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<p>Had physics for 2 years now on highschool, but there is a thing I am wondering about.</p>
<p>You know the in the height above the earth surface around where the satellites are (Or the ISS), I've calculated that there actually is a big amount of gravity-forces, even up there. (9.1 - 9.2 <code>m/s^2</code>) - How come that things aren't dragged down to earth, and why are you even weightless?</p>
<p>Why doesn't satellites fall down more frequently, and does it have something to do with their orbit-speed?</p>
<p>Okay, many questions here, but just a curious guy.</p>
| 33 |
<p>My book about quantum mechanics states that the hamiltonian, defined as $H=i\hbar\frac{\partial}{\partial t}$ is a hermitian operator. But i don't really see how I have to interpret this. First of all: from which to which space is this operator working? They are defining a vectorspace called the "wavefunctionspace $F$" which contains all square-integrable functions that are continious and infinite differentiable (and everywhere defined). But it looks to me, that if the hamiltonian acts on this space, it's not necessary true that the image of a random vector of $F$ is again in $F$. </p>
<p>I think in fact, that there are some vectors of $F$ so that the hamiltonian of those vectors is not an element of $F$ (so that it's not an endomorphism on $F$). And if the hamiltonian has to be hermitian, it has to be an endomorphism on some space. </p>
<p>If we define instead the vectorspace $V$, which is the same space as $F$ but where functions don't have to be square-integrable, the hamiltonian will be an endomorphism (so at first I thought this was the solution). But now the inner product on functions $<f,g> = \int_{-\infty}^\infty{f^*g}$ which was defined well on $F$ because the integral will always exist if $f$ and $g$ are function of $F$, is no longer properly defined. </p>
<p>I hope someone can clarify how I have to interpet this operator (the same question holds in fact for some other operators). </p>
| 1,975 |
<p>Imagine two charges A and B separated by some distance.</p>
<p>Charge A emits a photon which is absorbed by charge B.</p>
<p>Is the recoil momentum received by charge A always equal and opposite to the momentum gained by charge B?</p>
<p>Is this true both for static Coulomb fields and radiation fields from accelerating charges?</p>
<p>I suppose there is no momentum "left over" in the EM field after the interaction so that all the momentum lost by A is absorbed by B. Is this how it works?</p>
| 1,976 |
<p>Is the force which acts perpendicular to a wire due to another current wire in its vicinity consistent or it is just for a brief time? I thought it should be for a brief time because only for a moment all electrons will drift in the direction of force but after that the force will change its direction (it has to be perpendicular to velocity always, right?)
Further, does this force do work on the wire? (Caveat: Kindly keep in mind while answering that I'm just a 12th grader and I know nothing of quantum mechanics)</p>
| 1,977 |
<p>In Chapter II of Dirac's <em>Principles of Quantum Mechanics</em>, Dirac explains that in general it is very difficult to know whether, for a given real linear operator, that any eigenvalues/eigenvectors exist and (if they do) how to find them.</p>
<p>He then goes on to state that a special tractable case can be found in the event that a real linear operator, $\xi$ can be expressed as the algebraic expression:</p>
<p>$\phi$($\xi$) $\equiv$ $\xi$<sup>n</sup> + a<sub>1</sub> $\xi$<sup>n-1</sup> + a<sub>2</sub> $\xi$<sup>n-2</sup> + ... + a<sub>n</sub> = 0</p>
<p>Where the a<sub>i</sub> are all numbers. He then factorises this as:</p>
<p>$\phi$($\xi$) $\equiv$ ($\xi$- c<sub>1</sub>)($\xi$- c<sub>2</sub>)($\xi$- c<sub>3</sub>)...($\xi$- c<sub>n</sub>).</p>
<p>Where the c<sub>i</sub> are also numbers.</p>
<p>I'm unsure how this factorisation has been achieved. Since Dirac didn't explicitly state the difference between $\phi$($\xi$) and plain $\xi$, then I imagine that $\xi$ represents a given dynamical variable and $\phi$($\xi$) the corresponding operator. This may be incorrect however. This is the only step in the logic that I can't work out, I understand his subsequent arguments but this step is eluding me.</p>
| 1,978 |
<p>I first heard about the Tokamak in highschool 10 years ago and was wondering how far the technology has come since then. Can it sustain a reaction for more than a few seconds? Are these devices still huge or have they been made on a smaller scale?</p>
| 1,979 |
<p>Does anyone know the refractive index suppliers? I've found Cargille Labs (which customer service is terrible so far but the liquids may actually be OK), but nothing else comparable. I'd like to have a set of liquids with the refractive index in the range of 1.3...1.4. Are they so hard to produce that almost nobody does it or am I missing something?</p>
| 1,980 |
<p>As the title says, is it possible to have a Riemannian Ricci flat compact manifold with $U(1)\times{}SU(2)\times{}SU(3) $ <a href="http://en.wikipedia.org/wiki/Isometry_group" rel="nofollow">isometry group</a>?</p>
| 1,981 |
<p>I've read <a href="http://en.wikipedia.org/wiki/Quantum_computer">Wikipedia</a>, I've read <a href="http://www.howstuffworks.com/quantum-computer.htm">How Stuff Works</a>, I've read <a href="http://www.singularity.com/">The Singularity is Near</a>, but I still just don't get it. How does a Quantum Computer work? It sounds very intriguing, but I just can't wrap my mind around it. I would greatly appreciate it if someone could explain it to me as they would explain the basics of it to their 7 year old nephew (who apparently is probably about equal to me in their ability to understand this concept!) </p>
<p>Typically analogies work best when explaining concepts to the unenlightened, but this is quantum theory, so I'm not sure any analogy could exist that can explain such a bizarre concept ;)</p>
| 1,982 |
<p>I want to outline a solid argument (or bulletpoints) to show how weak is the idea of diff(M) being the gauge group of general relativity.</p>
<p>basically i have these points that in my view are very solid but i want to understand if there are misconceptions on my part that i'm simply not getting and if its so, i ask for help to make the case more solid, or understanding why it doesn't apply (to gravity):</p>
<ul>
<li><p><a href="http://www.mth.kcl.ac.uk/~streater/lostcauses.html#XXII">gauge groups are not the same as a symmetry group</a> (thanks to Raymond Streater for making that point completely clear)</p></li>
<li><p>gauge invariance in electrodynamics is an observation that physical observables are unchanged after a gauge transformation <strong>without changing coordinate frame</strong> ( we are ask to believe that in gravity someone did the same? that is, someone made the observation that physical observables are unchanged after a diffeomorphism-gauge-transformation, only to later argue that because of this, that there are no physical observables to begin with, that doesn't make a lot of sense, to not say that its just plain stupid circular argument )</p></li>
<li><p><a href="http://en.wikipedia.org/wiki/Maxwell%27s_equations_in_curved_spacetime">classic electrodynamics is also invariant (as in symmetry invariant, not as gauge-invariant) under Diff(M)</a>. The invariance is of course broken when the theory is quantized and $\hbar$ makes an appearance, because it assumes a preferred scale for certain energies. The key point here is: <strong>classical gravity is not special regarding having diff(M) as a symmetry group</strong></p></li>
<li><p>from bulletpoints 2 and 3, if i cannot infer that Diff(M) is a gauge-invariance of electrodynamics, the same should apply to gravity</p></li>
</ul>
<p>For this question, i would say that a valid answer would either disprove any of the arguments as fallacies themselves (hence showing a solid argument why gravity is special and diff(M) is without a doubt its gauge group), or improve the argument for making it bullet-proof (sorry for the pun)</p>
| 1,983 |
<p>In astrophysics, I often come across the speed of sound. I understand that, broadly, it represents the speed at which perturbations travel through a medium. But there's more than one speed of sound. The most common seem to be <em>isothermal</em> and <em>adiabatic</em>, which are defined as $c_s^2=(dp/d\rho)_T$ and $c_s^2=(dp/d\rho)_S$, respectively.</p>
<p>My question is, when do these different speeds apply? When do perturbations travel at the adiabatic sound speed, and when the isothermal? Are there any other useful sound speeds?</p>
| 1,984 |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/12435/einsteins-postulates-minkowski-space-in-laymans-terms">Einstein's postulates <==> Minkowski space. (In layman's terms)</a> </p>
</blockquote>
<p>In the spirit of Einstein's arguments using flashes of light, moving trains and mirrors;
what is the best way to go between Einstein's postulates [<a href="http://en.wikisource.org/wiki/On_the_Electrodynamics_of_Moving_Bodies" rel="nofollow">1</a>] of</p>
<ol>
<li>Relativity: Physical laws are the same in all inertial reference frames.</li>
<li>Constant speed of light: "... light is always propagated in empty space with a definite speed $c$ which is independent of the state of motion of the emitting body."</li>
</ol>
<p>to Minkowski's idea [<a href="http://en.wikisource.org/wiki/Space_and_Time" rel="nofollow">2</a>] that space and time are united into a 4D spacetime with the Lorentzian signature.</p>
<p>The argument can only use simple mathematics (algebra, geometry, a little calculus). I want an argument that a smart high school graduate would be able to understand.
