Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What is quantum discord? What is quantum discord? I stumbled upon this term on Quantum Computing: The power of discord, but have never heard of it before. Can you give a bit more mathematical explanation of the term here?
| It is basically a measure of the quantumness of some correlations, which is not vanishing for some separable state. It was introduced by Ollivier and Zurek (PRL/arXiv). It is the difference between two different generalizations of the classical (Shannon) conditional entropy to the quantum world, and is 0 for a pure bi... | {
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Can quantum annealing be used for factorization? It is known that there is a famous quantum factorization algorithm by Peter Shor. The algorithm is thought to be suitable only for quantum gate computer.
But can a an adiabatic quantum computer especially that which is capable of quantum annealing be used for factorizati... | Yes, though I don't think that we'll see D-Wave factoring even 20-bit numbers anytime soon. One of their tutorials shows how to model a NAND gate using 4 qubits. With a handful of those, I can make a carry-save multiplier cell, though surely it can be built more optimally. If I want to factor an N-bit number, I coul... | {
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Mechanical work to required battery power I have a very practical question where I've calculated the mechanical work needed by a simple mechanical system by solving the line integral $W = \int_C \ F \ dx$. However, since I have a black spot in my brain for electrical calculations I figured I could just (considering a 1... | From the specifications of your battery, that is 1.5V and 2700mAh, you can compute that there is $14580$ Joules of energy stored in your batteries.
The formula $P=U\cdot I$ relates power to voltage and current. You battery specs give voltage and capacity (that is total charge stored). The former is in Volt, the latter... | {
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Analyzing the motion of a ball rolling without slipping inside a hemispherical bowl Consider a solid ball of radius $r$ and mass $m$ rolling without slipping in a hemispherical bowl of radius $R$ (simple back and forth motion). Now, I assume the oscillations are small and so the small angle approximation holds. I wish ... | Your first derivation, using energy, uses two different meanings for the same symbol $\omega$. In one place, you interpret it as
$$\omega = \dot{\theta}$$
the time derivative of the angle of the line from the center of the ball to the center of the bowl with the vertical.
In another place, you interpret $\omega$ as th... | {
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what cools bottle of water faster: ice or snow Imagine you have a pile of snow and a pile of ice shards. You put a soda bottle which has a room temperature into both piles. Which bottle is going to cool down faster?
| The first thing to realize is that "ice" is a pile of small ice shards and snow is a pile of itty-bitty ice shards.
Assuming the snow and ice are at the same temperature, the answer to your question with come down to which one has more contact area and (to a much lesser extent) how that contact area is distributed. Al... | {
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Ascent rate and size of balloon I am part of a school project, Project Stratos to send a balloon to the edge of space (the closer side :P) and was wondering how you would work out the accent rate of a large balloon (roughly 1m^3 of helium with 100g of mass) and the size of it as it increases its Altitude. I am creating... | Your answer using drag assumes the balloon is rising very fast. At the low speeds, typical of a balloon, the dominant resistive force is the viscose downward displacement of the surrounding gas as the balloon rises upwards. This depends linearly on speed, not quadratically. Think lava lamp, not fighter jet.
The laborat... | {
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Direct exposure to the vacuum of space I was watching a few sci-fi movies and was wondering the real science explaining what would happen if you were to be subject to the conditions of outerspace.
I read the wikipedia article on space exposure, but was still confused. If a person was about the same distance from the su... | You'd freeze to death faster in the Atlantic ocean.
Space has essentially no thermal conductivity. All the heat you lose will be radiated away. According to the Stefan-Boltzman law, $W = \sigma T^4$, you would lose at most 500 watts per square meter of body surface area. By contrast, the convective heat transfer coe... | {
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What other shielding material than lead is effective against gamma rays? As the question in the title states I am wondering what material can be effectively used to shield gamma rays apart from lead? I believe concrete is often used, but it is nowhere near as effective as lead (6 cm to match 1 cm of lead as I understan... | There are three processes by which gamma rays interact with matter: the photoelectric effect, Compton scattering, and pair production.
The photoelectric effect is an interaction between the gamma ray and an electron. It's forbidden by conservation of energy and momentum unless there is some other body present as well, ... | {
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Why is the gravitational force always attractive? Why is the gravitational force always attractive? Is there another way to explain this without the curvature of space time?
PS: If the simple answer to this question is that mass makes space-time curve in a concave fashion, I can rephrase the question as why does mass ... | Artwork:
dipole +- <--- some distance ---> +- dipole
Two dipoles are always attractive (or a dipole and another charge).
If they are like this +- ... -+ or -+ ...+- the dipoles will rotate and the configuration become attractive +- ... +- or -+ ... -+ .
They obey a 1/r³ relation.
If you can consider that inside t... | {
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Why so many arguments for the transformation equations of generalized coordinates? For a system of $N$ particles with $k$ holonomic constraints, their Cartesian coordinates are expressed in terms of generalized coordinates as $$\mathbf{r}_1 = \mathbf{r}_1(q_1, q_2,..., q_{3N-k}, t)$$ $$...$$ $$\mathbf{r}_N = \mathbf{r}... | The $k$ holonomic constraints are used to eliminate $k$ $q$s, so reducing their number from $3N$ to $3N-k$. This then introduces the dependence of some of the transformation equations on t and other $q$s.
You have k holonomic constraints of the form $$\mathbf{f}_1(q_1, q_2,..., q_{3N},t) = 0$$ $$...$$ $$\mathbf{f}_k(q_... | {
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How is thermodynamic entropy defined? What is its relationship to information entropy? I read that thermodynamic entropy is a measure of the number of microenergy states. What is the derivation for $S=k\log N$, where $k$ is Boltzmann constant, $N$ number of microenergy states.
How is the logarithmic measure justified?
... | Hey you have the Thermodynamic definition which is :
$$\Delta S = \int \frac{dQ}{T}$$
and the statistical definition:
$S=k\log N$
N- the number of the possibly states of the system (including degeneration).
For mostly everything they are equivalent!!
note that you can not measure enytopy, but you can measure the $\Delt... | {
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In a gas of particles, how is the displacement vector related to the number density? Suppose I have a gas of particles that is initially uniformly distributed so that the number density is $n_0$ (number of particles per unit volume), and then I displace the particles by the vector field $\vec{d}(\vec{x})$ (i.e. the par... | A simple 1D calculation gives, at first order, something like
$$
\frac{1}{n} = \frac{1}{n_0}\left(1+\vec{\nabla}\cdot\vec{d}\right)
$$
but only if $\vec{d}$ is small enough. Otherwise, for calculating
$n(\vec{x})$, you need to evaluate the divergence at a point $\vec{x'}$
such that $\vec{x'}+\vec{d}(\vec{x'}) = \vec{... | {
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Linear polarizer and the angle of incidence It is known that when a beam of lineary polarized light falls perpendicularly on a linear polarizer, the intensity of polarization changes according to Malus' law and the direction of polarization changes as cosine of angle between polarization vector and polarizer vector.
