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<p>It seems to be common consensus that the world is non-deterministic and this is <em>proved</em> by <a href="http://en.wikipedia.org/wiki/Bell%27s_theorem#Overview">Bell's theorem</a>.</p>
<p>But even though Bell's experiments proved that the theory of quantum mechanics work, How does it prove the non-existent of <a href="http://en.wikipedia.org/wiki/Local_hidden_variable_theory">local hidden variables</a>?</p>
<p>Isn't it possible that there are hidden variables at work, and the results that were derived from these hidden variables coincide with the predictions of quantum mechanics?</p> | 6,103 | [
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<p>I am reading the paper <a href="http://cds.cern.ch/record/133713/files/" rel="nofollow">Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups - Weinberg, Erick J</a> .</p>
<p>In appendix C of this paper the author states, that the solution obtained (eqn 2.20) by embedding a SU(2) bps monopole, in a gauge theory of higher rank, can be categorized by a <strong>natural isospin $t$, and a hypercharge $y$</strong>. What is ispospin and hypercharge in this context?</p>
<p>I explain more about the solution. For each simple root $\beta^{(a)}$ of an arbitrary gauge group, you can define a SU(2) subgroup with generators, $t_1, t_2, t_3$ given in <strong>eqn 2.20,</strong> and a set of scalar and gauge fields, that satisfy the bps monopole equations of unit charge. </p>
<p>HE says the generators belonging to the cartan sub algebra H are isospin singlets with $y=0$. What does this mean? And also for other roots, $t_3$ and $y$ are given by <strong>(eqn C.1)</strong></p>
<p>$$t_3 E_{\alpha}=[t_3, E_{\alpha}]=[\frac{\beta \cdot H}{\beta^2},E_{\alpha}]=\frac{\beta \cdot \alpha}{\beta^2}E_{\alpha}$$
$$yE_{\alpha}=(\frac{h \cdot \alpha}{h \cdot \beta}-t_3)E_{\alpha}$$</p>
<p>Here, $\beta$ is any root of the gauge group, $E_{\alpha}$ is the raising operator, and $h$ is the vector formed by the components of the scalar field $\phi$ along generators of $H$.</p> | 6,104 | [
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<p>I've been studying electroweak theory and you need to keep the Lagrangian covariant by introducing covariant derivatives. What is a covariant derivative? And what does it mean to keep the Lagrangian covariant?</p>
<p>Also, in electroweak symmetry breaking, the gauge bosons attain their masses via the action of a 'covariant derivative' on the Higgs field. What does this mean in physical terms?</p> | 6,105 | [
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<p>I know that momentum and energy are always conserved in collisions, but if we have a perfectly inelastic collision in which an object sticks to another object $m_1 v_1 + m_2 v_2 = (m_1+m_2)v_{12}$, the kinetic energy is not conserved. I know that kinetic energy converts into thermal or sound energy, but I don't see how this would account for the whole of the lost kinetic energy.</p>
<p>Does the kinetic energy transform into some sort of potential energy between the bonding of the two objects? For example, if the two objects stick together with a small magnet (assuming the initial attraction between the objects is negligible) does the kinetic energy transfer to some sort of magnetic potential?</p> | 213 | [
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<p>I recently came across the definition of the Center of Mass of a system as the point about which the <strong>first</strong> <em>moment of mass</em> is zero.</p>
<p>Further, it defined <a href="http://en.wikipedia.org/wiki/Moment_of_inertia" rel="nofollow">Moment of Inertia</a> as the <strong>second</strong> <em>moment of mass</em>.</p>
<p>My question is, What is this '<strong>moment of mass</strong>'?</p> | 6,106 | [
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<p>I have an electric motor that can apply a pull force of $3000 \;\mathrm{lb}$ (electric winch), it draws $180 \;\mathrm{A}$ at $12 \;\mathrm{V}$.</p>
<p>I understand that power $P = I \cdot V = 2.1 \;\mathrm{kW}$. If I know the time this motor was running I can figure out the energy using $E = P \cdot t$. Why not use the capable force ($3000 \;\mathrm{lb}$) times the applied distance? </p>
<p>In addition, can electric motors function at 100% (fully running) at very short time scales, like 0.001 seconds - 0.020 seconds, using full power?</p> | 6,107 | [
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<p>The experiments of innovative Faraday and Joseph Henry in USA, conducted around 1830, demonstrated conclusively that electric currents were induced in closed coils when subjected to changing magnetic fields. </p>
<p>Maxwell developed a set of equations describing the laws of electricity and magnetism. Using these equations he derived what is known as wave equation from which he predicted the existence of electromagnetic waves. From the wave equation, Maxwell calculated the speed of electromagnetic waves in free space and he found that the theoretical value was very close to the measured value of speed of light. From this, he propounded that light must be electromagnetic wave. Thus, according to Maxwell, light waves are associated with changing electric and magnetic fields; changing electric field produces a time and space varying magnetic field and a changing magnetic field produces a time and space varying electric field. </p>
<p><img src="http://i.stack.imgur.com/KtLEu.gif" alt="enter image description here"> </p>
<p>Electromagnetic radiations are transverse waves. Transverse waves are moving waves that consists of oscillations occurring perpendicular (or right angled) to the direction of energy transfer. </p>
<p>I have question here. Electromagnetic radiations are transverse waves, which are referred as moving waves with changing electric and magnetic fields. We know that current can pass through skin, muscles, or hair of our body. It is also known that, the minimum current a human can feel depends on the current type (AC or DC) and frequency. A person can feel at least $1 mA$ (rms) of AC at $60 Hz$, while at least $5 mA$ for DC. </p>
<p>I thought that, if electromagnetic radiations are moving around us, the magnetic field must be linking with our body, as a result there must be emf induced in our body which should result in current through our body or else we can expect any conductor to conduct current, because the magnetic field of EMR is continuosly linking with it. If assume visible light it has frequency ranging from $4X10^{14}$ to $8X10^{14}$ which is far greater than $60Hz$ needed to produce current which can be felt by us. So, <em>would there be emf induced in our body due to electromagnetic radiations?</em> In reality, if we would had got shock if emf would have been induced in our body. But, this doesn't happen. I don't know whether I am wrong any where, or there is really emf induced. If any is the case please explain.</p> | 6,108 | [
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<p>Dark Matter appears to have more in common with phenomena related to spatial geometry then a particle. I thought in General Relativity, space can be curved without the presence of matter so gravitational lensing does not imply there is matter present but that the space in a region is curved. If Dark matter has more characteristics related to spatial geometry, why is it referred to as a kind of exotic particle (WIMP).</p> | 6,109 | [
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<p>I'm asked to find the linear acceleration of this object</p>
<p><img src="http://i.stack.imgur.com/zFdHp.jpg" alt="enter image description here"></p>
<p>for a given tension $T$ knowing that both discs have mass $M$ and we don't consider the mass of the bar.</p>
<p>The answer of the book is different than mine and I'm not sure where I have errors. What I did:</p>
<p>Considering $T= I\alpha$ being $\alpha$ the angular accelaration I have $a_{cm}=\alpha (R-r)$. I have two discs of mass $M$ which means $I=\displaystyle\frac{1}{2}(2M)(R^2) = MR^2$.</p>
<p>Then $T = (MR^2)\alpha = (MR^2)\left(\displaystyle\frac{a_{cm}}{R-r}\right) \implies a_{cm} = \displaystyle\frac{T(R-r)}{MR^2}$.</p>
<p>But the answer in the book is $a_{cm}=\displaystyle\frac{T(R-r)}{3MR}$. Maybe $I$ is not right?, but this is just a guess and I'm not sure why $3MR$ would be $I$ in this case.</p> | 6,110 | [
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<p>I was watching the speed skating event, and was wondering, why do the athletes use their right hand while accelerating? If they want to increase the moment of inertia, then they should move the hand away from themselves, but they don't do that.</p>
<p>Is it due to the shifting of the Centre of Gravity to the right (leading to an increased torque and more chances of toppling over) that they don't move their left hand at all?</p> | 6,111 | [
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<p>Does anyone knows a simple way to understand why the average value of the creation (or annihilation) operator should be equal to zero in the Canonical Ensemble? Why instead if I'm dealing with a Grand-Canonical ensemble the same averages can be different from zero? </p>
<p>I'm asking this because in the Bogoliubov approximation (in the case of weakly interacting Bose gas) basically we set</p>
<p>$a \sim \sqrt(N_0)$</p>
<p>so as far as I understood the average value of a should be different from 0 and the computation should be done in the Grand-Canonical ensemble.</p> | 6,112 | [
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<p>Why can't solar panels produce 1 Kw per 1 square meter? This is the energy of the Sun's radiation per square meter on Earth but solar panels don't come close. Why can't we trap all that energy? Where is the rest of the energy going?</p> | 6,113 | [
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<p>If I have a volume of $L$ liters of salt water at a concentration of $\approx N$ mM NaCl and I pour it into an electrophoretic apparatus (like this one: <img src="http://upload.wikimedia.org/wikipedia/commons/a/a6/Gel_electrophoresis_apparatus.JPG" alt="image">). Once we turn the apparatus on, and set the power level to some number of volts $V$, we would expect that there would be a Lorentz force on the individual Na+ and Cl- ions, pulling them towards the cathode and anode ends of the device, respectively. What does the physical distribution of Na+ and Cl- ions actually look like in the device as it operates? </p>
<p>Each ion will experience some Lorentz force, but separating the two ion types will have entropic penalties, so it's unclear to mean what the equilibrium distribution will look like with some voltage and current level.</p>
<p>A note on why this might be of interest: The apparatus for "gel electrophoresis" shown below is typically used to drag charged molecules (for example, nucleic acids or proteins) through a gel of some density, allowing for size sorting (where the gel leads to better size discrimination than the typical charge/mass ratio one uses to seperate molecular species for mass spectrometry). Proper molecular structure depends on having specific concentrations of specific anions or cations. Thus, I've always wondered if a gradient distributions of anions and cations over the length of distance between the anode and cathode had any undesirable effects. However, nowhere have I ever seen or heard this mentioned in the literature. </p> | 6,114 | [
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<p>I have a large cylinder made of a rigid thick plastic with a speaker inside of it. I want to be able to hear high pitched / high frequency noise from the outside but I'm primarily hearing bass. The treble is muffled. What can I do to be able to hear crisp sound from the outside? How should I modify the cylinder or speakers?</p> | 6,115 | [
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<p>How do scientists discover <a href="http://en.wikipedia.org/wiki/Superconductivity" rel="nofollow">superconductors</a>? Do they test properties of every material available on Earth? Or do they do something mathematically?</p> | 6,116 | [
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<p>How can the Anomalous Expansion of Water from 4$^\circ$C to 0$^\circ$C be explained with reference to subatomic particles?</p> | 6,117 | [
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<p>Is it possible that a metallic object will <em>not</em> be under the influence of a magnetic field at a certain <em>closeness</em> to a conductor, but will then experience the effect on moving to a particular distance (and onwards)? In other words, is there a threshold radius around a conductor <em>within</em> which the magnetic effect cannot be felt?</p> | 6,118 | [
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<p>Exist some relationship between irradiance units and wavelength of the incident sunlight?
