title: Can we generate infinite energy by successive fission and fusion reactions?

text: Fission divides one Helium atom into two Hydrogen (Deuterium) atoms. And fusion, once again, puts together those two Hydrogen atoms into one Helium atom. In both reactions, overall output energy is enormous. $ \begin{array}{rcrclclrl} \text{1 Neutron} & \+ & {}_2^4He & \to & {}_1^1H + {}_1^1H & \+ & \text{Energy} + \text{3 Neutrons} & \dots & (I) \\\ \text{2 Neutrons} & \+ & {}_1^1H + {}_1^1H & \to & {}_1^2H + {}_1^2H &&(somehow) & \dots & (II) \\\ \text{Energy} & \+ & {}_1^2H + {}_1^2H & \to & {}_2^4He & \+ & \text{Big Energy} & \dots & (III) \\\ \end{array} $ I don't know whether the reaction $(II)$ is possible with today's technology, or not. Neither I know if it is endothermic or exothermic. But, if we could realize it, would it be possible to generate infinite energy by looping these three reactions forever successively in the given order? I intuitively feel that the answer is "no", but I need an explanation on why it is not possible.


title: Antimatter collision - Energy Released

text: I think it's about time for me to ask this question, as I've been contemplating this for a while. $$E = mc^2.$$ This is Einstein's most famous equation. But what does it mean? On my own, I had to think a lot about it, since no one in my close surroundings can give me good answers. To me it means that the energy contained inside an object is proportional to the mass. Thus mass is energy. And if that object gets **annihilated** then its mass will be converted back into pure energy, such as light. Isn't that what happens when Antimatter collides with our ordinary matter? The masses cancel out and they turn into light (photons)? Here is a little fun I had last year in my Grade 9 Science class.               100g of H.     100g of anti-H.          They collide, and their masses, convert into energy. E = mc^2.     E = (100)*((299792458)^2);     E = 8.987551788E18 joules.      So that's the amount of energy produced. Is this correct? Did I use the wrong equation? What else can E=mc^2 be used for. If this is correct, boy that's a lot of energy contained in a hundred grams of Hydrogen.


title: How to show the oblique parameters S, T, and U are coefficients of d=6 operators

text: In Morii, Lim, Mukherjee, _The Physics of the Standard Model and Beyond._ 2004, ch. 8, they claim that the Peskin–Takeuchi oblique parameters _S, T_ and _U_ are in fact Wilson coefficients of certain dimension-6 operators. On page 212, they claim that the _T_ parameter is described by $$O_T=(\phi^\dagger D_\mu \phi)\phi^\dagger D^\mu \phi)-\frac{1}{3}(\phi^\dagger D_\mu D^\mu\phi)(\phi^\dagger\phi)\,,$$ and the _S_ parameter by $$O_S=[\phi^\dagger(F_{\mu\nu}^i\sigma^i)\phi]B^{\mu\nu}\,,$$ where $\phi$ is the Higgs doublet, $F_{\mu\nu}^i$ and $\sigma^i$ are the SU(2) weak isospin field strength and sigma matrices respectively, and $B^{\mu\nu}$ is the U(1) weak hypercharge field strength. On the next page (p. 213), problem **8.6** asks us to show that these are the operators. How do I precisely show that these higher-dimension operators give precisely the Peskin-Takeuchi parameters?


title: Entropy used to calculate energy?

text: I'm currently reading an online article, and below is a quote from that article: > The thermodynamic entropy to change $n$ memory cells within $m$ states is > $ΔS=k_B\ln(m^n)$, where $k_B$ is the Boltzmann constant. From the second law > of thermodynamics, $ΔS=\dfrac{ΔQ}{T}$, where $ΔQ$ is the energy spent and > $T$ is the temperature. So the energy required to write information into one > binary memory bit is $E_{bit}= k_BT \ln2$. But from what I've learned, $Q$ is heat transfer, not 'energy spent'. Why is it possible to use those 2 interchangeably, if it's possible?


title: Gauge fields -- why are they traceless hermitian?

text: A gauge field is introduced in the theory to preserve local gauge invariance. And this field (matrix) is expanded in terms of the generators, which is possible because the gauge field is traceless hermitian. Now why did we choose it as traceless Hermitian? What was the insight behind the choice that made us expand it in terms of the generators? I read somewhere that 'the gauge field belongs to the Lie algebra' and I tried to follow it up, but I can't make any sense out of what I read. Can anybody explain in clear, intuitive terms?


title: Energy Change in a Capacitor by Inserting Dielectric

text: This is a practice Physics Subject GRE problem. > A parallel-plate capacitor has plate separation $d$. The space between the > plates is empty. A battery supplying voltage $V_0$ is connected across the > capacitor, resulting in electromagnetic energy $U_0$ stored in the > capacitor. A dielectric, of dielectric constant _k_ , is inserted so that it > just fills the space between the plates. If the battery is still connected, > what are the electric field $E$ and the energy $U$ stored in the dielectric, > in terms of $V_0$ and $U_0$? I was able to figure out $E$ fairly easily. Since the voltage stays the same (by virtue of it being connected to a battery), $E = V/d$. I am having difficult understanding why the answer for $U$ is what it is though. The answer is $U = k^2U_0$. What equation(s) would give this result? I know $W = \frac{1}{2}VQ$, and with $V$ staying the same $Q$ must be the variable being multiplied by $k^2$. But $Q = CV$ so $C$ should also be increasing as $k^2$ but for a parallel plate capacitor $C$ only increases by a single $k$ when inserting a dielectric. How to resolve this discrepancy, or what am I missing?


title: Why aren't train headlights brighter?

text: I suspect a valid scientific, physics answer for this question, because I'd venture that train, insurance companies would've calculated and contemplated this question. Yet the train headlights at http://www.youtube.com/watch?v=0TY9Kdj5PJI don't appear to brighten/illuminate sufficiently far ahead. If an obstacle or hindrance were in front, then wouldn't the limited range of the headlights prevent a safe stop? Also, as can be seen at the 8:15 mark, the train's lights don't corner or turn together with the train. Why not? Wouldn't they befit and help such a train? Shouldn't such heavy, menacing trains be equipped with headlights of the 'lumens' resembling http://www.youtube.com/watch?v=jPKy1KAz8OM and http://www.youtube.com/watch?v=bWS30yHBuLQ _(same car and driver)_ , how gleaming so ever it is for a car?


title: amplification of magnetic field

text: can we by any means amplify magnetic signal as we can with electric signal. As both electric and magnetic field can be represented in the form of a wave the analogy seems to be natural. I want the input and output as magnetic signal.


title: Scaling in Vlasov equations

text: This question is in reference to the paper, http://arxiv.org/abs/1301.7182   * What exactly is the argument being made on page 6 and 7?  One deduces that the function $\Delta$ has to be such that, $\Delta^2(k,\tau) = \Delta^2(\frac{k}{\lambda ^{\frac{4}{n+3}}}, \lambda \tau )$. Now from this how does this follow that, the following holds, $\Delta^2(k,\tau) = \Delta^2(\frac{k}{k_{NL}})$ where $k_{NL}^{n+3} \propto \tau ^{-4} $ ?   * How does 2.26 follow from 2.2?  In 2.2 aren't all the $c_{*}^2$s dimensionless?


title: Fiber optics with broadband, incoherent light

text: I wonder if someone could help clarify waveguiding with broadband, incoherent light please. If we take a telecomms fiber, which is single-moded above ~1.4 μm and couple a laser beam in, we assume this excites the only mode, which is the fundamental mode. The mode-field diameter of the transverse mode is determined by the core radius and wavelength of light. I assume laser light here is coherent. But what happens if you couple light in from a broadband incoherent source (e.g. an incandescent bulb with spectrum from 1.5-3 μm)?. Can you say that a single mode will be excited containing all wavelengths from 1.5 to 3 μm? And what about if the spectrum extends from 1 to 3 μm - will there be multiple modes excited, since 1.4 μm is the cut-off for single mode behavior? Or is this picture invalid since the light is incoherent?


title: How to prove useful property of logarithm of generating functional in QFT?

text: How to prove that $\ln(Z(J))$ generates only connected Feynman diagrams? I can't find the proof of this statement, and have only met its demonstrations for case of 2- and 4-point.


title: (coordinates) Invariance/Covariance of Chern-Simons theory and Yang-Mills theory

text: It is known that 3D Chern-Simons(C-S) theory has no explicit metric involving in the Lagrangian density: $$ A \wedge dA + (2/3) A \wedge A \wedge A $$ while the 4D Yang-Mills(Y-M) theory has the metric $g_{\mu\nu}$involves. $$ F \wedge *F= (dA + A \wedge A) \wedge *(dA + A \wedge A) $$ More explicitly, for Abelian case, C-S gives the form without the metric(topological), $$d^3 x \epsilon^{\mu\nu\rho} A_\mu \partial_\nu A_\rho$$ Y-M gives the form with the metric: $$d^4 x (\partial_\mu A_\nu)( \partial^\mu A^\nu)=d^4 xg^{\mu\rho}g^{\nu\lambda}(\partial_\mu A_\nu)( \partial^\nu A^\lambda)$$ How about the statement of coordinate invariance of C-S and Y-M theory? **Are C-S or Y-M coordinate invariance? (i.e. does the Lagrangian density look different in other coordinates, such as cylindrical, spherical coordinates? or general curved coordinates? how does that Lagrangian look like in those generic coordinates?)** Is there some relations (if, only if or iff) between: (1) **gauge invariance** ; (2) **coordinate invariance** ; (3) **metric independence** (=diffeomorphism invariance?); (4) **covariant form in curved background**? for those gauge theories (e.g. Y-M) or for topological field theory (e.g. C-S)? ps. see also this post, which unfortunately does not directly answer my inquiries yet. Thanks.


title: Best time of the year to see the star Alpha Centauri in Chile, Santiago

text: If I'm in Chile, Santiago, what is the best time of the year to see the star Alpha Centauri at the beginning of the night?


title: Why do high current conductors heat up a lot more than high voltage conductors?

text: 120 volts x 20 amps = 2,400 Watts However, if I increased the voltage and lowered the current, you can also use a smaller wire size (more inexpensive), also have less heat and achieve the same watt Power. 1,000 volts x 2.4 amps = 2,400 Watts   1. Why doesn't it heat up like current?   2. To me this approach seems more efficient and less costly because you don't use as much material, so why isn't this common?


title: gravitational waves

text: Now that scientists found the primordial gravitational waves that formed shortly after the big bang,and we all now that just after the bang the 4 fundamental forces were unified can we consider that these waves are the strings that we're looking for,that unify again these forces?


title: How to determine day/night based on latitude, longitude and a date/time?