None of the group theory and coset/homogeneous spaces of <a href="http://physics.stackexchange.com/questions/12435/einsteins-postulates-minkowski-space/12438#12438">Marek's answer</a> to <a href="http://physics.stackexchange.com/q/12435/429">my previous question</a>. (Although, if you do have a little knowledge of Lie algebras, you should go read Marek's answer and references now!).</p>
| 34 |
<p>This is not a question pertaining to interpretations, after the last one I realized I should not open Pandora's Box ;) </p>
<p>For theories to be consistent, they must reduced to known laws in the classical domains. The classical domain can be summed up as: </p>
<p>$$\hbar=0 ; c=\infty$$</p>
<p>Which is OK. I need to know, however, is that if QM is an independent and fundamental <em>theory</em>, why does it rely so heavily on the classical formalism. Is it necessary for a classical formalism to exist in order to have a quantum formalism? From as far as I have read, it does not seem so, and I find this puzzling. Suppose you have a dissipative system, or an open system when you cannot write an autonomous Hamiltonian in the classical case, how then do we approach these quantum mechanically, when we cannot even write down the corresponding Hamiltonian. </p>
| 1,985 |
<p>When the shaft of the helicopter rotates, it creates a low pressure. Because of the low pressure, the helicopter lifts. Is my understanding that this is just an application of Bernoulli's theorem?</p>
| 17 |
<p>I am speaking about GR with classical fields and energy. One question, spread over three increasingly strict situations:</p>
<p>Is there an energy density limit in GR? (literally, can the energy density have an arbitrarily large value at some point in space at some point in time)</p>
<p>Is there an energy density limit beyond which a blackhole will always form?</p>
<p>Let's choose a small volume, for here I'll just choose the Planck volume. Is there an average energy density limit over this volume beyond which a blackhole will always form?</p>
<p><strong>Clarification:</strong></p>
<p>In light of <a href="http://en.wikipedia.org/wiki/Mass_in_general_relativity">http://en.wikipedia.org/wiki/Mass_in_general_relativity</a> , can those that are answering that the energy density is limited and referring to a mass $M$ in some equations please specifically state how you are defining the $M$ in terms of the energy density, or defining $M$ in terms of $T^{\mu\nu}$ the stress-energy tensor. Does your $M$ depend on coordinate system choice?</p>
<p>Also, reading some comments, it sounds like there is confusion on what energy density means. Based on wikipedia <a href="http://en.wikipedia.org/wiki/File:StressEnergyTensor.svg">http://en.wikipedia.org/wiki/File:StressEnergyTensor.svg</a> , it sounds like we can consider energy density = $T^{00}$ of the stress-energy tensor. If you feel this is not correct terminology, please explain and I'll edit the question if necessary.</p>
| 1,986 |
<p>In 2006 the IAU deemed that Pluto was no longer a planet because it fails to "clear" the neighborhood around its Kuiper Belt orbit. Presumably, this is because Pluto (1.305E22 kg) has insufficient mass to do the job. How massive must a body in Pluto's orbit (semi-major axis 39.5 AU) be to "clear" its orbit? Would Mars (6.24E23 kg) or Earth (5.97E24 kg) be declared planets if they were in Pluto's orbit?</p>
| 1,987 |
<p><a href="http://en.wikipedia.org/wiki/Hydrogen_ion" rel="nofollow">Hydrogen ion</a> doesn't have one electron which clearly mean that it has only one proton..So hydrogen ion is only a proton. Am I right, please make it clear. If hydrogen ion and proton are same that how to explain the reactivity with electron?</p>
| 1,988 |
<p>Here's a question inspired by <a href="http://physics.stackexchange.com/questions/7771/is-there-an-energy-density-limit-in-gr/7773#7773">Edward's answer</a> to <a href="http://physics.stackexchange.com/questions/7771/is-there-an-energy-density-limit-in-gr">this question</a>. </p>
<p>It's my understanding that the average energy density of a black hole in its rest frame is $\rho_\text{BH}(A)$, a function of surface area. I calculated $3c^2/2GA$ for a Schwarzschild black hole, but that's presumably not applicable here since I'm talking about an extended energy distribution. Anyway, suppose you are in a space filled with some sort of energy, matter, or whatever, which produces a potentially time-dependent stress-energy tensor. And further suppose that there is some finite, spherical region of surface area $A$ in this space, over which you measure the average energy density to be $\rho_\text{BH}(A)$, the net charge to be zero, and the total angular momentum of the matter within the region to be zero. (I'm assuming there is a measurement procedure available which can be carried out without entering the region, if it matters.) </p>
<p>Now, Edward's argument in the other question shows that there are at least two ways to produce that (average) energy density:</p>
<ol>
<li>The energy density arises from a fluid or other material at rest, such that the region is a black hole and there are no timelike geodesics exiting it</li>
<li>The energy density has been "augmented" by a Lorentz boost from some other frame, implying that there are timelike geodesics exiting the region</li>
</ol>
<p>Is it possible, in general, to distinguish between case 1 and case 2 by only looking at the other components of the stress energy tensor, without actually calculating the geodesics? If so, how? What would be the "signature" of a black hole in the components of $T^{\mu\nu}$ (or rather, their averages over the region in question)?</p>
| 1,989 |
<p>When an object enters water with high velocity, (like in <a href="http://physics.stackexchange.com/questions/106808/why-jumping-from-high-altitude-into-water-is-fatal">Why is jumping into water from high altitude fatal?</a>), most of it's kinetic energy will be converted, eg to accelerate water, deform the object etc. -<br>
What is the relevance of the surface tension to this? </p>
<p>Are the effects related to surface tension just a small part, or even the dominant part regarding the forces.</p>
| 1,990 |
<p>This post relates to <a href="http://physics.stackexchange.com/questions/71526/problems-with-putting-mass-on-yang-mills-theory-by-hand">this previous one</a>. My question is, what is the actual meaning of a theory being renormalizable?</p>
<p>There might be at-least two possibilities (correct me if I am wrong)</p>
<p><strong>1.Power-counting renormalizable</strong></p>
<p>If I understood correctly, the BHPZ theorem guarantees that all superficial divergences for a power-counting-renormalizable theory can be absorbed by counter terms. Formally, it might be possible that a counter term is outside the form of the Lagrangian.</p>
<p><strong>2.Stronger than power-counting renormalizable</strong></p>
<p>The counter term be produced from the original Lagrangian, such as QED. We need to look at all possible divergence explicitly and show how to regularize and renormalize them.</p>
<p><strong>(3. Any further possibility from non-perturbative aspect (I don't know))</strong></p>
<p>This problem also relates to 't Hooft and Veltman's achievement of proving Yang-Mills theory with Higgs mechanism is renormalizable. It cannot simply be power counting.</p>
<p>When people say a theory is renormalizable, what does it mean? Meaning 1 or 2? Is this distinction important? </p>
| 1,991 |
<p>I'm not a physicist and just making some research by the way of creating simple physics simulator, because of that, sorry if this is very dumb question, but I really need help with it.</p>
<p>Let's assume that some body (rectangle, square, N-polygon, etc.), exists in 2D world in rest (no friction, gravity, etc.) and can be freely moved in any direction.</p>
<p>If some pushing / pulling force will be applied to center of mass, then only translational force will exist, this case is very clear to me. But what if force will be applied on the edge of body? What will be if force will be applied at some angle to edge? I understand that this will involve a rotational forces. But how can I calculate the resulting translational vector in this case?</p>
<p>Here is image, demonstrating the problem. Force F2 will not involve any rotational forces, I can calculate net force (= F2) and get acceleration vector. All this question is about F and finding resulting translational vector after apply of F.</p>
<p><img src="http://i.stack.imgur.com/v8UwH.png" alt="example of forces-related question"></p>
| 1,992 |
<p>The average kinetic energy (KE) per molecule of a gas is $\frac{3}{2}kT$. While finding this we do </p>
<p>$$ \text{ Average KE} =\frac{1}{2} M \frac{1}{N}\sum v^2=\frac{3}{2}kT$$
But why do we not add rotational kinetic energy here?</p>
| 1,993 |
<p>Which is more appropriate regarding Bernoulli's principle</p>
<ul>
<li>fast moving air causes low pressure or</li>
<li>lower pressure causes fast moving air.</li>
</ul>
| 1,994 |
<p>The "<a href="http://www.vacuvin.com/270/Vacuum_Wine_Saver.html" rel="nofollow">Vacuum Wine Saver</a>" comes with the following "warning":</p>
<blockquote>
<p>Not for sparkling wines</p>
</blockquote>
<p>Intuitively and naively, I imagine that the <a href="http://en.wikipedia.org/wiki/Sparkling_wine#Bubbles" rel="nofollow">bubbles</a> (or the "bubble-potential"—my made-up terminology) will be sucked out of the wine by the pump and that this is also the reason for the "warning".</p>
<p>What is the better-formulated physical/chemical description and explanation? In other words: What happens and why?</p>
<hr>
<p>Extra: Is this (your answer) also a reason for not semi-compressing half-full flexible plastic cola bottles before closing them?</p>