What about irradiance? I want to establish a relationship between wavelength and irradiance, because I would try to model photosynthesis on Vensim. </p> | 6,119 | [
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<p>What is the maximum frequency of the Gamma Rays produced during supernovae? And how are these detected by telescopes without getting some serious damage done?</p> | 6,120 | [
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<p>I was wondering whether the rotational speed of a discus has any influence on the flight of the discus. Would slowing the rotation or speeding it up change the trajectory in any way or would the flight simply become unstable when slowing down?</p> | 6,121 | [
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<p>What exactly is the difference between 2-Level, 3-Level and 4-Level systems? Why can we not achieve stimulated emission in a two-level system using optical pumping?</p> | 6,122 | [
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<p>How can we theoretically calculate the boiling point of water at given pressure (other subtle parameters as well, if any)? What is the most accurate (minimum discrepancy with experimental value) computation that can analytically predict the
boiling point of water?</p>
<p>Possibly we need to invoke quantum mechanics for this. I anticipate that many answer would say that EXAXCT prediction is computationally infeasible, but please give the outline in algorithmic form regardless of computational cost.
My main goal is to learn how quantum mechanics can be applied to phenomena which can be observed by layman. Other example where quantum mechanics is used to predict physical properties of small molecules from first principle are also welcome.</p> | 6,123 | [
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<p>When we say Laser transverse modes. Is that mean what we will get at the output spot of laser beam ? secondly In practice , what TEM01 or TEMnm means ?</p>
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<p>The property of hermitian is the sufficient condition for eigenvalue being real.
Is there any non-hermitian operator on Hilbert Space with all real eigenvalues? If there exist, then can all eigenstates be orthogonal to each other? And these operators have any application in Quantum mechanics? </p> | 6,125 | [
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<p>I heard from Prof. Katrin Becker (in her "SUSY for Strings and Branes - Part 1" lecture) that the classical $SL(2,\mathbb{R})$ symmetry in type IIB String theory becomes $SL(2,\mathbb{Z})$ in Quantum because of charge quantization. However, I cannot see how does it work. Is there any rigorous Mathematical derivation for this? </p>
<p>Thank you.</p> | 6,126 | [
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<p>Assume I use a coil to create B-flux and put ONE Neodymium cylinder magnet (1"diameter & 0.25" thick) close to the flux, it would create 10 lbs force. Does it mean that I put TWO cylinder magnets (1"diameter & 0.25"+0.25" = 0.5" thick) would create 20lb force? </p> | 6,127 | [
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<p>So I'm in grade 10 but I finished all my physics classes, maths and further maths (Calculus). I would like to start with some harder stuff (university physics). What books do you recommend for both maths and physics? And if possible what steps should I take?</p> | 98 | [
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<p>This is from the beginning of Srednicki's QFT textbook, where he writes (approximately): </p>
<p>In QM we associate a unitary operator $U(\Lambda)$ to each proper orthochronous Lorentz transformation $\Lambda$. These operators must obey the composition rule </p>
<p>$$U(\Lambda'\Lambda) = U(\Lambda')U(\Lambda).$$</p>
<p>So far OK. </p>
<p>But where does he get the following from?
$$U(\Lambda)^{-1} = U(\Lambda^{-1})$$</p> | 6,128 | [
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<p>How exactly does a battery produce a current in the circuit connected across its ends? I dont want to know the chemical reactions in the battery core, but just the essence of it. I believe it doesn't do this by creating an excess of electrons at the -ve terminal and a deficit at the positive terminal. Moreover, how is the voltage and the EMF different in their definitions and value. Electric field being a conservative field, can the work done in motion of electrons in the conducting wire and all the components be compared to the work done in any other path across the terminals of the battery? And on a side note, how can we theoretically derive an relation between the potential difference and the electric current?</p> | 6,129 | [
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<p>To our time a light year is the distance that light travels in a vacuum but if we consider time of observer which moves at speed of light we found for light time and distance doesn't really exist.