My... | It depends on the polarizing material.
I assume below that it is about layer of absorptive material.
When wave travels through an anisotropic material, its phase shift and absorption is polarization-dependent. So you should be able to treat it in similar way as the Birefringence (giving a complex refraction index to ta... | {
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A No-Nonsense Introduction to Quantum Field Theory I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page here. pdf here), a 24-page overview of the topic, very helpful for beginning study. It all got me over the hump of learning the meaning of various terms associated with GR, most of ... | There is a great introduction called "This is How Quantum Field Theory Works" which, I think, is exactly what you are looking for.
All essential concepts are introduced and the basic idea how one gets from the fundamental equations to cross sections, i.e. quantities that can be measured in experiments is sketched.
| {
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Why aren't there compression waves in electromagnetic fields? I just started learning about optics, and in the book I'm reading they explain how the electrical field caused by a single charged particle could be described by a series of field lines radiating out of the particle; they compare these imaginary lines to rop... | Well, is not 100% percent accurate to say that there aren't longitudinal EM waves. In a waveguide there are allowed propagation modes that have non-zero electric and magnetic components in the direction of propagation:
http://en.wikipedia.org/wiki/Transverse_mode
| {
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Photon statistics of an incandescent light source We usually calibrate the cameras on our microscopes by capturing 20 images of a blurry (not sharp) fluorescent particle. For each pixel in this stack of 20 images we calculate the intensity variance. By plotting the variance against the intensity we obtain the scale fac... | I noticed this old answer and I don't think it's right. Surely a laser gives off photons with poisson statistics, but not an incandescent source. The reason is fairly intuitive, to the extent that these types of verbal arguments are ever correct: there are random intensity fluctuations associated with incandescent sour... | {
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Calculating time for a fully charged UPS I have a UPS of 1000 Volts connected with 2 batteries each of 150 Amp. How much time it will take to consume the whole UPS (after fully charged) when a device of 1Amp is getting electricity form that UPS.
Please also explain me the calculation.
| Don't think you can calculate this. I depends on the type, age and history of the batteries. All his factors make a big difference. If you rely need to know the TCT "total charge time" put them threw the cycle once and measure it. And remember this will change with time.
| {
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Why should one expect closed timelike curves to be impossible in quantum gravity? From the Wikipedia article, it seems that physicists tend to view closed timelike curves as an undesirable attribute of a solution to the Einstein Field Equations. Hawking formulated the Chronology protection conjecture, which I understan... | It's certainly possible that just as the holographic principle can save unitarity for black holes, that some generalization of the holographic principle coupled with cosmic censorship for closed timelike curves can save unitarity.
At any rate, the interior of a time machine is only real to the extent that memories and ... | {
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Gelfand-Yaglom theorem for functional determinants What is the 'Gelfand-Yaglom' Theorem? I have heard that it is used to calculate Functional determinants by solving an initial value problem of the form
$Hy(x)-zy(x)=0$ with $y(0)=0$ and $y'(0)=1$. Here $H$ is the Hamiltonian and $z$ is a real parameter.
Is it that si... | I was at a talk a while back by Gerald Dunne where he talked about the Gelfand-Yaglom theorem. He used it for calculating some Euler-Heisenberg type effective actions. A paper of his with Hyunsoo Min on the subject is A comment on the Gelfand–Yaglom theorem, zeta functions and heat kernels for PT-symmetric Hamiltonians... | {
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What happens to light in a perfect reflective sphere? Let's say you have the ability to shine some light into a perfectly round sphere and the sphere's interior surface was perfectly smooth and reflective and there was no way for the light to escape.
If you could observe the inside of the sphere, what would you observe... | As soon as the light shining in was turned off, the light in the sphere would disappear, not because observing depletes energy, it doesn't (but energy loss by the system is required for observation to occur). No one knows but this hypothesis that light beams persist when the light emitter is extinguished is just that. ... | {
"language": "en",
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Simplest interferometer I want to build simplest interferometer which should be able to measure movements down to fraction of wavelength.
What is the simplest scheme for that, and what are the requirements for a laser?
I have a bunch of laser diode-based ones, and I guess they might be not coherent enough...
Are green... | You should also consider the laser's frequency stability. My understanding is that the frequency of light can go up and down by some nanometers as temperature (and perhaps some of the electrical inputs) of a laser diode varies. Searching seems to turn up quite a few articles on stabilizing their output, exactly for thi... | {
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Projecting image without manual focussing I was wondering if it was possible to project a magnified image on a wall without the need of focusing, so just by dimensioning the lenses right.
I know I have to use the principal of Maxwellian View for the illumination of the slide. However, there are a lot of parameters left... | You can do it by correctly choosing the focal length of the lens(es) you're using. Is that what you mean? The drawback is that you can only use it in one specific setup. (I'm not sure if I understand correctly as this seems a bit trivial).
| {
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How fast does an ice cube melt in a microwave? I have noticed that when I microwave an ice cube it appears to melt more slowly than I would expect. For example, an equal volume of water starting at 0 deg C would probably be at boiling point before an ice cube that was at -15 deg C had melted. I realize there is enthalp... | The unusual thing is the really high absorption of microwaves by
bulk water, whereas the ice behaves more normal like most solids and liquids.
In liquid water we have an effect of relaxation of orientational polarisation.
The polarisation is achieved not by rotation (not possible in liquid water)
but by shift of hy... | {
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Can an object between two magnets reduce their attraction/repulsion? If you have two magnets (not in contact) and then put a non-magnetic object in between the two magnets, does that decrease the attraction/repulsion between the two magnets?
It seems that it wouldn't, because, if it would, then you could allow two magn... | Of course it's possible and it's completely the same like with electric materials. Google for terms (electric and magnetic) polarization, permitivity, permeability, susceptibility.
The problem with your perpetum mobile is that you don't account for bringing in the third object at all.
| {
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How beam focusing looks like in electron microscope? I mean I know there are electrostatic/electromagnetic lenses which does focus the beam, but I am not sure how it is possible to foсus beam down to a few 10nm while emitter might be 1mm thick while having large focusing distance (especially when looking at chromatic a... | "Why doesn't electrons widen the beam by repelling each other en-route?"
