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<p><strong>EDITED AND SOLUTION</strong>: In fact my stupid mistake was to take the wrong value for my $P_1$ and I was getting an 1.2998 that finally is a 1,9178 within just a difference about 7%. So at the end they are not equal but it is not a $1.9\neq1.3$, but $1,9\neq1,9278$. </p>
<p>In spite of everything, <em>it has been profitable to me to discuss</em> the possible conditions where the ideal gas law can be a good aproximation. </p>
<p>Thank you very much for your useful answers. </p>
<hr>
<p>I have made an experiment that consist of a gas inside a cylinder and I have a piston. I have this experiment connected to a computer and I can graph the temperature and the pressure. This system can lose temperature so when I push in the cylinder I can see that my temperature increases and estabilizes to my lab temperature after 5 seconds. </p>
<p>So, my question is: </p>
<p>Why am I getting a factor $\frac{V_1}{V_2}=1,9 \pm 0,1$ and a factor $\frac{P_1\ T_2}{P_2\ T_1}=1,2998\pm0,0001$?</p>
<p><strong>I know that they have to be different but I don't know why, so why I shouldn't be expecting them to be equal</strong> (taking in account the uncertainties)<strong>?</strong>
<strong>$$\frac{V_1}{V_2}=\frac{P_1\ T_2}{P_2\ T_1}?$$</strong></p>
<p>Thank you in advance. </p>
<p><em><strong>PLUS</em></strong>! I have added the image of the experiment. I pushed in the piston and stay making force for about 20 sec until I released the piston free</p>
<p><img src="http://i.stack.imgur.com/wDzPX.jpg" alt="I pushed in the piston and stay making force for about 20 sec until I released the piston free"></p>
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<p>How to show that
$$
\int d\Psi d\bar {\Psi}e^{i \int d^{4}x\bar {\Psi} \hat {A} \Psi} = det (\hat {A})?
$$
$\Psi , \bar {\Psi}$ refers to Dirac spinors (the second is $\bar {\Psi} = \Psi^{\dagger}\gamma^{0}$).</p> | 5,377 | [
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<p>In a lecture (<a href="http://teorica.fis.ucm.es/TAE2012/CHARLAS.DIR/MEISSNER.DIR/part2.pdf" rel="nofollow">look</a> at the chapter "The fermion determinant in a constant field", p. 5) I found some strange transformation, which is given by eq. 18. How to prove it? Exactly, I don't understand the appearance of some crossed symbols, especially in denominator.</p> | 5,378 | [
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<p>If I had a static thin (a few mm) film of water lying on a surface and I tried to push a squeegee across the surface in order to move the water. Would the water rise up in front of the squeegee? Would the angle be possible to calculate if the speed were to increase and or the force of gravity were to increase?</p> | 5,379 | [
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<p>What is the physical constraint that gauge invariance is a required condition for electromagnetic fields? What would happen if the electromagnetic fields were not gauge invariant?</p> | 5,380 | [
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<p>There was an announcement at a recent UCLA symposium on dark matter by the <a href="http://fermi.gsfc.nasa.gov/" rel="nofollow">FERMI collaboration</a> which hints at some evidence of dark matter. The results aren't yet published, but the <a href="http://m.ucla.edu/newsroom/item.php?name=News&path=http%3A%2F%2Fnewsroom.ucla.edu%2Fportal%2Fucla%2Ffiles%2Fmobile.xml&article=Possible+evidence+for+dark+matter+particle+presented&signature=18ef784085eaa0c6a3c40872eac84dbe&no_server_init" rel="nofollow">symposium news release is here</a>. Most of the news release is just general dark matter fluff, but it says that</p>
<blockquote>
<p>One search technique involves using the vast amount of dark matter in our galaxy. The NASA Fermi Satellite Telescope, an international collaboration involving NASA, the Goddard Space Flight Center and the SLAC National Accelerator Laboratory, searches for gamma rays — very high-energy light particles — from this dark matter.</p>
<p>There are models of dark matter that would allow a signal in the galactic dark matter consistent with the claims at the meeting and provide a small interaction consistent with the "null results" in the direct dark matter searches all over the world.</p>
</blockquote>
<p>This obviously doesn't contain much information. Can anyone closer to the field expound on the findings?</p> | 5,381 | [
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<ul>
<li>Suppose there is a habitable star with a significantly large mass, and thus a huge gravitation field. It has a clock on it that ticks each local second. And it also has a mirror. This is Star A.</li>
<li>Suppose there is another habitable star with a much smaller mass, also with a clock, called Star B. </li>
<li>Finally, suppose that these two stars somehow maintain a fixed distance between them. (Eg: the two stars have perfectly calibrated rocket thrusters pointing toward one another).</li>
</ul>
<p>Please correct me if I'm wrong: An observer on Star A looking through a telescope at clock B would see it ticking quickly. Likewise, an observer on Star B looking at the clock on Star A would see it ticking slowly.</p>
<p>Now, suppose a person on A sends a light pulse towards B and starts a clock. They measure it takes 10 seconds for it to come back.</p>
<p>Now, a person on B sends a pulse to A, and measures how long it takes to get back. Does it also take 10 seconds? If so, there's a pretty clear paradox. If not, how could it take light different times to travel the same distance?</p>
<p>Thanks</p> | 5,382 | [
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<p>Does the photino in super-symmetry have a mass, Or is this different in different super symmetric models?</p> | 5,383 | [
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<p>Quantum entanglement bridges space and time: entangled particles show correlations independently of where and when they are measured. This is most evident in "delayed choice quantum eraser" experiments, where the outcome of single measurments <em>now</em> depends on which measurements are done <em>in the future</em> (though there is no retro-causality in the strict sense).</p>
<p>I am looking for realistic interpretations which directly address this topic, i.e. discussions of underlying physical mechanisms or basic structures of the universe on which this correlations may be built.</p>
<p>So far I found John Cramers "Transactional Interpretation" of 1986; Bohmian mechanics may also be considered. Are there other physical interpretations or philosophical papers on this topic of correlations over spacetime?</p> | 5,384 | [
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<p>Why capacitors are used in flashlights of cameras instead of attaching the light directly to the battery? How this leads more light?</p> | 5,385 | [
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<p>I talked to a professor about solar panels and their efficiency. It seemed that the main reason solar panels aren't that efficient is because it can only accept a single energy input size. Anything below is ignored and anything above only gives the energy of that single limit.</p>
<p>That is, say the limit is 1W. A photon with 0.999W energy wouldn't give any voltage. A photon with 10W energy would give the same voltage as a 1W photon.</p>
<p>Does this mean I can get very high efficiency from a light source with a specific frequency? For example a solar-powered calculator in a room with only sodium lights. How high?</p>
<p>How does the efficiency change depending on the amount of light or the temperature of the solar cell? How about an extremely small amount of light, like 1nW, close to 0K?</p>
<p>This could be terribly wrong as there was quite a language barrier between us. I want to learn, so please point out any misstakes.</p> | 5,386 | [
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<p>I know the magnetic field strength increases as the number of turns in the solenoid increases.</p>
<p>However, I've learnt the field inside the solenoid is usually nearly uniform.</p>
<p>So, does the number of turns in the solenoid effect the uniformity of the field inside the solenoid? Does the field gets closer to uniform as the number of turns increases?</p> | 5,387 | [
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<p>Anthropic principle, at least in laymen explanations that I have encountered so far, sounds something like "the physical universe suits us exceptionally well because among all the possibilities we, the observers, tautologically encounter the one that can support us."</p>
<p>I was wondering whether this principle can be applied to specific observers. That is, suppose that Shroedinger performs his thought experiment with himself, rather than his cat. Would the anthropic principle imply <strong>from Shroedinger's viewpoint</strong> that he would always survive, at least according to many-worlds interpretation?</p>
<p>How about this setting, assuming many-worlds interpretation: two people decided to divorce by proceeding with their lives as window&widower in separate universes. They create a setup similar with Shroedingers, except that 2 boxes have been created in such a way that a person in exactly one of them would get killed, depending how a certain superposition collapses. Then the unhappy couple enters the chambers. Does the anthropic principle imply that <strong>each</strong> of them would experience the exiting the chamber as the sole surviving spouse?</p> | 5,388 | [
