question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>What's the proof of the light polarization that it happens to the electric field and not the magnetic field? How did Malus discover that the light is polarized although he didn't see the waves polarizing!</p> | g440 | [
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<p>If the magnetic field doesn't polarize does it follow the electric field path of propagation? or does it vanish?</p> | g440 | [
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<p>Why is the strength of a field (i.e. gravitational or electric) inversely correlated to the square of the radius?</p>
<p>It is clear to me why the further you get a way from a field, the field's enacted force decreases. However, this makes me hypothesize that the relationship should be:</p>
<p>$$F ~=~ k/r$$ </p>
<p>However, it is in fact:</p>
<p>$$F ~=~ k/r^2$$</p>
<p>Is this related to the fact that the surface area of a sphere is a function of the square of its radius? </p>
<p>An intuitive explanation would be very much appreciated. </p> | g441 | [
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<p>This probably sounds really naive. But, a strange discussion came up on Quora about computers possibly weighing more when information is added to them. </p>
<p>I tried looking around but couldn't find a definitive answer. There are a few threads where people have tried to ask something similar.</p>
<p>1) <a href="http://www.thenakedscientists.com/forum/index.php?topic=38844.0" rel="nofollow">http://www.thenakedscientists.com/forum/index.php?topic=38844.0</a></p>
<p>2) <a href="http://www.lolhappens.com/27706/does-a-computers-weight-increase-as-information-is-added-to-the-hard-drive/" rel="nofollow">http://www.lolhappens.com/27706/does-a-computers-weight-increase-as-information-is-added-to-the-hard-drive/</a></p>
<p>Both threads have people arguing about the possibilities, but I'm sure a more definitive, and painfully detailed answer must exist. I hope you have a good laugh and then help me out!</p>
<p>I don't have the rep to post more than two links so I'll just put the original thread in the comments.</p>
<p>Thank you!</p> | g442 | [
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<p>I read it on Yahoo Answers (link below) that the power of lens changes when the lens is placed inside water. But then, if we consider the formula f=c/2 , the radius if curvature of the lens still remains same, then, how can the focal length change? </p>
<p>While considering the definition (point where light rays meet) we see that the focal length changes.
But while considering the formula (f=c/2) focal length doesn't change.</p>
<p>Can anyone please explain this and please do mention whether the focal length actually changes or not.</p>
<p><a href="http://answers.yahoo.com/question/index?qid=20090217024946AAk1njB" rel="nofollow">http://answers.yahoo.com/question/index?qid=20090217024946AAk1njB</a></p> | g14164 | [
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<p>A <a href="http://www.google.com/search?q=sun+jar" rel="nofollow">sun jar</a> is an object that stores solar energy in a battery and then releases it during dark hours through a led.</p>
<p>Assume:</p>
<ul>
<li>a $65cm^2$ solar panel </li>
<li>a 12h/12h light/dark cycle</li>
<li>insolation of $2.61kWh/m^2/day$</li>
<li>perfectly efficient components (i.e. without violating Entropy laws or other theoretical limits)</li>
<li>light is emitted by an ideal "white" source</li>
</ul>
<blockquote>
<p>How bright can we make the jar so that it shines for 12 hours?</p>
</blockquote>
<p>Useful links:</p>
<ul>
<li><a href="http://en.wikipedia.org/wiki/Insolation" rel="nofollow">Insolation</a></li>
<li><a href="http://en.wikipedia.org/wiki/Peukert%27s_law" rel="nofollow">Peukert's law</a></li>
<li><a href="http://en.wikipedia.org/wiki/Solar_cell_efficiency" rel="nofollow">Solar cell efficiency</a></li>
<li><a href="http://en.wikipedia.org/wiki/Luminous_efficacy#Lighting_efficiency" rel="nofollow">Luminous efficacy</a></li>
</ul> | g14165 | [
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<p>What would be a good book or books for a sufficient prerequisite for Zee's book QFT in a nutshell?
I have had a course in QM and relativistic QM, but I think there are some gaps that needs to be filled. </p>
<p>Maybe someone who have read the book can tell me what other books they read or?</p> | g443 | [
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<p>I have a h/w question regarding the current in the armature of a motor when it is operating at half it's normal speed. The question is;</p>
<blockquote>
<p>A motor is designed to operate at 118V and draws a current of 12A when it first starts up. At it's normal operating speed, the motor draws a current of 2A. Compute: </p>
<p>a) the resistance of the armature of the coil. </p>
<p>b) the back emf developed at normal speed. </p>
<p>c) the current drawn by the motor at half the normal speed.</p>
</blockquote>
<p>I have done parts a) and b) but I don't know how to complete c).</p>
<p>My reasoning goes like this;</p>
<p>Voltage is a measure of how 'hard' you push the current around a circuit, so decreasing the voltage will decrease the amount of current in the circuit (since current is coulomb's per second) which will in turn result in a smaller magnetic force on the armature and hence the motor will be running at a lower speed. But I don't know how to quantify this - All I have managed to find online is that angular velocity is directly proportional to voltage...</p>
<p>I would really appreciate a general discussion of the concepts I need to understand to answer this question.</p>
<p>Thanks!</p> | g14166 | [
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<p>As a physics newbie I'm trying to get a grip on basic orbital mechanics. I think I'm beginning to get grasp on how bodies interact with each other. When a body approaches another body it accelerates due to gravity. It can reach a point where its velocity is high enough to keep falling but also keep missing the object it is falling towards. What keeps it from accelerating (because of gravity) and eventually reaching escape velocity? I feel like I'm either looking at things the wrong way or I have the entire thing wrong. </p> | g14167 | [
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<p>Neutinos are either Dirac particles or Majorana particles but can’t be both at the same time. Then how can we write a general mass term as the sum of a Dirac mass term and a Majorana mass term? When we write such a term what nature of neutrinos (Dirac or Mjorana) do we have in mind? </p>
<p>A massive Dirac field, has four independent degrees of freedom (DOF): $$\psi_L,\psi_R,(\psi_L)^c=(\psi^c)_R,(\psi_R)^c=(\psi^c)_L$$ In contrast with this, a Majorana fermion has only two independent DOF: $$\psi_L, (\psi_L)^c=(\psi^c)_R$$ Then, in particular, how is it possible to replace $\psi_L$ by $(\psi_R)^c$ <strong>in the Dirac mass term</strong> because $\psi_L=(\psi_R)^c$ is <strong>true only for Majorana particles</strong> and <strong>not for Dirac particles</strong>. This is the headache I have.</p> | g14168 | [
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<p>In math, I was taught to parameterize a scalar/vector <a href="http://en.wikipedia.org/wiki/Line_integral" rel="nofollow">line integral</a>. In physics, I remember doing problems where I didn't parameterize the problem and it still came out correct. </p>
<p>So, by parameterization, you'll always get the right answer. When can you do the line integral without parameterization (i.e., keep everything in terms of Cartesian coordinates and not replacing them with the parameter $t$)?</p>
<p>Wait, in general, a curve can be some squiggly thing where both $x$ and $y$ change simultaneously. So if the path is just a line along the $x$-axis or the path is just a line along the $y$-axis, parameterization is not needed? What about lines in general? </p> | g14169 | [
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<p><img src="http://i.stack.imgur.com/qEWny.jpg" alt="enter image description here"></p>
<p>The answer is same... That us the graph between P and I will also be a parabola.... Similar to the graph between V and I. But how? Can anyone explain through mathematical approach ?
I used $P=V^2/R$ , $P=i^2R$ or $P=VI$ . I differentiate to find the slope. Can anyone help ?</p> | g14170 | [
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<p>I read Griffiths EM today and it says something very interesting but a little bothering to me. It states for an atom, the position of center of mass of an electron cloud lies in the center of the proton.</p>
<p>But my question is why? What will happen if this is not true?</p> | g14171 | [
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<p>I am reading Srednicki's book on QFT and there's a thing I don't quite see in chapter 6 (Path integrals in QM)</p>
<p>equation (6.7) is</p>
<p>$\langle{}q^{''},t^{''}|q^{'},t^{'}\rangle=\int\prod_{k=1}^Ndq_k\prod_{j=0}^N\frac{dp_j}{2\pi}e^{ip_j(q_{j+1}-q_j)}e^{-iH(p_j,\bar{q_j})\delta t}$</p>
<p>where he says $\bar{q_j}=\frac{1}{2}(q_j+q_{j+1})$,$q_0=q'$, $q_{N+1}=q^{''}$ and takes the limit $\delta t\to{}0$
and he gets equation (6.8)</p>
<p>$\langle{}q^{''},t^{''}|q^{'},t^{'}\rangle=\int\mathcal{D}q\mathcal{D}p\cdot e^{i\int_{t'}^{t''}dt(p(t)\dot{q(t)}-H(p(t),q(t)))} $</p>
<p>My question is, where does the integral on the exponential come from?</p> | g14172 | [
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<p>I have seen the equation $V = \frac {V_0}{K}$, but also the equation $V=\frac{1}{2}CV^2$. The values of C and V increase in the same linear ration with K (because $C=KC_0$). However, as the energy is proportional to $C$ and $V^2$, the energy stored by the capacitor actually DECREASES with the employment of a dielectric.</p>
<p>Am I correct in this interpretation? Do I take it that merely knowing the capacitance is NOT enough to compute the energy stored - I must also know this about it's construction? </p>
<p>(I think this may explain the problem with on of my electronics project's in the past I see nothing to prevent two of the same capacitance from having a different energy store!) is it appropriate to summarize anything else one should be worried about when substituting
capacitors?)</p> | g14173 | [
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<p>What is the difference between rotational velocity & rotational frequency? Their units seem to be the same, and I've read that one is a 'scalar' and the other is a 'vector,' but how do they differ?</p> | g14174 | [
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<p>In case of any miscommunication let me describe my understanding of the meaning of "perturbative" and "<a href="http://en.wikipedia.org/wiki/Non-perturbative">non-perturbative</a>", and correct me if something is wrong:
In a perturbatively defined QFT the fields are quantized as free fields, and the interaction is constructed by multiplying free fields operators, hereafter particles can scatter with each other; non-perturbatively defined QFT is any QFT in which the interaction is not constructed by the above-described method, e.g. a lattice QFT. </p>
<p>Now I'm curious about the connection between two constructions. The possibilities I can imagine are the following:</p>
<ol>
<li><p>Perturbative and non-perturbative QFT are complementary to each other, they are both approximations of some underlying theory.There are things perturbative QFT can cover which non-perturbative QFT can't, and vice versa.</p></li>
<li><p>Perturbative QFT is contained in non-perturbative QFT, thus can be derived from it as some kind of limiting situation, however some calculations are more efficient in perturbative QFT.</p></li>
