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<p>Let's say I initially have an open, empty, soda can. I then turn it over and lower it into a bowl of water, and then release it. Obviously water rises to some level in the cup and then there is air at the top of the can, which was initially the bottom.</p>
<p>Are there only three forces on the can once it reaches equilibrium?</p>
<ol>
<li><p>Buoyant force from the water (up)</p></li>
<li><p>Weight of the can itself (down)</p></li>
<li><p>Air pressure inside the can acting on the water surface (down)</p></li>
</ol>
<p>Let me know if all of these are right, otherwise my equation for total forces is...</p>
<p>F_b = mg + P where m is the mass of the can, and P is the air pressure in the cup</p>
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<p>When construct spin liquid by projective symmetry group, we can classified spin liquids by the invariant group (IGG) of their mean field ansatze. For example, we can have Z2, U(1) and SU(2) spin liquids. In my understanding, IGG is equivalent to the low-energy gauge fluctuation. However, I am confused whether states with the same IGG actually have the same topological order? For example, do all the $Z_2$ spin liquid share the same $Z_2$ topological order? If so, is this $Z_2$ topological order corresponds to toric code or double semion?</p>
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<p>This is about continuity equation. What does the last integral mean?
$$\frac{\mathrm{d}Q_V}{\mathrm{d}t}=\iiint_V \mathrm{d}^3x \,\frac{\partial\rho}{\partial t}=-\iiint_V\! \mathrm{d}^3x\,\operatorname{div}\,\mathbf{j}=-\iint\limits_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf j\;\cdot\mathbf n\,{d}S\,,$$</p>
<p>EDIT:
And what does $\partial V$ mean? Why not S like surface?</p>
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<p>After recently going through a short program of self-study in quantum mechanics, I was surprised to find a quote attributed to Feynman essentially saying he was extremely bothered by the computational process of renormalization. It's "dippy" that anyone should have to subtract one infinity by another in order to arrive at a finite answer. </p>
<p>What's he referring to there, in rough terms? And what's the latest in attempts to replace this computational procedure with something more physically plausible, so that the theory can have more meaning and less dippiness? </p>
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<p>The canonical quantization of a quantum field prescribes that given a lagrangian, one can quantize the theory by imposing the commutation relations between the field operators and their conjugated momenta.The field operators are then obtained by solving the equation of motion for plane waves.</p>
<p>However, why is this correct? The equation of motions are derived in the classical theory from the requirement that the action be stationary. This requirement does not apply in quantum theory where all possible paths contribute to the action.</p>
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<p>Suppose you know kx,ky,kz points along with the corresponding energies. Basically, you know about the 4-D E(k) dispersion.</p>
<p>How you do then convert that data into the bandstructure plots you commonly see which show E(k) along a closed path through high-symmetry points through the Brillouin zone?</p>
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<p>This should be simple, but it keeps bothering me. If a rigid body has no fixed axis, and a torque (defined relative to a point $A$) is applied, it will rotate around $A$. But often I can also calculate the torque relative to another point $B$ (which often seems to be non-zero too). So does this mean that the rigid body will have an angular acceleration about both axises? This seems a bit strange to me. </p>
<p>(For a fixed axis I assume that a rotation around any axis (other than the fixed axis) is impossible, because there will always be zero torque around those axes.)</p>
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<p>Why if the earth is spinning at 1000mph a person falls from 10 stories his body didn't land about 1.4 miles away but right down as if the earth didn't spin at all</p>
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<p>I've been reviewing derivations of the spherical harmonics in quantum mechanics; mostly as review but also to make sure I understand where the concepts arise from. </p>
<p>However, every derivation I've seen makes use of the following differential equation/ identity that seemingly comes from nowhere. I've not yet been able to figure out where it comes from in looking through various texts. So, here I am to ask: where does this come from? </p>
<p>$$\frac{d}{d\theta}+l cot(\theta) \equiv \frac{1}{(sin(\theta))^l} \frac{d}{d\theta}(sin(\theta)^l)$$</p>
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<p>Going to word this question a bit more straightforward than I may have before. Also, I'm trying to use baby formulas so I can grasp exactly what's going on.</p>
<p>Object A has an elasticity of <code>Y</code>, and is propped against an effectively immobile rigidbody.</p>
<p>Object B is a rigidbody with mass <code>M</code>, and is colliding against Object A perpendicularly. Various Object B's may have a different shape by which to strike Object A. Some may be flat and apply strain uniformly across the whole of Object A, while some may be sharp and concentrate the strain in a smaller area.</p>
<p>Here's a diagram:
<a href="http://smg.beta.photobucket.com/user/TuahS/media/Collision_zps37a2afd6.jpg.html?sort=3&o=0" rel="nofollow">Diagram</a></p>
<p>I'm trying to figure out how quickly Object A's stress accelerates Object B in the opposite direction. <code>f=ma</code> has been thrown to me, but I'm a very visual person and don't exactly see where <code>f</code> is coming from. Intuition tells me that the collision area is important, and that the only area of Object A that matters is what's in the immediate collision area.</p>
<p>Is it simply Object A's stress multiplied by the area of impact?
And would it in-turn effectively accelerate Object B at a rate of stress/mass/sec^2?</p>
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<p>An electric charge $Q$ is distributed through out a nonconducting sphere of radius $r_ 0$ and has a spherical cavity of radius $r_1$ centered at the sphere's centre. Assume the charge $Q$ is distributed in the shell (i.e. between $r=r_1$ and $r=r_0$ ) and that the charge density varies as ρ= $(ρ_0 ∗r_1/r)$ Find the electric field as a fuction of $r$ for $r>r_0$ </p>
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<p>I did a Standard Model calculation and I want to compare my answer to a measured value.</p>
<p>Does anyone know the literature value for the forward-backward asymmetry $\frac{\sigma_F - \sigma_B}{\sigma_F + \sigma_B}$</p>
<p>for the process $e^+e^- \to \mu^+\mu^-$ on the $Z$ resonance (where $\sigma_F = \int_0^1 d\cos \theta \frac{d\sigma}{d \cos \theta}, \sigma_B = \int_{-1}^0 d \cos\theta \frac{d\sigma}{d \cos\theta}$)?</p>
<p>I'm unfamiliar with the literature, so I'd appreciate any help. Thanks!</p>
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<p>Imagine that two widely separated charged particles $A$ and $B$ exchange a photon.</p>
<p>Because they are far apart one can imagine that there is a major contribution to the photon propagator that travels at the speed of light from $A$ at a time $T_0$ to $B$ at a time $T_1$ where $T_1 > T_0$.</p>
<p>But in that case is there also a major contribution to the photon propagator that travels <em>backwards in time</em> at the speed of light from $B$ at time $T_1$ to $A$ at time $T_0$?</p>
<p>The forwards-in-time photon imparts momentum to particle $B$ whereas the backwards-in-time photon imparts a reaction momentum back to particle $A$.</p>
<p><img src="http://i.stack.imgur.com/j4eZO.jpg" alt="diag"></p>
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<p>I was talking with an acquaintance about lightning, and we came up with opposite theories and predictions for the frequency of lightning over ocean.</p>
<ul>
<li><p>My theory is that since seawater is a fluid riddled with ions, the charges can move to equalize with whatever field is applied to it; therefore it should take a much higher, much faster increase in the magnitude of cloud charge to cause the dielectric breakdown necessary for a strike--in other words, the clouds have to beat the ocean to the punch before it dissipates the increase. So I predict less frequent lightning over the ocean.</p></li>
<li><p>His theory is that the composition of the lower surface is irrelevant; it's the insulating effect of the air that contributes to favorable conditions for lightning generation. He predicts more or less equal frequency of lightning over land or sea.</p></li>
</ul>
<p>Wikipedia bears out my prediction (sourced from NASA data):
<img src="http://i.stack.imgur.com/BiXok.png" alt="NASA world lightning frequency"></p>
<p>According to the <a href="https://en.wikipedia.org/wiki/Distribution_of_lightning" rel="nofollow">distribution of lightning</a> page, strikes occur most frequently in the tropics, on land. What makes this possible? More importantly, <em>which of us is right?</em> ;)</p>
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] |
<p>PHYSICS of Brushing your teeth:
I spent a few weeks a few years ago, five minutes here and there, trying to figure out what is the optimal amount of water that you should put in your mouth to get the maximum rinsing effect after you brush your teeth. Do you fill your mouth half full, 1/3 full or what? If you want to rinse out a bottle with water then how full do you fill it before you shake it? With less water the water has more distance to travel. With more water there is more mass involved. Are you looking for energy transfer or momentum, one involves the square of the velocity and one only varies linearly with velocity. This kind of question actually comes up when you analyze tankers full of fuel and motorcycle design where they look at making high speed turns. The forces are not negligeable.</p>
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<p>Usually one is led to think of an electron moving from the valence band to the conduction band as an electron leaving the atom it is bound to in the lattice, and becoming free to move, while leaving apart a hole that is free to move as well. How accurate is that picture, how useful is it, and what does it really mean? </p>
<p>If I understand correctly, the (energy eigen)states in the valence band are such that the electron is more tightly bound to atoms in the lattice than it would be in an individual atom, though for every single state the electron is found with equal probability at every nucleus in the lattice, i.e. individual electrons are not bound to specific sites. </p>
<p>Electrons in the conduction band are more weakly bound than they would be in a single atom. Is it the particular combined state of all electrons that causes the probability to find an electron at some lattice point to be lower than at others (location of a hole), and the probability of finding an electron at some non-lattice point to be higher than at others (location of an electron that is free to move/not bound to any atom)?</p>
<p>Does a change in the state of one electron to a state that is nearby in the conduction band correspond to the movement of a free electron, and that of a state in the valence band to a nearby state to the movement of a hole?</p>
<p><strong>ADDED LATER</strong></p>
<p>I'll try to be more specific, assuming that my understanding outlined above is more or less correct. When introducing bands, usually a picture is drawn in which there are two very densely spaced ranges of energy eigenfunctions that can each be occupied by one (or two, when not taking spin into account) electrons. The combined ground state would have the valence band fully occupied, and the conduction band empty. </p>
<p>When an electron gets excited from the valence band to the conduction band, this is described as the electron moving to a higher energy level, leaving the lower energy level free, but at the same time as an electron leaving a fixed position (in the crystal lattice), and becoming free to move. </p>
<p>Since the energy eigenstates don't localize the electron at any particular lattice site, the equivalence of these two interpretations seems not at all obvious, nor how it could work. Is it that there is a change of basis in which the electrons are localized, and in which interchanging the coefficient of a state in the valence band with that of a state in the conduction band corresponds to a displacement of an electron. Does this have to do with the <em>Bloch states</em> and <em>Wannier states</em> mentioned in the answer to <a href="http://physics.stackexchange.com/questions/48529/semiconductors-and-localization-of-the-electrons">the question that John Rennie referred to in his comment</a>?</p>
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<p>I would like some book reference regarding the history of physics. I'm a civil engineering student, and I want to have some basics on the type of developments regarding my field of specialization (structures). For example, I want to look at something and know "No, this can't be it, because this is a physics conception already refuted by ... in ...; what is really going on now is ..etc.". Resuming, history book on physics to give a structural engineer a good insight in the areas he might see through his work. I know I gonna see classical mechanics, because I'm studying a lot of it, but I don't understand why. Didn't Einstein refuted that? I wasn't supposed to be seeing relativity?</p>
<p>Sorry if the question is stupid, I didn't had anywhere else to ask. Have a nice day.</p>
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] |
<p>What is the most common definition of <a href="http://en.wikipedia.org/wiki/Heavy-tailed_distribution#Definition_of_long-tailed_distribution" rel="nofollow">long tailed distribution</a> for physicists? I am looking for definition and examples. Examples should have arguments why the distribution is or is not long tailed.</p>
<p>I know that there are a few definitions.</p>
| 9,089 |
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<p>Normally water molecules are electrically neutral.