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<p>while studying scattering formula for the supercurrent (<a href="http://arxiv.org/abs/cond-mat/9611162" rel="nofollow">Beenakker</a>)
I encountered that the density of states for discrete and continuous spectrum can be simultaneously described by taking $\epsilon\ ->\ \epsilon + i\delta $ in the following formula:
$\rho(\epsilon) = -\frac{1}{\pi}Im\frac{d}{d\epsilon}\left\{lnDet\left[1 - S_{A}(\epsilon)S_{N}(\epsilon) \right] - \frac{1}{2}lnDet\left[S_{A}(\epsilon)S_{N}(\epsilon)\right]\right\}$.</p>
<p>I am wondering if one could argument this by referring to scattering theory and Green's function - eg. <a href="http://newton.phy.bme.hu/~szunyogh/Elszerk/Kkr-slides.pdf" rel="nofollow">Laszlo Szunyogh</a>.</p> | 5,389 | [
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<p>How to show with Maxwells Equations that nonaccelerating charges don't radiate?</p> | 5,390 | [
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<p>A wedge of mass $M$ rests on a rough horizontal surface with coefficient of static friction $\mu$. The face of the wedge is a smooth plane inclined at an angle $ \alpha$ to the horizontal. A mass $m_1$ hangs from a light string which passes over a smooth peg at the upper end of the wedge and attaches to a mass $m_2$ which slides without friction on the face of the wedge.</p>
<p>A) Find the accelerations of $ m_1, m_2 $ and the tension in the string when $ \mu $ is very large.</p>
<p>B)Find the smallest coefficient of friction such that the wedge will remain at rest.</p>
<p>Attempts:</p>
<p>No specification on whether or not any of the masses $m_i$ are bigger than the others, so let us assume that $m_1$ goes down and $m_2$ goes up the slope. Then A) is fine. (a minus error in the final answer for A) is introduced if I assume the other orientation)</p>
<p>As for B) if we consider the wedge+masses as a system, then to conserve linear momentum if the masses move as above, then the wedge must move rightwards. So the frictional force acts leftwards until the wedge slips. The only other force acting on the wedge is via the normal contact force from $m_2$. A component of this force acts to accelerate the wedge horizontally. Let's write this relative to some fixed inertial frame of reference with $x$ rightwards. Then the above recast into symbols gives $$-\mu (M+m_1+m_2)g - m_2 g \cos \alpha \sin \alpha = 0 $$ at the point of slip of the wedge. However, solving this for $\mu$ gives a negative result. Where did I go wrong?</p>
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<p>What do you mean by charge? Why should a particle have a charge?</p> | 189 | [
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<p>I know that the equation for it is $$v^2 = \frac{2GM}{r},$$ and with that, the rocket should be launched at that speed. But could it go much slower spending much more fuel to escape from gravity right? </p>
<p>Wouldn't it be easier to calculate it with energy? </p> | 5,392 | [
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<p>Is it possible to derive an uncertainty relation (Karolyhazy Uncertainty: <a href="http://dx.doi.org/10.1007/BF02717926" rel="nofollow">http://dx.doi.org/10.1007/BF02717926</a>) with photons? I brainstormed a bit to get the following:</p>
<p>$$ \Delta x_0 \Delta p_0 = \frac{\hbar}2,$$ </p>
<p>and then, </p>
<p>$$\Delta k_0=\frac{1}{2\Delta x_0}.$$</p>
<p>I need to derive a relation such that </p>
<p>$$\Delta x = (c)^a (\Delta x_0)^{1/3},$$ </p>
<p>where $c$ is a constant and $a$ is a power term. The other symbols retain their usual meaning.
How must I go about this, if it is possible? </p> | 5,393 | [
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<p>It is well known that if you blow horizontally on a bottle top it creates a sound. Pouring water to the bottle changes the pitch.</p>
<p>I have been doing experiments on the relation between the sound's main frequency (or rather the corresponding wavelength) and the vertical distance between the bottle top and the water level.</p>
<p>My (poor) theoretical thoughts were that by blowing on the top I create a standing wave exactly between the bottle top and the water surface, therefore the wavelength should be equal to the height of the air column.</p>
<p>Apparently, I was wrong, but not completely -- it's not $y=x$, but rather a linear relation $y=ax+b$. I have been conducting several experiments with different bottles, and the results are:</p>
<p>A 18cm high bottle gave me $a=5.5$ and $b=26.65$. A 21.7cm bottle gave me $a=7.94$ and $b=14.54$. A tall 32.5cm bottle resulted in $a=7.1$ and $b=34.21$. But my biggest surprise was to find a negative $b$, with a glass 19.3cm bottle (the rest were plastic), and $a=9.16$ and $b=-22.43$.</p>
<p>Is there a plausible explanation for this phenomenon?</p>
<p>(I didn't consider the actual shape of the bottle as I assumed a vertical standing wave will emerge. Most of the bottles are pretty constant in shape, except for the glass bottle which is closer to a cone. Looking at the signal itself one can clearly see a high energy peak at the pitch, and smaller peaks at the pitch's multiples. I noticed that the slopes are close to natural numbers or half thereof.)</p> | 5,394 | [
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<p>Many times in physics when we analyze a physical system mathematicly we get divergences, but when those divergences has no dependence on any actual physical quantity of interest we tend to disregard those "infinity Constants". </p>
<p>An example where such a thing happens is in the derivation of the Casimir force for two metal plates we get $\zeta(-3)$ which contains infinities.</p>
<p>One can provide many more examples where we make this analytical approach.</p>
<p>My question is why those infinities are treated this way, is there a deep mathematical reason why we do it?</p> | 190 | [
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<p>I was looking up for how polarisers work, I understood mostly everything except the part that explains that the polariser filters everything except light that is in a certain orientation.</p>
<p>Here are my questions. How do waves have different orientation except being either vertical or horizantal? What determines the orientation and how does that affect in absorption of the wave?</p> | 5,395 | [
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<p>Mathematician here with a speculative physical question -- feel free to boot me if the level isn't right.</p>
<p>Suppose one finds, or builds, a constellation of several black holes arranged in a circle. (To get a stable arrangement, presumably one could put a bunch of small positively charged black holes at equal angles around a central positively charged object, or alternatively suspend uncharged black holes gravitationally in a circle surrounded by a quickly rotating ring of heavy matter). Suppose moreover that the event horizons of neighboring holes overlap -- or if there's some reason this is theoretically impossible, suppose they're really, really close to being tangent, while leaving room for light and matter to pass through the middle of this ring. (Is this possible?)</p>
<p>My question is whether a trajectory from point A to point B that goes through the middle of the ring is causally related to one that does not. For example say a space explorer measures the spin of an electron, writes down the result and puts it in a box which he leaves at some fixed point in space (we've chosen a reference frame), then goes in a loop through the middle of the ring of black holes and comes back. When he comes back and opens the box again, will the recorded result be the same?</p>
<p>I got this question after someone told me about quantum decoherence, and I was curious whether the world can change significantly if you go around a loop that either cannot be contracted or cannot be contracted without at some point becoming ridiculously long (where it's up to you to decide the value of "ridiculously").</p> | 5,396 | [
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<p>Assume a small square block $m$ is sitting on a larger wedge-shaped block of mass $M$ at an upper angle $\theta$ such that the little block will slide on the big block if both are started from rest and no other forces are present. The large block is sitting on a frictionless table. The coefficient of static friction between the large and small blocks is µs. With what range of force $F$ can you push on the large block to the right such that the small block will remain motionless with respect to the large block and neither slide up nor down? </p>
<p>This question really is not too complicated without friction acting upon the small block (<a href="http://physics.stackexchange.com/questions/35978/preventing-a-block-from-sliding-on-a-frictionless-inclined-plane">Preventing a block from sliding on a frictionless inclined plane</a>) </p>
<p>But what happens when we add friction to the system? Why is it considered static, if at rest, the mass would slide down the plane? </p> | 5,397 | [
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] |
<p>What is the value of $g$ at the centre of the Earth? Is it zero or infinity?