</ol>
<p>Which one is correct? My sanity favors (1), but "non-perturbative" really sounds like a more powerful word to me so I can't help thinking (2) is possible. I'd really appreciate a comprehensive explanation on the issue.</p> | g14175 | [
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<p>Give an example of a situation in which there is a non-zero gravitational field and a zero gravitational potential at the same point?</p>
<p>$$dV=-\vec E\cdot d\vec r.$$</p>
<p>The above equation implies that such a situation is possible.</p> | g14176 | [
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<p>I have some questions about the statistics of Bell Tests. For convenience I'm going to refer to the test described in this paper:</p>
<p><a href="http://arxiv.org/abs/quant-ph/0205171" rel="nofollow">http://arxiv.org/abs/quant-ph/0205171</a></p>
<p>They show a coincidence rate of 300 counts with polarizers aligned. I'm wondering how many counts there would be if you took out both polarizers altogether, and how many of those would be coincidence counts. I'm interested in the ideal case of 100% detector efficiency and 100% downcoversion efficiency, but I also wonder how close the ideal case can be approached in practise.</p> | g14177 | [
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<p>In <a href="https://www.youtube.com/watch?v=IybCTI4aC5s" rel="nofollow">this video</a> we see a rather unorthodox bowling technique on display. The gentleman appears to knock over all of the pins using only a ping pong ball. It's a fake, of course: you could never knock over a bowling pin with a ping pong ball. Or could you? How fast would a ping pong ball need to travel in order to knock over a heavy object like a bowling pin? Naturally, you are free to make any simplifying assumptions and order-of-magnitude estimates you like.</p> | g14178 | [
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<p>So according to my notes, the field inside a conductor is zero. But what, exactly, is meant by inside?</p>
<p>I think we are in electrostatics for the purpose of this question.</p>
<p>The reason it is zero is because all the electrons are pushed to the edge of the conductor. So are these electrons assumed to be no longer inside the conductor (i.e. not strictly inside the conductor). If this is the case, does this mean that Gauss' Law applies to charges strictly inside a surface, and considers charges on the surface to be "outside" the surface, or more precisely, not strictly inside the surface?</p>
<p>Please let me know if I should write this more clearly.</p>
<p>physics</p> | g14179 | [
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<p>A recent <a href="http://arxiv.org/abs/1204.3924" rel="nofollow">arXiv</a> article measures the variation of gravitational potential in a local region around the solar system, and from that it tries to infer the mass density. Are there any valid counterarguments to their conclusion, i.e: that there is no dark matter near our vicinity?</p> | g14180 | [
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<p>if gravity travels at c(light speed), why aren't objects pulled to earth at that speed? </p>
<p>Since the velocity of gravity is 9.8 meters per second squared, will it eventually accelerate until it maxes out at c then hold constant? </p>
<p>And if that is the case, then why doesn't the gravitational pull between objects and earth immediately travel at c like photons?</p>
<hr>
<p>so the acceleration of gravity is 9.8 meters per second squared only on earth. </p>
<p>The gravitational pull is contingent on the body off mass and the distance between the masses.</p>
<p>Gravity waves travel at the speed of light.</p>
<p>So if a gravity wave extending from one primary object of greater mass to another object of lesser mass was to move a lights speed it wouldn't affect the speed or acceleration of the secondary object. the secondary object would just react to the primary object at the speed of light, but the reaction it self is dependent upon the size and distance between them?</p> | g14181 | [
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0.010655410587787628,
0.03339819237589836,
0.048431940376758575,
0.020228995010256767,
0.03258245065808296,
-0.0004915740573778749,
-0.08494701236486435,
-0.09823573380708694,
0.01390355546027422,
-0.010190342552959919,
0.0018257853807881474,
0.00... |
<p>I'm reading Einstein Gravity in a Nutshell (by Zee) and here he defines a vector as an object which is invariant under coordinate representation; concretely, if in one coordinate representation, $V$, $p_V=(p^1,p^2)$ then when we transform it via a rotation $p_W = R(\theta)p_V$ then we do not violate any physical laws. </p>
<p>To motivate the question further, I understand that individual terms after a transformation are not preserved but the law as a whole is: For example if $ma_V = F_V$ then $ma_W=F_W$ and although $F_W \neq F_V$ it is the case that the scalar (tensor) is preserved
$$ma_W-F_w=0=ma_V-F_V$$</p>
<p>The question that motivated this post is the following: Prove that if $p_V$ is a vector then $p'=(ap^1,bp^2)$ cannot be a vector unless $a \equiv b$. This seems easy enough to show</p>
<p>$$Rp'= (p_1a\cos(\theta)-p_2b\sin(\theta), p_1 a\sin(\theta) + p_2b\cos(\theta))^t$$</p>
<p>And clearly, we cannot just factor out the $a$ and $b$ unless $a\equiv b$. But what does this really mean? The converse must be true, namely if $p'$ is a vector then surely $p_V$ cannot be a vector.</p>
<p>I suspect if I keep reading there will be ample examples and it will click better (for example the force-mass-acceleration equation makes sense in how it transforms). I suppose my confusion rests in the idea that "well of course a vector is just a tuple and if rotate it that's another tuple and that old-new tuple pair was prescribed by a rotation so of course all tuples are vectors!"</p>
<p>EDIT: Here's another example to make the point (this is an actual exercise):
Suppose we are given two vectors ${p}$ and $q$ in ordinary 3-dimensional space. Consider this array of three numbers: $(p^2q^3,p^3q^1,p^1q^2)^t$. Prove that is not a vector, even though it looks like a vector. (Check how it transforms under rotation!) In contrast, $(p^2q^3-p^3q^2, p^3q^1-p^1q^3,p^1q^2-p^2q^1)^t$ does transform like a vector (so it's a vector). It is in fact the vector cross product $p \times q$.</p> | g14182 | [
0.02194667048752308,
0.02427881769835949,
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0.04078852757811546,
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0.0006114254938438535,
0.009978342801332474,
0.011807013303041458,
-0.041704218834638596,
-0.040... |
<p>Suppose there is an isolated system $A$ at time $(-\infty, t_1)$, whose entropy is $S=S_{max}$, i.e. it is at thermodynamical equilibrium.</p>
<p>Between moments $[t_1, t_2)$ the isolation is violated and system's entropy is decrased $S = S_{max} - S_d, \space\space\space 0<S_d <S_{max}$.</p>
<p>Question: the only way that this could happen is <strong>energy being added to system</strong>?</p> | g14183 | [
-0.0023708355147391558,
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0.0021080984733998775,
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0.01714199036359787,
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-0.0004529572615865618,
... |
<p>Where does an object "obtain" kinetic energy? I understand that an object often gets kinetic energy from another object. Where does the first object get the energy?</p> | g14184 | [
0.06661531329154968,
0.03393721207976341,
0.011450455524027348,
0.01498797070235014,
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0.013424326665699482,
-0.03655... |
<p><img src="http://i.stack.imgur.com/T1TPW.gif" alt="Free Body Diagram">
Hello,</p>
<p>I'm working on a small hardware project.</p>
<p>I have two load sensors located at distance $S_1$ ($x=0$) and $S_2$. Assuming we ignore the weight of the ramp ...</p>
<ul>
<li>What is the load on $S_1$ and $S_2$ as a function of $x$ where $x$ is an object's horizontal static position on the ramp?</li>
</ul>
<p>Here's what I have so far:</p>
<ul>
<li>As the object moves horizontally away from $S_1$, the load on $S_1$ monotonically decreasing.</li>
<li>As the object moves horizontally closer to $S_1$, the load on $S_1$ monotonically increasing.</li>
<li>When the object is directly over $S_1$ ($x=0$), the load on $S_1 = w=mg$.</li>
<li>When the object is directly over $S_2$ ($x = L = S_2$), the load on $S_1 = 0$.</li>
</ul>
<p>I have feeling adding an incline does not change the vertical forces acting upon $S_1$ and $S_2$. </p>
<p>My question is, can this problem be reduced to a <a href="http://theconstructor.org/structural-engg/analysis/influence-line-method-of-analysis/4361/" rel="nofollow"><strong>simply supported beam</strong></a> who's equations are:</p>
<p>$$
S1 = (\frac{L - x}{L})w
$$</p>
<p>and</p>
<p>$$
S2 = (\frac{x}{L})w
$$</p>
<p>Any other observations or insights would be great. Thanks!</p> | g14185 | [
0.049956291913986206,
-0.012272048741579056,
-0.022231994196772575,
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0.032817110419273376,
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0.00669874250888824... |
<p>A creationist website makes this argument for the 6,000 year old earth. I'm embarrassed to say I don't know how to do the math to evaluate the claim myself. However, the time scales involved seems to lend some credence to this argument. "The Moon is slowly drifting away from the Earth. If it is getting further, at one time it was much closer. The Inverse Square Law dictates that if the Moon were half the distance from the Earth, its gravitational pull on our tides would be quadrupled. 1/3 the distance, 9 times the pull. Everything would drown twice a day. Approximately 1.2 billion years ago, the Moon would have been touching the Earth. Drowning would be the least of our concerns! - See more at: <a href="http://www.allaboutcreation.org/how-old-is-the-earth.htm#sthash.LSHK4GQk.dpuf" rel="nofollow">http://www.allaboutcreation.org/how-old-is-the-earth.htm#sthash.LSHK4GQk.dpuf</a>"</p> | g14186 | [
0.01648138090968132,
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0.011065994389355183,
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0.005464146379381418,
0.04631560295820236,
0.00... |
<p>I've heard that clear things such as the gaseous components of the atmosphere or water reflect no light, and that is why they are clear. I've also heard that black things such as asphalt are such because they reflect no light. What is the physical reason for these things to reflect no light yet be totally opposite, such as black and clear? How can something be black or clear but have the same property of absorbing all visible light?</p> | g14187 | [
0.0034390734508633614,
0.007590690162032843,
0.026864588260650635,
0.01659609191119671,
0.050018031150102615,
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0.003495774231851101,
0.0662722960114479,
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0.08132556825876236,
-0.0031... |
<p>I am trying to understand how this linear motor works:</p>
<p><img src="http://i.stack.imgur.com/ymWB4.jpg" alt="enter image description here"></p>
<p>You can see a video <a href="http://www.youtube.com/watch?v=UX-_xt2m-pk%20%22%22" rel="nofollow">here</a> for more details. From what I know each permanent magnet consist a North and South poles so for a cylindrical magnet I have half of the magnet which is South and the other half North, so If I understand correctly the are positioned on this way:</p>
<pre><code> XXXXXXXXXXXXXXXXXX
_______ _______
| | || | |
| N | S || N | S |
|___|___||___|___|
..................