text: Is there a simple method of determining, given a UTC date/time, whether it is day or night at a given lat/long coordinate? I am currently using a formula based on a Sunrise/Sunset Algorithm from the US Naval Observatory, but unfortunately I am having trouble applying to arrive at a simple night/day indicator. Should I build upon this formula or is there some more efficient way of doing this that I am missing? _Disclaimer: I am a programmer, not an astronomer, so I find the formulas for astronomical calculations a bit confusing._ _Extra stuff: Ideally I would like to artificially shorten the period of "night" by two hours, for the purposes of eliminating some false positives from sensor data that occurs during twilight/dawn. In other words, if sunset occurs at 7 pm at a given location, I would like the option of padding the value by 60 minutes such that the output remains "day" until 8 pm for that location. (And apply the same padding prior to sunrise.)_ **Update:** I wound up calculating the sun's altitude for the location using a UTC timestamp and the location's lat/long coordinates. Using figures for various twilight amounts (6, 12, 18 or degrees below horizon) I am able to automatically select the portion of "night" that is sufficiently dark. (e.g. 6 degrees below horizon is not as dark as 12 degrees.) This approach was much easier than attempting to determine sunrise and sunset times for the locale's time zone (and all of the associated time zone headaches).


title: How much of sky can be seen on a typical night from a mid-latitude location?

text: I'm at about 40deg north so, assuming a clear southern horizon, I can't see things below about -30 or so (I actually don't know how far south). I also have a large portion that is circumpolar so it's always visible. I assume there's an equal size area south that is never visible. On an equinox, the average night, I have less than 12 hours of darkness, but as the Earth rotates some stars will set and other rise, so I'm guessing something approximating 70% of the sky will be visible west to east. So, how much of the sky is actually visible on a typical night?


title: Classical systems with strong coupling

text: I would like to have some examples of classical systems with "strong" coupling coefficient (in their action term). Specifically, I am looking for intermediate or cross-over ranges of coupling (~$\mathcal O(1) $), where it is neither possible to describe them by effective (composite) field theories with small coupling (like hadron model for QCD) nor possible to do perturbation. [A related question - "Can classical systems exhibit strong coupling?" \- had been asked here sometime back, where a few systems (dusty plasma, turbulence, granular materials etc) were mentioned. But I dont know if those systems are what I am looking for] Related question: I would like to have some examples of classical systems with negative beta function ie. coupling increases towards IR.


title: Travel at the speed of light

text: 1. Is it me who have a poor understanding, or does all matter have to become 'pure energy' in order to achieve speed-of-light speed?    2. If so, does that mean that no material can achieve the speed of light and remain in its original state of matter?


title: What is the extent of the universe?

text: Is there any realistic, understandable, provable (even in some extent) explanation/model for the extent of the universe? What is its shape? and Why? I mean physical explanations not philosophical since the question is about a physical entity, the universe. When I try to think about this it is almost I cannot think at all! note I am almost satisfied that there is no answer for this single question! I paid attention to all comments and spent time for watching the video-lectures recommended (I don't recommend) just to seek the answer, however, I got nothing about the question at all. The discussion and lectures are mathematical games far being physical to me. I respect all the science involved in cosmology but for this question even great researcher (some got Nobel prize recently) have nothing to say except playing with formulas and graphs. I was looking for physical meaning. I lost my interest in this question.


title: Microwave oven + water: dielectric heating or ion drag?

text: When you place a water or food in a microwave oven, it heats. Which process commits more energy to that: dielectric heating, or ion drag i.e. resistive heating? AFAIK, in distilled water (which is a dielectric) dielectric heating is close to 100%. What about regular (non-distilled) water? Mineral water? Sea water? Salty & wet food? Is dielectric heating still gives more energy to the water/food then the resistive heating i.e. ion drag?


title: How does energy depend on frequency in an alternating current circuit?

text: In what relation is the energy input in an alternating current circuit to its frequency? I'd guess I have to compute something like $$E=\int P(\omega,t) dt=\int U(\omega,t) I(\omega,t) dt, $$ but if say $$U(\omega,t)\propto\sin{(\omega t)},$$ then it seems part of the integral is $\propto\frac{1}{\omega}$, while I would expect the energy to _grow_ with $\omega$.


title: Experiment to find structure of water

text: Who first determined the structure of water (two hydrogen atoms stuck to an oxygen atom at approx 105 degrees), and, more importantly, how was this done?


title: How to calculate the evaporative cooling rate needed to protect a house from forest fire

text: Recently in our area there has been a large forest fire and I've been looking into home defense from such things. I am not a physicist - but can do some basic math. I was wondering how I could calculate if a 'evaporative mister' type system could be used for such to reduce the ambient air temp to stop the house catching fire (dont care about cosmetic damage). The goal would probably be to reduce temperature of air/surfaces of the house by approx 1000F to keep them below combustible temperatures. The area is very low humidity between 4% to maybe 15% during wildfire season. How can I calculate how much water/mist I need to put into the air to reduce temperature below 400F. Very rough simplest equations are fine - I know its not an exact science when dealing with wildfires. I found this formula on wiki but I don't know how to adapt it to use it to calculate water need for a temp drop of               TLA = TDB – ((TDB – TWB) x E)     TLA = Leaving Air Temp     TDB = Dry Bulb Temp     TWB = Wet Bulb Temp     E = Efficiency of the evaporative media.       Anything I forgot/missing - be appreciated to know. Some restrictions/thoughts I had   1. The roof would need to stay generally wet light continuous layer of water   2. Misting/irrigation could not use more then 12 gallons per minute (max well output)   3. Be nice to second use the misting system for outdoor aircon on off time (ie 20% capacity)   4. Windows/glass would need some of IR shielding to stop ignition of furniture inside the house.


title: How does Time traveling work in practice?

text: There are multiple theories about time traveling. One is "proven": The time slows down according to your speed. The satellites in space are traveling faster than us, thus their clocks slows down a bit. So by traveling at the speed of light, you would travel without the time. So the time stops when you are traveling with the speed of light. Then you would travel forwards in time, because when you slow down, the time around you will have gone in the "regular" speed, while being still in your time. Another completely "inverse" theory by Einstein is that extra dimension. The space time. So if you make a wormhole, you would be able to travel past the "bends" in the space time, thus traveling faster than the light. If you arrive before the light, then you would have traveled back in time. I also want to point out that some physicists have managed to send messages back in time with the help of photons, even though we are only talking about microseconds. (I just saw an interview on Discovery Channel..) Which of these (or both) is generally believed to be true, if any? And what about the paradoxes? Do you know any paradoxes regarding this? Maybe you are able to solve them? (One I've found is that if you travel into the future and grab a product that you start selling in the presence, the product will be in the future because you got it while time traveling. Who did make the product in the first place? I'm mostly interested in the paradoxes created while time traveling.


An astronaut camps on the moon for a period of one month as per the earth’s calendar. What would be the path of the earth seen by the astronaut in the lunar sky? (A) The earth remains approximately at a fixed altitude and direction. (B) The earth completes one revolution parallel to the lunar horizon in one month. (C) The earth completes one revolution from east (direction of rising sun) to west (direction of setting sun) in one month. (D) The earth completes one circle around the Pole Star in one month but never goes below the horizon.


title: A different proof for 6 degrees of freedom

text: I want a different proof of 6 degrees of freedom of a solid object made of $\ N$ particles. I am thinking along these lines: Definition of rigid body is $\ modulus[\vec{r_i}-\vec{r_j}]=constant \ \forall\ i,j$ This gives me $\ ^NC_2$ constraints. There exist in total $\ 3N$ equations. So the number of free variables should be $\ n= 3N- \ \ ^NC_2=\frac{N(5-N)}{2}$ Which is clearly not the answer as $\ n$ is $\ N$ dependent, but it should be $\ 6$. **What I want to do is show that :** $$\ number\ of\ constraints \ actually\ required= 3N-6$$ which is the correct answer since I know $\ n=6$ _I am aware of the proof given in Goldstein, Rana Joag etc. What I am asking is how to do it following this approach._


title: Spin-Statistics Theorem - Proof

text: Is this proof of spin-statistics theorem correct? http://bolvan.ph.utexas.edu/~vadim/classes/2008f.homeworks/spinstat.pdf This proof is probably a simplified version of Weinberg's proof. What is the difference? What is the physical meaning of $J^{+}$ and $J^{-}$ non-hermitian operators? I'm especially interested in the beginnig of proof of second lemma. How to get this: \begin{eqnarray} F_{AB}(-p^{\mu}) = F_{AB}(p^{\mu})\times (-1)^{2j_{A}^{+}} (-1)^{2j_{B}^{+}} \\\ \nonumber H_{AB}(-p^{\mu}) = H_{AB}(p^{\mu})\times (-1)^{2j_{A}^{+}} (-1)^{2j_{B}^{+}} \end{eqnarray} Also why under CPT field transform as \begin{eqnarray} \phi_{A}(x)\rightarrow \phi_{A}^{\dagger}(-x) \times (-1)^{2J_{A}^{-}} \\\ \nonumber \phi_{A}^{\dagger}(x) \rightarrow \phi_{A}(-x) \times (-1)^{2J_{A}^{+}} \end{eqnarray} conjugation is from charge reversal, - from space inversion and time reversal. What about $(-1)^{2J_{A}^{-}}$?


title: Is energy conserved in general relativity? Does $\nabla_aT^{ab}=0$ represent the conservation of energy and momentum?

text: For example, the radiation dominated cosmology, the energy density of radiation is propotional to $a^{-4}$ and the volume is propotional to $a^3$, where $a$ is the scale factor. So the total energy of radiation is propotional to $a^{-1}$. So where is the loss of energy of radiation? Is the gravitational field has the energy? Does $\nabla_aT^{ab}=0$ represent the conservation of energy and momentum of matter field in GR?


title: Error in variance

text: I've been exploring techniques in statistical physics, specifically applying them to spin ices. I'm in the canonical ensemble. By using the fluctuation dissipation theorem you can extract useful properties from the variance in energy and magnetization such as the heat capacity (constant V) and magnetic susceptibility respectively. I've included the formulas I'm using below: \begin{align} C_V & = \frac{\partial\langle E \rangle}{\partial T} \\\ & = -\frac{\beta}{T} \frac{\partial\langle E \rangle}{\partial\beta} \\\ & = \frac{\beta}{T} \frac{\partial^2\ln Z}{\partial\beta^2} \\\ & = \frac{\beta}{T} \frac{\partial}{\partial\beta}\left(\frac{1}{Z} \frac{\partial Z}{\partial\beta}\right) \\\ & = \frac{\beta}{T} \left[\frac{1}{Z} \frac{\partial^2Z}{\partial\beta^2} - \frac{1}{Z^2} \left(\frac{\partial Z}{\partial\beta}\right)^2\right] \\\ & = \frac{\beta}{T} \left[\langle E^2 \rangle - \langle E \rangle^2\right], \\\ \chi & = \frac{\partial\langle M \rangle}{\partial H} \\\ & = \beta \left[\langle M^2 \rangle - \langle M \rangle^2\right]. \end{align} Now for my question, is there another computable statistical property which acts as the error for the variance? Such that I can get errors for the heat capacity and susceptibility.


