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<p>If two identical masses are somehow "released" into deep space (that is, they're subject to no other gravitation forces but their own, and are initially at rest to each other). What decides whether they collide or orbit each other? I'm imagining for example two 1 kg masses initially at rest, say 10 m apart. What happens next?</p>
| 1,495 |
<p>we vistited yesterday a fun park and saw a ride which was a big centrifuge only in vertical.
this one had a speed meter but it was broken and i also wanted to know how much g-force is on there...</p>
<p>so my first thought was to calculate this with the centrifugal-accerleration. I have $\omega = \frac {0.5*2\pi} 1 [\frac {rad} s]$ and $r= 25[m]$, so the accerleration is $a_z = \omega^2r = \pi^2*25 = ~246$</p>
<p>then i can calculate the g force with $g_{force} = \frac {a_z} g$ which gives me about $24g$ that seems fairly too high! </p>
<p>what am i missing?</p>
| 1,496 |
<p>Not having studied General Relativity, I have sometimes been puzzled by references to the behaviour for "classic" black holes — as they are popularly portrayed — as being true for black holes which are not rotating and which have no charge. I don't understand the role rotation <em>does</em> play, but at least because it has to do with the motion of massive bodies, I can understand why it <em>could</em> play an important role. But I have no such intuition for electrical charge.</p>
<p>How does <em>charge</em> change the behaviour of a black hole, aside from the obvious role of electrostatic force? (It will preferentially attract particles of the opposite charge, obviously.) But it would seem that charge plays a more intriguing role than just this.</p>
<p>The current status of the <a href="http://en.wikipedia.org/wiki/Black_hole#Singularity" rel="nofollow">Wikipedia page on black holes</a> claims that you can theoretically avoid the singularity of a charged black hole. It also describes there that there is a theoretical upper bound on the charge/mass ratio of a black hole: that any would-be black hole exceeding it (which is generally thought to be impossible — see <a href="http://physics.stackexchange.com/q/6650/4976">this related question on trying to force saturation of the charge/mass ratio or black holes</a>) would lack an event horizon (and therefore presumably not be a black hole). Why should that be? Furthermore: from <a href="http://physics.stackexchange.com/q/9516/4976">this other related question on repulsion of pairs of charged black holes</a> (and from Willie Wong's comment, below), ir seems that the size of the event horizon may change depending on how close it is to being extremal! Why would the event horizon of a <em>highly charged</em> black hole be different than the event horizon of a <em>neutral</em> black hole, of similar mass?</p>
<p>Is there a clear reason for such an interplay is there between electrodynamics (aside from local Lorentz invariance) and general relativity that bring these things about?</p>
| 1,497 |
<p>I am reading up on the Schrödinger equation and I quote:</p>
<blockquote>
<p><em>Because the potential is symmetric under $x\to-x$, we expect that there will be solutions of definite parity.</em></p>
</blockquote>
<p>Could someone kindly explain why this is true? And perhaps also what it means physically?</p>
| 1,498 |
<p>when firing a proton (for example) to an atomic nucleus, from a distance $D$, the deflection angle of the proton $\alpha $ to the type of changes atomic nuclei? or always constant?</p>
| 1,499 |
<p>It's actually a teaching conflict at my school. They said that $$\text{Flux}=\frac{q}{\varepsilon_0}.$$ Say for a point charge at the centre of the sphere and let's say we not put water into the sphere, so now $E/ \varepsilon_0=K$. Thus $E= \varepsilon_0 K$.
So flux becomes $q/\varepsilon_0 K$. That means that any change in medium changes the flux.</p>
<p>However, in FIITJEE I was told that the addition of a medium won't change the flux since the number of electric field lines remains constant for any medium. So changing medium won't change the formula, $\text{flux}=q/\varepsilon_0$.</p>
<p>So, does flux actually change with change in medium or not? </p>
<p>$K$ is the dielectric constant.</p>
| 1,500 |
<p>Suppose we have a parallelepiped shaped box full of water on the surface of the sea. Suddenly the box disappears. What is the shape of the waves vs. time caused by the fall of the water contained in the box?</p>
| 1,501 |
<p>One of the most famous experiments in quantum mechanics in the context of wave-particle duality is certainly passing a beam of electrons through two slits, which results in an interference pattern being formed on a screen positioned after them.</p>
<p>Now, <strong>starting from the Schrödinger equation</strong> (which we know is obeyed by electrons), how can we derive the formula describing the interference pattern?</p>
<p>I am pretty sure we already know the answer, i.e. it is the same pattern generated by light going through two slits (so a sine squared modulated by a sinc envelope), but how do we get it <strong><em>from quantum mechanics</em></strong> ?</p>
| 1,502 |
<p>This is a historical question partly, and maybe too broad for this site, but would require some familiarity with modern physics research practice so hopefully appropriate here. </p>
<p>Einstein's later years, after general relativity, were (as I understand it) taken up predominantly by his effort to find a unified theory that explains both gravitation and electromagnetism and their interrelation. </p>
<p>And from what I understand his approach was mainly mathematical, trying variations of functions and so forth, looking for something that fit - and doing his work predominantly on paper. </p>
<p>Had he access to modern computers - programming languages, mathematica, etc. - how might that have changed his progress, and willingness to give up perhaps? And in what ways have computers in general changed / revolutionized theoretical & mathematical physics?</p>
| 1,503 |
<p>In QFT the principle of stationary action states that we choose fields that will make the action stationary but what if the action has many stationary points? What's the significance of these other solutions?</p>
| 1,504 |
<p>Through a bit calculation we can derive that in a cavity, the energy density $$u(f,T)=\overline{E(f)}\times G(f)=\frac{8\pi h}{c^3}\frac{f^3}{e^{h\nu /kT}-1}$$
If we take the integral over all frequency, we get
$$U(T)=\frac{8πh}{c^3}\frac{(kT)^4}{h^3}{\frac{π^4}{15}}=C_{onst}T^4$$
And Stefan-Boltzmann Law claims that for a perfect black-body
$$j^*=\sigma T^4$$
where $j^*$ is the radiant exitance, which is defined as the total energy radiated per unit surface area of a black body across all wavelengths per unit time.</p>
<p>And it just so happens that $\frac{\sigma}{C_{onst}}=\frac{c}{4}$, why is that?</p>
<p>P.S. The professor told me to refer to some thermodynamics book, where a more general case is discussed. But we don't have that book in our library and the professor's now out of town xD.</p>
| 1,505 |
<p>I have known the reason why skate can slide over ice is that water's melting curve in terms of pressure and temperature has a negative slope. If the pressure due to our mass increases sufficiently high, the ice starts to melt.</p>
<p>But someone says, according to latest research, it is not true because the time for which we pressure the ice is too short so the ice can't has enough time to melt.</p>
<p>Which is more reasonable between the two arguments?</p>
| 22 |
<p>The articles I found on radiation in the solar system mostly dealt with solar wind, I wonder about other types. Is there a breakdown that tells me, withhin an order of magnitude, at least what intensity I can expect for a the different spectra - hard gamma through to radio frequencies, and chargede particles - and how this varies depending on my position?</p>
| 1,506 |
<p>I've been reading up on nuclear reactors, and understand explanations of how it works, how water is heated to steam, which turns the turbines, etc.. I understand all of the safety features, and how control rods are used, and what they do with spent fuel.</p>
<p>However, what I can't figure out (after lookin at many websites and videos) is where the reaction actually starts. The fuel rods contain Uranium pellets, and then they're put in the reactor, where the reaction starts and neutrons start hitting each other to create heat? So is this happening all over the reactor, or just in each fuel rod assembly?</p>
<p>Also, you can hold a Uranium pellet in your hand (ideally wearing a glove) and it's not dangerous, so what <em>starts</em> a reaction? A lot of people say the reaction can start by itself, so why do uranium pellets not suddenly heat up and start spreading radiation by themselves? Is it because they haven't been <em>enriched</em>?</p>
<p>What if you dropped a Uranium pellet on the floor?</p>
| 1,507 |
<p>We know that a piece of ferromagnet, such as iron, can be magnetized by putting in a strong magnetic field to get domains parallel to the field grow. </p>
<p>I also remember from pop. culture and MacGyver old tv series that you can magnetize a piece of iron by hitting it hard, with a hammer say, along the same direction.</p>
<p>1-Is this way of magnetizing iron scientific? or is it pseudoscience?</p>
<p>and if it is scientific then:</p>
<p>2-what is the physical principle that will allow iron to get magnetized by hitting? and </p>
<p>3-how about nonferromagnetic materials?</p>
| 1,508 |
<p>We all know the effects of speed on time, and we have a formula for that, but I have a hunch, that time also is relative to pressure, and that by increasing the pressure on matter, in fact time will speed up for that matter. </p>
<p>I am not a physics expert ( I have a Masters Degree in Computer Engineering, and have hence taken several physics, math and chemistry classes ) so don't slaughter me, I would appreciate a talkative tone. </p>
<p>So I will say some "ideas" in my head that might be stupid, or assumptions from my understanding of how things are that are in fact wrong from an expert view, but please try to understand my <strong>intention</strong> or follow my idea of what I am thinking instead of focusing on details.</p>
<p>So, my thinking is that once something starts travelling near the speed of light, or the speed of light, it will start to dissolve, before turning into energy and becoming the lightest of all while dissolving = light, and hence is why it can travel at the speed of light. So if something is to travel at the speed of light, it actually have to be dissolved into energy.</p>
<p>The idea I have with pressure, is that if matter, in a pressure chamber, where pressure is turned up, the matter will eventually turn into pure energy as well = light. </p>
<p>I also have this thought, that once pressure is applied to matter, the atoms starts to vibrate, move faster, and a reaction that would normally take hundreds of years, can be achieved with quicker results in a pressure chamber because time for all that materia increases, not because of the pressure, but because time is happening faster, which supports my idea of time actually speeding up for those particles. </p>
<p>What happens with used reactor fuel in a pressure chamber today? How much can we speed up the halftime?</p>
<p>It appears to me that if this was true, it will be the contradiction to speed. A twin X travelling near the speed of light, will come back to visit an older twin Y on earth. </p>
<p>However, with pressure, it might just be the opposite, that twin X in the pressure chamber will in fact be older than twin Y outside.</p>
<p>Surely turning up pressure on a twin might not be so healthy, but neither is acceleration from 0 to the speed of light in 1s. So pressure is probably not a healthy way to speed up time for matter, it will probably destroy certain things in it. </p>
<p>Am I on something here? No?</p>
| 1,509 |
<p>I read about Goodwin's "proof" that $\pi = 3.20$, it's BS and I know that. What I am wondering is whether his technique may have stumbled on something ( a warped space) years before Einstein. So I guess my question is this: </p>
<p>Is it possible that somewhere in the universe (say the vicinity of a neutron star) where (due to the warped space) the ratio of the circumference to the radius is measured as something other than 3.14...? </p>
<p>Following from that, is it possible that we only measure $\pi$ as 3.14... because of the way <em>our</em> local space time is curved by the earth?</p>
| 1,510 |
<p>How can I recognize clearly when I deal with capacitors in parallel or capacitors in series? Can follow a "rule" or a intuitive method?