But I have seen somewhere ideas about electric energy generators mentioning that water droplets might be used in some applications as they are charged particles.</p>
<p>Is it really so? </p>
<p>I know that water droplets <a href="http://en.wikipedia.org/wiki/Triboelectric_effect" rel="nofollow">get charged</a> due to friction in the bottoms of waterfalls producing static discharges. But is there some other more fundamental process which makes evaporated or sprayed water droplets become charged? </p>
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<p>I have seen this post:</p>
<p><a href="http://www.nydailynews.com/news/politics/new-infrared-laser-weapon-shoot-drones-disable-ships-navy-article-1.1311093" rel="nofollow">New infrared laser weapon, the Laser Weapons System, could shoot down drones or disable ships: US Navy</a></p>
<p>You can watch the <a href="http://www.youtube.com/watch?v=OmoldX1wKYQ" rel="nofollow">video</a> as well. that exhibits a laser weapon which can burn a fighter aircraft.</p>
<p>I have two questions:</p>
<ul>
<li>How does it work?</li>
<li>Is it possible to create a <code>mirror</code> which can reflect the laser beam back ? If so, why won't the mirror burn up as well?</li>
</ul>
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<p>This might be a bit more of an engineering question, but I'm calculating air density drop-off with altitude, and I'm having some problems calculating the pressure (I'll run through my method). <a href="http://en.wikipedia.org/wiki/Density_of_air#Altitude" rel="nofollow">This has been very useful in explaining</a>, but the last bit lost me a little. </p>
<p>So we start with an ideal gas, then: </p>
<p>$$ pV = nRT $$ and using $$\frac{\rho V}{n} = M$$ where M is molar mass, you can calculate density to be:</p>
<p>$$ \rho = \frac{pM}{RT} $$ which implies a solution dependent only on pressure (p) and temperature (T). </p>
<p>Then define temperature using the Universal Standard Atmosphere lapse rate, $$T = T_0 - Lh$$ where L = 0.0065K/m and h is height in metres</p>
<p>Now at this point I'm a bit stuck. Wikipedia suggests the following equation: </p>
<p>$$p = p_0 \left(1 - \frac{L h}{T_0} \right)^\frac{g M}{R L}$$</p>
<p>Which, when calculated, provides values within a 5% tolerance - but where has it come from? I can't find any reference to its source or how it was derived. Can anyone help?</p>
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<p>I have a problem with the Hamiltonian, I don't think anything to solve it!!
So could you give me some hints!</p>
<ul>
<li>Knowing that:
$$\left[ {{{\hat p}_i},{{\hat q}_k}} \right] = \frac{\hbar }{i}{\delta _{ik}}.$$</li>
</ul>
<p>Hamiltonian is: </p>
<p>$$\begin{array}{l}
\hat H = \hat q_i^{},\hat q_i^2,\hat q_i^3,....,\hat q_i^n, \\
(n \in N) \\
\end{array}$$</p>
<p>Proof that:
$$\left[ {\hat H,{{\hat p}_i}} \right] = - \frac{\hbar }{i}\frac{{\partial \hat H}}{{\partial {{\hat q}_i}}}.$$</p>
| 9,093 |
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<p>It is stated in many popular science videos that one of the reasons that quantum mechanics is so wacky is that if you measure which slit the photon/particle went through on the way, then you no longer get the interference pattern. I want to ask how that is done? How do we detect which slit it went through?</p>
| 9,094 |
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<p>I'm new to field theory and I don't understand the difference between a "local" functional and a "non-local" functional. Explanations that I find resort to ambiguous definitions of locality and then resort to a list of examples. A common explanation is that local functionals depend on the value of the integrand "at a single point."</p>
<p>For instance, this functional is given as local, $$ F_1[f(x)] = \int_{a}^{b} dx f(x) $$ but this functional is not $$ F_2[f(x)] = \int_{a}^{b} \int_{a}^{b} dx dx' f(x) K(x, x') f(x') $$</p>
<p>To further compound my confusion, some references (see Fredrickson, Equilibrium Theory of Inhomogeneous Polymers) state that gradients make a functional non-local (or I have even heard the term semi-local), whereas others (see <a href="http://physics.stackexchange.com/questions/13624/why-are-higher-order-lagrangians-called-non-local">Why are higher order Lagrangians called 'non-local'?</a>) state that gradients do not make a functional non-local.</p>
<p>Is there a more rigorous definition of locality?</p>
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<p>Whenever you hear someone illustrating/describing the transmission of radio waves they always make it seem like they'd travel perfectly around the Earth to another distant location. For example, a radio wave sent by alternating current to be received from an intercepting device on the other side of the planet.