| 1,995 |
<p>Not sure if this is the right place to ask this but here goes.</p>
<p>If the north pole ice sheets melt, everyone agrees this would be a bad thing, however one of the reasons they state for this being a bad thing is the rise in sea level.</p>
<p>Given that the north pole is essentially a massive ice sheet floating on water, how can the melting of this ice raise the sea levels?</p>
<p>In my understanding the amount of water displaced by the ice, is equal to the amount of water that would be added to the ocean.</p>
<p>I tried an experiment where i marked the water level in a glass of water with ice, then waited for the ice to melt. the water level was identical.</p>
<p>Am I missing something here?</p>
| 35 |
<p>I'm really interested in quantum physics and would like to learn more. However, I don't know where to start and in what order I should learn things. So, ideally I'm looking for some sort of roadmap of what to learn. What physics topics do I need to know to start learning about quantum mechanics? (In addition to the mathematical topics mentioned at <a href="http://physics.stackexchange.com/questions/16814/what-is-the-math-knowledge-necessary-for-starting-quantum-mechanics">What is the math knowledge necessary for starting Quantum Mechanics?</a>)</p>
<p>My current knowledge is mostly popular science stuff, like tv shows on Discovery Science and National Geographic Channel. So I have a basic understanding of some basic principals. There's also a recent lecture from Brian Cox that I have watched which gave a bit more in-depth information.</p>
| 223 |
<p>I'm working on a physics problem in preparation for the MCAT and there's this particular problem that's troubling me. I don't know if it's a bad question or if I'm not understanding some sort of concept. I was hoping someone here can clarify. Here's the problem verbatim:</p>
<blockquote>
<p>A 1kg cart travels down an inclined plane at 5 m/s and strikes two billiard balls, which start moving in opposite directions perpendicular to the initial direction of the cart. Ball A has a mass of 2kg and moves away at 2m/s and ball B has a mass of 1kg and moves away at 4m/s. Which of the following statements is true?</p>
<p>a) the cart will come to a halt in order to conserve momentum</p>
<p>b) the cart will slow down</p>
<p>c) the cart will continue moving as before, while balls A and B will convert the gravitational potential energy of the cart into their own kinetic energies</p>
<p>d) these conditions are impossible because they violate either the law of conservation of momentum or conservation of energy</p>
</blockquote>
<p>At first glance, it appears to me that the answer is (D) because the system seemingly has more total momentum after the collision than before the collision. However, the answer explanation insists the correct answer to be (C) since it claims that "kinetic energy is not conserved; the system gains energy in this inelastic collision".</p>
<p>I can understand that this gain in energy can come from gravitational potential energy from the incline the cart is on; however, it is ambiguous if the cart is <em>accelerating</em> down the incline. In order for the scenario to be consistent with choice (C), does the cart have to be accelerating down the incline? Or do you take the problem to mean that the cart is leaving the incline at 5m/s? Or am I missing or not understanding something?</p>
<p>How would you interpret this problem and which explanation do you think is most consistent with the scenario? What assumptions do you have to make to arrive at your answer?</p>
<p>The answer key's explanation, verbatim is as follows:</p>
<blockquote>
<p>The law of conservation of momentum states that both the vertical and horizontal components of momentum for a system must stay constant. If you take the initial movement of the cart as horizontal and the two balls move in perpendicular directions to the horizontal, it means that the cart must maintain its horizontal component of velocity. Therefore, (A) and (B) are wrong. If the billiard balls move as described, then kinetic energy is not conserved; the system gains energy in this inelastic collision. (C) correctly describes how this scenario is possible.</p>
</blockquote>
| 1,996 |
<p>If we roll a normal egg and a boiled egg at the same time on a floor </p>
<p>1) with friction </p>
<p>2) without friction</p>
<p>which one will come to stop first (if they will stop at all) and why?</p>
<p>Can anyone tell me reason for this?</p>
| 1,997 |
<p>My research has led me to look into the idea of bubble universes which I don't know very much about. The first thing that I am looking for is understanding or visualising how could many bubbles co-exist geometrically, assuming each bubble universe is like ours (that is, a flat euclidean geometry). Are we talking about an n-manifold that has multiple bubbles embedded in it? Submanifolds? Or can we extend the idea of branes to the notion of bubbles? Is it perhaps a 3-sphere that houses multiple 2-spheres? Put simply, what is the theoretical geometry that engulfs all the bubbles and how would they be connected?</p>
| 1,998 |
<p>I've seen some discussions regarding the movement of a spinning object, say a curveball. However, all have been largely qualitative. I was wondering if anyone has seen or worked through a calculation of how far a curveball moves laterally on its way from the mound to homeplate - even in an order-of-magnitude sense.</p>
| 1,999 |
<p>Trying to determine the speed of a falling body with respect to traveled distance and initial speed. I've been provided with the following equation for acceleration as a function of distance and the grav. parameter(constant) of the attracting body :</p>
<p>$a=GM/r^2$ </p>
<p>Where:</p>
<p>$a$ - acceleration.<br>
$GM$ - gravitational parameter(constant).<br>
$r$ - distance to the attracting body.</p>
<p>I have entered inputs for $GM$ and $r$ and integrated this equation with respect to $r$. This obviously yielded total acceleration per traveled distance, in other words $m^2/s^2$ at the given altitude.</p>
<p>How do I proceed to determine speed at this altitude?</p>
| 1,000 |
<p>I was re-studying university physics last week, I'm now in the chapter about kinematics in 2 dimensions and specifically the one treating projectile motion. In page 86 of his book (Serway - Physics for scientists and engineers) he derives the equation of the range of the projectile motion to be: $$R=\frac{{v_i}^2\sin2\theta_i}{g}$$
But I don't know why he used one of his assumptions</p>
<p><img src="http://i.stack.imgur.com/9O7fi.png" alt="book"></p>
<p>$\color{red}{\bf Question1:}$ Why $v_{xi}=x_{x\rlap\bigcirc B}$? Where $\rlap\bigcirc {\,\sf B}$ is the time when the projectile stops.</p>
<p>$\color{darkorange}{\bf Question2:}$ Why did he use the particle under constant velocity model to derive that formula, whereas here we deal with a projectile under constant acceleration?</p>
<p>Any responses are welcome, I'm disappointed a lot about those matters!</p>
| 2,000 |
<p>I can't understand the concept of the curl of an electromagnetic wave. </p>
<p>$$
\nabla \times E = -\frac{\partial \textbf{B}}{\partial t}
$$</p>
<p>All of the examples I find show a current through a conductor, or that paddle wheel in water which I fail to see the distinction of that with an E-M wave. What I am trying to understand is the curl of say a laser beam light. </p>
<p>So lets say I have this sin wave which I plot in MATLAB which represents a section of a laser beam propagating through free space (We shall say it is the net product of $E_x$ and $E_y$):</p>
<p><img src="http://i.stack.imgur.com/yMbjt.png" alt="laser radiation"></p>
<p>How do you take the curl of it?
Where do you take the curl of it. eg the whole beam, a certain section? Can I do this in MATLAB to see visualization of the concept of curl?</p>
<p>I mainly seek descriptive or pictorial answers.</p>
<p>Thank you for your time.</p>
| 2,001 |
<p>There is a few questions that need to be answered in detail but in an easy way...</p>
<ol>
<li><p>What does it mean to describe the 'plane of polarisation' of electromagnetic waves?</p></li>
<li><p>Why will some antenna have rods which are horizontal and some which are vertical? What does this have to do with polarization of electromagnetic waves?</p></li>
</ol>
| 2,002 |
<p>I have to calculate the total number of electric field lines through a proton. I tried using Gauss' Law, i.e, $$\phi = \oint\boldsymbol E.d\boldsymbol s = {\frac{q}{\epsilon_0}} $$ $$So, \phi = {\frac{q}{\epsilon_0}} $$</p>
<p>$$ \textrm{Therefore}, \phi = \frac{1.6\times10^{-19}}{8.854\times10^{-12}}$$, as $q=1.6\times10^{-19}C$ and
$\epsilon_0 = 8.854\times10^{-12}C^2N^{-1}m^{-2}$.</p>
<p>But the answer is $0.18\times10^{-7}$ or something like that. How can that be the number of field lines? How can that be the number of anything? I mean it's a fractional number. Any help is appreciated. Thanks.</p>
| 2,003 |
<p>I wish to find an everyday situation that illustrates the following:</p>
<p>A rod is moving in a direction perpendicular to its axis. One end "gets caught" and the rod starts rotating around this end. THE SPEED OF THE OTHER END OF THE ROD WILL THEN INCREASE BY A FACTOR SQRT(3).</p>
<p>Here is an <a href="https://www.dropbox.com/s/71wk7k6y79wvekz/DSC_0154.JPG" rel="nofollow">illustration</a>.</p>
<p>Can someone please think of a simple situation in everyday life that illustrates this transition from translation to rotation. Of course it is not needed to see the increase in speed, but just a situation where you could ask a student what speed the rotating object will have. (Just rods flying through the air is not what you see every day.)</p>