I have to do difficult exercises regarding system of capacitors so I must understand when I have capacitors in parallel or in series. Can you explain me in a simple way?</p>
| 1,511 |
<p>I have been asked this question by a student, but I was able and in the same time incapable to give a good answer for this without equations, so do you have ideas how one can explain this in a simple way? </p>
<p>(Answers like we can take time as an imaginary, or our space is actually pseudo-Euclidean will be hard to grasp for new students.)</p>
<p>Note that the problem is <em>not</em> in visualizing the 4th dimension, that an easy thing to explain. The problem is more related to why we are in 3D that moving along 1D time dimension? In Differential geometry this interpreted by fiber bundles, but how to explain it to usual student.</p>
| 1,512 |
<p>I'm thinking about trying to do a numerical simulation of some very simple QM problems.</p>
<p>How much space do I need? To simulate the Hilbert space?</p>
<p>I'd like to eventually simulate the absorption or emission of a photon by a hydrogen atom. So at least three particles (two fermions, one boson). Let's generalize that to three particles with arbitrary spin, so I can look at three photons or three electrons if I want to.</p>
<p>In order to do a numerical simulation I need to replace the continuous spacetime with a rectangular grid or lattice. I'd like to eventually get more precision, but let's start with just ten cells per dimension to begin with. So including time, I need ten thousand cells in a four dimensional lattice. `</p>
<p>How many cells do I need to simulate the Hilbert space? and what goes in each cell? </p>
<p>If I put restrictions on the shape of the wavefunction, does that help?</p>
| 1,513 |
<p>I wanted to know why there is a hole in the ball (basketball, volleyball, handball) to fill the ball with air. Why can't the ball come with filled in air and fully sealed so that there is no loss of air?</p>
| 1,514 |
<p>I'm wondering if there is a textbook that describes the handiwork of a particle physics analysis. There are a bunch of books about theory, about the experimental aspects like detectors, and about statistical methods, but I haven't seen one that focused on the actual work of an analyzer.</p>
<p>I mean stuff like:</p>
<ul>
<li>How to conduct a search vs. a measurement</li>
<li>What backgrounds to consider for a final state, and how to model them</li>
<li>What distributions to look at -- pT of various objects or MET are obvious, but there are things like transverse masses, $\cos \theta^*$, aplanarity, the Florida variable (seriously), or ptBalance, that you first have to know about</li>
<li>How to choose signal regions, sidebands</li>
<li>How to determine systematic errors concretely</li>
<li>How to perform a cutflow</li>
<li>How to do tag-and-probe</li>
<li>How to perform a multivariate analysis, and how to choose btw. techniques</li>
<li>How to set limits, and how to perform combinations</li>
</ul>
<p>Most of this stuff is covered in various books, but mostly from a different perspective. For example, its nice to know how to solve an integral with Monte Carlo methods, and what the factorization theorem does. But for someone working on an analysis its more useful to know what the main differences between MC generators are, and how to deal with negative event weights in various situations. Similarly, there are a couple of textbooks about statistics for high energy physics, but those I've found tend to focus on derivations, instead of practical issues of the analysis.</p>
<p>Does anyone know of a book that fits my description?</p>
<p><em>(Note I don't believe this fits very well under the current <a href="http://meta.physics.stackexchange.com/questions/4697/are-resource-recommendations-allowed">book policy</a>. Resource recommendation questions tend to be fairly broad, and thus the answers have to be very descriptive. In this case, the question is already descriptive, so a brief answer would also be OK, even a negative answer (a la "I've been a expert for 20 years and can say for certain that such a book doesn't exist").)</em></p>
| 1,515 |
<p>I was studying a <a href="http://en.wikipedia.org/wiki/GRE_Physics_Test" rel="nofollow">GRE Physics Test</a> problem where optical light with a wavelength of 500 nm travels through a gas with refractive index $n$.</p>
<p>If we look at the equations for wave motion and index of refraction</p>
<p>$$c=\lambda_0\nu\quad\text{(in vacuum)}$$</p>
<p>$$v = \lambda\nu\quad\text{(in medium)}$$</p>
<p>$$n = c/v$$</p>
<p>we see that, if the frequency is constant, the <strong><em>wavelength decreases in the medium compared to vacuum</em></strong>. Is this a consistent property at all frequencies and for all mediums with refractive index real and greater than 1?</p>
<p>Are there dielectrics which change the frequency (still for <code>n</code> > 1), and is there an example of that?</p>
| 1,516 |
<p>One can expand any periodic function in sines and cosines. When calculating the coefficients $a_0$, $a_n$, and $b_n$ one find that $a_1>a_2>...>a_n>...$, similarly for $b_n$. </p>
<p>Is there an intuitive reason to understand this, I mean why would one expect this to happen? It looks miraculous and mysterious to me that the coefficients came out "ordered" in a way that made the convergence manifest.</p>
| 1,517 |
<p>Here is the problem:</p>
<p><img src="http://i.stack.imgur.com/iojG5.jpg" alt="Here is the problem"></p>
<p>In the above figure I want help on finding the potential difference between X and Y.
It is getting quite confusing due to the battery in the middle. I found the current in both the loops using Kirchhoff's Voltage law but then I'm confused on the proper method to find the potential drop between the two loops.</p>
| 1,518 |
<p>I have often seen diagrams, like <a href="http://en.wikipedia.org/wiki/Lens_%28optics%29#Imaging_properties">this one</a> on Wikipedia for a thin convex lens that show three lines from a point on the object converging at the image. Do all the other lines from that point on the object that pass through the lens converge at the same point on the image?</p>
<p>*<em>Updated question: *</em> to say, "from that point on the object"</p>
| 1,519 |
<p>I was at a lecture yesterday and there was a demo of a van de graff generator. He held the smaller metal globe which is attached by a wire, about 4cm from the main globe. This created a spark between the two globes.