You'd think of something like:</p>
<p><img src="http://i.stack.imgur.com/up1VA.jpg" alt="enter image description here"></p>
<p>Top frame shows how most media works, etc., would illustrate it: radio waves illustrated to go perfectly wrapped around Earth like a straight line until it gets to the other side.</p>
<p>Bottom frame shows how it should work (supposedly) if radio waves travel at all directions at the speed of light: will go right through the ground to the other side of the planet.</p>
<p>Basically, it will travel in all directions, but measuring how it gets there it should really appear like this, no?</p>
<p><img src="http://i.stack.imgur.com/usO1J.jpg" alt="enter image description here"></p>
<p>To put the question in perspective, will radio waves go right through the ground and reach the other point near instantly, all on the other side of the Earth? </p>
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<p>This is a question about terminology. To me, it's clear that the nucleus of an atom is still an atom. But a comment by Willie Wong at <a href="http://physics.stackexchange.com/questions/11562/is-nature-symmetric-between-particles-and-antiparticles/11563#comment-28303">Is nature symmetric between particles and antiparticles?</a> raises this question. Similarly, arguments go either way at the physics forums question: "is it possible for an atom to have no electrons?" <a href="http://www.physicsforums.com/showthread.php?t=50333" rel="nofollow">http://www.physicsforums.com/showthread.php?t=50333</a> </p>
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<p>As I understand it fusion inside a sun can produce heavier and heavier elements until some sort of "nucleus size limit" is reached. As far as I understand, the limit is thought to be reached with the element iron.</p>
<p>What accounts for this "fusion element limit"? Is it the battle between the nuclear strong force and the electromagnetic force which limits the size of the nucleus that can exist in a fusion environment?</p>
<p>Is the limit of what elements can be created the same for all types of suns?</p>
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<p>I am building a preheater for a maple syrup evaporator and am going to use the steam generated by the heating process to pre-heat the incoming sap from, say 5 degrees C to (hopefully) something on the order of 80-90 C. (the goal is to heat the sap/fluid before it gets into the evaporating pan so that we are more efficient - the steam used is "free" - it is a waste product of the process and capturing the heat and subsequent condensation for hot water is desirable)</p>
<p>My flow rate through the copper tubes will be on the order of 35 to 56 liters per hour (10 to 15 gallons per hour) (this is for the end points of the assembly)</p>
<p>I only know the outside diameter of the copper pipes - they will be 1/2" OD.<br>
There will be 5 parallel lines inside a hood and at each end a manifold - the incoming cold sap comes into the low side manifold and makes its way up to the high side manifold in one of the 5 pipes. The manifolds are 20 inches long and are perpendicular to the other pipes which are 40 inches long.</p>
<p>The heat exchanger will sit in a hood to provide a little back pressure for the steam and to collect the steam and force it to contact the pipes. The boiling surface area of the sap underneath the heat exchanger is larger than the heat exchanger and the hood but most of the steam rises through the hood and will transfer some heat to the copper which in turn heats the fluid.</p>
<p>So how can I calculate the some likely heat exchange/output temperature?</p>
<p>It seems to me that the issues are:</p>
<ul>
<li>efficiency of heat transfer from steam to copper</li>
<li>efficiency of heat transfer from copper to fluid</li>
<li>how much time the fluid is in the lines</li>
</ul>
<p>I guess I am looking for an upper bounds and lower bounds (I know I won't get the fluid over 100 C - that's about all I know for sure - well - I guess I can also be sure that the temperature will rise some - but not sure how much.)</p>
<p>Many people report output temps on the order of 95C but I am skeptical. </p>
<p>What can I do to improve the heat transfer to maximize the scavenged heat? I can try to find fins from a baseboard radiator, however this is for food product - so I am unsure if I will do that. </p>
<p>Some pictures of something I would like to do:</p>
<p><a href="http://s662.photobucket.com/albums/uu349/bkm_photos/Oil%20Tank%20Evaporator/?action=view&current=evap-096.jpg&newest=1#!oZZ80QQcurrentZZhttp%3A%2F%2Fs662.photobucket.com%2Falbums%2Fuu349%2Fbkm_photos%2FOil%2520Tank%2520Evaporator%2F%3Faction%3Dview%26current%3Devap-087.jpg%26newest%3D1" rel="nofollow">http://s662.photobucket.com/albums/uu349/bkm_photos/Oil%20Tank%20Evaporator/?action=view&current=evap-096.jpg&newest=1#!oZZ80QQcurrentZZhttp%3A%2F%2Fs662.photobucket.com%2Falbums%2Fuu349%2Fbkm_photos%2FOil%2520Tank%2520Evaporator%2F%3Faction%3Dview%26current%3Devap-087.jpg%26newest%3D1</a></p>
<p>and </p>
<p><a href="http://www.leaderevaporator.com/p-286-parallel-flow-sap-pre-heater.aspx" rel="nofollow">http://www.leaderevaporator.com/p-286-parallel-flow-sap-pre-heater.aspx</a></p>
<p>Wood is used as the heat source and one can assume a constant fire/heat source that will be providing 10 to 15 gallons of evaporation per hour from a 24" by 60" pan.</p>
<p><strong>EDIT (answering a comment)</strong></p>
<p>The wall thickness of the copper pipe is 0.569 inches.</p>
<p>There is only one fluid being heated - that is the sap from a maple tree. It is water with sugar in it - and by boiling it we can remove most of the water until it turns to maple syrup.</p>
<p>The level of the fluid (sap) in the evaporator pans is kept constant by a float valve. The sap in the pan boils - that is where the steam comes from. So the rate of evaporation will be the same (approximately) as the flow through the heating tubes. </p>
<p>The heat is generated by a wood fueled fire in a firebox just below the evaporator pans that hold the sap.</p>
<p>Maple sap is held in a storage tank above the whole contraption. Gravity feeds it into the evaporator (a 5'x2' pan) through the preheater/heat exchanger. The fluid flow/level is regulated by a float valve. Steam is a by-product of the process - and using the wasted heat from the steam (allowing it to condense on the copper pips and transferring heat then drawing that condensation away so as not to have to re-heat it) makes the process a little more efficient. One study that was done shows that there is approximately 15% improvement in boiling rate (best case) for preheating the sap before it goes directly into the pan that gets heated.</p>
| 9,099 |
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<p>This is a question taken from a past E&M exam</p>
<blockquote>
<p>A thick spherical shell (inner radius $R_1$ and outer radius $R_2$) is made of a dielectric material with a "frozen in" polarization $$P(r)=\frac{k}{r}\hat{r}$$ where $k$ is a constant and $r$ is the distance from the center. Find the electric field everywhere in space.</p>
</blockquote>
<p><code>attempt</code>: I tried using Gauss' law</p>
<p>$$\int D\cdot n \,da=Q_{enc\,,free}$$</p>
<p>However, there is no free charge, thus $D=0$ and therefore </p>
<p>$$\vec{D}=\epsilon_o \vec{E}+\vec{P}\,,\vec{D}=0\rightarrow \vec{E}=-\frac{\vec{P}}{\epsilon_0}=-\frac{k}{\epsilon_0r}\hat{r}$$</p>
<p>Is the electric field for all space. This doesn't seem right, I would think that the electric field differs inside the material of the shell vs. outside the shell or inside the cavity. What am I doing wrong?</p>
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<p>I recently came up with the following concept. It is very simple, and may have been thought of before.
A picture says more than a thousand words, so here is it explained in a picture:</p>
<p><img src="http://i.stack.imgur.com/DQhdL.png" alt="Conveyor belt using densities of gases to keep it in motion">
<em>Note that water was used to make the example easier to understand. Another gas (denser than Gas A and B) could be used instead, resulting in less friction than when using water.</em></p>
<p><br/></p>
<p>At first glance, it seems that this machine could run for an indefinite amount of time.</p>
<p>But I do not deem it possible to break the law of energy conservation. However, I have a hard time finding out what kind of force would cause this machine to slow down and stop.</p>
| 155 |
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] |
<p>Can you see or accurately visualise sub atomic particles or are they known only by maths and/or inference?</p>
| 9,101 |
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/11542/why-is-gravitation-force-always-attractive">Why is gravitation force always attractive?</a> </p>
</blockquote>
<p>I have heard that the attractiveness of gravitation is due to the fact that it is a spin 2 gauge theory. Why is this so? I find this very interesting and would love to understand this fact.</p>
| 81 |
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<p>Suppose we have two black holes of radius $R_b$ orbiting at a distance $R_r$. I believe semi-classical approximations describe correctly the case where $R_r$ is much larger than the average black body radiation wavelength due to Hawking radiation. </p>
<p>Do we have approximations for Hawking radiation temperature where the distance $R_r$ is of the same order, or in the case where it is much shorter than the radiation average wavelength?</p>
<p>In the absence of a concrete analysis for either one, <strong>Do we have any physical insight to affirm if Hawking radiation will be either inhibited or increased in the above situations?</strong></p>
| 9,102 |
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] |
<p>Why cant one see the tidal effect in a glass of water like in an ocean?</p>
| 9,103 |
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<p>What if we apply a very strong magnetic field to an electron so that it's position be a constant. Then if it's position is constant, it's momentum will also be a constant. But it is in violation of Heisenberg's uncertainty principle, so is such an experiment possible?</p>
| 9,104 |
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<p>If I take an electrolytic capacitor, remove the aluminium casing, unroll the foil/ electrolyte-soaked paper, if charged, will it still work? And what if I took of the cathode foil and wrapped the anode foil with the paper around a metal rod -- will it work if charged? If not, why? </p>
| 9,105 |
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<p>I'm hoping to understand the motivation for certain parts of the definition of a derivative operator $\nabla$ on a manifold $M$. In Wald's General Relativity, two clauses of the definition are:</p>
<blockquote>
<ol>
<li><p>Commutativity with contraction: For all tensors $\mathit{A} \in \mathscr{T}(k,l)$, $\nabla_{d}(\mathcal{A}^{a_1...c...a_k}_{b_1...c...b_l}) = \nabla_{d}\mathcal{A}^{a_1...c...a_k}_{b_1...c...b_l}$. (the parenthesis indicates contraction)</p></li>
<li><p>Consistency with the notion of tangent vectors as directional derivatives on scalar fields: for all functions $f \in \mathscr{F}:M \rightarrow \mathbb{R}$ and all tangent vectors $t^a \in V_p$, it is required that $t(f)=t^a\nabla_af$</p></li>
</ol>
</blockquote>
<p>What is the point of having derivative operators commute with contraction (where we sum over the vectors and dual vectors for some (i,j) slot in the tensor)? What theorems are not possible to prove if this commutativity isn't stipulated? The so-called "Leibnitz rule" for derivative operators on manifolds corresponds to the simple product rule in elementary calculus; does this commutativity-with-contraction rule correspond to something simple as well? </p>
<p>My second question is about the notation of clause 2. We know that the $t^a$ are tangent vectors in the tangent space $V_p$ at point $p$ on the manifold. Then what is $t$ supposed to be?</p>
| 9,106 |
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<p>As far as i know potential difference between 2 points is defined as the negative line integral of electric field between those 2 points.
I also know that when magnetic field changes curl of electric field is not 0 and potential difference makes no sense.