This does happen and can cause unwanted distortions. The reason it's not an overwhelming problem is that the electrons, once they get going, are not all that close together. For example, if you have a 1nA beam current, and the electrons are travel... | {
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Finding the position of a planet between two other planets of known mass and distance Here is the question:
A planet with mass $m$ and a second with mass $M$ are separated by a
distance $d$. A third planet with mass $m_3$ happens to be midway
between $M$ and $m$. Where could the third planet be positioned
(dista... | Check the signs in your equation. Draw the three planets in a line with the central planet at the origin. What is the direction of the force each of the side planets exert on the middle one?
If you resolve the above problem you can approach solving the equations. Notice that you have as many equations as you have unkno... | {
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Is the earth expanding? I recently saw this video on youtube:
http://www.youtube.com/watch?v=oJfBSc6e7QQ
and I don't know what to make of it. It seems as if the theory has enough evidence to be correct but where would all the water have appeared from? Would that much water have appeared over 60 million years? Also what... | There are several indicators that the Earth is both Growing ( increasing Mass ),
and Expanding ( increasing volume with or without mass increase ).
1) The continents and the submerged continental fragments fit together
on all the sides simultaneously at a radius of between 53.88 % R of the current
radius ( excluding ... | {
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Creation of matter in the Big Bang I appreciate your patience to my neophyte question. I am working on my dissertation in philosophy (which has nothing or little to do with physics) about the "problem of naming." Briefly what I am arguing is that when we name something, we stop it from being anything or everything else... | Without there being space or time before the big bang, the laws of physics wouldn't work. This means that everything possible AND impossible could and would happen in that instance. Without the conservation of matter in effect, matter was probably created at the big bang.
| {
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At what speed does our universe expand? Conceivably it expands with the speed of light. I do not know, but curious, if there is an answer. At what velocity, does our universe expand?
| The recessional velocity is given by Hubble's Law and it's proportional to the proper distance from the observer to the object (galaxy or other distant object):
$$v=H_0 D$$
where $H_0$ is Hubble's constant.
As you can see, the recessional velocity beyond a certain distance, known as the
Hubble distance, can be much gre... | {
"language": "en",
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In dimensional analysis, why the dimensionless constant is usually of order 1? Usually in all discussions and arguments of scaling or solving problems using dimensional analysis, the dimensionless constant is indeterminate but it is usually assumed that it is of order 1.
*
*What does "of order 1" mean? 0.1-10?
*Is... | The answer follows from considering why we use dimensional quantities in the first place. So, given that the laws of physics can be formulated in a dimensionless way, how come we've ended up with using dimensional quantities. The answer is that physical quantities that we can readily measure at the macroscopic scale h... | {
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Why does the weighing balance restore when tilted and released I'm talking about a Weighing Balance shown in the figure:
Press & Hold on onside of the horizontal beam and then release it. It makes some oscillations and comes back to equilibrium like shown in the figure.
Both the pans are of equal equal masses. When th... | If it would only be the weights exerting torque, the balance would be in equilibrium at all angles. What makes the balance go back to the horizontal position is the fact, that the center of mass is below the beam. consider this picture
The needle exerts a torque too, so you have more torque on the side, where the plat... | {
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Must the action be a Lorentz scalar? Page 580, Chapter 12 in Jackson's 3rd edition text carries the statement:
From the first postulate of special relativity the action integral must be a Lorentz scalar because the equations of motion are determined by the extemum condition, $\delta A = 0$
Certainly the extremeum con... | The key point made by Jackson here is that the Lagrangian is physically significant since it determines the equations of motion; via the extremum condition as it so happens.
Firstly, the action integral is taken along a path which is a Lorentz invariant. Secondly, since the Lagrangian is physically significant, then it... | {
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How can two different 12V batteries have different amperage for same resistance? My local car parts dealer presented me his inventory of car batteries. One 12V battery had a 'cold crank amperage' of 600amps. The other 12V battery had a 'cold crank amperage' of 585amps. Questions:[1] If the resistance, my truck, is cons... | It is due to non zero internal resistances being different. If you make a short circuit, the current won't be infinity but of a finite value. It is the internal resistance who limits high currents.
| {
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GUT that includes all 3 particle families into a large group? Explaining SU(5) GUTs (using the first particle family as an example) in the last SUSY lecture 10, Lenny Susskind mentioned that there are at present no ideas how to combine simultaneously all 3 particle families into a large GUT theory.
I somehow dont belie... | The problem of families in GUT is sometimes referred as an "Horizontal symmetry". There are two lines of work, roughly: those which get a continous symmetry, say SU(3), and then all the gauge malabars, and those which add a discrete symmetry, such as A4. Of course in both cases, a serious GUT should show everything emb... | {
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Introducing emf of a chemical cell as a hint towards quantum mechanics Today I had a discussion with a colleague who teaches electricity and magnetism to 2nd year undergraduate physics students. He is seeking the best way to explain how is the emf generated inside a battery with a minimal appeal to physics beyond class... | Each chemical species has a specific strength of oxidation and/or reduction. The Redox potential is what chemists use to calculate the electrode potential of a battery:
E°cell = E°red(cathode) – E°red(anode) = E°red(cathode) + E°oxi(anode)
Wikipedia has a nice compilation of Redox potentials, which are used in the abov... | {
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Why did my liquid soda freeze once I pulled it out of the fridge and opened it? This isn't a duplicate to "Why did my liquid soda freeze once I pulled it out of the fridge?". My question is why soda froze after it was opened. Opening a can or bottle seems to have a larger effect than just jostling it.
Is it because of ... | It is because of the Ideal Gas Law, PV=nRT. The soda is in equilibrium inside the sealed bottle or can. But when you open it, that equilibrium is disturbed. The pressure is decreased so the temperature will also decrease.
| {
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Physical interpretation of describing mass in units of length I'm working in Taylor and Wheeler's "Exploring Black Holes" and on p.2-14 they use two honorary constants: Newton's constant divided by the speed of light squared e.g. $G/c^2$ as a term to convert mass measured in $kg$ to distance.
Without doing the arithme... | I'm not sure it's terribly helpful, but it seems like the following analysis helps explain dmckee's response.
The force of gravity is
$F = G \frac{m M}{r^2}$.