My attempt: I know it's zero but applying law made me on fused.</p> | 50 | [
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<p>Folks, I have a naive question regarding the subject of dark energy and an accelerating universe:</p>
<p>From what I understand/read, it seems that the further we look out into deep space, the faster the objects are moving away from us - in all directions. </p>
<p>Is this basically what is meant by "accelerating universe"?</p>
<p>Because it seems that this situation is exactly what we should expect to see (according to Big Bang theory). The further out we peer into space, the further back in time we are "seeing", so wouldn't we expect to see higher rates of acceleration/expansion the further back in time we peer?</p> | 336 | [
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<p>I'm working on a problem with celestial bodies and for my purpose days and AUs are more appropriate units than seconds and meters. So I tried to convert the constant of gravitation, $G$, like this:</p>
<p>$$
k= \frac{\frac{\text{AU}^3}{\text{kg}\times \text{D}^2}}{\frac{\text{m}^3}{\text{kg}\times \text{s}^2}}=(\frac{\text{AU}}{\text{m}})^3(\frac{s}{D})^2=\frac{(1.496\times 10^{-11})^3}{(24\times 60\times 60)^2}=4.485\times 10^{-43}
$$
$$
G=6.673\times10^{-11}\times k = 6.673\times10^{-11}\times4.485\times 10^{-43}=2.993\times 10^{-53}
$$</p>
<p>Now I want to do some calculations with this value. First of all, what is the orbital period of a circular orbit around the sun?</p>
<p>$$
v_0=\sqrt{\frac{G M_\odot}{r}}
$$
$$
t = \frac{2\pi r}{v_0}
$$</p>
<p>The initial velocity has been adapted so that the centripetal force equals the force of gravitation, so the orbit will be circular.</p>
<p>For $r=1$ I expected that the orbital period would be a couple of hundred days, since it takes about 365 days for the earth to circle the sun and one AU is the distance between the sun and the earth. However, when I do the calculation I get that $t=8.14462\times 10^{11}$. What did I do wrong?</p> | 5,398 | [
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<p>There's some constant relating to electrons that also has the same value as the speed of light. What is it, what is the value, and how are they related?</p>
<p>EDIT: Is it the fine-structure constant?? Are there any other similar constants? If you posted that answer before, you shoulda left it (to the person who deleted their answer)!</p> | 5,399 | [
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<p>I've been looking for a long time and I've not had a lot of luck. I've found sources that <strong>use</strong> fermions in 3d Euclidean space but I can't find any that explain the Wick rotation from Minkowski space. </p>
<p>This <a href="http://arxiv.org/abs/hep-th/9608174" rel="nofollow">source</a> provides a nice explanation of the Wick rotation procedure for fermions in 4d. However it leaves the odd dimensional case as an open question.</p> | 5,400 | [
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<p>Will a CFL light bulb and an incandescent light bulb, in separate respective closed systems, produce exactly the same amount of overall temperature increase over time?</p>
<p>Assume you have two identical closed systems with gray walls, with a system input of 20 watts of power each. </p>
<p><strong>EDIT added for clarity: (On the packaging of the CFL light bulb the large print equivalent wattage is irrelevant... the input current of both bulbs is a consistent 20 watts of power each. The comparison wattage vs. the actual wattage of the CFL is off subject.)</strong></p>
<p>One has a CFL, one has an ordinary incandescent light bulb. Will both systems increase in heat the exact amount, every hour?</p>
<p>Due to conservation of energy it shouldn't matter if one light source is more efficient, right?... it's the same amount of energy input. One light makes more heat one makes more light, but the light when it hits the gray wall is converted to heat, right?</p>
<p>There is no such thing as loss of energy... it's just converted to another form of energy... and light is converted to heat, right?</p>
<p>The back story of this question is my wondering that if my wife leaves an incandescent light bulb on in the winter time it's not so bad because even though no one is in the room it's still heating up the room. On the other hand if she leaves on a CFL it's more efficient but it should still add heat to our "system," i.e., our home.</p> | 5,401 | [
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<p>This question is essentially a duplicate of <a href="http://physics.stackexchange.com/questions/67810/gibbs-paradox-why-should-the-change-in-entropy-be-zero">Gibbs Paradox - why should the change in entropy be zero?</a>. The question concerns the following situation: I have some gas of identical particles and they are in a box which has been partitioned into two halves by a removable divider. Now the question is "<strong>If I remove the divider, why should the change in entropy be 0?</strong>" The standard answer is given in the above-linked-to question. The main idea of the answer is that the particles are supposed to be considered indistinguishible. If you treat the particles this way, you find that there is no change in entropy when the partition is removed. </p>
<p>I understand this answer, and I suppose it should work for identical atoms, but you can easily imagine a situation where you have a collection of objects which are distinguishible, say some nanoparticles with differing numbers of constituent atoms. </p>
<p>Furthermore, you should be able to treat a gas of identical particles as classical distinguishable bodies, and still get the right answer from statistical mechanics. I would say this is a good check of understanding of statistical mechanics. </p>
<p>If this isn't enough motivation to come up with an alternate resolution to the paradox, consider this paradox, which requires essentially the same resolution that the gibbs paradox does: Imagine two systems initially in thermal contact and in thermal equilibrium. Now suppose they are separated. Here we might think the entropy will decrease in this process because in the initial configuration the energy of both systems were allowed to change as long as their sum remained constant. After separation, the systems' energies are fixed at some value. Clearly the set of final states is a subset of the set of initial states, so the entropy has decreased. This is the analogy of the gibbs paradox where instead of the systems exchanging particle number, they are exchanging energy. I would expect it to have essentially the same resolution.</p>
<p>So my question is, "<strong>Why should the change in entropy be zero, even in the particles are distinguishible?</strong>"</p> | 5,402 | [
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<p>I am confused about the current and voltage. My intuitive example would be that of a pipe of say water. The diameter of the pipe determines the amount of water flowing per second but the pressure is comparable to voltage. Am I right?</p>
<p>And what is the difference between voltage source and current source? In what class our electric sockets on the wall do fall?</p> | 5,403 | [
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<p>This question was asked to me.</p>
<p>My first thought was that electrons may ionise the air and potential difference that was applied may increase or decrease the current which should have been observed. I'd like to know whether this is the right reason or if there is any other reason which I should take into account.</p>
<p>$$hv-w.f=hv'=eV$$ where $V$ is stopping potential , my second question is:
if there isn't a vacuum will that stop potential change?</p> | 5,404 | [
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<p>what is the ram-facing side of a satellite? What does it mean and why is it called "ram"-facing?
