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<p>In a recent publication, <a href="http://prl.aps.org/abstract/PRL/v107/i17/e170404" rel="nofollow">Experimentally Faking the Violation of Bell’s Inequalities</a> (Gerhardt 2011) (<a href="http://lanl.arxiv.org/abs/1106.3224" rel="nofollow">arXiv version</a>), the statistics of quantum mechanics is faked using classical light sources.
But if it is possible for physicists to fake an experiment to imitate QM, how can we be sure that nature doesn't do the same trick on us? Can it be that QM is a fake, and in the end QM turns out to be an artifact of our imperfect measurement devices?</p>
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<p>Let's say I saw the barrel of a gun with a 45° angle, what would be the effect on the trajectory of a bullet fired through that barrel ?</p>
<p>Would the bullet be less stable (I guess), would it make the gun fire with an angle, and would that be toward the "small" end ?</p>
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/11321/confused-about-the-role-of-mass">Confused about the role of mass</a> </p>
</blockquote>
<p>why is it that two object of varying mass will fall at the same speed in a frictionless enviorment like the moon?
Is it because the object needs to overcome more momentum or what?</p>
| 85 |
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<p>In the steam bath at the health club, why is the "steam" thicker first thing in the morning before it has been used all day and the walls are "hotter"?</p>
| 5,554 |
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<p>I am kind of new to this eigenvalue, eigenfunction and operator things, but I have come across this quote many times: </p>
<blockquote>
<p>$\psi$ is the eigenfunction of an operator $\hat{H}$ with eigenvalue
$W$.</p>
</blockquote>
<p>First I need some explanation on how do we know this? All I know about operator $\hat{H}$ so far is this equation where $\langle W \rangle$ is an energy expected value: </p>
<p>\begin{align}
\langle W \rangle &= \int \limits_{-\infty}^{\infty} \overline{\Psi}\, \left(- \frac{\hbar^2}{2m} \frac{d^2}{d \, x^2} + W_p\right) \Psi \, d x
\end{align}</p>
<p>From which it follows that $\hat{H} = - \frac{\hbar^2}{2m} \frac{d^2}{d \, x^2} + W_p$. </p>
<hr>
<p><strong>Additional question:</strong></p>
<p>I know how to derive relation $\hat{H}\hat{a} = (W - \hbar \omega)\hat{a} \psi$ for which they state that: </p>
<blockquote>
<p>$\hat{a} \psi$ is an eigenfunction of operator$\hat{H}$ with
eigenvalue $(W-\hbar \omega)$.</p>
</blockquote>
<p>I also know how to derive relation $\hat{H}\hat{a}^\dagger = (W + \hbar \omega)\hat{a}^\dagger \psi$ for which they state that: </p>
<blockquote>
<p>$\hat{a}^\dagger \psi$ is an eigenfunction of operator$\hat{H}$ with
eigenvalue $(W+\hbar \omega)$.</p>
</blockquote>
<p>How do we know this?</p>
| 5,555 |
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<p>Could anyone explain what "extending the solution" beyond the past light cone means? Say, for example, if I have a metric (no coordinate singularities), how can I extend it to the outside of the past light cone?</p>
<p>Up to know, I only could find the extension argument in the context of Schwarzschild solution, where it seemed to be simply the procedure of removing a coordinate singularity. So what if I don't have a coordinate singularity, how do I show the extension of my solution? What mathematical techniques does "extending the solution" imply?</p>
| 5,556 |
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<p>I would like to consult a nice reference that explains the theoretical background of SC generation in optical fibers in detail but more or less self-contained. I would also like to have your opinions on nonlinear optic books that present material at introductory level.</p>
<p>Thanks in advance</p>
| 5,557 |
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<p><img src="http://i.stack.imgur.com/LKYC5.png" alt="enter image description here"></p>
<p>If we sprinkle iron fillings on a sheet of glass placed over a short bar magnet. The arrangement of iron fillings will be similar to the one shown above. </p>
<blockquote>
<p><a href="http://physics.stackexchange.com/questions/88876/why-do-some-of-the-iron-fillings-arrange-in-a-particular-pattern-when-sprinkled">Why do some of the iron fillings arrange in a particular pattern when sprinkled around a magnet, instead of getting attached to the magnet?</a><br>
All the filings are resting on a surface where there is friction. If the force due to the magnet does not exceed this friction, the filings won't accelerate to the magnet (only the closest ones experiencing the largest forces do).
Iron is also ferromagnetic, which means it can concentrate magnetic fields. So filings that are too far to be affected by the magnet itself can be attracted to adjacent filings which are concentrating the magnetic field better. This is why most of the filings seem to be more attracted to each other than the magnet itself. But essentially all the magnetic field is caused by the magnet.</p>
</blockquote>
<p>After this good answer by gregsan to the above <a href="http://physics.stackexchange.com/questions/88876/why-do-some-of-the-iron-fillings-arrange-in-a-particular-pattern-when-sprinkled">question</a>, I got a doubt here. Considering gregsan reason to be true, for gaps between the fillings around the magnet. I thought, if the reason for gaps in between the fillings is due greater field strength at those gaps (caused by displacement of fillings towards the magnet), and if the reason for those lines in between the gaps is due to lesser magnetic field at those locations (causing the fillings to remain at those same position). I thought iron fillings lines around the magnet exist if magnet can't exert more force to accelerate them against the frictional force, on the other hand in the gaps, fillings are more accelerated towards the magnet, so they get attached to the magnet causing gaps. Now, I assumed the lines around the magnet to be the locations where force due to magnet is less. So, if more is the lines around the magnet, greater will be locations where force due to magnet is less. Considering this, I thought, greater number of lines of force indicate less intensity of magnetic field around the magnet, but I have been taught in my school that, field strength to be more if greater is the lines of force around the magnet. Is it that magnetic field strength will be concentrated more at a shorter distance, if lines of force is more? I don't know whether I have misunderstood the answer of gregsan or is there any reason which would account for greater number of lines around the powerful magnet? If any is the case, please explain.</p>
| 5,558 |
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<p>Does the negative potential energy in the gravitational field have to be considered in calculating the total mass of the system in question (because of $E=mc^2$)? </p>
<p>If so it seems to me that the adding this negative energy to the calculation would slightly diminish the strength of the gravitational force over long distances. </p>
| 5,559 |
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] |
<p>Why is it that the <a href="http://en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates" rel="nofollow">Kruskal diagram</a> is always seen extended to all 4 quadrants when the definitions of the $U,V$ coordinates don't seem to suggest that the coordinates are not defined in, say, the 3rd quadrant. I can see that combining the definitions give equations that seem to allow that, but shouldn't the individual definitions of $U,V$ matter...? Physically, does it make sense?</p>
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] |
<p>What is the difference between <a href="http://en.wikipedia.org/wiki/Spin_glass" rel="nofollow">spin glass</a> and <a href="http://en.wikipedia.org/wiki/Quantum_spin_liquid" rel="nofollow">spin liquid</a>?</p>
<p>Do they both originate from frustration?</p>
| 5,561 |
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<p>I have a cylindrical pipe of internal diameter of around 5mm, with pressurised fluid flowing though it. If I have holes at the wall of the pipe, how do I calculate the pressure loss due to water leaking out through those holes?</p>
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<p>There is a analog between harmonic oscillator $x=\frac{1}{\sqrt{2\omega}}(a+a^\dagger)$ and quantum field $\phi=\int dp^3\frac{1}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_p e^{ipx}+a^\dagger e^{-ipx})$, which is used to quantize the field operator.</p>
<p>However, one thing confuse me is about the coefficient $\frac{1}{\sqrt{2\omega}}$. For field operator, this comes from Lorentz invariance, just because we have integrated time t. However, for harmonic oscillator, there seems no apparent Lorentz symmetry give me this. Is there any hidden symmetry behind the harmonic oscillator?</p>
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<p>My background is that of a mathematician. I have a question about the two Dimensional Ising Model. I think the terminology I use is similar to the physical.</p>
<p>I'm trying to understand the following passage in the article on the <a href="http://arxiv.org/abs/math/9907186" rel="nofollow">arXiv</a> about strong Markov property in two-dimensional Ising model.</p>
<blockquote>
<p>The strong Markov property of Gibbs measures,
stating that
$\mu(\cdot\,|\mathcal{F}_{\Gamma^c})(\omega) =\mu_{\Gamma(\omega)}^\omega$ for
$\mu$-almost
all $\omega$ when $\Gamma$ is
any finite random subset of $\mathbb{Z}^2$ which is em determined from
outside, in that
$\{\Gamma=\Lambda\}\in\mathcal{F}_{\Lambda^c}$ for all finite $\Lambda$, and
$\mathcal{F}_{\Gamma^c}$ is the $\sigma$-algebra of all events $A$ outside
$\Gamma$, in the sense that
$A\cap \{\Gamma=\Lambda\}\in\mathcal{F}_{\Lambda^c}$ for all finite $\Lambda$. (Using the
conventions $\mu_{\emptyset}^\omega=\delta_\omega$ and $\mathcal{F}_{\emptyset^c}=\mathcal{F}$
we can in fact allow that $\Gamma$ takes the value $\emptyset$.)
