title: What creates black streams in fountain-type fireworks?

text: For the New Year celebration of 2014, my nephews set off a series of fountain- type fireworks (as shown below). ![](http://i.stack.imgur.com/BgQYd.jpg) When one looks carefully into the shower of light, one notices that a fair number of "long, black and stringy streams of light" are coming out of the fountain. Note: I do not see any black streams in this picture! After reading this online article from the American Chemical Society, the colors of light are, of course, created from electrons jumping orbitals. However, how are these “black streams” created? I assume that somehow visible light is being absorbed to create these "black streams of light". What mechanism is responsible for this to occur? Are there small bits of matter that are large enough and cooled enough to absorb visible light? I really don’t know. Any help would be much appreciated.


title: How can we model intrinsic curvature?

text: Can it only be done in Euclidean space? Doesn't Euclidean space only model extrinsic curvature?


title: What is the fate of a 3-Torus universe?

text: Since it is flat, will it expand forever like a flat and open universe or collapse like a closed and curved universe?


title: How does an object regains its neutrality after being charged by rubbing?

text: Objects (like comb) can be charged by rubbing as charged particles, particularly electrons, are transferred from one object to other. This can be seen as the object (comb) attracts small bits of paper. After some time, the charge on the body seems to disappear. How does this charge disappear without any external influence?


title: What is the half-life threshold for an isotope to be considered stable?

text: What minimum half-life an isotope should have to be considered stable?


title: Why are black holes special?

text: A black hole is where it's mass is great enough that light can't escape at a radius above the surface of the mass? I've been told that strange things happen inside the event horizon such as space-time ceases to exist. Why does the escape velocity of light warrant space-time to not exist or the mass to be confined to a single point of infinite density. I mean what's make the escape velocity being the speed of light so special compared to other speeds?


title: Why 3He(n,p)3H nuclear reaction proceeds but 3He(n,gamma)4He heavily suppressed?

text: The neutron capture reaction 3He(n,p)3H is very useful for neutron detection as the Q value of ~700keV is converted to kinetic energies in the produced p and 3H. These charged products can then ionize gas mixed in with 3He in a gas chamber and then be detected. The cross-section for this reaction is massive at ~kilobarns for thermal neutrons (~2000m/s). My question is: why does the reaction 3He(n,gamma)4He not occur very often? The Q-value for this is ~20MeV! This is because the 4He nucleus is so tightly bound. A quick literature search for this puts the cross-section at ~microbarns. Am I missing something? Is there some selection rule I'm not aware of?


title: Gravitating sigma models

text: I am looking for a review or book on sigma models in (super)gravity theories, which arise from dimensional reduction.


title: Which CFTs have AdS/CFT duals?

text: The AdS/CFT correspondence states that string theory in an asymptotically anti-De Sitter spacetime can be exactly described as a CFT on the boundary of this spacetime. Is the converse true? Does any CFT in a suitable number of spacetime dimensions have an AdS/CFT dual? If no, can we characterize the CFTs which have such a dual?


title: Solution to the Schrodinger equation for periodically time dependent Hamiltonians

text: I have a Hamiltonian which is time dependent but possesses periodic symmetry: $H(t+t_0)=H(t)$. Is there any clever techniques to exploit this? Edit: In particular, I would like a practical method to simulate the dynamics of such a system (as opposed to naive time-slicing).


title: Could the cosmic microwave background radiation (CMBR) map be used as a backup for GPS navigation?

text: Using a sextant and a clock you can navigate by measuring the position of the observable stars and comparing them with the known map of the fixed stars. However, if it was cloudy couldn't you theoretically use the CMBR map instead? The cosmic microwave background radiation (CMBR) map is a constant pattern in the sky through which the earth travels and rotates. Given an accurate clock, microwave antenna and model of the earth's orbit, shouldn't it in principle be possible to match the patch of the the CMBR pattern above you with the overall CMBR map and therefore calculate where you are located on the earth's surface? Yes, I appreciate that measuring the CMBR sufficiently accurately at 160GHz is not trivial and needs a large antenna (preferably a phased array), probably with a cryogenically cooled microwave receiver. However, an antenna of this size should be easy to accomodate onboard a large military ship for example. There would be a tactical advantage in the USA turning off the GPS satellites and switching to CMBR-based navigation prior to launching an attack. Presumably for this application some of the the major sources of microwave interference that scientists normally have to carefully subtract in order to get the classic CMBR map could be left in the data if they are from outside the solar system (e.g. milky-way sources of microwaves)? What are the other practical issues and how might they be resolved to make a working system?


title: Variation - Electric pressure on a sphere?

text: I solved the following question(Answer is correct): > **Find the force with which two hemisperical parts of a uniformly charged > hollow sphere repel each other?(charge density: +$\sigma$)** > > Answer: ![enter image description here](http://i.stack.imgur.com/h2Blp.png) > > Radial force on strip is: > $$dF=\left(\frac{\sigma^2}{2\epsilon_0}\right)(2\pi R^2\sin\theta d\theta)$$ > Total force on hemisphere is: $$F=\int > dF\cos\theta=\int_0^{\frac{\pi}2}\frac{\pi > R^2\sigma^2}{\epsilon_0}\sin\theta\cos\theta d\theta$$ $$F=\frac{\pi > R^2\sigma^2}{2\epsilon_0}$$ * * * **_My question is:_ If the hollow sphere is uniformly charged on one half with a uniform charge density $+\sigma_1$ and its other half is also charged at charge density +$\sigma_2$.Now find the force with which the two halves repel?** Similiar to previous question force can be given as: $$F=\int \frac1{4\pi\epsilon_0}\sigma_1\sigma_2dS_1dS_2$$ But it doesn't give the answer, or I must say it can not be manipulated to an integrable form.Note that this is not a problem of integration.It is simple manipulation, as my teacher says, he suggests using previous problem. _Answer_ > $$F=\frac{\pi R^2\sigma_1\sigma_2}{2\epsilon_0}$$


title: Post Problem Analysis - Rod in a cylindrical time varying magnetic field?

text: **A metal rod of length $l$ is placed (as shown in figure) in a cylindrical time varying magnetic field. Find the potential difference across it.** ![enter image description here](http://i.stack.imgur.com/XgIjQ.png) My answer: As electric fields as forming circles around the centre with magnitude $$\frac12r\frac{dB}{dt}$$ whose magnitude is same along any chord at a fix distance from centre: $$\Delta V=E.l=\frac12r\frac32at^{\frac12}.l$$ $$\Delta V=\frac34arlt^{\frac12}$$ **_My question:_ Is $\Delta V =V_M-V_N$ or $\Delta V=V_N-V_M$ $\bf OR$ equivalently which side is at high potential?** Possible   * $(i)$ As Field lines are circular from $M$ to $N$, $M$ must be high potential.   * $(ii)$ As this field line apply a force on electrons- in the rod- towards left, then $M$ must have excess $e^-$ and $N$ must have deficiency; so $N$ would be high potential as $M$ is $(+)$ and $N$ is $(-)$.


title: Classical analogue of Heisenberg and Schrödinger pictures?

text: What do the Heisenberg and Schrödinger pictures in quantum mechanics correspond to in classical mechanics (if they correspond to anything)? It's kind of weird, because (if I understand it well) in classical mechanics the state of the system is determined by the dynamical variables positions and conjugate momenta, so the time dependence of the dynamical variables is the same as the time dependence of the state vector, I don't see whether the two could be separated. Nevertheless can it be done somehow?


title: What is the terminal velocity of a sheep?

text: _Inspired bythis question on Gaming.SE_ Using actual in-real-life physics, what would the terminal velocity of a sheep actually be? I would assume it would be around 50m/s, but I might be wrong. Bonus questions:   1. How big would the splat of the poor sheep be? (I'M JOKING. PLEASE DO NOT ANSWER THIS!)   2. What would the terminal velocity of a chicken be? Animal-Friendly answers preferred.


title: How to distinguish high-energetic muons and electrons in the CMS and ATLAS muon detectors?

text: At a typical energy of about 100 GeV, a muon has a Lorentz factor of about 1000, an electron about 200.000. The flight time to the detector should be around 30 ns (assuming d= 10m from the collision point). While e- would practically have the speed c, the muon's speed is about 0.9999995 c, causing a delay of about 15 fs, barely measurable I think. Is there a way to distiguihs e- from mu, unless we assume prior knowledge (that they have passed the electric calorimeter, about the penetrating power etc). Or, to put it in another way: what is the energy threshold below which they can be distinguished directly?


title: Day/night cycle in Greenland

text: I have heard that in Greenland there is day for 6 months and night for 6 months. Is this true? If so, how does it happen?


title: Electric field outside a hollow cylindrical conducting shell

text: Imagine that a point charge $+Q$ is located at radius $R$ and height $z=0$ inside of an infinitely long conducting cylinder shell of inner radius $a>R$ and outer radius $b$. From what we know of perfect conductors, we know that $Q_{induced}(r=a) = -Q$, $Q_{induced}(r=b) = +Q$, and the electric field inside the shell is $E(a<r<b)=0$. Is there a way to figure out the magnitude and direction of the electric field outside of the conducting shell as a function of position?


title: Why are there direct bandgaps?

text: This Question has been bugging me for sometime. Some semiconductors have direct bandgaps and indirect bandgaps. So what causes a direct bandgap to occur? The physics behind ,why there are direct bandgaps? I collected some data on a dozen compound semiconductors from handbooks (III-Vs, II-VIs and IVs) (35+ compound semiconductors if you count multiple crystalline phases of the same material) and performed anova with crystal structure, atomic number & location of constituting elements on the periodic table as variables. I found that the biggest influence on whether a semiconductor has a direct bandgap or indirect bandgap was atomic number of constituting elements and not crystal structure or location of the constituting elements on the periodic table. Could it be because a high atomic number entails a strong nuclear field from the constituting atoms in the unit cell that somehow aligns the conduction and valence bands in momentum space? Any ideas, opinions, relevant papers? Thanks


title: Transmittance of glass

text: Glass has low transmittance for infrared light. Does glass reflect or absorb infrared light? Greenhouses are able to reflect infrared as I understand it.


title: Geometry in diagonal matrix and inertia tensor

text: For this problem, can anyone explain to me why when $x_1$ axis is aligned with the diagonal of the cube, the resulting inertia tensor will become diagonal? How to interpret this result geometrically? I mean, is there some tricky way for some geometric shape that I don't have to compute the eigenvalue, eigenvectors to find the principal axises, but by observation, I can make a guess first. ![enter image description here](http://i.stack.imgur.com/HyEC3.png) ![enter image description here](http://i.stack.imgur.com/Rkpfz.png)


title: What is the physical meaning of group velocity for elastic waves through crystals?