Rearranging and dividing by $c^2$ gives
$\frac{G}{c^2} = \frac{F r^2}{M (m c^2)}$
where the $mc^2$ is the rest mass energy $(E_0)$ of the object experiencing the... | {
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How can it be that the beginning universe had a high temperature and a low entropy at the same time? The Big Bang theory assumes that our universe started from a very/infinitely dense and extremely/infinitely hot state. But on the other side, it is often claimed that our universe must have been started in a state with ... | Entropy is not the existence of heat or energy, but is more accurately described as the spread of energy. A universe with high heat and low matter density has very low entropy, the same way that a cup of hot water has low energy distribution when compared to a cold pool. If you throw the hot water into the cold pool th... | {
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Can superconducting magnets fly (or repel the earth's core)? If a superconducting magnet and appropriate power supply had just enough $I\cdot s$ (current $\cdot$ length) so that when it was perpendicular to the earth's magnetic field, the force of the interaction was just enough to excede the force exerted on the objec... | The bigger problem would be keeping it cool and not going over the magnetic threshold of the material. You really wouldn't need to worry about the spinning since your using the flux trapping property of the super conductors. Essentially once you produced the field needed you could trap it in a conducting loop, and as l... | {
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under what conditions happen the anti-Zeno effect? As you might know, the Zeno effect is intuitively expressed as what happens when a system is measured in intervals smaller than the half life of the state it is currently on. As a consequence, the state has a negligible probability of doing a transition and is kept 'st... | The Anti-Zeno effect is when you have a transition from a state enhanced by a decoherence source. I can show you a toy model where it happens:
consider four states A,B,E and Z. Z is the ground state, and A and B are two nearly degenerate excited states and E is a super-excited. B has no matrix element to Z and A has ma... | {
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Why does current alternate in an AC generator? I understand how generators work, but I can't for the life of me conceptualize why the current in an AC generator reverses every 180 degrees!!! I understand that, using the right hand rule, it can be seen that the current flows around the coil in a generator in one directi... | Set up a magnet around a coil, such that the Magnet has a field that is constant in magnitude, and has vector form ${\vec B} = B_{0}(\cos (\omega t) {\hat z} + \sin (\omega t) {\hat x})$. Orient the coil so that it lies in the $x-y$ plane and thus has a normal that points in the $z$ direction. If the overlap of the c... | {
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What determines the apparent radius of the rainbow? Let's say I know how to compute the apparent radius of a rainbow from the viewpoint of the observer: take a photo of the scene, measure the distance to a known reference object, and its dimensions. Using triangle similarity, I can extrapolate the radius of the rainbow... | It depends on where the sun is. If it is near the horizon (behind you) and in front of you there are water droplets, then you will see a rainbow with a radius (in angular measure) of about 42 degrees, because each water droplet returns a cone of light, whose axis is parallel to the direction to the sun and whose apertu... | {
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Experimental evidence for parallel universes/multiverses My idea of physics is that it is a collection of mathematical laws relating observables. And that one can perform alot of mathematical derivations on these laws to produce new laws between observables. My question is how does one translate a mathematical equation... | There are speculative theories that suggest areas of cold/hot patches in the cosmic microwave background are 'bruises' caused by collisions of expanding bubble universe... These are not 'parallel' in your sense though, more they are just different regions of space-time.
| {
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Why Do Hurricane Balls Spin So Fast? I was wondering if anyone could offer an explanation as to why the balls described in this video spin so fast.
Here's the setup: Two metal balls are wielded together. When spun with air, they acquire a massive amount of rpm.
| The balls never spin faster than the velocity of the air being blown on them. Notice that when the presenter blows on the hurricane balls, he angles the mirror towards himself. He does this so the balls aren't blown off the mirror (he's blowing pretty hard). Also, it seems they are spinning ridiculously fast due to ... | {
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Could the Schrödinger equation be nonlinear? Is there any specific reasons why so few consider the possibility that there might be something underlying the Schrödinger equation which is nonlinear? For instance, can't quantum gravity (QG) be nonlinear like general relativity (GR)?
| @Ron Maimon has given the canonical answer to this: the wavefunction is probabilities, and to preserve probabilities one must have a linear equation (indeed, also a norm-preserving evolution operator).
I offer another viewpoint, in the style of how Einstein thought about relativity, i.e. two postulates. The postulate i... | {
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Since the universe is expanding, does anything ever occupy the same point in space? Let's say we can observe expansion in a supercluster.
We define origin of our frame of reference at the center of the supercluster.
We observe an object/atom at point A at time T. The object is motionless relative to the origin.
We wait... | This seems to be dependent on the manner in which the super-cluster expands.
If expansion, mass, and energies expand perfectly synchronous relative to each other and the point defined as "center", then the "center" remains relative to all other points. We know this not to be the case, therefore, the "center"will consta... | {
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Acceleration vector - deceleration vs direction If acceleration of something $= - 10 \text{ m s}^{-2}$
And forwards is define as north.
Does that mean the object is getting slower (decelerating) or accelerating in the reverse direction (south)
How can you tell the difference?
|
Does that mean the object is getting slower (decelerating) or accelerating in the reverse direction (south)
It really doesn't matter. Basic kinematic formulas are designed to work just as well in either case, which is why physicists don't generally use the word "decelerating." It's just another kind of acceleration.
... | {
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How long does a permanent magnet remain a magnet? I have a bunch of magnets (one of those game-board thingies) given to me when I was a school-going lad over 20 years ago, and the magnets feel just as strong as it was the day it was given.
As a corollary to this question Do magnets lose their magnetism?, is there a wa... | If a permanent magnet could "decay" at the rate given in Rook's answer above there would be none found in geological strata.
A permanent magnet has a permanent orientation of the magnetic moments in a specific vectorially additive direction depending on small crystal domains. To change, i.e. be demagnetized, the magn... | {
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How can one localize the massless fermions in Dirac materials? I noticed that finite electric potential cannot localize the low energy excitations in a graphene sheet. Is it possible to localize the massless fermions in the surface band of topological insulators with a magnetic field?
I found a paper dealing with a s... | This issue is a well known problem in high energy physics which is called " Neutrino Billiards". You can find a full description about it in:
Ref:
Berry, M.V. and R.J. Mondragon, Neutrino Billiards: Time-Reversal Symmetry-Breaking Without Magnetic Fields. Proceedings of the Royal Society of London. A. Mathematical and ... | {
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Why are color values stored as Red, Green, Blue? I learned in elementary school that you could get green by mixing blue with yellow.
However with LEDs, TFTs, etc. you always have RGB (red, green, blue) values?