For a proof<br>
one simply splits $\Omega$ into the disjoint sets $\{\Gamma=\Lambda\}$ for
finite $\Lambda$.</p>
</blockquote>
<p>Could someone explain to me clearly an intuition about this property Strong Two-dimensional Ising model and the respective proof?</p>
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<p>Normally high-altitude balloon experiments end with the balloon popping and the payload falling back down to be reclaimed. </p>
<p>But if a second balloon was attached to the payload, one which was only partially inflated at launch, then could you keep the balloon aloft for a very long period of time? A sort of extremely-cheap very-low-orbit satellite.</p>
<p>And if so, then does anyone do this?</p>
| 5,565 |
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<p>"Nonlinear Wightman fields" are my current response to a wish to do interacting quantum field theory differently, no matter how successful what we currently do may be. The following image of a single page "poster" attempts to get across why I think the mathematics is interesting, with the intention that an ordinary physicist would find the hook curious enough to look at <a href="http://arxiv.org/abs/1211.2831v2" rel="nofollow">the 22 page arXiv paper</a>. The mathematics of section IV of that paper is really as simple as "use <a href="http://en.wikipedia.org/wiki/Hadamard_product_%28matrices%29" rel="nofollow">the Hadamard product of matrices</a>" to construct something nontrivial that might have more relevance to Physics than the Wightman axioms have had since they were created more than 50 years ago. This is at the same time familiar stuff and far up a different mountain, so there is some hope at the same time as there is concern that physicists generally will not understand the motivation or that I've made a mistake in the mathematics. [Note that the image itself is legible even if what is displayed inline is marginal.]</p>
<p><img src="http://i.stack.imgur.com/hzGN8.jpg" alt="Nonlinear Wightman fields -- a poster"></p>
<p>The paper this cites is something of an outcome from the thinking that led to my question <a href="http://physics.stackexchange.com/questions/9111/does-renormalization-make-quantum-fields-into-slightly-nonlinear-functionals-o">"Does renormalization make quantum fields into (slightly) nonlinear functionals of test functions?"</a>, 18 months ago, when I was using PhysicsSE quite actively as a way to help my research. Some of the content of the arXiv paper may also be found in a much rawer form as <a href="http://fqxi.org/community/forum/topic/1427" rel="nofollow">an entry in this year's FQXi essay competition</a> (so raw that I can't recommend that you chase the link). People who've been on PhysicsSE long enough may remember my attempts, for over a year, to use PhysicsSE as a tool for research, which I eventually felt to be counterproductive because it led to too little long-term thinking, and also because I felt unable to do much to help people whose research directions were different from mine.</p>
<p>I will submit the arXiv paper to a journal, probably JMathPhys, fairly soon, where it will hopefully generate a worthwhile critique either of the whole or of parts, but I would prefer to iron out kinks in the presentation or in the mathematics before doing so (or, if someone is kind enough to make a killing remark about the mathematics, you could save the editors or referees of JMathPhys or of some other journal some trouble).</p>
<p>As an aside, anyone who takes the time to read sections II and III of the arXiv paper will find calculations and an unconventional perspective on interacting quantum field theory that I would expect anyone who has thought for a while about foundational issues in QFT to find curious and perhaps useful.</p>
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<p>Given two parallel wires carrying a current (e.g. 2 and 3 Amperes) and the distance between them, 5 cm, how do I determine the magnitude of the magnetic field at a point M mid-distance between the wires (2.5 cm from each)?</p>
<p>The wires are located in a vacuum with ${\mu}=4\pi10^{-7}$.
If I use the formula
$$B=\frac{\mu*I}{2*\pi*r}$$
and calculate the magnetic field for both currents/wires, how do I find the resulting magnetic field?</p>
<p>How do I do that, assuming the wires are perpendicular and in the same plane? How does this generalise to more than two wires?</p>
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<p>Let's say a space-faring society wants to make a space station that has a large volume filled with air (or other gas), but no gravity. Using normal pressure tanks will require gathering an <a href="http://physics.stackexchange.com/questions/21286/amount-of-material-required-for-a-pressure-tank">amount of material proportional to the volume</a>, which is a ratio set by the tensile strength and desired pressure. It's likely that some other method for containing gas would be more economic for anything over a certain volume.</p>
<p>Could you confine a large volume of air in space using self-gravitation to hold the container together? Well obviously you can. Consider: a spherical volume of air surrounded by a solid sphere of matter through which the air cannot leak or diffuse and the pressure balances the gravity of the walls. Think of a big balloon ball in space, or alternatively, injecting the middle of the moon with air until it starts expanding. A hollow planet, if you will. There will be little gravity within the air because the walls don't contribute to the gravity inside and air has a low density.</p>
<p>So here is what I'd like to ask:</p>
<ul>
<li>For a given pressure, what surface mass density ($kg/m^2$) would you need? What would the wall thickness be?</li>
<li>Going by the amount of material required, at what size would this approach be more economic?</li>
<li>How stable would this thing be?</li>
<li>Hypothetically, could you use the same principles to drape a airtight tarp over Mars and keep atmosphere from leaking out? It would be the surface mass density that determines the altitude at which it rests, right?</li>
</ul>
<p>Disclosure type statements:</p>
<p>I can do a lot of the calcs for this myself, but I don't want to because I have doubts about certain parts and I want to avoid influencing other people with my potentially incorrect thought process. If you look at my Physics SE activity, you might notice that I'm <a href="http://physics.stackexchange.com/questions/10670/what-nonlinear-deformations-will-a-fast-rotating-planet-exhibit">fascinated</a> by <a href="http://physics.stackexchange.com/questions/9830/tension-in-a-curved-charged-wire-electrostatic-force-does-wire-thickness-mat">self-gravitation</a> <a href="http://physics.stackexchange.com/questions/16197/at-what-size-will-self-gravitation-contribute-more-to-stability-than-surface-ten">problems</a>. I came up with this question reading <a href="http://physics.stackexchange.com/questions/21247/keeping-air-in-a-well">Keeping air in a well</a>.</p>
| 5,568 |
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<p>I just had this idea of orbiting a planet just by jumping and then flying upon it on its orbit kind of like superman. So,</p>
<p>Would it be theoretically possible or is there a chance of that small body to be & remain its unity?</p>
<p><img src="http://i.stack.imgur.com/MNhD5.jpg" alt="Orbiting an asteroid by jumping"></p>
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<p>I need help with a physics problem, I don't know much about dampers, how can this be solved?</p>
<p><img src="http://i.imgur.com/ybpcQ.png" alt="spring"></p>
<p></p>
<p>we have
$y_0(x)=\mu\sin(\Omega x)$</p>
<p>We arrive at this equation for motion (where we define $b$ and $w_0$ ourselves, and $z=y(t)-y_0(t)$)</p>
<p>$$\displaystyle\frac{d^2z}{dt^2} + b\displaystyle\frac{dz}{dt} +w_0^2z = \mu\Omega^2U^2\sin(\Omega Ut)$$</p>
<p>Can someone show me the steps in between for determining this equation of motion</p>
<p><strong>EDIT:</strong> What I have is (with $y(ii)$ meaning second derivative of $y$, and $y(i)$ first):</p>
<p>$$m(y(ii)-y_0(ii))=-K(y-y_0)-C(y(i)-y_0(i))$$</p>
<p>which simplifies as</p>
<p>$$(y(ii)-y0(ii))+\frac{c}{m}(y(i)-y_0(i))+\frac{k}{m}(y-y_0)=0$$</p>
<p>which $\implies$ $z(ii)+bz(i)+w_0^2z=0$ (which is wrong)</p>
<p>Maybe I could be shown a proper free body diagram by someone if my idea of the forces are wrong?</p>
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<p>I read somewhere that a quantum field can be thought of as a tiny bowl at every point in space with a ball doing SHM (quantum harmonic oscillator). It was given that the amplitude of this SHM is quantized, and each quantum signifies a particle. (i.e. if the ball rolls with minimum amplitude, there are no particles in that point of space. If it has the next amplitude, then there is one particle and so on).</p>
<p>What I don't get is how this analogy relates to quantum fields which are not exactly quantized at every point of space. For example, a single electron has a wavefunction spread out over some space. At every point in this space, we can say that "there is a fraction of the electron over here". But, If I model this as a bunch of oscillators, I can't have a fraction of an electron as the amplitude of SHM, as its supposed to be quantized.</p>
<p>I'm quite sure there's a flaw in my interpretation, but I can't figure it out. Could someone give a more detailed explanation of quantum harmonic oscillators?</p>
<p>Note that I do not understand the mathematics behind quantum mechanics, so though I don't need layman's terms, I would rather stay away from the equations.</p>
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<p>Let's say a spinning star radiates mass-energy only from it's pole regions. How does the loss of mass-energy effect the angular momentum of the star?</p>
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<p>Suppose that Alice and Bob are both holding speakers emitting sound at a frequency $f$. Alice is stationary while Bob is moving towards Alice at twice the speed of sound.</p>
<p>In the case of Alice, if I forget for a minute that she is holding a speaker herself, and just think about the Doppler effect from Bob moving towards her, I get $$f_{\text{effective}}=f\frac{1}{1-\frac{2v_a}{v_a}}=-f$$</p>
<p>I do not know what "negative" frequencies mean in the context of sound waves, and so I do not really know how to describe what Alice will hear as Bob becomes very close to her.</p>
<p>I also do not know how the fact that she is emitting sound at a frequency $f$ will affect, if at all, what she hears.</p>
<p>And, from Bob's perspective, I get $f_{\text{effective}}=3f$, which is a bit more meaningful, but does not factor in the fact that Bob is emitting sound himself.</p>
<p>Any clarification is appreciated.</p>
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<p>Ok, so I understand the eye has 3 different types of receptors and I've seen the process of converting from RGB to CMYK. However if in physics I can specify a color using a single number (its frequency) why do computers need 3 (RGB) or 4 (CMYK) numbers to specify the same color? Is there some kind of disagreement in the amount of degrees of freedom involved?</p>
<p>Thanks a lot.</p>
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] |
<p>Does string theory explain the weird things that happens at the quantum level, especially wave-particle duality? </p>
| 5,575 |
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<p>Just wondering. I know a negative electric charge moving though a coil will induce a voltage in the coil. My question is, would a positive charge, say an ion beam, moving though a coil also induce a voltage?</p>
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<p>The metaphor of a surface (typically a pool table or a trampoline) distorted by a massive object is commonly used as a metaphor for illustrating gravitationally induced space-time curvature. But as has been pointed out <a href="http://physics.stackexchange.com/questions/3009/how-exactly-does-curved-space-time-describe-the-force-of-gravity">here</a> and elsewhere, this explanation seems (to a layman like me, at least), to be "hopelessly circular", and in the end contributes little to an understanding of how modern theories of gravitation work.</p>
<p>Are there other (or additional) metaphors that might be helpful in illustrating to lay readers (a) what motivates modern gravitational theory and (b) why it has greater explanatory power than Newtonian gravitation?</p>
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<p>What is the basis for black hole evaporation?</p>
<p>I understand that Hawking-radiation is emitted at the event horizon, a theoretical result originating in General Relativity and Quantum Field Theory, but it seems to me that additionaly one has to assert an integral conservation law for mass/energy, ie. for a sphere surrounding the black hole.</p>
<p>Does such a conservation law hold for the simplest case of a Schwarzschild metric?</p>
<p>I am grateful for any related classic paper references.</p>
<p><strong>EDIT:</strong> The usual heuristic for understanding Hawking-radiation is: virtual pair, one falls in, one goes out; the ones going out are called Hawking-radiation. But what about the ones going in? Naively, it seems there should also be Hawking-radiation going inward, which would actually increase the black hole's mass.</p>
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<p>In Griffiths' ED book he derives the field of a moving charge by two ways:</p>
<ol>
<li><p><a href="http://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential" rel="nofollow">LW retarded potential</a>.</p></li>
<li><p>Lorentz transformation of EM fields.</p></li>
</ol>
<p>(eq10.68 and eq12.92 and the discussion that follows,3rd edition)</p>
<p>Now my question is: <em>fundamentally</em>, what is the relation between the potential retardation and the L transformation of the EM fields? Can we totally replace the function of one by the other? Can we derive one formula from the other? </p>
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<p>I use several shape, several type of material (glass, metal, plastic), I use two different balances with 0.01g of accuracy. I put oil on gasket, and put upside down (like that I can see if water escape). But always it's the same result, when I put one, two or more effervescence tablets, the weight decrease:</p>
<p>one tablet => -0.03g</p>
<p>two tablets => -0.06g</p>
<p>three tablets => -0.09g</p>
<p>Sure the difference is not big. But if I put an object without effervescence tablet, the weight is always the same (move sometimes +0.01 or -0.01g but never more). The time for decreasing is about 2 minutes so it's not enough for change something from temperature I think especially with glass container.</p>
<p>So, maybe someone has done this experimentation before and know where is my error ? Or maybe someone can test and try this experimentation ?</p>
<p>@Luboš Motl: "Recall that the air density is about 1.3 grams per cubic centimeters", you're sure ? it's not 0.0013 ?