title: Is it possible that 5 planets can revolve around a single star in a single orbit?

text: I'm writing a novel and I'm quite confused if this system could be possible in the real universe. Is it possible that a system exist, where 5 identical planets which could be of same characteristics (Inclination, speed, planetary mass and others) revolve around a single star. Also, What effects would the 5 planets undergo if they are so close? (including the climatic changes and the gravitational, magnetosphere interference.)


title: What is the coefficient $\mu_\text{air}$?

text: I am answering some exercises in thermodynamics, and I am still in trouble with some values and constants. In the exercise, it is given: $\mu_\text{air}=1.8\cdot10^{-5}~\text{kg/m s}$. What for is this value used? In the case, I need to find some tensions in given points, and I know the speed profile of the air. Other question: As I need the tension in some points, and it is about air, is it the same thing as pressure?


title: Two masses attached to a spring

text: I'm trying to understand the solution of the following problem. > Two masses $m_{1}$ and $m_{2}$ slide freely in a horizontal frictionless > track and are connected by a spring whose force constant is $K$. Find the > the frequency of oscilatory motion for this system. In the solutions manual, it is considered that $x_{1}$ and $x_{2}$ are the coordinates of $m_{1}$ and $m_{2}$, respectively, and the length of the spring at equilibrium is $l$. Then, it is defined that, the equations of motion for each mass are: $$ m_{1}\ddot x_{1} = -k(x_{1} - x_{2} + l), \\\ m_{2}\ddot x_{2} = -k(x_{2} - x_{1} - l).$$ And, with some algebraic manipulations, we arrive at the answer. My question is about the right hand side of these two equations. Why is the displacement in the restoring force equal to the difference between the positions plus the length of the spring in the first equation and minus on the second? What is the behavior of the system during the move? What changes in the analysis when I consider the frictional force? Could I consider that this motion has some relationship with the center of mass of the system?


title: Period of oscilation

text: Two masses $m_1$ and $m_2$ are connected by a spring of spring constant $k$ and slide freely without friction along horizontal track. What is period of oscillation? No force influence.


title: Comparing Lagrangian in Special Relativity vs General Relativity for a weak gravitational field

text: This is a sequel to this question. Who knows a difference between the Lagrangian in SR and GR for a weak gravitational field in non-relativistic case? What is the reason of this difference?


title: Relativity conclusions from Michelson-Morley Experiment

text: This is what my textbook says about the Michelson-Morley experiment: "This invariance of the speed of light between inertial reference frames means that there must be some relativity principle that applies to electromagnetism as well as to mechanics. That principle cannot be Newtonian relativity, which implies the dependence of the speed of light on the relative motion of the source and observer." Question: Why must there be a relativity principle that applies to electromagnetism and to mechanics? Why can't they be separate?


title: What is the Fermi energy of (undoped) graphene?

text: All of the sources I have found for this online have been wildly unclear. Many use the phrase "Fermi energy" to refer to the "Fermi _level_ " (which is emphatically _not_ what I'm looking for; I want the Fermi energy as defined in this Wikipedia article: http://en.wikipedia.org/wiki/Fermi_energy ). Fermi energy is always greater than zero. Has anyone ever measured the Fermi energy of graphene? Is there any way to calculate it from known quantities, such as the Fermi velocity, which is approx. $10^6$ m/s? i.e. is there a reason why the usual formula $E_F = \tfrac{1}{2}m_e v_F^2$ wouldn't work here? I read that the Fermi energy for undoped graphene is equal to the energy at the Dirac points, but I read elsewhere that that value is less than zero, which makes no sense because, again, Fermi energy is always greater than zero.


title: true three index tensors

text: is such a _tensor_ , $T_{\alpha\beta\, \gamma}$, possible such that $$T_{\alpha\beta\, \gamma}=T_{\beta\alpha\, \gamma}=-T_{\alpha\gamma\, \beta}=-T_{\gamma\beta\, \alpha}$$ That is, symmetric under two indices, but antisymmetric under the third with the previous too. If so can it be build up by a linear combination and "multiplication" of 4-vectors? Thanks,


title: Hinged bridge statics problem

text: ![enter image description here](http://i.stack.imgur.com/twSPw.jpg) For part (a), is the normal force by the hinge on the bridge at an angle or is it horizontal? For part (b), I know how to resolve forces horizontally and vertically, and to take torques about the hinge, but the information is still insufficient for me to figure out what the tension force is. Any help would be much appreciated!


title: Calabi Yau compactification based on U(1) charges

text: In Green-Schwarz-Witten Volume 2, chapter 15, it is argued (roughly) that we need 6-dimensional manifolds of $SU(3)$ holonomy in order to receive 1 covariantly constant spinor field. And it turns out that Calabi Yau manifolds satisfy this property. Now I understand this reasoning just fine, but I occasionally find in some papers, that Calabi Yau manifolds are "demanded" based on the fact that the sum of all $U(1)$ charges sums to 0? Could someone enlighten me on why this yields the Calabi Yau condition?


title: Is the electric field zero inside an ideal conductor carrying a current?

text: By an ideal conductor, I mean one with zero resistance. Inside an ideal conductor with no current, the electric field is zero, but is the electric field still zero with the ideal conductor carrying a current?


title: Maximize Magnetic Self-Inductance Through a Wire

text: You are given a long length W of copper wire. How would you arrange it to obtain the maximum self-inductance? Why? I am trying to use the equation $$L=\mu_o n^2 l A$$ I try to solve it using a fixed length wire of 10 units, width 1mm and winding it into a solenoid. I plug in values of circumference 10, 5, 2.5 and finding the inductance through number crunching. However, I am getting a larger values for multiple loops but the answer is a single loop (ie. a circle) rather then a solenoid. Here are the sample values I got: $n=1; C=10; r=1.59; L=0.079 \mu_o$ $n=2; C=5; r=0.79; L=0.156\mu_o$ $n=4; C=2.5; r=0.3978; L=0.318\mu_o$ If anyone could enlighten me on the proper way of solving this, I'd appreciate it.


title: Measure the voltage of a resistor without error

text: We have a simple circuit given, a resistor $R_x$ and a fixed current source with $I = 50 \, \mathrm{\mu A}$. Now over the resistor there is a currentmeter which has an internal resistance. In any case some of the current will go through the currentmeter and therefore the result will be slightly off. The question asks us to rearrange that circuit so that no measurement error is made. We can use additional parts like a power source or a resistor with variable resistance or anything else. Is there some way to do this other than using a currentmeter with a higher internal resistance?


title: Blasius boundary layer solutions

text: I'm trying to understand the Blasius boundary layer solution, but I'm having some difficulties. Using wikipedia, I wonder how they get the first formula: http://en.wikipedia.org/wiki/Blasius_boundary_layer. $$\frac{U^2}{L}\approx\nu \frac{U^2}{\delta^2}$$ And how they get to the fourth formula: $$\delta(x) \approx \sqrt{\frac{\nu x}{U}}$$ I feel that those formulas are correlated somehow, but I don't really see how they derive those. I hope someone can help.


title: Which color of an umbrella is more effective against sunlight?

text: It's usually said that black umbrellas are best against sun, since black absorbs most of the radiation . The common umbrellas in market(atleast in India) are painted black outside and silvery inside. However I think the reverse(silvery outside, black inside) should be more effective. The outer color(silvery) will reflect most of radiation, while the black color inside will absorb anything passing through outer layer. Now my questions are :                  1. Which color scheme is more effective ?        2. What is the logic behind the common (black-outside, silvery-inside) scheme ?


title: Unpolarized light vs. randomly rotating polarized light?

text: I am confused with physical picture about unpolarized light. Is unpolarized light very fast rotating polarized light? or co-existing state of two orthogonal polarization? (or something else?) If there is a linear polarizer which rotates very very fast and randomly (the polarizer in imagine), the output light is same to unpolarized light? I don't think so but I am not sure. \-- or, instead of linear polarizer, _a Faraday rotator with magnetic field whose amplitude is randomly chnaged_ can be considered, I think.


title: container with low pressure inside of the high pressure container

text: How will act low pressure container, or what would happen inside the low pressure container when it is placed inside the container with high pressure? And if it is high pressure container inside the high pressure container? Will the container which is inside stay in the centre?


title: accelerated charged particles and interaction with magnetic field

text: In high school we are taught that magnetic field perpendicular to velocity of an charged particle experience perpendicular force that causes it to move in circular path by relation $$qvB=\frac{mv^2}{r}$$ but in drawbacks of Bohr's theory it was proposed that accelerated charged electron orbiting along nucleus will immediately loose energy in form of electromagnetic waves and collapse into nucleus.So My question basically is are we taught wrong about this relation that charged particle according to Lorenz's force will perform circular motion as far as required conditions in equations are provided but will it eventually loose energy in form of electromagnetic radiation and halt it's circular orbit ?


title: numerical diagonalisation comparison of complex Hermition matrix and real matrix

text: we are doing K space calculation(transnational invariant basis) of Hamiltonian, and trying to compare with exact method for same nos of sites and particles, we are getting big difference in ground state energy. Is it coming because of Hamiltonian is complex in K-space calculation and real in exact calculations.I am using complex(ZHEEVR),real(DSYEV) these Lapack subroutines....


title: (Euclideanized) QFT on $S^d$ vs $S^{d-1}\times S^1$

text: * Broadly I would like to understand what is the difference in the physical interpretation of a (Euclideanized) QFT which is on space-time $S^d$ and which is on a space-time $S^{d-1}\times S^1$.  In the later case I am comfortable thinking of it as being a theory actually on a Lorentzian space-time where the spatial manifold is $S^{d-1}$ but the theory is heated to a temperature equal to the circumference of the $S^1$ factor. But for the first case what is the interpretation?   * Specifically consider the action of a conformally coupled Euclidean scalar on $S^d$ space-time as, $S = \frac{1}{2} \int_{S^d} d^dx \sqrt{G} \left [ (\nabla \phi )^2 + \frac{d-2 }{4(d-1) }R \phi^2 \right ]$. (where $R$ on $S_d$ is $\frac{d(d-1) }{a^2 }$) Knowing this is it obvious as to how to write down the action for the same conformally coupled scalar theory on a spatial $S^{d-1}$ at a finite temperature?