</code></pre>
<p>Where 'X' is the current going into and '.' is the current getting out. So If I understand correctly I will have opposite forces that cancels each other. Analyzing the current of the top ('X') North poles gives me a force going to the right, but the South pole gives me a force going to the left so I have no force, so, how exactly this linear motor moves?</p> | g14188 | [
0.019405212253332138,
-0.01451015379279852,
0.003614161629229784,
-0.006561878602951765,
0.052239518612623215,
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0.06057039275765419,
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-0.025600824505090714,
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0.022013304755091667,
-0.028786828741431236,
-0... |
<p>Hypothetically, I have a circuit with a two $10\Omega$ resistors in parallel. I supply them say, $2V$. How do I calculate the current?</p>
<p>What if, say, the circuit now has a $10\Omega$ resistor and a $5\Omega$ resistor in parallel with $2V$. Will anything change? I'm looking for calculations here.</p> | g14189 | [
0.03731584921479225,
0.021460263058543205,
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0.06172217056155205,
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0.01716584526002407,
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0.07757050544023514,
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0.03401742... |
<p>Is the fine tuning that cosmologists talk about (that our Universe is fine tuned for intelligent life) is the same as the fine tuning of the squared mass parameter of the Higgs in the Standard Model? And that in SUSY models?</p>
<p>Also, could anyone refer me to a source that explains the fine tuning issue in general?</p> | g14190 | [
0.028492528945207596,
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0.07427755743265152,
0... |
<p>This is perhaps a simple tensor calculus problem -- but I just can't see why...</p>
<p>I have notes (in GR) that contains a proof of the statement </p>
<blockquote>
<p><em>In space of constant sectional curvature, $K$ is independent of position.</em></p>
</blockquote>
<p>Here </p>
<blockquote>
<p><em>$$R_{abcd}\equiv K(x)(g_{bd}g_{ac}-g_{ad}g_{bc})$$
where $R_{abcd}$ is the Riemann curvature tensor and $g_{ab}$ is the metric of the spacetime.</em></p>
</blockquote>
<p>The proof goes like this: </p>
<blockquote>
<p><em>Contract the defining equation with $g^{ac}$, giving $$R_{bd}=3Kg_{bd}.$$
and so on.</em></p>
</blockquote>
<p>Problem is I don't understand why the contraction gives $$R_{bd}=3Kg_{bd}.$$ I can see the first term gives $$g^{ac}g_{bd}g_{ac}=4g_{bd}$$ since it's 4D spacetime. But as far as I can tell, the second term gives $g^{ac}g_{ad}g_{bc}=\delta_{bd}$ which is not necessarily $g_{bd}$.</p>
<p>Where have I gone wrong?</p> | g14191 | [
0.045871175825595856,
0.04812745749950409,
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0.0317654050886631,
0.03283641114830971,
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0.02805074118077755,
0.023283421993255615,
0.05836857110261917,
0.010855275206267834,
-0.01936... |
<p>The pressure for the ultrarelativistic Bose gas is </p>
<p>$$p~=~U/(3V) ~\propto~ (kT)^4/(hc)^3.$$ </p>
<p>It looks to me like it diverges for $h \to 0$. Looking at the derivation, it diverges because $h$ is the unit volume in phase-space and letting it go to zero allows for an infinite number of states per volume. But I don't understand the physics. </p>
<p>My question is threefold: </p>
<ol>
<li><p>Is it correct that the pressure diverges in the limit $h\to 0$ or is there some hidden $h$ dependence that I've missed? </p></li>
<li><p>Is this indeed the right classical limit? If not, what is? </p></li>
<li><p>What does that mean physically?</p></li>
</ol> | g14192 | [
0.016134625300765038,
0.07045470923185349,
0.00187089410610497,
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0.06075773388147354,
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0.0012846547178924084,
0.0793890655040741,
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-0.01779322326183319,
-0.021790800616145134,
-0.018251748755574226,
-0.06804372370243073,
-0.02... |
<p>Why do the four spin 3/2 $\Delta$ baryons have nearly identical masses and lifetimes despite their very different $u$ and $d$ quark compositions?</p> | g14193 | [
0.023233233019709587,
-0.04699544236063957,
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0.0010930635035037994,
0.052642256021499634,
0.07541994005441666,
0.045078277587890625,
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-0.046499501913785934,
-0.046377092599868774,
0.008456683717668056,
-0.004544059745967388,
0.00011947616440011188... |
<blockquote>
<p>What is an example for a system, which is in <a href="http://en.wikipedia.org/wiki/Chemical_equilibrium" rel="nofollow">chemical equilibrium</a>, but not in <a href="http://en.wikipedia.org/wiki/Thermodynamic_equilibrium" rel="nofollow">thermodynamical equilibrium</a>? </p>
</blockquote>
<p>And what about the other way around?</p>
<p>It seems to me, that as long as Parameters like temperature $T$ and pressure $p$ are changing, there cannot not be chemical equilibrium, since chemical reactions depend on these quantities temperature and pressure. Hence, if there is chemical equilibrium the parameters are not changing, enforcing thermodynamical equilibrium.</p> | g14194 | [
0.01127293799072504,
0.018350927159190178,
0.006682623643428087,
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0.04269680380821228,
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0.007794835139065981,
-0.040309157222509384,
-0.002186285564675927,
-0.012610391713678837,
0... |
<p>In many popsci articles it is claimed that String Theory (ST) birthed SUSY. Yet ST was originally invented as a bosons-only theory, that later on brought fermions into the fold. This was only possible After SUSY was incorporated. Hence the old moniker, Superstrings.
My understanding is that string theory (ST) is a `house of cards' i.e., collapses & dies if SUSY is falsified. Is this true?</p> | g14195 | [
0.058785732835531235,
0.04970259591937065,
0.020908145233988762,
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0.02070038393139839,
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-0.00033882114803418517,
0.06751330196857452,
0.020... |
<p>The force $F$ to carry a plate of area $A$ with velocity $v$ in a fluid of depth $d$ <a href="http://en.wikipedia.org/wiki/Viscosity" rel="nofollow">is given by</a></p>
<p>$$\frac{F}{A}=\eta\frac{v}{d}.$$</p>
<p>Hence if the depth is $kd$, the force becomes $F/k$. </p>
<blockquote>
<p>Do this relations hold for a ship in water?</p>
</blockquote> | g14196 | [
0.042431529611349106,
0.026953058317303658,
-0.010640773922204971,
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0.08576709777116776,
0.041888054460287094,
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0.01705453172326088,
0.0416131392121315,
0.019056715071201324,
-0.0212... |
<p>For my level of understanding the only explanation of mass to energy, ie nuclear weaponry, is limited to a simple summing game where a mass deficit is expressed as energy. For the 'reverse' process, ie in the LHC at CERN, it is a similar story, energy in, mass out. </p>
<p>Is there a more detailed physical explanation of what is occuring and if so is it mirrored by the two processes? </p>
<p>(Obviously pure physical theory at some level is just numbers in, numbers out but that alone doesn't preclude the possibility of some physical description between high level text book and base theory.)</p> | g14197 | [
0.07001038640737534,
0.04673150181770325,
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0.04772848263382912,
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-0.004420650657266378,
0.0120888352394104,
-0.017443425953388214,
0.06544959545135498,
0.01... |
<p>I have heard many times that we can treat a moving particle as a: </p>
<ol>
<li><p>classical particle</p></li>
<li><p>non-relativistic</p></li>
<li><p>relativistic particle</p></li>
<li><p><strong>ultra-relativistic</strong> particle</p></li>
</ol>
<p>While I know equations for 1, 2, & 3, I really don't know what is the difference between ultrarelativistic and relativistic particle. Can anyone explain a bit or provide some hyperrefs.</p> | g14198 | [
0.025927642360329628,
0.041954901069402695,
-0.02566966600716114,
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0.09596633911132812,
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0.05195486173033714,
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-0.028579413890838623,
-0.025416424497961998,
0.039437972009181976,
0.015954263508319855,
-... |
<p>I was wondering what the electric field of a uniformly charged <a href="http://en.wikipedia.org/wiki/Spherical_cap" rel="nofollow">spherical cap</a> is? Thereby I am referring to a spherical shell that was sliced into two pieces and we are only looking at one part of it. So in spherical coordinates it would mean that you would have a shell with radius $R$, it contains a full revolution of $2\pi$, but the polar angle does not go from $0$ to $\pi$ but rather from $0$ to some $\theta \in (0,\pi)$. And now I am looking for an equation that gives me the electric field for a given charge $Q$ on the shell.</p>
<p>It would be sufficient if somebody could give me the integral, that I have to evaluate!</p> | g14199 | [
0.03244192898273468,
-0.010255315341055393,
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-0.05025443062186241,
0.08895396441221237,
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0.011094373650848866,
0.012034622021019459,
0.04406789317727089,
0.07595362514257431,
-0.06287076324224472,
-0.003862655721604824,
0.012319930829107761,
-0.04... |
<p>Sorry about my poorly worded question as i'm not to good at explaining but bare with me so here i go.</p>
<p>Does sound come as straight lines like ||||| and become diffracted into curves when it passes through a slit so it looks like )))))?</p>
<p>If this is the case (as most diagrams on the net show), my question is what causes this to curve? In the Young's experiment with the slit how does light not pass straight through as ||||| : ----- ? In diagrams it is shown like this |||| : )))).</p>
<p>Can someone explain diffraction a bit more clearly and easy for me to understand why it curves?</p>
<p>Question 2: Why do light waves look like like this? And when passed through a slit, how do they curve into ))))?</p> | g14200 | [
0.026566311717033386,
-0.022738022729754448,
0.0004681859863922,
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0.04146358743309975,
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-0.034852877259254456,
0.0031839008443057537,
0.029876520857214928,
0.0444679893553257,
0.07099... |
<p>I'm looking for the exact correspondence between
Lorentz transfer four vector </p>
<p><img src="http://i.stack.imgur.com/5Ws5L.png" alt="Lorentz transfer four vector"></p>
<p>and the four vector of scalar and vector potential $A^\mu = (\phi(t,\vec{x}),\vec{A}(t,\vec{x}))^{T}$.</p>
<p>Does $ct=A(t), x=\phi(t),y=\phi(x), z=\phi(x)$?</p> | g14201 | [
0.04274531081318855,
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0.007646496407687664,
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0.05042486637830734,
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0.06388888508081436,
-0.044293906539678574,
0.013374343514442444,
-0.008646802976727486,
0.04... |
<p>I am very confused about orbital velocity for satellite launched from earth. It is states that:
$$
v=\sqrt{\frac{GM}{r}}
$$
Some says that it is equal to 8000 m/s and some say 3.1 km/s. Please remove my doubt. </p> | g14202 | [
0.005131634417921305,
0.011972622945904732,
0.0030768224969506264,
0.03156657889485359,
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0.00016827313811518252,
0.08795668929815292,
0.03746034577488899,
-0... |
<p>If we write something like: </p>
<p>$\partial_a X_{\mu} \partial^a X^{\mu}$</p>
<p>Does that mean the first derivative is only applied to the first X? </p>
<p>($\partial_a X_{\mu})( \partial^a X^{\mu}$)</p>
<p>Or is the first derivative applied to the object $X_{\mu} \partial^a X^{\mu}$, such that second derivatives would appear?</p> | g14203 | [
0.06565672159194946,
-0.028684353455901146,
-0.004351684357970953,
-0.029020296409726143,
0.06635033339262009,
-0.013096910901367664,
0.01712695322930813,
0.03748120740056038,
-0.04710058495402336,
-0.035148926079273224,
-0.028981393203139305,
0.03404569625854492,
0.004793384578078985,