But when we have an inductor in a rlc circuit then people always say that there is a potential drop across the ends of inductor,but since magnetic field is changing potential difference should make no sense.
please help. </p>
| 9,107 |
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<p>Consider you have a slab waveguide having n1=3.5 and n2=1.45. The value of critical angel is 24.5 degree approx. Similarly effective refractive index will be in between 1.45 and 3.5. How can we find the eigenvalue for this optical waveguide and plot in Matlab or some other software. </p>
<p>Thanks and hope it is clear.</p>
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<p>While the fasted emitted electrons comes from the fermi level of the material in UPS measurement, where does the slowest, which is called secondary electron cut-off orginate from? I really can't figure it out.
Also, why isn't the smallest kinetic energy zero? At least it should be nearly zero considering a rather continuous distribution of energy states of electrons.</p>
<p>(ultraviolet photoelectron spectroscopy(UPS) involves photons of a certain energy exciting electrons out of the solids and kinetic energies of the electrons are measured)</p>
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<p>I was recently startled to find that the Earth's North Magnetic Pole is moving at upwards of 40 km per year, with an additional ~80 km daily elliptical drift about its mean position due to variations in solar wind. The <a href="http://en.wikipedia.org/wiki/North_Magnetic_Pole">Wikipedia article on the NMP</a> has a wealth of information, including this image:</p>
<p><img src="http://i.stack.imgur.com/OQtk0.png" alt="enter image description here"></p>
<p>I'm particularly surprised at the existence of "modelled" data, showing a lot of detail, about the NMP's location for centuries before anyone went there. Neither that Wikipedia article nor <a href="http://en.wikipedia.org/wiki/Earth%27s_magnetic_field">this one on the Earth's magnetic field</a>, which include the image, mention where the modelled data come from.</p>
<p>I get the impression from <a href="http://www.ngdc.noaa.gov/geomag/GeomagneticPoles.shtml">sources like this</a> that the model is derived from historical measurements of <a href="http://en.wikipedia.org/wiki/Magnetic_declination">magnetic declination</a>. If that is the case I would be disinclined to trust the model much: the Earth's magnetic field has a complex enough structure that the magnetic north and south are not antipodal, with nontrivial spatial variations in magnetic declination at any given time.</p>
<p>Has anyone seen references that explain this model and what measurements they are based on?</p>
| 9,110 |
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<p>Could a dying star in one brane ( assuming that we live in a world of multiple branes { not a Randal-Sumdrum model of a single brane}) be the start of the birth of the star ( more precisely Super Nova) in another brane? If so is the black hole merely the "Shadow" of the star's gravity in another brane ( because gravity is not confined to a single brane) ? Could it be that as the black hole eventually dies in one brane it becomes stronger in another (as the star keeps traveling further away from the "origin brane { assuming the number of branes are infinite}) ? That means the star never "actually" dies right? but what happens when the black hole grows to big and becomes a "Black Pancake"? Could this be true in any way? </p>
| 9,111 |
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<p>I have seen multiple papers talking about the manifold, $M$ of the Neel order for an $SU(N)$ magnet is</p>
<p>$$M~=~\frac{U(N)}{U(m)\times U(N-m)}.$$</p>
<p>So for instance, a $SU(2)$ magnet has manifold</p>
<p>$$M ~=~ \frac{U(2)}{U(1)\times U(1)} ~\sim~ S^2.$$</p>
<p>Could someone explain to me physically how I could see why this is the appropriate manifold?</p>
<p>References:</p>
<ol>
<li>Subir Sachdev, <em>NATURE OF THE DISORDERED PHASE OF LOW-DIMENSIONAL
QUANTUM ANTIFERROMAGNETS,</em> lectures (1990) page 13. The pdf file is available <a href="http://qpt.physics.harvard.edu/c6.pdf" rel="nofollow">here</a>.</li>
</ol>
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<p>Is the oscillation of a simple pendulum in vacuum a case of perpetual motion? I recently read Feynman's lectures and he said perpetual motion is impossible in real life. But this pendulum in vacuum is pretty straightforward to achieve. </p>
| 301 |
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<p>I am currently working on the measurement of the coefficient of thermal expansion of copper. In order to compare my experimental results with theory or experiments made by others, I am looking for abacus or theoretical curves showing the latter coefficient (as a function of temperature).</p>
<p>The range of temperature I'm working with is 298K-500K.</p>
<p>Has anyone ever seen such data ? If so, are they easily available ? Anyway, I'm interested with any kind of data (easily available or not).</p>
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<p>On my last HW set, we were asked to show that the operator
$$\hat T = \exp(-ic\hat p /\hbar)$$
acts as a translation operator ($\hat T^\dagger q\hat T=q+c)$. This was simple to show using commutators and other such things. The same thing can be said with a momentum operator.</p>
<p>Can I have a translation operator that will take some operator
$$\hat A=(\hat p-p_0)(\hat q -q_0)$$
and translate this to eliminate both of the C numbers? I feel like this could be something useful for a multidimensional 'number' type operator that raises some form of state.</p>
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<p>While there is no confirmation that quark stars exist, is there any theoretical limit analogous to (but different from) the <a href="http://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_limit" rel="nofollow">Tolman–Oppenheimer–Volkoff limit</a> for neutron stars?</p>
<p>In other words, what is the maximum pressure for quark matter?</p>
| 9,115 |
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<p>What is the conceptual difference between minimizing the availability of a thermodynamic system and maximizing the entropy of a thermodynamic system? I am under the impression that these are the same thing for the most part but occasionally have slightly different meanings. </p>
| 9,116 |
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<p>Is interstellar flight possible in the near future in a way that would keep our civilization alive?
I mean is it practically possible to obtain technology that would enable us to travel to nearby habitable earth-like planets to keep our civilization alive? </p>
<p>For example, consider this <a href="http://projectavalon.net/forum4/showthread.php?72620-Amazing-Design-for-NASA--s-Star-Trek-style-Space-Ship-the-IXS-Enterprise" rel="nofollow">design for NASA’s Star Trek-style Space Ship, the IXS Enterprise</a>. Do you know any good site which goes into detail on both latest practical and theoretical development of this interstellar flight?</p>
| 9,117 |
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<p>Is it possible to utilize gravitational waves as a delivery system for information between two observers straddling the event horizon of a black hole? And why ?</p>
| 9,118 |
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<p>Can velocity and acceleration reach maximal values during the SHM simultaneously? Can you explain why?</p>
| 9,119 |
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<p>Consider a lattice of massive points connected by harmonic springs, with zero or periodic boundary conditions. If we make a repeating pattern of $N$ varying masses, the system will have $N$ bands of eigenfrequencies with real wave vectors and band gaps between these bands, where wave vectors are imaginary. If we then put these lattices around another lattice with some eigenfrequencies in band gap of outer lattices, we'll get something like "quantum well" for mechanical waves (similar to phonon confinement in heterostructures). This way we'll get evanescent waves in outer lattice.</p>
<p>But this model has a problem: its evanescent waves are envelope waves, i.e. in the limit of lattice constant $a\to0$ the waves won't have smooth waveform. To have a smooth waveform for evanescent waves one'd need a band gap between zero frequency and bottom-most band. But as I add smaller and smaller eigenfrequencies in the first band for inner lattice (so that they were smaller then smallest eigenfrequency of outer one), I only get linear waveforms in outer lattice - they never curve enough to become exponential, i.e. the wavevector never becomes imaginary.</p>
<p>I begin to think that at least in purely mechanical case evanescent waves must be envelope waves, and there's no way to make a true (non-envelope) wave with imaginary wave vector.</p>
<p>Is this true? How can this be (dis)proved?</p>
<p><strong>EDIT</strong>: as noted by @WetSavannaAnimalAkaRodVance, setting up a medium with different wave velocities allows one to get true evanescent waves in a faster medium via total internal reflection. This works fine, I've checked it. But total internal reflection requires at least two dimensions, so I still wonder whether true evanescent mechanical waves can be created in one dimension.</p>
<p>Rephrasing my question with the remark above in mind: can a one-dimensional purely mechanical system be created, in which evanescent waves <em>without oscillating structure</em> would exist? If not, how to prove this impossibility?</p>
<p>Here's what I mean by wave with oscillating structure - it is <strong>not</strong> what I'm looking for:
<img src="http://i.stack.imgur.com/HXb63.png" alt="enter image description here"></p>
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<p>When you look out at the white-caps on a wind-swept lake, you can see a dark, undulating pattern under the crests of the white-caps.</p>
<p><em>Could this shadow-like area explain the sightings?</em> Revised, see below.</p>
<p><strong>Edit</strong> First of all, it must be a rogue wave, <img src="http://i.stack.imgur.com/rL4cC.jpg" alt="rogue wave">, so it stands out from the rest of the waves (if any). This could be the hump of some monster just breaking the surface!</p>