Why is that? From what you learned in elementary yellow would be the 'natural' choice instead of green.
| The inherent difference is things that emit colors, e.g. LEDs, and things that place substances on a surfaces to color them, e.g. printers. In the latter case, the CMYK (cyan, magenta, yellow, black) space is commonly used, rather than RGB, so you were on the right track with yellow. BTW, black is there because the bla... | {
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Is there some explanation for $y_t=1$ The Yukawa coupling of the top quark is Dirac-natural in a too excellent way, it is within one sigma experimentally, and within 99.5% in absolute value, of being equal to one. Without some symmetry, it seems too much for a quantity that is supposed to come down from GUT/Planck scal... | This is a very naive answer or, in fact, it is not an answer. Among all numbers of order one, is not $y_t=1$ the most likely value, i.e., the statically expected value? Why do we need an explanation for $y_t=0.995$ and not for, say, $y_t=0.629$?
| {
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Superluminal neutrinos
I was quite surprised to read this all over the news today:
Elusive, nearly massive subatomic particles called neutrinos appear to travel just faster than light, a team of physicists in Europe reports. If so, the observation would wreck Einstein's theory of special relativity, which demands tha... | Suppose this is real, that the neutrinos arrive very slightly faster than light would through the vacuum. Wouldn't that point to there being a slightly higher c which actually limits speeds, and some slight slow-down for light from this maximum due to interactions of the electromagnetic field with other particles, incl... | {
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What is the "shape" of atomic/subatomic particles? I apologize in advance for my ignorance if this is a question with an obvious answer... I am not experienced in this field. But are such particles in the universe points with a charge, or are they very small spheres with a charge? Or does it not even matter in the e... | continuing with @lusken 's answer, the atom is perceived as a fuzzy ball with a highly dense nucleus (mainly point size, compared to the size of the atom itself) and the fuzzy boundary because of the electron cloud.
The electron cloud themselves appear in different probability distribution, which gives different "shap... | {
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How do you find the uncertainty of a weighted average? The following is taken from a practice GRE question:
Two experimental techniques determine the
mass of an object to be $11\pm 1\, \mathrm{kg}$ and $10\pm 2\, \mathrm{kg}$.
These two measurements can be combined to
give a weighted average. What is the unce... | I agree with @Ron Maimon that these ETS questions are problematic. But this is (i think) the reasoning they go with. Unlike @Mike's assumption you should not take the normal average, but as stated in the question the weighted average. A weighted average assigns to each measurement $x_i$ a weight $w_i$ and the average i... | {
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Is there a mathematical way to describe how a flame flickers? I love the way candles flicker. It's a great effect and I almost want to see it replicated in an actual lightbulb. I was curious if there is any way to express that mathematically? I'm not that familiar with physics but I go in assuming that most things can ... | If you want to determine physical causes of flame shape evolution, you would have to consider all processes taking place (chemical, phase changes, fluid dynamics, heat, ...); they are described using known differential equations, i.e. in one point in space. The exact global solution then requires those equations to hol... | {
"language": "en",
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understanding time: Is time simply the rate change? Is time simply the rate of change?
If this is the case and time was created during the big bang would it be the case that the closer you get to the start of the big bang the "slower" things change until you essentially approach a static, unchanging entity at the begin... | Time is what is measured by clocks.
But how is time modelled in physical theories ?
In the Schrödinger equation time enters as an external parameter. How does this parameter correspond to the time measured by clocks ?
The following reference might be a good introduction to this and related questions concerning time and... | {
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What is the difference between electric potential, electrostatic potential, potential difference (PD), voltage and electromotive force (EMF)? This is a confused part ever since I started learning electricity. What is the difference between electric potential, electrostatic potential, potential difference (PD), voltage ... | EDIT: Put simply, potential difference is the work done by electrostatic force on a unit charge, while EMF is the work done by anything other than electrostatic force on a unit charge.
I don't like the term "voltage". It seems to mean anything measured in volts. I'd rather say electric potential and electromotive forc... | {
"language": "en",
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Numerical software to manipulate a light beam in its plane wave representation? Any light field can be expressed as a sum of plane waves. Such an ensemble of plane waves is called the plane wave spectrum of the light field. The plane wave spectrum is the Fourier transform of the light field in the real space representa... | I use pylab numpy scipy matplotlib (and matplotlib.mlab)
examples f.i. here and doc and nice ref here
or use the online integrated python environment sagenb.org (open account or download package, upload files and start working anywhere)
nice plots ...
to do digital filters explore the online book
The Scientist and E... | {
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Open quantum systems and measuring devices The Copenhagen interpretation by Niels Bohr insists that quantum systems do not exist independently of the measuring apparatus but only comes into being by the process of measurement itself. It is only through the apparatus that anything can be said about the system. By necess... | ''that quantum systems do not exist independently of the measuring apparatus but only comes into being by the process of measurement itself'' is a gross distortion of the Copenhagen interpretation. The latter only asserts that the particular value of measuring quantum variables of a system that exists objectively (othe... | {
"language": "en",
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What ring weave disposition should be the most resistant against stabbing and/or how to determine it In a website that I am studying so I can build a Chain Mail, I have found a page featuring a lot of different Ring Weaves to build them.
I want to determine which one is the best to provide resistance against stabbing s... | I will hand wave on this:
The best resistance against stabbing must be metal plate, i.e. no holes where a knife can enter.
The weave is the result of trying to introduce flexibility so that a dress can be made out of the material that would allow agile motion.
The best weave is the weave that when projected against the... | {
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Mathematical definition of Bogomol'nyi–Prasad–Sommerfield (BPS) states What is the mathematical definition of Bogomol'nyi–Prasad–Sommerfield (BPS) states, independent of any specific physical theory.
| It's a state annihilated by $E-Q$ where $E$ is the energy, or another dynamical/isometry generator, and $Q$ is the sum of multiples of other conserved charges such that one may write
$$ E - Q = \sum_{i,j} c_{ij}\{Q_i,Q_j\} $$
i.e. the difference between energy and charges may be obtained as an anticommutator of some s... | {
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Quick question concerning the Heisenberg model I got a small, rather technical question concerning the Heisenberg model.
(It is technical indeed.)
Consider the Heisenberg Hamiltonian:
$H = \sum_{(i,j)} S_{i} S_{j}$ = $- \frac{J}{V} \sum_{q} \gamma_{q} S_{q} S_{-q}$.
with
$\gamma_{q} = 2 \sum_{\alpha=x,y,...}cos(q_{... | The thing to keep in mind is that that formula only holds because you are coupling nearest-neighbor spins. Let's pretend we're in 1D (the generalization for higher dimensions is trivial). When you replace the operators by their fourier transformed representations that you provided, you get
$$
J\sum_i S_i \cdot S_{i+1}... | {
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Does the speed of sand flow in a hourglass depend on a height of a sand column above the hourglass neck? In a hourglass, does the sand flow through the neck depend on the amount of sand in the upper glass? If we consider a sand flow analogous to fluid flow, then it should depend linearly, but in that case amount of san... | Fluid approximations do not work well at the scale of sand in hourglasses for most hourglasses. Almost all of the sand is statically braced against the walls and floor of the hourglass. Instead, you have a small region of instability above the hole where it is not possible for the sand to be braced; as that unstable ... | {
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why making a surface "super" smooth increases the coefficient of friction? I read that:
If you take a rough surface and make it smooth, the coefficient of friction decreases. But if you make it super smooth, then the coefficient of friction increases. How come?
| What do you mean by super smooth?
I remember a note (again) by Feynmann that said if you made your test surface so clean that there is absolutely no dirt or impurities on it, then the super clean surface would actually attach to anything sliding on it, making the apparent friction coefficient higher.