<p>If the situation is free of gravity (moving horizontally), it would be a better illustration, I believe.</p>
<p>(A related situation, but too complex and different is if you sit on the top of a telegraph pole. If the pole breaks at the bottom you will suffer less injury (theoretically) if you jump off the pole immediately rather than going down with it. (Speed less by a factor sqrt(1.5) I believe.))</p>
<p>A pair of ice skaters meeting with speed and taking each others hands and starting to rotate together would resemble the situation a little. But the mass of the skaters is concentrated to their bodies and the only thing accelerating would be their hands if they held them out.</p>
<p>(The classical illustration of a skater making a pirouette by pulling in the arms will not help here, of course.)</p>
<p>Thanks</p>
| 2,004 |
<p>I have studied about the two types of doping which result in p and n type semiconductors. I also came to know that they are neutral. But, how can it be? </p>
<p>Is it that the positive charge(holes) in p-type and negative charge in n-type are negligibly small to affect the overall neutrality of the substance? But, in that case with very few holes or negative charges how can semiconductors work the way it actually does? </p>
<p>So, I think there is another possible explanation and I would like to know the correct one. </p>
| 2,005 |
<p>In case of solar system,we can explain "Why Sun would not revolve around any other planet?",by giving the reason that Sun is heavier than any other planets. </p>
<p><a href="http://physics.stackexchange.com/questions/81648/why-heavier-bodies-produce-greater-gravitational-pull-than-the-lighter-bodies">Heavier the body,greater will be the gravitational strength produced by it</a>.Thus,Sun being heaviest,produces greater gravitational pull,and keeps other planets revolving around it. </p>
<p>In case of atom,we can consider coulomb's law.Here,we can see that both protons and electrons have same charge in magnitude(Don't consider electron to have less charge than proton,because of negative sign.It just implies that electron is resinously charged i.e charge similar to amber). </p>
<p>So,in case of atom we don't have electrons and proton with different charge in magnitude,as like we had Sun to be heavier than other planets,to make other planets to revolve around the sun.Thus,we can also expect protons to revolve around the electron.But,this doesn't happen.So,what is the reason for protons not revolving around the nucleus cotaining electrons and neutrons? </p>
| 2,006 |
<p>I have hacked a FitDesk exercise bike to output the RPM of the pedals and the position of the resistance control within its range of travel.</p>
<p>I want to characterize the energy that is required to pedal the bike at different RPMs and resistance settings.</p>
<p>My approach is to determine the torque required to the turn the bike at different settings.</p>
<p>My first idea is to use a variable speed drill to turn the bike while measuring the amperage the drill is pulling. Keeping the drill speed constant, I would change the resistance setting and observe the change in amperage. I would also baseline the amperage pulled with no load on the drill.</p>
<p>I am able to turn the bike using the drill, but I am worried that the measurements will be non-linear because the amount of heat generated by the drill changes quite a bit as resistance is added and I don't know how this relates to the amperage reading.</p>
<p>My second idea is to drop a weight which will turn the bike using a simple pulley arrangement. If I know the weight and can measure the angular acceleration of the bike, I should be able to calculate how much torque the weight is overcoming at different resistance settings.</p>
<p>But I am worried that after setting all that up, the differences in acceleration will be too small for meaningful comparison. (I really have no idea if this would be a problem or not.)</p>
<p>So I ask the experts: what is the easiest way to accomplish my goal?</p>
| 2,007 |
<p><img src="http://i.stack.imgur.com/dBS2M.png" alt="This is the image of the paragraph from the book"></p>
<p>Why should an equation (<a href="http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation" rel="nofollow">TDSE</a>) in which first time derivative is related to second space derivative have a solution that contains $i$?The wave function is supposed to be complex, but I am unable to understand why it can also be assumed to be complex directly from my previous statement as stated in Quantum Physics by <a href="http://www.google.com/#q=Eisberg+Resnick" rel="nofollow">Eisberg & Resnick</a>. Can anyone help me develop an intuition?</p>
| 36 |
<p>If you have, say, a proton it has gluon field fluctuations around it. Those flux tubes between the quarks suppresses the gluon field fluctuations and create a true vacuum between them(correct me if I'm wrong), but how does that bind the quarks together?</p>
<p>I've read that it costs energy to clear the vacuum out, but I still don't quite get it.</p>
<p>Thank you!</p>
| 2,008 |
<p>I need an inexpensive instrument to measure cryogenic temperatures (down to -200C).</p>
<p>I can build a thermistor-based thermometer using an Arduino that is accurate to under 1 degree for 0 to 100C.</p>
<p>First of all, can ordinary NTC thermistors be used at cryogenic temperatures?
Second, if I were to try to use this approach, I would need ways to calibrate the device.</p>
<p>I have found a chipset from Analog Devices that would let me use a thermocouple down to that range.</p>
<p>I would take other ideas on how to build one, but then I need some equipment to calibrate whatever I build. Is there anything I can buy for < $100, I don't need huge accuracy, but I need something.</p>
| 2,009 |
<p>If we have two parallel charged plates, equal and opposite in charge:</p>
<p>What is the flux felt on a Gaussian surface between them? surely it sum to 0 as each amount of flux will enter and then leave? This must be wrong as it would mean the field between the two plates is also zero?</p>
<p>Let me know what i'm missing, thanks!</p>
| 2,010 |
<p>If we imagine a object made up of Hydrogen gas that is optically thick to all radiation, and is in thermal equilibrium, then, microscopically, photons will be emitted and absorbed as emission/absorption lines.</p>
<p>However, the overall object should emit radiation according to <a href="https://en.wikipedia.org/wiki/Planck_function" rel="nofollow">Planck’s Law</a>, which describes intensity as a continuous function of wavelength (and temperature).</p>
<p>How does this occur and where do the photons we detect at wavelengths between spectral lines of hydrogen come from originally?</p>
| 2,011 |
<p>Current in wire + moving charge next to wire creates magnetic force in the stationary reference frame OR electric force in the moving reference frame from special relativity due to change in charge density etc.... I think I understand this and I think it's super cool. Now here's the rub...</p>
<p>Current in wire + <strong>stationary</strong> charge next to wire creates no net charge. This is how nature behaves. I get it. My question is why can't I use the same special relativity logic as above, that is, current in wire cause electrons in wire to contract in accordance with special relativity so there has to be a net charge on the wire, which then acts on stationary charge next to wire.</p>
<p>I have been reading and reading and reading and I have come up with the following:</p>
<p>(1) When electrons in wire get accelerated to create current the distance between them actually expands in accordance with special relativity - something to do with bells spaceship paradox - which I am not going to pretend to understand</p>
<p>(2) This expansion from (1) above is exactly opposite and equal in magnitude to the contraction special relativity then causes and the expansion and contraction cancel out to keep the charge density in the wire constant and therefore no net charge on the wire</p>
<p>Here are my questions:</p>
<p>Is the explanation above correct? If so, please elaborate because i dont understand</p>
<p>If not correct, what is going on?</p>
<p>This is driving me absolutely nuts. </p>
| 780 |
<p>In M. Salmhofer's "Renormalization, An Introduction" Wick ordering is defined as follows:</p>
<blockquote>
<p>Let $C = C_\Gamma$ be a nonnegative symmetric operator on $\mathbb{C}^\Gamma$. For $J: \Gamma \to \mathbb{C}$, let</p>
<p>$$\mathcal{W}_\Gamma (J, \phi) = e^{i(J,\phi)_\Gamma + \frac{1}{2} (J, CJ)_\Gamma},$$</p>
<p>where $\Gamma = \Gamma_{\varepsilon,L} = \varepsilon \mathbb{Z}^d / L \mathbb{Z}^d$. Let $\mathcal{P}_\Gamma$ be the algebra of polynomials in $(\phi(x))_{x \in \Gamma}$. Wick ordering is the $\mathbb{C}$-linear map $\Omega_C: \mathcal{P}_\Gamma \to \mathcal{P}_\Gamma$, that takes the following values on the monomials:</p>
<p>$$\Omega_C(1) = 1,$$</p>
<p>and for $n \geq 1$ and $x_1, \dots, x_n \in \Gamma$ (not necessarily distinct)</p>
<p>$$\Omega_C(\phi(x_1) \dots \phi(x_n)) = \left[ \prod_{k=1}^n \frac{1}{i} \frac{\delta}{\delta J(x_k)} \mathcal{W}_\Gamma (J, \phi) \right]_{J=0},$$</p>
<p>where $\frac{\delta}{\delta \phi(x)} = \varepsilon^{-d} \frac{\partial}{\partial \phi(x)}$.</p>
</blockquote>
<p><strong>Question 1:</strong> What exactly does the $J=0$ part in the last equation do? Also, I don't quite understand the part $\frac{\delta}{\delta J(x_k)}$. We multiply over $k$ and $J$ is a map $\Gamma \to \mathbb{C}$, so $J(x_k) \in \mathbb{C}$ for all $k$. How does it make sense to derive with respect to a constant complex number?</p>
<p>Later, the following theorem is proven (I will only copy the relevant part):</p>
<blockquote>
<p>For all $n \geq 1$:</p>
<p>$$\int \, \mathrm d \mu_C(\phi) \; \Omega_C(\phi(x_1) \dots \phi(x_n)) = 0,$$</p>