text: In a chapter about phonons they define group speeds for elastic waves in crystals as the derivative of the dispersion relation: $$v_g = \frac{d{\omega}}{d{k}} $$ I wonder though how they come to this equation, i.e. what is the physical meaning of $v_g$? I find on the internet information about the physical meaning about the group velocity of wave packets, but I don't see how I can interpret an elastic wave as a wave packet. So I hope someone can clarify the meaning of 'group velocity' for this particular case of elastic waves in a crystal.


title: What is an intuitive picture of the motion of nucleons?

text: I understand the "motion" of electrons within an ordinary atom (say argon at room temperature and pressure). They are moving in "orbits" defined by quantum mechanical wavefunctions where the "orbits" are smeared out in space with some locations more probable than others but they don't possess a definite trajectory. But in some sense, we know they are moving around the nucleus in some rough shape orbits even if we can't hope to describe the motion in a Newtonian sense. My question is what is the similar "intuitive" picture of nucleons in an ordinary atom. Is the location of the nucleons fundamentally more "locked down" than for electrons? If so, does the nucleus look similar to a solid where the individual nucleons are vibrating (maybe w/ some QM smearing) around equilibrium positions? Also, recognizing the strong force will dictate what is possible, can nucleons "jump" around their neighbors to a different "location" in the nucleus (maybe say with a coincident jump of a similar particle exchanging positions)?


title: Stationary Solutions

text: An unbelievably basic question, but it's something I've never been taught. Am I right in thinking that the following defines a stationary solution? Let $\phi$ be some dynamical variable satisfying a differential equation $D(\phi)=0$ with respect to some parameter $t$. Then $\phi$ is called a **stationary solution** or a **stationary state** if all $t$ derivatives of $\phi$ are zero. Could someone point me to a resource where this is defined? A quick google threw up nothing useful, but perhaps I was looking in the wrong place!


title: Benefits of the sign convention for electrons?

text: Benjamin Franklin considered electrons to be positive, but J.J. Thompson considered them negative. We obviously went with J.J. Thompson's convention. Why? What were the benefits of moving to J.J. Thompson's convention when Benjamin Franklin had already established a convention? Related: Why is the charge naming convention wrong? Related: Why are electrons defined to have negative charge?


title: What are the Electric and Magnetic Properties of Aluminum Oxynitride?

text: Is Transparent Aluminum (Aluminum Oxynitride) a good conductor of electricity? Also, is it attracted by a magnet?


title: Acceleration of pendulum

text: **At what point of a pendulum's swing is its acceleration the greatest? What does this tell you about where the forces act in a pendulum?** Is my answer correct? The force that causes the acceleration of the pendulum is due to the weight of the pendulum. The weight is constant but if the pendulum is still, hanging in a direct downwards position, then the weight does not make the pendulum swing. This is because the force is vertical and the pendulum's possible motion is horizontal when it's at the bottom. If we pull the pendulum some distance to the side and release it, then it will swing. That's because when the pendulum is taken to the side, a component of the weight acts in the direction that the pendulum can move - along the arc. It's often convenient to take a vector (like the pendulum's weight) and resolve it into 2 components that are perpendicular. For a pendulum, the components of the weight that help us are along the string (or rod) and perpendicular to the string. A perpendicular to the string would be tangential to the arc of possible motion. Give the symbol Wt to the component that is tangential to the arc. When we take it to the side (so far that the string (or rod) was horizontal), then the weight would of course point downwards and that direction would be tangential to the arc of the pendulum's possible movement. In that case, Wt is equal to the weight. So, the entire weight provides force for the acceleration of the pendulum. However big the swing is, the pendulum's acceleration is greatest when the component of the pendulum's weight lies tangential to the arc of possible motion.


title: What is the need to consider a singular spacetime?

text: To have a consistent superstring theory (which is to avoid the conformal anomaly on the worldsheet CFT) we are forced to build our theory on the critical dimension $n=10$. However, the Standard Model, seen as an effective low energy theory lives on $n=4$. So we are forced to compactify the background spacetime for the string theory, as to be of the form $\mathbb{R}^4\times M$ where $M$ is a compact and "very small" riemannian manifold. $M$ could be a torus, for example. To save some of the supersymmetry after compactification we are furtheremore forced to take $M$ to be Kahler. Given this, my question is: From a physical viewpoint, why do we usually consider nowadays $M$ to admit singularities? In other words why should $M$ be an orbifold and not just a smooth manifold?


title: Are two touching conductors connected in parallel or in series?

text: Consider the following problem: There are two spherical conductors $A, B$, with capacitances $C_A, C_B$ resp. Conductor $A$ is supplied some charge and is found to have a potential of $160 \space V$. Conductor $B$ is also supplied some charge and is found to have a potential of $50 \space V$. They are then connected so that their charges equalize. Now, their common voltage is $140 \space V$. Find $C_A: C_B$. I started off with the basic relation, $Q_A = C_AV_A = 160\space C_A$ similarly, $Q_B = 50C_B$. Now, when they are connected the total charge will equal $Q_T = Q_A + Q_B = 160C_A + 50C_B$. Now, the total capacitance of the combination of these spheres will be $C_T$. I can't seem to decide if these spheres should be considered to be connected in parallel or in series.


title: Is there a Transparent, Non-Magnetic Conductor?

text: I am looking for a transparent (visual wavelength: 390 to 750 nm), non- magnetic (not attracted by a magnet) electrical conductor that could be used for a physics demonstration. Is there such a substance? If yes, is there a cheap one?


title: Entropy of a naked singularity

text: According to the wikipedia article http://en.wikipedia.org/wiki/Naked_singularity: "Some research has suggested that if loop quantum gravity is correct, then naked singularities could exist in nature, implying that the cosmic censorship hypothesis does not hold. Numerical calculations and some other arguments have also hinted at this possibility." The entropy of a black hole is proportional to its horizon area. What is the entropy of the black hole if the cosmic censorship hypothesis fails to hold? Do we assume this hypothesis for the expression of the entropy?


title: What is the correct Orientation of Earth's Rotational-axis w.r.t Ecliptic at Equinox?

text: I am boggled with the position of earth relative to the sun at the "Equinoxes". According to the wikipedia: > an equinox occurs twice a year (around 20 March and 22 September), when the > tilt of the Earth's axis is inclined neither away from nor towards the Sun, > the center of the Sun being in the same plane as the Earth's equator. My confusion starts from here: if earth's rotational-axis is neither tilted towards nor away from the sun then it means that celestial-equator and ecliptic become parallel to each other at equinox. But which is, of course, ridiculous because it would mean that earth's rotational axis's tilt of $23.5^o$ reduces to $0^o$ at equinox. If above is not true then what is the exact orientation of the earth in space at equinox? Help in the matter will be highly appreciated.


title: Special relativity and quantum mechanics

text: I know how the Dirac's equation about the relativistic quantum mechanics works. Can anyone tell me how can one combine special relativity and quantum mechanics as a whole - special relativity is valid only under constant speed while the speeds of electrons in quantum mechanics vary with positions.


title: Calculating Joule heating in magnetic field

text: I have problem with calculating Joule heating in alternating magnetic field perpendicular through circulate plate with radios a and height h. Lets say that alternating magnetic field is in form of this equation $\mathbf B=\mathbf B_0\cos(\omega t)$, so I guess by Maxwell-Faraday equation you can get out E field (because of eddy currents): $$\oint_l\mathbf E\cdot d\mathbf l=-\int_a\frac{\partial\mathbf B}{\partial t}\cdot d\mathbf A$$ So I inserted here for circle and I get out this: $$ 2\pi r\cdot\mathbf E=-\pi r^2\cdot\frac{\partial \mathbf B}{\partial t} \\\ 2\pi r\cdot\mathbf E=-\pi r^2\cdot\omega\mathbf B_0\sin(\omega t) \\\ \mathbf E=\frac r2\omega\cdot\mathbf B_0\sin(\omega t) $$ I take Joule heating equation $$ P=\mathbf J\cdot\mathbf E $$ and united with this equation, $\mathbf J=\sigma\mathbf E$, and get this $$ P=\sigma\frac{r^2}{4}\omega^2B^2\sin^2(\omega t) $$ and I said $\sin^2(\omega t)=\frac12$ so that to get rid of $\sin(\omega t)$ and get this: $$ P=\sigma\frac{r^2}{8}\omega^2B_0^2 $$ The total power I get by integrating over the volume of plate: $$ P_d=\frac{\sigma}{8}\omega^2B_0^2\int_0^ar^2\cdot2\pi\cdot h\cdot rdr \\\ P_d = \frac{1}{16}\sigma\pi ha^4B_0^2\omega^2 $$ But the right solution to this is $$ P_d = \frac{1}{16}\gamma\pi ha^4B_0^2\omega $$ First I think my volume is wrong and how do you get rid of $\omega^2$ and how can I get $\gamma$. Can someone please help me with this?


title: If photons carry 1 spin unit, why does visible light seem to have no angular momentum?

text: Spin 1 silver atoms have a definite spin axis, e.g. up or down along an axis labeled X. This in turn means that they carry angular momentum in an overt, visible fashion. However, spin 1 photons do not seem to display an experimentally meaningful version of a spin axis, unless I'm completely missing something (very possible!). Instead, photons in the form of light display an effect we call "polarization," by which we mean the light has a definite vibrational orientation in space. This effect follows the same 90$^\circ$ rules as the basis states for massive spin 1 particles, but lacks the directionality of those states. So for example, if X is horizontal and Y is vertical, vertically polarized light could be interpreted as exhibiting a rotation in YZ plane, which is the same plane of rotation that gives rise to -X and +X spins for particles with mass. But since photons have no mass and travel at $c$, there is no way to assign $\pm$ to this nominal rotation. Instead, the light appears to be composed of particles with no visible spin, or (perhaps) alternatively as superpositions of equal and cancelling quantities of -X and +X spin. Circular polarization seems at first glance to provide a solution by providing distinct clockwise and counterclockwise directions. I've gone that route myself, but the more I look at it, the more sure I am that it's a bogus assignment. If nothing else, circular polarization can always be decomposed into two planar polarization that have a relative phase shift. Furthermore, the idea of a spin axis pointing along the infinitely compressed direction of propagation of a massless particle is problematic at very best. Circular polarization still seems to me the most promising path for finding real angular momentum in photons, but if it is the solution, I must admit that the more I look at it the less I see how. So, at last, my question: If there is no way to demonstrate experimentally that an arbitrarily small unit of light carries explicit, non-zero angular momentum, how then does a photon manage to convey the 1 unit of spin required needed for it to balance angular momentum in particle interactions?