At the same time the spark happened the speakers in the hall would click loudly, the projector (on the other side of the room) would turn yellow and the text moved down, then flashed black and back to normal. And the plasma globe that was next to the van de graff generator which was switched off (but on at the wall) would briefly turn on. </p>
<p>Is it possible for a spark to do that? Or is there something else happening at the same time? </p>
| 1,520 |
<p>As far as I've read online, there isn't a good explanation for the <a href="http://en.wikipedia.org/wiki/Born_rule" rel="nofollow">Born Rule</a>. Is this the case? Why does taking the square of the wave function give you the Probability? Naturally it removes negatives and imaginary numbers, but why is it the square, not the fourth or some higher power?</p>
| 23 |
<p>While reading a paper I ran into this particular way of writing a $\cal{N}=3$ fields (in a theory with $N_f$ hypermultiplets) that I couldn't relate to anything I had seen before in the text-books (typically Weinberg's) The claim is that $q^{Aa}$ and $\psi_{\alpha}^{Aa}$ are scalar and fermions such that $a,b$ are $SU(R)_R$ indices, $A,B$ are denoting them to transform in the fundamental representation of $USp(2N_f)$ (why?) and $\alpha, \beta$ are $SO(2,1)$ spinor indices (theory is in $2+1$) </p>
<p>Apparently these fields satisfy some reality conditions given by, the following equations,</p>
<p>$(q^\dagger)_{Aa} = \omega_{AB}\epsilon_{ab}q^{Bb}$</p>
<p>and</p>
<p>$\bar{\psi} ^\alpha _{Aa} = \omega_{AB} \epsilon_{ab} \epsilon ^{\alpha \beta} \psi _{\beta} ^{Bb}$</p>
<p>(where $\omega$ is some symplectic form, which I have no clue about) </p>
<p>I find the above equations very unfamiliar. For one thing why do the scalar and the fermion have $R$ charge indices? (I am only familiar with the supercharges having a R-symmetry when the central charges are absent) Also I don't understand the $USp(2N_f)$ index. </p>
<p>Apparently this can be related to usual $\cal{N}=2$ fields $(Q,\tilde{Q})$ as,</p>
<p>$q^{A1} = (Q,\tilde{Q})$</p>
<p>and</p>
<p>$q^{A2} = (-\bar{\tilde{Q}}, \bar{Q})$</p>
<p>I am completely unfamiliar with such a relationship or this thinking of $\cal{N}=2$ fields as being thought of as a pair of $Qs$. </p>
<p>Once I understand the meaning of the above I will post another about its curious way of writing the supersymmetry transformation and the lagrangian with this field content. </p>
| 1,521 |
<p>A thin spherical shell made of plastic carries a uniformly distributed negative charge of -Q coulombs. Two large thin disks made of glass carry uniformly distributed positive and negative charges S coulombs and -S coulombs. The radius of the plastic spherical shell is R1, and the radius of the glass disks is R2. The distance from the center of the spherical shell to the positive disk is d.</p>
<p>I want to know how to find two things:</p>
<ul>
<li><p>The potential difference V1-V2. Point 1 is at the center of the plastic sphere, and point 2 is just outside the sphere.</p></li>
<li><p>The potential difference V2-V3. Point 2 is just below the sphere, and point 3 is right beside the positive glass disk.</p></li>
</ul>
| 1,522 |
<p>Can one measure the Higgs field? Or is the higgs field not measurable?</p>
<p>I know that the higgs boson is a indication for the presence of the higgs field. But it is the only way of the presence of the higgs field?</p>
<p>When the higgs field is not measurable, what is the reason?</p>
| 1,523 |
<p>Really short question, but I cannot find anything on the internet.</p>
<p>What is meant <em>proton polarisation</em>?</p>
<p>Is it to do with the spin of the proton?
I guess the spin of the proton is obtained from the vector addition of the 3 quarks' individual spins, so it can't be 0...
Can we have <em>unpolarised</em> protons then?</p>
<p>Thanks!</p>
| 1,524 |
<p>Approaching the speed of sound in an aircraft is relatively difficult, because the closer you get to Mach 1, the denser the pressure is around you (sound accumulates causing vibrations).</p>
<p>Is there a similar effect as you approach the speed of light? Does the Doppler Effect apply for light as it does with sound? Will light accumulate around your aircraft causing heat? </p>
<p>Speaking strictly hypothetical.</p>
| 1,525 |
<p>(I apologize if this question is too theoretical for this site.)</p>
<p>This is related to the answer <a href="http://physics.stackexchange.com/a/11124">here</a>, although I came up with it independently of that. $\:$ Suppose we
<br>
have a unit mass planet at each integer point in 1-d space. $\:$ As described in that answer, the sum
<br>of the forces acting on any particular planet is absolutely convergent. $\;\;$ Suppose we move planet_0
<br>
to point $\epsilon$, where $\: 0< \epsilon< \frac12 \:$. $\;\;$ For similar reasons, those sums will still be absolutely convergent.
<br>
Now we let Newtonian gravity apply. $\:$ What will happen?</p>
<p><br><br></p>
<p>If it's unclear what an answer might look like, you could consider the following more specific questions:
<br><br><br>
planet_0 will start out moving right, and all of the other planets will start out moving to the left.
<br>
Will there be a positive amount of time before any of them turn around?
<br>
(As opposed to, for example, each planet_n for $\: n\neq 0 \:$ turning around at time 1/|n|.)</p>
<p>Will there be a positive amount of time before any collisions occur?</p>
<p>"Obviously" (at least, I hope I'm right), planet_0 will collide with planet_1. $\:$ Will that be the first collision?</p>
<p>How long will it be before there are any collisions? $\:\:$ (perhaps just an approximation for small $\:\epsilon\:$)
<br><br></p>
| 1,526 |
<p>We know that the light gets refracted when it enter a medium low/high refractive index. </p>
<p>But why light is not refracted when it comes out from the vertex of a prism.</p>
| 1,527 |
<p>Consider the quantum system $\mathcal{B}(\mathbb{C}^d\otimes\mathbb{C}^d)$ and $|\psi\rangle=\frac{1}{\sqrt{d}}\sum_{i=0}^{d-1}|i,i\rangle$ be the (standard) maximally entangled state. Consider the state </p>
<p>$\rho_\lambda=\lambda \frac{\mathbb{I}_{d^2}}{d^2}+(1-\lambda)|\psi\rangle\langle\psi|.$</p>
<p>Now for some values of $\lambda$ this state is entangled (example $\lambda=0$ it is $|\psi\rangle\langle\psi|$) and hence its entanglement can be detected by partial transpose operation. </p>
<p>Can $\rho(\lambda)$ be an entangled state which is positive under partial transpose (known in literature as PPT entangled state) for some values $\lambda$? My intuition tells me that this is the case. However, I was told (without reference) that this is not the case and for the values of $\lambda$ we get only separable states or not PPT entangled states. I could not find the corresponding paper. May be I am not giving the proper string for searching. Advanced thanks for any suggestion, reference or comment.</p>
| 1,528 |
<p>I'm currently learning about symmetry between particles. For a simple case of two non-interacting particles at $x_1$ and $x_2$, we know that the wavefunction can be written as $\psi_{n_1, n_2} = \phi_{n_1}(x_1) \phi_{n_2}(x_2)$</p>
<p>Let's consider two cases in ground state and first excited state.</p>
<p>(a) Two particles are not identical, and have spin zero</p>
<p>(b) Two identical particles, each with spin zero</p>
<p>We know that the energy is given by $E_n = (n_1 + n_2 + 1)\hbar \omega$.</p>
<p><strong>For case (a)</strong></p>
<p>Since they are not identical, the wavefunction at ground state would be $\phi_1(x_1) \phi_1 (x_2)$ right? Then the degeneracy would be 0 right? Since $n_1 = n_2 = 1$.</p>
<p>For the first excited state, the wavefunction would be $\phi_2(x_1)\phi_1(x_2)$, assuming $E_2(x_1) < E_2(x_2)$, meaning we just take whatever is lower. The degeneracy would be 0, since they are distinguishable?</p>
<p><strong>For case (b)</strong></p>
<p>Now they are identical, ground state wavefunction would still be $\phi_1(x_1)\phi_1(x_2)$ right? Degeneracy of ground state would be 0, since $n_1=n_2=1$?</p>
<p>But for the first excited state, the degeneracy would be 2, since either $n_1=2$ and $n_2=1$ or $n_1=1$ and $n_2=2$? Spin 0 particles are bosons, so the wavefunction must be symmetric right? So I'm thinking $\psi = \frac{1}{2} \left[ \phi_2(x_1)\phi_1(x_2) + \phi_1(x_1)\phi_2(x_2)\right]$</p>
<p>The concept of symmetry and exchange symmetry is still new to me, I'd appreciate any response!</p>
| 1,529 |
<p>The force for revolution of earth is provided by the gravitational force of attraction between earth and the sun. What provides the force(torque) for the rotation of earth? </p>
| 1,530 |
<p>What kind of significant impacts have originated from $E=mc^2$.</p>
<p>Generally, it is regarded as the most famous equation of all time. Except for nuclear energy (fission and fusion) I do not know any other way in which this equation has made an impact on the world. </p>
<p>Can somebody list some developments and impacts based on this equation?</p>
| 1,531 |
<p>The process of exchange of energy between a photon and an electron only occur after a specific energy called work-function of the material. Thus, the energy transferred is quantised due to the fact that the electron can reside only in quantised orbits. </p>
<p>But, why doesn't the process happen in steps? I mean the electron getting excited to a higher orbit and before the electron gets de-excited another photon gives it energy to escape from the metal. Is it theoretically possible?</p>
| 1,532 |
<p>Why is electron presented in books, pictures as a sphere, when in fact it's not?</p>
| 1,533 |
<p>Is it possible to know whether a lightning bolt travel from the ground to the sky or from the sky to the ground? </p>
<p>Alternatively, it could be both sides approaching</p>
| 1,534 |
<p>I'm having trouble understanding what a problem I have is seeking.</p>
<p>To simplify the problem:</p>
<blockquote>
<p>A particle reaches a speed of 1.6 m/s in a 5.0 micrometer launch. The speed is reduced to zero in 1.0 mm by the air. Assume constant acceleration and find the acceleration in terms of g during a) the launch and b) the speed reduction. </p>
</blockquote>
<p>The basic strategy to find acceleration I am using is to calculate two velocity equations: one between (0 m/s, 0 m) and (1.6 m/s, 5.0 micrometers); the second between (1.6 m/s, 5.0 micrometers) and (0 m/s, 1.0 mm). Then I will derive the acceleration value for each. Because acceleration is constant I can expect a linear velocity equation. </p>
<p>What is confusing me is that we are to assume constant acceleration. Thus the acceleration equation will merely be some real number. So, what exactly is expected if it is to be in terms of g? Is my strategy to find acceleration incorrect?</p>
| 1,535 |
<p>How does the nonlinear absorption coefficient depend on the band gap?