<p>where $\mathrm d \mu_C(\phi) = (\det 2 \pi C)^{-1/2} e^{-\frac{1}{2} (\phi, C^{-1} \phi)} \mathrm d^N \phi$.</p>
</blockquote>
<p><strong>Question 2:</strong> Does this imply that the integral of any Wick ordered polynomial vanishes since Wick ordering is $\mathbb{C}$-linear? </p>
<p>Thank you in advance for any help.</p>
| 2,012 |
<p>Usually in texts about Physics that uses tensors defines them as multilinear maps. So if $V$ is a vector space over the field $F$, a tensor is a multilinear mapping:</p>
<p>$$T:V\times\cdots\times V\times V^\ast\times\cdots\times V^\ast\to F.$$</p>
<p>In texts about multilinear algebra, however, a tensor is defined differently. They consider a collection $V_1,\dots,V_k$ of vector spaces over the same field, consider the free vector space $\mathcal{M}=F(V_1\times\cdots\times V_k)$, consider the subspace $\mathcal{M}_0$ genereated by vectors of the form</p>
<p>$$(v_1,\dots,v_i+v_i',\dots,v_k)-(v_1,\dots,v_i,\dots,v_k)-(v_1,\dots,v_i',\dots,v_k)$$</p>
<p>$$(v_1,\dots,kv_i,\dots,v_k)-k(v_1,\dots,v_i,\dots,v_k)$$</p>
<p>And then define the <a href="http://en.wikipedia.org/wiki/Tensor_product" rel="nofollow">tensor product</a> $V_1\otimes\cdots\otimes V_k = \mathcal{M}/\mathcal{M}_0$ and define tensors as elements of such space, which are equivalence classes of functions with finite support in $V_1\times\cdots\times V_k$.</p>
<p>Now, is there some cases in Physics where it's better to think as tensors as such equivalence classes rather than multilinear mappings? If so, how then we get some physical intuition behind those objects?</p>
| 2,013 |
<p>Suppose a particle with mass $m_1$ and speed $v_{1i}$ undergoes an elastic collision with stationary particle of mass $m_2$. After the collision, particle of mass $m_1$ moves with speed $v_{1f}$ in a direction of angle $\theta$ above the line it was moving previously. Particle with mass $m_2$ moves with speed $v_{2f}$ in a direction of angle $\phi$ below the line which particle with mass $m_1$ was moving previously. Using equations for conservation of momentum and kinetic energy, how can we prove these two equations</p>
<p>$\frac{v_{1f}}{v_{1i}}=\frac{m_1}{m_1+m_2}[\cos \theta \pm \sqrt{\cos^2 \theta - \frac{m_1^2-m_2^2}{m_1^2}}]$</p>
<p>and</p>
<p>$\frac{\tan(\theta +\phi)}{\tan(\phi)}=\frac{m_1+m_2}{m_1-m_2}$
?</p>
<p>EDIT. Here is what I've done:</p>
<p>For the first one, set the $xy$ coordinate system so that the positive direction of the $x$ axis points toward the original path of the particle with mass $m_1$. So we have three equations:</p>
<p>$m_1v_{1i}=m_1v_{1f}\cos \theta + m_2v_{2f} \cos \phi$</p>
<p>$0=m_1v_{1f}\sin \theta - m_2v_{2f}\sin \phi$</p>
<p>$m_1v_{1i}^2=m_1v_{1f}^2+m_2v_{2f}^2$.</p>
<p>From the second one, we get:</p>
<p>$v_{2f}=\frac{m_1v_{1f}\sin \theta}{m_2 \sin \phi}$</p>
<p>Plotting this into third equation, we get</p>
<p>$v_{1i}^2=v_{1f}^2(1+\frac{m_1 \sin^2 \theta}{m_2 \sin^2 \phi})$ (1)</p>
<p>From the first equation, we have</p>
<p>$\cos \phi =\frac{m_1(v_{1i}-v_{1f}\cos \theta)}{m_2v_{2f}}$</p>
<p>which after applying the equation we have for $v_2f$ becomes</p>
<p>$\sin^2 \phi = \frac{1}{1+\frac{(v_{1i}-v_{1f}\cos \theta)^2}{\sin^2 \theta \times v_1f^2}}$</p>
<p>Plotting this into equation (1), gives us an equation in terms of $m_1$, $m_2$, $v_{1f}$, $v_{1i}$ and $\theta$, but it is too far from what I expected.</p>
<p>For the second one, assigning the $xy$ coordinate in a way that the positive direction of the $x$ axis points toward the final path of the particle $m_2$, will give us three equations (two for conservation of linear momentum and one for conservation of kinetic energy), but I don't know what to do next.</p>
| 429 |
<p>I'm trying to help a child research a science project on refrigeration.
Refreshing my incredibly rusty thermodynamics skills....</p>
<p>The ideal gas law: $PV=nRT$. Let's take air at STP:</p>
<p>$P = 101\,kPa$
$V = 1\,L = 0.001\,m^3$
$R = 8.3\,J/mol\cdot K$
$T = 298\,K$</p>
<p>$n=PV/RT = (101000) (.001) / (8.3 \cdot 298) = 0.04\, moles$?</p>
<p>If we compress the air to ~7atm adiabatically
$P_2 = 7P$</p>
<p>I would think the volume goes to $\frac{1}{7V}$</p>
<p>$V_2 = \frac{V}{7}$</p>
<p>then I would expect the gas to be hotter. But I'm obviously confused because with that pressure and volume, the temperature is obviously the same. I'm assuming that I'm wrong about what the volume would be for an ideal gas if I compress to $7\,atm?$</p>
<p>$T_2 = \frac{P_2V_2}{nR} = ???$</p>
<p>The specific heat of air: $c_p = 1.006\,kJ/kg\cdot K$</p>
<p>Of course air is not quite ideal. I would also appreciate someone explaining what the non-ideal behavior is due to. Is it related to the mixing? Some kind of chemical interaction between the different components? </p>
<p>What I want to know is how to calculate the temperature of a gas given an initial temperature, pressure, heat capacity and final pressure, Adiabatically.</p>
| 2,014 |
<p>In the following image,three cases have been mentioned. $N$ is the normal force acting on the object inside the lift and $mg$ is the force of attraction due to gravity.<br>
In case 1, $N = mg$.<br>
In case 2, $N = m(g+a)$ and<br>
in case 3, $N = m(g-a)$. Why is it so in 2nd and 3rd case?
<img src="http://i.stack.imgur.com/xdA80.png" alt="enter image description here"></p>
| 2,015 |
<p>Let's say I know the size of the container, size of the hole the air leaks through, pressure the air is under and temperature of the air if that helps anything. Is it possible to calculate this only from these variables? What is the formula for how fast air leaks out of a hole?</p>
| 2,016 |
<p>I read an article which tells power consumption by many devices. It say that a desktop computer (computer and monitor) use 400 to 600 watt.<br>
While when i checked my computer and monitor with meter, it was about 60 + 60 = 120 watt (computer + 17" CRT monitor) after loading windows xp and running an application. The voltage is 220V here.<br>
Which one is correct? How much power does it consume?</p>
| 2,017 |
<p>In the time-independent Schrödinger's equation:</p>
<p>$$ -\frac{\hbar^2}{2m} \frac{d^2} {dx^2} u + Vu ~= Eu, $$</p>
<p>why there is a minus sign before the first term?</p>
| 2,018 |
<p>Mass m is connected to the end of a cord at length R above its rotational axis (the axis is parallel to the horizon, the position of the mass is perpendicular to the horizon). It is given an initial velocity, V0, at a direction parallel to the horizon. The initial state is depicted at position A in the image.</p>
<p>The forces working on the mass are MG from the earth and T the tension of the cord.</p>
<p>How can I calculate the tension of the cord when the mass is at some angle $\theta$ from its initial position (position B in the image)?</p>
<p><img src="http://img535.imageshack.us/img535/8167/76300324.png" alt="image">.</p>
<p>Here's what I thought:</p>
<p>Since the mass is moving in a circle then the total force in the radial direction is T - MG*$\cos\theta$ = M*(V^2)/R</p>
<p>and so T = MG*$\cos\theta$+M*(V^2)/R</p>
<p>but since MG applies acceleration in the tangential direction then V should also be a function of $\theta$ and that is where I kind of got lost. I tried to express V as the integration of MG*$\sin\theta$, but I wasn't sure if that's the right approach.</p>
| 2,019 |
<p>In Peskin and Schroeder's QFT book, page 189, equation 6.38, how do they get from the first line to the second line?</p>
<p>In particular, I am stuck on the transition from what I perceive to be:
$$ k'_\alpha \gamma^\alpha m \gamma^\mu + m k_\alpha \gamma^\alpha \gamma^\mu $$
into:
$$ -2m(k+k')^\mu $$</p>
<p>what am I missing?</p>
<p>I thought it might be using the Dirac equation because it works on $u(p)$, but that can't be it since $k\neq p$. Also couldn't figure out how to use the anticommutation relations of the gamma matrices.</p>
| 2,020 |
<p>I read a lot about the classical twin paradox recently. What confuses me is that some authors claim that it can be resolved within <a href="http://en.wikipedia.org/wiki/Special_relativity">SRT</a>, others say that you need <a href="http://en.wikipedia.org/wiki/General_relativity">GRT</a>. Now, what is true (and why)? </p>
| 249 |
<p>What are the different death scenarios for a black hole? I know they can evaporate through Hawking radiation - but is there any other way? What if you just kept shoveling more and more mass and energy into the black hole?</p>
| 2,021 |
<p>Imagine a circuit with a voltage source, a switch and an inductivity all connected in series.</p>
<p>First, the switch is open and there's no current and no magnetic field around. If we close the switch, the potential difference of the voltage source is instantaneously applied to the inductivity. Lenz's Law tells us that the induced voltage from the inductivity will always be such that the change in the magnetic flux is reduced. And we have Faraday's Law which tells us that the induced voltage is equal to the change in the magnetic flux.</p>
<p>What is the theoretical reason why the change in magnetic flux must be smaller than the applied voltage? Why does for t -> infinity always run a current trough the inductivity as it would be just a resistor? Is it just because the wires have a resistance? What would then happen when taking superconductors instead of wires? Is it the inner resistivity of the voltage source then?</p>
| 2,022 |
<p>Given the solution of the Von Neumann equation
$\rho(t) = e^{-i H t/\hbar} \rho(0) e^{i H t/\hbar}$</p>
<p>How can we justify if it will be stabilized as $t\rightarrow\infty$ in general?</p>
<p>For example, $H=\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}, \rho(0)=\begin{pmatrix}\frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & \frac{1}{2}\end{pmatrix}$, it will simply be fixed? But is it normal? Shouldn't there be some wave dynamics before reaching equilibrium?</p>