title: about the Atiyah-Segal axioms on topological quantum field theory

text: Trying to go through the page on Topological quantum field theory - The original Atiyah-Segal axioms \- "Let $\Lambda$ be a commutative ring with 1, Atiyah originally proposed the axioms of a topological quantum field theory (TQFT) in dimension d defined over a ground ring $\Lambda$ as following": $(1):$ A finitely generated $\Lambda$-module $Z(\Sigma)$ associated to each oriented closed smooth d-dimensional manifold $\Sigma$ (corresponding to the **homotopy axiom** ). $(2):$ An element $$Z(M) \in Z(\partial M)$$ associated to each oriented smooth (d+1)-dimensional manifold (with boundary) $M$ (corresponding to an **additive axiom** ). Pardon my question is really stupid, if not just naive: **Questions** : $\bullet (i)$ How do I see this axiom $(2)$: $Z(M) \in Z(\partial M)$ is correct? Instead of $Z(M) \ni Z(\partial M)$? It seems $M$ is one higher dimension than its boundary $\partial M$, so why not more intuitively $Z(M) \ni Z(\partial M)$? Or is that a misleading typo in Wiki, instead we have $$Z(\Sigma) \in Z(\partial M)$$ with $M=M^{d+1}$ being one higher dimensional than $\Sigma=\Sigma^{d}$? $\bullet (ii)$ How do I _physically intuitively digest_ (1) as a **homotopy axiom** and (2) as an **additive axiom**? ps. I suppose we shall view $Z(\Sigma)$ as a TQFT partition function on the manifold $\Sigma$.


title: How many particles are created in the strong electromagnetic field?

text: Consider a vacuum of charged massless scalar field. Then the uniform and isotropic electric field $E$ is turned on for a time interval $\tau$. The question is, how many scalar particles are created?


title: Does this* refraction experiment correctly conclude faster than light travel?

text: This question asks if a particular experiment is correct in its conclusion. This experiment, conducted by Alfred Leitner, is shown in a 1975 physics instructional movie. It claims that the experiment proves faster than light travel by the phase speed of the light. Is this conclusion correct, based on the experiment?   * The experiment video can be found here: http://alfredleitner.com/refraction.html The claim can be seen at about 3/5 and 7/8 ths in the movie, however you will really need to watch the whole thing if you want to understand the claim. dont worry, you will find it easy to watch and worth watching.


title: Elegant approaches to quantum field theory

text: I have been reading _Quantum Mechanics: A Modern Development_ by L. Ballentine. I like the way everything is deduced starting from symmetry principles. I was wondering if anyone familiar with the book knows any equally elegant presentation for quantum field theory. Weinberg's books start off nice with the irreducible representations of the Poincare group/algebra but the later chapters lose me with the notation. Also, most books I've read on QFT (Srednicki, Peskin and Schroeder, Mandl and Shaw) make a valiant initial attempt at a nice consistent framework but end up being a big collection of mathematical recipes and intuitive insights that seem to work but the overall structure of the theory seems to be sewn up. The relativistic equations crop out of rather flimsy arguments, the canonical anti/commutation relations are imposed out of density indeterminate air, functional methods are developed cause we know no better, infinities come about with renormalization theory to the rescue but it seems very alien from the initial context. Is there any approach that ties all these things together in an elegant mathematical framework which accounts for all the patch up work that is needed? I am not talking about axiomatization just a global point of view that encompasses all the issues.


title: How to use Legendre polynomials in order to determine the (an)isotropy of an on-lattice cluster aggregate?

text: I am currently testing various models of on-lattice (square lattice in two dimensions) cluster growth for anisotropy. I end up with a cluster, the boundary of which, in case of a truly isotropic model, should look like a circle. In anisotropic cases the cluster boundary will deviate from the circular shape. I've been told that the Legendre polynomials can be used in order to determine the anisotropy of a cluster, but I'm not exactly sure of how I can use these Legendre polynomials in order to say something about the isotropy or otherwise of the clusters. I gather that one can write the angular functional dependency of the cluster boundary in terms of a Legendre series due to the orthogonal nature of the Legendre polynomials, but once I've calculated the coefficients of the series I'm not sure how to interpret them in terms of anisotropy of the cluster or even if this is the correct thing to be doing. Any hints, tips or further reading would be appreciated. I am a humble mathematician, so please go easy on the physics jargon as I may not be well versed in it. Thanks for your time and help.


title: Pure state - density matrix - real life example of boxes in warehouse

text: So if there are a billion boxes in a warehouse, I would like to know conceptually how to tell if it is in a pure state. I know that if it is in a pure state (not mixed) that the density matrix has only one nonzero diagonal element and that the trace is 1, whereas a mixed state would not be idempotent and the trace would be less than 1. I'm thinking that the warehouse resembles a microcanonical ensemble or a canonical ensemble since the box count is fixed. I also think it wise to imagine it is well-insulated (isolated) so that there is no entanglement with the environment. Would a good way to tell if it is in a pure state would be to measure each box's temperature? (Too many, right) Or instead measure a few times several boxes to make sure the measurement doesn't change and is the same for all in the sample? Or would one just look at the thermostate? ha ha please forget that last remark.


title: Experiment to measure initial speed of high speed tennis ball?

text: I want to devise a way to measure the initial speed of a tennis ball fired from a tennis ball cannon, but without using any speed-measuring devices. Just plan distance-measuring and physics formulas. This question stems from a friend of mine who built a tennis ball cannon, but doesn't know how high it can go. I already know that answer if the cannon is fired straight up (so it's the maximum height of the maximum angle), which is $Y_{max} = \frac{1}{2}\frac{V_0^2}{g}$. But the flaw in that formula is you have to know how fast it's already going as it leaves the cannon. I know of the bullet experiment, as I like to call it, where a bullet is fired into a block of wood tied to a long string. Using the energy equations, we can easily calculate the initial speed of the bullet based on the maximum height that the block of wood swings to. The result is $v_{i,bullet} = \sqrt{\frac{2y(m_{bullet} + m_{wood})}{m_{bullet}}}$ where $y$ is the maximum height of the wood and bullet. The failure of that kind of experiment, though, when measuring a tennis ball's initial velocity is that the tennis ball is elastic. I got that formula above by equating the kinetic energy of the bullet with the potential energy of the bullet-block of wood mass, because initially the bullet has only kinetic energy but no potential energy, and at the maximum height of the bullet-wood, it has only potential energy. With a tennis ball, it won't stick to a block of wood. So the energies there aren't as easy, and you'll still have to know some final speeds. And of course, that's hard to time manually because of how fast it will be going, and the point of this question is an experiment that you can do manually. I was thinking about getting a large mass of something, putting it on the floor, firing at it, and then measuring the distance it moves after the ball hits it. But that stuff requires estimating the coefficient of friction to the floor (which, fair enough, can be estimated by textbooks), but it's still an elastic collision. I can't quite visualize how it will go down because the tennis ball bouncing will still have energy when it bounces off. I could also just fire the ball straight up, wait for it to come back down, and time that amount to get $t_{max}$. I could do it several times and get a value within some good margin of error. But that sounds inelegant and, frankly, not fun at all. Is there an experiment that we can do that will just let us measure distances things move, and from there work out the initial speed of the tennis ball? I guess the largest difficulty is it's very hard to get an inelastic collision if you shoot a tennis ball at a block of wood.


title: Sitting on the bob of a pendulum

text: Walter Lewin's best performance was the pendulum demonstration, and I copy the transcript now: > Would the period come out to be the same or not? > > [students respond] > > Some of you think it's the same. > > Have you thought about it, that _I'm a little bit taller than this object > and that therefore maybe effectively the length of the string has become a > little less if I sit up like this_? And if the length of the string is a > little less, the period would be a little shorter. Why would the length decrease? Shouldn't it increase, as the string is stretchable? If this concerns centre of mass, a diagram would be much appreciated!


title: Charging an object by induction

text: when charging a sphere by induction using a (-) charged object , and we put it to the right side of the sphere, electrons are pushed to the left side , so we ground the left side and the excess electrons escape. but what if we grounded the right side ( which has less electrons than usual ) wouldn't electrons flow from the ground to neutralise this side?


title: Why doesnt gravity speed up light?

text: We know that gravity speeds up a body; for instance, a meteor which enters the earth gets constantly accelerated up by earth's gravity. And from relativity we know that light bends near a massive body, because Newton's law of gravitation is just an approximation and actually gravity depends on energy and momentum. So my question is: If a ray of light is aimed exactly at the center of a body, then will it get accelerated like a meteor? And if does get accelerated, then won't it surpass the universal speed limit of 3,00,000 km/s (approx.)?


title: Rolling in 3D using Torque, Angular Momentum/Velocity

text: I'm stuggling to get a simulation working correctly. Below you can see what I am attempting to do. You can also view it here. Can you spot where I'm going wrong? ## (Calculated at start) ## 1) Inertia Sphere $$ I = \frac{2}{5} MR^2 $$ (I = 1.161) $$ I_{body} = \begin{bmatrix} 1.161 & 0 & 0 \\\ 0 & 1.161 & 0 \\\ 0 & 0 & 1.161 \end{bmatrix}$$ $$ I_{body}^{-1} = \begin{bmatrix} 0.861 & 0 & 0 \\\ 0 & 0.861 & 0 \\\ 0 & 0 & 0.861 \end{bmatrix}$$ ## 2) Inverse Inertia Tensor $$ I^{-1} = RI_{body}^{-1}R^T $$ * * * ## (Calculated each update) ## 3) Torque CP = Vector from center of mass to contact point.   SumF = impulse force + friction. (impulse was converted by: impulse / dt) $$ T = CP \times \sum_{F} $$ ## 4) Angular Momentum $$ L = L + T *dt $$ ## 5) Angular Velocity $$ w(0) = I^{-1}L $$ ## 6) Skew Matrix $$ w(^*) = \begin{bmatrix} 0 & -w_z(t) & w_y(t) \\\ w_z(t) & 0 & -w_x(t) \\\ -w_y(t) & w_x(t) & 0 \end{bmatrix} $$ ## 7) Rotation Matrix $$ R = R + dt \times w(^*) \times R $$


title: How was the sinusoidal model for propagation developed?

text: It's a little difficult to explain this question .. but I'll try anyway. To the best of my knowledge propagation models - audio, RF - are modelled as travelling in a sinusoidal form. Surely if a model was constructed based on observation, and then verified by experiment the experiment would more often yield the desired result than not. Is the model for sinusoidal motion/waves deemed true because the equations are proved true by experiment? How do we know these waves are actually sinusoidal? How was this model developed?