How can that coefficient be calculated theoretically? (Preferably with an example)</p>
| 1,536 |
<p>The latent heat of vaporization of water is what we normally use to calculate the heat transfer that occurs at 373 K when liquid water transits to vapor phase. But there are curves for latent heat of vaporization at different temperatures. What is meant by latent heat of vaporization at a temperature different from its boiling point?</p>
| 1,537 |
<p>If we consider a classical field theory for a massless particle of integer spin $s$, in a curved space-time, one finds that it is "naturally" conformal in a space-time of dimension $2+2s$</p>
<p>For instance, the free massless scalar field theory is conformal in $2$ dimensions, the electromagnetic field theory is conformal in $4$ dimensions, etc...</p>
<p>But does it work for half-integer spin, for instance is a spin $\frac{1}{2}$ field theory conformal in a $3$ dimensional space-time , and is a spin $\frac{3}{2}$ field theory conformal in a $5$ dimensional space-time ?</p>
| 1,538 |
<p>I have the cross-sections as a function of $\sqrt{s}$ for a process with a $u$-quark and $u$-antiquark in the initial state (eg.: $u \bar{u} \to e^- e^+$). I have a standard parton distribution function table (say, CTEQ). With these, how do I find the corresponding cross-sections for a process with protons in the initial state (e.g. $p p \to e^- e^+$ as at the LHC)?</p>
<p>Specifically, should I use some sort of convolution? How?</p>
| 1,539 |
<p>It is said that the universe is expanding and the galaxies are moving apart. I understand that the space between every two galaxies is increasing. Doesn't this seem to imply that the galaxies will have relative motion and so have a moving velocity. According to relativity and the modern belief in physics, it is said that everything depends on relative motion and nothing else (I am talking about the concepts such as Time Dilation etc.). So in brief I would like to ask that why is it said that galaxies do not move even though the distance between them is increasing.</p>
| 1,540 |
<p>To derive Bose-Einstein and Fermi-Dirac distribution, we need to apply grand canonical ensemble:$Z(z,V,T)=\displaystyle\sum_{N=0}^{\infty}[z^N\sideset{}{'}\sum\limits_{\{n_j\}}e^{-\beta\sum\limits_{j}n_j\epsilon_j}]$. There is a constraint $\sideset{}{'}\sum\limits_{\{n_j\}}$ for quantum particles(bosons and fermions) in grand canonical ensemble:$\sum\limits_{j}n_j=N$, but why is there no such a constraint for classical particels?</p>
| 1,541 |
<p>The figure shows an LR circuit with a switch and a 240-volt battery. At the instant the switch is closed the current in the circuit and the potential difference between points a and b, Vab, are</p>
<p><img src="http://i.stack.imgur.com/Xs9ak.png" alt="enter image description here"></p>
<p>Choices : </p>
<pre><code>a. 0 A, 0 V
b. 0 A, -240 V
c. 0 A, +240 V
d. 0.024 A, 0 V
e. 0.024 A, +240 V
</code></pre>
<p>Answer : c. 0 A, +240 V</p>
<hr>
<p><strong>My Questions</strong></p>
<ul>
<li><p>When the battery discharging, the voltage will drop continuously, the voltage across a and b at the start instant should be equal to the original voltage of the battery 240V. However, how can we determine whether Vab is +240V or -240V?</p></li>
<li><p>Moreover, if the potential different at the start instant is 240V, why should the current equals 0A?</p></li>
</ul>
<hr>
<p>Thank you for your help.</p>
| 1,542 |
<p>The spatially flat FRW metric in cartesian co-ordinates is given by:
$$ds^2 = -dt^2 + a^2(t)(dx^2 + dy^2 + dz^2)$$
As I understand it there are Killing vectors in the $x$, $y$, $z$ directions implying that momentum is conserved but there is no Killing vector in the $t$-direction which implies that energy is not conserved. I don't know much about Killing vectors. Is this correct?</p>
<p>If I transform the time co-ordinate $t$ to conformal time $\tau$ using the relationship:
$$d\tau = \frac{dt}{a(t)}$$
the metric now becomes:
$$ds^2 = a^2(\tau)(-d\tau^2 + dx^2 + dy^2 + dz^2)$$
Does this metric now have a Killing vector in the $\tau$-direction as well as in the $x$, $y$ and $z$ directions?</p>
| 1,543 |
<p>The Lagrangian of the Yang-Mills fields is given by
$$
\mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu}
D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+
\bar{c}^a(\partial\cdot D^{ab})c^b
$$
where the metric is $(-,+,+,+)$, and the conventions are the following:
$$
[D_{\mu},D_{\nu}]=-igF_{\mu\nu},\quad
D_{\mu}=\partial_{\mu}-igA^a_{\mu}t^a, \quad
D^{ab}_{\mu}=\delta^{ab}\partial_{\mu}-gf^{abc}A^c_{\mu}
$$</p>
<p>Let $\epsilon$ be an infinitesimal anticummuting parameter, and consider the BRST transformation:
$$
\delta\psi=ig\epsilon c^at^a\psi,\quad
\delta A^a_{\mu}=\epsilon D^{ab}_{\mu}c^b,\quad
\delta c^a=-\frac{1}{2}g\epsilon f^{abc}c^bc^c,\quad
\delta\bar{c}^a=\frac{1}{\xi}\epsilon\partial^{\mu}A^a_{\mu}
$$</p>
<p>I have calculated the corresponding Noether current as
$$
j_{BRST}^{\mu}=-g\bar{\psi}\gamma^{\mu}c^at^a\psi-F^{a\mu\nu}D^{ab}_{\nu}c^b-
\frac{1}{\xi}(\partial\cdot A^a)D^{ab\mu}c^b+
\frac{1}{2}gf^{abc}(\partial^{\mu}\bar{c}^a)c^bc^c
$$</p>
<p>I am not sure whether the result is correct or not, so I would like to check that $\partial_{\mu}j^{\mu}_{BRST}=0$. Even though I have used the equation of motion
$$
\partial_{\mu}F^{a\mu\nu}=-g\bar{\psi}\gamma^{\nu}t^a\psi-
gf^{abc}A^b_{\mu}F^{c\mu\nu}-\frac{1}{\xi}\partial^{\nu}
(\partial\cdot A^a)-gf^{abc}(\partial^{\nu}\bar{c}^b)c^c
$$
$$
(i\gamma^{\mu}D_{\mu}-m)\psi=0,\quad \partial^{\mu}D^{ab}_{\mu}c^b=0
$$
and spent about four hours, I still cannot get it right. Could someone help me check this? Thanks a lot.</p>
| 1,544 |
<p>Any finite & non empty set of masses has a computable center of gravity:
$\vec{OG} = \frac{\sum_i m_i \vec{OM}_i}{\sum_i m_i}$ .</p>
<p>Does the contrapositive permits to conclude that a mass system with
physical evidence that it doesn't have a gravity center is an infinite
set of mass (i.e. of cardinal larger than $\aleph_0$) ?</p>
<p>On the other hand,
an infinite set of masses may have a computable center of gravity.