Does distance really exist?</p>
<p>($d\tau=dt\gamma^{-1}$ where the at speed of light $\gamma^{-1}=0$)</p>
<p>isn't universe just a point for observer at light speed?</p>
<hr>
<p>it is not duplicate guys!.</p> | 195 | [
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<p>I'm new to this forum so I hope this post falls under the guidelines of what's acceptable.</p>
<p>I'm currently finishing my grade 11 year of high school and I have hopes of attending one of the prestigious schools in the US such as MIT, Harvard, Stanford, Princeton, etc. I would love to be able to study physics in university and, since my school's physics courses are lacking any difficulty, I've been taking it upon myself to learn physics. I have a very strong ability to do the necessary math and have taken university calculus courses to prepare.</p>
<p>However, the field is brimming with a wealth of resources and I'm just not sure what to choose and was hoping you would be able to help me out a little.</p>
<p>I currently own Stephen Hawking's books: The Grand Design, The Universe in a Nutshell, and A Brief History of Time. Now I know these are written without the technical aspects, but I'm sure they'd make great reads when I find time. However, I'm more looking into resources which actually teach the math behind the ideas.</p>
<p>I've found countless courses on MIT OpenCourseware and other online course resources including Leonard Susskind's The Theoretical Minimum courses. As far as books go, I've been interested in Leonard Susskind's two main books. I've also taken a great interest in Richard Feynman's work and so I'm interested in purchasing the Feynman Lecture on Physics boxed set with the accompanying exercise book being published this summer.</p>
<p>I would like to listen to any recommendations any of you may have as to which resources I should use to gain a good understanding of physics. I would really like to learn using Feynman's lectures although I hope it isn't considered to be too old to be of much value.</p>
<p>Any advice would be very much appreciated!!</p> | 98 | [
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<blockquote>
<p>Two people, Micah and Lyra, with different near points are equally
close to an object. Both inspect the object through the same magnifier
by holding the lens close to the eye. Micah's near point is located
farther away from his eye than Lyra's near point is located relative
to her eye. Micah will experience a larger magnification for which of
the following reasons?</p>
<p>The answer is: </p>
<ul>
<li><p>When the object is located at his near point, the angular size of the object is smaller for Micah than for Lyra.</p></li>
<li><p>The angular size of the image relative to the angular size of the object at the near point is greater for Micah than for Lyra.</p></li>
</ul>
</blockquote>
<hr>
<p>My question is why the 1st point? Not really able to visualize whats happening ... Also, why is "Micah can see the image clearly from a larger distance than Lyra can." not correct too? He has a larger near point so he can see the image from a larger distance? </p> | 6,130 | [
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<p>The following is the question that very commonly appears in all HS textbooks.<br>
A hollow sphere with a hole is taken to a depth of 40cm when the water starts entering the hole. if the surface tension of water is 70dyne per cm find the radius of the hole.<br>
All the textbooks solve it in a similar manner as given below:-
When water enters the sphere, radius of the bubble of air formed, will be equal to radius of the hole say r. Then excess pressure inside the bubble equals the external pressure at the depth of 40cm and thus on equating 2T/r to h*d*g, they find the answer.</p>
<p>but i dont find this explanation satisfying at all. why should a bubble form only at that depth and that too of the radius of hole. cant it form at any depth and the radius depend on the depth with maximum being equal to the radius of the hole.?</p> | 6,131 | [
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<p>If you have two particles of the same species , Quantum mechanics says that $\Phi_{m_{1},x_{1},p_{1},m_{2},x_{2},p_{2}}=\alpha\Phi_{m_{2},x_{2},p_{2},m_{1},x_{1},p_{1}}$
But I don't understand why $\alpha$ doesn't depend on $x$ , $p$ . If $\alpha$ depends on $SO(3)$ invariants as $x^2 , x.p , p^2$ etc then it will be the same on all reference frame why does one require that it doesn't depend on these variables? Even if it depends on $p ,x$ $\alpha$ is a phase factor so it doesn't affect anything why should this be important?</p>
<p>EDIT : I figured out the answer to the second question , for $\alpha$ is a complex number that carries no indices so it cannot change </p> | 6,132 | [
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] |
<p>In an answer to a previous question of mine, <a href="http://astronomy.stackexchange.com/questions/888/are-the-inner-planets-on-planar-orbits-because-there-was-more-dust-in-the-inner-s">one that asked about the planar orbits of inner planets</a>, I was told the following (emphasis mine):</p>
<blockquote>
<p>On the subject of different solar systems, I would expect tidal
disturbances from close passes with neighboring stars to be the most
dominant effect in determining how closely planets' orbital planes
coincide. So... "urban" star areas would have more close passes than
"rural" ones, and also more metal pollution. <strong><em>Ergo, if anything I would
expect systems with higher metals to be less coplanar.</em></strong></p>
</blockquote>
<p>Now, this last sentence got me thinking whether or not there was any evidence for this, so do stars of higher metallicity have more planets in highly-inclined Pluto-like orbits? (higher metallicity means more dust, I'd presume - but would it significantly increase the gas to dust ratio?) I actually would expect the opposite hypothesis (at first), since there might presumably be more friction with more dust (and the amount of dust wouldn't really affect the amount of gas, since gas still forms the overwhelming majority of particles)</p> | 6,133 | [
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<p>I understand that you get coffee rings on a table as a result of solute migration (solutocapillarity) towards the pinning of the circumference of the coffee ring <a href="http://www.nature.com/nature/journal/v389/n6653/abs/389827a0.html" rel="nofollow">[Deegan et al.]</a>.</p>
<p>Below is an observation that I made with coffee in a mug. I notice several rings forming along the inside circumference of the mug and these rings seem to be equidistant. Two things, at the very least, hit me:</p>
<ol>
<li>Is the equidistance in the rings only because of a generally constant sip volume?</li>
<li>Is there a penetration depth from the surface where most of the solute collects and migrates in. I am assuming based on brewing observation that coffee grounds (the solute) are less dense than water and float on top.</li>
<li>If the second hypothesis is correct, I suppose the rings would be closer or further away depending on how much coffee I use?</li>
<li>Is there a physics/chemistry coupling to this problem?</li>
</ol>
<p><img src="http://i.stack.imgur.com/EL0ZK.jpg" alt="Mug ringsin coffee cup"></p> | 6,134 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/25070/why-can-we-see-the-cosmic-microwave-background-cmb">Why can we see the cosmic microwave background (CMB)?</a> </p>
</blockquote>
<p>We all have seen evidence of radiation left from the Big Bang, but how is it still detectable? Why didn't it disperse early on?</p> | 214 | [
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<p><strong>The actual number:</strong></p>
<p>How far apart are galaxies on average? </p>
<p><strong>An attempt to visualize such a thing:</strong></p>
<p>If galaxies were the size of peas, how many would be in a cubic meter?</p> | 6,135 | [
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<p>I have written a computer simulation of the driven damped pendulum, pretty much as the one <a href="http://www.cmp.caltech.edu/~mcc/Chaos_Course/Lesson2/Demos.html" rel="nofollow">shown here</a>, only that I did it Python. Next, I have found some parameters for which the pendulum behaves chaotic. Now I want to extract the <a href="http://en.wikipedia.org/wiki/Lyapunov_exponent" rel="nofollow"><strong>Ljapunov exponent</strong></a> from the system. To do this, I let the system run two times, one time at the found parameters for chaos, a second time with the same parameters plus a very small deviation in the initial position of the pendulum. Then I plot the difference in the displacement of the two pendulums as a function of time, as shown in the figure below (taken from <a href="http://rads.stackoverflow.com/amzn/click/0131469908" rel="nofollow">Giordano, Computational Physics</a>). </p>
<p>I can <strong>qualitatively</strong> extract the Ljapunov exponent, by doing this several times and fitting a line to the data. </p>
<p>The <strong>question</strong> is, however, how would I do this <strong>quantitatively</strong> or even <strong>analytically</strong>? </p>
<p><img src="http://i.stack.imgur.com/GAAWt.png" alt="Extracting the Ljapunov exponent from plotting $\Delta \Theta(t)$ vs. t"></p> | 6,136 | [
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] |
<p>Taking it to the bottom of layman's terms, what would be the shortlist of significant <em>things</em> in the universe?</p>
<p>A list I could think of myself would put</p>
<ul>
<li><strong>Energy</strong> (at whatever wavelength travelling through space)</li>
<li><strong>Gas</strong> (Atoms and molecules floating interplanetary, interstellar and intergalactic space)</li>
<li><strong>Rocks</strong> (Anything from dust to planets)</li>
<li><strong>Stars</strong> (In more general terms, anything that is or were a star... would include also black holes, magnetars and novae)</li>
<li><strong>Galaxies</strong>..</li>
</ul>
<p>Things that does not fit very well in this classifications however are:</p>
<ul>
<li>The super massive black hole of galaxies (although I could simply put it in galaxies)</li>
<li>Dark matter (but I do not worry too much until it has been properly measured :) )</li>
<li>Wormholes (if they even exist..)</li>
<li>Anything else</li>
</ul>
<p>What else is to be put in either list?</p>
<p>cheers!</p> | 6,137 | [
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<p>I was wandering around the <a href="http://pdg.lbl.gov/2011/tables/rpp2011-sum-mesons.pdf" rel="nofollow">particle date group</a> page for meson and couldn't find a meson for top-bottom, which from symmetry you would expect. </p>
<p>Q1: Is this because it hasn't been found?