title: Solving coupled nonlinear ODEs, controlling numerical instability through numerical viscosity

text: I'm solving a problem numerically that takes the form $ Q_{ij} \ddot{y}_j +S_{ijk}\dot{y}_j\dot{y}_k +V_i=0$, where $(Q_{ij},S_{ijk},V_i) $ are all low order polynomial functions of the dependent variables $y_i$. The dependent variables are all functions of the variable t. The resolution of this spectral model is controlled by the number of $y_i$, denoted N. Now, when these equations become stiff, or I integrate for long times, numerical instability becomes apparent. If I increase the resolution, these spurious growths are attenuated, but it is not feasible to make N large enough so that they don't appear at all. If one looks at the time history of the higher modes, it seems like their large growth corresponds to the onset of the instability, so I want to attenuate these (un-physical) fast growing components of the solutions. To this end, I have added a term to the leading order term, so that the equation takes the form $Q_{ij}( \ddot{y}_j +\nu j^2 \dot{y}_j)+S_{ijk}\dot{y}_j\dot{y}_k +V_i=0$, where $\nu$ is a numerical viscosity to be prescribed later on. This does an OK job at attenuating the instability (e.g. I get accurate solutions for an twice as long), based on how I choose $\nu$, and the constraints of the problem. I have played around with the power of j as well, and found varying success in different contexts. The issue is, for long times this scheme breaks down, and the solution greatly deviates from the expected solution, making me think I'm not doing addressing the issue very rationally. Indeed, I am doing all of this very naively, and am having trouble finding similar types of problems in the literature. Does anyone have experience damping numerical instabilities in equations that take this form? In particular, is there a way to essentially add a dissipation that removes these fast growing modes? References to relevant literature are also greatly appreciated. Thanks! Nick


title: Does transverse flow always assist in mixed convection?

text: I am dealing with both natural convection and transverse forced convection over a flat plate. There are 4 different situations:   1. Upward-facing cold plate   2. Downward facing cold plate   3. Upward facing hot plate   4. Downward facing hot plate For mixed convection there is the relationship $$Nu^n=Nu_{F}^{n} \pm Nu_{N}^{n}$$ I was reading that for transverse flow, forced convection always assists natural convection but I was wondering if that is true for each of the 4 scenarios. I know that it is true for an upward facing hot plate but it doesn't seem plausible for the other 3 cases.


title: Exact wavefunction of superconducting state

text: Eventhough we know the mechanism of superconductivity (conventional superconductors) why couldn't we obtain the exact wavefunction of this state? Edit: is there any simpler example in which we know the approximate wavefunction which captures the physics but the exact wavefunction is not known?


title: Suggestions on a particular arXiv publication on math needed for theoretical physicists

text: I'm going to start my PhD in a year and I'll be taking a gap year doing other stuff. But I also wanted to fill in the gaps in my math knowledge and I came across an arXiv publication called "Mathematics for Theoretical Physicists." This is the link. I was wondering if anyone has read it/skimmed through it and if so, do you suggest that it's a good book? Thanks!


title: How to calculate beam spread of a non-point light source via an aspheric lens

text: I need to determine the angle, or rate of divergence of light from a single aspheric lens when I place a non-point light source (e.g. LED array) at a given distance from the lens which is less than the focal length of the lens. This seems to fall outside of the normal emphasis on image size and location in all the beginner optic info I'm finding on the WWW; I don't care about the virtual image this creates, I just want to know what the angle of divergence is so I can predict the spot size at an arbitrary distance from the lens. I can also say that I've seen plenty of examples which have collimated light on one side of the lens; as near as I can tell, they won't work, as they assume the light is collimated and thus don't take into account the light source beam angle. My best guess is that the equation to solve for the divergent angle would just need: *light source's beam angle *the focal length of the lens, *distance between the light source and the lens, *and possibly the radius of the non- point light source. I also suspect that the equation is probably the same for other types of lenses.


title: Does spatial coupling prohibit resonances due to an external source field?

text: The harmonic oscillator coupled to a sinodial external source $$\tfrac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$ has the solution $$x(t)=x(0)\cos(\omega_0 t)+C \sin(\omega_0 t) +\frac{F_0}{\omega_0^2-\omega_\text{ext}^2}\sin(\omega_\text{ext} t),$$ with a constant of integration $C$. So here we have a resonance for $\omega_\text{ext}=\omega_0$. If we consider the Klein-Gordong equation with nonvanishing coupling and with a source function $F$ $$\tfrac{\partial^2 \phi(t,x)}{\partial t^2}-c^2\nabla_x^2\ \phi(t,x) +\omega_0^2\ \phi(t,x)=F(s,x,t),$$ (one dimensional, three dimension, whatever you can deal with) is there also an family of functions $F(s,t,x)$, (family w.r.t. the parameter s), such that we have a singularity at $s=\omega_0$? Maybe you go about similar as with the Helmholtz equation, except than you get a shifted coefficient $\omega_0+k^2$. I think that could be the case as a damping term $\delta\cdot x'(t)$ also destroys the resonance, at least for a sinodial source.


title: Relationship between dynamical entropy and chaotic noise

text: I am interested to know if Kolmogorov Sinai Entropy of a system also known as Kolmogorov Complexity in information theory or popularly known as metric entropy increases with increase in dynamical noise. The dynamical noise can be in the form of deterministic chaotic noise. Consider, a linear system like an Auto Regressive (AR) model that is perturbed with chaotic noise. Will the entropy (Kolmogorov Sinai) of the output of the AR model increase? Intuitively, any kind of entropy increases with presence of noise. I am unable to find a proof or any relationship (preferably in literature or books) which have a relationship between entropy and noise. Can somebody please provide any guidelines as to how I should proceed to show that reduction in chaotic noise means decrease in Kolmogorov Sinai entropy and vice versa? Thank you


title: At the smallest level, how do things move?

text: When we see something moving on a screen it's usually just pixels being turned off at one location and turned on at another. For example: This would render a dot moving from A to C. Turn on pixel A, Turn off pixel A, Turn on pixel B, Turn off pixel B, Turn on pixel C In a real world scenario - how do things actually move? How does the tiniest physical space get covered? There must be a tiniest physical space right? If not then from my reckoning we shouldn't move at all. To move 1 step forward I'd have to first move half a step, but before that I'd have to move a quarter of a step, before that an eighth, etc. I would always be moving forward but I would never reach 1 full step. So assuming there is a tiniest physical space, does matter get turned off at point A and on at point B etc?


Does gravity slow the expansion of the universe? I read through the thread http://www.physicsforums.com/showthread.php?t=322633 and I have the same question. I know that the universe is not being stopped by gravity, but is the force of gravity slowing it down in any way? Without the force of gravity, would space expand faster? Help me formulate this question better if you know what I am asking.


title: Torque of Air Resistance on Ellipsoid

text: Imagine an non-rotating arbitrary free, rigid ellipsoid with in some arbitrary direction with velocity $\vec v$. Assume linear drag ($\vec F=KA\vec v$ for some constant K, where A is the cross section area). What is the total torque of air resistance on the ellipsoid? One question I think might be important is that is the symmetry of arbitrary ellipsoids sufficient to guarantee zero torque, no matter which direction the ellipsoid's velocity is. I decided it might not be and decided to post the question here after my calculations got quite a bit too involved.


title: Making and keeping a reading list

text: Seeing this as an academic community, I hope this question is on-topic. Academia is still a long way from beta `:(` I have a few questions about reading journal papers in the field of engineering/applied physics.   1. How do you keep and schedule a reading list?   2. From the more recent papers, how do you track down the one (or few) papers that started an idea or technology?   3. Then conversely, how do you move forward in time to trace how that technology evolved? How do you decide which is the next paper to read?   4. (I think being able to do the tasks of 2 and 3 could help me formulate my own research questions in the future)   5. How do you retain the gist of the information you read from an article?   6. How do you do the dirty work of the above? What software do you use, if at all? If you write it down in a notebook, what are the essential data points? Like the date you read the paper, publication date, title, author, then writing down (or illustrating) what you see with your mind's eye the information that the article presented, and... anything else?   7. I envision a notebook with the ideas I learned, then posing my own questions after reading each article. How do you do it? You may (or may not) answer those questions one-by-one, but they're there to give you an idea of what I want to find out. Offers to make this community wiki are very welcome.


title: Wave function of a photon?

text: consider a single photon. Since it is not possible to create a photon with a certain frequency it can be characterized by a normalized frequency distribution $f(\nu)$ that is peaked around some mean frequency. Now I sometimes hear or read that the fourier transformation of $f(\nu)$ is considered as the wave function of the photon (interpreted as the probability density in space). This is especially done in quantum optics. But I don't understand that. The reason is the following: In classical optics it's completely clear to consider the wave vector and the position as conjugate variables. Also in standard textbook QM this is clear due to the commutator relation of the Position and Momentum Operator (dealing with massive particles). But for a single photon, described by a creation operator, I can not find a reason to interpret the fourier transformation of $f(\nu)$ as the spatial probability density of the photon.


title: Is there a better alternative to assuming $a=0$ and then calculating acceleration? (Exam question: radiated energy after Coulomb scattering)

text: My classmates and I are having some debate about how to solve this problem which came up on one of our comprehensive exams. A full, step-by-step solution is not needed, an outline is enough. A solution does not need to be relativistic, as we are interested in both cases. > Find the total energy radiated in the collision of a relativistic ($\gamma > >> 1)$ particle of charge $q$, mass $m$, velocity $v$ (in the lab), impact > parameter $b$ against a fixed target of charge $Q$, in the limit of small > deflections. Write the condition for "small deflections" in terms of the > parameters of the problem. The current strategy assumes that $a=0$ but calculates the acceleration anyway from Newton's laws -- then, applying the Larmor formula, finds the total power radiated. This doesn't really satisfy me. I realize that for soft scattering that the velocity doesn't change much, but I was hoping there was a better way. However if you can justify this strategy then that is okay too.


title: Fine-Tuning, the Hiearchy Problem, and Mass in the Standard Model

text: In Chapter 1 of his book _String Theory in a Nutshell_ , Kiritsis states the following. > The [Standard M]odel is unstable as we increase the energy (hierarchy > problem of mass scales) and the theory loses predictivity as one starts > moving far from current accelerator energies and closer to the Planck scale. > Gauge bosons are protected from destabilizing corrections because of gauge > invariance. The fermions are equally protected due to chiral symmetries. The > real culprit is the Higgs boson. Let $\phi$ be a quantum field and define $G(p,q):=\langle \widehat{\phi}(p)\widehat{\phi}(q)\rangle$ (this is of course a vacuum expectation value). Then, it turns out that, $G(p,q)=\delta (p+q)H(p^2)$. Under the assumption $H$ has a unique pole which is a non-negative real number (anybody have a proof of why this would be true in general?), define the mass of $\phi$ to be the square-root of this pole. My understanding was that this mass is _given to us_ by experiment; instead, in calculations, we use this condition to calculate the _counter-terms_ , not the _mass_. Is my understanding of this in-correct? For some reason I was interpreting his words to mean something along the lines of "In quantum field theory, you can calculate particle masses via perturbation theory, and sometimes certain symmetries tells us that anomalies cannot arise, but in the case of the Higgs boson, there is no such symmetry, and so for the result to come out correct, some crazy cancellation has to occur." (now that I think about it, my assumption regarding his meaning here must have been heavily influenced by what I have been told about the Hierarchy Problem from other sources). This of course, doesn't jive with my aforementioned understanding of masses in quantum field theory (i.e. that you don't calculate them). Can somebody explain to me the Hierarchy Problem given my understanding of mass in quantum field theory? What precisely are the theorems that "protect" gauge bosons and fermions? I've seen time and again people talk about some how finely-tuned cancellation needs to happen regarding the Higgs. Could somebody tell me _very explicitly_ just what this cancellation is, and where and how it comes up? How does this imply the instability of the Standard Model? Thanks much in advance.