Ex. : within a 2D infinite plan, an infinite set of equal masses linearly distributed along the x and y axis will have a gravity center at its origin O.
Unfortunately, this example doesn't have a center of gravity since the integral of masses in this particular topology doesn't converge. </p>
| 1,545 |
<p>Why do the propellers on helicopter appear to be so slow when the propellers is going at full speed? Can you please explain this particular optical illusion to me? </p>
| 1,546 |
<p>$u^{\mu}$ - 4-velocity</p>
<p>$b^{\mu}$ - 4-vector of magnetic field</p>
<p>$
u_{\mu}u^{\mu}=-1, \qquad u_{\mu}b^{\mu}=0
$</p>
<p>$$
u_{\beta}u^{\alpha}\nabla_{\alpha}b^{\beta}-u_{\beta}b^{\alpha}\nabla_{\alpha}u^{\beta}+\nabla_{\alpha}b^{\alpha}=0
$$
I don't understand why this equation gives this
$$
u^{\alpha}u^{\beta}\nabla_{\alpha}b^{\beta}+\nabla_{\alpha}b^{\alpha}=0
$$</p>
<p>Help me please!</p>
| 1,547 |
<p>OK, so my textbook says that in time dilation and length contraction, the proper time and the proper length is "That which is in the frame of reference of the observer at rest relative to the event". </p>
<p>This means that the proper time/length is that which is observed by the observer moving close to the speed of light, and the dilated time and contracted length is that which is observed by an observer moving relative to the event, i.e. is watching something move close to the speed of light. Am I correct so far?</p>
<p>So, for example, if we have a beam of protons moving with a velocity of 0.99c and a stationary electron watching them, the proper time/length is that which the protons observe whereas the dilated time/contracted length is that which the electrons would see. </p>
<p>Assuming I am correct so far (which I very well may not be, please tell me if I'm wrong), I have just been confused by an exam question. Here it is:</p>
<blockquote>
<p>In an experiment, a beam of protons moving along a straight line at a
constant speed of $1.8$x$10^8$$ms^{-1}$ took 95ns to travel between
two detectors at a fixed distance $d_0$ apart. Calculate the distance
$d_0$ between the two detectors in the frame of reference of the
detectors.</p>
</blockquote>
<p>Well, according to my understanding above, this would be the contracted distance, since the observer (detectors) are in motion relative to the event. However, they calculate the distance using $d=vt$, which would mean it's the proper distance.</p>
<p>Someone please explain. </p>
| 1,548 |
<p>I would like to know how one could show and prove that a given motion is simple harmonic motion.</p>
<p>Once given an answer, I'll apply that technique to an example I am trying to figure out. </p>
<p>Thank you in advance!</p>
<p>I believe a motion can be proved simple harmonic, if the relation between its is as such:
$$
a_x = - \omega^2\cdot x
$$</p>
<p>And as such the period time is:
$$
T =\frac{2\pi}{\omega}
$$</p>
<p>Question-so-far: How do you prove such for a given force $F = \frac{G\cdot m_e \cdot M}{R_E} \cdot r$ ? Or any force that has non-trivial constants?</p>
| 1,549 |
<p>David Albert is a philosopher of Science at Columbia. His book "Time and Chance" includes this example (p 36). </p>
<p>A gas is confined on one side of a box with a removable wall. "Draw the wall out, <em>slowly</em>, and <em>perpendicular</em> to its surface, like a piston. Now it happens to be the case, it happens to be a consequence of the Newtonian laws of motion, that a billiard ball which bounces off a receding wall will move more slowly <em>after</em> the collision than <em>before</em> it. (Footnote. Proof: consider the fame of reference in which the wall is at rest.) And so gas particles that bounce off the wall as it it's being drawn out will have their kinetic energy somewhat <em>depleted</em>."</p>
<p>Why is that? We are assuming that an externally applied force is pulling the wall out. It's not the gas that is pushing the wall out. So why is energy lost. Why doesn't that violate conservation of energy.</p>
<p>Another way to look at it is to assume a series of walls very close to each other. Remove them one by one parallel to the surface. There will be no change in the total kinetic energy of the gas. Why is this different?</p>
| 1,550 |
<p>I've been told to revise the derivation that proves $\frac{\mathrm{d}P}{\mathrm{d}r} =\frac{GM(r)p(r)}{r^2}$ where brackets indicate a function of, P is pressure and p is density. Rather helpfully he hasn't given us it to revise, so if anyone knows it I'd be really grateful. Thanks. </p>
| 1,551 |
<p>With all the recent discoveries of supermassive black holes being at the center of nearly every galaxy, and the proposed "at least one planet" around (probably) every star.</p>
<p>Does this affect the estimated total mass of our universe?</p>
<p>Is Dark Matter necessary when planets and black holes are included in the calculation?</p>
| 1,552 |
<p>An object of mass m is slowly lowered into a black hole of mass 1000 m. Is the amount of braking energy larger than $0.6 mc^2$? </p>
<p>Now what if, after lowering the mass close to the event horizon, we wait the black hole to shrink to mass 100 m, by emitting Hawking radiation, and then we lower the mass some more? Is the braking energy of the second lowering process larger than $0.5 mc^2$? </p>
<p>I wonder can we extract more than $E=mc^2$ energy from mass m?</p>
<p>(In this thought experiment we use a wire and a winch, or anything that works)</p>
| 1,553 |
<p>Well, that's easy: the sand is wet, and my shoes are wet, and hydrogen bonding adheres the wet sand to my wet feet and to my shoes.</p>
<p>But then I walk home, and my shoes dry, and the sand on them dries, and some of the sand falls off. But some does not. It's really stuck: even several days later I can turn the shoe upside-down and it won't fall off. What holds it on?</p>
<p>Sand sticks to my feet after my feed dry and the sand dries. Is this the same?</p>
| 1,554 |
<p>Can anyone give an example of when infinite-dimensional <a href="http://en.wikipedia.org/wiki/Hilbert_space" rel="nofollow">Hilbert spaces</a> are required to describe a physical system? The standard answer to this question is yes, and I'm sure some of you will be quick to point out several clear examples:</p>
<p>Ex. 1: Photon number states $\left\{ |0\rangle,|1\rangle,...,|n\rangle \right\}$</p>
<p>Ex. 2: Harmonic oscillator number states (same as above).</p>
<p>Ex. 3: Continuous-variable basis of a single free particle $\left\{ |x\rangle \right\} \forall x \in \mathbb{R}$</p>
<p>From the infinite number of basis vectors in these examples, it is generally concluded that the dimension of the Hilbert space is also infinite.</p>
<p>However, it is clear that a photon number state such as $|\psi\rangle=|100\rangle$ is unphysical (to be clear, this is the <a href="http://en.wikipedia.org/wiki/Fock_state" rel="nofollow">Fock number state</a> with $n=100$, not a tripartite state with one photon in one channel). If you dispute this, I would suggest you try preparing such a state in a single-mode fiber in an optics lab. For this reason, we can apply a (somewhat arbitrary) cutoff value of $n$ and recover a finite-dimensional Hilbert space.</p>
<p>Similarly, the <a href="http://en.wikipedia.org/wiki/Cardinality" rel="nofollow">cardinality</a> of the basis set for a free particle is actually $\mathbb{N}$, not $\mathbb{R}$ (due to the properties of the function space), and although this set of orthogonal functions is infinite, we can also apply a similar cutoff for any reasonably behaved wavefunction.</p>
<p>Can anyone give an example of a system described by an infinite-dimensional vector space for which such a cutoff cannot be applied?</p>
| 1,555 |
<p>Let's consider an electron-positron pair with total spin equal to zero. When it annihilates it can not emit only one photon because it would have zero momentum and nonzero energy. The pair emits two photons with opposite momenta but on the momentum-energy plain it looks like the particle goes through a forbidden state (red path on the picture below).</p>
<p>The first question is: How is it possible? I suppose this is because of the energy-time uncertainty. The annihilation process is instant (at least looks like on Feynman diagram) and the energy of the intermediate state is not determined. Is it correct?</p>
<p>If we can go through any forbidden state, why doesn't the annihilation go the blue path? This is the second question.</p>
<p>And the third question: Why do electron-hole pairs in semiconductors always emit photons with energy equal to the band gap? Is it just because the interaction with one photon has higher probability or there is a fundamental difference?</p>
<p><img src="http://i.stack.imgur.com/XtNu2.png" alt="enter image description here"></p>
| 1,556 |
<p><img src="http://i.stack.imgur.com/v7mfP.png" alt="enter image description here"></p>
<p>The question asked was "what should be the acceleration such that the pressure at both the points marked by thick dots be equal? the vessel is <strong>open</strong> and cubic with side 5m?" </p>
<p>Initially i considered the diagram to be resembling the figure B where $$\tan(\theta)=a/g$$