<p><a href="http://cogsci.stackexchange.com/questions/5154/eyewitness-perceptions-of-the-loch-ness-monster">Question on Cognitive Science.SE about eyewitness perceptions.</a></p>
<p><strong>Edit</strong> You are walking along a country lane, when a sudden motion on the water catches your eye. Followed by the sound of a crashing wave. Within seconds, only ripples remain on the surface. You remember the image as shown above. It could be a white-cap on a wave, but everyone who has been to the beach knows that waves come in one-after-another, and there are no other waves, so it can't be a wave. You notice the darker area under the white-cap and realize the only possible explanation is: you have just seen a large animal dive under the surface. Like a sounding whale. (Or monster?).</p>
<p>Loch Ness is located near a major fault line that has seismic activity. Physicists can explain that a wave created by seismic activity is a rogue wave or tsunami. They can also explain why the wave does not reach shore and, why the area under the white-cap is always darker.</p>
<p><strong>So, could a collaboration between physics and psychology show this illusion is a possible explanation for Nessi?</strong></p>
| 9,121 |
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<p>I am reading <a href="http://books.google.co.uk/books?id=Quv8awSN-RYC&printsec=frontcover&dq=magnetic%20techniques%20for%20the%20treatment%20of%20materials%20pdf&hl=en&sa=X&ei=ePKuUu2lH8yThQfs64D4CA&ved=0CDIQ6AEwAA#v=onepage&q&f=false" rel="nofollow">this</a> book, the part in particular about Eddy-current separation starting at Page 246, in it there is an equation for calculating the "characteristic time with which the induced magnetic field decays in the particle".</p>
<p>$$
\tau = \mu_0\sigma_psb^2
$$</p>
<p>Where:</p>
<ul>
<li>$\mu_0$ is the permeability of free space</li>
<li>$\sigma_p$ is the specific electric conductivity of a particle [S/m]</li>
<li>$s$ is the shape factor of the particle</li>
<li>$b$ is the particle radius</li>
</ul>
<p>I am hoping someone can reflect some light on what $s$ is and how to calculate it, "shape factor" isn't very descriptive and I cannot find anywhere in the book describing it in further detail.</p>
<p>This shape factor is also used in the force equations that I am intersted in...</p>
<p>Another part of the equation I am unclear on is $b$, what if the particle is a cube or cuboid, what should the radius be then?</p>
| 9,122 |
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<p>A black hole would radiate mass optimally for interstellar-travel applications in the range between $10^7$ and $10^8$ kilograms. Assuming a light-only radiation emission spectrum, with a parabolic reflector with efficiency $f$, this would create an acceleration</p>
<p>$$ a = \frac{f P}{mc}$$</p>
<p>$$ a = \frac{ f \hbar c^5 }{ 15360 \pi G^2 M^3}$$</p>
<p>$$ a = \frac{ f 10^{24} m \times sec^{-2}}{M^3} $$</p>
<p>The problem is that the schwarzschild radius at this mass is a few attometers, which creates a host of problems:</p>
<p>1) the rate at which it can feed from normal matter is too small compared to the rate BH mass is being radiated</p>
<p>2) any electric charge we throw in the BH will be quickly radiated by super radiance effects and Schwinger pair production, so it will stay neutral most of the time.</p>
<p>3) only super hard gamma rays have (to my limited knowledge) the short enough wavelength in order to scatter against such a tiny BH</p>
<p>By the 3 points above, it is unclear how to apply a back-force on the black hole so that a payload, comprising at least of the parabolic reflector, can be accelerated with it</p>
<p>are there any ideas out there about how to exert a force or moment on such a tiny black hole?</p>
| 9,123 |
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] |
<p>The Klein-Gordan equation describing a spinless scalar field is one of the first things one studies in a QFT course, but there are no elementary spin-0 fields in nature.</p>
<p>Is the scalar field to QFT like the frictionless plane in high school physics, an aid to get us started?</p>
<p>Or is it deeper than that?</p>
| 9,124 |
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<p>Suppose I put water in a closed vessel and heat it, so the vessel becomes pressurized above ambient pressure. Now, there should be liquid and gaseous water inside the vessel. Since it's under pressure, when I open the vessel at the bottom, the liquid starts to flow out. If I wait until all liquid is expelled, and close the opening before the water vapor exits too, what state do I have in the vessel? Specifically:</p>
<ul>
<li>Releasing pressure from a system usually means it cools down. What does that mean for the vessel's inside? If I want the vessel to stay at the temperature it was, do I have to reheat (if we ignore ordinary heat dissipation for now)?</li>
<li>The pressure inside the vessel now is lower, does that mean water vapor will condense and the system moves toward a new equilibrium? If I keep the temperature constant, will it be the same pressure as before?</li>
<li>Does it matter for this question to what extent the vessel is filled at the beginning? If I understood vapor pressure correctly, the contents will reach an equilibrium of liquid and gaseous such that the pressure reaches a point which is solely dependent on temperature.</li>
<li>Does it matter for the purpose of this question how quickly I expel the liquid phase?</li>
<li>I'm not sure what influence the ambient pressure has on this question.</li>
</ul>
<p>If you need sample values, assume 100 kPa (i. e., normal atmosphere) for the ambient pressure, 200 °C for the water and 1.555 MPa inside the vessel when I open the valve.</p>
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<p>Since pH is a measure of the effective concentration of $\mathrm{H}^+$ ions a solution, I expect that an electric field applied to a solution will create a pH gradient. The higher concentration of $\mathrm{H}^+$ ions (corresponding to lower pH) should be close to the anion, and a lower concentration of $\mathrm{H}^+$ ions (corresponding to higher pH) should be closer to the cation.</p>
<p>This is a simple yes or no question. Does an electric field create a pH gradient as I described above? (If not, can you please provide an explanation?)</p>
| 9,126 |
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<p>A particle moving towards the origin has initial conditions $x(t=0) = 1$ and $\dot{x}(t=0)=0$</p>
<p>If the Lagrangian is L:=$\frac{m}{2}\dot{x}^2 -\frac{m}{2}ln|x|$ </p>
<p>This should satisfy Euler Lagrange Equation $$\frac{d}{dt} (\frac{\partial L}{\partial \dot{x}}) = \frac{\partial L}{\partial x}$$</p>
<p>Prove the particle reaches the origin at $\Gamma(1/2) = \sqrt{\pi}$</p>
<p>1) okay to begin I simply plug in and expand the D.E.</p>
<p>$$\frac{d}{dt}[(\frac{\partial \frac{m}{2} \dot{x}^2}{\partial \dot{x}}) - \frac{\partial\frac{m}{2}ln|x|}{\partial \dot{x}}] = \frac{\partial \frac{m}{2}\dot{x}^2}{\partial x} - \frac{\partial \frac{m}{2}ln|x|}{\partial x}$$</p>
<p>2) since $x(t)$ and $\dot{x}(t)$ are functions of time, the cross partials dissapear and I am left with:</p>
<p>$$\frac{d}{dt}(\frac{\partial \frac{m}{2} \dot{x}^2}{\partial \dot{x}}) = - \frac{\partial \frac{m}{2}ln|x|}{\partial x}$$</p>
<p>Which reduces to:</p>
<p>$$m \frac{d}{dt}(\dot{x}) = - \frac{m}{2x}$$</p>
<p>This is equivalent to:
$$\ddot{x} = - \frac{1}{2x}$$</p>
<p>3) Now I will separate and Integrate (Keeping in mind the particle starts from Rest):</p>
<p>$$\dot{x} = \frac{dx}{dt} = -\frac{1}{2}ln|x|$$
$$t = -2 \int^{x}_{x_0} \frac{dx}{ln|x|}$$</p>
<p>All I really want to know is that Up until this point, Have I done everything correct? Because I feel like I haven't. I don't think I can even Integrate this because I put it into wolfram and I got a mess.</p>
| 9,127 |
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] |
<p>how can we find out the effective mass of a hole,since a hole in the valence band is just an absence of electron?</p>
| 9,128 |
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] |
<p>A book, <a href="http://rads.stackoverflow.com/amzn/click/0465060714" rel="nofollow">Exercises for the Feynman Lectures on Physics</a>, has recently been published. It consists of homework problems to provide practice with the techniques and concepts used in the famous Feynman lectures, which had not had published problem sets to accompany them since they came out in 1964. I bought a copy, found what I considered to be an error in the answer given for one of the problems, and, as a matter of professional courtesy, emailed one of the book's editors, M. Gottlieb, to report the erratum. Dr. Gottlieb insists that I'm wrong. I'll quote the question here and give my own answer below.</p>
<blockquote>
<p>3.12 In making laboratory measurements of $g$, how precise does one have to be to detect diurnal variations $\Delta g$ due to the Moon's gravitation? For simplicity, assume that your laboratory is so located that the Moon passes through the zenith and nadir. Also, neglect earth-tide effects.</p>
</blockquote>
<p>The answer given in the back of the book is:</p>
<blockquote>
<p>$\Delta g/g=7\times10^{-6}$</p>
</blockquote>
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<p>I don't know much about string theory, apart from it being a theory of everything which brings QM, QED and nuclear forces and gravity under one single roof. I am curious to know from a mathematical view point, how the quantization of space-time is achieved in super string theory.</p>
| 9,130 |
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<p>I want to solve the transient heat equation on a ball. The boundary condition is the same over the hole outer surface. So this should reduce to a one-dimensional problem in radial direction. However I cannot use the one-dim heat equation, since the surface through which the heat flows goes quadratic with the radius.</p>
<p>Is the following approach correct: Take the heat equation, transform it into sperical coordinates and eliminate the derivatives in angular directions. I think the last part is justified, because of the rotational symmetry of the boundary condition. So I end up with this equation:</p>
<p>$$