title: Potential energy during vertical fall

text: Suppose I have a weightless spring connected perpendicularly to the ground, and it has on top of it some weightless surface. Now, I release some sticky object from height $h$ above the system of light spring-surface. The object eventually hits the surface and the spring is starting to contract till all the kinetic energy of the object is transformed to elastic potential energy. And the system continues to oscillate harmonically. I want to find the maximal contraction of the spring, therefore, I did: (we assume that no energy is lost during the collision) $U_{GR}=E_{k,max}=U_{SP, max}$ $mgh=\frac{1}{2}kx_{max}^2$ where $k$ is the stiffness coefficient. Therefore: $x_{max}=\sqrt{\frac{2mgh}{k}}$ I've chosen my 0 level for gravitational potential energy to be on the same level as 0 level of potential elastic energy. Suppose I want to choose another 0 level for GPE, e.g. at maximum contraction. Then my equation would be: $mg(h+x_{max})=\frac{1}{2}kx_{max}^2$ It obviously leads us to a slightly different $x_{max}$ value. According to the numbers in the answer in my book it seems like the second equation is correct. My question is - how then correct equations should look like if I want to arbitrary choose my PE 0 level at any point? Or why the first one is wrong? Also, I'm wondering why the amplitude of the oscillations is not $x_{max}$ (according to the book it is slightly less the correct $x_{max}$ value, even though we assumed that no kinetic energy was lost. Interesting coincidence: the amplitude on the contrary, according to the book, equals to the $x_{max}$ value of my first equation).


title: Why is Einstein gravity not renormalizable at two loops or more?

text: (I found this related Phys.SE post: Why is GR renormalizable to one loop?) I want to know explicitly how it comes that Einstein-Hilbert action in 3+1 dimensions is not renormalizable at two loops or more from a QFT point of view, i.e., by counting the power of perturbation terms. I tried to find notes on this, but yet not anything constructive. Could anybody give an explanation with some details, or a link to some paper or notes on it?


title: Physics Applications of Fredholm Theory:

text: I find Fredholm theory beautiful, especially the Liouville-Neumann series for solving Fredholm integral equations of the second kind. There seems to be a consensus that these equations are quite useful for physicists, but all I have read is "these are useful in physics but we don't have time for that here . . . blah, blah, blah compact operators blah blah blah existence and uniqueness blah blah blah Banach spaces blah blah blah". (I love all these topics, but the point stands.) So my question is: Is there a simple problem in physics, perhaps suitable for advanced undergraduates, that contorts itself into a Fredholm integral equation? I reject the Poisson equation as an example, because it is too simple and there is no reason to learn Fredholm theory to solve it.


title: The relation between Gauss's law and Coulomb law and why is it important that the electric field decrease proportionally to $\frac{1}{r^{2}}$?

text: My question relates to the third MIT's video lecture about Electricity and Magnetism, specifically from $21:18-22:00$ : http://youtu.be/XaaP1bWFjDA?t=21m18s I have watched the development of Gauss's law, but I still don't quite understand the link between Gauss's law and Coulomb law: How does Gauss's law change if Coulomb law would of been a different one. I also don't understand why is it so important for Gauss's law that the electric field decrease proportionally to $\frac{1}{r^{2}}$ ? For example, what would of happened if the electric field decrease proportionally to $\frac{1}{r}$ , or $\frac{1}{r^{3}}$ ?


title: How we can find the kinetic energy?

text: A solid disk of mass m is rolling along a surface its center has velocity v what is the kinetic energy of disk?I cannot solve the problem,


title: How can a deSitter space have finite size?

text: a deSitter space is a maximally symmetric solution of Einstein equations, I have some problem picturing one thing: this space is past and future (time) infinite but spatial slices have finite size, how can we have finite size in slicing at constant time, and infinite time size when slicing at constant radial coordinate if the solution is supposed to be symmetric in the plane (t,r).


title: Why do we need Higgs field to re-explain mass, but not charge?

text: We already had definition of mass based on gravitational interactions since before Higgs. It's similar to charge which is defined based on electromagnetic interactions of particles. Why did Higgs need to introduce concept of universe-wide Higgs field to define mass, based on interactions with it? And nobody cared about the charge of an electron (for example), which is also basic attribute and constant?


title: General solution to the Helmholtz wave equation with complex-valued frequency in cylinderical coordinates

text: The Helmholtz equation is expressed as $$\nabla^2 \psi + \lambda \psi = 0$$. This equation occurs, for eg., after taking the Fourier transform (with respect to the time coordinate) of the wave equation in free space. While this equation for the case of $\lambda$ real is reasonably well discussed in the literature, the case where the coefficient $\lambda$ is complex-valued is not much discussed in the literature. However, such an equation does come up for the components of the electric and magnetic fields when we try to solve Maxwell's equations within a conductor. So my question is, what is the general solution of the equation $$\nabla^2 \psi + \lambda \psi = 0$$, where $\lambda$ is complex-valued(having both real and imaginary parts), in cylinderical coordinates? Also, can you quote a good reference from where I can get some good information about this?


title: Why is the radial direction the preferred one in spherical symmetry?

text: I am learning about electricity and magnetism by watching MIT video lectures. In the lecture about Gauss's law, while trying to calculate the flux through a sphere with charge in it, the lecturer states that the direction of the electrical field is radial, since it is the only preferred direction that there is (since the problem have spherical symmetry). But why is this the only preferred direction? I think that there is also the direction perpendicular to the sphere, but since this is actually a two dimensional subspace of $\mathbb{R}^{3}$ I think that I can rule this out. Is my conclusion, that since I can't determine any direction (which corresponds to a one dimensional subspace of $\mathbb{R}^{3}$) in any other way, then indeed the redial direction is the only preferred direction?


title: Do gases reflect some IR radiation?

text: The usual definition given for a greenhouse gas is that it absorbs infrared radiation. Of course, then the gas emits its own thermal radiation, and it does so without preference for direction (assuming homogeneity). I was looking at the greenhouse effect heat balance and noticed a larger downward flow from the atmosphere than upward. ![Wikipedia greenhouse effect](http://i.stack.imgur.com/RvKA4.png) I can think of two ways you could explain this:   * the top of the atmosphere is colder than the bottom   * the atmosphere reflects IR from the surface While the first point is trivially true, that doesn't rule out IR reflection. This isn't a completely pointless distinction. Since the atmosphere is cooler than the surface, the temperature of the down-coming IR radiation would be higher if there was reflection going on. So is there some reflection? Or is the downward flow of IR radiation from the atmosphere completely from absorption and remission?


title: Two Qubit problem

text: A two-qubit system was originally in the state $ \frac{3}{4}|00\rangle-\frac{\sqrt{5}}{4}|01\rangle+\frac{1}{4}|10\rangle-\frac{1}{4}|11\rangle $ , and then we measured the first qubit to be 0 . Now, if we measure the second qubit in the standard basis, what is the probability that the outcome is 0 ?


title: Multiquark states and molecular QCD

text: Due to some recent "discoveries" (yet to be completely confirmed), we have hinted the existence of tetraquark particles. **Why QCD exotics like multiquark states beyond n=2,3 (mesons, protons,neutrons,...) like tetraquarks, pentaquarks,...or even glueballs could be useful for new physics? And more generally: Quark spectroscopy and "molecular" QCD/quark chemistry...What could they be useful for?**


title: Do all forces act in the same way where gravity is close to zero?

text: Suppose that I put in the outer space (where gravity from other bodies is negligible) a large, perfectly round sphere totally filled with water. At the bottom (even though "bottom" doesn't make much sense in the deep space) of the sphere there are several marbles, all touching each other. If I make rotate the sphere, all marbles should stay exactly where they are. Right? Is that true regardless of the force that I apply? And what happens, instead, if I strongly shake the sphere?


title: Shape of a string/chain/cable/rope/wire?

text: The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall) and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc length) . **What shape does it take?** My try so far: minimise potential energy of the whole string, $$J(x,h, \dot{h})=\int_0^l gh(x) \rho \frac{ds}{l}=\frac{g \rho }{l}\int_0^l h(x) \sqrt{1+\dot{h}^2} dx$$ With the constraint $$\int_0^l \sqrt{1+\dot{h}^2} dx- l=0$$ If it helps, it's evident that $\dot{h}(\frac{l}{2})=0$. Generally, this kind of equation is a case of a constrained variational problem, meaning that the integrand in $$\int_0^l \frac{g \rho }{l}h(x) \sqrt{1+\dot{h}^2} +\lambda(\int_0^l \sqrt{1+\dot{h}^2} dx- l)dx$$ Must satisfy the Euler Lagrange equation. The constraint must also be satisfied. But, in truth, by this point I am clueless. $\lambda$ is worked through $\nabla J = \lambda \nabla(\int_0^l \sqrt{1+\dot{h}^2} dx- l)$. I have tried this , but get nonsensical answers. Is this method the best? If so, in what ways am I going about it wrongly thusfar?


title: Why is there a potential difference?

text: ![enter image description here](http://i.stack.imgur.com/R70Fu.png) The question then asks for the potential difference between $X$ and $Y$, which is claimed to be $3.6\text{ volts}%$. Why would there be a potential difference in this case? If I connect a lightbulb on $X$, and another on $Y$, it seems very obvious that the brightness would be the same. Or is the standard direction of current important? So the current "encounters" the 60 ohm "first" when flowing to $X$, and the 30 ohm "second" when flowing to $Y$? That seems a little crackpot to me. So if we change the resistor to the left of $X$ to 100 ohms, and the resistor to the right of $Y$ to be 0 ohms, the differing definitions of current flow would actually cause a difference in measurement of potential?!?! The correct answer is worded: ![enter image description here](http://i.stack.imgur.com/kpT1i.png)


title: What if Felix Baumgartner went the other way?

text: How much harder would it have been for Felix to use some powered sled and head for the ISS when he stepped out of his capsule? He was already above most of the atmosphere. BTW, Is that capsule still up there? Why don't more missions use balloons for the first stage?


title: Rotate vector in spherical coordinates

text: I have two arbitrary vectors $\vec{x}$ and $\vec{x}'$ given in spherical coordinates $(|\vec{x}|=x,\theta,\phi)$ (as convention I take the "physics notation" given on Wikipedia http://en.wikipedia.org/wiki/Spherical_coordinate_system). I now want to rotate the coordinate system so that it's $z$-direction points along $\vec{x}$. That means, $\vec{x}$ would have the values $(0, 0, x)$. I now need to compute the angles of $\vec{x}'$. The absolute value does not change, but the angles do. I need to figure out how the angles are in the new coordinate system. With the help of rotation matrices, one is able to get: $\vec{x}' = x' (\sin(\theta')\cos(\phi'-\phi)\cos(\theta)-\sin(\theta)\cos(\theta'),\sin(\theta')\sin(\phi'-\phi),\sin(\theta')\cos(\phi'-\phi)\sin(\theta)+\cos(\theta)\cos(\theta')) \equiv x' (\sin(\alpha')\cos(\beta'),\sin(\alpha')\sin(\beta'),\cos(\beta')) $ Now $\alpha', \beta'$ are the angles in the normal sense but in the new coordinate system. I need a converting rule $\theta', \phi' \to \alpha', \beta'$. Anyone a hint? **Edit (some further explanations):** I need this to compute an integral of the form $\int \mathrm{d}^3x' g(\theta',\phi')f(|\vec{x}-\vec{x}'|)$ and I converted $\mathrm{d}^3x'=x'^2\mathrm{d}x\mathrm{d}\phi' \sin(\theta')\mathrm{d}\theta'$ to spherical coordinates. The problem is that $|\vec{x}-\vec{x}'|=x^2+x'^2-2xx'[\sin(\theta')\cos(\phi'-\phi)\sin(\theta)+\cos(\theta)\cos(\theta')]$ contains angles of both vectors and I need to get rid of the unprimed angles (which is possible in transforming the coordinate system under the integral to point with it's z-direcion along $\vec{x}$).