but then i realized since the both points are the midpoints of the respective sides, the height of the liquid above the lower point must be half of the height above the point on the side. I took the diagram then to resemble D. Then i got the answer as $a=2g$. Is this CORRECT?<br>
<strong>If this had been a closed vessel what would the answer have been?</strong> Figure C That is my question.</p>
| 1,557 |
<p>My question is fairly simple, but I do need clarification on how to get the inverse of the <a href="http://en.wikipedia.org/wiki/Lennard-Jones_potential" rel="nofollow">Lennard-Jones</a> potential V(x).</p>
<p>I am working with the following expression:
$$
V(x) = e\times[(R/x)^{12} -2\times(R/x)^6]
$$</p>
<p>So given a value $V$, how can I find $x(V)$ ?</p>
| 1,558 |
<p>I'm currently consuming a course on QFT where we need to define the unitary time-evolution to get the time evolution of the wave function in the interaction picture:</p>
<p>$\hat{U}(t_1,t_0) = \exp\left(\frac{i}{\hbar}\hat{H}_0t_1\right)\exp\left(-\frac{i}{\hbar}\hat{H}(t_1-t_0)\right)\exp\left(-\frac{i}{\hbar}\hat{H}_0t_0\right)$ .</p>
<p>Now one can show that this operator follows a Schrödinger equation by simply taking the derivative to time:</p>
<p>$i\hbar\frac{d}{dt}\hat{U}(t,t_0) = \hat{H}_1^I(t)\hat{U}(t,t_0)$ .</p>
<p>Where $\hat{H}_1^I$ is the perturbation to our free-field Hamiltonian $\hat{H}_0$.</p>
<p>Now I started wondering whether $\hat{U}(t_1,t_0)$ shouldn't also follow a Heisenberg equation since it's an operator.</p>
<p>I believe it shouldn't since $\hat{U}(t_1,t_0)$ gives a unitairy time-evolution which is a transformation, while the Heisenberg equation applies to observables. I was woundering if someone could confirm my reasoning or disprove it?</p>
| 1,559 |
<p>In the 19th century, most astronomers adopted an island universe model, in which our galaxy was the only object in an infinite space. They didn't know that the "spiral nebulae" were other galaxies. This model had the advantage of being dynamically stable (unlike Newton's infinite and uniform cosmology), and of avoiding the fact that Poisson's equation doesn't have unique solutions for an infinite and uniform universe. Ca. 1830, the geologist Lyell advocated a theory of uniformitarianism, in which the universe would have had uniform conditions going back infinitely far in time. There was some debate between Lyell and physicists such as Kelvin, who objected that the sun would have run out of energy, the earth would have lost its internal heat, and so on, but this was inconclusive because they didn't know enough thermodynamics and didn't know about the atomic nucleus.</p>
<p>But by 1850, the second law of thermodynamics had been formulated, and this would seem to have been solid proof that the universe could not possibly have existed for an infinite time in the past. (This level of understanding of thermodynamics would also, I'd imagine, allow them to show that stars would gradually evaporate out of the galaxy, since the velocity distribution would have a high-velocity tail.) Kelvin did attack Lyell with the second law, but it doesn't sound like people at the time appreciated that this was a decisive argument.</p>
<p>With the benefit of hindsight, we can say that it was decisive, and from 1850 to 1905, people should have been considering only cosmological models that used Newtonian mechanics and that stretched back a finite time into the past. Are such models possible?</p>
<p>For example, I suppose you could make a Newtonian big bang, in which, as many students today imagine, there was an explosion at a specific point in otherwise empty space. Extrapolating the motion of all particles back in time using the laws of physics, one would find their trajectories all converging on a point, then diverging from it again on the other side, i.e., it would look like a big crunch/big bang "singularity," -- it would be a singularity of the matter density, temperature, etc. Thermodynamically, it would look like an extreme thermodynamic fluctuation, which is no worse than the thermodynamic implausibility of the low-entropy big bang in modern GR-based theories. There would be an upper bound on ages of objects in today's universe, because everything was destroyed in the singularity.</p>
<p>Another possibility I can imagine is that you could start off with a universe containing an infinite amount of matter and an infinite amount of energy thermodynamically available to do work. After an infinite time, you would have expended an infinite amount of energy to do work, but you would still have an infinite amount left. The modern counterpart of this kind of thinking would be calculations of whether you can do an infinite calculation in various cosmological models (Dyson 1979, Krauss 1999).</p>
<p>Related: <a href="http://physics.stackexchange.com/questions/6897/why-didnt-newton-have-a-cosmological-constant">Why didn't Newton have a cosmological constant</a></p>
<p><em>References</em></p>
<p>Dyson, Time without end: Physics and biology in an open universe, Reviews of Modern Physics 51 (1979), pp. 447–460, doi:10.1103/RevModPhys.51.447; described in <a href="http://math.ucr.edu/home/baez/end.html">http://math.ucr.edu/home/baez/end.html</a></p>
<p>Krauss and Starkman, 1999, Life, The Universe, and Nothing: Life and Death in an Ever-Expanding Universe, <a href="http://arxiv.org/abs/astro-ph/9902189">http://arxiv.org/abs/astro-ph/9902189</a></p>
| 1,560 |
<p>In the last 40 years (approximately) people have been "discovering", "rediscovering" and "studying" SUSY as a powerful tool and "symmetry principle". </p>
<p>Question: </p>
<p>What if SUSY is not realized in Nature at the end? Is SUSY the only path to "relate" fermions and bosons or what else? Remark: SUSY has not been discovered yet, so keep you totally conservative. What if there is no SUSY?</p>
<p>Bonus:</p>
<p>What are the merits of SUSY? What are its main issues? I do know some answers to this, but I think it could very enlightening if we "listed" pros and contras of current supersymmetric theories to see where we are NOW. </p>
| 1,561 |
<p>So electrons of specific atoms have a minimum amount of energy needed to escape the atom, called the work function, W. Now let's say that you emit a certain frequency of light, and $hf<W$. However, from my understanding, this work function is just a form of kinetic energy, and if an electron has enough kinetic energy, its inertia will be greater than the centripetal force and the electron will escape. So even though $hf<W$, the object being illuminated will still heat up from the light. This heating up means that the material is gaining internal energy, which means that the electrons are gaining kinetic energy. If the material gets hot enough and the electrons keep gaining speed, couldn't the they escape anyway even though $hf<W$? Thanks! </p>
| 1,562 |
<p>I have this problem. I have an ideal gas that goes through an irreversible adiabatic decompression. I have the initial state (P,T,V), and the final pressure, and I have to calculate the entropy difference of the proccess. So, what I know is that I can make up any reversible proces bewteen the initial and final state because entropy is a state function, and integrate the heat over that process, but I can't solve it. I'm aplying $P_1V_1^\lambda=P_2V_2^\lambda$ to get the final state, but as I am creating the final point of the adiabatic, I get entropy difference of $0$ for an invented reversible path. That way of getting the final state is not correct, right? I have $PV=nRT$ but I only have the final $P$ so I need another equation.</p>
<p>EDIT: I have tried also to use $\Delta U=W\Rightarrow C_v\Delta T=P_{ext}\Delta V$, get $T_{final}$, and go on, but I don't get the correct result either. I thought this was general: $dU=C_vdT$, when can I apply that equation?</p>
| 1,563 |
<p>I am having trouble understanding electromagnetic radiation (or waves in general, be it EM or sound). If I have a 1 Watt speaker, is it infinitely divided and spread out so that everyone in every direction around the speaker can hear it?</p>
<p>I do not believe they have "height", to reach more than one person at once, but if they did they would probably collide at one point. How do sound waves travel "backwards" (i.e. you are behind a speaker), are they scattered by air particles or itself so that people behind could hear it (at reduced amplitude)?</p>
<p>I am just unsure how to wrap my head around it.</p>
| 1,564 |
<p>I often see the term "net mechanical efficiency" used in literature, but I am not quite sure what it means, and what the difference is between it and "normal" efficiency. Take this sentence for example: <code>... increased the effectiveness, while reducing net mechanical efficiency.</code> What does exactly does this mean?</p>
| 1,565 |
<p>It is usually said that existence of discrete spacetime violates Lorentz symmetry. What quantity is used to quantify such violation? I mean could someone points a reference for a derivation that shows such analysis.</p>
<p>My other question is that: if, and this is a big fat if, OPERA result was true (and I believe it is not) would that prove that spacetime is discrete?