| 2,023 |
<p><img src="http://www.a-levelphysicstutor.com/images/matter/E-r-graph.jpg" alt="potential energy vs intermolecular distance r"></p>
<p>I'm trying to understand this curve better, but I can't quite figure out what "negative potential energy" means.</p>
<p>The graph should describe a molecule oscillating between $A$ and $B$, however where I'm stuck in reasoning this is that the PE is equal in $A$ and $B$, but then why does this mean $r$ will increase in $A$ (repel) and decrease in $B$?</p>
| 2,024 |
<p>This is a question on the synchronization of clocks. If a girl on a train has the same clock that a guy has on the platform and they synchronize their clocks at 12am together when the train and the platform are both stationary with respect to each other. Then if the train runs and some time later (a random time later) the girl says, "Stop". When she says this both the guy and girl stop their clocks. They turn it off so that the clock reads the time it was at when they stopped it. Then the girl gets off the train and she compares her clock with the guy. Which one would be slow? They were both moving with respect to each other so both their clocks should run slow. I don't understand that./?</p>
| 2,025 |
<p>Starting with the Maxwell action for a $U(1)$ vector gauge boson with a general metric and (I'm assuming) using a plane wave ansatz for the vector, is it possible to derive the action for a massless point particle?</p>
<p>EDIT: More information on what I'm trying to do. The Maxwell action and the action for a massless point particle are written in very different language (field values integrated over spacetime vs. particle trajectory integrated over time). But if I want to follow, say, the front of an EM wave, I should be able to get the massless point particle action from Maxwell. Does anyone know if this can be done and if so where?</p>
| 2,026 |
<p>Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that proves it?</p>
| 2,027 |
<p>This brand new published result (nature):</p>
<blockquote>
<p><strong>Experimental non-classicality of an indivisible quantum system</strong><br> by
Radek Lapkiewicz, Peizhe Li, Christoph Schaeff, Nathan K. Langford, Sven Ramelow, Marcin Wieśniak & Anton Zeilinger</p>
</blockquote>
<p>(see <a href="http://www.nature.com/nature/journal/v474/n7352/full/nature10119.html" rel="nofollow">here</a>, for a more popular article about it see <a href="http://www.newscientist.com/article/dn20600-quantum-magic-trick-shows-reality-is-what-you-make-it.html?DCMP=OTC-rss&nsref=physics-math" rel="nofollow">here</a>; also for a pre-print see the ArXiv <a href="http://arxiv.org/abs/1106.4481" rel="nofollow">here</a>)</p>
<p>seems to support the Copenhagen interpretation.</p>
<p><strong>My question</strong> <br>Does this definitely rule out the many-worlds interpretation - or are there still loopholes? How could a many-worlds interpretation of this experiment possibly look like (if possible)?</p>
<p>Thank you</p>
<p><strong>EDIT</strong><br>
Because I obviously created some confusion, how I came to that question: at the end of the NewScientist-article it says:</p>
<blockquote>
<p>Niels Bohr, a giant of quantum
physics, was a great proponent of the
idea that the nature of quantum
reality depends on what we choose to
measure, a notion that came to be
called the Copenhagen interpretation.
"This experiment lends more support to
the Copenhagen interpretation," says
Zeilinger.</p>
</blockquote>
| 2,028 |
<p>What is the centripetal acceleration and angular velocity of a child located 8.2 m
the center of a carousel? The speed (size of the tangential velocity) of the child is
2.1 m / s</p>
<p>A train moves in a straight path north until it turns to west.
If the road segment used to change direction is shaped like a quarter circle of radius 30 m and the train takes 30 seconds to traverse that part of the road,
What is it the speed (size of the velocity vector) and the centripetal acceleration acts on the train as it traverses the curve.</p>
<p>I am reviewing some concepts like centripet force, <code>ar = ( v^2 ) / r</code>
also this:</p>
<blockquote>
<p>The direction of the centripital
acceleration is always inwards along
the radius vector of the circular
motion. The magnitude of the
centripetal acceleration is related to
the tangential speed and angular
velocity as follows:</p>
</blockquote>
<p><img src="http://i.stack.imgur.com/XGojw.png" alt="enter image description here"></p>
<p>Can you please guide me to solve the 2 problems above?</p>
<p>for the fisrt one is it only :</p>
<p><code>(2.1 m / s)^2 / 8.2 m</code> ?</p>
| 2,029 |
<p>I was looking for a derivation of the expression for the energy density at any point in a static magnetic field. I do know that it is $\dfrac {1}{2 \mu_0}\left|\vec{B}\right|^2$ -- I was just wondering if there was a derivation that could be built up the way one derives the energy density $\dfrac {\epsilon_0}{2}\left|\vec{E}\right|^2$ at any point in an <em>electric</em> field, by considering the energy needed to build up a 'source' charge bit by infinitesimal bit.</p>
<p>Whatever proof I have come across seems to bring <em>inductance</em> into the picture -- is there a way of doing it without that? I ask because the corresponding proof for the electric field does not seem to need the definition of capacitance anywhere...</p>
<p>Thanks... </p>
| 2,030 |
<p>If p-type semiconductor and n-type semiconductor of a diode are equally doped, and if the diode is forward biased, then holes will move toward the n-type semiconductor and electrons will move toward the p-type semiconductor and they will diffuse with each other. Then will there be any electron that will go to the positive terminal of the battery if all of them have diffused with each other? I can't understand, please help me! </p>
| 2,031 |
<p>The human brain is said to produce a magnetic field resulting from the action potentials released inside the brain. What's the nature of such a field in terms of size and strength, and what is the potential for manipulation of brain functions by interfering with it by means of electromagnetic radiation?</p>
| 2,032 |
<p>Hi I'm trying to solve this textbook example but I don't know where to begin;</p>
<blockquote>
<p><em>NASA has decided to send an experimental probe to Mars. Its weight on earth is $40 kg_f$. When the probe is near the planet it will be
attracted by the its gravitational field ($g_{Mars} = 3.75\ m/s^2$). Determine the parachute’s diameter so that the probe will touch Mars’ surface with a velocity of $3 m/s$ (which is equivalent of dropping the probe from 0.5 m height on Earth). ($A_{chute} = π \frac{D^2}{4}, C_D = 1.4$, the density of Mars’ atmosphere is $\frac{2}{3}$ of Earth’s).</em></p>
<p><em>[$C_D$ is the drag coefficient of the parachute $C_D = 1.4$ (no dimensions, dimensionless number, or clear number,) and where $A$ is the projected area of the solid on a plane perpendicular to the body’s motion.]</em></p>
</blockquote>
<p>My knowledge of phyics is still at a beginner-intermediate level. I've been working on this problem for more than an hour and understand the concepts of drag coefficient, and force of a falling object.
What I don't understand, and couldn't find good resources for, is how to measure the speed of a falling object attached to a parachute (aka calculate the drag the parachute has on the fall), how to figure the density of Earth's atmosphere (isn't it different everywhere?) and how to figure out what the speed of the probe would be without a parachute. </p>
| 2,033 |
<p>This was another question from my son's workbook. It said:</p>
<pre><code>Ever jumped into a pool on a warm day and still felt cold, even after measuring the
temperature of the water with a thermometer and finding that it is the same temperature as
the air? Would this be conduction, convection or radiation then?
</code></pre>
<p>Interesting question. When he asked me, I immediately thought of convection, as that is 'conduction' of fluids, right? But I wasn't too sure, and I asked some friends. Both conduction and convection came as answers.</p>
<p>Which one is it? Why?</p>
| 2,034 |
<p>Assuming that I calculated the electric field in a single point between a uniform charged positive sphere and an infinite long wire charged positive uniformly.
Now, I want to calculate the velocity of a given particle q+ which will be set free from the point (A) which I calculated the field at, while hitting the surface of the sphere.
It is very clear that the electric field will change at any point during the particle q movement, but can I still use the Line Integral of the electric field in point A to calculate the Voltage between point A and the surface of the sphere? or do I need to calculate individualy the potential of the wire and sphere and these 2 points?</p>
<p><img src="http://i.stack.imgur.com/ciIzD.gif" alt="enter image description here"></p>
| 2,035 |
<p>We typically say that forces cause acceleration inversely proportionate to mass. Would it be any less correct to say that acceleration causes forces proportionate to mass? Why?</p>
<p>(Note that the underlying question in my mind - essentially, what distinguishes cause from effect - is far more general. But this seems like a good place to start.)</p>
| 2,036 |
<p>From a paper on tunnel design I've been reading: (<a href="http://www.sciencedirect.com/science/article/pii/0886779887900113" rel="nofollow">http://www.sciencedirect.com/science/article/pii/0886779887900113</a>)</p>
<blockquote>
<p>In the present application, the solu-
tion corresponding to a sinusoidal load
in an infinite elastic medium is sought.