Is this what you ... | {
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Does the Opera result hint to a discrete spacetime? Could the Opera result be interpreted as some kind of hint to a discrete spacetime that is only seen for high enough energy neutrinos?
I think I've read (some time ago) something like this in a popular article where among other things tests of quantum gravity theories... | In several theories, space itself is discrete, somewhat in relation to the Planck length, $$l_p = \sqrt{\frac{\hbar G}{c^3}} \simeq 1.616199 \times 10^{-35}\quad m$$ .
More specifically in loop quantum gravity, Carlo Rovelli's 1998 overview paper states the following:
The spin-networks picture of space–time is mathema... | {
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Orbital radius of Geo-stationary satellite Could you please tell, Why all the geo-stationary satellites are to be dropped at same height from earth? Why can't it be closer or away from its regular orbit(ie, 35,000 km)? If all satellites are dropped in the same orbit, then will not those collide one another?
| Geostationary satellites are less likely to collide since they are all moving in the same direction. But they aren't all perfectly positioned and so do drift - even 'perfectly' positioned ones do drift in a figure of 8 around their intended point.
But if there ever is a collision, or an explosion, the debris is going... | {
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What are quarks made of? So atoms are formed from protons and neutrons, which are formed from quarks.
But where do these quarks come from? What makes them?
| The standard mainstream answer is to consider them as fundamentals. Another standard, but not mainstream, answer is that we call generically "preons" to the hypothetical components of quarks and leptons. The most stablished -arguably- preon theory is Harari-Shupe, sometimes referred to as "rishon theory", but there are... | {
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Know altitude and speed of an object in orbit, with true anomaly I'm quite stuck with this problem.
I know that I have an object in orbit. I know the eccentricity of that orbit, as well as the semi-major axis of the orbit.
Giving a true anomaly, how do I find the speed and altitude of that object? The true anomaly is... | As far as I can tell the true anomaly is the same type of angle used in the standard solution of the Kepler problem since there we assume the sun is at a foci.
When solving the equations of motion for a Keplerian orbit we obtain $r\left(\theta\right)=\frac{a\left(1-e^{2}\right)}{1\pm e\cos\theta}$ (- if $r\left(0\rig... | {
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Dependence of Friction on Area Is friction really independent of area? The friction force, $f_s = \mu_s N$. The equation says that friction only depends on the normal force, which is $ N = W = mg$, and nature of sliding surface, due to $\mu_S$.
Now, less inflated tires experiences more friction compared to well inflat... | It is all about the distribution of pressure under the contact. For a block of uniform weight the pressure can be assume almost constant under the area and so when traction is broken it will happen all at once all over with a force of $\mu N$ as you stated.
But for other geometries, or for elastic parts (like tires, or... | {
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Are specific heat and thermal conductivity related? Are there any logical relationship between specific heat capacity and thermal conductivity ?
I was wondering about this when I was reading an article on whether to choose cast iron or aluminium vessels for kitchen.
Aluminium has more thermal conductivity and specific ... | This is in address to your last two questions:
*
*Which retains heat better?
*How does mass effect heat retention?
You introduce two material properties (mass, specific heat) that seemingly affect the heat retention but do not give you the whole picture in of themselves. However, we can combine them to give u... | {
"language": "en",
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Inverted Harmonic oscillator what are the energies of the inverted Harmonic oscillator?
$$ H=p^{2}-\omega^{2}x^{2} $$
since the eigenfunctions of this operator do not belong to any $ L^{2}(R)$ space I believe that the spectrum will be continuous, anyway in spite of the inverted oscillator having a continuum spectrum ar... | The wave functions that are not $L^2$-integrable play no direct physical role. You may get such "mathematically nice" functions e.g. by the analytical continuation from the stable (non-inverted) harmonic oscillator but they won't have the same interpretation. That's easy to see: as you noticed, the analytic continuatio... | {
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Why egg cooks slowly in mountains? A quick Google tells me "Because water boils at a lower temperature at high altitudes". But I am not being able to understand this answer and fill-in the gap. Like, how does an egg cook in the first place? What does it mean when we say that water boils at lower temperature? In fact, I... | Since at higher altitudes, the air pressure is lower, the boiling point of water decreases, since it's easier for the energy insde the water to get free.
When A liquid starts to boil, you reach a critical point where the liquid loses a lot of heat, much more than when not boiling, thus requiring much more energy for th... | {
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The Energy-Momentum Tensor and the Ward Identity I have a question regarding a homework problem for my quantum field theory assignment.
For the purposes of the question, we can just assume the Lagrangian is that of a real scalar field:
$$\mathcal{L}=\frac{1}{2}\left( \partial _\mu \phi\right) ^2-\frac{1}{2}m^2\phi ^2$$... | The Noether current is a conserved quantity in classical field theory. In quantum theory, it is mirrored by the Ward identity. You may possibly find this formula looking into the derivation for Schwinger-Dyson equations.
It is derived in chp 22 of Srednicki's book: http://web.physics.ucsb.edu/~mark/qft.html.
| {
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Classical car collision I have a very confusing discussion with a friend of mine.
2 cars ($car_a$ and $car_b$) of the same mass $m$ are on a collision course. Both cars travel at $50_\frac{km}{h}$ towards each other.
They collide. Ignoring any shreds and collateral damage, what is the speed of collision that the driver... | I think you are asking how much damage would be done to the driver in the two cases you described. If that is your question, then the single car that is driven at a speed of $50\frac{km}{hr}$ into an infinite mass wall would experience the same damage as two identical cars being driven exactly head on at a speed relat... | {
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What is lepton number? What exactly is a lepton number of a particle? With the charge (eg proton is just 1, not the exact charge), I can understand because it's a physical property, put a particle with charge + next to another particle with charge + and they will repel.
What is the lepton number in similar terms? Or i... | Electric charge is a "special" kind of physical property because it corresponds to a very simple physical effect. But that's not true of most physical properties. The lepton number doesn't have any force associated with it, the way electric charge does, because it's not a coupling constant.