Q2: There is an underlying reason why it can't exist?</p> | 6,138 | [
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<p>The Lorentz force on a charged particle is perpendicular to the particle's velocity and the magnetic field it's moving through. This is obvious from the equation:</p>
<p>$$ \mathbf{F} = q\mathbf{v} \times \mathbf{B} $$</p>
<p>Is there an <em>intuitive</em> explanation for this behavior? Every explanation I've seen simply points at the equation and leaves it at that.</p>
<p>I can accept <em>mathematically</em> why $\mathbf{F}$ will be perpendicular to $\mathbf{v}$ and $\mathbf{B}$ (assuming the equation is correct, which it is of course). But that doesn't help me picture what's fundamentally going on.</p>
<p>Trying to create an analogy with common experiences seems useless; if I were running north through a west-flowing "field" of some sort, I wouldn't expect to suddenly go flying into the sky.</p>
<p>I'm hoping there's a way to visualize the reason for this behavior without a deep understanding of advanced theory. Unfortunately, my searching for an explanation makes it seem like something one just has to accept as bizarre until several more years of study.</p> | 6,139 | [
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<p>I am recently reading Xiao-Gang Wen's paper (http://dao.mit.edu/~wen/pub/edgere.pdf) on edge excitation for fractional quantum hall effect. On page 25, he claimed that it is easy to show that there exist a bijective correspondence between a symmetric polynomial and edge excitation of the fractional quantum hall droplet. As we all known that Laughlin state is a zero-energy eigenstate for Haldane pseudopotential. And it is easy to see that if a symmetric polynomial times the Laughlin wave function, then that increases the relative angular momentum for particles, thus that wave function is still a zero-energy eigenstate for Haldane pseudopotential. However, Wen claimed that the reverse also holds, but I am not quite convinced by his argument in his paper. Does anybody know how to rigorously show that the reverse is also true, that is every zero-energy eigenstate is of the form of a symmetric polynomial times the Laughlin wave function?</p> | 6,140 | [
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<p>In P.A.M. Dirac's <em>The Principles of Quantum Mechanics,</em> Chapter 10 (Observables), pp. 40, at the end of the chapter there is a proof that I don't understand at all.</p>
<p>Here is a pdf link to the book readable online: <a href="http://www.fulviofrisone.com/attachments/article/447/Principles%20of%20Quantum%20Mechanics%20-%20Dirac.pdf" rel="nofollow">http://www.fulviofrisone.com/attachments/article/447/Principles%20of%20Quantum%20Mechanics%20-%20Dirac.pdf</a></p>
<p>The proof in question is on pp. 50 using the pdf reader's numbering and on pp. 40 using the books original numbering. I'm curious about the part starting with "We can now see..." until the end of the chapter.</p>
<p>Would somebody be so kind to explain me what happens there? </p> | 6,141 | [
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<p>I'm trying to derive the equation for work done by a vibrating string, but I'm running into problems. The easiest way - the method used by the other question by this name - makes the approximation $\sin\theta\approx\tan\theta$, that is, the small angle approximation.</p>
<p>I'm fairly sure this doesn't reflect some underlying physical concept that changes the expression for high-amplitude high-frequency waves - for starters, I do have another derivation, but it makes the assumption without justification that $\frac{dK}{dx}=\frac{dU}{dx}$, $K$ kinetic energy and $U$ potential energy. So can anyone explain an alternate derivation, or else justify that assumption?</p> | 6,142 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/3158/why-quantum-entanglement-is-considered-to-be-active-link-between-particles">Why quantum entanglement is considered to be active link between particles?</a> </p>
</blockquote>
<p>I am a layman trying to read into quantum mechanics. As I understand it quantum entanglement is an experimentally proven mechanism by which the quantum state of two particles become 100% correlated, that is, measuring the quantum state of one object causes you to know the quantum state of its entangled particle with 100% certainty (they're opposite). </p>
<p>Where I don't understand is why this is used to imply that information is "traveling", faster than light or not. Where is the intuition coming from that the correlation between two separated particles has anything to do with one particle effecting the other? For me, a much stronger explanation for why these two particles are correlated is that the entanglement itself effects the particles, that is, upon becoming entangled their quantum states are individually governed by some formula (as a function of time alone) where those formulas produce exact opposite results for each particle. Separating the particles doesn't have to change the formula, so if you measure one you know the other just because they must be opposite.</p>
<p>Yet from what I've read it's taken for granted that quantum entanglement = information is traveling from one to the other. Do we have a reason for thinking that? Have we shown that we can definitely modify the quantum state of one particle and therefore change the quantum state of its entangled partner, or anything else to show that information is traveling? It's the old question of "causation vs. correlation." In principle, the concept of measurement itself modifying the Universe itself (beyond any observer effects) strikes me as somewhat silly.</p> | 61 | [
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<p>The following is the question from my school.</p>
<p><strong>A source emits sound uniformly in all directions. A radial line is drawn from this source. On this line, determine the positions of two points,
1.00m apart, such that the intensity level at one point is 2.00dB greater than the intensity level at the other.</strong></p>
<p>I have no idea what to do because I haven't met a question about determining the positions by dB.</p>
<p>How can I deal with this question?</p>
<p><em><strong>Thank you for your attention.</em></strong></p> | 6,143 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/937/how-does-gravity-escape-a-black-hole">How does gravity escape a black hole?</a> </p>
</blockquote>
<p>How can gravity get out of a black hole? If a black hole is so powerful that even light does not travel fast enough to get out, and gravity, or rather, gravitational waves, travel at the speed of light, how does gravity get out?</p>
<p>And please don't say that the black hole creates a "well" in space that other masses "slide" down. Such a well would be unstable and, if two black holes pass near each other, neither would be able to "slide" down the other since both are infinitely deep. These wells would make gravity selective.</p> | 215 | [
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<p>The below explanation why magnetism exists is superb in <a href="http://www.youtube.com/watch?v=1TKSfAkWWN0" rel="nofollow">this video</a>. The explanation about magnets is also great in <a href="http://www.youtube.com/watch?v=hFAOXdXZ5TM" rel="nofollow">this video</a>.</p>
<p>A magnet has atoms with unpaired electrons forming mini magnets. The crystals in the magnet align the atoms in the same direction. If you use a magnet you can align permanently the atoms in some iron ores (e.g. ferrite).</p>
<p>The plane of moving charges inside the magnet has many directions, that are approximately in the plane and perpendicular to the magnetic field lines. The magnet attracts or repels other magnet, with the same type of moving charges.</p>
<p><img src="http://www.umkcradres.org/Spec/RADPAGE/Magnet1.jpg" alt="magnetic_field"></p>
<p>I have a big question about this.</p>
<ol>
<li>Imagine a moving charge passing between 2 magnets with speed $\mathbf{v}$ orthogonal to the magnetic field $\mathbf{B}$. This generates a force $\mathbf{F}$ orthogonal to both.</li>
</ol>
<p><img src="http://www.school-for-champions.com/science/images/magnetism_lorentz__right_hand_rule.gif" alt="hand_rule"></p>
<ol>
<li>Imagine a magnet between 2 magnets. The average moving charges from a central magnet is approximately perpendicular to the line that links the 2 magnets.</li>
</ol>
<p><img src="http://ww2.valdosta.edu/~csparlor/magnets.jpg" alt="three magnets"></p>
<p><strong>Why are the $\mathbf{B}$ magnetic field lines perpendicular to the force $\mathbf{F}$ in situation 1, whereas they both are parallel in situation 2?</strong></p>
<p>I can see a path to a possible answer.</p>
<p>Wikipedia <a href="http://en.wikipedia.org/wiki/Force_between_magnets" rel="nofollow">states that</a></p>
<blockquote>
<p>The forces of attraction field of magnets are due to microscopic currents of electrically
charged electrons orbiting nuclei <strong>and the intrinsic magnetism of fundamental
particles</strong>. </p>
</blockquote>
<p>The <a href="http://van.physics.illinois.edu/qa/listing.php?id=17176" rel="nofollow">Ask Van physics FAQ at the University of Illinois website</a> says that</p>
<blockquote>
<p>a lot of the magnetism in ordinary permanent magnets comes from
this <strong>intrinsic spin</strong> magnetism of the electrons".</p>
</blockquote>
<p>Trying to explain spin, Wordpress blog <a href="http://quantummoxie.wordpress.com/2010/05/07/" rel="nofollow">Quantum Moxie</a> comments that </p>
<blockquote>
<p><strong>spin isn’t just angular momentum</strong>. [...] the total angular momentum of
an electron in an atom can be given by the sum of the orbital angular momentum
and the spin [...] the rotation of an electron ought to include rotation of its
electric field [...] As such, at the most fundamental level, <strong>magnetism is a purely
relativistic effect.</strong> [...] It is not clear that a intrinsic property exists
for magnetism (though some have conjectured spin fits the bill, but it
depends on how we interpret spin!).</p>
</blockquote>
<p>I would be grateful for simple and intuitive explanations that do not depend on formulas.</p> | 6,144 | [
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<p>Fission divides one Helium atom into two Hydrogen (Deuterium) atoms. And fusion, once again, puts together those two Hydrogen atoms into one Helium atom. In both reactions, overall output energy is enormous.</p>
<p>$ \begin{array}{rcrclclrl}
\text{1 Neutron} & + & {}_2^4He & \to & {}_1^1H + {}_1^1H & + & \text{Energy} + \text{3 Neutrons} & \dots & (I) \\
\text{2 Neutrons} & + & {}_1^1H + {}_1^1H & \to & {}_1^2H + {}_1^2H &&(somehow) & \dots & (II) \\
\text{Energy} & + & {}_1^2H + {}_1^2H & \to & {}_2^4He & + & \text{Big Energy} & \dots & (III) \\
\end{array}
$</p>
<p>I don't know whether the reaction $(II)$ is possible with today's technology, or not. Neither I know if it is endothermic or exothermic. But, if we could realize it, would it be possible to generate infinite energy by looping these three reactions forever successively in the given order?</p>
<p>I intuitively feel that the answer is "no", but I need an explanation on why it is not possible.</p> | 6,145 | [
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<p>I think it's about time for me to ask this question, as I've been contemplating this for a while.</p>
<p>$$E = mc^2.$$</p>
<p>This is Einstein's most famous equation. But what does it mean?</p>
<p>On my own, I had to think a lot about it, since no one in my close surroundings can give me good answers. </p>
<p>To me it means that the energy contained inside an object is proportional to the mass. Thus mass is energy.</p>
<p>And if that object gets <strong>annihilated</strong> then its mass will be converted back into pure energy, such as light.</p>
<p>Isn't that what happens when Antimatter collides with our ordinary matter? The masses cancel out and they turn into light (photons)?</p>
<p>Here is a little fun I had last year in my Grade 9 Science class.</p>
<pre><code>100g of H.
100g of anti-H.
They collide, and their masses, convert into energy. E = mc^2.