0.0... |
<p>when a body is subjected to $0 K$ temperature, it becomes rigid. hence if we see in terms of quantum the lattice vibration decreases, resulting in no change in the direction of the Random velocity, then can we increase the degree of probability of finding of an electron in an given sys</p> | g14204 | [
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0.03569... |
<p>The glasses that we use for 3D viewing does it allow infrared rays to pass through them. Infrared rays pass through normal glass right? I need the pupil illuminated through infrared LEDs so I need to know does the infrared rays pass through each and every kind of glass.</p> | g14205 | [
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<p>My intuitive understanding is that although atoms are mostly empty space, the nucleus is solid. Thus a neutron or a neutrino can collide with it and do things like deflect or cause a nuclear reaction. </p>
<p>But does this intuition reflect the underlying reality? Since we usually think of a solid in reference to substances comprised of atoms, how does the concept of solid extend into the subatomic realm? Thanks </p> | g14206 | [
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<p>I am trying to start from:
\begin{align*}
[\phi(x),\pi(x')] = i\hbar\delta(x-x') \\
[\phi(x),\phi(x')] = [\pi(x),\pi(x')]=0
\end{align*}
to derive:
\begin{align*}
[a(k),a(k')^\dagger]=\delta_{kk'}\\
[a(k),a(k')]=[a(k)^\dagger,a(k')^\dagger]=0
\end{align*}</p>
<p>So starting with:
\begin{align*}
\phi(x) = \sum_k \left(\frac{\hbar c^2}{2\omega_k}\right)^\frac{1}{2}[a(k)u_k(x)+a(k)^\dagger u_k(x)^*]
\end{align*}
where $u_k(x) = \frac{1}{\sqrt{V}}e^{i(k \cdot x - \omega_k t)}$ and $\pi(x) = \frac{1}{c^2}\dot{\phi}(x)$
\begin{align*}
&[\phi(x),\pi(x')] \\
&=-i\sum_{k,k'} \frac{\hbar}{2}\sqrt{\frac{\omega_k}{\omega_{k'}}}\left([a(k)^\dagger,a(k')]u_k(x)^*u_k(x')-[a(k),a(k')^\dagger]u_k(x)u_k(x')^*\right)
\end{align*}</p>
<p>I'm not sure how to continue...</p> | g14207 | [
0.005577240604907274,
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0.04358300194144249,
0.009497221559286118,
... |
<p>I took quantum mechanics from our school's electrical engineering department. It was a grad level class designed for students working in device physics, thus it covered a lot of materials: from the basics (Schrodinger's equation, tunneling, the harmonic oscillator), to statistical physics (variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions), as well as some solid state physics basics (simple models for metals, semiconductors).</p>
<p>I then went on to take solid state physics, which used Ashcroft&Mermin, and Lundstrom.</p>
<p>Now I no longer plan to work in device physics for my phD, but I still want to have a good understanding of QM and Solid state physics.</p>
<p>I was working through the Griffith text, hoping to graduate toward the Shankar text when I came across Dirac's book. It seemed really elegant and focuses on intuition first. I was wondering if anyone would recommend going through Dirac's text before going to Griffith's? It makes more sense to me but most curriculums never even touches Dirac's book.</p>
<p>Thanks,
Al</p> | g14208 | [
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0.020074406638741493,
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0.04455117881298065,
-0... |
<p>There is no atmosphere for comets to get hot and burn and show tails but they still have tails. Why do they?</p>
<p>Edit: Isn't the answer "acceleration"?</p>
<p><img src="http://i.stack.imgur.com/bdR0F.gif" alt="enter image description here"></p> | g14209 | [
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<p>We are told to wear light clothes in summer as they are better at reflecting sunshine and keeping us cool. And dark clothes absorb sunshine and keep us warm.</p>
<p>But is it really relavent? If I buy identical t-shirts, one in black and one in white, will I feel significantly cooler or warmer? I have noticed that black surfaces get much warmer, but do they make the person warmer too?</p> | g14210 | [
-0.014861089177429676,
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... |
<p>According to <a href="http://www.guardian.co.uk/science/blog/2012/jul/04/higgs-boson-discovered-live-coverage-cern" rel="nofollow">http://www.guardian.co.uk/science/blog/2012/jul/04/higgs-boson-discovered-live-coverage-cern</a>, the reporter says that higgs boson things are little over <a href="http://en.wikipedia.org/wiki/General_Certificate_of_Secondary_Education" rel="nofollow">GCSE</a> physics. So, English learn a lot about physics in high school? Quantum mechanics is usually learned in university-level courses, right?</p>
<p>By the way, wow. A new particle that looks like Higgs boson.</p> | g14211 | [
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0.039437953382730484,
-0.... |
<p>Will this unite some theories, or cause some other change in physics, and perhaps our undertanding of the universe?</p> | g14212 | [
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-0.... |
<p>We already had definition of mass based on gravitational interactions since before Higgs. It's similar to charge which is defined based on electromagnetic interactions of particles.</p>
<p>Why did Higgs need to introduce concept of universe-wide Higgs field to define mass, based on interactions with it? And nobody cared about the charge of an electron (for example), which is also basic attribute and constant?</p> | g217 | [
0.07656977325677872,
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0.074611... |
<p>The relationship between the steady state theory and the notion of Higgs boson is not clear to me. What does the discovery of Higgs boson mean for steady state theory? Or are the two ideas purely orthogonal?</p> | g14213 | [
0.07715760916471481,
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0.01376940868794918,
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0.017217816784977913,
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0.023496655747294426,
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-0.06107523292303085,
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-0.04577505588531494,
0.006520354654639959,
0.03... |
<p>I have a question that I am just curious about.</p>
<p>Two principles: </p>
<p>Magnetic fields and Magnetic susceptibility </p>
<p><a href="http://en.wikipedia.org/wiki/Supercavitation" rel="nofollow">Supercavitation</a> is the use of cavitation effects to create a bubble of gas inside a liquid large enough to encompass an object traveling through the liquid, greatly reducing the skin friction drag on the object and enabling achievement of very high speeds.</p>
<p>Can a magnetic field hold a state of supercavitation if a magnetic field could be placed inside of the bubble of the supercavitation?</p> | g14214 | [
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0.005754917394369841,
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0.021924151107668877,
0.019953465089201927,
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-0.03156096488237381,
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-0.040112413465976715,
-0.002864968031644821,
0.0... |
<p>Through unit analysis, one can identify the following relationship linking energy, action and power:
$energy^2 = action \times power$</p>
<p>Alternatively, we rewrite this expression as:</p>
<p>$power = \frac{energy^2}{action}$</p>
<p>or;</p>
<p>$action = \frac{energy^2}{power}$</p>
<p>In light of this tight relationship, it seems odd that physicists prefer only to discuss energy and action when it comes to quantum field theory. It would seem that the inverse relationship between action and power would lead to an alternative formulation where the goal is to find extremum of power instead of action. So why is there very little discussion of power in physics?</p> | g14215 | [
0.02485661581158638,
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0.010071026161313057,
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0.0151413874... |
<p>What "breakthrough" from a theoretical point of view is needed for solar energy to become feasible energy alternative?</p> | g14216 | [
-0.011253902688622475,
0.09027723222970963,
0.016240114346146584,
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<p>In late 2003, Edward Witten released a <a href="http://arxiv.org/abs/hep-th/0312171">paper</a> that revived the interest in Roger Penrose's twistors among particle physicists. The scattering amplitudes of gluons in $N=4$ gauge theory in four dimensions were expressed in a simple way using the twistor variables. Witten also proposed a particular model, the topological B-model on the $CP^{3|4}$ twistor space, to generate all these amplitudes.</p>
<p>These methods began their own life but the topological B-model became largely silent, perhaps partly because the phenomenologists who fell in love with these things haven't been trained in string theory, especially not in the topological one. However, many twistor-related discoveries in the recent 3 years - which were made without Witten's constructive picture - lead me to ask whether Witten's theory actually knows about these matters.</p>
<p>In particular, the "dual superconformal symmetry" was first noticed by <a href="http://arxiv.org/abs/hep-th/0607160">Drummond et al.</a> in 2006 and derived by stringy methods by <a href="http://arxiv.org/abs/0710.1060">Alday & Maldacena</a> in 2008 or so. The 3+1 dimensions on the CFT boundary may be T-dualized to produce another copy of the Yang-Mills theory that is superconformally invariant once again. Scattering amplitudes have been converted to the expectation values of piecewise linear Wilson loops in the dual theory - the segments have the directions and length of the light-like momenta of the scattering particles. My question is</p>
<blockquote>
<p><strong>Can you also "T-dualize" Witten's topological B-model to obtain another one in which the scattering amplitudes are computed in a different way?</strong></p>
</blockquote>
<p>If you think that the answer is Yes, I would also like to know what is the "dual prescription" for the supersymmetric Yang-Mills amplitudes and whether the D1- and D5-branes in Witten's original models are replaced by other D1- and D5-branes or, for example, by D3-branes.</p> | g14217 | [
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0.014684636145830154,
0.044509775936603546,
0.023305226117372513,
0.06059041991829872,
0.026651451364159584,
-0.0272475928068161,
-0.02495449408888817,
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0.054710324853658676,
-0... |
<p>So I'm pretty sure I'm approaching this problem in the wrong way and I need some guidance (my first hint is that I think I'm thinking about a quantum mechanical problem too classically)</p>
<p>Suppose there is an isolated molecule in the gas phase with an average cross-sectional area to be exposed to radiation of $A$. (For my specific problem, the molecule is trapped in a superfluid Helium droplet, but I think the calculation should be roughly the same). If the radiation source has a flux $f$ (in units of photons/second/square area/0.1% BW) at energy $E$, what is the probability of the molecule absorbing a photon within a given interaction time $t$ if the absorption probability at a given energy is $P(E)$?</p>
<p>This is pretty easy to calculate if I treat the whole problem classically, i.e. like a ball and a target model. For some reason, though, I get numbers that seem to be way too low if I do this. I know it has to be more complicated than that, since light is a wave also. What am I missing?</p>
<p>I understand that transition probabilities are related to wavefunction overlap, etc. Also, I should note that the radiation in my specific problem is in the hard x-ray region, though I don't think that should change the answer.</p>
<p>Thanks in advance for your help.</p> | g14218 | [
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0.058567170053720474,
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0.0023380450438708067,
0.014723172411322594,
0.009367446415126324,
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<p>I did not understand if a current I above a conducting surface why we take image of current to find magnetic field intensity why not take the effect of actual current only . And is this method and equations to satisfy boundary condition at the surface </p>
<p>Also is there any good tutorial that explain methods of images in magneto-static because I did not find any thing for magneto-static.</p> | g14219 | [