Since no closed-form solution to this
problem exists, a numerical procedure
should be used. The procedure involves,
first, deriving the solution to the case of
a constant pressure applied to a finite
strip in an infinite body. The solution
for a sinusoidal distribution of loading
then can be found by dividing the
wavelength into several segments and
assuming the pressure on each segment
to be constant. In the present case, this
procedure is applied to calculate the
displacements under a sinusoidal line
load. Each wavelength was divided in 10
and 20 segments and a line load of 4, 6, 8
and 10 wavelengths were considered. It
was found that the calculated displace-
ments became insensitive to the number
of wavelengths when the latter exceeded
6, and that 10 segments were enough to
represent each wavelength.
As a result of this analysis, the vertical
displacement under a sinusoidal load
may be approximated by</p>
<p>$$u_y = \frac{(3-4\nu)}{16\pi(1-4\nu)G}\sigma L\sin\frac{2\pi x}{L}$$</p>
</blockquote>
<p>The authors refer to the plane strain solution to Kelvin's problem before this.</p>
<p>Can you suggest how I would go about deriving this as mentioned in the paper—from going for a finite strip in an infinite body to applying a <em>numerical</em> solution and getting the result for displacement?</p>
<p>Note: $\nu$ poisson's ratio, $L$ Length of strip, $G$ is the shear modulus.</p>
| 2,037 |
<p>I need to find a parachutist's displacement after a given height (nearly 37000m) and at a given latitude. I have his mass, area, parachute area, drop height, parachute deployment height, data about the atmosphere, and other assorted values. I don't have velocity and Temperature so I'm stuck. Please help.</p>
<p>My issues:</p>
<p>finding pressure change without temperature: $V(dP/dt) = nR(PV/NR)$ (doing that would result in the original pressure for pressure change...)?</p>
<p>using pressure change to find density change: again, no temperature, and if you substitute temp for PV/NR you end up canceling the pressure terms making using the pressure derivative futile? $ Density = (P*Mw)/(RT)$</p>
<p>using density change to find drag change: No velocity given so what do I do?
$Drag = Cd*A*.5*r*v^2$, where $r = drag$</p>
<p>using drag to net force to find acceleration: $drag/m = a$? </p>
<p>repeat last few steps for the parachute:...</p>
<p>Find how fast the earth rotates, and use the two velocities (earth/person) to find salient times: ?</p>
<p>Use the above to find: total displacement</p>
<p><em>Note</em> I'd need to stick to the above process and I didn't give values because I'd prefer to get help with strategies. </p>
| 2,038 |
<p>The eigenfunctions of a Hermitian operator are real. But consider a function $\psi(x)=e^{-\kappa x}$, $x\in\mathbb{R}$, where $\kappa$ is a real constant. Then, $$\hat p \psi(x)=-i\hbar \frac{d}{dx}e^{-\kappa x}=i\kappa \hbar \psi(x).$$ This gives a pure imaginary eigenvalue. Is it not a contradiction? Or am I missing some crucial point?</p>
| 2,039 |
<p>On page 160 Peskin & Schroeder, they say: </p>
<blockquote>
<p>Therefore we expect $\mathcal{M}^\mu(k)$ to be given by a matrix element of the Heisenberg field $j^\mu$: $$\mathcal{M}^\mu(k) = \int \mathrm{d^4}x \; \exp(\mathrm{i}k \cdot x)\langle f | j^\mu(x) | i\rangle.$$</p>
</blockquote>
<p>Why do they expect that?
Where does this come from? I've seen similar expressions with e.g. two Lorentz indices and so on. I've been taught (obviously not enough) qft through path integrals and have a hard time to make connections between the different formalisms. </p>
| 2,040 |
<p>In quantization of scalar field theory we impose commutation relation between the field operators <strong>by hand</strong> and similarly we impose anti-commutation relation between Dirac field operators <strong>by hand</strong>. As a consequence one gets Bose-statistics (two-particle wavefuction is symmetric) in the first case and the Fermi statistics (two-particle wavefuction is anti-symmetric) in the second case. But does it really <strong>prove</strong> the <a href="http://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem" rel="nofollow">spin-statistics theorem</a>?</p>
| 2,041 |
<p>Where can one find some concrete physical problems (with solutions) that illustrates the uselfullness and power of QFT? These must not be solvable by QM or SR alone.</p>
<p>It would be good if the problem utilizes the most central QFT concepts. I am trying to learn QFT but it looks like only some mathematical definitions.</p>
<p>Concrete QFT calculations which shows agreement with physical experiment to high accuracy.</p>
| 2,042 |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/2175/is-it-possible-for-information-to-be-transmitted-faster-than-light-by-using-a-ri">Is it possible for information to be transmitted faster than light by using a rigid pole?</a> </p>
</blockquote>
<p>On one episode of <a href="http://www.qi.com/" rel="nofollow">QI</a> they asked the question, "How fast do electrons move travelling around an electric current."</p>
<p>The answer is (more or less) "very slowly", with the explanation that it's not the electrons that move fast, it's the force (I think). They likened it to pushing on one end of a long tube of touching marbles and observing how quickly one fell out the other end.</p>
<p>This made me think about the tube. I realise that this tube cannot allow a force to propagate through the tube instantaneously because that would be faster than the speed of light, so my question is, why not?</p>
<hr>
<p><strong>TL;DR;</strong> Why doesn't a marble exit a long tube filled with touching marbles immediately when a force is applied to the marble at the other end?</p>
| 4 |
<p>Considering the fact that electrons tend to take the maximum conductance path to flow from A to B. This is justified by saying that $\vec{E}$ is larger in conductors. But once similarly it was thought for gravitation, that if in a region the gravity was stronger, the mass more likely took that path, then later it was found it is actually a geodesic in space time as gravity curves space time. So is there some underlying geodesic for motion caused by electromagnetic force?</p>
| 543 |
<p>Hi, I am thinking about acceleration. Let's think we have a force of $1$ N and a particle of $1$ kg, then acceleration will be $1$. So the speed gets higher every second and $c$ seconds later, <em>in Newtonian mechanics</em>, the particle will reach the speed of light. In relativity, of course, something like that cannot happen. So, what are the equations that describe acceleration in relativity?</p>
| 37 |
<p>Is there any reason for the names of the decay chains? As shown in this chart (<a href="http://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Radioactive_decay_chains_diagram.svg/2000px-Radioactive_decay_chains_diagram.svg.png" rel="nofollow">larger version here</a>):
<img src="http://i.stack.imgur.com/0LVtw.png" alt="enter image description here"></p>
<p>only the Thorium chain starts on an isotope of the element it takes its name from, and it can also start from Uranium.</p>
<p>My bet is that they were given that name because it was thought those were the starting elements, and it was later discovered that there were parent isotopes. Am I right?</p>
| 2,043 |
<p>I have two coherent point sources of light, $A$ and $B$, separated by a distance $L$, which I focus down to the diffraction limit using a high-powered objective (e.g. a $\approx 100x$ objective). If I turn on $A$ and turn off $B$, I have an Airy disk at position $c_1$, and I turn off $A$ and I turn on $B$, I have an Airy disk at position $c_2$. Given that both light sources are sent through the same objective, what is the minimum distance between $c_1$ and $c_2$? Is it simply $L$ scaled down by the objective (i.e. $\frac{L}{100}$)? Or does something odd happen because of e.g. curvature of the lens in the objective?</p>
<p>EDIT: A restatement of this question would be the following - Assuming all of the optics are perfect, if I shine a laser at a point (x,y) on an objective, and then shine the laser at a point (x2,y2), will the peak of the Airy disk move the same distance?</p>
| 2,044 |
<p>I read in wiki that the speed of light is 88km/s slower in air than it is in a vacuum.</p>
<p>Do neutrinos travel faster than light in air?</p>
| 2,045 |
<p>A lot of textbooks and exam boards claim that light incident at exactly the critical angle is transmitted along the media boundary (i.e. at right-angles to the normal), but this seems to violate the principle of reversibility in classical physics. How would a photon or ray travelling in the reverse direction "know" when to enter the higher refracting medium? It can't know, so I conclude that such light is simply reflected?</p>
<p>Is this correct?</p>
| 722 |
<p>RHIC has been the dominant player in heavy ion physics, producing tantalizing evidence in support of the entropy/viscocity formula from AdS/CFT.
What's the potential of the LHC's Pb ion collsions? What can it achieve which RHIC can't? What measurements will be improved?</p>
| 2,046 |
<p>I don't know how this "paradox" can be solved. I'm given the following system: A permanent magnet with a magnetic field given by ($\hat{a}$ are unit vectors in the x and y directions)</p>
<p>$$\vec{H}=H_0\hat{a}_y$$</p>
<p>and a parallel plane capacitor with an electric field</p>
<p>$$\vec{E}=E_0\hat{a}_x$$</p>
<p>Poynting's vector is given by:</p>
<p>$$\vec{S}=\vec{E}\times\vec{H}=H_0E_0\hat{a}_z \neq 0$$</p>
<p>The funny part comes when the professor told that in a system like that "clearly" there is not propagation (wich I know will imply some short of energy flux) in the $z$ direction, hence the "paradox". Is there or is there not propagation of energy?</p>
<p>Any hint will be appreciated, thank you for your time.</p>
| 2,047 |
<p>The only explicit computation I have seen is the planar 1-loop one, but there should be a way to write the multi-loop case in terms of boundary states as well. </p>
| 2,048 |
<p>I had a test on Quantum mechanics a few days ago, and there was a problem which I had no clue how to solve. Could you please explain me?</p>
<p>The problem is:</p>
<blockquote>
<p>Let's look at the $\hat H=E_0[|1 \rangle \langle 2| + |2 \rangle \langle1|]$ two-state quantum system, where $E_0$ is a constant, and $\langle i|j \rangle=\delta_{ij}$ $(i,j=1,2)$.
\begin{equation}
\hat O= \Omega_0 [3 |1 \rangle \langle1|- |2 \rangle \langle2|]
\end{equation}
is an observable quantity, and its expectation value at $t=0$ is: $\langle \hat O \rangle =-\Omega_0$, where $\Omega_o$ is a constant.