title: Discord for partially decohered bell state

text: To illustrate discord and its use, Zurek in his paper on discord (NB pdf) gives example of a partially decohered bell state i.e. $$\rho_{AB}=\frac{1}{2}(|00\rangle\langle 00|+|11\rangle\langle 11|) + \frac{z}{2}(|00\rangle \langle 11|+|11\rangle \langle 00|)$$ using the measurement basis for Alice's side. $$\\{\cos\theta |0\rangle + e^{i\phi} \sin\theta |1\rangle,\ e^{-i\phi} \sin\theta |0\rangle + \cos\theta |1\rangle\\}$$ He plotted it in the Fig.1. Now my problem is that I have not been able to reproduce this result. Here is what I got. I can not seem to locate what could be the source problem. The Mathematica code which I used is here. Can anyone see what might be going wrong here.


title: Mechanical Waves

text: In the book Young and Freedman 13th edition, the wave equation is      $y(x, t) = A\,\text{cos}(kx-wt)$      The problem is, I find it hard to console with the fact that      $y(x, t) = A\,\text{sin}(wt-kx)$.      How to derive $A\,\text{sin}(wt-kx)$ from $A\,\text{cos}(kx-wt)$?


title: What algorithms are used for track reconstruction in cloud chambers?

text: In particular I'm interested in any algorithms that can separate multiple tracks from one another reliably.


title: What is the difference between a one-particle state in the fock space and single particle wave function (in momentum representation)

text: If I consider one single Dirac electron in momentum representation, I use the wavefunction $u(p)e^{-ipx}$, however if I consider an one-particle state in the Fock space I use $|p\rangle$. Should it not be same? Obviously the Dirac 1-particle wavefunction is a bispinor, and probably $|p\rangle$ is not a spinor. But could it not be spinor? For a 2-particle wavefunction $|p,k\rangle$, I would use $$\frac{1}{\sqrt2}(u_1(p)u_2(k)e^{ipx_1+ikx_2} - u_2(k)u_1(p)e^{ipx_2 + ikx_1})$$ or something similar. I regret my limited way of expressing correctly. Certainly there is the problem if I consider instead of a half-spin particle a scalar particle, then I would have to build my multi-particles state out scalar wave function instead of spinor wave functions. May be my understanding of the Fock space is incomplete.


title: Orbital speed in an elliptic orbit

text: I want to have a general solution for calculating orbits. Wikipedia says how to put object on circle orbit. We must give it speed $v_1 = \sqrt{g(h_o +R)} $ Where $h_o$ - is the orbit height, and $R$ - Earth radius. But how to calculate the speed that the object must have, if we want to place it in an elliptical orbit? For example: Having massive massive spherical object with mass $M$ and radius $R$. which speed $V$ we must to give to this object to put it on elliptical orbit with eccentricity $\epsilon = E$ , and perihelium $P$?


title: Speed to run a loop

text: So this guy was the first to run a loop and in this (german) article (and also in the video) a certain speed (13.8km/h) is mentioned. Why must he run at this speed and not just "as fast as possible"? My intuition says it has to do with to much centrifugal force and him not being used to it $\rightarrow$ trip hazard.


title: What is the significance of the difference in the eigenvalue equations of Bloch functions for electrons vs photons?

text: any text on photonic crystals will highlight the almost perfect analogy between electrons in a periodic potential and photons in a periodic dielectric. The analogies are: $$V(\vec r + \vec R) = V(\vec r) \Leftrightarrow \epsilon(\vec r + \vec R) = \epsilon(\vec r)$$ $$\psi(\vec r)=e^{i\vec k\cdot \vec r}u_n(\vec r) \Leftrightarrow \vec H(\vec r)=e^{i\vec k\cdot \vec r}\vec u_n(\vec r)$$ But they have a slight difference in their respective operators in their eigenvalue equations: $$(\frac{-\hbar^2}{2m}\nabla^2 + V(\vec r))\psi = E\psi \Leftrightarrow \nabla^2\vec H= \epsilon(\vec r) (\frac{\omega}{c})^2\vec H$$ That is, the QM version _adds_ the periodic part, whereas the EM version _multiplies_ it. Why is this, and is it significant? I don't know enough about differential equations, so maybe it's very insignificant and you could represent either in either way. If I had to guess, I'd say it's related to the fact that electrons and photons have different $k$ dependencies in their dispersion relations ($k^2$ and $k$), but I don't see how the two are related.


title: What does the magnitude of the acceleration mean?

text: I am a little confused as to what the magnitude of acceleration is and what it means.


title: Voltage in a circuit?

text: > The voltage of the battery signifies the difference in voltage between the > positive and negative terminal What does this mean? The definition of voltage difference I'm familiar with is the amount of potential energy charge one coloumb of charge would undergo from point A to point B. At first I thought the quote was saying the voltage of the battery signifies the difference in potential energy one 1 C of charge would have if it were moved from the positive to the negative terminal. But my interpretation of batteries is that they "push" electrons into the wire which push the electrons in front of them ahead which push the electrons in front of them ahead and so on. How can I connect the two concepts of voltage being the difference in potential energy a charge would have if it moved from the positive to the negative terminal with the "pushing" power of a battery?


title: phospholipid bilayer

text: I'm a high school student. The head is hydrophilic, the tail is fatty acid,in other words hydrophobic. Here is the thing I don't understand, all textbooks state that water is repelled by hydrophobic tail, why? The hydrophilic head is composed of polar molecule,and water is polar,so they will attract each other. But why hydrophobic tail will repel polar molecule?Isn't hydrophobic tail is just composed of nonpolar molecules?


title: How to realize long-range interaction of colds atom in an optical lattice?

text: In the Bose-Hubbard model of cold atoms in an optical lattice, we consider only the short-range interaction or on-site interaction. Is it possible to realize long-range interaction similar to Coulomb interaction in the cold atom experiment?


title: Water pressure in free fall

text: The increasing water pressure as you go deeper is generally explained in terms of the weight of the water column above the observation point pressing down. The question, then, is what would happen if you had a big blob of water in free fall, say 100m in diameter-- not big enough to produce large gravitational forces on its own-- and swam to the center of it. I'm imagining some sort of contained environment, here-- a giant space station, or the planet-sized envelope of air in Karl Schroeder's Virga novels, that sort of thing-- so you don't worry about the water boiling off into vacuum or freezing solid, or whatever. Would there be any pressure differential between the surface of the blob and the center of the blob? At first glance, it would seem not, or at least not beyond whatever fairly trivial difference you would get from the self-gravity of the water. But it's conceivable that there might be some other fluid dynamics thing going on that would give you a difference. For that matter, what difference would you expect between the pressure inside the water and outside the water? We know from shots of astronauts goofing around that water in free fall tends to stay together in discrete blobs. This is presumably some sort of surface tension effect. Does that lead to a higher pressure inside the water than out? How much of a difference would that be? Or would you not particularly notice a change from sticking your head into a blob of free-falling water? (Other than, you know, being wet...) (This is just an idle question, brought on by thinking about the equivalence principle, and thus free-falling frames. It occurred to me that somebody here might know something about this kind of scenario, so why not post it?)


title: Are signals exchanged between a rotating frame and a central frame assymetric?

text: This question pertains to EM signals exchanged between an inertial central clock and an orbiting clock i.e. non-inertial frame. (I edited out the variables connected with gravity and separation between bodies) This is how I found the frequency and wavelength received by clock (orbiting) as sent from clock (central). Hereafter let $$c=1$$ and angular speed as the proportion of c $$rω/c=β$$ so that the length contraction factor $$\gamma$$ for each instant in a rotating frame is given as $$γ=\sqrt{1-β^2}$$ Clock 2 is situated at the centre of clock 1’s uniform rotation. We can use the simplified formula $$f_1=f_2/\sqrt{1-β^2}$$ to determine the frequency of a signal that rotating clock 1 receives from central clock 2's emitted frequency. Let central clock 2’s frequency=1, so $$f_2=1$$ Therefore, a familiar relation appears $$f_1 = 1/\sqrt{1 - β^2}$$ or just $$f_1=1/γ$$ The frequency of a signal and its wavelength in relation to the speed of light is given by $$c=fλ$$ Let's view this relation from rotating clock 1's frame. So, $$c_1=(1/γ*f_1)(γλ_1)$$ but from central clock 2's frame, we get the reciprocal $$c_2=(γf_2)(1/γ*λ_2)$$ Is this correct?


title: Rational ratio of frequencies leads to isolating integral of motion

text: Padmanabhan's discussion of dynamics mentions that in general the two dimensional harmonic oscillator fills the surface of a two torus. He further notes that there will be an extra isolating integral of motion provided that the ratio of frequencies is a rational number. > $ > -\frac{\omega_{x}}{\omega_{y}}\cos^{-1}\left(\frac{y}{B}\right)+\cos^{-1}\left(\frac{x}{A}\right)=c$ > > This quantity $c$ is clearly another integral of motion. But- in general - > this does not isolate the region where the motion takes place any further, > because $\cos^{-1}z$ is a multiple-valued function. To see this more > clearly, let us write > > $ > x=Acos\left\\{c+\frac{\omega_{x}}{\omega_{y}}\Big[Cos^{-1}\left(\frac{y}{B}\right)+2\pi > n \Big]\right\\}$ > > Where $Cos^{-1}z$ (with an uppercase C) denotes the principal value. For a > given value of $y$ we will get an infinite number of $x$'s as we take $n=0, > \pm 1, \pm 2, \dots $ > > Thus, in general, the curve will fill a region in the $(x,y)$ plane. > > A special situation arises if $(\omega_{x}/\omega_{y})$ is a rational > number. In that case, the curve closes on itself after a finite number of > cycles. Then $c$ is also an isolating integral and we have three isolating > integrals: $(E_{x}, E_{y}, c)$. The motion is confined to closed (one- > dimensional) curve on the surface of the torus. This last part is not still clear to me. Can someone please explain why a rational ratio of frequencies make a candidate integral of motion single valued and therefore the motion takes place on a closed (one dimensional) curve on the surface of the two torus?