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<p>Is there anything known about the spatial configuration of the quarks within a proton of pion? Or are they just considered to be two or three overlapping points?</p> | g14220 | [
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<p>I have been (independently) working on Problem 2.13 in Kleppner and Kolenkow's <em>An Introduction to Mechanics</em> and come to an answer which conflicts with the hint the authors provided in the book. The problem is this:</p>
<blockquote>
<p>A "pedagogical machine" is illustrated in the sketch. All surfaces are frictionless. What force $F$ must be applied to $M_1$ to keep $M_3$ from rising or falling?</p>
</blockquote>
<p><img src="http://i.stack.imgur.com/8OXPf.png" alt="MS Paint approximation of original picture"></p>
<p>(Note that $M_1$ is sitting on a level plane which is not drawn in my reproduction of the original sketch.)$\\$</p>
<p>I have three or four pages of matrix manipulations and derivations which led me to my answer, but since I think my error is in my force equations and not in my manipulations I won't post everything I've done unless someone requests that I do so. Let $\vec{F}_{M_3}$ be the force on $M_{1}$ from $M_{3}$, let $\vec{F}_{M_{1}}$ be the force on $M_3$ from $M_1$, and let $\vec{a}_n$ be the acceleration vector for $M_n$. For each vector $\vec{u}$, let $\vec{u}=\left<u_{x},u_{y}\right>$ and $\vert\vec{u}\vert=u$. The vectors $\vec{T}_1$ and $\vec{T}_2$ are tension forces.</p>
<p>$$\vec{F}_{M_3}+\vec{F}=m_{1}\vec{a}_1\\
\vec{T}_{2}=m_{2}\vec{a}_{2}\\
\vec{T}_{3}+\vec{F}_{G_3}+\vec{F}_{M_1}=m_{3}\vec{a}_{3}$$</p>
<p>Since $a_{1x}=a_{1}=a_{3x}$, $F_{M_3}=F_{M_1}$, and $T_{2}=T_{3}$, I find (letting $a_{3y}=0$),</p>
<p>$$
F-F_{M_3}-m_{1}a_{3x}=0\\
T_{3}-m_{2}a_{3x}=0\\
F_{M_3}-m_{3}a_{3x}=0\\
T_{3}=m_{3}g
$$</p>
<p>Putting the corresponding matrix into row reduced echelon form gives</p>
<p>$$F=\frac{m_{3}g\left(m_{3}+m_{1}\right)}{m_{2}}.$$</p>
<p>The hint provided in the book says:</p>
<blockquote>
<p>For equal masses, $F=3Mg$.</p>
</blockquote>
<p>My answer gives $F=\frac{Mg(M+M)}{M}=2Mg$. Have I properly accounted for all forces which do not cancel in my force equations?</p> | g14221 | [
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0.0... |
<p>If i have 2 coordinate systems (CS) which are travelling one towards another. CS $xy$ with an observer in its origin and CS $x'y'$ with a source in its origin. Correct me if I am wrong, but i think that I have to use this variation of an equation for a <a href="http://en.wikipedia.org/wiki/Relativistic_Doppler_effect" rel="nofollow">relativistic Doppler effect</a>:</p>
<p>$$\nu = \nu' \sqrt{\frac{c+u}{c-u}}$$</p>
<p>Here $\nu$ is a frequency that observer receives and $\nu'$ is a frequency which source transmits. Correct me if I am wrong.</p>
<p><strong>Question:</strong>
Do I have to swap $\nu$ and $\nu'$ in the equation above if I put observer in CS $x'y'$ and source in CS $xy$? A brief explanation will do just fine.</p> | g14222 | [
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<p>From everything I've read about quantum mechanics and quantum entanglement phenomena it's unobvious for me, why quantum entanglement is considered to be active link. I.e. it's stated every time that measurement of one particle <em>affects</em> another.</p>
<p>While in my head there is less magic explanation: the entangling measurement affect both particles in the way which makes their states identical, though unknown. In this case measuring one particle will reveal information about state of the other, but without magic <em>instant</em> modification of remote entangled particle.</p>
<p>Obviously, I'm not the only one who had this idea. What are the problems associated with this view and why <em>magic</em> view is preferred?</p> | g61 | [
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<p>Some of you may know this experience (<a href="http://www.youtube.com/watch?v=0i2lhO3bSjQ">Grape + Microwave oven = Plasma video link</a>):</p>
<ul>
<li>take a grape that you almost split in two parts, letting just a tiny piece of skin making a link between each half-part.</li>
<li>put that in a microwave oven, and few seconds later, a light ball which seems to be a plasma appears upon that grape</li>
</ul>
<p>Looking through google to understand why this phenomena happens, I have found either laconic or partial answers to that question.</p>
<p>In the big lines, this what I understand :</p>
<ol>
<li><p><strong>Micro waves seems to create an electric current in the grape because of ions.</strong></p>
<ul>
<li><em>Why do grapes contains ions ?</em></li>
</ul></li>
<li><p><strong>Suddenly the tiny link between the two half-parts is broken which creates an electric arc</strong></p>
<ul>
<li><em>How is that link broken ?</em></li>
</ul></li>
<li><p><strong>In parallel, the grape is warmed up and a gas is raised upon the grape</strong></p>
<ul>
<li><em>What is this gas made of ? water ? sugar ?</em></li>
</ul></li>
<li><p><strong>The combination of the electric arc in that gas creates a plasma</strong></p>
<ul>
<li><em>What is the necessary condition for a gas crossed by an electric arc to create a plasma ?</em></li>
</ul></li>
</ol>
<p>Is that correct ? </p>
<p><em>Are there any relevant parameters (microwave frequency, grape size, grape orientation) that make it works ?</em></p>
<p><em>Any idea of order of magnitude for the intensity involved, the voltage of such an arc, the temperature reached (I've read 3000 degrees !) ?</em></p>
<p>Has someone a complete explanation to provide (reference to physical principle would be appreciated !) ?</p> | g14223 | [
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<p>Take a displacement in three dimensions and reduce the number of dimensions by one. The original displacement loses one degree of freedom; giving it two parameters to specify a magnitude and an orientation. Now reduce the number of dimensions to just one, leaving just a magnitude... or does it?</p>
<p>For a displacement in just one dimension, does this mean there is no sense of direction and therefore a "forwards" and "backwards"?</p> | g14224 | [
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<p>What math do I want to focus on for 1) quantum computing and 2) quantum physics?</p>
<p>I am interested in studying quantum computing and the Higgs Boson (quantum physics?) and ultimately working in some capacity at the CERN in Europe. I am learning by myself and making progress, self-tested have succeeded in Calculus, Matrices Algebra and more. Not sure of the right track. I enjoy reading the life and the math explorations of Srinivasa Ramanujan and this math keeps me compelled to want to explore and do more. Would appreciate a line of math courses to help me play with quantum computing and quantum physics. Thank you.</p> | g14225 | [
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<p>I'm trying to find Susskind and Glogower's original paper,</p>
<blockquote>
<p>L. Susskind and J. Glogower, <em>Quantum mechanical phase and time operator,</em> Physics 1 (1964) 49-61,</p>
</blockquote>
<p>where they propose their exponential and sine-cosine phase operators (i.e. $\widehat{\textrm{exp}}(i\phi)=\sum_{n=0}^\infty |n\rangle\langle n+1|$ and friends). This paper has a huge number of citations, both from papers that discuss the formalism directly, as well as papers that deal with other formulations of the quantum phase.</p>
<p>However, it was published in a pretty obscure and apparently short-lived journal and I can't find it either online or in print. (I'm also beginning to question how many people have actually read this paper...) Can anyone point me to an online resource that has this or to a print library (preferably in England) that has it?</p> | g14226 | [
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... |
<p>I will formulate my question in the classical case, where things are simplest.</p>
<p>Usually when one discusses a continuous symmetry of a theory, one means a one-parameter group of diffeomorphisms of the configuration space $M$ which fix the action functional $S:P\rightarrow \mathbb{R}$, where $P$ is the space of time evolutions, ie. differentiable paths in $M$. The idea is that, given some initial configuration $(x_0,v_0)\in TM$, there is a path in $P$ passing through $x_0$ with velocity $v_0$ and minimizing $S$ among all such paths. I will assume that this path is unique, which is almost always the case. Thus, if a diffeomorphism fixes $S$, it commutes with determining this path. One says that the physics is unchanged by taking the diffeomorphism.</p>
<p>Now here's the question: are there other diffeomorphisms which leave the physics unaltered? All one needs to do is ensure that the structure of the critical points of $S$ are unchanged by the diffeomorphism.</p>
<p>I'll be more particular. Write $P_{x_0,v_0}$ as the set of paths in $M$ passing through $x_0$ with velocity $v_0$. A diffeomorphism $\phi:M\rightarrow M$ is a symmetry of the theory $S:P\rightarrow \mathbb{R}$ iff for each $(x_0,v_0) \in TM$, $\gamma \in P_{x_0,v_0}$ is a critical point of $S|_{P_{x_0,v_0}}$ iff $\phi \circ \gamma$ is a critical point of $S|_{P_{\phi (x_0),\phi^* (v_0)}}$.</p>
<p>It is not obvious to me that this implies $S = S \circ \phi^{-1}$, where $\phi^{-1}$ is the induced map by postcomposition on $P$. If there are such symmetries, what can we say about Noether's theorem?</p>
<p>A perhaps analogous situation in the Hamiltonian formalism is in the correspondence between Hamiltonian flows and infinitesimal canonical transformations. Here, a vector field $X$ can be shown to be an infinitesimal canonical transformation iff its contraction with the Hamiltonian 2-form is closed. This contraction can be written as $df$ for some function $f$ (and hence $X$ as the Hamiltonian flow of $f$) in general iff $H^1(M)=0$. Is this analogous? What is the connection? It's been pointed out that this obstruction does not depend on the Hamiltonian, so is likely unrelated.</p>
<p>Thanks!</p>
<p>PS. If someone has more graffitichismo, tag away.</p> | g14227 | [
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<p>Background:</p>
<p>It is well known that the quantum mechanics of $n$ identical particles living on $\mathbb{R}^3$ can be obtained from the geometric quantization of the cotangent bundle of the manifold $M^n = \frac{\mathbb{R}^{3n}-\Delta}{S_n}$, where $\Delta$ is the set of coincidences and $S_n$ is the permutation group of $n$ elements acting naturally on the individual copies of $\mathbb{R}^3$, please see, for example, <a href="http://books.google.com/books?id=4tBrbryIKQAC&printsec=frontcover&dq=Souriau%20%2b%20Structure%20of%20dynamical%20systems&hl=en&ei=nBu5ToXbBtGyhAelvMW6Bw&sa=X&oi=book_result&ct=book-thumbnail&resnum=1&ved=0CDgQ6wEwAA#v=onepage&q&f=false">Souriau: Structure of dynamical systems</a>. $T^*M^n$ is multiply connected with $\pi_1(T^*M^n) = S_n$. Given the canonical symplectic structure on $T^*M^n$,the set of inequivalent quantizations has a one to one correspondence to the set of character representations of the fundamental group $\mathrm{Hom}(\pi_1(M^n), U(1))= \mathbb{Z}_2$ corresponding to the identity and the parity characters. These
quantizations correspond exactly to the pre-quantization of bosons and fermions. The boson and fermion Fock spaces modeled on
$\mathrm{L}^2(R^3)$ emerge as the quantization of Hilbert spaces corresponding to these two possibilities.</p>
<p>Many authors pointed out that the removal of the coincidence set from the configuration space may seem not to be physically well motivated. The standard reasoning for this choice is that without the removal, the configuration space becomes an orbifold rather than a manifold. Some authors indicate also that without the removal, the configuration space is simply connected thus does allow only Bose quantization (Please, see for example the reprinted article by Y.S. Wu in <a href="http://books.google.com/books?id=mCgy_y8PAkoC&printsec=frontcover&dq=Wilczek%20Fractional%20statistics&hl=en&ei=fz65TsvKF8WohAfr6qjTBw&sa=X&oi=book_result&ct=book-thumbnail&resnum=1&ved=0CC8Q6wEwAA#v=onepage&q&f=false">Fractional statistics and anyon superconductivity By Frank Wilczek</a>.</p>
<p>My question:</p>
<p>Are there any known treatments or results of the problem of geometric quantization of the configuration space as an orbifold (without the removal of the coincidence set), in terms of orbifold line bundles, etc.?