Thanks.</p> | 5,405 | [
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<p>Wired magazine ran an <a href="http://www.wired.com/magazine/2011/04/st_equation_sodapop/" rel="nofollow">article</a> this month on carbonation in soft drinks.</p>
<p>If all soft drinks are manufactured effectively identically, why do some types fizz more than others?</p>
<p>For example, root beer is always extremely fizzy (and <a href="http://billybrew.com/beer-lacing" rel="nofollow">laces</a> well).</p>
<p>In similar fashion, lemon-lime drinks like Sprite and Sierra Mist are very fizzy - but do not lace like root beer.</p>
<p>Compare those to diet colas, which fizz slowly and/or minimally, and one is left to ponder.</p>
<p>What is it about some types of drinks that make them hold and release their carbonation differently?</p> | 5,406 | [
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<p>More specifically, in quantum field theory books, we usually have this:</p>
<p>\begin{equation}
Z = \int D(\bar{\psi}, \psi) e^{-S + \int_0^\beta d\tau \sum_l [\bar{\eta}_l (\tau) \psi_l (\tau) + \bar{\psi}_l (\tau) \eta_l (\tau) ]} \hspace{10mm} (1)
\end{equation}</p>
<p>where $S = \int_0^\beta d\tau \sum_l (\bar{\psi}_l (\tau) \partial_\tau \psi_l (\tau ) +H(\bar{\psi},\psi))$ is the action, and $H$ is the Hamiltonian of the system.</p>
<p>Can I instead start off with the Hamiltonian in diagonal form and include the source term in, say, a momentum basis? So that</p>
<p>\begin{equation}
Z = \int D(\bar{\psi}, \psi) e^{-S + \int_0^\beta d\tau \sum_k [\bar{\eta}_k (\tau) \psi_k (\tau) + \bar{\psi}_k (\tau) \eta_k (\tau) ]}
\end{equation}</p>
<p>where $S$ is now $\int_0^\beta d\tau \sum_k (\bar{\psi}_k (\tau) [\partial_\tau +\epsilon_k]\psi_k (\tau ))$.</p>
<p>Or do I have to start off with equation (1) and apply various transformations to the Hamiltonian and the rest of the exponent until $H$ it is in a diagonal basis? - If this is the case, the resulting source term in the momentum basis could be extremely complicated after the transformations are performed.</p>
<p>Thanks! </p> | 5,407 | [
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<p>First of all, I know there's a much alike question <a href="http://physics.stackexchange.com/questions/15762/what-is-a-wave">here</a> but this is not duplicate since I couldn't find there the answer I'm seeking. My problem is the following: I know that intuitively we have a wave when we have some quantitiy (that as I see can be anything) oscilating at each point in space. So for instance, electromagnetic waves are composed of electric and magnetic fields oscilating on each point of space.</p>
<p>Now, this is vague and imprecise. It is not clear at first how to model this mathematically and what properties this thing should have. However there's the wave equation:</p>
<p>$$\nabla^2 \psi = \dfrac{1}{v^2} \dfrac{\partial ^2}{\partial t^2}\psi,$$</p>
<p>but asking some physicists they told me that not every wave obeys that equation. That anything obeying that equation is really a wave, but that there are waves which evolve differently, some that are nonlinear and all of that.</p>
<p>In that case it seems everything is totally vague. A wave is something that moves like a wave, some of those things obeys a certain equation and the others can obey equations totally different. In that case it becomes a little bit difficult to grasp what really is a wave and how do we treat waves with precision.</p>
<p>So, what is a wave and how waves are preciselly dealt with in some mathematical framework?</p> | 5,408 | [
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<p>In order to derive the Lorentz transformation one can use the picture of a light clock. A Photons bounces back and forth between two mirrors. This is then observed in two different inertial systems. If the relative speed of the inertial systems is perpendicular to the propagation direction of the photon deriving, extracting the Lorentz transformation is easy and there are hundreds of examples on the web: </p>
<p><a href="http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/lightclock.swf" rel="nofollow">http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/lightclock.swf</a></p>
<p>However, I am trying to calculate this scenario if the relative motion between the Inertial systems is parallel to the direction of the light propagation:</p>
<p><img src="http://i.stack.imgur.com/XfeMN.png" alt="Depiction of clock moving parallel to light propagation"></p>
<p>In this case I simply get for the standing observer:</p>
<p>$T_{Periode} = \frac{2 h}{c}$</p>
<p>and for the moving observer:</p>
<p>$ T_{Periode} = \frac{h + v_{rel} t}{c} + \frac{h - 2v_{rel} t}{c} = \frac{2h - v_{rel}}{c}$</p>
<p>I can't see how this would lead me to the Lorentz transformation.</p> | 5,409 | [
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<p>The formula for centripetal (radial) acceleration is well known, and there exist many proofs for it: $$||a_c|| = \frac{||v||^2}{r}$$</p>
<p>However, all the proofs I've seen rely on the fact that it is <em>uniform</em> circular motion and the magnitude of the tangential velocity vector does not change. For instance, take the classic proof using similar triangles — the similarity can only be established if the final tangential velocity vector and the initial one are of the same length.</p>
<p>In addition, take <a href="https://www.khanacademy.org/science/physics/two-dimensional-motion/centripetal-acceleration-tutoria/v/calculus-proof-of-centripetal-acceleration-formula" rel="nofollow">this</a> calculus based proof from Khan Academy, outlined as follows:</p>
<p><img src="http://i.stack.imgur.com/7ysrf.png" alt="Image 1">
<img src="http://i.stack.imgur.com/lzHw6.png" alt="Image 2"></p>
<p>For this proof to work, $\frac{\text{d$\theta $}}{\text{dt}}$ must be considered a constant, $\omega$, that does not depend on time. In the case of non-uniform circular motion, however, this is not always true as since there exists a tangential acceleration along with a radial one, $\omega$ must depend on time and is not necessarily a constant value.</p>
<p>Intuitively I understand that the centripetal/radial acceleration depends only on the difference in orientation between two tangential velocity vectors, and that their magnitudes do not matter -- hence the formula intuitively holds true in the non-uniform case. However, how would you go about modifying either of the proofs presented so that they are still valid in this case? Or alternatively, is there another proof that holds valid even when there exists tangential acceleration?</p>
<hr>
<p>As per the suggestion of one of the answers, I let $\omega$ vary with time and took its derivative as $\alpha(t)$. This is my work so far. Unfortunately, I am stuck after the last step.</p>
<p>$$\overset{\rightharpoonup }{p}(t)=r \cos (\theta (t))\cdot\hat{i}+r \sin (\theta (t))\cdot\hat{j}$$
$$\overset{\rightharpoonup }{v}(t)=-r \sin (\theta (t))\cdot\omega(t)\cdot\hat{i}+r \cos (\theta (t))\cdot\omega(t)\cdot\hat{j}$$
$$\overset{\rightharpoonup }{a}(t)=(-rcos(\theta(t))\cdot\omega(t)^2 - rsin(\theta(t))\cdot\alpha(t))\hat{i} + (-rsin(\theta(t))\cdot\omega(t)^2 + rcos(\theta(t))\cdot\alpha(t))\hat{j}$$</p>
<blockquote>
<p>From here on, $\theta(t)$ is represented as just $\theta$ for brevity
and clarity</p>
</blockquote>
<p>$$\overset{\rightharpoonup }{a}(t)= -\omega(t)^2(rcos\theta\cdot\hat{i} + rsin\theta\cdot\hat{j}) -\alpha(t)(rsin\theta\cdot\hat{i} - rcos\theta\cdot\hat{j})$$</p> | 5,410 | [
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] |
<p>After reading <a href="http://www.nasa.gov/topics/technology/features/new-nano.html" rel="nofollow">this NASA article</a> about the "blackest material", the following stuck out to me.</p>
<blockquote>
<p>The tiny gaps between the tubes absorb 99.5 percent of the light that hits them</p>
</blockquote>
<p>Is it possible to create a material that absorbs, not just all visible light, but all electromagnetic radiation?</p> | 561 | [
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<p>I am reading the two concepts mentioned in the title. According to the definition of torque and moment of inertia, it would appear that if I pushed on a door, with the axis of rotation centered about its hinges, at the door-knob, it would be difficult, relative to me applying a force nearer to the hinges. However, I just experimented with my front door, and it would appear to be the converse, what am I misunderstanding?</p>
<p>Definition of torque: $\tau=r\times\vec{F}$, where r is the length of the lever arm (the distance from the axis of rotation to the point of application of the force).</p>
<p>EDIT:</p>
<p>Also, what does it mean for torque to be perpendicular to the rotation?</p> | 5,411 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/7584/how-do-we-know-that-some-radioactive-materials-have-a-half-life-of-millions-or-e">How do we know that some radioactive materials have a half life of millions or even billions of years?</a> </p>
</blockquote>
<p>I understand how to calculate decay, but it seems to me that the formula leaves a lot to be desired. I learned in chemistry that radioactive decay occurs completely at random, which is why we have assigned half life times to radioactive isotopes. But how can we know for sure the half life of an isotope unless one waits for exactly half the sample to decay?
For all we know, uranium has a much shorter half life, and all the samples are about to decay to half mass.