title: What techniques can be used to prove that a spacetime is not asymptotically flat?

text: The modern coordinate-indepenent definition of asymptotic flatness was introduced by Geroch in 1972. You can find presentations in Wald 1984 and Townsend 1997. The definition is in terms of existence of something -- a certain type of conformal compactification -- and in many cases such as the Schwarzschild metric, it's straightforward to think up a construction that proves existence. But to prove that a spacetime is _not_ asymptotically flat, you have to prove the _nonexistence_ of any such compactification, which seems harder. What techniques could be used to prove that a spacetime is _not_ asymptotically flat? The only example of such a technique that I've been able to think of is the following. Suppose we want to prove that an FLRW spacetime is not conformally flat. Wald gives a theorem by Ashtekar and Hansen that says that if a spacelike submanifold contains $i^0$, it admits a metric that is nearly Euclidean, so that, e.g., the spatial Ricci tensor falls off like $O(1/r^3)$. This implies that there can't be any lower bound on the Ricci tensor, but an FLRW spacetime can have such a lower bound on a constant-time slice, since such a slice has constant spatial curvature. Townsend, http://arxiv.org/abs/gr-qc/9707012 Wald, General Relativity


title: What does the Froude number represent?

text: While reading on Wikipedia, I read the following > _The Froude number is defined as:_ > > $$\mathrm{Fr} = \frac{v}{c}$$ > > _where $v$ is a characteristic velocity, and $c$ is a characteristic water > wave propagation >velocity. The Froude number is thus analogous to the Mach > number. The greater the Froude >number, the greater the resistance._ While reading the following paper on shallow water waves, I could not understand how/why the Froude number was given to be $$\mathrm{F} = \frac{gt_0^2}{L}$$ Where $t_0$ is the time scale, and $L$ is the length scale along the X and Z axes. Note that the scale for the amplitude of the surface above the mean depth is some other $A$ and not $L$. Please explain how the author has defined the Froude number. Is it the same as the one given on Wikipedia? If so, then please provide a step-by-step reasoning to show that they are indeed the same. If not, then please explain what the Froude number mentioned in the paper represents. EDIT: I'd like to add another minor question as it is related to the abovementioned paper. It mentions that the surface tension is accounted for but I do not understand how that is possible given that there is no term containing the surface tension $\gamma$ explicitly.


title: Is $Q=CV$ still acceptable formular on the capacitor charged by the transformed circuit?

text: Assume there is a 100V to 1000V transformer and the capacitor connected in the second circuit.(You know, transformers have two circuits) The second circuit's voltage is 1000V, but the amount current is lower than the first circuit.(because of the power conservation) So my question is that the formula $Q=CV$ still stands in the case of decreased current?


title: Polar ice caps and thermal radiation

text: I was reading an article on global warming and it said that the polar ice caps, because they are white, reflect a lot of the sun's radiation. The article also has a picture of some houses in England that are painted all white and supposedly these houses keep cooler in the summer and warmer in the winter. I understand that the warmth that one feels from standing outside in the sun is due to infrared radiation from the sun. I also understand that the more infrared radiation an object reflects, the whiter it looks. At least, that is what the article I was reading impressed on me. Anyways, here are some questions:   1. If I expose an object to EM radiation only from the infrared spectrum, will it only reflect back infrared? Is this true for other types of EM radiation?   2. Is it possible to make an object that looks white and absorbs a lot of infrared radiation?   3. If an object reflects most of the EM radiation that it receives of a particular wavelength $\lambda$, will it also reflect most of the radiation it receives of wavelengths less than $\lambda$ (and absorb most of the radiation of wavelengths larger than $\lambda$)? Is this why objects that reflect most visible light (and hence look white) also reflect most infrared radiation (since infrared waves have a shorter wavelength)?


title: Greenhouse gases

text: A post (below) on the Bishop Hill blog relating to climate change asserts that no warming effect can be attributed to $\mathrm{CO_2}$. I don't know whether the author is really a physicist but it sounds impressive (Planck spectra and black-body radiation etc). Can someone explain in layman's language whether the assertions are valid. Quote from http://www.bishop-hill.net/blog/2012/4/5/greenhouse-reversal.html               There is no greenhouse, so it can't be reversed.          Many so-called skeptics are not really basing their arguments on the true     physics of the atmosphere. By failing to do so, they are demonstrating     that they also have fallen for the IPCC bluff that radiation from a cooler     atmosphere (including so-called backradiation, but also initial radiation)     can transfer thermal energy to a warmer surface.          This is not correct physics and the sooner this is made clear to the     public the better. True physics, backed up by basic phenomena such as the     fact that radiation in a microwave oven is not absorbed in the usual sense     of the word, shows why this is the case. No one has ever proved anything     to the contrary in any empirical experiment, and never will.          The only thing any such radiation from the atmosphere can do is slow down     that third or so of surface cooling which occurs by way of radiation that     does not escape to space via the atmospheric window. Radiation from the     atmosphere can have absolutely no effect on evaporative cooling, chemical     processes or sensible heat transfer. These non-radiative components plus     the radiation to space make up about 70% of all surface     cooling. Furthermore, the effect of carbon dioxide with its limited     frequencies is far less than a true blackbody, and less per molecule than     water vapor. No gas can radiate outside its Planck spectrum (i.e. more than     a true blackbody) and so there is no way that carbon dioxide (1 in 2,500     molecules) can contribute a very large amount of radiation anyway.          The other cooling processes merely accelerate and compensate for any     minuscule slowing of radiative cooling. Thus there is absolutely no     warming attributable to carbon dioxide. It is time for skeptics to get     their facts right and stop giving in to part of the hoax. Only truth will     prevail in the long run.       EDIT: The author of the blog post was 'Doug Cotton', who has published a related paper at http://principia- scientific.org/publications/psi_radiated_energy.pdf and has a website at http://climate-change-theory.com/


title: Is it safe to observe the sun through binoculars with welding glass in front?

text: I asked this on Reddit but didn't get much of a response. So here goes! I'm looking for low-cost ways to observe the Transit of Venus this summer. Since I'll only be able to see a few hours of it from my location, and it very well may be cloudy, I don't want to spend big bucks on solar filters. I've been reading though that shade 14 welding glass will block enough light. What I want to know is if it's still safe to view the sun through binoculars **after** light has passed through the welding glass. Here's how I'm thinking the arrangement would look:               Eyes  <-  Binoculars  <-  Shade 14 welding glass  <-  Sunlight      Thanks!


title: Does a Force on the block $M_1$ in this diagram have an effect on the block $M_2$?

text: Suppose we have two blocks: ![enter image description here](http://i.stack.imgur.com/7ZmYU.jpg) There is no friction. Does $F$ has the same effect on $M_2$?


title: Is the "Great Attractor" an indicator of the "Multiverse"?

text: I have heard a bit about the Great Attractor (the gravitational anomaly that seems to be "sweeping" our universe in one direction). Someone (and forgive me, I do not recall the specifics) has hypothesized that this may be an indication of an other universe affecting us gravitationally. I am interested in people's opinions on this. Would this be an experimentally provable phenomenon of string-theory (in all its different incarnations)? Or are there more viable hypotheses that would explain this?


title: Question on notation in Shankar's Quantum Mechanics - math intro on vector spaces

text: I'm just beginning Shankar's 2nd edition Quantum Mechanics and having some trouble with notation. He defines his vectors as "$\left|V\right>$" . And with a scalar multiplier as "$a\left|V\right>$" . When he gets into inner products a couple of pages later he does this: $$\left<V\right|\Bigl(a\left|W\right>+b\left|Z\right>\Bigr) \equiv \left<V|aW+bZ\right>$$ My question is whether $aW$ and $bZ$ has meaning? Or, is this just a definition of a new notation to simplify $\left<V\right|\Bigl(a\left|W\right>+b\left|Z\right>\Bigr)$? If so, does this mean that aW shouldn't be used outside of this specific case?


title: From the perspective of an observer inside a black hole's horizon, where does the energy for Hawking radiation come from?

text: Would energy be seen to "flow" to the outside of the black hole? Through what mechanism?


title: What does it take to derive the ideal gas law in themodynamics?

text: > How can the ideal gas law be derived from the following > assumptions/observations/postulates, and these only ? > >   1. I'm able to measure pressure $P$ and volume $V$ for gases. >   2. I notices that if two systems of gases come into thermodynamical > equilibrium, that the quantities $PV$ for gas 1 and gas 2 coincide. >   3. I assume there is an energy function $U$. >   4. The first and the second law of thermodynamics hold by axiom, together > with all the consequences, which can abstractly derived from the two. >   5. For a free expansion of my gas $(\Delta U=\Delta Q=\Delta W=P\Delta > V=0)$ I find that the expression $PV$ for my gas is the same before and > after the experiment. > If I'd postulate $PV=nRT$, then I'd easily see that $U(T,V)$ is only a function of $T$ and I can derive everything else, pretty much even without the second law. Here I know of the second law, which gives me a bunch of expressions and I wonder if that suffices to identify the temperature. > If it's not possible, are there other experiments I can do in my position > which would do the job? * * * Here is a weaker version of the question: > Can the ideal gas law be derived if I additionally know that $U$ is really > only a function of $T$, or even that $U(T,V)=C_V T\ $? * * * > And what role does the zeroth law of thermodynamics play here? The essence of the question is not necessarily gas physics. It's rather about how temperature is defined by the laws of Thermodynamics, if there is merely the assumption that the system can be described by internal energy $U$ and is experimentally accessible only by its parameters like $P,V,M,H,\dots$. And there is no connection to a theory lying above.


title: Boundary condition for water waves generation

text: I am trying to model water wave propagation in 2D with CFD. What would be a suitable boundary condition to generate the waves on the left boundary? Currently I vary the fraction of water above the initial water level as a sine of time. I get some results, but not too good so far. I also tried a dynamic mesh following a tutorial but results seem very hard to control. Ideally I need a condition which would allow me to generate waves with desired characteristics (period, speed etc.) I am doing it in Fluent, so implementational advises are also appreciated as a bonus, but I guess the question isn't that much related to it. That's why I place my question here, not in the scicomp exchange.


title: How can some optical microscopes measure height differences of different sample planes with nanometer accuracy?