Partial results or special cases are welcome. Does this quantization allow the possibility of Fermi statistics?</p> | g14228 | [
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0.0... |
<p>Centre of mass of a system cannot change its state of motion, unless there is an external force acting on it. Yet the internal force of brakes can bring a car to rest. Then what stops the car?</p> | g14229 | [
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<p>If an electron and positron are accelerated towards each other, at distances quite far away, there wouldn't be any significant electrostatic attraction, hence they need to be accelerated. But when they do come close, the Coulomb force is significant. So why do we accelerate the particle antiparticle pair, when they get attracted by electromagnetic forces? What is the need for getting them to collide at high speeds? Doesn't annihilation occur when an electron comes in the field of the positron?</p> | g14230 | [
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0.08359751850366592,
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0.011412032879889011,
-0.00702542532235384,
-0.01597... |
<p>I do a bit of hobby programming and I often search the internet for little oddities that are fun to ponder over. I have read a few passages that try to explain quantum computing to the layman like myself. I have read of the <a href="http://en.wikipedia.org/wiki/Qubit" rel="nofollow">Qubit</a>, the more 'power' version of the bit, and its bad habit of being in superposition. This, to me, sounds as if it sits halfway between 1 and 0.</p>
<p>So, I reason that one can create a qu-binary number with these; something resembling a ternary number, made from 0's, 1's and 1/2's (or Q's). I have read that a quantum computer has more 'power' when it comes to computation because one qu-value is a possibility between at most n^2 regular values in n bits. I have constructed a little problem with this value when you try to store a specific set of regular values in a qu-value.</p>
<p>Imagine a value is a superposition between 2 and 3. In qu-binary, I would write "10 or 11 -> 1Q", as the last bit is "both". OK, so this works. But what about real values 2, 3 and 4 in superposition? in my ternary notation "QQQ" is potentially any of the possibilities 0 through 7, and so actually represents a whole lot more values than I want!?</p>
<p>My question is, how does it really work? Am I thinking about it all wrong? Because this is how the whole subject of Quantum computing looks like from the outside. Or is this an example of quantum computing's non-determinism? I assume all bits are completely isolated from one another and have no qu-knowledge of any other. Maybe something obscure like quantum gates sharing information between bits could explain the problem; or if the bits represent continuous probabilities. I don't know. Could someone explain it for me?</p> | g14231 | [
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... |
<p>The maximum achievable probability of the Clauser-Horne-Shimony-Holt game is $\cos^2(\pi/8)\approx85.355\%,$ which can be proved with Tsirelson's inequality. But I don't imagine that this remained unknown until Tsirelson's 1980 paper. When was it first known that this constant is optimal?</p>
<p>I must admit—shamefully—I have not read the famous 1969 paper, so if the strategy's optimality is proved there my apologies.</p> | g14232 | [
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-0... |
<p>Lets put an ice cube on a fairly precise scale and take readings over a period of several hours. The ice cube is situated in a saucer so that the water is retained after melting. </p>
<p><strong>What will the recorded curve look like?</strong></p>
<p>Suppose ambients conditions: 25°C, RH40% and 1013 mbar.</p> | g14233 | [
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-0.02361150085926056,
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0.04440254345536232,
-0.01657017320394516,
... |
<p><img src="http://i.stack.imgur.com/Lnk3k.png" alt="enter image description here"></p>
<p>Could someone show the math behind it?</p>
<p>Source : "A vortex is a bunch of air circulating around itself. The axis around which the air is rotating is called a vortex line. It is mathematically impossible for a vortex line to have loose ends" --- <a href="http://www.av8n.com/how/htm/airfoils.html#sec-circulation-vortices" rel="nofollow">http://www.av8n.com/how/htm/airfoils.html#sec-circulation-vortices</a></p> | g14234 | [
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-0.03289179131388664,
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0.028286801651120186,
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0.04... |
<p>Consider force $F$ acting on a body of mass 1000kg and the displacement be $s$. So energy required to do so is $F$x $s$. Now consider the same force causing same displacement on body of mass 1kg. Here to energy required(according to equation) is same. But certainly more energy is required in the first case. How is this possible? Does it mean that no more energy is needed for prolonged application of force? This is the main reason I don't understand why work/energy is force times displacement .Instead force times time makes more sense to me.</p> | g14235 | [
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<p>Why is it that in <a href="http://en.wikipedia.org/wiki/Electro-osmosis" rel="nofollow">electro osmosis</a> the liquid will be attracted to the electrode having the same polarity sign as the one of the capillary walls but in <a href="http://en.wikipedia.org/wiki/Electrospray" rel="nofollow">electro spraying</a> the liquid, once escaping the needle will be attracted to the electrode having the opposite sign from the needle ?</p>
<p>In one case the walls will give their polarity to the liquid (electrospray), in the other it is like the global polarity of the liquid (the force on the liquid to be exact) is opposite from the walls.</p>
<p>The 2 processes have a lot of similarities, but, to be more specific, can you help me make sense of the electro osmosis force (EOF) without burying me under cryptic equations? Why would the electric charges of the liquid near the walls drag more liquid than the opposite charges in the center of the liquid ? </p> | g14236 | [
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0.04161... |
<p>A ferromagnet is attracted to a solenoid's magnetic field. I understand that now the ferromagnet produced a magnetic field, from that process is there an induced $EMF$? </p>
<p>Can ferromagnets that are not permanent magnets( i.e low magnetic remanence ) induced $EMF$ in the solenoid? </p> | g14237 | [
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-0.... |
<p>Suppose I have a pure magnetic dipole $\mathbf{\vec m} = m\hat z$ located at the origin. What is the magnitude of the field $|\vec B|$ as $r\to 0$? In other words, what is $\lim_{r\to 0}\frac{\hat{r}\cdot \vec{p}}{4\pi\varepsilon_0r^2}$? Is it just zero? $\infty$? Do I have to use some sort of quadripole term?</p> | g14238 | [
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<p>I am reading trough chapter one of Moshinsky's <a href="http://books.google.be/books?id=RA-xtOg4z90C&pg=PA20&dq=moshinsky%20harmonic%20oscillator%20states%20expressed%20in%20terms%20of%20creation%20operators&hl=en&sa=X&ei=ygilUeqQH-GP0AXrwoBo&ved=0CDoQ6AEwAA#v=onepage&q=moshinsky%20harmonic%20oscillator%20states%20expressed%20in%20terms%20of%20creation%20operators&f=false" rel="nofollow">"The harmonic Oscillator in Modern Physics"</a>. However i am having some trouble with the mathematics in section 8 of chapter 1. I will sketch a summary of what the author is trying to do and then point out my problem. </p>
<p>In the 3D quantum harmonic oscillator a general state may be constructed trough,
$$
|n_1 n_2 n_3 \rangle = [ n_1! n_2!n_3!]^{-\frac{1}{2}} \eta_1^{n_1} \eta_{2}^{n_2} \eta_{3}^{n_3} | 0 \rangle
$$
with $\eta_j$ the creation operators,
$$
\eta_j = \frac{1}{\sqrt{2}} (x_j - i p_j)
$$
The above state is valid for a Cartesian basis. If we want to characterize the state in function of the eigenvalues of $H, L^{2}$ and $L_z$, namely $N,l,m$, we must construct a homogeneous polynome of degree $N$ in the creation operators $\eta_i$'s. It turns out that the following state
$$
| n l m \rangle \equiv A_{nl} (\boldsymbol{\eta} \cdot \boldsymbol{\eta} )^{n} \mathcal{Y}_{lm}(\boldsymbol{\eta}) | 0 \rangle
$$
with
$$