Thanks for any help in clarifying. </p> | 191 | [
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<p>Some metal containers such as the Nissan Thermos ones, even if 100 C water is filled inside, the container is still cold to the touch on the outside. It won't be even warm:</p>
<p><img src="http://i.stack.imgur.com/E3Cbs.jpg" alt="enter image description here"></p>
<p>At the same time, some that look similar are so hot on the outside that holding it for a couple of seconds won't be possible:</p>
<p><img src="http://i.stack.imgur.com/gg9pq.jpg" alt="enter image description here"></p>
<p>Also, some teapot at Chinese restaurant or Vietnamese Restaurant, it can be boiling hot water inside, but the handle is also cold to the touch:</p>
<p><img src="http://i.stack.imgur.com/mc5il.jpg" alt="enter image description here"></p>
<p>The question is, for the Nissan one and the ones at Chinese restaurants, if the metal part is all connected, from where the liquid is, to the part that the hand can touch, why isn't the handle or outside too hot to hold, but can be not much different from room temperature?</p>
<p>(the Nissan one is vacuum inside, but the metal container part is all part of a single piece.)</p> | 5,412 | [
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<p>When I whistle, I find that I can vary the volume by pushing more or less air through my mouth at once. However, when I increase volume past a point, I start to hear a blend of rushing air and a faint whistle sound. Why? Is the air just subtly pushing my lips out of shape, or is there some other maximum (such as size/shape of my mouth) that I'm encountering? Is there any adjustment I can make after I cross this point to continue whistling louder?</p>
<p><strong>EDIT</strong></p>
<p>Why is it possible for people to whistle louder with their fingers in their mouth?</p> | 5,413 | [
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<p>Recently, I have stumbled upon a YouTube video by Veritasium describing the conductivity of fire. My question is: how exactly does fire conduct electricity? I am a high school student; therefore appropriate language is expected. </p>
<p><a href="http://youtu.be/a7_8Gc_Llr8?hd=1">http://youtu.be/a7_8Gc_Llr8?hd=1</a></p> | 354 | [
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<p>I read according to 'Newtonian' Mechanics any set of physical activity of particles can be reversed ( I think) so a set of complicated dynamic systems of particles and matter can reverse their 'behaviour'. Yet a Star collapsing towards a 'Black Hole' will probably not 'stop' and reverse it's behaviour. So could Gravity be considered part of the 'Arrow of Time'? Since entropy is part of this 'Arrow' could entropy have 'qualities similar to the qualities of Gravity?</p> | 5,414 | [
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<p><strong>EDIT</strong>: I haven't forgotten to accept answer, the question is still open.. </p>
<hr>
<p>I need a clarification about Poisson brackets. </p>
<p>I'm studying on Goldstein's Classical Mechanics (1 ed.).</p>
<p>Goldstein proves that Poisson brackets are canonical invariants for any functions F and G. </p>
<p>But there is a step that I can't understand.</p>
<p>After some steps, he says that: </p>
<p>$$ \tag{1} [F, G]_q,_p = \sum_k ( \frac { \partial G}{\partial Q_k} [F,Q_k]_q, _p +\frac {\partial G}{\partial P_k}[F, P_k]_q, _p)$$ </p>
<p>After other steps, he writes:</p>
<p>$$ \tag{2}[F,Q_k]= - \frac {\partial F}{\partial P_k}$$.</p>
<p>and $$ \tag{3}[P_k, F]_q, _p = \sum_j \frac {\partial F}{\partial Q_j} [P_k, Q_j] + \sum_j \frac {\partial F}{\partial P_j}[P_k, P_j]$$ -></p>
<p>$$ \tag {4} [F,P_k]=\frac {\partial F}{\partial Q_k}$$ </p>
<p>and now he replaces these relations in the first expression I have written, obtaining:</p>
<p>$$\tag {5}[F, G]_q, _p=[F, G]_Q, _P$$</p>
<p>Why does he obtain in the second last step $\frac {\partial F}{\partial Q_k}$ and not $-\frac {\partial F}{\partial Q_k}$? $[P_k, F]=-[F, P_k]$ isn't it?</p>
<p><strong>EDIT</strong>:
Golstein starts from (1) and substituites $Q_k$ to $F$ and $F$ to $G$ and so he obtains (2). </p>
<p>Then he substitutes $P_k$ to $F$ and $F$ to $G$ and obtains (3). </p>
<p>Immediately after he writes (4), that according to me is opposite to (3). </p>
<p>And so I have thought to a printing error. I have tried to substitute $-P_k$ to $F$ and I have obtained </p>
<p>$$[-P_k, F]=\frac {\partial F}{\partial Q_k}$$</p>
<p>Then, as $[-P_k, F]=[F,P_k]$,
I can say that $$ [F,P_k]=\frac {\partial F}{\partial Q_k}$$. </p>
<p>And so I can obtain (5).</p>
<p>Could you confirm that my argumentation is correct? Many thanks</p> | 5,415 | [
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<p>I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 nested integrals (3 for each particle $dm$ and 3 for integrating the potential energy for all other particles).</p> | 5,416 | [
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<p>Trying to get a better understanding of the relation between a SU(N) Yang Mill theory and its number of "color" <a href="http://www.stat.physik.uni-potsdam.de/~pikovsky/teaching/stud_seminar/Classical_Yang_Mills.pdf" rel="nofollow">space</a>.</p>
<p>Most of the description I've found so far are either way to complex/specific. Yiannis answer on <a href="http://physics.stackexchange.com/questions/102941/how-many-physical-degrees-of-freedom-does-the-mathrmsun-yang-mills-theory">this post</a> is almost what I'm looking for, except I was hoping someone could provide addition sources and readings corresponding precisely to what he is describing. </p> | 192 | [
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] |
<p>What is thermal velocity? What is it's physical significance?
<a href="http://en.wikipedia.org/wiki/Thermal_velocity" rel="nofollow">Wikipedia says</a>: </p>
<blockquote>
<p>The thermal velocity or thermal speed is a typical velocity of the thermal motion of particles which make up a gas, liquid, etc. Thus, indirectly, thermal velocity is a measure of temperature. </p>
</blockquote>
<p>But I cannot understand and comprehend it.</p> | 5,417 | [
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] |
<p><a href="http://www.mazda.com/mazdaspirit/skyactiv/engine/skyactiv-g.html" rel="nofollow">Here's a description</a> of new combustion engine improvement by Mazda, called SkyActive-G. They claim that in a "generic" engine...</p>
<blockquote>
<p>when the exhaust manifold is short, the high pressure wave from the gas emerging immediately after cylinder No. 3’s exhaust valves open, for example, arrives at cylinder No.1 as it finishes its exhaust stroke and enters its intake stroke. As a result, exhaust gas which has just moved out of the cylinder is forced back inside the combustion chamber, increasing the amount of hot residual gas</p>
</blockquote>
<p>I always though, that exhaust manifold and intake manifold are separated, so exhaust gases just can't possibly enter other cylinders combustion chambers as described in the above quoted text.</p>
<p>Can exhaust gases be diverted into other cylinders as claimed in that text? </p> | 5,418 | [
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<p>For a time dependent wavefunction, are the instantaneous probability densities meaningful? (The question applies for instances or more generally short lengths of time that are not multiples of the period.)</p>
<p>What experiment could demonstrate the existence of a time dependent probability density?</p>
<p>Can an isolated system be described by a time dependent wavefunction? How would this not violate conservation of energy?</p>
<p>I see the meaning of the time averaged probability density. Is the time dependence just a statistical construct?</p> | 5,419 | [
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<p>First of all, I should note that I'm a programmer and have only an extremely basic understanding of physics; I only know how to explain my question in layman's terms and I apologize if I'm unclear or unnecessarily verbose.</p>
<p>If there's a rigid square object of size 1x1 and mass 1 on a two-dimensional frictionless plane, and while stationery it is struck by a force of strength 1 at exactly halfway along one of its sides from directly perpendicular to said side, like so:</p>
<p><img src="http://i.stack.imgur.com/f8Pp0.png" alt="a picture of a square being struck by a force perpendicular to one of its sides"></p>
<p>then my intuitive understanding is that it will begin traveling at a speed of 1 in the direction of the force.</p>
<p>Similarly, if it is struck exactly on a corner by a force of strength 1 that is exactly perpendicular to the square's diagonal (at a 45* angle to its side), like so:</p>
<p><img src="http://i.stack.imgur.com/bQF8O.png" alt="a picture of a square being struck by a force hitting it on the corner"></p>
<p>then my intuitive understanding is that it will begin spinning (I don't know how fast) but remain stationery.</p>
<p>What I don't know is how to work out what will happen if it is struck at any other point or from any other angle. For example, if struck three-quarters of the way down a side at an angle perpendicular to the side, like so:</p>
<p><img src="http://i.stack.imgur.com/4qvUk.png" alt="a picture of a square being struck by a force partway down one of its sides"></p>
<p>It seems as though it should cause it to begin moving (in some direction, at some speed) and spinning (at some speed), and the less perpendicular to the square's center of gravity the force is, the more it will spin and the less it will move. Is there a formula that, given the magnitude, angle, and impact point of the force, exactly how fast it will spin vs. how fast and in what direction it will move?</p>
<p>More generally, how does one work out the answer to this sort of problem when applied to objects of other shapes/sizes/masses when impacted by other forces? Does it make a difference if the object is already moving or spinning? </p>
<p>(Also, are any of my intuitive understandings actually entirely incorrect?)</p> | 5,420 | [
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<p>I have asked this question before on other forums, but only got the classical answer of the impossibility of the probability interpretation for single particle in QFT. Now, there seems to be also doubt in multi particle interpretation of the Dirac "sea". while in QFT the multi particle seems to be the result of promoting the wavefunction to an operator. And some people claimed it is a multi picture of a single particle. So, is there any clearer explanation?</p> | 5,421 | [
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<p>Is the structural similarity between atoms ( smallest) and universe (biggest) a coincidence? Or there can a reason for this beyond imaginations?</p>
<p>It seems like, if one starts travelling out from atoms... and grows bigger and bigger, one ends in a similar structure somewhere in the universe. Kind of a circular ring. </p>
<p>PS: By structural similarity I mean : single nucleus and electrons revolving around in an atom, is structurally similar to planets revolving around the sun.</p> | 5,422 | [
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<p>I am very puzzled by the quintet of Higgs bosons in the MSSM: two charged, two scalars and a pseudoscalar. I wonder if they could be understood better if they were considered jointly with the three "bosons" that are "eaten" by the Higgs mechanism. For instance, if they were two charged bosons and a pseudoscalar one, then the whole set should be four charged, two pseudoscalars and two scalars, which seems more sensible if you wish, for instance, reorder them into chiral and dirac supermultiplets jointly with the higgsinos.</p>
<p>I have been reminded of this question because it seems that now LHC is trying to guess if the discovered Higgs boson is a pseudoscalar or an scalar, and they are doing this by looking how it couples to ZZ, if it is to transversal or to longitudinal modes.</p> | 5,423 | [
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<p>I read what is <a href="http://en.wikipedia.org/wiki/Computational_science" rel="nofollow">computational science</a> in Wikipedia but the explanation and understanding are not very clear. </p>
<p>So, I could you please give a simple example computational science project and what all basic skills a person should have?</p>
<p>Also, </p>
<ol>
<li>Does computational science involves programming?</li>
<li>How different are computational science and computational materials science?</li>
<li>I am from Electrical and Computer Science (basically programming) background. I was assigned a computational materials science project. So, is it in my scope?</li>
</ol>
<p>Probably, the prof assigned based on what individual subjects I studied (Engineering Math, Engineering Physics, Engineering Chemistry, Probability, Programming).</p> | 5,424 | [
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] |
<p>Do you know why in the quantization of SU(2) Yang Mills Gauge Theory, it is always chosen the Weyl (temporal) gauge to derive the Hamiltonian?</p>
<p>Is it possible to fix another gauge?</p> | 5,425 | [
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<p>What will be the tensor product of two doublets
$$
(x_1,x_2) ~\text{and}~ (y_1,y_2)?