Yes, I have the same values for glass (2 mm of thickness and one of 3 mm of glass) with a metal cover of 0.8 mm of metal. I done about more than 100 measures. After 2 minutes, the tablet is full dissolved in water and weight move very few after (-0.01g next 2 minutes) but never more.</p>
<p>Maybe I found: when bubbles move up in water, they have gas in it (CO2), this gas move up with a speed, so there is a quantity of movement, the weight losses is the sum of mass of bubbles multiply by speed. Like quantity of movement is conserved, the weight don't change. </p>
<p>It's possible to use the formula of Newton: force=2mv if top speed is 0.25 m/s the weight losses is 2*0.3/1000*0.25/10 = 0.015 g with 0.3 g of CO2, image show speed that I found on Internet. If it's that, the weight must change with a ball full of air (ping-pong ball) in water. But the CO2 in a tablet is very powerfull, 0.3g give 0.187 liter of CO2, even the ball move faster the volume is not great in a bottle. The ball must be down before close the container. And the gas must relax when the ball reached surface. </p>
<p>Is it possible it is the rotation of Earth that change the pressure in water due to the centripetal forces ? This give -0.03N for each kg of water.</p>
<p>Good day</p>
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<p>In paper by Barnich and Brandt <a href="http://arxiv.org/abs/hep-th/0111246" rel="nofollow">Covariant theory of asymptotic symmetries,
conservation laws and central charges</a> they defined the Riemann tensor like this:</p>
<p>$$R_{\rho\mu\nu}^{\quad \ \ \lambda}~=~\partial_\rho \Gamma_{\mu\nu}^{\ \ \ \ \ \lambda}+\Gamma_{\rho\sigma}^{\ \ \ \ \ \lambda}\Gamma_{\mu\nu}^{\ \ \ \ \ \sigma}-(\rho\leftrightarrow\mu).$$</p>
<p>Now I have taken the 'normal' definition of Riemann tensor and raised the first index, and lowered the last one, and if I do the same with original (lower the first one and raise the last one) I get the same expression, which means that this is ok.</p>
<p>But, why such definition? And does that mean that the Christoffel symbols have different definition compared to usual? I mean raised first and lowered last index.</p>
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<p>Wick rotation of quantum field theories to Euclidean path integrals with a nonnegative measure everywhere is a wonderful tool. Not so with Lorentzian path integrals. Events far separated in coordinates can have zero or arbitrarily tiny interval separation in relativity. Ultraviolet divergences crop up for infrared separations at arbitrarily high boosts. The integrand becomes highly oscillatory phasewise around null separations. Absolute convergence is nonexistent, only mere convergence which is so sensitive to integral reorderings it raises warning flags. Changing the regulator or the order of limits can change the answer drastically. Are such path integrals even well-defined?</p>
| 5,582 |
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<p>Every year millions of car tires are worn down on our highways, yet the roads are not all black from the rubber, neither are the sides of the roads black. Where does all the rubber go?</p>
| 5,583 |
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<p>I am preparing to teach Grade 9 Static Electricity next week and am going crazy trying to figure out what is happening in one of my experiments. I have a short piece of PVC pipe, 4 inches diameter, and I rub it with wool to charge it negatively. I can observe excellent repulsion when I touch it with my foil bit (dangling from a thread). Here is the problem: I am holding down the PVC pipe down on a wooden base with two brass-plated wood screws, and these screws somehow collect an INSANE amount of positive charge, even when I am very careful not to touch them with the wool. The foil bit is strongly attracted to the screws, and when it touches them it bounces off more violently than anything I've seen in any of my other static electricity experiments.</p>
<p>Can anybody explain what I am seeing?</p>
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<p>For my electrical engineering course, we had to build a simple DC motor that can lift a coin. I have tested the motor, and here are the results:</p>
<ul>
<li>rotational speed (no load): 3630 RPM (380 rad/sec)</li>
<li>Current with load (9g): 3A (limited)</li>
<li>Current with no load: 0.7A</li>
<li>Maximum weight lifted: 0.1422 N</li>
<li>Max voltage 12V</li>
</ul>
<p>I now want to plot a torque-speed curve and calculate its efficiency. My problem is that the weight it lifted is a force quantity. To convert it to a torque quantity, I multiply by the axle radius (6mm) which gives 0.00085 Nm. This seems wrong to me becausekjg when I calculate the efficiency $\epsilon = \frac{\omega \tau}{VI}$ I get $\epsilon = 0.9 \% $ which seems extremely low.</p>
<p>Is this the correct way to calculate the torque produced by an axle when lifting a load?</p>
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<p>Is there a way to describe interactions between systems with particles of different species, that is to say with different statistics?</p>
<p>For example:
I am placing a boson next to a free fermion gas. How can I write down interaction
Hamiltonians that make sense? By interaction Hamiltonians I mean Hamiltonians that
contain products of fermion and boson operators? </p>
<p>Somewhat I am puzzled with this question, since both the boson and fermion operators act on different Hilbert spaces. </p>
<p>Might bosonization or fermionization a solution (at least for 1D systems)? </p>
<p>Best.</p>
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<p>Given a 2-loop divergent integral $\int F(q,p)\,\mathrm{d}p\mathrm{d}q$, can it be solved iteratively? I mean</p>
<ol>
<li>I integrate over $p$ keeping $q$ constant</li>
<li>Then I integrate over $q$</li>
</ol>
<p>In both iterated integrals I use dimensional regularization.</p>
<p>Can it be solved iteratively? I presented a paper to a teacher of mine about regularization of integrals using the Zeta regularization. He told me that for one dimensional integrals (or one loop integrals) it was fine, but that my method could not handle multi loop integrals. I argue back that you could apply the regularization method by introducing a regulator of the form</p>
<p>$$(a+qi)^{-s}$$</p>
<p>I could make the integral on each variable by iterated regularization, that is applying the algorithm iteratively.</p>
<p>EDIT: i think they have cheated me :) making up excuses not to put me atention</p>
<p>by the way , how can i insert math codes on my posts ?? is just setting <code>$</code> at the beginning and the end of the equation ??</p>
<hr>
<h2>Edit: 19th of July</h2>
<p>thanks :) your answer was quite useful :)</p>
<p>however can I not insert a term $(qi+a)^{-s} $ on each variable and then apply the regularization iteratively ??</p>
<p>I say so because I made a paper <a href="http://vixra.org/abs/1009.0047" rel="nofollow">http://vixra.org/abs/1009.0047</a> to regularize integrals using the regulator $(q+1)^{-1}$ and tried to extend it to several variables, however that was my doubt, if i could apply my regularization scheme to every variable :) thanks again</p>
<p>I mean for a one dimensional integral $\int dx (x+a)^{m-s}$, I know how to regularize it by using the Euler-Maclaurin summation formula plus the Riemann Zeta function $ \zeta (s-m)$</p>
<p>Then for multiloop integrals, I had thought that i could introduce the $s$-regulators (x+a)^{-s}(y+a)^{-s}.. and so on on each variable, and then apply iterated integration... :)</p>
<p>so this is a resume of my method..</p>
<p>a) i know how to use Zeta regularization to get finite values for the integral $ \int dx(x+a)^{m-s} $ in terms of the Riemann Zeta function $ \zeta (s-k) $ with k=-1,0,1,....,m</p>
<p>b) for a more general 1-dimensional integral $ \int dx f(x)(x+a)^{-s}$ i add substract a Polynomial $K(x+a)(x+a)^{-s} $ to get a finite part and then regularize the divergent integrals $dx(x+a)^{m-s} $ </p>
<p>c) for a more complicate 2-loop integral $ \iint dpdq F(q,p)(p+a)^{-s}(q+a)^{-s} $ to obtain a regularization of it i do the sema method , first on 'p' considering 'q' a constant and i treat it as a one dimensional integral over 'p' and then over 'q' by substracting a Polynoamials $ K(q,p+a)(p+a)^{-s} $ and so on</p>
| 5,587 |
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<p>Recall that the <a href="http://en.wikipedia.org/wiki/Fermion_doubling">fermion doubling</a> is the problem in taking the $a \to 0$ limit of a naively discretized fermionic theory (defined on a lattice with lattice spacing $a$). After such a limit one finds themselves with an additional amount (precisely $2^d$) of fermionic fields. One can fix this by considering different discretizations of the action that make unwanted fields decouple in the continuum limit. The downside is that the additional terms have to spoil some nice features of the theory (chiral symmetry, locality, lattice symmetry, ...).</p>
<p>Now, I wonder what is the true reason for the appearance of new fields. Is it the fermionic nature of the theory? (In other words, is a similar problem ruled out for bosonic fields?) And do all (naive?) fermionic theories (that is, independent of the continuum form of the action) suffer from this problem?</p>
<p>More generally, how can one tell <em>a priori</em> what will the field content of a lattice theory in the continuum limit be? Or is the field content fundamentally a continuum limit property that has to be calculated?</p>
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<p>I am going through the introductory chapter's of Schwinger's <a href="http://physics.stackexchange.com/questions/98694/source-theory-alternative-to-qft">Source theory</a>. He writes,</p>
<blockquote>
<p>It [Source Theory] is a phenomenological theory, designed to describe the observed particles. No speculations about the inner structure of the particles are introduced. No abstract definition of particle is devised. The theory is thereby firmly grounded in space-time, where the experimenter manipulates his tools, <strong>but the question of ultimate limitation to microscopic space-time description is left open, with the decision reserved to experiments. Correspondingly, no Operator-fields are used.</strong></p>
</blockquote>
<p>Now in this regard, I would want to know how operator fields answer the question of ultimate limitations to microscopic space-time (If they are related to each other)?</p>
<p><strong>EDIT 1 :</strong> It just struck me that the limitation could be due to canonical commutation between field operators and their conjugates. However, I don't see how to formalize a restriction using this commutation.</p>
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<p>Hotels usually install peepholes in their doors so that a person inside a suite can see who is at the door without having to open it.</p>