\frac{\partial T}{\partial t} = \alpha \frac{1}{r^2}\frac{\partial}{\partial r} \left( r^2\frac{\partial T}{\partial r}\right)
$$
with thermal diffusivity $\alpha$. Is this the correct reformulation of the heat equation on a ball to a one-dimensional problem?</p>
<p>EDIT: When I solve this with the finite element method, will there be a problem in the centre of the ball? The $1/r^2$ factor might cause a problem.</p>
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<p>You know energy is necessary for the occurrence of an event . Time is also exactly neccessary for the occurrence of an event. If there is no time , there will be no event. I mean time is a type of energy ?</p>
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<p>I need to know which formulas and the step-by-step answers for the following physics questions:</p>
<blockquote>
<p><em>1. You throw a ball upward with an initial speed of 7.0 m/s, and it returns to your hand o.92 seconds later, ( assuming air resistance can be ignored).</em></p>
<ul>
<li><em>(a) What is the average acceleration vector of the ball?</em></li>
<li><em>(b) Find the highest up ward distance that ball can get.</em></li>
</ul>
<p><em>2. A ball was thrown at an angle of 45.0 degrees above the horizontal, that it traveled a horizontal distance of 496ft, and that it was caught at the same level from which it was thrown.</em> </p>
<ul>
<li><em>(a) What was the ball's initial speed?</em></li>
<li><em>(b) How long was the ball in the air?</em></li>
</ul>
</blockquote>
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0.0019943276420235634,
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] |
<p>For light travelling in a medium with refractive index greater than one:</p>
<p>The "average" speed of light is slower than the speed of light in a vacuum. As far as I know, the instantaneous speed of light in a medium is equal to the speed of light in a vacuum.</p>
<p>Is this correct?</p>
<p>If so, is this because it takes some non-zero time for photons to be absorbed/remitted? Is this because of some backscattering? Is there some other phenomenon at work?</p>
<p>PS: We're Bringing back Joel Spolsky's subreddit -- <a href="http://joel.reddit.com" rel="nofollow">joel.reddit.com</a>.</p>
| 298 |
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<p>How can I convert my self-similar boundary layer solution that is a function of the nondimensional wall-normal coordinate $\eta$ to be a function of dimensional $y$? For instance, if I determine from my boundary layer solution that $\delta_{99}$ occurs at $\eta = 5$, for a given set of dimensional parameters how do I determine the corresponding physical coordinate? This is very straight forward for Blasius flow but is not as obvious to me for compressible flow. The definition of $\eta$ is shown below. The integral dependence on $y$ is what is throwing me off.</p>
<p>$$\eta = \frac{U_e}{\sqrt{\int_0^x\rho_eU_e\mu_edx}}\int_0^y\rho dy$$</p>
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<p>I'm trying to make an orbit simulator, and I want to draw the orbit of a satellite given its position and velocity vectors in a 2-D plane. I found <a href="http://physics.stackexchange.com/questions/72203/calculating-specific-orbital-energy-semi-major-axis-and-orbital-period-of-an-o">this other question</a> which tells how to calculate eccentricity and semimajor axis, but how do I figure out the orientation of the major axis (if e > 0)?</p>
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<p>I am a science fiction writer. </p>
<p>I know how to time travel to the future (using black hole or speed). But I need to argue in my novel that time travel to the past might not be possible. Is there a way to do this without using a formula? And how basic would argument look like ?</p>
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] |
<p>Can a semi-conductor ( germanium or silicon) or a semi-metal ( graphite ) carry an induced charge ?</p>
| 9,137 |
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<p>Currently working on this question, however I'm not sure how to solve it. </p>
<blockquote>
<p>As a pendulum swings in simple harmonic motion at the surface of the Earth, the angle the pendulum makes relative to its equilibrium position is given by $\theta(t) = (0.140 \:\mathrm{rad})\cos(5.72t)$ where t is in seconds. What is the length of this pendulum?</p>
<p>a) 0.140 m</p>
<p>b) 0.250 m</p>
<p>c) 0.300 m</p>
<p>d) 0.439 m</p>
<p>e) 0.801 m</p>
</blockquote>
<p>The equation provided indicates that this is a torsional pendulum, correct? </p>
<p>Therefore the length of the string with torsion supporting the disc at the bottom does not matter at all? If so, why?</p>
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] |
<p>Can someone provide a trigonometry/geometry insight to deduce the angle of the plane is the same as the angle of the component of the weight?</p>
<p><img src="http://i.stack.imgur.com/W5OfC.jpg" alt="enter image description here"></p>
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<p>I'm supposed to shoot a projectile from the origin to a point $(x_0 , y_0)$ with minimal initial velocity $v_0$. (no air resistance; regular gravity)</p>
<p>The flight time should be $T=\frac{x_0}{v_x}$. Plugging in to the equation for y, I get
$$y_0=\frac{-g}{2}\frac{x_0^2}{v_x^2}+\frac{x_0v_y}{v_x}$$</p>
<p>Recalling that $v_x = v_0\cos{\theta}$ and $v_y = v_0\sin{\theta}$ and some algebra yields: $$v_0=\sqrt{\frac{gx_0^2}{2\cos^2{\theta}(x_0\tan{\theta}-y_0)}}$$</p>
<p>To minimize initial velocity, I figure I have to take $\frac{dv}{d\theta}$, set it to 0 and hope for a minimum. This is prohibitively complicated. Am I missing some intuition about how the components are independent of each other in finding the minimum velocity (maybe minimize $v_y$ separately)? $\theta=\frac{\pi}{2}$ seems to make $v_0$ the smallest (by blowing up the denominator), but that would be shooting the object straight up, which doesn't make sense.</p>
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<p>Inspired by the wording of <a href="http://physics.stackexchange.com/a/62847/10851">this answer</a>, a thought occurred to me. If a photon and a neutrino were to race along a significant stretch of our actual galaxy, which would win the race?</p>
<p>Now, neutrinos had better not be going faster than the speed of light <em>in vacuum</em>. However, an energetic enough neutrino can have a velocity arbitrarily close to $c$. Say we took a neutrino from a typical core-collapse supernova. It would have a speed
$$ v_\nu = (1 - \epsilon_\nu) c $$
for some small $\epsilon_\nu > 0$. What is the order of magnitude for $\epsilon_\nu$?</p>
<p>At the same time, photons can also travel slower than $c$. The interstellar medium is not completely devoid of matter, and in fact much of this matter is ionized plasma. As such, it should have a plasma frequency $\omega_\mathrm{p}$, and so it should effectively have an index of refraction depending on the ratio $\omega/\omega_\mathrm{p}$. Then the speed of a photon will be
$$ v_\gamma = (1 - \epsilon_\gamma) c, $$
where $\epsilon_\gamma$ is in general frequency-dependent. What is the order of magnitude for this deviation? I know it comes into play at radio frequencies, where in fact even the variation of $v_\gamma$ with frequency is detected: Pulses from pulsars suffer dispersion as they travel over hundreds to thousands of parsecs to reach us.</p>
<p>For simplicity, let's assume there are no obstructions like giant molecular clouds or rogue planets to get in the way of the photon. <strong>Is it possible that some photons will be outpaced by typical neutrinos?</strong> How big is this effect, and how does it depend on photon frequency and neutrino energy?</p>
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] |
<p>A human cannon has a spring constant of 35 000 N/m. The spring can be extended up to 4.5m. How far horizontally would a 65kg clown be fired if the cannon is pointed upward at 45 degrees to the horizontal?</p>
| 9,142 |
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<p>RCFT's (rational conformal field theories) in two dimension are very well-studied, but it seems that there is no any gravity dual of such theories has been found. Is there example of the holographic dual of RCFT?</p>
| 9,143 |
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<ul>
<li><p>One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - <a href="http://en.wikipedia.org/wiki">http://en.wikipedia.org/wiki</a>/Poincaré_group..) or equations 2.4.18 to 2.4.24 of Weinberg's volume 1 of his QFT books?</p>
<p>What confuses me is that in deriving the commutation relations between $J^{\mu \nu}$ and $P^\mu$ he did use quantum theoretic arguments about the Hilbert space operator $U$ but I guess there is nothing quantum about the Lie algebra he derives in the aforementioned equations. Is that right? </p></li>
<li><p>This quantum confusion steepens when one looks at the $K_i$ (..relatvistic boost along the $i^{th}$ spatial direction..), $P_j$ (..linear momentum along the $j^{th}$ spatial direction..) commutator being non-zero. This is justified by saying that the exponential action of the boosts and the translations on the Hilbert space states do not commute and that is being reflected here. (..they pick up an extra phase proportional to the mass and the dot product of the boost velocity and the displacement vector..) </p></li>
</ul>
<p>But if the afore mentioned equations are really the Lie algebra of the isometry group of the Minkowski spacetime then in the Galilean limit shouldn't they be instead reflecting the fact that Galilean boosts and translations when acting on the spacetime coordinates do infact commute. But the $K_i$ and $P_j$ commutation continues to be non-zero even when the Galilean limit is taken on page 62.</p>
<p>This makes me strongly suspicious that the equations 2.4.12 to 2.4.14 are not the Lie algebra of the isometry group of the Minkowski spacetime but are the Lie algebra of the group whose elements are $U(\Lambda, a)$ (..using Weinberg's notation..)…right? </p>
<ul>
<li><p>So is the "low velocity" limit taken on page 62 recovering non-relativistic quantum theory ? (and not Newtonian physics)</p></li>