text: I could use last week an optical microscope, didn't seem special in any way, 50x magnification, image viewable per a CCD camera on a computer screen besides through the ocular. But the software of this microscope had a feature to show a 3D calculated topography view of the sample (silicon wafer with some laterally structured micron sized 40 nanometer high SiO2 squares). So in the software you could see the height of these squares (30-50 nm there, so some error) and also do virtual profilometer over these squares. There these height measurements were separated for green, red, blue, so 3 lines showing a 30-40 nm difference from silicon to a SiO2 square. The manual didn't tell how the physics work, so can has someone here an idea how this might work. It looked like a cheap normal microscope, I suppose that it uses somehow the CCD data and reflected intensity of the squares, the height of the bigger squares was more accurately measured/extrapolated than smaller squares. Also I can exclude it is a Normaski microscope http://en.wikipedia.org/wiki/Differential_interference_contrast_microscopy there were no polarisators or prisms inside the microscope. https://snf.stanford.edu/SNF/equipment/characterization-testing/zygo/Zygo This technique seems to come near, white light interferometry, but resolution is much better. So can someone explain to me how this technique that is probably used in this microscope is called and what the accuracy is, what limits it? Link to the specific model https://www.micro- shop.zeiss.com/?s=12128207d6c5cf&l=en&p=us&f=e&i=10247&o=&h=25&n=0&sd=490950-0002-000#490950-0002-000


Have some trouble finding a useful reference to answer the following questions:   * What's a typical electron-hole recombination time of semiconductors? And how does it depend on the temperature and the band gap? If there's no formula, examples will do.   * What's the probability of an electron being kicked into the conduction band merely by thermal motion? Is it $\exp(-\Delta E/T)$, where $\Delta E$ is the band gap and $T$ the temperature? That thermal excitation should lead to noise in the system, is that correct?


title: Maximum pressure at a compressor outlet and molecular weight

text: I am puzzled by some data I see for a compressor. From what I read, the maximum discharge pressure reachable with a reciprocal compressor would vary depending on the nature of the gas used, and its molecular mass (maximum pressure lower with a heavier gas). This does not seem to fit with my quickly jotted notes from a perfect gas point of view, in which molecular mass shouldn't matter. Any explanation ?


title: Is there a relationship between Berry-Pancharatnam phase and CP violation in quark mixing?

text: Berry-Pancharatnam phase is the phase that quantum systems exhibit when they pass through a sequence of states and return to their original state. It's a complex phase and it is different from the usual complex phases in that it does not depend on the arbitrary complex phases present in quantum states. For an encyclopedia-level introduction to B-P phase for the purpose of this question, see   Péter Lévay, Encyclopedia of Mathematical Physics, Elsevier 2006, "Geometric Phases"   http://arxiv.org/abs/math-ph/0509064v1 When a quark interacts with the weak force it typically changes flavor and emits or absorbs an electron and a neutrino (or anti-electron / anti-neutrino, as appropriate). This process is generally assumed to require a unitary matrix called the CKM matrix. The elements of this matrix can be measured in high dollar physics experiments but only in absolute value. That is, the complex phases are unknown. So when the data is fit to a unitary CKM matrix, physicists have a choice in how to arrange the complex phases. There are four degrees of freedom in the data and five degrees of freedom in the arbitrary complex phases. The usual method is to use three of the degrees of freedom to (approximately) define the transition probabilities between generations. That is, one has $\\{\theta_{12},\; \theta_{13},\; \theta_{23}\\}$ for the "mixing angles" between the 1, 2, and 3 generations. (This is only approximate because the probability for going from the 1st to 3rd generation is not equal to the probability for going from the 3rd to the 1st generation.) The fourth degree of freedom is chosen to be $\delta$. If this fourth parameter is zero, then there can be no CP violation. The wikipedia article is a good introduction:   http://en.wikipedia.org/wiki/Cabibbo%E2%80%93Kobayashi%E2%80%93Maskawa_matrix The $\delta$ angle enters the CKM matrix as a complex phase, that is, it appears as $e^{\pm i\delta}$. The other parameters $\theta_{12},\; \theta_{13},\; \theta_{23}$ are used in cosines and sines and are usually abbreviated for example as $\cos(\theta_{12}) = c_{12}$. In both these cases the central object, Berry-Pancharatnam phase and the $\delta$ angle, is a complex phase. And neither has anything to do with the arbitrary complex phases of quantum states. So my question is this: Can CP violation be defined in terms of a Berry-Pancharatnam phase?


Does the unpredictability in the "micro world" means that everything is if we can look at it close enough imperfect? I mean, there is a saying "You will never stand in the same river again" or something like that. So, if nothing in our makro world is the same, if we look close enough (no two people or flowers are the same; and if they seem, it just means you are not looking carefully or cose enough ;) Is this also true in the micro world? If yes, does that mean that e.g no two atoms of hydrogen are the same and the sign $H$ is only some kind of reference for "from-to" or "plus-minus- something-like-that" tolerance? And the same principle can be applied for smaller particles or even strings etc.? Does that mean that there is no such thing as two identical proto particles and everything is slighty different? And my final concern is... Do we live in "The Imperfect Universe"? ;)


title: Whirlpools and Tornados

text: This may not be a great question. But whenever you drain water, a small whirlpool happens, obviously. This got me thinking... Can we model tornados with this effect, would it even be beneficial?


title: Heterotic string as worldvolume theory of two coincident 9-branes in 27 dimensions?

text: The heterotic string is a combination of right-moving excitations from a D=10 superstring and left-moving excitations from a D=26 bosonic string, with the left-movers behaving as if the extra 16 dimensions are compactified. The heterotic string is also derived from D=11 M-theory, as an open 2-brane stretched between two "end-of-the-world" 9-branes (spatial boundaries; this is M-theory compactified on a line segment, and the 9-branes lie at the ends). So I am led to imagine a 27-dimensional theory, containing branes. We compactify 16 dimensions, and consider the worldvolume theory of two parallel 9-branes. When they are coincident, we get the heterotic string; when they are slightly separate, we get "heterotic M-theory". A 27-dimensional fundamental theory has been discussed before (hep-th/9704158 section 4; hep-th/0012037; arXiV:0807.4899), but I don't see this particular line of thought discussed.


title: The Big Bang in an infinite universe

text: If the universe is _spatially infinite_ (and assuming, if it makes a difference, that we don't have eternal inflation), what actually happened 13.7 billion years ago? Was the energy density infinite (or "very large") at each point in **R** 3? Or did **R** 3 itself collapse to some other structure?


Why do Faddeev-Popov ghosts decouple in BRST? What is the physical reason behind it? Not just the mathematical reason. If BRST quantization is specifically engineered to make the ghosts decouple, how does this engineering work?


title: What experiments, other than Hubble Expansion, support the Dark Energy theory?

text: Dark energy is introduced as a constant inside Einstein's equations. Its primary purpose, from what I understand, is to make Einstein's equations compatible with the _accelerating_ expansion of the universe. As a consequence, of the "predictions" of dark energy is the expansion of the universe according to Hubble's law. I know there are numerous experiments that verify this expansion (and its acceleration), and thus indirectly support the dark energy theory. My question is:   **Are there _other_ factors that give credit to the existence of dark energy?**   Are there any experiments that support this theory, but not only through the verification of Hubble expansion?


title: Paralel light conditions after passing from a sphere

text: ![enter image description here](http://i.stack.imgur.com/FJDSp.png) Is it possible to get such result that light will be parallel after passing from the sphere? what is the total condition for such result if possible? Thanks for answers


title: combination of 5 identical capacitors

text: Given 5 identical capacitors, each EMF. Draw the proper combination of all these 5 capacitors.. 1.) 2.5 2.) 4.17 I really do not know how to solve this thing and if anyone of you knows the title of this lesson please comment it here so I can study it further. We will be having our finals tomorrow.


title: Wilson Loops as raising operators

text: Consider a U(1) Chern Simons theory on a torus $\mathbb{T}$: \begin{align} L &= \frac{k}{4\pi} \int_{\mathbb{T}} a \partial a \end{align} where a is some U(1) gauge field, $k\in\mathbb{Z}$ and we used the short hand notation $a \partial a \equiv \epsilon^{\mu \nu \lambda} a_\mu \partial_\nu a_\lambda$. Consider Wilson Loops of the form \begin{equation} W(C) = \mathcal{P} e^{i \oint_C a \cdot dl}. \end{equation} Here $\mathcal{P}$ denotes path ordering and $C$ denotes some closed loop on the torus $\mathbb{T}$. Consider the two non-contractible loops on $\mathbb{T}$ denoted by $\mathcal{a}$ and $\mathcal{b}$. (For a picture see: http://share.pdfonline.com/7e91df64f6e84f43bff166c6911972d6/torus_a_b.htm) THe ground state manifold of of the theory is $|k|$-fold degenerate. Consider a basis that consists of wrapping "quasiparticles" around the b loop of the torus: $\left| n \right\rangle$ with n=0...$|k|-1$. Then the Wilson loop operators act as \begin{align} W(b)|n \rangle &= |n + 1 \text{ mod } |k| \rangle, \nonumber \\\ W(a) |n \rangle &= e^{2\pi i n /k} |n \rangle. \end{align}. What is the reason for this? I assume it must somehow be related to the explicit construction of the ground state manifold? Since I am working myself into Chern Simons theory at the moment I would also be happy for some advice on readable literature with a focus on condensed matter problems. Best regards.


title: Temperature and resistance?

text: Why does resistivity increase with temperature? The explanations I have heard so far are that increasing temperature increases vibrations in the lattice structure resulting in the number of collisions increasing. But the vibrations from thermal energy are random, so around half of the vibrations would result in the atoms moving _out_ of the electrons way and half would result in atoms moving _into_ the way of the electrons. And since half of the vibrations result in increasing the drift speed and half reduce it, shouldn't the average drift speed remain the same?


title: Expansion of ideal gas

text: Consider an ideal gas in a chamber (A), separated from another chamber (B) by a diaphragm, in the following two situations: (1) Instantaneously burst the diaphragm   (2) Plug in an isentropic nozzle so that the gas escapes gradually Are the two cases identical? I believe there should be some work done in the second case, because the opposing pressure in chamber B increases gradually, so the work done by the gas would increase as it reaches steady state. Is this reasoning correct, or should both cases have zero work done?


title: How do capacitors work?