<p>I understand that there should be a convex lens within the peephole so that the person inside can easily see the person outside, but what I'm wondering about is the trick such that the person outside can only see blurred shapes if he tries to look though the peephole. Surely, there is more to it than specially-arranged convex lenses!</p>
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] |
<p>I have a question in my book</p>
<p><img src="http://i.stack.imgur.com/7yZhT.png" alt="http://i.imgur.com/P5R55sR.png"></p>
<p>The question is very easy, but then my solutions manual gave me unexpected answers</p>
<p><img src="http://i.stack.imgur.com/cam6h.png" alt="http://i.imgur.com/tSMmJEY.png"></p>
<p>I don't get how in d) they conclude the vectors go in the opposite direction, but in b) they go in the same direction. The only thing I could guess is that there's some assumed current direction but I can't find anything in my book about that. Thanks for any help</p>
| 5,591 |
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<p>I have read about the <a href="http://en.wikipedia.org/wiki/Uncertainty_principle" rel="nofollow">uncertainty principle</a>. And it applies to electrons. Then how is it that we can get exact tracks of electrons in cloud chambers?? That is to say that how is it that the position is fixed? I think I am missing a crucial point here. Please help.</p>
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] |
<p>Anyone knows where I can find an errata (or any related material, such as solution sheets, etc) for this book? Thanks.</p>
<p>Note: This is not a physics question, but this book is so popular among physicists that I can't think of anyone else better to answer it.</p>
| 5,593 |
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] |
<p>What numbers did Halley, Cook, et al. have? What was the strategy by which they calculated the AU? </p>
| 5,594 |
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<p>When changing the curved space co-ordinate into a flat space co-ordinate if a cone. I got the result transformation that i cannot get a transformation at the vertex(apex) why?</p>
| 5,595 |
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<p>Pretty much what the title says. My base question is this. Assuming I take a piece of steel, and a piece of PVC plastic and I measure both their temperatures and find they are the same. I then take a look at the vibration speeds of the individual molecules would they be the same as well?</p>
<p>Here's a rough example:</p>
<p>I measure both the steel and PVC and find them both at 100F, and then I measure the vibrations of a molecule in the steel and find it to be moving at 10 miles an hour. Would the PVC molecules also be moving at 10 miles an hour?</p>
<p>I'm sure I'm not using the correct units of measure to measure the vibration, but I didn't know what the correct unit of measure is for something like that. Hopefully it gets the point across.</p>
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<p>As I've understood it, the area under $F$-$s$-graph is the work done, so then :$$W(s)=\int{F(s)ds}$$
I am also given this equation ($W_k$ is kinetic energy, which is equal the work done to set the object in motion):
$$W_k=\frac{1}{2}mv^2$$
Does this mean that work is also the area under a $m$-$v$-graph, like so:
$$W(v)=\int{m(v)dv}$$
Could anyone explain why this is, or isn't true?</p>
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<p>An identity exists for CG coefficients:
$$\langle j_1 m_1 j_2 m_2 |J M \rangle = (-1)^{j_1+j_2-J} \langle j_2 m_2 j_1 m_1|J M\rangle,$$</p>
<p>But why is there a phase factor $(-1)^{j_1+j_2-J}$?</p>
<p>It seems to me that
$$|JM\rangle =\sum_{m_{1},m_{2}}|j_{1}m_{1}\rangle\otimes|j_{2}m_{2}\rangle\langle j_{1}m_{1}j_{2}m_{2}|JM\rangle
=\sum_{m_{1},m_{2}}|j_{2}m_{1}\rangle\otimes|j_{1}m_{2}\rangle\langle j_{2}m_{2}j_{1}m_{1}|JM\rangle
$$</p>
<p>And since $|j_{1}m_{1}\rangle\otimes|j_{2}m_{2}\rangle$ and $|j_{2}m_{1}\rangle\otimes|j_{1}m_{2}\rangle$ are the same physical state, there should be no difference between $\langle j_1 m_1 j_2 m_2 |J M \rangle$ and $\langle j_2 m_2 j_1 m_1|J M\rangle$. What do I get wrong?</p>
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] |
<p>A particle in a cyclotron requires more and more force to maintain the same acceleration as it accelerates.</p>
| 5,599 |
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<p>The observer is outside the water; the stones are underwater (say, 1 m below surface, if that matters). This produces a higher pitched sound for the observer than when both the observer and the stones are in air.</p>
<p>Is this because it takes more energy for sound waves to travel through water than through air, and so the ones that we hear from outside the water are the ones that had higher frequencies immediately after the collision to begin with?</p>
<p>Does the density of the medium which is disturbed by a rigid body collision have any effect on the frequency distribution of sound waves that are generated by the collision? For example, does the higher "stiffness" of the cage of water molecules surrounding the vibrating stones post-collision mean higher frequency normal modes for water (than for air)?</p>
<p>Finally, does refraction at the water-air interface play any role?</p>
| 5,600 |
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<p>Before this post gets marked as duplicate, I've checked book <a href="http://physics.stackexchange.com/questions/12175/book-recommendations">book recommendations</a> among other posts but I don't think they really answer this fairly niche question.</p>
<p>I am looking to compile a list of books, online courses, or other resources, that <strong>assume an advanced level of mathematical comprehension</strong> (graduate level at least), and yet no more than a <strong>junior-senior highschool level physics understanding</strong>.</p>
<p>I've been working as a mathematician for several years, specifically in the information security industry, and I am interested in steering my career in the direction of computational physics, purely due to curiosity.</p>
<p>More specifically, I'm after something that is,</p>
<ol>
<li>More fast paced than a first year - university text book,</li>
<li>Takes the student from topics of, for eg. the 17th century to the present, </li>
<li>Assumes very little physics understanding, </li>
<li>When presenting physics problems or exercies, emphasizes deriving computational models rather than analytic solutions to trivial questions,</li>
<li>At the very least, presents a roadmap of what to learn (excluding mathematical prerequisites) above teaching it</li>
</ol>
<p>Note 1: Apologies again if this can be marked as duplicate. However I can't find a suitable resource for a mathematician who is a beginner in physics. I've always found books progress either too slowly that I need to skim faster than I can comfortably skim a book without missing out on the good parts, or assume too much physics knowledge without redirecting to background reading. </p>
<p>Note 2: If this is indeed not a duplicate, I will be sure to add it in to the book recommendations thread.</p>
<p>If you can spare a moment or two to point me in the right direction, I hope I will be able to repay this forum with more constructive questions and answers in the future if I can reach the same level as you.</p>
| 201 |
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<p>I am trying to understand intuitively what a <a href="http://en.wikipedia.org/wiki/Phonon">phonon</a> is, but for the moment I find it quite difficult (having a limited background in quantum mechanics, an undergraduate course in non-relativistic QM). In fact, I find it hard to formulate good questions, so I hope my questions below make some sense.</p>
<p>I read that phonons are (the quantum mechanical analog of) normal modes of vibration in a crystalline system of atoms or molecules, so I guess a superposition, i.e. a general vibration should also be a phonon. Is that so? Why would they then be described as normal modes?</p>
<p>Could we say that a phonon is a particle whose position wave function extends over the whole crystal? Are the quantum mechanical frequency and wave vector the same as the frequency and wave vector of the corresponding classical oscillation (vibration in the crystal)?</p>
<p>In what sense is it (like) a particle? In that it is always observed or it always interacts at a specific location?</p>
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] |
<p>I assume it is some kind of quantity. Google only made things more confusing. </p>
<p>I get that it has something to do with circuits. </p>
<p>I also get what a <a href="http://en.wikipedia.org/wiki/Elementary_charge#Quantization" rel="nofollow">discrete charge</a> is. In fact, I thought charges were, by definition, discrete - because each individual proton/electron/hole contributed one unit of charge. </p>
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<p>My problem is when I take a picture (a close one) the straight edge looks a little curved. In a standard camera, like a CyberShot. </p>
<p>I would like to know if there is some relationship between the curvature of the glass and that effect or if you know more information about that.</p>
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] |
<p>Background:</p>
<p>Currently I am studying a course on non-linear dynamics. We have been studying about
attractors only intuitively, so I do not have a definition for an attractor. Let me give you a couple of examples.</p>
<p>Consider a problem where a ball is slipping in a parabolic valley. It is clear
intuitively and quantitatively that the lowermost point of the parabola is the
attractor for it. </p>
<p>Say we are talking about a <a href="http://en.wikipedia.org/wiki/Lorenz_attractor" rel="nofollow">Lorenz system</a>. We may not guess intuitively that
there is an attractor, a priori, but using simulations for different values of
initial conditions, we may qualitatively (and maybe quantitatively too) compare the trajectories for different initial conditions and convince ourselves that we have an attractor.</p>
<p>Problem:</p>
<p>Consider the <a href="http://en.wikipedia.org/wiki/Logistic_map" rel="nofollow">logistic map</a> given as </p>
<p>$$x_n = ax_{n-1}{(1-x_{n-1})}.$$</p>
<p>Let us fix a value of the parameter where we "know" that the logistic map exhibits
chaos. Say $a=3.9$.</p>
<p>Let us take the definition for the term attractor from <a href="http://en.wikipedia.org/wiki/Attractor" rel="nofollow">Wikipedia</a>:</p>
<p>An attractor is a subset $A$ of the phase space characterized by the following three
conditions:</p>
<ul>
<li>$A$ is forward invariant under $f$: if $a$ is an element of $A$ then so is