Lepton number is just a math... | {
"language": "en",
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Can there be black light? I mean is it possible to devise a machine that outputs darkness? I understand there are various colours that light can have. But i was wondering why there is no 'black' light. What is the logical explanation for this? I mean I am expecting an answer that goes beyond mentioning the spectrum det... | It may be worth looking into an alternative theory of colour eg. Goethe. He proposes that colour arises from the interplay of light and darkness. Darkness, then, is not the absence of light but the polar opposite. It is my opinion that human consciousness is not ready to arrive at a true understanding of the phenomenon... | {
"language": "en",
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Quality factor for a quantum oscillator? I've been reading papers about nanomechanical oscillators, and the concept of quality factor often pops up. I understand to some extent about Q factor in classical sense, but since nanomechanic oscillators are often treated quantumly, what does Q factor mean then?
| If you have a hydrogen atom in empty space in the a p-state and ask about the transition to the ground state, Quantum Mechanics tells you that the coupling between the states is given by something called Fermi's Golden Rule. There is also something called the Einstein A coefficient which gives the probability per unit ... | {
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What does transport equation represent in terms of physical quantities? In my math course we're taught to solve PDE (partial derivative equations) like transport equation:
$$
c\frac{\partial u}{\partial x} +\frac{\partial u}{\partial t}~=~0.
$$
If $u(x,t)$ is the quantity transported and $c$ has speed dimension (accord... | $\frac{\delta u}{\delta t}$ does not always have the dimension of speed. It is the change rate of physical quantities respect to time, $u$ can be mass or concentration of electric charge (density) or probability density $\rho$ in quantum physics.
So if we only consider the classical physics (i.e. heat conduction can b... | {
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Chiral anomaly and decay of the pion I am told that if all classical symmetries were reflected as quantum symmetries, the decay of the neutral pion $$\pi^0 ~\longrightarrow~ \gamma\gamma$$ would not happen. Why would the conservation of the axial current in QED prevent the decay of the pion? What is the non-conserved c... | Neutral Pion would not decay (in Your discussed case) only if the constituent quarks forming the neutral pion were massless. The professional answer to Your question can be found here:
http://www.scholarpedia.org/article/Axial_anomaly .
It clearly states (between Eq. 14 - 15 and Eq. 24 - 25), that zero mass of Fermi-Di... | {
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Total Resistance of Infinite Resistor Grid? The problem of the infinite resistor grid is very common. The solution for the resistance between any 2 nodes in an infinite resistor lattice is all over the internet.
My question is somewhat similar but more pragmatic.
If we had a grid that was very large but yet finite... T... | The total resistance of the grid is infinite when the grid is two dimensional and large.
If you place two point probes at location x and y on an infinite 2-d resistor grid, and impose the voltage V(x)=1 and V(y)=0, the potential obeys the discretized Laplace equation: V(up) + V(down) + V(left) + V(right) - 4 V(center) ... | {
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superconductor levitating in earth's magnetic field?
Possible Duplicate:
Can superconducting magnets fly (or repel the earth's core)?
I've seen superconductors levitating on magnets. But is it possible for superconductors to levitate on Earth from Earth's magnetic field?
| The lift generated by magnetic field B on a superconductor of area S is:
\begin{equation}
F = \frac{B^2S}{2\mu_0}
\end{equation}
disregarding lateral forces and assuming superconducting cylinder (or similar shape) with area S at the top and bottom and height h, we need three forces to remain in the equilibrium: magneti... | {
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Can Plasma Ignite? This question on Scifi.se: Why does warp plasma burn green? mentions a fictional type of plasma called 'Warp Plasma' that is capable of igniting and when it does it sprays plasma flames/gas out of pipes as if it were oil or some other form of fuel.
Wikipedia says that the sun consists of hot plasma i... | Ignition in what sense? Chemical energy is out of the question, because plasma by definition are mostly ions unbound of their electrons, which is needed for chemical binding.
Nuclear fusion ignition, well, that is the whole point behind nuclear fusion research. So if someone finds how to "ignite" plasma, it will revolu... | {
"language": "en",
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What is the force between two magnetic dipoles?
*
*What is the force between two magnetic dipoles?
*If I have two current loops parallel to each other with currents $I_1$ and $I_2$ and radii $R_1$ and $R_2$ a distance $z$ from each other, what is the force between them?
*What would change if they were two solenoids... | The equation for the force depends on how far you are from the current source.
If you are far away, then the dipole-dipole interaction formulas can be used. In that case, all of the configurations will give the same force if they have the same dipole moments. If you are closer, then more complicated specific equations... | {
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Hamiltonian with position-spin coupling I am solving a Hamiltonian including a term $(x\cdot S)^2$.
The Hamiltonian is like this form:
\begin{equation}
H=L\cdot S+(x\cdot S)^2
\end{equation}
where $x$ is the position operator, $L$ is angular momentum operator, and $S$ is spin operator. The eigenvalue for $L^2$ and $S^2... | I would solve it using a matrix representation.
If we multiply Pauli matrices by $\frac{\hbar}{2}$ we can work in the following basis:
$$|n;S_z = +\rangle, |n ; S_z = -\rangle$$
Note that
$$S\cdot L = S_xL_x +S_yL_y +S_zL_z$$
$$X\cdot S = XS_x$$
$$[L,S] =0$$
You get some matrix in the $S_z$ base ($2\times 2$) and dia... | {
"language": "en",
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What are some interesting calculus of variation problems? That I could create as a classical mechanics class project? Other than the classical examples that we see in textbooks (catenary, brachistochrone, Fermat, etc..)
| While studying classical mechanics I did the following simulation:
*
*Consider a motion in Coulomb potential: $U(r) = \frac{\alpha}{r}$
*Fix starting and final points $p_1$ and $p_2$, and consider different paths in a form: $$p_1 + (p_2 - p_1)\lambda + \vec{a}\sin(\pi\lambda) + \vec{b}\sin(2\pi\lambda) + \vec{c}\si... | {
"language": "en",
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Is it possible to recover Classical Mechanics from Schrödinger's equation? Let me explain in details. Let $\Psi=\Psi(x,t)$ be the wave function of a particle moving in a unidimensional space. Is there a way of writing $\Psi(x,t)$ so that $|\Psi(x,t)|^2$ represents the probability density of finding a particle in classi... | The short answer: No, does not exist any wavefunction in Hilbert space which reproduces classical mechanics.
The classical limit of quantum mechanics is studied with some deep in Ballentine textbook. For instance, section 14.1 is devoted to the Ehrenfest theorem and it is shown that the theorem is neither necessary nor... | {
"language": "en",
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Physical laws prior the big bang (quantum fluctuations) A theory among scientists says that quantum fluctuations caused the big bang and created the universe. This seems plausible to me.
What I can't grasp yet is how a quantum fluctuation can even start without an existing universe. Aren't all physical laws created wi... | Indeed, there exist some pre-big-bang theories that arose from string theory. A notable name in this area is Gabriele Veneziano. You can find some information here. This article is somehow technical but should convey the right flavor of these ideas. As you can read from this, there is a two-dimensional space where stri... | {
"language": "en",
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This Expansion-of-the-Universe-Diagram Confuses Me The following blue-cone Wikipedia diagram confuses me.
At any point of cosmological time the encircling horizontal lines in the diagram are of finite circumference. That is indicative of a closed model of the universe.