\mathcal{Y}_{lm}(\boldsymbol{r}) \equiv r^{l} Y_{lm} (\theta, \phi)
$$
satisfies the following equations
\begin{aligned}
(H - \frac{3}{2}) | n l m \rangle & = \boldsymbol{\eta} \cdot \boldsymbol{\eta}^{\dagger} | n l m \rangle = N | n l m \rangle \\
L^{2} | n l m \rangle & = l(l+1)| n l m \rangle \\
L_z | n l m \rangle & = m | n l m \rangle
\end{aligned}</p>
<p>The last two equations I can easily derive using that
$$
[\eta^{\dagger}_i, \eta_j] = \delta_{ij}, \hspace{20pt} [\eta^{\dagger}_i, \eta^{\dagger}_j ] = [\eta_i,\eta_j] = 0
$$
we can derive,
\begin{aligned}
{} [L_k, \eta_m \eta_m] & = -i [ \varepsilon_{ijk} \eta_{i} \eta^{\dagger}_{j}, \eta_m \eta_m] \\
&\propto \varepsilon_{ijk} \eta_{i} \eta^{\dagger}_{j} \eta_m \eta_m - \varepsilon_{ijk} \eta_m \eta_m \eta_{i} \eta^{\dagger}_{j} \\
&= \varepsilon_{ijk} \eta_{i} \eta^{\dagger}_{j} \eta_m \eta_m + 2 \varepsilon_{ijk} \eta_i \eta_m \delta_{jm} - \varepsilon_{ijk} \eta_{i} \eta^{\dagger}_{j} \eta_m \eta_m \\
&= 2 \varepsilon_{ijk} \eta_i \eta_j = 0
\end{aligned}
As we can see from the definition of the state, we can drag the vector operator $\vec{L}$ trough all the products $(\boldsymbol{\eta} \cdot \boldsymbol{\eta})$ up to the spherical harmonics $Y_{lm}(\theta, \phi)$. This gives us the last two eigenvalue equations.</p>
<p>In order to prove the first equation we need the commutator
\begin{aligned}
\left[ \eta_{i}^{\dagger}, \eta_{j} \eta_{j} \right] = 2 \delta_{ij} \eta_{j}
\end{aligned}
Hence dragging the operator $\eta_{i}$ trough the $n + \frac{l}{2}$ factors $(\boldsymbol{\eta} \cdot \boldsymbol{\eta} )$ will deliver a term $ \propto 2(n+\frac{l}{2} ) \eta_i$,
\begin{aligned}
\boldsymbol{\eta} \cdot \boldsymbol{\eta}^{\dagger} | n l m \rangle & = \eta_{i} \eta_i^{\dagger} | n l m \rangle \\
& = \eta_{i} \eta_i^{\dagger} A_{nl} (\boldsymbol{\eta} \cdot \boldsymbol{\eta} )^{n} \mathcal{Y}_{lm}(\boldsymbol{\eta}) | 0 \rangle \\
&= A_{nl} \eta_{i} \eta_i^{\dagger} (\boldsymbol{\eta} \cdot \boldsymbol{\eta} )^{n} (\boldsymbol{\eta} \cdot \boldsymbol{\eta} )^{\frac{l}{2}} Y_{lm} | 0 \rangle \\
& = A_{nl} \eta_{i} (\boldsymbol{\eta} \cdot \boldsymbol{\eta} )^{n+\frac{l}{2}} \eta_i^{\dagger} Y_{lm} | 0 \rangle + (2n + l)A_{nl} \eta_{i} \eta_i (\boldsymbol{\eta} \cdot \boldsymbol{\eta} )^{n+\frac{l}{2}-1} Y_{lm} | 0 \rangle \\
& = A_{nl} \eta_{i} (\boldsymbol{\eta} \cdot \boldsymbol{\eta} )^{n+\frac{l}{2}} \eta_i^{\dagger} Y_{lm} | 0 \rangle + N | n l m \rangle,
\end{aligned}
with $N = 2n+l$. Now I really don't see why the first term here,
$$
\propto \eta_{i} \eta_i^{\dagger} Y_{lm} | 0 \rangle
$$
should be zero. The author gives some handwaving arguments that $\eta_i^{\dagger}$ can be interpreted as $\frac{\partial}{\partial \eta_{i}}$ and thus this could be seen as
$$
\eta_{i} \frac{\partial}{\partial \eta_{i}} Y_{lm} = \boldsymbol{\eta} \cdot \boldsymbol {\nabla} Y_{lm} = 0
$$
analogues to
$$
\mathbf{r} \cdot \boldsymbol{\nabla} Y_{lm} = 0.
$$
However the author is very wary not to write $ \eta^{\dagger} \equiv \frac{\partial}{\partial \eta_{i}}$ as the equivalence is only valid if the operators are acting on a polynome of $\eta_{j}$'s. I really don't see how a spherical harmonic could be seen as a polynome in $\eta_{j}$'s or how one could prove that
$$
\propto \eta_{i} \eta_i^{\dagger} Y_{lm} | 0 \rangle = 0
$$
with ($\hbar = 1$)
$$
\eta_{i} = \frac{1}{\sqrt{2}} ( x_{i} - i p_{i} ) = \frac{1}{\sqrt{2}} ( x_{i} - \frac{\partial}{\partial x_{i}} )
$$
rigourously without using (the somewhat, in my eyes, dirty trick) $\eta_{i}^{\dagger} \rightarrow \frac{\partial}{\partial \eta_{i}}$</p>
<p>I hope this post will not get flagged as too localized as the mathematics involved are extensively used in quantum mechanics.</p> | g14239 | [
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0.01675337180495262,
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0.04752938821911812,
0.03345... |
<p>I'm solving an exercise about small oscillations and I have a doubt about coordinates that I have to use.</p>
<p>This is the text of the exercise:
"A bar has mass M and lenght l. Its extremity A is hooked to a coil (with lenght at rest $l_0$), its extremity B is hooked to the point O that is the origin of axes. "</p>
<p>I have considered three coordinates: $x$, $y$ (that are the coords of the extremity A on the x-axes and y-axes) and $\theta$ that is the angle that the bar forms with a parallel to the y-axes.</p>
<p>I have to find the points of equilibrium.</p>
<p>I have written the coordinates of the center of mass of the bar as:
$M=(x+l/2 \sin \theta, -y-l/2 \cos \theta)$
and the potential energy as $ V=\frac{1}{2}k(x^2+y^2)-Mg(y+\frac{l}{2}\cos \theta)$</p>
<p>Then I have posed $gradV=0$ and I have obtained:</p>
<p>$y=\frac{Mg}{k}$</p>
<p>$x=0$</p>
<p>$\theta=0, \pi$</p>
<p>My doubt is about the result of y.. I was waiting for a negative value.. could you "clarify" my ideas and tell me where I'm making a mistake?</p> | g14240 | [
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0.0286524910479784,
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0.035126760601997375,
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<p>What is the size of the magnetic dipole moment $\vec m$ of a superconducting diamagnetic sphere $radius=R$ in a uniform magnetic field $\vec B_0$? Since there is no free current, we can solve for $\Phi_m$, the scalar potential of $\vec H$.</p>
<p>The boundary conditions that I see are $r\to 0 \Rightarrow \Phi_m \lt \infty$ and $r\to\infty\Rightarrow\Phi_m\to r\cos\theta$</p> | g14241 | [
0.005067004822194576,
0.0772547721862793,
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0.008206278085708618,
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<p>We have </p>
<ol>
<li>A point charge,</li>
<li>a homogeneously charged insulator with total charge $Q''$ which is a ball with radius $R$,</li>
<li>a conducting metal ball with charge $Q'$, radius $R$ and a grounded metal (no charge). </li>
</ol>
<p>The things I named are all separated by vacuum. I am supposed to identify the boundary conditions. Does anybody know how to do this? The only thing I know is that the potential inside the grounded metal is zero. </p> | g14242 | [
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-0.005678698420524597,
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0.08879106491804123,
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<p>The <a href="http://en.wikipedia.org/wiki/Gibbs%E2%80%93Duhem_equation" rel="nofollow">Gibbs-Duhem equation</a> states </p>
<p>$$0~=~SdT-VdP+\sum(N_i d\mu_i),$$ </p>
<p>where $\mu$ is the chemical potential. Does it have any mathematical (about intensive parameters) or physical meaning?</p> | g14243 | [
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0.08283959329128265,
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0.006110903806984425,
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0.014935668557882309,
-0.03282183036208153,
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0.06271512806415558,
-0... |
<p>Why is the Higgs boson spin 0? Detailed equation-form answers would be great, but if possible, some explanation of the original logic behind this feature of the Higgs mechanism (e.g., "to provide particles with mass without altering their spin states") would also be appreciated.</p> | g14244 | [
0.03729543834924698,
0.0161434393376112,
0.01052332017570734,
0.005792226176708937,
0.05350218713283539,
0.033085908740758896,
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0.005072304513305426,
0.0059911... |
<p>Consider a (classical) system of several interacting particles. Can it be shown that, if the Lagrangian of such a system is Lorenz invariant, there cannot be any space-like influences between the particles?</p> | g14245 | [
0.0384596511721611,
0.00788130983710289,
0.011097943410277367,
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0.0017939545214176178,
0.07240758836269379,
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0.045... |
<p>I have a a coin infinitely thin, rotating along the diameter.
How to derive the formula for it's moment of inertia passing through the diameter.</p>
<p>I was suggested to use the surface density and infinitely small part of the surface area, equidistant from the axis of rotation (marked as $dS$ on the picture).</p>
<p><img src="http://i.stack.imgur.com/q6KEX.jpg" alt=""></p>
<p>I've already figured out that:</p>
<p>$$I~=~\int r^2dm~=~\int \rho r^2 dS. $$</p>
<p>And now I'm stuck.</p>
<p>Any help would be much appreciated.