$$
I am very much confused in determining this.</p> | 5,426 | [
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<p>I'm contemplating particle-hole symmetry, and as an example I am looking at either an electron moving along a hypothetical lattice of hydrogen ions, or a hole moving along a hypothetical lattice of helium atoms. </p>
<p>According to some lecture notes I found, the hopping integral I get when I treat this in a tight-binding ansatz is positive for holes and negative for electrons, and now I want to see why this is so. </p>
<p>For electrons, I can understand the result: The atomic wavefunctions are just the 1s hydrogen wavefunctions, and they are positive everywhere, so the matrix element with the kinetic energy operator gives something negative. </p>
<p>Now, for holes I am not sure how I would have to proceed. Can I just say that the relevant Hamiltonian for holes is the negative of the Hamiltonian for electrons because, after all, a hole with energy $E$ would be an electron with energy $-E$ missing?</p>
<p>Of, if that's wrong, how would I come to the conclusion that the hopping integral for electrons is negative and for holes it's positive?</p> | 5,427 | [
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<p>Could you please suggest the software, where I can load my 3D model and see how it behave on various conditions (speed - preferably including supersonic, temperature, pressure)?</p>
<p>Both free & commercial variants are interesting.</p> | 5,428 | [
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<p>A physical quantity can be represented by the following form:</p>
<p>$A = a_1\sigma_1 + a_2\sigma_2 + a_3\sigma_3$ where $\sigma$ matrices are Pauli matrices.
Also suppose that there is $B = b_1\Sigma_1 + b_2\Sigma_2 + b_3\Sigma_3$.</p>
<p>A. I read that $a_1,a_2,a_3$ are direction vectors, and when the sum of A's representing real quantity and B's is zero, as each quantity can only be 1 or -1, probability $AB$ being 1 or -1 depend on the value of $-a_1b_1 - a_2b_2 - a_3b_3$. </p>
<p>The question would be: isn't $a_1,a_2.., b_1,b_2,..$ only direction vectors? If so, how can probability of finding $AB$ being 1 change? I do get this mathematically, but I am unable to picture the situation with $a,b$ being direction vectors.</p>
<p>B. I read that when the sum of A's representing real quantity and B's is zero, determining a value on one direction of $A$ set the value of the whole $A$. Is this true? Can anyone explain this?</p> | 5,429 | [
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<blockquote>
<p><strong>Question:</strong> The maximum range of projectile is $R$ and the maximum height attained by the particle is <em>H</em>. </p>
<p>If the area covered by the particle between its path and horizontal line is $A$, then $A$ =</p>
<ol>
<li><p>$\frac{2}{5}$</p></li>
<li><p>$\frac{2}{3}$</p></li>
<li><p>$\frac{4}{5}$</p></li>
<li><p>$\frac{1}{3}$</p></li>
</ol>
</blockquote>
<p>I know the formula for maximum range $R$ and maximum height $H$</p>
<p>$R=\frac{U^2}{g}$, $U$ is initial veocity and $g$ is acceleration due to gravity </p>
<p>$$H=\frac{U^2 \sin^2\theta}{2g}$$</p>
<p>I can't find the way to realte this formula with the question.</p> | 5,430 | [
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<p>My nephew is 3 and weighs around 30 pounds I am guessing. However, I would like to weigh him at home. I have kitchen scales, one flat one that goes up 1kg and one that looks like this picture that goes up to 5kg. <img src="http://i.stack.imgur.com/u3rsam.jpg" alt="enter image description here"></p>
<p>What is a safe and practical way I can weigh my nephew at home?</p> | 5,431 | [
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<p>The textbook explanation is that, at <a href="http://en.wikipedia.org/wiki/Brewster%27s_angle" rel="nofollow">Brewster's angle</a>, the electric dipoles excited by the incident light can't reradiate to the reflection direction since it's aligned with the dipole moments.</p>
<p>Is there a deeper understanding of the microscopic physics picture? For example, is there an actual calculation of these electric dipoles induced by the near field?</p> | 5,432 | [
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<p>Antimatter and matter particles annihilate. But does <a href="http://en.wikipedia.org/wiki/Dark_energy" rel="nofollow">dark energy</a> annihilate energy?</p>
<p>We consider energy to be photons, and such, correct? So when we say energy, we're actually talking about some bosons, right? </p>
<p>So photons and anti-photons would annihilate, gluons and anti-gluons.</p>
<p>I am not sure if anti-bosons are hypothesized so please forgive. I am amateur to this.</p> | 5,433 | [
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<p>Why does Mother Nature allow bound states in arbitrarily weak attractive potential in 2D but not in 3D?</p>
<p>See, for example, this article: <a href="http://scitation.aip.org/content/aip/journal/jmp/44/2/10.1063/1.1532538" rel="nofollow">http://scitation.aip.org/content/aip/journal/jmp/44/2/10.1063/1.1532538</a></p> | 5,434 | [
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<p>There are lots of models of gravity mediated SUSY breaking with various spectra as well as various general gauge mediation models. Are there any "smoking gun" experimental singnatures that could definitely distinguish between the two scenarios? Would this be possible to do at the LHC or would we need an ILC-type machine to do that?</p> | 5,435 | [
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<p>The phenomenon of high temperature superconductivity has been known for decades, particularly layered cuprate superconductors. We know the precise lattice structure of the materials. We know the band theory of electrons and how electronic orbitals mix. But yet, theoreticians still haven't solved high Tc superconductivity yet. What is the obstacle to solving it? What are we missing?</p> | 5,436 | [
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<p>When computing the first order perturbative corrections to string theory over a curved background, we find the background has to be Ricci-flat if the dilaton is constant and we have no fluxes. Such is the case for Calabi-Yau compactifications. However, to fourth order in perturbation theory, we find nonzero contributions to the beta function. But this can be resolved by perturbative modifications to the background metric which cancels the beta function order by order in perturbation theory.</p>
<p>Does this procedure work for a generic time-varying background which is Ricci-flat to first order in perturbation theory? If not, does that tell us we can't apply first quantized string theory to such backgrounds?</p> | 5,437 | [
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<p>In the strong coupling limit of type IIA and heterotic E8 string theory, we get 11 dimensional M-theory in which we have no strings. Instead, we have M2 branes.</p>
<p>Are there any other backgrounds in string theory which can't be described by first quantized string theory?</p> | 5,438 | [
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] |
<p>What are possible effects of electromagnetic pulse / EMP on superconductor-based devices/equimpent/transportation?</p>
<p>Are they resilient or more sensitive to EMP?</p> | 5,439 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/36131/friction-between-atoms-in-spring">Friction between atoms in spring</a> </p>
</blockquote>
<p>thanks john:when we apply a stress within elastic range of metal/spring,due to flow of atoms the particular void(defect) region getting filled by atoms & get organised crystal structure in that region,when we released that force the atoms filled in void region doesnt return to its previous position right,due to this the spring could not obey the same in 1st&2nd cycles,is my statement true? one more doubt, after few cycles, voids of springs are filled by atoms& now the springs obey different from the spring with void right,if my statemnt true, then in books the oscillation decay of springs in constant rate(1/e) it should be false right..then the oscillation decay should be a variable depends on defects in spring material.... can u give some more papers for my reference?</p> | 193 | [
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<p>I can't find any numbers about table tennis. What accelerations occur during a forehand smash for example?</p>
<p>Thanks in advance & kind regards,
Hans</p> | 5,440 | [
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<p><img src="http://i.stack.imgur.com/Vl3a6.jpg" alt="Picture of gravity"></p>
<p>We assume that the earth planet is a black hole.