$f(t,a)$, for all $t > 0$.</li>
<li>There exists a neighborhood of $A$, called the basin of attraction for $A$ and
denoted $B(A)$, which consists of all points $b$ that "enter $A$ in the limit $t →
∞$". More formally, $B(A)$ is the set of all points $b$ in the phase space with the
following property: For any open neighborhood $N$ of $A$, there is a positive
constant $T$ such that $f(t,b) ∈ N$ for all real $t > T$.</li>
<li>There is no proper subset of $A$ having the first two properties.</li>
</ul>
<p>How might we demonstrate/convince ourselves of/disprove the statement that the logistic map does have an attractor for a particular choice of the parameter at which the map exhibits chaos?</p>
| 5,604 |
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<blockquote>
<p>The result of an imbalance of electrons between objects is called static electricity. It is called "static" because the displaced electrons tend to remain <em>stationary</em> after being moved from one insulating material to another.</p>
</blockquote>
<p>Please can any one explain to me what does it mean by the word <em>stationary</em> in the definition? Does it mean that the displaced electrons do not spin around the nucleus in another material's atom? </p>
| 5,605 |
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<p>Lets suppose a spaceship travels with v = 0.9c relative to the Earth. The time inside the spaceship would pass slower than on Earth. Would the astronauts measure a different speed (that means, a different one that the observer on Earth does) in relation to the same reference frame (Earth)?</p>
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<p>I was wondering how Young's Modulus effects the resonant harmonics of a vibrating (string instrument) string. I know that the string's fundamental frequency is $$\frac{1}2 \times \text{Length} \times \frac{\text{Tension}}{\text{linear density}^{1/2}}$$ that Young's Modulus for a material is - $$\frac{\text{Force}\times \text{original length}}{\text{original cross section} \times \text{change in length}}$$ and that resonant harmonics of a string are even multiples of the string's fundamental frequency. Does the fundamental frequency of the string material itself (which I can calculate by figuring out the speed of sound in whatever material the string is made from and how thick the string is) effect the frequencies it vibrates at under tension?</p>
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<p>If you look at the commutation relation of the position and momentum operators (in 1D position space), you get:</p>
<p>$$[\hat{x}, \hat{p}_x] = [x,-i \hbar \frac{\partial}{\partial x}] = i \hbar$$</p>
<p>All this says to me is that if you prepare a system in state (A) and measure the position, the system is now in state (B), which is an eigenstate of the position operator. You then measure the momentum of state (B) and now you're in state (C), which is an eigenstate of the momentum operator. Note that these must be consecutive measurements.</p>
<p>Alternatively, let's assume you reversed the order of the measurements. Beginning with state (A) again, you measure momentum first and put the system in state (D), an eigenstate of the momentum operator, but not necessarily state (C) [right?]. You then measure position, and put the system in state (E).</p>
<p>$$(B) \neq (E)$$
$$(C) \neq (D)$$</p>
<p>That's all HUP says to me. It says nothing about simultaneous measurements of position and momentum — is that even possible? (What operator would that be?) It only says how much the final wavefunctions of two systems that started out the same differ if you perform two measurements in a different order.</p>
<p>Where is the uncertainty? You know the position and momentum exactly — right when you measure them. You get some random value weighted by the coefficients of the eigenfunctions in the linear combination that forms $\psi$.</p>
<p>So I don't think it's accurate to say you can't "simultaneously know position and momentum to arbitrary precision", because as far as I can tell, you can't even measure the two at the same time.</p>
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<p>If the mass of the universe were cut in half, would it affect the speed of light?</p>
<p>Would it be twice as fast?</p>
<p>Would it stay the same?</p>
<p>Do we have instruments that are sensitive enough to measure the speed of light at different positions relative to high-mass objects to empirically answer this question?</p>
<p>The speed of light is (something of) a universal constant, but is it really dependent on the universe or on something intrinsic to photons?</p>
<p><strong>EDIT:</strong></p>
<p>Related question:</p>
<p>Since gravity is a relationship between one atom and every other atom in the entire universe, and it takes all the energy in the universe to travel at the speed of light, is there something about the energy/gravity/mass of the universe that "slows" light from going a faster speed?</p>
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<p>I need to consider a couple of examples of systems which have energies that are intensive variables - not extensive. I'be been thinking about this and I am not coming up with anything. My understanding is that extensive variables (at least wrt usual energies) scales with mass or length (system size). It also seems that some 'energies' depend upon the model used, such as how strong the interactions are in neighbors of atoms or dipoles, etc., or whether one is considering chemical potential or not, etc.</p>
<p>Any good suggestions?</p>
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<p>In physics, a pseudo-scalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion such as improper rotations while a true scalar does not.</p>
<p>Can someone show me the graphical picture or illustration that how a scalar changes under rotations? </p>
<p><strong>Why we can't say it as vector, if just the sign of the quantity changes? What is the fundamental difference between a vector and pseudo-scalar?</strong></p>
<p><strong>Why is the Klein-Gordon equation an equation of motion for a pseudo-scalar field?</strong></p>
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<p>How does ice become thinner in a no-frost fridge? I thought ice can't evaporate at all since, well, it's below freezing temperature and it's solid, too. In my other yes-frost fridge, the ice never becomes thinner, but thickens over time, so I have to de-frost it.</p>
<p>I don't believe the no-frost fridges have some patented magical mechanisms that make ice evaporate, but it has to somehow occur naturally, and they just speed up the process by drying the air. Still, I don't understand how the ice evaporates.</p>
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<p>I'm currently going through statistical physics, especially on Fermi energy when I came across a term called "quasi-continuum", what exactly is it?</p>
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<p>I am having a little bit of trouble with this following problem - </p>
<p>Suppose a particle has initial velocity and is moving with a constant acceleration. After t seconds its velocity is v. What will its displacement be in 2t seconds?</p>
<p>I have tried to solve this on my own with the help of these equations - </p>
<ol>
<li>v = u + at ( a is acceleration, u is initial velocity)</li>
<li>s = ut + 1/2 at^2 ( s is the displacement)</li>
<li>v^2 = u^2 + 2as</li>
<li>s = (u+v)*t/2</li>
</ol>
<p>I tried to replace all the acceleration parameter using equation 1(a = (v-u)/t) in all other equations. I've also tried some other ways but they didn't help.</p>
<p>but I couldn't figure out how to do it.</p>
<p>I wish I could have tagged it as <code>high-school physics</code>, but couldn't find such tag.</p>
<p>Any help is appreciated!!!!!</p>
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<p>Russian officials are seriously talking about <a href="http://gizmodo.com/report-russia-will-shut-down-all-u-s-gps-stations-wit-1575641874" rel="nofollow">shutting down US GPS ground stations within their borders</a> and <a href="https://twitter.com/DRogozin/status/466224135018782722" rel="nofollow">Deputy Prime Minister of Russia tweeted on the subject</a>.</p>
<p>What will happen to the GPS? My assumption would be that its accuracy will get worse, at least in some parts of the globe. If it is correct, then where, and by how much exactly?</p>
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<p>If I put a ping pong ball in a vacuum, would it pop? If so, at what point would it happen? Any standard table ping pong ball is acceptable.</p>
| 5,616 |
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<p>I am working on a problem in which I shall find the normalised solution to the 1D particle in a box. Solving for the particle in an asymmetric potential is quite straight forward, but I run into trouble when the potential is symmetric:</p>
<p>$$
V(x) = \begin{cases} \infty & x < -\tfrac{L}{2} \\ 0 & - \frac{L}{2} \leq x \leq \frac{L}{2} \\ \infty & x > \frac{L}{2} \end{cases}
$$</p>
<p>The problems arise with the boundary conditions. We have</p>
<p>$$
\frac{d^2\Psi (x)}{dx^2} = -k^2 \Psi (x)
$$</p>
<p>where $k^2 = \frac{2mE}{\hbar ^2}$. The general solution is</p>
<p>$$
\Psi (x) = Ae^{ikx} + Be^{-ikx}
$$</p>
<p>Due to continuity and the nature of the potential, we must have</p>
<p>$$
\psi (-\tfrac{L}{2}) = \Psi (\tfrac{L}{2}) = 0
$$</p>
<p>Plugging in:</p>
<p>$$
\psi (-\tfrac{L}{2}) = Ae^{-ikL/2} + Be^{ikL/2} = 0 \\
\psi (\tfrac{L}{2}) = Ae^{ikL/2} + Be^{-ikL/2} = 0
$$</p>
<p>I know that when the potential is symmetric, we will find even ($A=B$) and odd ($A=-B$) wave functions. We will see that for even functions, $n$ has to be odd whole numbers, and for odd functions $n$ has to be even whole numbers. This leads to a sequence of sine and cosine curves as $n$ increases by 1.</p>
<p>I am trouble getting there, however, from those boundary conditions, and I would really appreciate pointers and help.</p>
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] |
<p>I'm looking for the resistivity and magnetic permeability of molten gallium arsenide, but can only seem to find the values for the solid material at room temperature (e.g., <a href="https://en.wikipedia.org/wiki/Electrical_conductivity#Resistivity_of_various_materials" rel="nofollow">Wikpedia</a>). Not even temperature-dependency of these parameters seems to be available.</p>
<p>Is this because the value just doesn't change with temperature? If it does, what's a good resource for such parameters?</p>
| 5,618 |
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<p>Around 9pm (GMT) on June 9th, we noticed that the two security cameras had gone dark. Around the same time, a photo voltaic sensor responsible for keeping the yard lights on at night also failed.</p>