<li><p>On page 89 of the same book he derives the topology of the inhomogeneous Lorentz group as being $R^4 \times R^3 \times S^3/Z_2$. Since this is a connected manifold, I guess that by the term ``inhomogeneous Lorentz group" he is meaning only the proper orthochronous component of the full relativistic symmetry group. right? </p></li>
<li><p>I can't see how the above topology matches with the semidirect product structure for posibly the same thing as given on this Wikipedia page -http://en.wikipedia.org/wiki/Poincaré_group ? </p></li>
</ul>
<p>When people talk of the Poincare group is the full symmetry group of relativity is what is being referred to or is it just its proper orthochronous component (and not the other 3 components) ? </p>
<ul>
<li>I am familiar with the notion of "central charge" as in the "first" term on the RHS of the TT OPE of CFT…what also has the interpretation as the zero-point energy when doing the plane-minus-point<->cylinder conformal transformation.</li>
</ul>
<p>In this light it is not clear to me as to what is meant when one says that one can add in the "mass" as a central charge to the Galilean group..an extra generator which commutes with all the rest so that with this "central extension" the free particles will lie in the unitary representations of the Galilean group rather than the projective representations before the extension.</p>
<p>I would be grateful if someone can shed light on this issue and help reconcile the two "different" notions of central charge. </p>
<ul>
<li>When one takes a "low velocity" limit of the Poincare algebra to get the Galilean algebra then is one taking just a non-reltivistic limit or is one also taking a non-quantum limit ? </li>
</ul>
<p>(..I guess this will depend on my first query about whether what Weinberg calls as the Poincare algebra in the quoted equations has any quantum effect encoded in it {as it seems to be!} or is it just the Lie algebra of the isometry group of the Minkowski spacetime..) </p>
| 9,144 |
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<p>Consider a charged spherical shell of radius $R$ and surface charge density $\sigma$. Choose a point on the surface of the shell and cut a spherical cap of radius $a \ll R$. What is the electric field intensity in the middle of the hole?</p>
<p>This was made up intended as a relatively easy problem to solve, it turns out however it is probably not, as every edition of the textbook shows a different answer and professors at our physics department can't agree upon one. What do you think?</p>
<p>My attempt: First I calculated the intensity on the axis of a disc and integrated over the disc elements: $\vec E = \int_0^{2R-{a^2 \over 2R -1}} {\sigma \over 2\epsilon} ({ \sqrt{2Rh} - |h| })dh$. This, using the fact that $a \ll R^2$ evaluates to ${\sigma R^2 \over 3\epsilon} $, which is wrong.</p>
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<p>The Maxwell-Boltzmann velocity distribution in 3D space is
$$
f(v)dv = 4\pi \left(\frac{m}{2\pi k_B T}\right)^{3/2} v^2 \exp\left(-\frac{m v^2}{2k_B T}\right)dv$$
It gives the probability for a single particle to have a speed in the intervall $[v,v+dv]$. But this probability is not zero for speeds $v > c $ in conflict with special relativity.</p>
<p>Is there a generalization of the Maxwell-Boltzmann velocity distribution which is valid also in the relativistic regime so that $f(v) = 0$ for $v>c$ ? And how can it be derived? Or can a single particle distribution simply not exist for relativistic speeds, because for high energies, we always have pair-production meaning the particle number is not conserved and a single particle distribution can not be defined in a consistent way? </p>
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<p>I would like to know if there is some formula / graph which would provide / show the efficiency of a certain type of propeller in space. Specifically, I'm interested in the acceleration attainable at certain speeds.</p>
<p>I'm writing a science fiction book and I'm trying to make it as correct as possible, fact wise. The propeller I'm talking about is the <a href="http://en.wikipedia.org/wiki/Ion_drive" rel="nofollow">ion drive</a></p>
<p>Now, my book takes place in a world where fusion power is finally ours.</p>
<p>So, please, let us assume that we have unlimited energy so you could power a dozen huge ion drives non stop. OK, there's the question of argon/xenon fuel, let's assume we have 1 year of that.</p>
<p><strong>So... the question is... what speed could you reach?</strong></p>
<p>If a continuous acceleration of $10\frac{\mathrm{m}}{\mathrm{s}}$ is applied (I put that number because it would also constitute an advantage for my crew - living in Earth's gravity), that would mean that a ship would reach the speed of light in just 347 <strong>DAYS</strong></p>
<p>But I know that's impossible because the EFFICIENCY of the ion drive would DECREASE as the ship's speed would approach the exhaust speed of the drive's "nozzle" (well, it doesn't have a nozzle per-se, as you can see in Wiki, but anyway...)</p>
<hr>
<p>Please do not fear to elaborate on top of my question. Let's suppose for example that maybe the ion drives of the future have a much higher thrust/efficiency/nozzle exhaust speed.</p>
<p>This isn't only about currently POSSIBLE facts but also about THEORETICAL limitations which might be overcome in the future (such as fusion energy).</p>
| 9,147 |
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<p>I watched some videos on the <a href="http://en.wikipedia.org/wiki/Unified_field_theory" rel="nofollow">unified field theory</a>, specifically interviews with Michio Kaku and John Hagelin, and want to learn a bit more about it. I looked up the theory of everything, string theory and unified field theory but most of it goes over my head.</p>
<p>In one of the <a href="http://www.youtube.com/watch?v=OrcWntw9juM" rel="nofollow">interviews</a> with John Hagelin he describes the unified field as being the deepest level of the universe. He refers to it as intelligence or a field that has the potential for matter. So, what does this consists of if it isn't the smallest form of matter?</p>
<p>Also, is there a definite view in the scientific community that the unified field exists and what it is?</p>
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<p>Suppose there is a positron and an electron, and they both collide, and we get $E=2mc^2$ of energy from the collision. Now, the charge also got vanished. Now suppose, I create neutrinos from the collision's energy, which are neutral and that doesn't violate conservation of charge, now the mass-energy of the neutrinos is same as the mass energy of the positron and electron destroyed.</p>
<p>But instead if I make electron and positron pair again from that energy, it doesn't violate conservation of charge either, but this implies that creating one kind of charge requires positive energy and creating the other requires negative energy in some form. Isn't it ?</p>
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<p>Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating about an axis which is perpendicular to the force and which goes through the center of mass.</p>
<p>What is the proof of this?</p>
| 9,150 |
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<p>As far as I understand, the motivation for using representation theory in high energy physics is as follows. Assume that a theory has some (internal or external) symmetry group which acts on a vector space. Then fields satisfying the theory will have to transform under some representation of that symmetry group, by construction.</p>
<p>What happens if we have some internal or external symmetry structure that is no longer acting on a vector space? The gauge group diffeomorphisms of general relativity spring to mind. Is there some more general 'representation' type theory which comes to our aid? And are there any examples of internal symmetries where this viewpoint is needed?</p>
<p>Apologies if this question is imprecise or flawed - I'm just starting to get my head around the foundations of the subject! Many thanks in advance!</p>
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] |
<p>I wonder if the refractive index of acetone, ethanol, methanol, heptane was measured in the range above 830 nm. The site <a href="http://refractiveindex.info" rel="nofollow">refractiveindex.info</a> provides it only for visible, and I couldn't find any other data so far.</p>
| 9,152 |
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<p>Before asking, I swear that, for how it may seem strange, this is all true. Very briefly, when my pc is off and I am near it, it turns on. I do not touch anything. Nobody else have the same effect. I just have to still near it for 3-5 seconds and it will boot. It begun 1-2 weeks ago. The first time was at night, and I was sleeping, so I wasn't really near to it. It is not "scheduled". It doesn't happen at 3:00 every day, just random.</p>
<p>Some days before it started I had a radiography on my head. May I have absorbed some X-rays, which are now creating some sort of magnetic field around me? I'm quite scared from this thing, even if at first it seemed funny...</p>
<p>Thank you in advance, and excuse me for my poor english.</p>
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<p>I am currently busy with some magnetism and quite shockingly (to me at least) I haven't yet read anything about the difference between the north pole and the south pole of a magnet. Before I started with magnetism I learned electricity, here there 2 opposite charges: negative charges (electrons) and positive charges (protons). Although I know for the people on this forum, that is very rudimentary, I at least find at a satisfactory explanation; different particles have different charges; a positive or a negative one. With magnetism I haven't stumbled across this yet. </p>
<ul>
<li><p>My teacher told me you can't say there is a positive and negative 'magnetic charge' (I don't know how to call it); but why? </p></li>
<li><p>Also, what causes the difference between the 2? </p></li>
<li><p>And, now that I'm thinking about it; are there actually magnets with only a north pole or a south pole (if not, why are the 2 so fundamentally connected that you can't have one without the other)?</p></li>
</ul>
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<p>Why does Lagrangian of free particle depend on the square of the velocity ?