(this is like the inverse to the 1st part of this post, if space-time is discrete then Lorentz symmetry is violated, what if Lorentz symmetry is violated, does that imply space-time is discrete? or not necessarily?)</p>
| 1,566 |
<p>I'm having some trouble calculating the 2nd order energy shift in a problem.
I am given the pertubation:</p>
<p>$\hat{H}'=\alpha \hat{p}$,</p>
<p>where $\alpha$ is a constant, and $\hat{p}$ is given by:</p>
<p>$p=i\sqrt{\frac{\hbar m\omega }{2}}\left( {{a}_{+}}-{{a}_{-}} \right)$,</p>
<p>where ${a}_{+}$ and ${a}_{-}$ are the usual ladder operators.</p>
<p>Now, according to my book, the 2nd order energy shift is given by:</p>
<p>$E_{n}^{2}=\sum\limits_{m\ne n}{\frac{{{\left| \left\langle \psi _{m}^{0} \right|H'\left| \psi _{n}^{0} \right\rangle \right|}^{2}}}{E_{n}^{0}-E_{m}^{0}}}$</p>
<p>Now, what I have tried to do is to calculate the term inside the power of 2. And so far I have done this:</p>
<p>$\begin{align}
& E_{n}^{1}=\alpha i\sqrt{\frac{\hbar m\omega }{2}}\int{\psi _{m}^{*}\left( {{{\hat{a}}}_{+}}-{{{\hat{a}}}_{-}} \right)}\,{{\psi }_{n}}\,dx=\alpha i\sqrt{\frac{\hbar m\omega }{2}}\left( \int{\psi _{m}^{*}\,{{{\hat{a}}}_{+}}{{\psi }_{n}}\,dx-\int{\psi _{m}^{*}\,{{{\hat{a}}}_{-}}{{\psi }_{n}}\,dx}} \right) \\
& =\alpha i\sqrt{\frac{\hbar m\omega }{2}}\left( \sqrt{n+1}\int{\psi _{m}^{*}\,{{\psi }_{n+1}}\,dx-\sqrt{n}\int{\psi _{m}^{*}\,{{\psi }_{n-1}}\,dx}} \right)
\end{align}
$</p>
<p>As you can see, I end up with the two integrals. But I don't know what to do next ? 'Cause if $m > n$, and only by 1, then the first integral will be 1, and the other will be zero. And if $n > m$, only by 1, then the second integral will be 1, and the first will be zero. Otherwise both will be zero.
And it seems wrong to have to make two expressions for the energy shift for $n > m$ and $m > n$.</p>
<p>So am I on the right track, or doing it totally wrong ?</p>
<p>Thanks in advance.</p>
<p>Regards</p>
| 1,567 |
<p>In Statistical Mechanics, we often postulate that for an isolated system, the phase-space density of all accessible microstates (i.e all microstates consistent with the energy) is the same. This is equivalent to assuming that the system is ergodic. This postulate leads us to the assertion that at any given time, the system is most likely to be found in that macrostate which has the maximum number of consistent microstates, and from then on, we calculate the entropy for this macrostate and get the fundamental relation for entropy, and hence, other thermodynamic quantities.
My question now is: Is this assumption of equal a-priori probabilities too strong to obtain the second assertion? In other words, can we not say that the macrostate with the maximum number of microstates <em>is</em> the observed thermodynamic state, while being non-committal as to whether indeed they are all equally probable or not? Or am I losing some information by not considering their probability distribution (maybe, say fluctuations)?</p>
| 1,568 |
<p>I'm wondering if there is more than the empty theory (no local fields, identically vanishing stress energy tensor) that can have central charge $c$ equals to $0$?</p>
<p>My intuition tells me no, the stress energy tensor would transform as a primary field and so would only contain primary fields but there are none except for the identity operator. So there could only be (topological) degrees of freedom on the boundary. Is this reasoning wrong?</p>
<p>ps: I'm only thinking at unitary theories, otherwise, sure it could be possible to combine in a balanced way fields carrying positive and negative central charge.</p>
| 1,569 |
<p>Why does production of white light using a LED require combining a short wavelength LED such as blue or UV, and a yellow phosphor coating?</p>
<p>Why can't a single LED produce pure white light?</p>
| 1,570 |
<p>Suppose you have a U tube filled with a liquid. The height of the liquid column in both the arms of the U tube is not the same. Will the pressure be the same at two points in the two arms of the U tube which are at the same height from the base of the U tube or will it vary depending on height of liquid column above these two points?</p>
| 1,571 |
<p>If I try to add up neutrino masses (let's assume 1 eV rest mass equivalent each) to count as DM, do I use the rest mass or relativistic mass?</p>
| 1,572 |
<p>About the meta questions <a href="http://meta.physics.stackexchange.com/questions/1193/full-migration-of-theoretical-physics-se-questions-to-physics-se">1193</a> and <a href="http://meta.physics.stackexchange.com/questions/2609/why-theoretical-physics-has-been-closed">2609</a>, I've heard parallelly, that the complete branch <a href="http://en.wikipedia.org/wiki/Theoretical_physics" rel="nofollow">theoretical physics</a> is already done and that there isn't any thing else to do in this field, how true is it?</p>
| 1,573 |
<p><strong>The Setup</strong>: Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric </p>
<p>$ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$. </p>
<p>It seems to me that in the usual discussion (e.g. di Francesco, Ginsparg, Polchinski), one proceeds to consider an analytic continuation of the CFT to $\mathbb C^2$ with coordinates $z^1, z^2$ and complex metric</p>
<p>$ds^2 = (dz^1)^2+(dz^2)^2$</p>
<p>and then, one performs the coordinate transformation $z = z^1+iz^2$ and $\bar z = z^1-iz^2$. In this way the coordinates $z$ and $\bar z$ can be considered "independent" because they are coordinates on a complex two-dimensional manifold. Also, in these coordinates the metric becomes</p>
<p>$ds^2 = dz\,d\bar z$</p>
<p>and it becomes clear that conformal mappings consist of mappings: $(z, \bar z)\to (f(z), g(\bar z))$.</p>
<p><strong>My confusion is this</strong>: Since our original theory was on $\mathbb R^2$, books say that when we do calculations, we should consider the physical theory as living on the copy of $\mathbb R^2$ embedded in $\mathbb C^2$ given by the condition $\bar z = z^*$. But consider the mapping $(z, \bar z)\to (z^2, \bar z)$. This is a conformal mapping on $\mathbb C^2$, but it does not map the surface $\bar z = z^*$ to itself; for example the point $(z, \bar z)=(2,2)$ gets mapped to the point $(z^2, \bar z) =(4,2)$ and $2$ is clearly not equal to $4^*$. In particular, it seems to me that analytic continuation to a CFT on $\mathbb C^2$ enlarges the set of mappings one can have, so what relevance does it really have to the original CFT on $\mathbb R^2$? (my apologies for the long post)</p>
| 1,574 |
<p>I'm trying to learn how to apply WKB. I asked a <a href="http://physics.stackexchange.com/questions/90157/how-to-apply-the-wkb-approximation-in-this-case">similar question</a> already, but that question was related to finding the energies. Here, I would like to understand how to find the wave functions using WKB.</p>
<blockquote>
<p><em>An electron, say, in the nuclear potential</em>
$$U(r)=\begin{cases}
& -U_{0} \;\;\;\;\;\;\text{ if } r < r_{0} \\
& k/r \;\;\;\;\;\;\;\;\text{ if } r > r_{0}
\end{cases}$$
<em>What is the wave function inside the barrier region ($r_{0} < r < k/E$)?</em></p>
</blockquote>
<p>Shouldn't the wave function have the following form?</p>
<p>$$\psi(r)=\frac{A}{\sqrt{2m(E-U(r))}}e^{\phi(r)}+\frac{B}{\sqrt{2m(E-U(r))}}e^{-\phi(r)}$$
where
$$\phi(r)=\frac{1}{\hbar}\int_{0}^{r} \sqrt{2m(E-U(r))} dr'$$</p>
| 1,575 |
<p>Is there any temperature dependence of relaxation time in impurity scattering of conducting electrons? It seems to me that there is none. But, some people claim that there is.</p>
<p>So if you could explain, how temperature dependence comes into play if it does at all?</p>
| 827 |
<p>The problem I am working on is:</p>
<blockquote>
<p><em>Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 300 kg, and a minute hand 4.20 m long with a mass of 100 kg (see figure below). Calculate the total rotational kinetic energy of the two hands about the axis of rotation. (You may model the hands as long, thin rods rotated about one end. Assume the hour and minute hands are rotating at a constant rate of one revolution per 12 hours and 60 minutes, respectively.)</em></p>
</blockquote>
<p>(Converted) Angular Speed of Clock Hands:</p>
<p>Hour Hand $1.45\cdot10^{-4}~rad/s$</p>
<p>Minute Hand $1.75\cdot10^{-3}~rad/s$</p>
<p>Rotational Moment of Inertia:</p>
<p>Hour Hand $I=1/3(300~kg)(2.70~m)^2=729~kg\cdot m^2$</p>
<p>Minute Hand $I=1/3(100~kg)(4.20~m)^2=243~kg\cdot m^2$</p>
<p>Rotational Kinetic Energy:</p>
<p>$K_{rot}=1/2(729~kg\cdot m^2)(1.45\cdot10^{-4}~rad/s)^2+1/2(243~kg\cdot m^2)(1.75\cdot10^{-3}~rad/s)^2$</p>
<p>When I calculate this, it comes out incorrect, what has happened?</p>
| 1,576 |
<p>I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable (self-adjoint operator) in quantum mechanics? </p>
<p>E.g. an operator $A$ with the Hamiltonian $H$?</p>