Queries:
1. Why does the author use a closed mod... | If you look at the top view of the cone in the Wikipedia article you linked to, you'll notice that it's not actually a closed cone. So this diagram represents the evolution of a 1D open curve in a timelike slice of spacetime, not the whole universe. It doesn't say anything about instantaneous large-scale structure.
Eve... | {
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Is it necessary to embed a 4D surface in 5D space? Lets consider the line element:
$$ds^2=dr^2+r^2[d\theta^2+\sin^2\theta d\phi^2]$$
There are three variables r,theta and phi.
If we use a surface constraint like r=constant the number of
independent variables is reduced by one--now we have two independent
variables.Thes... | Any enclosing space is outside of the problem domain of GR: All results can be obtained from within the space-time. Physically, it makes no sense to talk about an enclosing space which has no impact whatsoever on measurements. In particular, even though we say space-time is curved, the question Where does it curve to? ... | {
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Why do 3d spheres and gravity tend to rotating discs on one plane? Whether is it our solar system or a whole galaxy, there is usually a massive object (star or black hole) at the centre with gas and objects rotating around it.
The gravitational effect of the star/black hole extends uniformly (more or less) in every di... | The way I look at this is to wonder what would happen if things weren't in the same plane.
*
*The obvious issue is collisions - space may be quite empty but if you have a large amount of dust orbiting in different planes there will be collisions
*Gravitational forces - more likely than collisions, when bodies come ... | {
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How can I prevent being zapped by static electricity every time I touch a doorknob or handle in the office? I don't know what it is about this office, but it seems everything I touch (doorknob, bathroom faucet, edge of kitchen sink in the break room), I get zapped by static electricity. It's getting old. I feel like ... | Touch it with a key or something metal first.
| {
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How should one combine the uncertainties from the ATLAS and CMS measurements? First off, a naive theorist question - How are measurements divided between the different detectors at the LHC? I would imagine that for a short run time, say, the CMS detector is active and all the others are turned off (the beam just passes... | Have a look at the recent discussions where the experiments are combined:
http://motls.blogspot.com/2012/02/higgs-signal-grew-from-38-to-43-sigma.html
and error estimates discussed :
http://blog.vixra.org/2012/02/10/some-technical-points-about-combining-sigmas/
Here are the recent individual ones:
http://www.science20.... | {
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Can you magnetize iron with a hammer? We know that a piece of ferromagnet, such as iron, can be magnetized by putting in a strong magnetic field to get domains parallel to the field grow.
I also remember from pop. culture and MacGyver old tv series that you can magnetize a piece of iron by hitting it hard, with a hamm... | Seems that it can be done, and here are instructions
Copying from the link
Strike an iron nail squarely and sharply several times with a hammer while keeping the nail positioned in a north-south orientation. The impact of the hammer with the iron nail causes the magnetic domains within the nail to break loose from the... | {
"language": "en",
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How does gravity work underground? Would the effect of gravity on me change if I were to dig a very deep hole and stand in it? If so, how would it change? Am I more likely to be pulled downwards, or pulled towards the edges of the hole? If there would be no change, why not?
| Assuming spherically symmetric mass distribution within Earth, one can compute gravitational field inside the planet using Gauss' law for gravity. One consequence of the law is that while computing the gravitational field at a distance r < R (with R being the radius of the Earth), one can ignore all the mass outside t... | {
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Are proton, antiproton, electron, positron the only observed subatomic particles that can freely exist and don't decay, i.e. are stable? Are proton, antiproton, electron, positron the only subatomic particles that can freely exist (i.e. I don't want particles that only exist in bound state as constituents such as quark... | No. At a minimum neutrinos and anti-neutrinos are also stable{*} and exist in unbound systems.
Additionally the electromagnetic carrier boson (i.e. the photon) can exist for arbitrarily long times in the reference frames of massive objects (it's proper time is necessarily zero). The same could be said for the graviton ... | {
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What does a unitary transformation mean in the context of an evolution equation? Let be the unitary evolution operator of a quantum system be $U(t)=\exp(itH)$ for $t >0$.
Then what is the meaning of the equation
$$\det\bigl(I-U(t)e^{itE}\bigr)=0$$
where $E$ is a real variable?
| If the dimension of the state space is finite, say $n$, then your question makes sense since the determinant makes sense.
Now suppose that $E$ is a real number such that (for all $t$) $$\det (I-U(t)e^{itE} ) =0.$$ Your equation implies that $I-U(t)e^{itE}$ is not invertible (if it were invertible, its determinant wou... | {
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Effects of a Coiled Cable Okay, I've got a little bit of a layman's question here.
We're doing a bit of spring cleaning in our office and we've found a cabinet with boxes upon boxes of stored wires, so naturally, this discussion arose...
Picture a normal, bog-standard wire, with a plastic outer coating. Now, quite ofte... | You are talking about the inductive effects of the coil of wire. Essentially a wrapped up coil of metal with electrons running through it creates a linear magnetic field since moving electrons through a wire creates a redial field and if you approximate the coil to have infinite loops the field becomes liner.
But, this... | {
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Spin angular momentum of a system of particles : Is there any energy associated with it? Consider a system of point particles , where the mass of particle $i$ is $μ_i$ and its position vector is $\vec{r}_i$. Let $\vec{r}_\text{cm}$ is the position vector of the center of mass of the system. Considering the system from ... | The energy associated with the internal rotations is the rotational energy
http://en.wikipedia.org/wiki/Rotational_energy
given by the formula
$$ K = \frac 12 I \omega^2 $$
where $\omega$ is the angular frequency and $I$ is the moment of inertia with respect to the axis of rotation
http://en.wikipedia.org/wiki/Momen... | {
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Elasticity of Space; How does the expansion of Space affect gravity? Does space have an elastic quality?
What I was thinking about was if space is expanding, is it being 'stretched', like a balloon being blown up, and if so, is this causing gravity to weaken? Imagine space as a 2 dimensional sheet (got this from one of... | But, how do gravitational waves propagate unless there were some form of fluidity to the space between bodies? There is a very fluidic like behavior of wht we refer to as the "fabric" of spacetime. Even with local large mass gravitational distortion, once the object moves from a given reference point the fabric returns... | {
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Simple applications of group theory which can be understood by a senior undergrad I am looking for references (books or web links) which have "simple" examples on the use of group theory in physics or science in general.
I have looked at many books on the subject unfortunately they usually require extensive technical ... | I recommend " The Theory of Groups and Quantum Mechanics " by Hermann Weyl http://books.google.co.uk/books?id=jQbEcDDqGb8C&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
Although the book is written in a old school way, I found it interesting!
| {
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"url": "https://physics.stackexchange.com/questions/18909",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 3,
"answer_id": 1
} |
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