text: Say you have a battery, with a wire connecting the negative and positive terminal. Initially, (the transient state) the electric field is not uniform and is perpendicular to the surface of the cross section of the wire. This forces the surface charges to rearrange, and the surface charges keep moving until the electric field in the wire is uniform and at any point, the electric field is perpendicular to the cross section of the wire at that point. This is the steady state, and is when current is flowing. Now consider a circuit that consists of a battery and a capacitor connected to the both the terminals. Could someone walk me through how the capacitor is charged using the concepts of surface charge redistribution discussed above? **Please note I am not looking for a general explanation, I'm looking for an explanation that shows how the surface charges redistributing themselves during the transient state to ensure the electric field is perpendicular to the wire results in the capacitor charging.**


title: Finding release angle and final velocity of projectile when the target has a different coordinations

text: I am trying to write some codes for auto-snowball mechanism which seems like a regular projectile but instead of hitting the targets on the ground it is going to be able to hit the target in the air or with different(x,y) coordination. Here is the blueprint of the mechanism: ![enter image description here](http://i.stack.imgur.com/WVU9j.jpg): Simply The mechanism will be able to get the (x,y) of the target and then mechanism will have a constant initial velocity(Vo). I used regular Velocity equations to find the Vox and Voy of Initial Velocity(Vo). Here is my Velocity and Delta X and Delta Y formulas: ![enter image description here](http://i.stack.imgur.com/jmqWP.jpg) My questions are: 1-Is a(acceleration) still going to be a=0 for Delta X and a=-g=-9.8 m/s^2 2-How am I going to find the final Velocity(Vf)? 3-Is this a correct equation to find Release Angle(Theta)?![enter image description here](http://i.stack.imgur.com/EW867.jpg)


title: Angular Momentum Expectation in Magnetic Field

text: I am trying to find the time dependent expectation value for J ($\langle J(t) \rangle$) for a spin 3/2 particle in a uniform magnetic field (in the z direction). My method is as follows: $$H=-\frac{\mu B}{\hbar}J_z$$ Then to find the equaions of motion for $J_i$: $$i\hbar \dot J_i=[J_i,H]$$ $$\dot J_x=\mu B/\hbar \space \space J_y$$ $$\dot J_y=-\mu B/\hbar \space \space J_x$$ $$\dot J_z=0$$ Now I am given tha t the particle is initially in an eigenstate of $J_x$, with eigenvalue +3/2$\hbar$. So I know that: $$J^2|j,m\rangle=\frac{15\hbar^2}{4}|j,m\rangle$$ $$J_x|j,m\rangle=3/2 \hbar|j,m\rangle$$ So to calculate $\langle J(t) \rangle$, I need to know the equations, which I have solved. But then I need to know what $J_y,J_z$ acting on $|j,m\rangle$ is. For the z component of J. $$\langle J_z(t)\rangle=\langle j,m|J_z(0)|j,m\rangle$$ In order to find what $J_z(0)$ is, do I have to create a new raising operator, which would be $Jy\pm iJ_z$ and then find what I initially have in terms of J squared and the x component?


title: Two ways of looking at weak current?

text: A weak current of the form: $$j^\mu=\bar u_e \gamma^\mu \frac{1}{2}(1-\gamma^5)u_\nu$$ implies that it automatically selects the left- handed neutrino. This current can also be written as: $$j^\mu=\bar u_e \frac{1}{2}(1+\gamma^5)\gamma^\mu u_\nu$$ which seems to imply that only left- handed electrons take part in weak interactions. Which statement is right?


title: How can it be that the beginning universe had a high temperature and a low entropy at the same time?

text: The Big Bang theory assumes that our universe started from a very/infinitely dense and extremely/infinitely hot state. But on the other side, it is often claimed that our universe must have been started in a state with very low or even zero entropy. Now the third law of thermodynamic states that if the entropy of a system approaches a minimum, it's temperature approaches absolut zero. So how can it be that the beginning universe had a high temperature and a low entropy at the same time? Wouldn't such a state be in contradiction to the third law of thermodynamics?


title: Is rocket propellant meaningfully a form of "space junk"

text: I imagine that most people are familiar with the concept of space junk (or space debris), which is a hazard to space exploration that grows with every item that humans leave in space. Wikipedia lists the following types of space junk:   * spent rocket stages    * defunct satellites    * erosion, explosion and collision fragments I'm extremely curious, **how much sense would it make to add ejected rocket propellant to this list?** To the extent of my understanding, for at least a fraction of the flight the products of the reactions that power a rocket will be left in space and maybe in orbit (?). In the case of LOX/LH2 fuel, for instance, I believe this ejected material would be water vapor. Normally this wouldn't be a problem, but if that gas is occupying an orbit, or is suspended as a part of the upper-atmosphere I wonder about detrimental effects such as:   * Increasing the gas content of near-space would cause greater drag on spacecraft   * In the case of high specific impulse thrusters, the propellant wouldn't be following the normal thermal distribution... so maybe that could lead to radiation damage   * Space could be polluted by activities on the ground, due to use of Helium, which escapes the atmosphere (and can thus contribute to increased orbit drag)   * Couldn't it increase the effective temperature of space? If you assume a constant growth rate in energy use humans will inevitably cook themselves. It might be easy to dismiss this is negligible, but I find the outcome non- obvious for several (basic physics) reasons. Firstly, the mass of rocket propellent would probably exceed the mass of other space junk, since it is not reusable and because the ratio of payload to propellant is so poor for many trips. Although Earth's atmosphere is large, the orbits that this propellant could affect only have an extremely sparse population of gas molecules. Adding a few drops to a small bucket can still make a difference. Some velocities:   * LOX / LH2 fuel: $v_e = 4,400 m/s$   * Ion thruster: $v_e = 29,000$   * LEO orbit speed: $V = 7,800 m/s$   * Earth and moon escape velocities: $11,200 m/s$, $2,400 m/s$ Similar to how anthropogenic CO2 emissions slowly affected the climate of Earth, could a scale-up of space traffic ultimately lead to problems by stretching out the upper edges of our atmosphere, injecting weird thermal distributions into space, and giving the moon a man-made atmosphere? Even though the moon can't "hold" an atmosphere, a quick glance at the velocities above reveals that many plausible ejection vectors could leave it bouncing around for a good long time. Just so that I don't leave this untouched, Project Orion (using nuclear bombs for propellant) seems like it could do the same thing for space that atmospheric testing did for the radiological environment we live in. The further out you go, the more space you have, but also the higher speed propellant you need, so it seems like this is a potential problem at several stages of space development.


title: The BRST construction for YM with or without auxiliary field

text: I'm learning BRST symmetry for Yang-Mills theory and I see that there are two ways of writing BRST differential. In some books (for example Ryder's and Ramond's textbooks) BRST differential acts as \begin{gather} \delta A_\mu^a =-D_\mu c^a, \\\ \delta c^a= -\frac{1}{2} f^a_{bc} c^b c^c ,\\\ \delta \bar{c}^a= f^a, \end{gather} where I skipped coupling constant, and $f^a$ is a gauge-fixing function, for example $f^a=\partial^\mu A_\mu^a$. But in Srednicki's or Peskin and Schoeder's textbooks differential $\delta$ acts on $\bar{c}$ as $$ \delta \bar{c}^a= B^a, $$ where $B^a$ is the auxiliary field. For me it seems that first approach is a simple elimination of the auxiliary field $B^a$ from the differential and from the action using condition $f^a=B^a$. Is that so? I just want to be sure I'm not missing something. What form of BRST is "preferable" i.e. what are reasons to choose BRST transformation with or without auxiliary field?


title: Would you see a rainbow from refraction when the sun is in front of you?

text: I know how rainbows are formed, and why. Usually it is said that the Sun must be **behind** the observer, in order for its light to be totally reflected inside the droplet and then reach the observer. But surely not all the light is totally reflected? There must be some radiation refracting from inside the droplet to the air: since different wavelengths refract through different angles, shouldn't we also see a rainbow when the Sun is in front of us?


title: Lever Mechanics - How to formulate an ideal lever launch

text: Let's say I have a simple lever as shown below, and the lever is massless and the pivot is frictionless and there is no air resistance. I'm thinking the cradle for the projectile would have to have a specific shape to dictate the launch angle, but for the context of a general equation $\theta$ will be the angle the lever makes parallel to the ground, and will have some value where the object will leave the lever. $\theta_{launch}$ will refer to the angle the lever is at when the object 'launches', so the lever will have swept $\theta_0 - \theta_{launch}$. $t_0$ is the initial time the weight is released and $t_{launch}$ = launch time. ![Lever Launching](http://i.stack.imgur.com/dN2fz.png) # Height Functions $h_{weight}(\theta) = h_{pivot} + l_{shortArm}cos(\theta)$ $h_{projectile}(\theta) = h_{pivot} - l_{longArm}cos(\theta)$ # Desired Equations   * Potential Energy of the system at Initial Conditions   * Velocity of Projectile at Launch   * KE of Projectile at Launch   * Efficiency of machine


Is there any quantum interpretation which isn't "crazy" at all? Exponentially many parallel worlds in MWI, superdeterministic conspiracies, and/or nonlocality in hidden variables, idealism and the idea measurements and observations create the outcome in Copenhagen, retrocausality, negative probabilities which can never be observed, etc. . Is Nature really "stark raving mad"?


title: converting daily global radiation into hourly values

text: I would like to convert daily global radiation into hourly solar radiation. While I do not know the terms, I tried using below equations I found in the papers but I have negative radiation values range between -75 to 100 j/m2/s. Any suggestions are welcome.               # radi(h) = r * radi(daily)      > r <\- (pi/24) * ( a + b * cos_d (w))* ((cos_d(w) - cos_d(ws)) / > (sin_d(ws)-((pi/180) * ws * cos_d(ws))) ) > > a <\- 0.409 + 0.5016 * sin_d(ws - 60) > > b <\- 0.6609 - 0.4767 * sin_d(ws - 60)                # W = hour angle of the sun      > w <\- (360/24) * (h-12.0) # h = time of the day (hour) > > ws <\- acos_d(-tan_d(phi)*tan_d(sigma))) # ws = sunset hour angle (degree) > > phi= 36.20 # phi = location latitude angle               # sigma= declination angle of the sun [degree]      > sigma = 23.45 * sin_d (360* ((284+day)/365)) # day=DOY


What is relation between Holographic principle and Hologram? The holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon.


title: Theoretical String Landscape Question

text: Could it be plausible that the same theoretical string "shape" occurs twice. As in two or more universes with the same amount of dark energy and string shape. The term "shape" I'm defining as based on the way Brian Greene was implying in this video: Why is our universe fine-tuned for life? Please forgive my ignorance if this question is nonsensical as I'm very interested in physics but mostly just read around.


title: Surviving Free Fall with the Help of Mr. Bernoulli

text: What is the best strategy to survive a free fall naked out of a jetliner at cruising altitude (ignoring temperature)? For instance, my strategy would be to streamline my fall so that my terminal velocity was very high. Then at some critical distance above the ground I would pitch upward and attempt to use my forward velocity to achieve lift. Presumably this would slow my fall to some survivable speed. (This is roughly what the space shuttle does after all.) Would it work? And idea if it would be survivable?


title: What fraction of nuclear excited states are known?