E = (100)*((299792458)^2);
E = 8.987551788E18 joules.
</code></pre>
<p>So that's the amount of energy produced. </p>
<p>Is this correct? Did I use the wrong equation? What else can E=mc^2 be used for.
If this is correct, boy that's a lot of energy contained in a hundred grams of Hydrogen.</p> | 6,146 | [
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<p>In Morii, Lim, Mukherjee, <i>The Physics of the Standard Model and Beyond.</i> 2004, ch. 8, they claim that the Peskin–Takeuchi oblique parameters <i>S, T</i> and <i>U</i> are in fact Wilson coefficients of certain dimension-6 operators. On page 212, they claim that the <i>T</i> parameter is described by
$$O_T=(\phi^\dagger D_\mu \phi)\phi^\dagger D^\mu \phi)-\frac{1}{3}(\phi^\dagger D_\mu D^\mu\phi)(\phi^\dagger\phi)\,,$$
and the <i>S</i> parameter by
$$O_S=[\phi^\dagger(F_{\mu\nu}^i\sigma^i)\phi]B^{\mu\nu}\,,$$
where $\phi$ is the Higgs doublet, $F_{\mu\nu}^i$ and $\sigma^i$ are the SU(2) weak isospin field strength and sigma matrices respectively, and $B^{\mu\nu}$ is the U(1) weak hypercharge field strength.</p>
<p>On the next page (p. 213), problem <b>8.6</b> asks us to show that these are the operators.</p>
<p>How do I precisely show that these higher-dimension operators give precisely the Peskin-Takeuchi parameters?</p> | 6,147 | [
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<p>I'm currently reading an online article, and below is a quote from that article:</p>
<blockquote>
<p>The thermodynamic entropy to change $n$ memory cells within $m$ states is $ΔS=k_B\ln(m^n)$, where $k_B$ is the Boltzmann constant. From the second law of thermodynamics, $ΔS=\dfrac{ΔQ}{T}$, where $ΔQ$ is the energy spent and $T$ is the temperature. So the energy required to write information into one binary memory bit is $E_{bit}= k_BT \ln2$.</p>
</blockquote>
<p>But from what I've learned, $Q$ is heat transfer, not 'energy spent'. Why is it possible to use those 2 interchangeably, if it's possible?</p> | 6,148 | [
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<p>A gauge field is introduced in the theory to preserve local gauge invariance. And this field (matrix) is expanded in terms of the generators, which is possible because the gauge field is traceless hermitian. </p>
<p>Now why did we choose it as traceless Hermitian? What was the insight behind the choice that made us expand it in terms of the generators? I read somewhere that 'the gauge field belongs to the Lie algebra' and I tried to follow it up, but I can't make any sense out of what I read. Can anybody explain in clear, intuitive terms?</p> | 6,149 | [
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<p>This is a practice Physics Subject GRE problem.</p>
<blockquote>
<p>A parallel-plate capacitor has plate separation $d$. The space between the plates is empty. A battery supplying voltage $V_0$ is connected across the capacitor, resulting in electromagnetic energy $U_0$ stored in the capacitor. A dielectric, of dielectric constant <em>k</em>, is inserted so that it just fills the space between the plates. If the battery is still connected, what are the electric field $E$ and the energy $U$ stored in the dielectric, in terms of $V_0$ and $U_0$?</p>
</blockquote>
<p>I was able to figure out $E$ fairly easily. Since the voltage stays the same (by virtue of it being connected to a battery), $E = V/d$. I am having difficult understanding why the answer for $U$ is what it is though. The answer is $U = k^2U_0$. What equation(s) would give this result? I know $W = \frac{1}{2}VQ$, and with $V$ staying the same $Q$ must be the variable being multiplied by $k^2$. But $Q = CV$ so $C$ should also be increasing as $k^2$ but for a parallel plate capacitor $C$ only increases by a single $k$ when inserting a dielectric. How to resolve this discrepancy, or what am I missing?</p> | 6,150 | [
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<p>I suspect a valid scientific, physics answer for this question, because I'd venture that train, insurance companies would've calculated and contemplated this question. </p>
<p>Yet the train headlights at <a href="http://www.youtube.com/watch?v=0TY9Kdj5PJI" rel="nofollow">http://www.youtube.com/watch?v=0TY9Kdj5PJI</a> don't appear to brighten/illuminate sufficiently far ahead. If an obstacle or hindrance were in front, then wouldn't the limited range of the headlights prevent a safe stop? </p>
<p>Also, as can be seen at the 8:15 mark, the train's lights don't corner or turn together with the train. Why not? Wouldn't they befit and help such a train?</p>
<p>Shouldn't such heavy, menacing trains be equipped with headlights of the 'lumens' resembling <a href="http://www.youtube.com/watch?v=jPKy1KAz8OM" rel="nofollow">http://www.youtube.com/watch?v=jPKy1KAz8OM</a> and <a href="http://www.youtube.com/watch?v=bWS30yHBuLQ" rel="nofollow">http://www.youtube.com/watch?v=bWS30yHBuLQ</a> <em>(same car and driver)</em>, how gleaming so ever it is for a car?</p> | 6,151 | [
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<p>can we by any means amplify magnetic signal as we can with electric signal. As both electric and magnetic field can be represented in the form of a wave the analogy seems to be natural. </p>
<p>I want the input and output as magnetic signal. </p> | 6,152 | [
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<p>This question is in reference to the paper,
<a href="http://arxiv.org/abs/1301.7182" rel="nofollow">http://arxiv.org/abs/1301.7182</a></p>
<ul>
<li><p>What exactly is the argument being made on page 6 and 7? </p>
<p>One deduces that the function $\Delta$ has to be such that, $\Delta^2(k,\tau) = \Delta^2(\frac{k}{\lambda ^{\frac{4}{n+3}}}, \lambda \tau )$. Now from this how does this follow that, the following holds, </p>
<p>$\Delta^2(k,\tau) = \Delta^2(\frac{k}{k_{NL}})$ where $k_{NL}^{n+3} \propto \tau ^{-4} $</p>
<p>?</p></li>
<li><p>How does 2.26 follow from 2.2? </p>
<p>In 2.2 aren't all the $c_{*}^2$s dimensionless? </p></li>
</ul> | 6,153 | [
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<p>I wonder if someone could help clarify waveguiding with broadband, incoherent light please.</p>
<p>If we take a telecomms fiber, which is single-moded above ~1.4 μm and couple a laser beam in, we assume this excites the only mode, which is the fundamental mode. The mode-field diameter of the transverse mode is determined by the core radius and wavelength of light. I assume laser light here is coherent.</p>
<p>But what happens if you couple light in from a broadband incoherent source (e.g. an incandescent bulb with spectrum from 1.5-3 μm)?. Can you say that a single mode will be excited containing all wavelengths from 1.5 to 3 μm? And what about if the spectrum extends from 1 to 3 μm - will there be multiple modes excited, since 1.4 μm is the cut-off for single mode behavior? Or is this picture invalid since the light is incoherent?</p> | 6,154 | [
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<p>I want to learn physics and the math required, but I never got the chance to learn properly in school due to mental illness. But, now, as a 22 year old, I wish I can start learning. Attending a college is not an option as I do not think I would find one that is willing to provide the psychological support a person suffering from psychotic depression/schizoaffective disorder needs in my city in India. Anyway, so I think I should start learning from resources online and by buying some (not too expensive) books. The problem is I'm not very good at math, as my knowledge of basics and foundation is very weak, probably worse than middle school level. Though I can probably do basic algebra, I'm not even sure I know what set theory is. My trigonometry and geometry is poor also and I doubt I would be able to do even simple problems. Physics is the same. So I really want something that will help me build my knowledge from ground up, as I now have an genuine interest in learning the subject. What got me interested was reading Stephen Hawking's Brief History of Time and some topics on quantum mechanics. So I want to learn now to be able to comprehend such stuff someday. So please recommend good resources/books I can use to start from VERY basic level, as most similar questions and discussions elsewhere that I found were asking for resources for the high school level and up. Also, it would be nice if the books were very interesting and not dry, maybe like Bill Bryson or how Cecil Adams would do it.</p>
<p>Edit with regards to Qmechanic's setting the question as duplicate: The resources mentioned in the other question do not seem to me to be aimed at a very basic level of math and physics (starting from middle school level, so to speak.) and they appear to be aimed at those who possibly have some well-to-do knowledge of at least the basics or the foundation, unlike what I asked for. However, I could be wrong, but their question does mention 'high-school level'.</p> | 98 | [
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<p>How to prove that $\ln(Z(J))$ generates only<a href="http://en.wikipedia.org/wiki/Feynman_diagram#Connected_diagrams%3a_linked-cluster_theorem" rel="nofollow"> connected Feynman diagrams</a>? I can't find the proof of this statement, and have only met its demonstrations for case of 2- and 4-point.</p> | 6,155 | [
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<p>It is known that 3D Chern-Simons(C-S) theory has no explicit metric involving in the Lagrangian density: </p>
<p>$$
A \wedge dA + (2/3) A \wedge A \wedge A
$$</p>
<p>while the 4D Yang-Mills(Y-M) theory has the metric $g_{\mu\nu}$involves.</p>
<p>$$
F \wedge *F= (dA + A \wedge A) \wedge *(dA + A \wedge A)