For example, $L(v^4)$ also doesn't depend on direction of $v$. </p>
| 9,155 |
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<p>My question is simple, when you have a small lump of sugar, it's hard to break it with your bare hands, but when you blow in it, it appears to be more easy. (it's a piece of advice i learned for my gran, and it works !)</p>
<p>Is it due to humidity of the breath? or the spacing between sugar cristals? or something else?</p>
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<p>What is wrong if I define temperature of a small system (I mean, a system which has not a large number of particles) by</p>
<p>$$1/T = dS/dE$$</p>
<p>?</p>
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<p>In relation to this question:</p>
<p><a href="http://physics.stackexchange.com/questions/48574/how-can-a-black-hole-produce-sound">How can a black hole produce sound?</a></p>
<p>Which notes that the hole "produces" sound. The top answer states that:</p>
<blockquote>
<p>What you think of as the hard vacuum of outer space could just as well be seen as a very, very, very diffuse, somewhat ionized gas. That gas can support sound waves as long as the wavelength is considerably longer than the mean free path of the atoms on the gas.</p>
</blockquote>
<p>I get that there is "stuff" in space, what I don't get is how sound travels it. I learnt in high school that sound was a wave - as an example, you could fix a shoelace at one end and vibrate the other - voila, a wave forms.</p>
<p>And then sound kind of moves in the same way through, say, air, because of the slight molecular attraction between individual molecules is enough to create a similar waveform.</p>
<p>And then you get to space, and there aren't any molecules nearby to irritate each other, so there's no sound.</p>
<p>If that's the case, why does it matter <em>how</em> long the wavelength is, if there isn't a molecule nearby for the initial molecule to affect, how can sound travel?</p>
<p>I'd understand a <em>little</em> better if the particle a just <em>hit</em> particle b (like a pool ball) and b carried the sound - but that has little to do with waves and wavelengths.</p>
<p>Or is it that the "jet" that is thrown out travels along as a contiguous blob, with a sound wave embedded within it?</p>
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] |
<p>I am seeking references to the first articles regarding the observation of polaritons. </p>
| 9,159 |
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<p>I am taking a course in Computer Graphics, and the teacher said we could put materials in there main categories:</p>
<ul>
<li>mirror like</li>
<li>glossy or specular</li>
<li>diffuse</li>
</ul>
<p>He suggested that the law of reflection is immutable and applies to all types of surfaces but that glossy and diffuse surfaces appeared the way they do because of their microstructure. The roughness of these surfaces causes light rays to be reflected in random directions, thus blurring incoming light. So far, so good.</p>
<p>He also insisted on the idea that surfaces (expected in the case of metals) reflects the incident light color. In other words, if the incident light striking a mirror is white, reflected light is white (and not yellow as it is with gold, but again metal is a different case).</p>
<p>What I don't understand is that: if you use "roughness" to explain why some materials are shiny and others diffuse, diffuse surfaces too reflect incoming light color as mirror surfaces do. Therefore if mirror like surface do not have a color of their own (since they only reflect the incoming light color) so should diffuse surfaces. But diffuse objects have a color of their own (which mirror surfaces don not have). Thus, there's a flaw in the reasoning which I can't resolve.</p>
<p>I understand the object's color comes from the fact that electrons making up the atoms the material is made of, selectively absorb photons of some specific wavelength, and reflect the others. However does it mean it reflects these photon always in the mirror like direction? How and why does that happen that way if this is the case?</p>
<p>I am trying to put in one single pictures all the pieces of the puzzle together. Light can only be either reflected or refracted, however objects are coloured because they absorb some light frequencies, but I am told that "mirror reflection" does not affect the incident light color (in other words, that the reflected light color and the incident light color are the same in the case of mirror like reflections).</p>
<p>I am totally lost and would really appreciate if someone could shed light on this mystery.</p>
| 9,160 |
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] |
<p>This is a know rule when baking: </p>
<blockquote>
<p>Don't open the oven until your cake is finished, otherwise it will "fall".</p>
</blockquote>
<p>Why/how does this happen?</p>
| 9,161 |
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<p>As far as I understand, the basic reason why we are not able to solve QCD at low energies is because it is a strongly coupled quantum field theory, and a part from exceptional situations in simplified models (involving for instance supersymmetry), we have no tools to fully analyze such regimes. Correct me if I am wrong, but this is a rather technical obstruction.</p>
<p>Is there thus a simple, non-technical reason why proving confinement is such a difficult problem?</p>
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<p>This question concerns the following exercise from an old exam:</p>
<blockquote>
<p>The vibrational motion of a linear diatomic molecule can be approximated as simple harmonic motion.</p>
<ul>
<li><p>A CO molecule has a bond with force constant $k = 1900 \, Nm^{-1}$. What frequency of radiation would excite transitions between the different vibrational enery levels? (C and O have masses of $12 \, m_u$ and $16\, m_u$ respecitvely, where $m_u$ is the atomic mass unit.)</p></li>
<li><p>Explain why electromagnetic radiation can not excite vibrational transitions in an $O_2$ or $N_2$ molecule. How is this important for the heating of the earth's atmosphere by the sun (the greenhouse effect)?</p></li>
</ul>
</blockquote>
<p>For the first part I know the energy levels of a harmonic oscillator (in center of mass reference frame)</p>
<p>$$E_n = \hbar\omega(n+1/2),\quad \text{where }\omega = \sqrt{\frac{k}{\mu}}, \quad \mu = \frac{m_Om_C}{m_O + m_C}$$</p>
<p>and the energy of a photon of frequency $\nu$ is given by $E_{ph} = h\nu$. The photon energy must be the energy difference between two states:
$E_{ph} = E_n - E_m = \hbar \omega (n-m)$. This gives me the frequency</p>
<p>$$\nu = \frac{(n-m)}{2\pi}\sqrt{\frac{k}{\mu}}$$</p>
<p>Or minimum frequency $\nu_0 = \frac1{2\pi}\sqrt{\frac{k}{\mu}}$, right?</p>
<p>However, now to my actual question: I don't know why we cannot do the exact same thing for the other two molecules? What is different for $O_2$ and $N_2$?</p>
<p>I'd appreciate some help, thanks! =)</p>
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<p>I am reading 't Hooft's notes on Black Holes. I want to find the solutions of the Klein-Gordon equation $(\tilde{x},\tilde{y}, \rho, \tau)$ in the Rindler coordinates which are $$x=\tilde{x}\,\,\,\,\ y= \tilde{y}\,\,\,\,\,\,z=\rho \cosh{\tau}\,\,\,\,\,t=\rho \sinh{\tau}$$.</p>
<p><img src="http://i.stack.imgur.com/r47yg.png" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/3Tm7d.png" alt="enter image description here"></p>
<p>Firstly looking at the solution at first glance, why are there two parameters $\omega$, $\mu$, when the Klein-Gordon solution in Minkowski space has a solution with a parameter $\omega$ satisfying the mass on-shell condition. </p>
<p>Secondly, how do you get that solution? Following 't Hooft's advice, I wrote the usual solution with $k_3=0, k_0=\mu$ in terms of the Rindler coordinates and fourier transformed with time. </p>
<p>$$\Phi_{\mu}=\int d{\tau}\, e^{i{\tilde{k} \cdot \tilde{x}-\mu \rho \frac{e^{\tau}-e^{-\tau}}{2}}} e^{i\omega \tau}$$</p>
<p>Setting $s=e^{i\tau}$, I get the first expression of equation 17.7, but without the $e^{\tau}$ factors for $\alpha, \beta$.
I am obviously, going wrong somewhere, I am Fourier transforming to frequency space, so why is $\tau$ still there? Shouldn't it be just $\mu$ and $\omega$ or $\mu$ and $\tau$?</p>
| 9,164 |
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<p>In many theories of CMT, we assume the nature of quasi-particles (without giving proper justifications). For example, we assume nature of quasi-particles to be fermionic in case of a interacting fermion system we began with and impose anti-commutation relations accordingly. Like in BCS theory, while using the Bogoliubov-Valatin transformation to diagonalize the Hamiltonian, we assume that the new operators are also fermionic in nature. Please explain more on this step and how is it justified.</p>
| 9,165 |
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<p>The specifics of a question I am working on are, "After a 0.280-kg rubber ball is dropped from a height of 1.80 m, it bounces off a concrete floor and rebounds to a height of 1.45 m."</p>
<p>Why doesn't the ball return to the same height?</p>
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<p>I've been working on a project that involves thermoacoustics, and one of the commonly-used values in this field is know as the thermal penetration depth. It is calculated as follows:</p>
<p>$$\delta_k = \sqrt{2K / (C_p 2 \pi f \rho)}$$</p>
<p>where $K$ is the thermal conductivity of the fluid in question (helium)
$C_p$ is the isobaric specific heat of the fluid
$f$ is the frequency of vibration
$\rho$ is the density of the fluid</p>
<p>For my project, I've been using <a href="http://kilby.sac.on.ca/physics/SPH4U/LabInfo/Design%20of%20thermoacoustic%20refrigerators%20Cryogenics%202002a.pdf" rel="nofollow">this document</a> as a reference guide</p>
<p>In it, the given $\delta_k$ is 0.1 millimeters.
The given frequency is 400 $Hz$.
The fluid is helium at 10 bar.</p>
<p>Based on this information, I found the density of helium (~1.6 $g/mL$), the thermal conductivity of helium (~0.15 $W/mK$), and its isobaric specific heat (5.193 $J/gK$). </p>
<p>However, when I plug these values into the equation, I get delta_k = 0.00379 mm, which is considerably off.</p>
<p>Am I doing something wrong here? Is this widely-cited paper incorrect on such a basic fact?</p>
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