When a light beam is fired.
The only way that even light can move is A and B which means this is impossible that light move on other ways C, D, E</p>
<p>Isn't it true?</p> | 5,441 | [
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<p>Let's assume that the aircraft is 1000kg and it is flying in a air density of 1.225kg/m^3 at the speed of sound in air. </p>
<p>Just how much energy does it require per second to maintain flying at this speed.(Please make other necessary assumptions.) </p>
<p>Thank you.</p> | 5,442 | [
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<p>Force-Weight <a href="http://en.wikipedia.org/wiki/Pinewood_derby" rel="nofollow">Pinewood Derby</a> Car.</p>
<p>I'm trying to make a fast derby car. I was wondering if I could make a car that can drop/eject weight once it comes off of the incline. Would that increase speed or would it make it slower?</p> | 5,443 | [
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<p>I understand mathematically how one can obtain the conservation equations in both the conservative
$${\partial\rho\over\partial t}+\nabla\cdot(\rho \textbf{u})=0$$</p>
<p>$${\partial\rho{\textbf{u}}\over\partial t}+\nabla\cdot(\rho \textbf{u})\textbf{u}+\nabla p=0$$</p>
<p>$${\partial E\over\partial t}+\nabla\cdot(\textbf{u}(E+p))=0$$</p>
<p>and non-conservative forms. However, I am still confused, why do we call them conservative and non-conservative forms? can any one explain from a physical and mathematical point of view?</p>
<p>Many off-site threads deal with this question (<a href="http://www.cfd-online.com/Forums/main/75621-conservative-versus-non-conservative-forms.html" rel="nofollow">here</a> and <a href="http://www.cfd-online.com/Forums/main/10994-conservative-non-conservative-form.html" rel="nofollow">here</a>), but none of them provides a good enough answer for me!</p>
<p>If any one can provide some hints, I will be very grateful.</p> | 5,444 | [
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<p>Similar question has been asked but did no get good answers.</p>
<p>We know that black hole can confine light, but can we create an ocean black hole -
which can confine surface water waves or sound waves in water?</p>
<p>Definition:</p>
<ul>
<li>What is a static water flow which can CONFINE water waves?</li>
<li>Is there a configuration confining only surface waves?</li>
<li>Is there a configuration confining volume waves?</li>
</ul>
<p>Description:</p>
<p>Inside a confined region any water density perturbations can not propagate outside.</p>
<p>PS:</p>
<ul>
<li>Overall volume of water in the "tank" can not change so the solution
when the water is removed faster then the waves travel is ruled out.</li>
<li>There possibly can be additional objects presented in the water
"tank".</li>
<li>It can be some unsual liquid or gas, whith additional "new"
properties.</li>
</ul>
<p>Thanks for your answers.</p> | 5,445 | [
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<p>Non-linear waves do not superimpose to each other, but why?
What characteristics give this property?</p> | 5,446 | [
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<p>I am looking at a 2 Nucleon potential of the form
$$V(r)=V_0(r)[a+bI_1\cdot I_2]$$
Where a and b are constants. $I_1,I_2$ are isospins. $V_0(r)$ is of the square well form. My goal is to find an equality for a and b, given that deuteron exists, and that diproton and dineutrons do not. </p>
<p>My approach has been the following:</p>
<p>2 nucleons can either be in an isosinglet or an isotriplet. The Isosinglet has I=0 and is the following:
$$|00\rangle=\frac{1}{\sqrt2}(pn-np),I_1\cdot I_2=-\frac34$$
The isotriplet has I=1 and
$$|11\rangle=pp,I_1\cdot I_2=\frac12$$
$$|10\rangle=\frac{1}{\sqrt2}(pn+np),I_1\cdot I_2=\frac12$$
$$|1-1\rangle=nn,I_1\cdot I_2=\frac12$$
So I get the following equations based on V</p>
<p>$$\text{Isosinglet: }\frac{V(r)}{V_0(r)}=a-\frac34 b$$
$$\text{Isotriplet: }\frac{V(r)}{V_0(r)}=a+\frac12 b$$</p>
<p>Now I am supposed to use the fact that $V_0(r)$ is of the square well form to create inequalities, but I am unsure of where the inequalities come from.</p> | 5,447 | [
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<p>This question is not about phase velocity changed which causes refraction, but about the real time itself being slower by the gravity of any object (from general relativity).</p>
<p>If so, would this mean any light traveling inside a glass would be slower than in the air because it is directly affected by gravity of glass? Does this effect also contribute to refraction? How much this effect cause the light to slow down?</p> | 5,448 | [
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<p>This problem is similar, but also different question from my previous question. They are both unfortunately long.</p>
<p><strong>Problem/Solution #1</strong></p>
<p><img src="http://img215.imageshack.us/img215/6696/problem2f.jpg" alt="">!