What is the $|\psi(0) \rangle$ state of the system at $t=0$, and what is the minimum $t>0$ time, that is needed for the system to be in the state: $|\psi(t) \rangle =|1 \rangle$?</p>
</blockquote>
<p>I never came across a problem like this, I tried to construct the time evolution operator, $\hat U$, but I couldn't, and I have no idea how to start. </p>
| 2,049 |
<p>A copy of <a href="http://math.stackexchange.com/questions/687534/are-continuous-mathematical-models-of-discrete-physical-phenomena-messy-because">my question on Mathematics</a>:</p>
<p>Examples from statistical mechanics and continuum mechanics abound: a discrete phenomenon (e.g. kinetic energy of molecules) is "averaged" out over the constituents of the system to which it applied (continuing the example: temperature, or pressure), and then calculations are simplified for certain special cases (e.g. ideal gases), at the cost of increasing "messiness" as increasingly general cases are considered (e.g. non-ideal gases).</p>
<p>I am not familiar with combinatorics and discrete mathematics, so please be gentle: are there trains of thought being explored in modern research that wonder if discrete physical phenomena might be better modelled by discrete mathematics?</p>
<p>If such a direction is not being seriously looked into because discrete math doesn't model discrete phenomenon in a neater way, why are discrete math models of discrete physical phenomena as messy as continuous math models of discrete physical phenomena?</p>
<p>P.S. What resources could I use to further read about related subjects?</p>
| 38 |
<p>I know ice floats in water because it's crystalline structure causes $H_20$ solid to be less dense than $H_20$ liquid. Is the same true for salt because it is crystalline? If not why?</p>
| 2,050 |
<p>In the popular culture the XIX-XX century competition between Thomas Edison and Nikola Tesla is well-known. The example could be the <a href="http://www.imdb.com/title/tt0482571/" rel="nofollow"><em>Prestige</em></a> movie, where there are some "Edison's agents" who sabotage Tesla's efforts. From electrical engineers' point of view the most known problem between them is whether to use DC or AC (the <a href="http://en.wikipedia.org/wiki/War_of_Currents" rel="nofollow">War of Currents</a>).</p>
<p>We can say that Edison is better known, because of the invention of a bulb or his first urban electricity system. Tesla is almost unknown, some people say about magic and so on. (That's why I recall the <em>Prestige</em> movie.)</p>
<p>In electricity it seems that Tesla has won, even if he's widely forgotten. We use AC mainly because of it's easy in transformers. We have an SI unit $\text{T}$ (tesla), which is for measuring magnetic induction.</p>
<p>But -- we can't forget Edison's impact on electricity. Even if he was mostly a great businessman, no-one can say he's done nothing but the bulb. <a href="http://en.wikipedia.org/wiki/List_of_Edison_patents" rel="nofollow">Here is some list of his patents</a>.</p>
<p>So why isn't he honored (like Tesla, Ampère, Volta, Siemens, Ohm, Faraday, ...) by his "own" unit in physics?</p>
| 2,051 |
<p>The diagram in <a href="http://physics.stackexchange.com/questions/36092/why-are-l4-and-l5-lagrangian-points-stable">Why are L4 and L5 lagrangian points stable?</a> shows that the gravitational potential decreases outside the ring of Lagrange points — this image shows it even more clearly:
<img src="http://i.stack.imgur.com/JMnkQ.gif" alt="Potential surface"></p>
<p>If I understand correctly, using the rubber-sheet model analogy, an object placed in the field moves as if a marble rolls on the sheet with downward gravity. That's fine for objects inside the Lagrange ring: They move towards either mass.</p>
<p>But outside it, it implies that they move <strong>away</strong> from both masses. Is that really what happens? If so, why? If not, why does the surface slope downwards?</p>
| 2,052 |
<p><img src="http://i.stack.imgur.com/sUvHk.png" alt="enter image description here"></p>
<p>As you see, this is the electric field generated by a point charge moving at constant speed v. I know that when $v$ -> 0, $E$ is just the Coloumb Law. But how do you interpret $E$ when $v$ -> $c$ ? </p>
<p>Can I just interpret it as the field of electromagnetic wave, because it moves at the speed of light?</p>
<p><img src="http://i.stack.imgur.com/LvWkF.png" alt="enter image description here"></p>
| 2,053 |
<p>If while calculating a band gap, the band just below the Fermi level touches the Fermi level, can we say the material is semiconducting?</p>
| 2,054 |
<p>I'm currently reading the Seiberg-Witten paper on $N=2$ supersymmetric Yang Mills pure gauge theory (i.e. no hypermultiplets). I have the following question:</p>
<p>How does one understand that the metric on the moduli space of the full quantum theory is the same as the metric obtained from the Kahler potential for the scalar field (or in general the $N=1$ chiral superfield) in the low-energy effective theory? On the face of it, the two things seem quite different - while the moduli space is the space of all gauge-inequivalent vacua in the full theory, the Kahler metric is derived from the Kahler potential in the low energy theory. </p>
| 2,055 |
<p>I'm swimming in the ocean and there's a thunderstorm. Lightning bolts hit ships around me. Should I get out of the water?</p>
| 2,056 |
<h1>Problem</h1>
<p>If you had a long bar floating in space, what would be the compressive force at the centre of the bar, due to the self-weight of both ends?</p>
<p>Diagram - what is the force at point X in the middle of the bar?:</p>
<pre><code><----------------------L--------------------->, total mass M
=======================X====================== <- the bar
F---> X <---F
</code></pre>
<h1>Summary</h1>
<p>You should be able to simplify by cutting the bar into pieces, but that gives a different answer depending on how many pieces you use (see below). So the simplification must be wrong - but why?</p>
<h1>My approach</h1>
<h3>Split bar in two</h3>
<p>So, one approximation would be to cut the bar in half - two pieces of length L/2, mass M/2:</p>
<pre><code> (M/2)<-------L/2------->(M/2)
#1 X #2 <- bar approximated as blobs #1 and #2
</code></pre>
<p>Force at X is G(M1.M2)/(R^2) = G (M/2)^2 / (L/2)^2 = G M^2 / L^2</p>
<p>Or Fx / (G. M^2 / L^2) = <strong>1</strong></p>
<p>But is that really valid? If so, shouldn't you get the same answer if you split the bar into four pieces?</p>
<h3>Split bar into four</h3>
<pre><code> (M/4)<-L/4->(M/4)<-L/4->(M/4)<-L/4->(M/4)
#1 #2 X #3 #4
</code></pre>
<p>My assumption is that the force at X is the sum of the attractions of each blob on the left to every blob on the right.</p>
<p>Force at X = #1<>#3 + #1<>#4 + #2<>#3 + #2<>#4</p>
<p>('<>' being force between blobs #x and #y).</p>
<p>Fx / (G.M^2 / L^2) = (2/4)^-2 + (3/4)^-2 + (1/4)^-2 + (2/4)^-2 = <strong>1.61</strong></p>
<p>This is bigger than the previous result (1.61 vs 1).</p>
<h3>Split bar into six</h3>
<p>Similarly, if you split into 6 blobs, the total force comes out as:</p>
<p>Fx / (G.M^2 / L^2) = (3/6)^-2+(4/6)^-2+(5/6)^-2 + (2/6)^-2+(3/6)^-2+(4/6)^-2 + (1/6)^-2+(2/6)^-2+(3/6)^-2</p>
<p>Fx / (G.M^2 / L^2) = <strong>2.00</strong></p>
<h3>So what's wrong with my approach? And what is the real answer?</h3>
<p>So it seems the more pieces we split the bar into, the larger the result gets. There's clearly something wrong with my assumptions! - but what?</p>
<p>I'd be very glad if someone here could explain this. Thanks!</p>
<p><strong>EDIT</strong>
As Peter Shor pointed out, my calculations had some dodgy algebra and I'd calculated $$L^2/M^2$$ values rather than $$M^2/L^2$$. I've now corrected that - the value still increases as you divide into more masses.</p>
<p>I'll do a bit more work with more divisions and see if this leads to convergence or not.</p>
| 2,057 |
<p>The Lippmann-Schwinger equation in the first Born approximation, in the far field, is the Fourier transform of the potential. The scattering potential for an electron beam incident on a crystal is by the Coulomb potential which can be recast as crystal electron density by the Poisson equation. The scattering field is then the Fourier transform of the charge density.</p>
<p>Far field x-ray scattering in a crystal is the Fourier transform of the charge density. But the x-rays are not scattered off of the Coulomb potential. So, how does one go from the Lippmann-Schwinger to the Fourier transform of the charge density for x-ray scattering?</p>
| 2,058 |
<p>Does the nature of the assortment of virtual particles depend upon the warping of spacetime in a direct manner ?</p>
| 2,059 |
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