$$
More explicitly, for Abelian case, </p>
<p>C-S gives the form without the metric(topological),
$$d^3 x \epsilon^{\mu\nu\rho} A_\mu \partial_\nu A_\rho$$</p>
<p>Y-M gives the form with the metric:</p>
<p>$$d^4 x (\partial_\mu A_\nu)( \partial^\mu A^\nu)=d^4 xg^{\mu\rho}g^{\nu\lambda}(\partial_\mu A_\nu)( \partial^\nu A^\lambda)$$</p>
<p>How about the statement of coordinate invariance of C-S and Y-M theory? <strong>Are C-S or Y-M coordinate invariance? (i.e. does the Lagrangian density look different in other coordinates, such as cylindrical, spherical coordinates? or general curved coordinates? how does that Lagrangian look like in those generic coordinates?)</strong></p>
<p>Is there some relations (if, only if or iff) between: </p>
<p>(1) <strong>gauge invariance</strong>; </p>
<p>(2) <strong>coordinate invariance</strong>; </p>
<p>(3) <strong>metric independence</strong> (=diffeomorphism invariance?); </p>
<p>(4) <strong>covariant form in curved background</strong>?</p>
<p>for those gauge theories (e.g. Y-M) or for topological field theory (e.g. C-S)?</p>
<p>ps. see also <a href="http://physics.stackexchange.com/questions/56598/">this post</a>, which unfortunately does not directly answer my inquiries yet. Thanks.</p> | 6,156 | [
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<p>If I'm in Chile, Santiago, what is the best time of the year to see the star <a href="http://en.wikipedia.org/wiki/Alpha_Centauri" rel="nofollow">Alpha Centauri</a> at the beginning of the night? </p> | 6,157 | [
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<p>120 volts x 20 amps = 2,400 Watts </p>
<p>However, if I increased the voltage and lowered the current, you can also use a smaller wire size (more inexpensive), also have less heat and achieve the same watt Power.</p>
<p>1,000 volts x 2.4 amps = 2,400 Watts</p>
<ol>
<li>Why doesn't it heat up like current?</li>
<li>To me this approach seems more efficient and less costly because you don't use as much material, so why isn't this common?</li>
</ol> | 6,158 | [
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<p>Now that scientists found the primordial gravitational waves that formed shortly after the big bang,and we all now that just after the bang the 4 fundamental forces were unified can we consider that these waves are the strings that we're looking for,that unify again these forces?</p> | 6,159 | [
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<p>Is there a simple method of determining, given a UTC date/time, whether it is day or night at a given lat/long coordinate?</p>
<p>I am currently using a formula based on a <a href="http://williams.best.vwh.net/sunrise_sunset_algorithm.htm" rel="nofollow">Sunrise/Sunset Algorithm from the US Naval Observatory</a>, but unfortunately I am having trouble applying to arrive at a simple night/day indicator.</p>
<p>Should I build upon this formula or is there some more efficient way of doing this that I am missing?</p>
<p><em>Disclaimer: I am a programmer, not an astronomer, so I find the formulas for astronomical calculations a bit confusing.</em></p>
<p><em>Extra stuff: Ideally I would like to artificially shorten the period of "night" by two hours, for the purposes of eliminating some false positives from sensor data that occurs during twilight/dawn. In other words, if sunset occurs at 7 pm at a given location, I would like the option of padding the value by 60 minutes such that the output remains "day" until 8 pm for that location. (And apply the same padding prior to sunrise.)</em></p>
<p><strong>Update:</strong></p>
<p>I wound up calculating the sun's altitude for the location using a UTC timestamp and the location's lat/long coordinates. Using figures for various twilight amounts (6, 12, 18 or degrees below horizon) I am able to automatically select the portion of "night" that is sufficiently dark. (e.g. 6 degrees below horizon is not as dark as 12 degrees.) This approach was much easier than attempting to determine sunrise and sunset times for the locale's time zone (and all of the associated time zone headaches).</p> | 6,160 | [
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<p>I'm at about 40deg north so, assuming a clear southern horizon, I can't see things below about -30 or so (I actually don't know how far south). I also have a large portion that is circumpolar so it's always visible. I assume there's an equal size area south that is never visible.</p>
<p>On an equinox, the average night, I have less than 12 hours of darkness, but as the Earth rotates some stars will set and other rise, so I'm guessing something approximating 70% of the sky will be visible west to east.</p>
<p>So, how much of the sky is actually visible on a typical night?</p> | 6,161 | [
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<p>I would like to have some examples of classical systems with "strong" coupling coefficient (in their action term). Specifically, I am looking for intermediate or cross-over ranges of coupling (~$\mathcal O(1) $), where it is neither possible to describe them by effective (composite) field theories with small coupling (like hadron model for QCD) nor possible to do perturbation.
[A related question - <a href="http://physics.stackexchange.com/questions/72387/can-classical-systems-exhibit-strong-coupling">"Can classical systems exhibit strong coupling?"</a> - had been asked here sometime back, where a few systems (dusty plasma, turbulence, granular materials etc) were mentioned. But I dont know if those systems are what I am looking for]</p>
<p>Related question:
I would like to have some examples of classical systems with negative <a href="http://en.wikipedia.org/wiki/Beta_function_%28physics%29" rel="nofollow">beta function</a> ie. coupling increases towards IR.</p> | 6,162 | [
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<ol>
<li><p>Is it me who have a poor understanding, or does all matter have to become 'pure energy' in order to achieve speed-of-light speed? </p></li>
<li><p>If so, does that mean that no material can achieve the speed of light and remain in its original state of matter?</p></li>
</ol> | 6,163 | [
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<p>Is there any realistic, understandable, provable (even in some extent) explanation/model for the extent of the universe?
What is its shape? and Why? I mean physical explanations not philosophical since the question is about a physical entity, the universe.
When I try to think about this it is almost I cannot think at all!</p>
<p>note I am almost satisfied that there is no answer for this single question! I paid attention to all comments and spent time for watching the video-lectures recommended (I don't recommend) just to seek the answer, however, I got nothing about the question at all. The discussion and lectures are mathematical games far being physical to me. I respect all the science involved in cosmology but for this question even great researcher (some got Nobel prize recently) have nothing to say except playing with formulas and graphs. I was looking for physical meaning.</p>
<p>I lost my interest in this question.</p> | 6,164 | [
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<p>When you place a water or food in a microwave oven, it heats.
Which process commits more energy to that: <a href="http://en.wikipedia.org/wiki/Dielectric_heating">dielectric heating</a>, or ion drag i.e. <a href="http://en.wikipedia.org/wiki/Joule_heating">resistive heating</a>?</p>
<p>AFAIK, in distilled water (which is a dielectric) dielectric heating is close to 100%.</p>
<p>What about regular (non-distilled) water? Mineral water? Sea water? Salty & wet food?</p>
<p>Is dielectric heating still gives more energy to the water/food then the resistive heating i.e. ion drag?</p> | 6,165 | [
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<p>In what relation is the energy input in an alternating current circuit to its frequency?</p>
<p>I'd guess I have to compute something like</p>
<p>$$E=\int P(\omega,t) dt=\int U(\omega,t) I(\omega,t) dt, $$</p>
<p>but if say </p>
<p>$$U(\omega,t)\propto\sin{(\omega t)},$$</p>
<p>then it seems part of the integral is $\propto\frac{1}{\omega}$, while I would expect the energy to <em>grow</em> with $\omega$.</p> | 6,166 | [
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] |
<p>Who first determined the structure of water (two hydrogen atoms stuck to an oxygen atom at approx 105 degrees), and, more importantly, how was this done? </p> | 6,167 | [
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<p>Recently in our area there has been a large forest fire and I've been looking into home defense from such things.</p>
<p>I am not a physicist - but can do some basic math.</p>
<p>I was wondering how I could calculate if a 'evaporative mister' type system could be used for such to reduce the ambient air temp to stop the house catching fire (dont care about cosmetic damage).</p>
<p>The goal would probably be to reduce temperature of air/surfaces of the house by approx 1000F to keep them below combustible temperatures.</p>
<p>The area is very low humidity between 4% to maybe 15% during wildfire season.</p>
<p>How can I calculate how much water/mist I need to put into the air to reduce temperature below 400F.</p>
<p>Very rough simplest equations are fine - I know its not an exact science when dealing with wildfires.</p>
<p>I found this formula on wiki but I don't know how to adapt it to use it to calculate water need for a temp drop of </p>
<pre><code>TLA = TDB – ((TDB – TWB) x E)
TLA = Leaving Air Temp
TDB = Dry Bulb Temp
TWB = Wet Bulb Temp
E = Efficiency of the evaporative media.