<p>In the morning the cameras were back to normal, which means that only the LEDs, responsible for night vision on the cameras, had failed. The cameras are powered by a 12V/2A power supply, which makes it even less likely that a power surge is responsible for the LEDs (and only the LEDs) burning out.</p>
<p>Checking upon the space weather, I noticed that there was a solar flare (M5.9) emitted right around this time. I don't know much about solar flares, but from what I gather M5.9 is on the very low end of things.</p>
<p><strong>Could this be the reason 2 cameras and one photo voltaic sensor failed at the same time?</strong> Or what else should I look into?</p>
<p><em>Mods, sorry if the question is somewhat open ended. Feel free to close the question if not appropriate.</em></p>
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<p>Is it possible to measure gravity other than cause and effect. Gravity is a principle which can only be measured by cause and effect. Ie since an object falls we assume there must be something pushing it down and since this principle holds true for a variety of scenarios, we hold it as true. Is that all we have to go on with gravity? To put it into perspective electricity can be measured by other methods than turning on a light switch and observing the filament glowing. Infrared waves can be measured by heat. For gravity other than seeing an object fall, what other proofs do we have? (Info sourced by RMMS). </p>
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<p>This <a href="http://physics.stackexchange.com/q/67561/">question</a> quotes Hawking saying: </p>
<blockquote>
<p>[...] <em>you enter a world where conjuring something out of nothing <strong>is</strong> possible (at least, for a short while). That's because at this scale particles, such as protons, behave according to the laws of nature we call "quantum mechanics", and they really can appear at random, stick around for a while, and then vanish again to reappear somewhere else.</em></p>
</blockquote>
<p>Nowever, is empty space really nothing? is there a distinction between non-existence and the "nothingness" of space?</p>
<p>Perhaps space is something, we just cannot grasp exactly what it is. Anyone can shed light on whether space is something and what exactly that "something" is.</p>
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] |
<p>From <a href="http://www.atomicarchive.com/Effects/effects3.shtml" rel="nofollow">The Blast Wave</a></p>
<blockquote>
<p><em>A fraction of a second after a nuclear explosion, the heat from the fireball causes a high-pressure wave to develop and move outward producing the blast effect. The front of the blast wave, i.e., the shock front, travels rapidly away from the fireball, a moving wall of highly compressed air.</em></p>
</blockquote>
<p>From <a href="http://en.wikipedia.org/wiki/Shock_wave" rel="nofollow">Wikipedia</a></p>
<blockquote>
<p><em>A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium (solid, liquid, gas or plasma) or in some cases in the absence of a material medium, through a field such as the electromagnetic field. Shock waves are characterized by an abrupt, nearly discontinuous change in the characteristics of the medium. Across a shock there is always an extremely rapid rise in pressure, temperature and density of the flow. A shock wave travels through most media at a higher speed than an ordinary wave.</em></p>
</blockquote>
<p>How shock wave differs from ordinary wave, and how it can travel faster then ordinary wave in same medium. In first ex, In nuclear explosion why shock wave is traveling faster then fireball, when both are in same medium. Can someone please explain the phenomenon in detail.</p>
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<p>Would like to ask a question, but first i would like to say <strong>Hello Everybody</strong> in a way that plays the system, since some geniouses decided that one should not be able to say hello in a question.</p>
<p>The <a href="http://en.wikipedia.org/wiki/Uncertainty_principle" rel="nofollow">uncertainty principle</a> in quantum mechanics is well known and considered one of most basic properties of natural reality. The <a href="http://en.wikipedia.org/wiki/Second_law_of_thermodynamics" rel="nofollow">2nd Law of thermodynamics</a> is also well known and also considered one of the most basic processes of natural reality.</p>
<p>The uncertainty principle uses and is related to <a href="http://en.wikipedia.org/wiki/Planck_constant" rel="nofollow">Planck's constant</a>.
Planck's constant has the dimensions of <em>action</em> and in a statistical mechanics approach, also relates nicely with the partitioning of the phase-space providing the basic measure for the entropy functional (<a href="http://physics.stackexchange.com/a/63325/44176">this answer</a> provides a nice outline of this).</p>
<p>Apart from that, there are <a href="http://arxiv.org/pdf/1205.6894v1.pdf" rel="nofollow">relatively recent papers</a> which relate the Heisenberg Uncertainty Principle in quantum mechanics directly and intuitively to the 2nd Law of Thermodynamics.</p>
<p>Is this relation correct? And if so can we derive one from the other?</p>
<p>Thank you</p>
<p>PS. One can also check <a href="http://physics.stackexchange.com/q/60905/44176">this question</a>, which although not the same, is related in an interesting way.</p>
<p>UPDATE:</p>
<p>anna's answer is accepted since by mentioning the derivation of (part of) the 2nd law from unitary dynamics, answers the question at least in one way. Please consider this as still open so you can add another answer. There are more alternatives (and one of which is my stance, ie thermodynamics -> uncertainty)</p>
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<p>I am trying to see if I am doing a problem correctly. Problem </p>
<blockquote>
<p>Suppose you carry a 50kg sack of potatoes up two flights of stairs, a total height of 10m. How much work did you do? If it took you 20seconds, what was your power outlet?</p>
</blockquote>
<p>(I am NOT looking for the answer, I am just trying to see if I am doing this correctly).</p>
<p>Based on what I have learned to find Work you must do this equation:
$W = Fd$ (force x displacement)</p>
<p>This is where I am a little confused. Not sure what the force is, but going off of my notes to find the force you must do this equation:
$F = ma$ (mass x acceleration).</p>
<p>I already know the mass is 50kg, but to find acceleration I must find it in m/s^2. (Where I think I am getting this wrong). So I know that our meters is 10, and our seconds is 20 (10 m high, and 20 seconds going up stairs), but to find it squared I would do 10/20 / 20 m/s^2 which equals 0.025 m/s^2 for my acceleration.</p>
<p>Going back to finding force I can now plug in my acceleration of 0.025 as follows:</p>
<p>$F = (50kg) \times (0.025m/s^2) J$</p>
<p>$F = 1.25 N$</p>
<p>$W = (1.25) \times (10)$</p>
<p>$W = 12.5 J$</p>
<p>Did I do this correctly? If not, instead of answers, let me know what I did wrong, and maybe like a hint at what I should do next. I appreciate any help given. </p>
| 5,624 |
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<p>This question has a flavor which is more mathematical than physical, however it is about a mathematical physics article and I suspect my misunderstanding occurs because the precise mathematical definition of the concepts used is different than what I think. But then again, it might be some foolish mistake on my part.</p>
<p>I'm reading "<a href="http://arxiv.org/abs/hep-th/0410178">Topological strings and their physical interpretation</a>" by Cumrun Vafa and Andrew Neitzke. On p. 14 they introduce the "deformed conifold" (really complex 3-sphere) which is given by the equation</p>
<p>xy - zt = μ (equation 2.27 in the article)</p>
<p>in C^4 with coordinates (x, y, z, t) and μ a constant. According to the article, μ plays the role of a complex structure modulus, that is, varying μ we get diffeomorphic manifolds with different complex structure.</p>
<p>On p. 14 below equation (2.27) they write</p>
<blockquote>
<p>This gives a Calabi-Yau 3-fold for any value μ ∈ C, so μ spans the 1-dimensional moduli
space of complex structures</p>
</blockquote>
<p>Also on p. 16 they write</p>
<blockquote>
<p>In summary, we have two different non-compact Calabi-Yau geometries, as depicted in
Figure 5: the deformed conifold, which has one complex modulus r and no Kahler moduli,
and the resolved conifold, which has no complex moduli but one Kahler modulus t</p>
</blockquote>
<p>Here μ was replaced by r since they change coordinates to rewrite (2.27) in the form</p>
<p>x_1^2 + x_2^2 + x_3^2 + x_4^2 = r (equation 2.30 in the article)</p>
<p>However, for any lambda non-zero, multiplication of the coordinates by lambda yields a biholomorphic mapping between the complex manifolds corresponding to μ and lambda^4 μ. Thus they are all isomorphic.</p>
<p>What am I missing here?</p>
| 5,625 |
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<p>Consider $N$ qubits. There are many complete sets of $2^N+1$ mutually unbiased bases formed exclusively of stabilizer states. How many?</p>
<p>Each complete set can be constructed as follows: partition the set of $4^N-1$ Pauli operators (excluding the identity) into $(2^N+1)$ sets of $(2^N-1)$ mutually commuting operators. Each set of commuting Paulis forms a group (if you also include the identity and "copies" of the Paulis with added phases $\pm 1$, $\pm i$). The common eigenstates of the operators in each such group form a basis for the Hilbert space, and the bases are mutually unbiased. So the question is how many different such partitions there exist for $N$ qubits. For $N=2$ there are six partitions, for $N=3$ there are 960 (as I found computationally).</p>
<p>The construction above (due to Lawrence et al., see below) may be an example of a structure common in other discrete groups - a partition of the group elements into (almost) disjoint abelian subgroups having only the identity in common. Does anyone know about this?</p>
<p>Reference:</p>
<p>Mutually unbiased binary observable sets on N qubits - Jay Lawrence, Caslav Brukner, Anton Zeilinger, <a href="http://arxiv.org/abs/quant-ph/0104012" rel="nofollow">http://arxiv.org/abs/quant-ph/0104012</a></p>