text: I was reading a paper today claiming observation of a new $2^+$ state in $^{12}\mbox{C}$, which would correspond to a sort of rotationally excited Hoyle state. Looking at NuDat reveals that this region of excitation energy seems well probed, with many states known above and below the new state. This got me to wondering: What fraction of excited states are known in the light nuclei? (Presumably, heavier nuclei have very many states and must be less completely known. Also, let's assume we stay below the single-nucleon ejection energy so that we have a definite upper bound.) Are there some regions where we know that all excited states are known? (Probably "yes" for systems such as the deuteron: there aren't any.) Are there enough too-broad states such that we can never really know if we've got them all? (This new state is 0.8 MeV wide at 10.0 MeV above ground.)


title: How to perform contour integral in Nekrasov's formula

text: My question is technical. It is about instanton counting calculation (see this paper). The partition function of SU(N) gauge theory with $N_f$ fundamental multiplets in k instanton background is given by (3.10) $$Z_k(a,\epsilon_1,\epsilon_2)=\frac{\epsilon^k}{k!(2\pi i\epsilon_1 \epsilon_2)^k }\oint \prod_{I=1}^{k} {{\rm d}{\phi}_I \ Q({\phi}_I) \over {P({\phi}_I) P({\phi}_I + {\epsilon})}} \ {\prod}_{1\leq I < J \leq k} {{{\phi}_{IJ}^2 ( {\phi}_{IJ}^2 - {\epsilon}^2)}\over{({\phi}_{IJ}^2 - {\epsilon}_1^2)({\phi}_{IJ}^2- {\epsilon}_2^2)}} $$ where: $ Q(x) = \prod_{f=1}^{N_f} ( x + m_f) $ & $ P (x) = \prod_{l=1}^{N} ( x - a_l)$, $ {\phi}_{IJ}$ denotes ${\phi}_I - {\phi}_J$, and ${\epsilon} = {\epsilon}_1 + {\epsilon}_2$ . Then the pole of the integral corresponding to $\vec Y$ is at ${\phi}_I$ with $I$ corresponding to the box $({\alpha},{\beta})$ in the $l$'th Young tableau (so that $0 \leq {\alpha} \leq {\nu}^{l,{\beta}}, \ 0 \leq {\beta} \leq k_{l,{\alpha}}$) equal to: $ {\vec Y} \longrightarrow {\phi}_{I} = a_l + {\epsilon}_1 ({\alpha}-1) + {\epsilon}_2 ( {\beta}-1)$. After the path intagral, the result is (3.20) $$ \eqalign{&R_{\vec Y} = {1\over{({\epsilon}_1 {\epsilon}_2)^k}} \prod_{l} \prod_{{\alpha}=1}^{{\nu}^{l,1}} \prod_{{\beta}=1}^{k_{l,{\alpha}}} {{\mathcal{S}_{l}({\epsilon}_1 ({\alpha}-1) + {\epsilon}_2 ({\beta}-1))}\over{({\epsilon} ({\ell}(s)+1) - {\epsilon}_2 h(s))({\epsilon}_2 h(s) - {\epsilon} {\ell} (s))}} \times \prod_{l < m} \prod_{{\alpha}=1}^{{\nu}^{l,1}} \prod_{{\beta}=1}^{k_{m,1}} \left( {{\left( a_{lm} + {\epsilon}_1 ({\alpha} - {\nu}^{m,{\beta}})+{\epsilon}_2 (1-{\beta}) \right) \left( a_{lm} + {\epsilon}_1 {\alpha} + {\epsilon}_2 ( k_{l,\alpha} + 1 - {\beta}) \right)}\over{\left( a_{lm} + {\epsilon}_1 {\alpha} + {\epsilon}_2 ( 1 - {\beta}) \right) \left( a_{lm} + {\epsilon}_1 ({\alpha} - {\nu}^{m,{\beta}}) + {\epsilon}_2 ( k_{l,{\alpha}} + 1 - {\beta}) \right)}}\right)^2 } $$ where we have used the following notations: $a_{lm} = a_l - a_m$, $ \mathcal{S}_{l}(x) = {Q(a_l + x) \over { \prod_{m \neq l} ( x + a_{lm} ) (x + {\epsilon} + a_{lm} )} }$, and $ {\ell}(s) = {k}_{l,{\alpha}} - {\beta}$, $ \qquad h(s) = {k}_{l,{\alpha}} + {\nu}^{l,{\beta}} - {\alpha} - {\beta} +1 $ **My question is how to get formula (3.20). Any references about this calculation are welcome.**


title: What is $\Delta t$ in the time-energy uncertainty principle?

text: In non-relativistic QM, the $\Delta E$ in the time-energy uncertainty principle is the limiting standard deviation of the set of energy measurements of $n$ identically prepared systems as $n$ goes to infinity. What does the $\Delta t$ mean, since $t$ is not even an observable?


title: Ideal suborbital hop

text: This is actually regarding Kerbal Space Program, but it's more of a physics question than one about the game. If I have a rocket on the surface of a rotating spherical body without an atmosphere, with an infinite TWR, how can I calculate the amount of delta-v required to do a suborbital hop to another given point on the body? Is there a closed-form solution? Or if not, at least a good approximation? The answer is upper-bounded of course by the amount of delta-v required to get into orbit and land again.


title: Atomic nucleus consisting of only neutrons?

text: Is it true that the nucleus of all atoms (including radioactive isotopes) contain at least one proton? Is there an atomic nucleus consisting entirely of neutrons? (Let's exclude neutron stars for the moment.) If so, how does one name them? (since Periodic Table starts from atomic number 1, not 0.)


title: Can (quantum) angular momentum $L$ be zero?

text: I am trying to calculate the _orbital magnetic moment_ , $\bar{\mu}$, for Sodium, which has an electron configuration of $1s^2 2s^2 2p^6 3s^1$. The full shells do not contribute to $\bar{L}$ and $\bar{S}$ so only the outer shell electron will contribute to them. The $3s$ shell corresponds to $l=0$. And $\bar{L}=\hbar\sqrt{l(l+1)}$ which gives $\bar{L}=0$. Is this possible? Doesn't that mean that the electron isn't "oribiting" the nucleus? I am thinking that $\bar{L}^2$ tells you if the electron is "orbiting" the nuclues, but then what is the significance of $\bar{L}$? **Extra question:** The z-component of the orbital magnetic moment is given by $\mu_z = -m_l\mu_b$. Since $m_l$ varies as $-l\le m_l\le l$ does that mean that there are more than one values for the z-component? Strange, no?


title: Infinite Wells and Delta Functions

text: In considering a delta potential barrier in an infinite well, I can just enforce continuity at the potential barrier-it doesn't have to go to zero. Why then does it need to go to zero at the walls of the infinite well? These two cases seem to be very similar to be, I even feel like the well wall is equivalent to a summation of delta functions... Where is my logic faulty?


title: Resonance modes of a cubic box of water which we shake

text: I don't know hydrodynamics, but I wonder how one would compute resonance modes of a cubic box of water which we shake. I believe the waves would directly depend on the height of water and the width and length of the box. Is it a bit like a waveguide for electodynamics?


title: Finding a research area with a not-too-steep learning curve

text: In theoretical physics, I'm torn between high-energy and condensed matter physics. Is it true that the former has a much steeper learning curve than the latter, assuming I don't pick a well-trodden area like high temperature superconductivity? I'd like to start becoming productive as early as possible, and I don't necessarily want to spend more time than needed in getting up to speed. Does that rule out high-energy theory for me?


title: Huygens-Fresnel principle

text: Huygens principle states that 1) Every point on a given wavefront may be considered as a source of secondary wavelets which spread out with the speed of light in that medium. 2) The new wavefront is the forward envelope of secondary wavelet at that instant. What does this actually mean in both **_theoretical_** and **_practical view_**? Does this explain in this way: Taking sun as a source, As the light from sun reaches every object, Do each & every object actually act as a new source of that light"..? Or a ray of light inside a room causes its walls to reflect the light. Then, do the walls act as a new source? Explanation and examples related to both principles would be helpful...


title: Do arXiv links last for the forseeable future?

text: If I give someone an arXiv link, say http://arxiv.org/abs/0707.0118 , will this link last for the foreseeable future?


title: What is the meaning of non-compactness in the context of $U(1)$ in gauge theories?

text: In John Preskill's review of monopoles he states > Nowadays, we have another way of understanding why electric charge is > quantized. Charge is quantized if the electromagnetic U(l)em gauge group is > compact. But U(I)em is automatically compact in a unified gauge theory in > which U(l)em is embedded in a nonabelian semisimple group. [Note that the > standard Weinberg-Salam-Glashow (35) model is not "unified" according to > this criterion.] The implication of the third sentence is that, in some circumstances, the $U(1)_{em}$ gauge group may _not_ be compact. How could this be? Since $U(1)$ as a differentiable manifold is diffeomorphic to $S^1$ isn't it automatically always compact? The following paragraph: > In other words, in a unified gauge theory, the electric charge operator > obeys nontrivial commutation relations with other operators in the theory. > Just as the angular momentum algebra requires the eigenvalues of $J_z$ to be > integer multiples of $\frac{\hbar}{2}$, the commutation relations satisfied > by the electric charge operator require its eigenvalues to be integer > multiples of a fundamental unit. This conclusion holds even if the > symmetries generated by the charges that fail to commute with electric > charge are spontaneously broken. is OK, but I don't follow what that has to do with the compactness of $U(1)$.


title: How does energy transfer between B and E in an EM standing wave?

text: I'm trying to understand how an electric field induces a magnetic field and vice versa, its associated energy, as well as relating it to my understanding of waves on a string. Using a standing wave as an example, I came up with the equations $\vec{E}=A\sin(\omega t)\sin(kx)\hat{y}$ $\vec{B}=\frac{Ak}{w}\cos(\omega t)\cos(kx)\hat{z}$ I checked them against Maxwell's equations, and they're self-consistent. At time 0, this reduces to: $\vec{B}=\frac{Ak}{w}\cos(kx)\hat{z}$ Since the electric field is 0, based on the Poynting vector, there's no energy transfer at this time. At this time, at a node where $\vec{B}=0$, there's neither electric field nor magnetic field. If there's no energy transfer, and no energy stored in either field, then how can an electric field exist at this point at some time later? How is the energy stored, or transferred from elsewhere?


title: Period of small oscillations

text: > _A light elastic string is stretched between two points, one lying > vertically below the other. A particle is attached to the mid-point of the > string, causing it to sink a distance h. Assuming that the string below the > particle does not go slack, show that the period of small vertical > oscillations about its equilibrium position is $2\pi(h/g)^{1/2}$._ My attempt: The string seems to be acting like a spring so from Hess's law we have the tension $T = kh$ and resolving downwards we have $mg = kh$ so $k = \frac{mg}{h} $, this was as far as I was able to go - how else would I proceed? I've tried using $F = ma$ but no luck.