Greg</p>
<p>edit:</p>
<p>My coin is infinitely thin, so it's two-dimensional object (only $X$ any $Y$ axis). So let's assume that my rotating axis is equal to Y axis. So I have to integrate from $R$ to $-R$ on the $X$ axis. And every $dS$ will have different surface area. But I know, that total area is $S=\pi r^2$. From Pythagorean theorem I know, that $ r^2 + h^2 = R^2 $. And my integrate is $$I ~=~ \int\limits_{-R}^{R} 2\rho r^2 \sqrt {R^2 - r^2} dr $$
<s>But now I'm confused how to solve that - every time I get different solution than in <a href="http://www.wolframalpha.com/input/?i=integral%20r%5E2%20sqrt%28R%5E2%20-%20r%5E2%29%20dr" rel="nofollow">Wolfram Alpha calculator</a> </s></p>
<p>Ok, I've solved that - final answer is $ I = \frac {1}{4}MR^2 $</p> | g14246 | [
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0.0035420972853899,
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<p>I would like to clarify my understanding on why mass terms in Lagrangians of gauge theories are forbidden.</p>
<p>It's often repeated that particle masses are forbidden by electroweak symmetry because it is a chiral theory. I want to make a distinction between fermionic masses and gauge boson masses. </p>
<p>Looking through the transformations of gauge boson mass terms, it seems that these are in fact always forbidden by their respective gauge symmetry. Is this correct? (So if there was no SU(2) symmetry, the photon and gluon would still need to be massless?)</p>
<p>In which case, the electroweak symmetry is actually responsible for forbidding all other mass terms (i.e. weak boson masses and fermion masses) due to the usual chiral arguments. Is this correct?</p> | g14247 | [
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0.05... |
<p>Just a question out of curiosity, what would happen if the event horizons of 2 black holes of the same mass were to come into contact? Would both gravitational accelerations be canceled where the event horizons overlap?</p> | g444 | [
0.06803053617477417,
0.01154667790979147,
0.06379105150699615,
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0.031849928200244904,
0.01266165915876627,
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0.00... |
<p>If the densities of the moon and the earth are related by $\rho_m / \rho_e =3/5$, and if $g_m /g_e = 1/6$,
then what is $R_m /R_e$? ($g=$ acceleration due to gravity and $R=$ Radius)</p> | g14248 | [
0.06617113947868347,
0.033736634999513626,
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0.023346493020653725,
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0.010471198707818985,
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0.01974639855325222,
0.04... |
<p>I am currently reading <a href="http://arxiv.org/abs/quant-ph/0108137" rel="nofollow">this</a> paper. I understand how the <a href="http://en.wikipedia.org/wiki/Bloch_sphere" rel="nofollow">Bloch sphere</a> $S^2$ is presented as a geometric representation of the observables of a two-state system:</p>
<p>$$ \alpha |0\rangle + \beta |1\rangle \quad \alpha,\beta\in\mathbb{C} \quad \longrightarrow \{(\langle\sigma_x\rangle ,\langle\sigma_y\rangle ,\langle\sigma_z\rangle )\} = S^2 \subset\mathbb{R}^3$$</p>
<p>I also understand how $S^3$ is presented as a geometric representation of the same two-state system:</p>
<p>$$ \alpha |0\rangle + \beta |1\rangle \quad \alpha,\beta\in\mathbb{C} \quad \longrightarrow {(Re(\alpha),Im(\alpha),Re(\beta),Im(\beta))}=S^3 \subset \mathbb{R}^4$$</p>
<p>I see that the Bloch sphere representation loses the information about a global phase, but I do not understand why we <em>need</em> a non-trivial (Hopf) fibration of $S^3$ to preserve this phase information. Why can't we simply assign to every point of the Bloch sphere a phase $e^{i\phi}$? Why does the two-state system demand a non-trivial fibration (and why specifically the Hopf fibration)?</p>
<p><strong>PS (and a possible partial answer)</strong>: Since the Bloch sphere contains all of the observable information about the system, the $S^3$ representation has to be "decomposable" into pieces such that one of the pieces is the Bloch sphere. Since $S^3\not = S^2\otimes S^1$, we need a more complicated decomposition, e.g. the Hopf fibration. But this still leaves the question: is there no other decomposition of $S^3$ that will do the trick?</p> | g14249 | [
0.027257563546299934,
0.009583232924342155,
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0.04194575920701027,
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<p>If an heavy object (e.g. 10 tons) orbiting around Earth at 370 miles high, is connected with a cable back to Earth, we assumed either Earth is going to pull the mass or vice versa (or it will fall back to Earth). Assuming correct pressure/release/pull can be applied from the ground to prevent the fall, or it naturally starts spinning around in a circular motion - what do you think about its power generation capability?</p>
<p>This was a fun chat between friends, so just wanted to run it by.</p> | g14250 | [
0.012477589771151543,
0.02717362530529499,
0.0028210156597197056,
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0.014457443729043007,
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... |
<p>I am reading an <a href="http://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.115406" rel="nofollow">article</a> about <a href="http://www.google.com/search?as_q=floquet+bloch+state" rel="nofollow">Bloch-Floquet state</a>. My questions is in <em>Part II.B</em> and <em>Appendix A</em> of this paper, I will describe them below.</p>
<p>The original Schordinger equation we consider is: </p>
<p>$$i\hbar\frac{\partial}{\partial t} \tilde{\Psi}(r,t)=\tilde{H}(t)\tilde{\Psi}(r,t)$$</p>
<p>where: </p>
<p>$$\tilde{H}(t)=\frac{1}{2m_e}(\frac{\hbar}{i}\nabla+\frac{e\vec{A}(t)}{c})^2+V_c(r) $$</p>
<p>with $A(t)$ periodic in time and $V_c(r)$ periodic in space. </p>
<p>According to Floquet theorem, this time-periodic Hamiltonian has the wave function in the form:</p>
<p>$$\tilde{\Psi}(r,t)=e^{-i\tilde{\epsilon}(k)t/\hbar}e^{ik\cdot r}\tilde{\phi}_{\tilde{\epsilon},k}(r,t)$$
with $\tilde{\phi}_{\tilde{\epsilon},k}(r,t)$ periodic in space and time, we call $\tilde{\epsilon}(k)$ the Bloch-Floquet quasienergy.</p>
<p>The author did a following transform to avoid dealing with the square term of $A(t)$:</p>
<p>$$\tilde{\Psi}(r,t)=\exp(-\frac{ie^2}{2m_e\hbar c^2}\int^t dt'A^2(t'))\Psi(r,t)$$</p>
<p>Substitute this to the original Schordinger equation we arrive at:</p>
<p>$$i\hbar\frac{\partial}{\partial t} \Psi(r,t)=H(t)\Psi(r,t)$$</p>
<p>where:</p>
<p>$$H(t)=H_0+\frac{e}{m_ec}\vec{A}(t)\cdot \frac{\hbar}{i}\nabla$$
$H_0$ is the field free Hamiltonian.
Finally, the author claimed that the physics quantities are invariant under such a transformation and give an example of the invariance of the current density(I can see the identity).</p>
<p>My question is:</p>
<ul>
<li><p>Since this transformation is just a gauge transformation(see my comments). I heard that the physical quantities is unchanged by the gauge transformation. If this is true, is the floquet quasienergy a physical quantity in my second question? What about the quantity in my third question?</p></li>
<li><p>After the transformation, the author is using this new Schordinger equation to calculate the Bloch-Floquet quasienergy, is these qusienergies same as the ones obtained using the original Schordinger equation?</p></li>
<li><p>If I calculate this quantity $\int d\vec{r}\Psi^*H\Psi$ and $\int d\vec{r}\tilde{\Psi}^*\tilde{H}\tilde{\Psi}$ , what's the physical meaning of them? One can easily see that they are not equal. Also what's the difference and relation between this quantity and
the floquet energy?</p></li>
</ul>
<p>Please help if you have answer(s), also any comments are welcomed.</p> | g14251 | [
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0.033176884055137634,
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0.03014584258198738,
-0.0070573920384049416,
... |
<p>$E$ = $mc^2$
And also
$E$ = $hf$ (f - frequency)</p>
<p>And hence Einstein said $m$ = $hf\over c^2$
And so photons have mass</p>
<p>But later he also said</p>
<p>$M$ = $M_0\over \sqrt {1-v^2/c^2}$ </p>
<p>Where if we put $v = c$ we get</p>
<p>$M = M_0/0 \leftrightarrow M=\infty$ </p>
<p>And so photon travelling at the speed of light ($c$) have undefined mass (or $\infty$)</p>
<p>And so in one equation it is said photons have mass and in one it is said they have $\infty$ mass.</p>
<p>So do i have a problem in understanding or is there really any discrepancy ?</p> | g14252 | [
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... |
<p>Is there any general purpose stellar evolution simulation engine or software? Something to throw in properties of the star and to watch how (and why) they change along the timeline - with or without visualization (but preferably with).</p>
<p>The best of what I have found on the net is this site:</p>
<p><a href="http://outreach.atnf.csiro.au/education/senior/astrophysics/stellarevolution_links.html" rel="nofollow">http://outreach.atnf.csiro.au/education/senior/astrophysics/stellarevolution_links.html</a></p>
<p>however, there is no good simulation software behind the links there (or at least I don't see one).</p> | g14253 | [
-0.007201785687357187,
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0.004312440752983093,
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0.0... |
<p>Consider a yield-stress liquid in gravity. I assume that the buyouncy of a small gas-bubble will not be enough to overcome the yield stress (so the liquid doesn't behave liquid), thus leaving the bubble trapped. Is this so in theory, or is there a flaw in my thinking?</p>
<p>Sme argue that there are no yield-stress liquids in sense of one stress, below wich there is no yield, but rather a very high apparent viscosity. Would this imply that even miniscule bubbles will rise, but very slowly?</p>
<p>Lastly, have there been tries to measure viscosity or apparent viscosity or some measure for yield stress from rising bubbles?</p> | g14254 | [
-0.01462414488196373,
0.04304647445678711,
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0.02264421060681343,
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0.057657934725284576,
0.023813389241695404,
... |
<p>The ideia is to show that, because of Goldstone modes, 2d systems are quite different from 3d ones. So, considering the Heisenberg model, I'll post here what I'm asked to and my current thoughts on the subject in hope you can give me further assistance.</p>
<p><strong>1. fluctuations on Heisenberg model should destroy long-range spin order</strong> (solved but more info is wellcome)</p>
<p>I can calculate the mean square value of the fluctuations $<(\delta\vec{S}(\vec{r}))^2>$ and get the integral
$$\int_0^\Lambda dq \;q^{d-1}\frac{1}{q^2}$$
which tells me the lower critical dimension (next question) and how bidimensional lattices can´t have a phase transition, but how can I relate this with long-range order destruction?</p>
<p><strong>2. a bidimensional lattice can't be stable</strong></p>
<p>It seems I gave the wrong idea here. This here differs from the above in that we want to show that the fluctuations of the atom's position is so that the lattice can't be stable in 2d! I think this is associated with a divergence in phonons momentum, but how can I prove this?</p>
<p><strong>3. lower critical dimension of antiferromagnetic heisenberg model</strong></p>
<p>In this one I assume it is $d=2$ because Heisenberg model has continuous symmetry and it follows directly from Mermin-Wagner theorem. But it seems it is not enough! Antiferromagnetic behaviour is quite different of ferromagnetic one, specially concerning sin waves dependence on momentum (linear and quadratic, respectively, if I'm not wrong). So, following the same calculations I did on topic 1, this linear dependence will give me a lower critical dimension $\neq 2$ and I think I'm missing something, because this can't be right according to the theorem stated above. Any ideas?</p>
<p>Sorry for any typos. Hope someone can enlight me!
Thanks in advance.</p> | g14255 | [
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0.027525003999471664,
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0.... |
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