title: How can it be that the sun emits more than a black body?

text: As far as I know, a black body is an ideal emitter. So how can it be that a non-ideal emitter emits more radiation than a black body? This happens only in a very limited area at **around 500nm** , but it still happens: it looks like at the maximum it is around 15% above black body. This seems impossibile for my understand of a black body. Especially because just for that there is the **emissivity value ε** , or better **ε(λ)** > **Wikipedia Emissivity:** Quantitatively, emissivity is the ratio of the > thermal radiation from a surface to the radiation from an ideal black > surface at the same temperature. The ratio varies from 0 to **1** Means **0 ≤ ε(λ) ≤ 1** What is the right interpretation? What is the sun doing there, seems like ε(500nm)=1.15? ![Solar spectrum](http://i.stack.imgur.com/yTUFf.png)


title: Why does ebonite rod gets negatively charged when rubbed with fur

text: What I think is : The protons are present at the centre of the atom with rotating electrons around it so when it is rubbed by fur the electrons get passed from the ebonite rod to the fur leaving the rod negatively charged. But in reality the rod is negatively charged Why ?


title: electrons in elecrtostatic force(please read specification given below)

text: when comb is rubbed with hair, and brought near small pieces of papers, small paper pieces gets a towards comb. Here the comb gets negatively charged and when brought near piece of paper where do electrons go because after sometime attraction of paper pieces towards comb stops and comb doesnt have negative charge then. Why does it happen so ? What is the reason for it ? If a glass rod is rubbed with silk, rodna and silk gets positive or negative charge respectively, an when they are seperated after charge gets nuetral. Why does it happens? What is the reason behind this ?


title: How does rubbing cause the transfer of electrons from one object to the other?

text: I have just learnt about electrostatics. Why would there be a transfer of electrons? Is it because of the difference of the materials (i.e. triboelectric series)? So in the case of two different materials **contacting** each other, will there still be transfer of electrons?


title: If the S-matrix has symmetry group G, must the fields be representations of G?

text: If the fields in QFT are representations of the Poincare group (or generally speaking the symmetry group of interest), then I think it's a straight forward consequence that the matrix elements and therefore the observables, are also invariant. What about the converse: > If I want the matrix elements of my field theory to be invariant scalars, > how do I show that this implies that my fields must be corresponding > representations? How does this relate to S-matrix theory?


title: BICEP2 and string theory

text: Can anybody elaborate on the implications of the BICEP2 result for string theory? The discussion here What experiment would disprove string theory? suggests that refuting string theory is rather difficult. It did not mention that planned/ongoing experiments in the near future could exclude many string models by measuring the polarization of the CMB. I now read that the BICEP2 result might rule out lots of string theory models. Is that true? If so, why? Is this result in the so-called "swampland"? How big a blow is this for string theory?


title: understanding the oscillating part of the Gutzwiller trace

text: given the density of states according to Gutzwiller's trace formula $ g(E)= g_{smooth}(E)+ g_{osc}(E) $ i know that the 'smooth' part comes from $ g_{smooth}(E)= \iint dxdp \delta(E-p^{2}-V(x)) $ for one dimensional system however how it is the oscillating part of the trace obtained ?? :D i mean the sum over lenghts of the orbit (in the phase space) also how does the condition for WKB energies appear ?? $ \oint _{C} p.dq= 2\pi \hbar (n+ \alpha) $ from the Gutzwiller trace ??


title: Detecting Polarization States of Quantum Field

text: (Background) In the scenario where a gauge symmetry is spontaneously broken and the gauge field eats the Goldstone boson to acquire a mass, the massive gauge field acquires a longitudinal polarization. I have seen the argument that the massless field has only two physical polarizations, and I have heard the hand-waving argument that now we can boost into the frame of the massive gauge boson, so I think I understand conceptually what has happened. However, I still don't understand how to show mathematically and rigorously that the new polarization has appeared, and I can't find any really decent explanation. This raises the following question > Given only the Lagrangian of some QFT, and assuming that one does not > already know anything about the answer from more elementary arguments, how > does one (mathematically, rigorously) find the polarizations of a given > field appearing therein? The proof that a massless vector field has only two physical polarizations (at least the one from my QFT I class) assumes the Lorentz gauge condition; this suggests the question > Can one find the polarizations of a field in general gauge? Thank you in advance.


title: Why are there two metric signature conventions?

text: I understand that it is more common in GR for the metric to be given a $(-,+,+,+)$ signature and more common in particle physics (or field theory, as Peskin & Schroeder tells me) to use the $(+,-,-,-)$ metric signature. I'm wondering why. Is there any advantage in these disciplines in terms of actual physics to using one over the other, or it simply an entrenched arbitrary convention?


title: Intuition for actions written as integrals over spacetime

text: Right now I'm simply looking for an intuitive explaination of actions that integrate over a 4-volume element, $d^4x$ rather than a parameter say $\lambda$. More specifically I'm well versed in action principles that say have an action as $\int L d\lambda$. But in trying to understand actions such as the Einstein Hilbert action for example that are an integral over a volume element, in the form $\int(whatever)d^4x$. I'm not exactly seeing from an intuitive stance how these are pieced together, and how/if they relate to the extremization methods I am more familiar with. I do understand the notation of metrics, and GR and all that, that's not the problem. I just don't have any experience working with actions that are integrals over volumes. If anyone can try to point me in the right direction here, or recommend a good text perhaps it would help.


title: can silence happens when 2 sound waves destroy each other

text: Hi is there any possibility that you located between 2 sound sources and u hear nothing? as we know 2 wave in opposite direction will destroy each other...


title: Where does energy go in destructive interference?

text: I have read that when two light waves interfere destructively, the energy contained within is transferred to other parts of the wave which have interfered constructively. However, I am having some trouble grasping this. While in experiments such as Young's Double Slit experiment, there are visible bright bands of higher energy, I would imagine that it be possible to configure light waves to propagate linearly such that the waves interfere only destructively and not at all constructively. Is such an arrangement possible? And if so, to where is the energy in the wave transferred? Similarly, how does the energy transfer from one part of a wave which is interfering destructively to another part which is interfering constructively? These regions may be several meters apart for long wavelength light, and I find it strange that energy can travel between these potentially distant and non-interacting regions.


title: How accurately can we measure human electromagnetic fields?

text: How accurately can our current technological tools measure the human bio- electromagnetic field emitted by a person? Or, to put it differently, does each person have a different electromagnetic field signature, and can we measure that with enough accuracy to tell two people apart by their frequencies?


title: Superspace as the Hilbert Space for Quantum Gravity

text: Let $\mathcal{A}$ be the Ashtekar connection. Since $^{(3)}g_{AB}=i\frac{\delta}{\delta\mathcal{A}^{AB}}$ (see R. Penrose, 2004: Road to Reality. Vintage Books, 1136 pp.), the Ashtekar connection, in a way, represents the graviton. Let $\mathcal{Riem}$ denote the configuration space of GR. If one managed to quantize the metric to yield the graviton, it would make sense to say that the $\mathcal{Riem}$ is also quantized, i.e., Wheeler's superspace becomes a Hilbert space with elements as gravitons. There is an complex inner product defined between the ``de-projections'' (the inverse projection mapping) of gravitons $\mathcal{A,A}_1$, defined as $\langle\mathcal{A}|\mathcal{A}_1\rangle$. An algebra of self-adjoint unbounded operators (of which the Hamiltonian is an element) on this quantum superspace corresponds to a set of all observables. The set of all possible states corresponds to the projective superspace. Thus, is it possible to interpret the superspace as a Hilbert space (as mentioned above)and provide a rigorous mathematical formulation of quantum gravity?


title: Why is the metric linearized to determine the mass spectrum of five dimensional Kaluza-Klein?

text: In this review about Kaluza-Klein theories, (page 1115) in order to determine the mass spectrum of the 5 dimensional theory the metric is expanded to first order. Why this? Why not retain the full metric? Why does it consider only small perturbations? Is it because doing considering the full metric is just too complicated or is something else behind this?


title: Numerical aperture of a lens

text: Using a laser setup, I was asked to determine the aperture of a given lens and then use some geometrical arguments and compare the theoretical value from the manufacturer and the experimental value. However, when I did this, the values _differed by orders of magnitude_. The way I got the aperture was to let the laser light pass through the lens onto a white screen and then keep the screen at a fixed distance from the lens and measure the radius of the light spot obtained. Then I used geometry to determine the angle and thus its sine. Could diffraction be the reason of such a large error?


title: Is the plasma state always visible?

text: All the examples of plasma I have come across are visible. Is there any plasma which is not visible? For example, during a dark lightening we don't see the radiation because its gamma radiation. Is plasma formed during a dark lightening?


When we calculate electric field intensity for a point charge at any point inside electric field the field intensity is $E = F/q$ where $F$ is the force acting on charge $q$. In this case, the charge $q$ should be very small. The practical value of $q$ cannot be so small as needed. In defining electric field by measuring value $F/q$ is smaller than the actual value. **My question:** How can the accurate value of electric field intensity be calculated?   I'm quite confused. Can someone point me out?


title: Deriving the Angular Momentum Commutator Relations by using $\epsilon_{ijk}$ Identities

text: I've been trying to derive the relation $$[\hat L_i,\hat L_j] = i\hbar\epsilon_{ijk} \hat L_k $$ without doing each permutation of ${x,y,z}$ individually, but I'm not really getting anywhere. Can someone help me out please? I've tried expanding the $\hat L_i = \epsilon_{nmi} \hat x_n \hat p_m$ and using some identities for the $\epsilon_{ijk} \epsilon_{nmi}$ which gives me the LHS as something like $-\hbar^2\delta_{ij}$ but I've got no further than this.


title: How to design a deliberately biased coin?

text: For demonstrating basic probability concepts, it would be nice to have a coin- like object that lands heads/tails not in 50/50% ratio, but biased in a way that can be revealed in a short experiment. What I'd like is to make an object satisfying:   * Thin disk shape, say thickness around 1/10 to 1/20 of diameter.   * Lands heads/tails with some given lopsided ratio such as 60/40.   * Feels evenly balanced to the students' hands.   * Can be made by the average machinist, hobbyist woodworker, or 3D printing designer.   * Size not important, but maybe 10-20cm diameter. It's meant to be a theatrical prop visible to a small audience, not an actual coin. Would a disk with an interior hollow zone closer to one side than the other do the job? I doubt it, since the coin will still rotate uniformly in the air, exposing both sides equally to any direction, including the floor. Making both sides "heads" is too obvious a cheat, and I don't want 100/0% probabilities anyway. Note I'm not asking for any practical how-to workshop details, just the physical principle for designing such an object.


title: Why/When can the gauge superfield and/or chiral superfield kinetic term in $(2,2)$ SUSY be ignored?

