potential of a non-interacting Bose gas must be exceed the energy of the ground state single particle energy of that gas. If there are (as say, in $^4\rm He$) repulsive interactions between the particles, the chemical potential can be anything.
| {
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At what point is the spin determined in a Stern-Gerlach Apparatus Consider a particle with spin that travels through a Stern Gerlach box (SGB), which projects the particle’s spin onto one of the eigenstates in the $z$-direction. The SGB defines separate trajectories for the particles that travel through it depending on... | The spin is determined when observed or measured. At this point the particle must take only one position. A big issue in experimental physics is that when you observe or measure something, you are actually changing it yourself for example when observing a stream of electrons, you are exerting photons onto it, thus chan... | {
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"answer_id": 3
} |
If a Goldstone boson is an excitation moving between degenerate vacua, how do symmetries remain broken? In spontaneous symmetry breaking, moving around the circular valley of the Mexican hat potential doesn’t change the potential energy. These angular excitations are called Goldstone bosons. But doesn't the change of a... | Not sure I understand the question. The symmetry is broken because you're in the valley. As you say correctly, moving around in the valley doesn't change anything about that.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/92440",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 4,
"answer_id": 3
} |
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