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<p>In their proof, Hohenberg and Kohn (<a href="http://prola.aps.org/abstract/PR/v136/i3B/pB864_1">Phys Rev 136 (1964) B864</a>) established that the ground state density, $\rho_\text{gs}$, uniquely determines the Hamiltonian. This had the effect of establishing an implicit relationship between $\rho_\text{gs}$ and the external potential (e.g. external magnetic field, crystal field, etc.), $V$, as the form of the kinetic energy and particle-particle interaction energy functionals are universal since they are only functions of the density. This implicit relationship defines a set of densities which are called $v$-representable. What is surprising is that there are "a number of 'reasonable' looking densities that have been shown to be impossible to be the ground state density for any $V$." (<a href="http://books.google.com/books?id=dmRTFLpSGNsC&printsec=frontcover&dq=Electronic%20Structure%20Martin&hl=en&src=bmrr&ei=HsF8TrDrM8S2sQKCiZVI&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDEQ6AEwAA#v=onepage&q&f=false">Martin</a>, p. 130) On the surface, this restriction looks like it would reduce the usefulness of density functional theory, but, in practice, that is not the case. (See the proof by Levy - <a href="http://www.pnas.org/content/76/12/6062.abstract?sid=11ea2824-f673-4d3f-95dd-78ab6f9e036e">PNAS 76 (1979) 6062</a>, in particular.) However, research continues into the properties of the $v$-representable densities, and I was wondering if someone could provide a summary of that work.</p>
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<p>I am currently studying affine Lie algebras and the WZW coset construction. I have a minor technical problem in calculating the (specialized) character of $\widehat{\mathfrak{su}}(2)_k$ for an affine weight $\hat{\lambda} = [k-\lambda_1,\lambda_1]$. Given the generalized theta function
$$\Theta_{\lambda_1}^{(k)}(z,\tau) = \sum_{n\in\mathbb Z}e^{-2\pi i\left[knz+\frac 12\lambda_1 z-kn^2\tau-n\lambda_1\tau- \lambda_1^2\tau/4k\right]}$$
I want to evaluate
$$\chi^{(k)}_{\lambda_1} = \frac{\Theta^{(k+2)}_{\lambda_1+1} - \Theta^{(k+2)}_{-\lambda_1-1}}{\Theta^{(2)}_1 - \Theta^{(2)}_{-1}}$$
at $z=0$. Putting $z=0$ directly, both the numerator and denomerator vanish (since there is no difference between $\lambda_1$ and $-\lambda_1$ due to the sum). So my question is; what is the appropriate way to take the limit $z\rightarrow 0$? [This is from <a href="http://books.google.dk/books?id=keUrdME5rhIC&dq">Di Francesco et al</a>, section 14.4.2, page 585]. The result should be
$$\chi^{(k)}_{\lambda_1} = q^{(\lambda_1+1)^2/4(k+2)-\frac 18}\frac{\sum_{n\in\mathbb Z}\left[\lambda_1 + 1 + 2n(k+2)\right]q^{n[\lambda_1+1+2(k+2)n]}}{\sum_{n\in\mathbb Z}\left[1+4n\right]q^{n[1+2n]}}$$
where $q=e^{2\pi i\tau}$.</p>
<p>Since I fear the solution to my question is rather trivial, I have a bonus question. Do you know any paper which works out the details for the coset
$$\frac{\widehat{\mathfrak{su}}(N)_k\oplus \widehat{\mathfrak{su}}(N)_1}{\widehat{\mathfrak{su}}(N)_{k+1}}$$
for arbitrary $N$? I am thinking about something like what Di Francesco et al. does in section 18.3 for $N=2$. It would be nice if the reference relates this to $\mathcal W$-algebras.</p>
| 5,628 |
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<p>I just bought a small <a href="https://www.sparkfun.com/products/11676" rel="nofollow">OLED screen</a> and was wondering is it possible to make a screen surface a little bit bigger ( 2x ) by projecting it through some optics on translucent surface. It reminds me of viewfinders in some old cameras or SLR lens adapters or DIY LCD projectors.</p>
<p>Does it even make any sense?</p>
<p>I'm positive that some fresnel lenses will be needed but can't get a grasp on their configuration for this to work. </p>
<p>I've found pretty simple <a href="http://physics.bu.edu/~duffy/java/Opticsa1.html" rel="nofollow">lens simulator</a> and it makes it look like it can be done with only 2 lenses. But it don't seem right.</p>
<p>I know that with LCD projectors you need a fresnel lens and a triplet. Can it be simplified at the expense of image distortion?</p>
| 5,629 |
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<p>Why do we assume that in normal modes, particles oscillate in form cos (wt) ?</p>
<p>How do we know that the general motion of particles can be expressed as a superposition of normal modes?</p>
<p>In both French and Crawford, the assumption of harmonic motion is made without any proof, please help.</p>
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<p>In the Lorenz gauge, we have a beautiful relation between the four-current and the four-potential:</p>
<p>$$\Box A^{\alpha} = \mu_0 J^{\alpha}$$</p>
<p>To get $A$ in terms of $J$, however, we have to use a considerably uglier formula; or, at least, this is the formula presented in textbooks:</p>
<p>$$A^{\alpha}(t, \mathbf{r}) = \frac{\mu_0}{4\pi} \int \frac{J^{\alpha}\left(t - \frac{1}{c}\|\mathbf{r} - \mathbf{r}'\|, \mathbf{r}' \right)}{\|\mathbf{r} - \mathbf{r}'\|} d^3\mathbf{r}'$$</p>
<p>The first equation is evidently Lorentz covariant. The second one, on the other hand, doesn't look covariant at all. The integrand has some messy dependence on $(t, \mathbf{r})$ and the integration goes over only the spatial dimensions.</p>
<p>Can we rewrite the second equation in a covariant form? If not, then why not?</p>
| 5,631 |
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<p>In the frame of photon does time stop in the meaning that past future and present all happen together?</p>
<p>If we have something with multiple outcomes which is realized viewed from such frame? Are all happening together or just one is possible?</p>
<p>How the communication between two such frame s work meaning is there time delay for the information as $c$ is limited? If there is time delay does it mean that time does not stop?</p>
<p>My question does not concern matter at that speed rather how it looks viewed from the photon reference.</p>
<p>Thanks Alfred! I think I understand it now.</p>
| 195 |
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] |
<p>According to Einstein's <a href="http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence" rel="nofollow">mass-energy relation</a> mass and energy are interchangeable. Can you provide some examples where:</p>
<ol>
<li><p>Mass gets converted into energy.</p></li>
<li><p>Energy gets converted into mass.</p></li>
</ol>
| 46 |
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<p>I was browsing the NEXRAD radar feeds (I'm not an expert, just figuring them out) and I came across the following signature (visit the link to view the radar image)</p>
<p><a href="http://cl.ly/3n0y0p0g2M0K2B313g3U" rel="nofollow">http://cl.ly/3n0y0p0g2M0K2B313g3U</a></p>
<p>The radar in question was operating in clear air mode and the "ray" varies from about 0-16 dBZ. There were several of these all covering the Midwest, and I picked up one as far west as Kansas, at about the same return signal strength. Further west they weren't visible.</p>
<p>Could this be caused by a cosmic phenomenon?</p>
<p>IMMEDIATE FOLLOW-UP:</p>
<p>I'm tracking it across the United States right now. I'll be following it below with updates.</p>
<ul>
<li>9:16 PM: appears on KIND Indianapolis composite reflectivity</li>
<li>9:30 PM: appears on KSGF Springfield base tilt 1 and 2, KICT Wichita base tilt 2</li>
<li>9:31 PM: updated KSGF now shows only on base tilt 1, not 2</li>
<li>9:34 PM: now appears only on KICT Wichita base tilt 3? This doesn't make sense if it's a "stationary" cosmic object, that would mean it should be shifting to lower tilts. Might just be an outlier</li>
<li>9:37 PM: visible now on KDDC Dodge City base tilt 4, KICT tilts 2 and 3. Also now appears on KAMA Amarillo base tilts 4 and 3 (weaker on 3)</li>
<li>9:43 PM: visible on KICT base tilt 2 only</li>
</ul>
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<p>Is there any speed different between blue or red color? Is there speed different? or there are same speed? </p>
| 5,633 |
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<p>Let's say I would want to light up Venus, such that we can see Venus all day long and not have to wait for a Venus Transit. What kind of light would I need for it? How powerful would it need to be?</p>
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<p>Let me explain.</p>
<p>My shower is inconsistant in how hot it gets. Whenever I turn on the shower, I always put my hand really close to the water, but not touching it, so I can feel the heat radiate from the shower. That way, if I can feel it from a distance, I know it is too hot.</p>
<p>I also notice that if the water is very cold, I can feel it as well. Do I feel the absence of radiating heat? Am I actually touching the water and not noticing it?</p>
<p>Sorry if the questions isn't technical enough; it's more of an everyday physics question.</p>
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<p>My understanding is that dark energy, or equivalently a positive cosmological constant, is accelerating the expansion of the universe and I have read that this gives empty space-time positive curvature, ie de Sitter geometry. I also understand that parallel geodesics converge when curvature is positive and diverge when it is negative. I would expect accelerating expansion of space to make parallel space-time geodesics diverge and thus make curvature negative. Is there a nice visual explanation why dark energy actually produces positive curvature?</p>
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] |
<p>I need a concise definition of a fluid flux and an accompanying example. I've never taken a single physics course before, but I'm required to understand this concept so I can do the calculations for a Complex Analysis class. </p>
| 5,637 |
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<p>As I understand neutrinos, there are three different flavors, all with different masses. Although the masses of these neutrinos have not been directly measured, their mass differences have been. Current experiments, KATRIN and Project8 are going to measure neutrino masses and we shall know soon enough. Regardless, their mass states change as they travel through space. This leads to my question...</p>
<p>Since an object's gravitational field is related to its mass and neutrinos have different mass states while they are traveling, it must mean that every point in space must be constantly altering in gravity intensity!</p>
<p>Although every object alters the gravitational field intensity as it travels and passes a given point, neutrinos would do it differently because they keep changing mass states!</p>
<p>Let's assume a constant stream of neutrinos pass by a point in space versus neutrinos that don't oscillate (This is hypothetical) doing the same thing. Wouldn't these extremely weak gravitational waves be different given oscillations than not?</p>
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<p>How can someone calculate the power in watt that a runner produces, when he runs uphill and downhill?</p>
<p>Is there any algorithm? It is important to take under consideration the uphill and downhill elements of the run.</p>
<hr>
<p>Thank you for your answers but i am confused since i don't have a background in physics.