text: This is in reference to the argument given towards the end of page $61$ of this review paper. There for the path-integral argument to work the author clearly needed some argument to be able to ignore the kinetic term(Kahler potential). But I can't get the argument fully. Just above equation 5.5 in that review the author says, _"..since the Kahler potential is irrelevant we may choose it at will,and in particular we may choose it very small. To a first approximation, in fact, we may ignore it..."_ And on Page 62 in his point 1, he says, _"..Nothing in our argument assures that the resulting kinetic term in the Calabi-Yau sigma model will be sufficiently “large” to ensure that sigma model perturbation theory will be valid.."_   * It would be great if someone can help make precise as to what the above argument means (..espeically the second part about "alrge"..) and flesh out its contents in may be an equation form or something.. Conceptually I would think that trying to ignore the kinetic term of the chiral fields is _different_ than trying to ignore the kinetic term of the gauge fields. like say as written in equation 2.22 on page 11 of this paper.   * Now one can see that in the above paper (unlike in the initially linked review) the author is trying to ignore the gauge kinetic term by trying to take the gauge coupling $e \rightarrow \infty$ limit as in Page 30 of the above paper by Witten.  ..but naively one might think that large gauge coupling is precisely the region where perturbative arguments would have started to fail and the entire idea of trying to minimize the classical potential would have started to become bad..   * But unlike in the review as linked to earlier, Witten's argument crucially needs the kinetic terms of the scalar chiral superfields (..from where the $F^2$ and the Yukawa terms come..). And Witten's argument also crucially needs the gauge kinetic term (from there the $D^2$ terms come..) Then why is he trying to justify the $e \mapsto \infty$ limit? Like he comments towards the end of Page 60, _``..the effects of finite e, are believed to be “irrelevant” in the technical sense of the renormalization group.."_ It would be great if someone could explain these two arguments about ignoring the kinetic term of the gauge fields and the chiral fields.


title: Why isn't there a Heterotic string theory which tensors the fermionic state with the Type II state?

text: The Heterotic (HO and HE) string is found by tensoring the left movers of the bosonic string theory state and the right movers of the Type II string theory state: $$|\psi_{\operatorname{H}}\rangle=|\psi_{\operatorname{B}}\rangle\otimes|\psi_{\operatorname {II}}\rangle$$ The bosonic state is of course based on the Polyakov Action. Now, what if we had another state (I'll call it the k-heterotic state) which is formed by tensoring the fermionic string theory state and the type II state. $$|\psi_{\operatorname{H}}\rangle=|\psi_{\operatorname{F}}\rangle\otimes|\psi_{\operatorname {II}}\rangle$$ The fermionic string theory state is based on the Dirac Action: $$S_F=S_{RNS}-S_B$$ Why is this theory not consistent? Whether the bosonic state is chosen or the fermionic state, how does that matter? Is it because the Dirac Action is imaginary (since it has an i outside the integral if one expands out the Dirac matrix fermionic field product)? Does it have anything to do with that?


title: Spectrum of a quantum relativistic "distance squared" operator

text: This question disusses the same concepts as that question (this time in quantum context). Consider a relativistic system in spacetime dimension $D$. Poincare symmetry yields the conserved charges $M$ (a 2-form associated with Lorentz symmetry) and $P$ (a 1-form associated with translation symmetry). The center-of-mass trajectory $x$ is defined by the equations $$x \wedge P + s = M$$ $${i_P}s = 0$$ I'm implicitely identifying vectors and 1-forms using the spacetime metric $\eta$ Define $X$ to be the point on the center-of-mass trajectory for which the spacelike interval to the origin is maximal. Substituting $X$ into the 1st equation, applying $i_P$ and using the 2nd equation and $(P, X) = 0$ yields $$X = -\frac{{i_P}M}{m^2} $$ Passing to quantum mechanics, this equation defines $X$ as vector of self- adjoint operators, provided we use symmetric operator ordering the resolve the operator ordering ambiguity between $P$ and $M$. In particular these operators are defined on the Hilbert space of a quantum mechanical particle of mass $m$ and spin $s$. > What is the spectrum of the operator $X^2$, for given $m$, $s$ and $D$?


title: Spin of a particle and spin quantum number

text: what actually does the spin quantum number of a particle describe about? What it means when we say photon has spin 1, Higgs boson has spin 0, etc..?? What actually does that numerical value explain? I do hope the + or - sign definitely talks about direction of spin! (kindly elaborate!)


title: Law for tap water temperature

text: I was wondering if anyone put together a law to describe the rising temperature of the water coming out of a tap. The setup is fairly simple: there's a water tank at temperature T, a metal tube of length L connected to it and a tap at the end where temperature is measured. The water flows at P l/s. Given that the metal tube is at room temperature initially, what law describes the temperature of the water at any instant? What is the limit temperature of the water? Thanks.


title: Boiling water and salt

text: I would like to have a good understanding of what is happening when you add salt to boiling water. My understanding is that the boiling point will be higher, thus lengthening the process (obtaining boiling water), but at the same time, the dissolved salt reduce the polarization effect of the water molecules on the heat capacity, thus shortening the process. Is this competition between these two effects real ? Is it something else ?


title: Reference request: statistical inference with real world (chaotic) data, e.g. climate/weather data

text: I'm interested in the process that goes from, for example, huge data sets of temperature, pressure, precipitation etc readings to a model of the atmosphere. I'd like to know about how much relies on a priori knowledge of Navier-Stokes, and how much curve fitting is done. Some sort of general overview of the process (ideally a fairly accessible one) would be perfect. **Edit** I'm looking for a reference, specifically. I know more or less the science from talking to people who do this stuff, but I would like to have some summary article or book chapter overview I can refer to in written work.


title: Modeling falling spheres

text: The following situation interests me and I was wondering if there is software to model it? A large set of n spheres of uniform density and discrete sizes, mass proportional to volume, are dropped together on a narrow inclined plane under low gravity (so they are free to bounce and sort themselves) . The spheres are assigned mutual repulsion and attraction functions according to size, such that balls of a certain size are at equilibrium a certain distance apart. This doesn't reflect any physical phenomenon I am aware of, but it seems like the sort of thing a physicist might model. I have seen physical contraptions that drop balls into slots so they sort themselves into a more or less "normal" distribution, and this is not unlike what I have in mind. But the situation is a little more complicated and I don't really have any preconceived idea about the results. It may be there is no simple program that does this sort of thing, and that too would be an answer. Suggestions appreciated. Thanks.


Magnetic monopole predicted by Dirac nearly a century ago was found in spin ice as quasi-particle(2). My question is Why magnetic monopole found in spin ice don't modify the Maxwell's Equations? (I know they are not elementary particles but quasi-particles.) (1) Dirac, P. A. M. Quantised singularities in the electromagnetic field. Proc. R. Soc. A 133, 60–72 (1931) (2) Castelnovo, C., Moessner, R. & Sondhi, S. Magnetic monopoles in spin ice. Nature 451, 42–45 (2008).


title: Why do clusters of stars eventually dissipate?

text: Why don't the stars in a star cluster attract each other gravitationally, forming one big star? What causes a cluster to disperse the stars in it?


title: Force and Natural Units

text: Today in my Physics lecture I suddenly thought of something. We all know that gravitational force is proportional to the two masses and inversely proportional to the square of the distance between them. So, naturally, there exists a system of natural units which equates the proportionality by setting $G=1$. Here I'm referring to Planck Units. But I realized that even though numerically using this system of units $F=\frac{m_1m_2}{r^2}$, dimension-wise that is wrong because the units do not correspond to the unit of force as defined by Newton's Second Law. Similarly, the electrostatic force, when making $k=1$, has the wrong unit as well. Why do we have to throw in those proportionality constants to convert the units? Shouldn't the units work out to be the same?


title: Mass/light ratio of galaxies

text: I'm really stuck. I need to figure out the mass/light ratio of a galaxy in solar units. I know its mass is 5.7 x 1010 solar masses. I know its absolute magnitude (-17.3) and distance (29 Mpc). I'm feeling dumb here because I think this ought to be clear to me, but I'm getting hung up at the magnitude - luminosity - light part. Here's what I think: mass/light = 100.4*(Magnitude galaxy-magnitude Sun) x (mass galaxy/mass Sun) I get a mass to light ratio of around 90. Am I doing this right?


title: Zero entropy change

text: If you put a object in contact with a heat reservoir that is infinitesimally higher in temperature than the object and allow equilibrium to be reached the entropy change is zero right?


title: Stability of moons around tidally locked exoplanets

text: Can someone send me pointers to work (either theoretical or simulations) showing (in)stability of satellite orbits around tidally locked exoplanets? I want to know firstly if satellite orbits can survive the inward migration and secondly if once the planet becomes tidally locked if that has any implications for the orbits of its satellites - do they too become tidally locked? How do the tidal interactions from the star impact their orbits? In particular, I'm interested in what happens to orbits of earth-sized moons around gas giants that are in the HZ.


title: What is the physical origin of scintillation?

text: The twinkling of stars, or scintillation, occurs because the optical path length of the atmosphere varies in both space and time due to turbulence. This means that when the wavefront from a distant star enters a telescope, it is distorted from the flat wavefront expected for an object at infinity. Because the fundamental Fourier mode of this wavefront varies in time, the average position of the PSF on the retina of a human observer also changes in time; the star appears to shake back and forth. (By this I mean that the wavefront at the telescope may be considered a superposition of plane waves. One particular plane wave is the strongest, or is the median; that is the one I mean by "fundamental Fourier mode". I'm not sure if I'm using exactly the right term. When I worked with an adaptive optics team one summer, we had a "tip-tilt mirror" specifically to correct for this mode, and then the deformable mirror corrected for higher-order aberrations. ) That much makes sense to me. However, I have read on Wikipedia that this is not the dominant effect in what we observe as scintillation. Instead, the overall apparent brightness of the star varies. I presume this has essentially the same physical origin. The wavefront is complicated and dynamic, and so interference effects sometimes reduce and sometimes increase the brightness. What are the details of how this works? How can one work out that this effect should occur? Perhaps a specific example of what a wavefront might do and how this would result in varying brightness would be helpful.


title: How to make a moondial?

text: A question came up on Outdoors StackExchange, How to tell time at night. I wrote an answer to that question, and in my answer I said that a standard sundial wouldn't work without some fiddling, but that an astronomer would know what fiddling was required. (I invite/encourage any qualified astronomers to go there and answer the question, BTW.) So I did some searching around, and some thinking about it. Here's the question. Suppose we have an ordinary horizontal sundial, at a fixed latitude (in the Northern hemisphere), which has been calibrated to correctly show solar time at that latitude. The sundial _works_. Now, suppose there's a Full moon. What adjustments would be necessary, what additional information is needed, what would it take to transform/convert the ordinary sundial into a moondial? The definition of "success" would be that we could look at the shadow and get the "correct" time, where correct might mean up to the precision of an ordinary sundial which might neglect the Equation of Time (is a different equation needed?). One website I read said that no adjustment was necessary, but I'm not sure I agree. If that's not too bad, how would the answer change if we were some days _off_ of a full moon? (Obviously, if we are sufficiently far off then there will not be enough light to make a discernible shadow.) **EDIT:** I've been thinking about it a lot, and thinking about the E.o.T.. The EoT has two (dominant) parts: the Kepler eccentricity part, and the oblique axis part. At first I thought the Kepler part wouldn't matter, but then I learned that the Moon/Earth eccentricity (0.055) is even bigger than the Earth/Sun eccentricity (0.017). So it would seem any reliable moondial would need to be corrected for this problem. I'm still wrapping my head around the obliqueness part. I understand that the style of the gnomon must be angled from the horizontal (equal to the latitude), but that's to make sure the style points toward true north. In fact, even if a horizontal sundial is used at an incorrect latitude, we can fix it by angling the whole sundial so the style points north. Clearly the Moon is in another orbital plane (apparently by about 5 degrees, I'm guessing that's an average), but if we change the angle of the style to compensate for the Moon then it wouldn't be pointing north anymore. So, at the moment, I'm thinking to leave the sundial as-is and then figure (somehow) the sine-wave that describes the Moon's obliqueness. The further this goes the more it looks like I'm talking about figuring an Equation of Moon Time or similar.