| 651 |
<p>Please can anyone explain the concepts of <a href="http://en.wikipedia.org/wiki/Electromagnetically_induced_transparency" rel="nofollow">electromagnetic induced transparency</a>? I am having problem with the technicality of the explanation on wikipedia. Please I am an engineer with a physics background though and would love if this can be explained with little to no jargons . I am working on optical buffers and studying recent technologies and would love and explanation on this.</p>
| 1,577 |
<p>Photons have no mass but they can push things, as evidenced by <a href="https://en.wikipedia.org/wiki/Laser_propulsion">laser propulsion</a>. </p>
<p>Can photons push the source which is emitting them? If yes, will a more intense flashlight accelerate me more? Does the wavelength of the light matter? Is this practical for space propulsion? Doesn't it defy the law of momentum conservation?</p>
<p><em>Note: As John Rennie mentioned, all in all the wavelength doesn't matter, but for a more accurate answer regarding that, see the comments in <a href="http://physics.stackexchange.com/a/112870/46604">DavePhD's answer</a> .</em></p>
<p><em>Related Wikipedia articles: <a href="https://en.wikipedia.org/wiki/Ion_thruster">Ion thruster</a>, <a href="https://en.wikipedia.org/wiki/Spacecraft_propulsion">Space propulsion</a></em></p>
| 483 |
<p>I'm reading that general relativity let's us describe physics from the point of view of both inertial and accelerated observers. What does that actually mean in terms of doing actual physics? For example, say a physicist performed Millikan's oil drop experiment or Young's double slit experiment or decomposed white light with a prism:
(1) in deep space, far from any gravitational field,
(2) on Earth,
(3) near a black hole.
I'm assuming she would get different results, and I'm assuming that in some way this is near the heart of what's important regarding GTR, but how exactly? In other words, what are the implications of GTR for understanding these experiments?</p>
<p>Thank you</p>
| 1,578 |
<p>The anthropic principle has become a very popular explanation among theoretical physicists lately. Life is unlikely, but only life can observe, so we find ourselves in an unlikely position, so to speak. What I would like to ask is just how unlikely is life? Is the evolution of life generic for most laws of physics, or extremely unlikely with extreme fine-tuning? What is so controversial about the anthropic principle? No one is surprised to find themselves on an Earth-like planet orbiting a long lived star at just about the right distance from the star with plenty of liquid water, a thick atmosphere and plenty of carbon amidst the sterile antiseptic reaches of space. What are the major pros and cons? String theory conveniently provides a multiverse and a landscape.</p>
| 1,579 |
<p>I was recently reading <a href="http://en.wikipedia.org/wiki/Siphon#Explanation_using_Bernoulli.27s_equation" rel="nofollow">the explanation for the behaviour of a siphon</a> on Wikipedia, which uses Bernoulli's equation in its proof. The argument is generally pretty easy to follow, except for one key point: how can we assume that the velocity of the water is constant at all points throughout its flow through the tube? This tacit assumption is made at various point, not least in the terming of "the siphon velocity" (implying there's only one). I would be grateful if someone could clarify this.</p>
<p>Note: I've done a hefty amount of classical mechanics in my time, but barely any fluid mechanics I'm afraid. First principles explanations would be appreciated.</p>
| 1,580 |
<p>Amorphous metals are often referred to as metallic glasses due to their quenched atomic disorder. Do they fracture in the same fashion as silicate glasses? If not, what failure mode(s) do they have?</p>
| 1,581 |
<p>When comparing two light sources, for example, a light bulb at 20W and a light bulb at 100W, what is it about the incoming light that makes the latter look brighter than the former? Are there different reasons why different light sources looks different in brightness (High five for cramming three instances of "different" in the same sentence)? For example, in <a href="http://physics.stackexchange.com/questions/3145/sensitivity-of-eye">this</a> thread, it is stated that the human eye is most sensitive around 555nm, something that I guess translates to meaning that given a light of the same intensity (whatever that means, hence my question), it is going to be perceived as most bright when hitting 555nm. Does this question have different answers depending on if you're seeing light as a particle vs a wave?</p>
| 1,582 |
<p>Does the internal structure of a neutron star resemble anything like that of an atomic nucleus? I.e., are the neutrons arranged in a shell like structure with different energy levels, and without a distinct location for each neutron?</p>
<p>I know that the force holding a neutron star is gravity, compared to the strong interaction inside atomic nuclei, but does this matter?</p>
| 1,583 |
<p>While watching the first 4 seconds of <a href="http://www.gizmodo.com.au/2011/11/driving-at-745kmh-is-ludicrous-from-any-angle/" rel="nofollow">driving at 745 km/h is ludicrous from any angle</a>
wondered </p>
<p>1)If we knew the curvature of the earth in a "flat" desert, what would be the speed of the car?</p>
<p>2)Assuming we don't know the curvature of the earth, how long would it take for the car to go around the earth ( assuming a "flat" desert all the way travelling on a great arc)?</p>
<p>Using my ninja pause skills it seemed it took 2 seconds from the time the car appeared ( as a dot ) in horizon to the time it passed by the camera, although 2 second window of observation seems to lead to a great error in overall estimates, using the 745 as the value for 1 and 2 the error of human observation could be calculated (?) </p>
| 1,584 |
<p>The book I'm reading about optics says that an anti-reflective film applied on glass* makes the glass <em>more</em> transparent, because the air→film and film→glass reflected waves (originated from a <a href="http://en.wikipedia.org/wiki/Paraxial_approximation" rel="nofollow">paraxial</a> incoming wave) interfere destructively with each other, resulting on virtually no reflected light; therefore the "extra" light that would normally get reflected, gets transmitted instead (to honor the principle of conservation of energy, I suppose?).</p>
<p>However, <a href="http://physics.stackexchange.com/questions/10410/why-dont-waves-erase-out-each-other-when-looking-onto-a-wall/10439#10439">this answer</a> states that <em>"Superposition is the principle that the amplitudes due to two waves incident on the same point in space at the same time can be naively added together, but the waves do not affect each other."</em></p>
<p>So, how does this fit into this picture? If the reflected waves actually continue happily travelling back, where does the extra transmitted light come from?</p>
<p><sub>* the film is described as (1) having an intermediate index of refraction between those of air and glass, so that both the air-film and film-glass reflections are "hard", i.e., produce a 180º inversion in the phase of the incoming wave, and (2) having a depth of 1/4 of the wavelength of the wave in the film, so that the film-glass reflection travels half its wavelength back and meets the air-film reflection in the opposite phase, thus cancelling it.</sub></p>
| 1,585 |
<p>For some electric devices, like a fan or air conditioner, I read about their power consumption in watts on their specification guide.</p>
<p>Does it tell about the power at normal or full speed? or Does the speed even affect the power consumption? Can I find the consumption at different speeds?</p>
| 1,586 |
<p>Why is electricity not transmitted wirelessly such that we don't need to span cables on the earth's surface? As in: electricity is transmitted wirelessly from the power plant to the household.</p>
| 1,587 |
<p>The book I'm reading about optics says at some point that "each color (wavelength) contained in the white light interferes only with itself". But why is this so?</p>
<p>Edit: I moved the rest of the question <a href="http://physics.stackexchange.com/q/12208/4283">elsewhere</a>.</p>
| 1,588 |
<p>Could anyone suggest a recent review article or book on gas chromatography instrumentation? My interest is in the devices themselves, rather than using them for a particular application.</p>
<p><a href="http://rsi.aip.org/resource/1/rsinak/v61/i11/p3317_s1" rel="nofollow">This article</a>, "Gas Chromatography" in Review of Scientific Instruments is the sort of thing I'm going for; I'm just checking to see if there's a more recent or superior introduction.</p>
| 1,589 |
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