To make thinks simple, i have some values, and using these values and maybe some constants like gravity, i want to create a calculator for real time watt production.
These values are:</p>
<p>INSTANT VALUES: speed, distance, hr, kcal, ascent, descent, duration.
OTHER VALUES: body mass, vertical speed (average), ascent time, descent time, max hr, rest hr, vo2max.</p>
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] |
<p>if you have water flowing through a 6 or 4 inch pipe what would the pressure be if tapped off through a 1/2 inch BSP tap. What would the equation be to find out the pressure at different flows?</p>
| 5,640 |
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<p>As we know electrons continuously revolve around the nuclus without falling in it at a high velocity beating it's force of attraction. My question is where do electrons get energy to revolve around the nucleus and withstand its force of attraction.</p>
| 202 |
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<p>In an unbiased PN junction, when the carriers recombine to form a depletion layer , it is said that immobile ions are formed.</p>
<p>We know that the conduction band electrons in N type are not associated with any particular atom. So when the conduction band electron diffuses to the P type region, which atom becomes an ion?</p>
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<p>First let me state that I am not, nor ever have I been, a physics student. I am working on an idea for a book I'm writing.</p>
<p>This is a thought experiment that posits the existence of a computer system that, to cut right to the point, has within its memory banks the thoughts, memories, and experiences of every human being who has ever died on Earth, and this data is continuously updated in real time. Also, this computer system has a constant stream of data fed to it from a network of planetary sensors that record every physical event that occurs on the planet, from the shifting of tectonic plates beneath the Earth's crust to the ol' hackneyed flapping of a butterfly's wings. This computer system is able to process this data through a realizable causal filter that allows it to create an unimaginably detailed model of, well, everything.</p>
<p>This computer system should therefore be asymptotically omniscient, in regard to past and ever-present events that occurred and are occurring. Its data would not be 100% reliable, as there is a distinct difference between observed past (which is subject to interpretation), and actual past (which is indelible), and keep in mind that the physical data fed to it by the planetary sensors would also be considered as observations. I feel that the sheer amount of raw data available would make it so that, when looked at as a whole, multitudinous patterns of causation would emerge.</p>
<p>My question is this: In the example that I described, is there anything that would physically prevent the computer system from anticipating (within specific parameters) future events to a given degree of probability, the accuracy of which would be proportional to the magnitude of the event, and inversely proportional to the time interval between the predicted event and the present? </p>
<p>Furthermore, would it be conceivable that the computer system, when analysing a given prediction, could indicate (within a degree of probability) specific critical points in time and space that, if interfered with by the computer system's operator, could drastically raise or lower the odds of the original predicted event actually occurring? </p>
<p>Further still, the computer system should also be able to simultaneously calculate the potential effects of such an interference, and suggest a course of action that is least likely to create unwelcome consequences further down the road.</p>
<p>Assumptions:
The computer system possesses near-infinite processing power and internal storage.</p>
<p>The computer system is programmed to constantly scan for future catastrophic events within a specific magnitude, and when such an event is detected, the computer system is programmed to analyse the various patterns of causation leading up to the event, and suggest optimal points of interference, with the goal of averting the catastrophe.</p>
<p>The computer system operates within a stochastic universe, thus 100% accurate predictions are asymptotically impossible.</p>
| 5,642 |
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<p>Vafa proposed <a href="http://arxiv.org/abs/hep-th/0008142" rel="nofollow">a duality</a> when embedding <a href="http://arxiv.org/abs/hep-th/9811131" rel="nofollow">the Gopakumar-Vafa duality</a> into superstring theory. Vafa's duality is about a correspondence N=1 supersymmetric gauge theory and superstring propagating on noncompact CY manifolds with flux turned on. I am puzzled about this relation. </p>
<p>a) On superstring theory side, is the total dimension six or ten? In the other words, it is the duality about ordinary string theory or topological string theory?</p>
<p>b) Where does the N=1 gauge theory come from? IIA superstring theory compactification on conifold internal space with $D_6$ branes wrapped around 3-cycles, its geometric transition counterpart, or $D_6$ branes world volume theory?</p>
<p>Thanks in advance.</p>
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<p>A ball (radius $R$) has three layers. For $0<r<a$ it is a conductor with free charge $+Q$. For $a<r<b$ it is a linear dielectric $\epsilon$ with free charge embedded in it with density $\rho_{free}(r) = \left(\frac{\rho_0}{a^2}\right)r^2$. From $b<r<R$ it is a conductor again with some amount of charge on it $q$ which makes the field vanish for $r\lt R$. I'm supposed to:</p>
<ol>
<li>Find the polarization $\vec P$ in the dielectric</li>
<li>Find bound volume charge density in the dielectric</li>
<li>Find free and bound surface densities at each surface $r=a,b,R$</li>
</ol>
<p>So I tried using Gauss's law here with a sphere of radius $a<r<b$ as my surface to get $\vec P$:$$\oint \vec D\cdot d\vec A =Q_{free}+\int_a^r \rho_{free} dr$$$$D = {Q+\frac{\rho_0}{3a^2}(r^3-a^3)\over4\pi r^2}$$</p>
<p>Using $\vec D = \frac{\vec E}{\varepsilon}$ and $\vec P = \varepsilon_0\chi_e\vec E$ and $\rho_b=-\nabla\cdot\vec P$ I calculated: $$\vec P = \frac{\varepsilon_0\chi_eQ}{4\pi\varepsilon r^2}+\frac{\varepsilon_0\chi_e\rho_0}{12\pi\varepsilon}({r\over a^2}-{a\over r^2})\hat r$$$$\rho_b = \frac{\varepsilon_0\chi_e}{2\pi\varepsilon}(\frac{Q}{2r^2}-\frac{\rho_0r}{3a^2}+\frac{\rho_0}{6r^2})$$</p>
<p>Two questions:</p>
<ol>
<li><p>Is that right?</p></li>
<li><p>How do I use that to calculate the surface charge densities $\sigma_b$ and $\sigma_f$ for each surface?</p></li>
</ol>
| 5,644 |
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<p>In a previous question (<a href="http://physics.stackexchange.com/questions/65979/calabi-yau-manifolds-and-compactification-of-extra-dimensions-in-m-theory">Calabi-Yau manifolds and compactification of extra dimensions in M-theory</a>), I was told that the $G(2)$ lattice can be used to compactify the extra 7 dimensions of M-theory and preserve exactly $\mathcal N=1$ supersymmetry.</p>
<p>However, since there is only 1 $G(2)$ lattice, there should be only 1 4-dimensional M-theory. Then, why is there such a huge fuss about the M-theory landscape?</p>
<p>Thanks!</p>
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] |
<p>Two light sources emit light at the same moment but in opposite directions. At what speed the distance between two light fronts is increasing? <strong>c</strong> or <strong>c</strong> * 2?</p>
<p>Note, that there is only one coordinate system here - a system, where these two light sources are placed and they don't move.</p>
| 109 |
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