Josh Hill, 9, Oakdale Elementary has always talked Theory of Relativity and Astrophysics etc., I can answer most but lately he has stumped me and has been begging me to ask a pro, so here it is.... "What happens when Dark Matter comes in contact with the event horizon of a large Black Hole?” Josh Hill & Mike Hill (DAD) P.S. we should probably anticipate “ What happens when Dark Energy comes in contact with a Black Hole?” as the follow up question , just so we kill 2 birds with one stone , Thanks.


title: What are the various physical mechanisms for energy transfer to the photon during blackbody emission?

text: By conservation of energy, the solid is left in a lower energy state following emission of a photon. Clearly absorption and emission balance at thermal equilibrium, however, thermodynamic equilibrium is a statement of the mean behaviour of the system, not a statement that the internal energy is constant on arbitrarily short timescales. The energy has to come from somewhere during emission, and go somewhere during absorption. Energy in a solid can be stored as kinetic and potential energy of electrons and nuclei, either individually or in collective modes such as phonons and plasmons. In thermal equilibrium energy will be stored more or less in various forms depending on the temperature and material. However, even if most of the thermal energy in a particular solid at temperature $T$ is stored in the form of phonons, it could be that phonons primarily interact with light indirectly via electrons, e.g. a phonon excites an electron in a phonon-electron interaction, which can interact with light via the EM field. Given that light is an EM field, it makes sense to me that it is emitted and absorbed by charged particles. The electron-photon interaction is probably dominant for visible and ultraviolet light, given that metals are opaque, while semiconductors and insulators are transparent to (visible and UV) light with energy lower than their bandgap. However, once you get into energies in the IR and below, or X-rays and above, other mechanisms apparently take over. For example, on the high-energy end of the spectrum I've heard that gamma rays can interact directly with nuclear degrees of freedom, which is reasonable considering that gamma rays are emitted during a lot of nuclear reactions. A review of absorption spectroscopy might give clues to important light-matter interactions over a broad range of wavelengths. Whether all of the these processes are involved in blackbody emission is a somewhat different question. What physical processes mediate energy transfer during blackbody emission, and in which energy ranges are the various processes dominant?


title: Energy of black body radiation

text: Does radiated energy of black body radiation due to the transition of electrons to higher energy state? or due to the increasing vibration of atoms themselves?


title: Why is the black body radiation so important?

text: In the derivation of the black-body radiation formula the assumption is made that the system is an electromagnetic cavity, so that it can be considered in thermal equilibrium. Leaving aside the fact that I don't see why one would make that assumption (what are its mathematical consequences in the derivation?), most everyday sources are not in thermal equilibrium, so how can we adjust the black-body radiation formula for them? Or is it still applicable? Also: in a black-body, the spectral energy density is not a constant, which means that some frequencies contribute more to the energy than others: shouldn't we naively expect that each frequency would carry an equal weight? What is the physical meaning of there being "preferred" frequencies?


title: Equations of motion for a pendulum and spring system

text: The question is available here: ![enter image description here](http://i.stack.imgur.com/MLall.png) I've modeled the building as a rod on a torsional spring (with a pendulum hanging from the top). $\phi$ is the angle from the centre for the pendulum and $\theta$ is the angle from the centre for the building. Taking the Lagrangian, $$L = T - V,$$ we have to find $T$ and $V$. Inertia of the pendulum was given as $mL^2$ and the building (rod) was given as $\frac{mh^2}{3}$, therefore $$T = \frac{1}{2}(mL^2)\dot \phi^{2} + \frac{1}{2}(\frac{mL^2}{3})\dot \theta^2.$$ Potential energy of the pendulum is $-mgL \cos\phi$ and $\frac{1}{2}k\theta^2$, therefore $$V = -mgL \cos\phi + \frac{1}{2}k\theta^2.$$ So, $$L = \frac{1}{2}(mL^2)\dot \phi^{2} + \frac{1}{2}(\frac{mL^2}{3})\dot \theta^2 + mgL \cos\phi - \frac{1}{2}k\theta^2.$$ Evaluating: $$\frac{\partial d}{\partial dt}(\frac{\partial L}{\partial \phi}) = \frac{\partial dl}{\partial d\phi}$$ and $$\frac{\partial d}{\partial dt}(\frac{\partial L}{\partial \theta}) = \frac{\partial dl}{\partial d\theta},$$ I get $$mL^2 \ddot{\phi} = mgL\sin \phi - r_{\phi}\dot{\phi}$$ and $$\frac{mh^2}{3}\ddot{\theta} = k\theta - r_{\theta}\dot{\theta},$$ where $r_{\phi}$ and $r_{\theta}$ are the damping forces on the pendulum and torsional coil respectively. I'm reasonably certain that this is incorrect? This is a coupled system meaning that there should be variables from one in the equation of the other. I'm not entirely sure how to get that. Any pointers in the correct direction would be appreciated. If anything is unclear in my post (such as what variables are or something messed up in latex), please let me know and I will try to correct/clarify.


title: Why Gauss' law is applied?

text: Why Gauss' law is applied? Why is there a need of finding electric field by Gauss' law if we can find the electric field through Coulomb's law? or has it got more applications than Coulomb's law?


Who proposed the bulk-edge correspondence principle? The principle is often quoted in counting the number of zero energy states localized on the interface between two insulators with distinct band topology. However, I could not retrieve who was the first to say that.


title: Why are diffraction gratings not called interference gratings?

text: It seems to me that diffraction gratings are completely described by the double slit experiment-why then is it called a diffraction grating?


title: Can light exist without spacetime?

text: Since the medium in which light propagates is spacetime, would light be able to exist if spacetime did not exist? Is this like one of those chicken/egg problems, or can light be thought of as a legitimately independent entity? This might be bordering on an philosophical question, so if it is, let me know and I'll delete it.


title: periodic boundary conditions for vortex in a square lattice

text: I am trying to follow this paper and track the dynamics of vortex motion on a discrete (square) lattice. The idea is to simulate the time evolution of the Gross-Pitaevskii (GP) equation, which reads (in rescaled units) $$i \partial_t \psi = - \nabla^2 \psi + |\psi|^2 \psi.$$ As initial condition one takes a wavefunction of the form of Eq. (10) in the above-mentioned paper, $$\psi(z) = \prod_{z_+ \in [Z_+]} \frac{(z-z_+)}{|z-z_+|} \prod_{z_- \in [Z_-]} \frac{(z^*-z_-^*)}{|z-z_-|}$$ where $z=x+iy$ are complex coordinates. This wavefunction describes a set of vortices (V) with coordinates $z_+$ in $Z_+$ and a set of anti-vortices (AV) with coordinates $z_-$ in $Z_-$. This is equivalent to using a wavefunction of the type $e^{i \phi}$ (polar coords.) for vortices and $e^{-i \phi}$ for anti- vortices, with $\phi$ the polar angle. One can calculate the velocity as gradient of the phase of the complex wavefunction. An example of the associated velocity field, for a V at (x,y)=(0,2.5) and AV at (0,-2.5) is shown below. ![velocity-lines](http://i.stack.imgur.com/nLZqZ.png) This should correspond to Fig. 1 in the paper. However, there are several things I do not understand. First, why do the authors say that they cannot look at the dynamics of just one vortex, but must include an anti-vortex in the initial conditions to satisfy the periodic boundary conditions? Second, apart from the initial V-AV pair, they also seem to include "a few mirrow images with respect to the boundary". However, they do not specify how many nor where they are positioned. (I assume that the mirrow image of a V is and AV and vice-versa, please correct me if I'm wrong). Lastly, they mention "evolving the system in imaginary time" in order to "cool it down" (although no temperature is included in the model!) and then "turning on a superflow" and continuing the evolution in real-time. I though all was needed was the discretization of the GP equation and following its evolution given the initial wavefunction and periodic boundary conditions ($\psi(\text{left margin})=\psi(\text{right margin})$ and $\psi(\text{top margin})=\psi(\text{bottom margin})$). **Edit** Following the suggestion of @BebopButUnsteady, I repeated the 'unit' of my system, the V-AV pair, until obtaining the following tiling pattern (vortices are circles, AVs are squares) ![tiles](http://i.stack.imgur.com/OQSXa.png) Let us first look at the real (left) and imaginary (right) parts of the wavefunctions for the initial V-AV pair: ![initial-boundaries](http://i.stack.imgur.com/ECgmG.png) One can see that, especially in the imaginary part, the values on the boundaries are not equal. Now we start adding copies of the "unit cell" along the x axis, and plot a cut though the imaginary part of the wf: ![boundaries-tiled](http://i.stack.imgur.com/VVDSm.png) It appears that, as we increase the number of copies, the values at the ends get closer and closer to 0, which would be the ideal periodic case. Of course this is just numerics, I have no formal proof yet that this procedure actually converges.


title: Intensity of particles with zenith angle dependence

text: The intensity of particles come to sea level depend to the zenith angle $I=Iv (\cos(z))^n$, where $z$ is the zenith angle and $n$ depend to the particle. I know the vertical intensity depend to the energy or momentum of the particle, for exemple, to muons, $n$ is about 2 and vertical intensity is $0.0094\, \mathrm{cm}^{-1}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ to $>0.35 \mathrm{GeV/c}$. I would like to know what is the vertical intensity and the $n$ for electrons, positrons, protons and hadrons.