</code></pre>
<p>Anything I forgot/missing - be appreciated to know.</p>
<p>Some restrictions/thoughts I had</p>
<ol>
<li>The roof would need to stay generally wet light continuous layer of water</li>
<li>Misting/irrigation could not use more then 12 gallons per minute (max well output)</li>
<li>Be nice to second use the misting system for outdoor aircon on off time (ie 20% capacity)</li>
<li>Windows/glass would need some of IR shielding to stop ignition of furniture inside the house.</li>
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<p>There are multiple theories about time traveling. One is "proven": The time slows down according to your speed. The satellites in space are traveling faster than us, thus their clocks slows down a bit. So by traveling at the speed of light, you would travel without the time. So the time stops when you are traveling with the speed of light. Then you would travel forwards in time, because when you slow down, the time around you will have gone in the "regular" speed, while being still in your time.</p>
<p>Another completely "inverse" theory by Einstein is that extra dimension. The space time. So if you make a wormhole, you would be able to travel past the "bends" in the space time, thus traveling faster than the light. If you arrive before the light, then you would have traveled back in time.</p>
<p>I also want to point out that some physicists have managed to send messages back in time with the help of photons, even though we are only talking about microseconds. (I just saw an interview on Discovery Channel..)</p>
<p>Which of these (or both) is generally believed to be true, if any? And what about the paradoxes? Do you know any paradoxes regarding this? Maybe you are able to solve them? (One I've found is that if you travel into the future and grab a product that you start selling in the presence, the product will be in the future because you got it while time traveling. Who did make the product in the first place?</p>
<p>I'm mostly interested in the paradoxes created while time traveling.</p> | 6,169 | [
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<p>An astronaut camps on the moon for a period of one month as per the earth’s calendar.
What would be the path of the earth seen by the astronaut in the lunar sky?</p>
<p>(A) The earth remains approximately at a fixed altitude and direction.</p>
<p>(B) The earth completes one revolution parallel to the lunar horizon in one month.</p>
<p>(C) The earth completes one revolution from east (direction of rising sun) to west (direction of setting sun) in one month.</p>
<p>(D) The earth completes one circle around the Pole Star in one month but never
goes below the horizon.</p> | 6,170 | [
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<p>I want a different proof of 6 degrees of freedom of a solid object made of $\ N$ particles. I am thinking along these lines:</p>
<p>Definition of rigid body is</p>
<p>$\ modulus[\vec{r_i}-\vec{r_j}]=constant \ \forall\ i,j$</p>
<p>This gives me $\ ^NC_2$ constraints. There exist in total $\ 3N$ equations. So the number of free variables should be $\ n= 3N- \ \ ^NC_2=\frac{N(5-N)}{2}$ Which is clearly not the answer as $\ n$ is $\ N$ dependent, but it should be $\ 6$.</p>
<p><strong>What I want to do is show that :</strong> </p>
<p>$$\ number\ of\ constraints \ actually\ required= 3N-6$$</p>
<p>which is the correct answer since I know $\ n=6$</p>
<p><em>I am aware of the proof given in Goldstein, Rana Joag etc. What I am asking is how to do it following this approach.</em> </p> | 6,171 | [
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<p>Is this proof of spin-statistics theorem correct?</p>
<p><a href="http://bolvan.ph.utexas.edu/~vadim/classes/2008f.homeworks/spinstat.pdf" rel="nofollow">http://bolvan.ph.utexas.edu/~vadim/classes/2008f.homeworks/spinstat.pdf</a></p>
<p>This proof is probably a simplified version of Weinberg's proof.
What is the difference?</p>
<p>What is the physical meaning of $J^{+}$ and $J^{-}$ non-hermitian operators?</p>
<p>I'm especially interested in the beginnig of proof of second lemma. How to get this:
\begin{eqnarray}
F_{AB}(-p^{\mu}) = F_{AB}(p^{\mu})\times (-1)^{2j_{A}^{+}} (-1)^{2j_{B}^{+}} \\ \nonumber
H_{AB}(-p^{\mu}) = H_{AB}(p^{\mu})\times (-1)^{2j_{A}^{+}} (-1)^{2j_{B}^{+}}
\end{eqnarray}</p>
<p>Also why under CPT field transform as
\begin{eqnarray}
\phi_{A}(x)\rightarrow \phi_{A}^{\dagger}(-x) \times (-1)^{2J_{A}^{-}} \\ \nonumber
\phi_{A}^{\dagger}(x) \rightarrow \phi_{A}(-x) \times (-1)^{2J_{A}^{+}}
\end{eqnarray}
conjugation is from charge reversal, - from space inversion and time reversal.
What about $(-1)^{2J_{A}^{-}}$?</p>
<p>Where can I find similar proofs?</p> | 767 | [
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<p>For example, the radiation dominated cosmology, the energy density of radiation is propotional to $a^{-4}$ and
the volume is propotional to $a^3$, where $a$ is the scale factor. So the total energy of radiation is propotional to $a^{-1}$. So where is the loss of energy of radiation? Is the gravitational field has the energy?
Does $\nabla_aT^{ab}=0$ represent the conservation of energy and momentum of matter field in GR?</p> | 6,172 | [
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<ol>
<li><p>What is the mass of a photon moving at the speed of light? </p></li>
<li><p>And if it does not have mass, how is it affected by gravity?</p></li>
<li><p>Also why does Einstein's general relativity support that a gravitational wave must travel at the speed of light?</p></li>
</ol>
<p>I'm just an A-level student. So, I would appreciate it if you could explain it as idiotically as possible.</p> | 195 | [
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<p>I've been exploring techniques in statistical physics, specifically applying them to spin ices. I'm in the canonical ensemble. By using the fluctuation dissipation theorem you can extract useful properties from the variance in energy and magnetization such as the heat capacity (constant V) and magnetic susceptibility respectively.</p>
<p>I've included the formulas I'm using below:
\begin{align}
C_V & = \frac{\partial\langle E \rangle}{\partial T} \\
& = -\frac{\beta}{T} \frac{\partial\langle E \rangle}{\partial\beta} \\
& = \frac{\beta}{T} \frac{\partial^2\ln Z}{\partial\beta^2} \\
& = \frac{\beta}{T} \frac{\partial}{\partial\beta}\left(\frac{1}{Z} \frac{\partial Z}{\partial\beta}\right) \\
& = \frac{\beta}{T} \left[\frac{1}{Z} \frac{\partial^2Z}{\partial\beta^2} - \frac{1}{Z^2} \left(\frac{\partial Z}{\partial\beta}\right)^2\right] \\
& = \frac{\beta}{T} \left[\langle E^2 \rangle - \langle E \rangle^2\right], \\
\chi & = \frac{\partial\langle M \rangle}{\partial H} \\
& = \beta \left[\langle M^2 \rangle - \langle M \rangle^2\right].
\end{align}</p>
<p>Now for my question, is there another computable statistical property which acts as the error for the variance? Such that I can get errors for the heat capacity and susceptibility.</p> | 6,173 | [
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<p>I'm writing a novel and I'm quite confused if this system could be possible in the real universe. Is it possible that a system exist, where 5 identical planets which could be of same characteristics (Inclination, speed, planetary mass and others) revolve around a single star. Also, What effects would the 5 planets undergo if they are so close? (including the climatic changes and the gravitational, magnetosphere interference.)</p> | 6,174 | [
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<p>I am answering some exercises in thermodynamics, and I am still in trouble with some values and constants.