<img src="http://img59.imageshack.us/img59/4281/sol2pp.jpg" alt="">!</p>
<p><strong>Quick Concept Check</strong></p>
<p>a) Could someone briefly explain to me why the block on top can accelerate, but the one hanging on the pulley does not?</p>
<p><strong>Problem/Solution #2</strong></p>
<p>Consider the set up below. What is the minimum force required so that the 3kg block remains on the 8kg block? Given that the coefficient of static friction between the blocks is 0.8 and the coefficient of kinetic friction between the 8kg block and the surface is 0.4.</p>
<p><img src="http://img714.imageshack.us/img714/1299/contr.jpg" alt="">!</p>
<p><img src="http://img163.imageshack.us/img163/5941/contrd.jpg" alt="">!</p>
<p>$\sum F_x' = F - (N' + \mu_k n) = 8a$</p>
<p>$\sum F_y' = n = (8g + \mu_ s N)$</p>
<p>$\sum F_x = N' = 3a$</p>
<p>$\sum F_y = \mu_s N = 3g$</p>
<p>Solving the systems of equations above, you should get that $F_{min} = 11g(\mu_k + \frac{1}{\mu_s}) = 177.87N$</p>
<p><strong>Point of the question and why the heck is this so long</strong></p>
<p>Notice how the 3kg block is actually "attached" tot he 8kg block, yet the solution here didn't include it in its free-body diagram and they even included the reaction force from the 3kg on the 8kg.</p>
<p>Compared with the cart problem where the hanging mass is also touching the cart, no reaction force was drawn and they even treated the three mass as a single mass. David explained this to me last night and I thought I got it, but I went to bed and started thinking about it and it became even more confusing!</p>
<p>Could you have solved the first problem with the cart WITHOUT taking all three mass into the cart's free body diagram? Is there another way of applying Newton's Second Law to the cart problem?</p> | 5,449 | [
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<p>So - a little bit of background. Obviously from Einstein's equations it's shown that energy can be converted to matter and vice versa; in essence, energy and matter are different manifestations of the same "stuff". </p>
<p>Now, I've done a bit of reading about the interplay between space and time. Some of what I've read would seem to indicate that just like energy and matter, space and time are different manifestations of the same "stuff", though the majority of what I've read seems to indicate that this isn't the case.</p>
<p>So I got to thinking...what if space and time aren't the same thing, but there's interplay between them? What if one is a function of the other? And so I come to my question:</p>
<p>Could space be a function of time? Or vice versa?</p>
<p>From what I've gathered, our universe is expanding at a faster and faster rate. If space is a (seemingly exponential) function of time, then it makes complete sense that as more and more time passes, the amount of space in existence would increase.</p>
<p>In addition (also from what I gather), nothing can go faster than the speed of light. We know that the closer to the speed of light that something is going, the more time slows down for that something, until the speed of light is reached and time stops for whatever it is. </p>
<p>Since we're outside observers, a light year is the distance <em>we perceive</em> light to travel in one year. But since (for the light) time stops completely, "how far it travels in a year" becomes meaningless to the light itself. Because no time is passing for it, wherever light goes, it effectively goes that distance in a relative time frame of zero seconds.</p>
<p>This phenomenon would also make sense if space is a function of time; if there is no time affecting that light, there would be no space affecting it either. If from the light's perspective time has stopped completely, then from its perspective there would be no distance between it and any destination in the universe; any journey the light made would be instantaneous. Again, that's from the perspective of the light itself, not the perspective of someone who's observing the light.</p>
<p>So does that make any sense? Could space be a function of time?</p>
<p>Note: I am not a physicist. I am a lay-scientist, in the very loosest definition of that term. I ask this question assuming there are glaring errors and inaccuracies, which is why I'm asking it here - so you can all point me in the right direction.</p> | 11 | [
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<p>How is the speed of an object in space measured? Also more importantly how do you measure your own speed in space? On the road we use a speedometer which tells us the speed easily. How is it done in space?</p> | 5,450 | [
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<p>When did astronomers realise that the stars were similar to the Sun? I'm not asking for when this was established, but when also the hypothesis was first proposed. </p> | 5,451 | [
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<ol>
<li><p>We all know that wavefunction collapse when it is observed. Uncertainty principle states that $\sigma_x \sigma_p \geq \frac {\hbar}{2}$. When wavefunction collapse, doesn't $\sigma_x$ become $0$?, as we will know the location of the particle. Or does standard deviation just become smaller?</p></li>
<li><p>After collapse occurs, what happens to the particle? Does the particle resurrect into a wavefunction form?</p></li>
<li><p>What can be an observer that triggers wavefunction collapse? (electron wavefunction does not collapse when meeting with electrons; but some macroscopic objects seem to become observers....)</p></li>
<li><p>What happens to the energy of a particle/wave packet after the collapse?</p></li>
</ol> | 5,452 | [
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<p>If a body is under non-uniform circular motion, will it experience or will there be any impact of centrifugal force on the body upon eliminating the centripetal force?
update-sorry.the title of question was incorrect.</p> | 5,453 | [
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<p>How can I determine the direction of the force acting due to gyroscopic couple on a car's wheels when it is taking a turn to it's left side?</p> | 5,454 | [
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<p>In "String Theory and M-Theory: a modern introduction" by K.Becker, M. Becker and J.H.Schwarz, they say that BPS D-brane is stable as it preserves half of the Supersymmetry. I really want to understand more about this statement and see detail calculations. What is the mechanism of D-brane stability? Is there any derivation for the instability of space-filling D-brane (so that open string tachyon will be eliminated from the theory)? </p>
<p>Thank you.</p> | 5,455 | [
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] |
<p>How does the temperature vary along the length of the rod if its both ends are at different temperature. As an example, consider the problem:</p>
<blockquote>
<p>20 cm long rod has rod at one end 100 ºC and another end at 0 ºC. Find the temperature at the center of the rod when it's in thermal steady state.</p>
</blockquote> | 5,456 | [
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<p>I was looking at rockets and stuff and thought about how they move through a vacuum using newtons 3rd law, and then I started thinking of any other ways you could move through a vacuum without using this and then I thought about the photon. I then thought how does the photon move through a vacuum? So I searched it online and couldn't find an answer. So my question is simply how does a photon move through a vacuum? Is it because its massless? Is it because it is thrown from an electron or whatever like a rock from a slingshot? Or is it something completely different? I'm very curious!</p> | 5,457 | [
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<p>Galileo discovered that the distance fallen is proportional to the square of the time it has been falling.Why is it proportional to the square of the time and not just time?
i.e $d \propto t^2$ why not just $d \propto t$</p>
<p>I know this question involves some common sense which i'am not able to use for some reason!</p> | 5,458 | [
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<p>I have used a new term <a href="https://drive.google.com/file/d/0B5sD2PI0YoRvMmwyeE04emptTzQ/edit?usp=sharing" rel="nofollow">spinning apparatus</a> as I was unable to name it.
I have tied a thread to a stone and was spinning it and I heard a sound something like that of a rotating propellor of a helicopter and then this idea stuck my mind </p>
<p>can i calculate it? if yes then how can any one suggest me something and also if any extra information any one needs regarding that apparatus feel free to comment</p> | 5,459 | [
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<p>We know that a simple application of Gauss's law tells us that the field inside of a uniformly charged spherical shell is zero. Does this hold for all uniformly charged closed surfaces? If so, how could we prove this? Or does it hold only for certain shapes? </p> | 5,460 | [
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<p>I saw this in an art museum:
<img src="http://i.stack.imgur.com/LLO24.jpg" alt="Floating Rock"></p>
<p>How is this possible? The materials used to make this were foam, wood, stone dust, paint, electromagnets, and metal. I would like to know how this was make and how I could make something similar.</p>
<p>Thank You.</p> | 5,461 | [
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] |
<p>In this <a href="http://arxiv.org/abs/1108.3003v1" rel="nofollow">article</a> it is claimed that certain type of string theory called EGBd allows for traversable wormhole solutions that do not require exotic matter.</p>
<p>What is this EGBd model and how it fits in the grand scheme of things of string theory? is this fringe science or is serious? (i know that there might be fringe authors in ArXiv). But my main concern is how general or realistic is this result?</p> | 5,462 | [
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<p>The following blue-cone <a href="http://en.wikipedia.org/wiki/Metric_expansion_of_space#Understanding_the_expansion_of_Universe" rel="nofollow">Wikipedia diagram</a> confuses me.</p>
<p><img src="http://upload.wikimedia.org/wikipedia/commons/3/32/Embedded_LambdaCDM_geometry.png" alt=""></p>
<p>At any point of cosmological time the encircling horizontal lines in the diagram are of finite circumference. That is indicative of a closed model of the universe.</p>
<p>Queries:
1. Why does the author use a closed model of the universe to explain his point?</p>
<p>2.Can we conclude "It is also possible for a distance to exceed the speed of light times the age of the universe, which means that light from one part of space generated near the beginning of the Universe........." if we draw the same diagram on a flat sheet of paper[instead of using the cone we take a flat surface],remembering that the null geodesics are always straight lines in the flat spacetime context? </p> | 5,463 | [
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<p>Some authorities have stated publicly and without explanation that if the theories of Special and General Relativity were not taken into account in the design of the <a href="http://en.wikipedia.org/wiki/Global_Positioning_System#History" rel="nofollow">GPS</a> (by building the satellite clocks to run 38us/day slower than GPS time before launch aka 'the factory offset), the position indicated by an earthbound GPS user device would drift by about 11km/day. I've considered this for various GPS models but can only predict much smaller effects. That multiplying the 38us/day uncorrected difference from GPS time by the speed of light yields 11.6km/day, does not for me seem to relate to GPS receiver function. Please reply with references if possible. I'd be very glad for any pointers.</p> | 5,464 | [
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<p>I was running the washing up water this morning, and started to think about why the cold tap isn't hot, and why the water doesn't get hotter the faster it is flowing (if anything, the cold tap gets colder the faster it flows).</p>
<p>From my understanding</p>
<p>$K.E = \frac{mv^2}{2}$</p>
<p>and temperature is directly proportional to kinetic energy.</p>
<p>I know that the $v$ in the above equation is really the mean speed of the particles and therefore some are moving backwards and some moving forwards, it is the speed that is used. But surely the particles of water in the tap are all moving faster, therefore they should all be hotter. Perhaps the particles in the stream are moving at a much higher mean speed than the water is flowing, so the temperature increase is negligible... Am I correct in thinking this? or otherwise, why doesn't the cold tap get hot the more you turn it on?</p> | 5,465 | [
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