In the exercise, it is given: $\mu_\text{air}=1.8\cdot10^{-5}~\text{kg/m s}$. What for is this value used? In the case, I need to find some tensions in given points, and I know the speed profile of the air.</p>
<p>Other question: As I need the tension in some points, and it is about air, is it the same thing as pressure?</p> | 6,175 | [
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<p>I have two masses connected by a spring. They are horizontal and are not affected by friction or gravity.</p>
<p><img src="http://i.stack.imgur.com/S34Hs.png" alt="Mass Spring System"></p>
<p>The spring's stiffness constant is $k$, and $x_1$ and $x_2$ are the displacements of the masses from their equilibrium positions.</p>
<p>The system is set in motion when $m_1$ is kept in its equilibrium position and $m_2$ is displaced distance $a$ to the right. </p>
<p>I'm trying to figure out the forces on each mass. So far I have </p>
<p>$$m_1 \ddot x_1 = km_2x_2$$</p>
<p>$$m_2 \ddot x_2 = -km_1x_1$$</p>
<p>Is this at all correct? I also need to write it in matrix form.</p> | 216 | [
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<p>This is a sequel to <a href="http://physics.stackexchange.com/q/24188/2451">this</a> question.</p>
<p>Who knows a difference between the Lagrangian in <a href="http://en.wikipedia.org/wiki/Special_relativity" rel="nofollow">SR</a> and <a href="http://en.wikipedia.org/wiki/General_relativity" rel="nofollow">GR</a> for a weak gravitational field in non-relativistic case? What is the reason of this difference?</p> | 6,176 | [
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<p>This is what my textbook says about the Michelson-Morley experiment:</p>
<p>"This invariance of the speed of light between inertial reference frames means that there must be some relativity principle that applies to electromagnetism as well as to mechanics. That principle cannot be Newtonian relativity, which implies the dependence of the speed of light on the relative motion of the source and observer."</p>
<p>Question: Why must there be a relativity principle that applies to electromagnetism and to mechanics? Why can't they be separate? </p> | 6,177 | [
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<p>All of the sources I have found for this online have been wildly unclear. Many use the phrase "Fermi energy" to refer to the "Fermi <em>level</em>" (which is emphatically <em>not</em> what I'm looking for; I want the Fermi energy as defined in this Wikipedia article: <a href="http://en.wikipedia.org/wiki/Fermi_energy" rel="nofollow">http://en.wikipedia.org/wiki/Fermi_energy</a> ). Fermi energy is always greater than zero.</p>
<p>Has anyone ever measured the Fermi energy of graphene? Is there any way to calculate it from known quantities, such as the Fermi velocity, which is approx. $10^6$ m/s? i.e. is there a reason why the usual formula $E_F = \tfrac{1}{2}m_e v_F^2$ wouldn't work here? I read that the Fermi energy for undoped graphene is equal to the energy at the Dirac points, but I read elsewhere that that value is less than zero, which makes no sense because, again, Fermi energy is always greater than zero.</p> | 6,178 | [
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<p>is such a <em>tensor</em>, $T_{\alpha\beta\, \gamma}$, possible such that
$$T_{\alpha\beta\, \gamma}=T_{\beta\alpha\, \gamma}=-T_{\alpha\gamma\, \beta}=-T_{\gamma\beta\, \alpha}$$
That is, symmetric under two indices, but antisymmetric under the third with the previous too. If so can it be build up by a linear combination and "multiplication" of 4-vectors?</p>
<p>Thanks,</p> | 6,179 | [
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<p><img src="http://i.stack.imgur.com/twSPw.jpg" alt="enter image description here"></p>
<p>For part (a), is the normal force by the hinge on the bridge at an angle or is it horizontal?</p>
<p>For part (b), I know how to resolve forces horizontally and vertically, and to take torques about the hinge, but the information is still insufficient for me to figure out what the tension force is.</p>
<p>Any help would be much appreciated!</p> | 6,180 | [
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<p>In Green-Schwarz-Witten Volume 2, chapter 15, it is argued (roughly) that we need 6-dimensional manifolds of $SU(3)$ holonomy in order to receive 1 covariantly constant spinor field. And it turns out that <a href="http://en.wikipedia.org/wiki/Calabi%E2%80%93Yau_manifold" rel="nofollow">Calabi Yau manifolds</a> satisfy this property.</p>
<p>Now I understand this reasoning just fine, but I occasionally find in some papers, that Calabi Yau manifolds are "demanded" based on the fact that the sum of all $U(1)$ charges sums to 0? Could someone enlighten me on why this yields the Calabi Yau condition?</p> | 6,181 | [
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<p>By an ideal conductor, I mean one with zero resistance. Inside an ideal conductor with no current, the electric field is zero, but is the electric field still zero with the ideal conductor carrying a current?</p> | 6,182 | [
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<p>You are given a long length W of copper wire. How would you arrange it to obtain the maximum self-inductance? Why?</p>
<p>I am trying to use the equation</p>
<p>$$L=\mu_o n^2 l A$$</p>
<p>I try to solve it using a fixed length wire of 10 units, width 1mm and winding it into a solenoid. I plug in values of circumference 10, 5, 2.5 and finding the inductance through number crunching. However, I am getting a larger values for multiple loops but the answer is a single loop (ie. a circle) rather then a solenoid.</p>
<p>Here are the sample values I got:</p>
<p>$n=1; C=10; r=1.59; L=0.079 \mu_o$</p>
<p>$n=2; C=5; r=0.79; L=0.156\mu_o$</p>
<p>$n=4; C=2.5; r=0.3978; L=0.318\mu_o$</p>
<p>If anyone could enlighten me on the proper way of solving this, I'd appreciate it.</p> | 6,183 | [
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<p>We have a simple circuit given, a resistor $R_x$ and a fixed current source with $I = 50 \, \mathrm{\mu A}$. Now over the resistor there is a currentmeter which has an internal resistance. In any case some of the current will go through the currentmeter and therefore the result will be slightly off.</p>
<p>The question asks us to rearrange that circuit so that no measurement error is made. We can use additional parts like a power source or a resistor with variable resistance or anything else.</p>
<p>Is there some way to do this other than using a currentmeter with a higher internal resistance?</p> | 6,184 | [
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<p>I'm trying to understand the Blasius boundary layer solution, but I'm having some difficulties. Using wikipedia, I wonder how they get the first formula: <a href="http://en.wikipedia.org/wiki/Blasius_boundary_layer" rel="nofollow">http://en.wikipedia.org/wiki/Blasius_boundary_layer</a>. $$\frac{U^2}{L}\approx\nu \frac{U^2}{\delta^2}$$
And how they get to the fourth formula: $$\delta(x) \approx \sqrt{\frac{\nu x}{U}}$$
I feel that those formulas are correlated somehow, but I don't really see how they derive those. I hope someone can help.</p> | 6,185 | [
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<p>It's usually said that black umbrellas are best against sun, since black absorbs most of the radiation . The common umbrellas in market(atleast in India) are painted black outside and silvery inside. </p>
<p>However I think the reverse(silvery outside, black inside) should be more effective. The outer color(silvery) will reflect most of radiation, while the black color inside will absorb anything passing through outer layer.</p>
<p>Now my questions are :</p>
<pre><code> 1. Which color scheme is more effective ?
2. What is the logic behind the common (black-outside, silvery-inside) scheme ?
</code></pre> | 6,186 | [
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<p>I am confused with physical picture about unpolarized light.</p>
<p>Is unpolarized light very fast rotating polarized light? or co-existing state of two orthogonal polarization? (or something else?)</p>
<p>If there is a linear polarizer which rotates very very fast and randomly (the polarizer in imagine), the output light is same to unpolarized light? I don't think so but I am not sure.</p>
<p>--</p>
<p>or, instead of linear polarizer, <em>a Faraday rotator with magnetic field whose amplitude is randomly chnaged</em> can be considered, I think. </p> | 6,187 | [
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<p>How will act low pressure container, or what would happen inside the low pressure container when it is placed inside the container with high pressure?</p>
<p>And if it is high pressure container inside the high pressure container?
Will the container which is inside stay in the centre?</p> | 6,188 | [
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<p>In high school we are taught that magnetic field perpendicular to velocity of an charged particle experience perpendicular force that causes it to move in circular path by relation
$$qvB=\frac{mv^2}{r}$$ but in drawbacks of Bohr's theory it was proposed that accelerated charged electron orbiting along nucleus will immediately loose energy in form of electromagnetic waves and collapse into nucleus.So My question basically is are we taught wrong about this relation that charged particle according to Lorenz's force will perform circular motion as far as required conditions in equations are provided but will it eventually loose energy in form of electromagnetic radiation and halt it's circular orbit ? </p> | 6,189 | [
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<p>we are doing K space calculation(transnational invariant basis) of Hamiltonian, and trying to compare with exact method for same nos of sites and particles, we are getting big difference in ground state energy. Is it coming because of Hamiltonian is complex in K-space calculation and real in exact calculations.I am using complex(ZHEEVR),real(DSYEV) these Lapack subroutines....</p> | 6,190 | [
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<ul>
<li><p>Broadly I would like to understand what is the difference in the physical interpretation of a (Euclideanized) QFT which is on space-time $S^d$ and which is on a space-time $S^{d-1}\times S^1$. </p>
<p>In the later case I am comfortable thinking of it as being a theory actually on a Lorentzian space-time where the spatial manifold is $S^{d-1}$ but the theory is heated to a temperature equal to the circumference of the $S^1$ factor. But for the first case what is the interpretation? </p></li>
<li><p>Specifically consider the action of a conformally coupled Euclidean scalar on $S^d$ space-time as, $S = \frac{1}{2} \int_{S^d} d^dx \sqrt{G} \left [ (\nabla \phi )^2 + \frac{d-2 }{4(d-1) }R \phi^2 \right ]$. (where $R$ on $S_d$ is $\frac{d(d-1) }{a^2 }$)</p>
<p>Knowing this is it obvious as to how to write down the action for the same conformally coupled scalar theory on a spatial $S^{d-1}$ at a finite temperature? </p></li>
</ul> | 6,191 | [
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