4 element super conductor without oxygen and iron

I am trying to find a list with super conductors. In particular I am searching for a superconductor, that consists of 4 elements none of which is Oxygen. The reason I rejected Oxygen, is because(from the kinematic factor) the maximum energy from scattering with the Oxygen is about $730 keV$. Therefore-unfortunately-I have to reject _YBCO_ superconductors. In particular I have to analyse an RBS spectrum of a supposed 4-element well known super conductor. I can't find any 4-element-superconductor without oxygen. Is there anyone, or it might be the case where the sample is bad described? Just for reference the RBS spectrum is ![enter image description here](http://i.stack.imgur.com/eEndF.png) **EDIT** I also tested iron based superconductors, but it seems that I need a heavier element. For instance a superconductor containing $Ba, K, Fe, As$ has the following RBS spectrum ![enter image description here](http://i.stack.imgur.com/P5ssM.png) Please ignore the concentrations... The analysis indicates that the superconductors consists of 4 elements which are   * Bi(28.5%)   * Sr(28.4%)   * Cu(28.2%)   * K(14.8%) Does a superconductor like that really exists? I mean OK about Bismuth or Copper or even Strontium...How about Potassium? The combination of those doesn't seem right to me...


Radio vs optical telescope imaging

As I understand, the visible light from an optical telescope is focused on a sensor which correlates light exposure to an electrical voltage, which is then converted to an image. A single antenna radio telescope's signal is focused on some sort a sensor but this signal represents only a single 'pixel.' To generate a composite image of an object, a time intensive scan pattern needs to be carried out. Why does this difference exist? Why does a radio telescope see a single pixel, while optical telescopes see an entire image? Are radio telescope sensors only a single pixel, or is a radio telescope itself, regardless of the sensor, only capable of seeing a single pixel?


How do I calculate the power consumed by a lightbulb?

I'm studying a lightbulb and its variable resistance, given by the expression: $R(T) = Ro[1 + α(T-T_0)]$, where $R_0$ is the resistance of the lamp at $T_0$. In this case, $R$ is not given by Ohm's law ($V=Ri$). So, which expression can I use to calculate the power consumed by a lightbulb?   * $P = R\cdot i^2$   * $P = \frac{V^2}{R}$   * $P = V\cdot i$ (I don't think I can use this one) I have measured the current and the e.p.d. at the bulb using instruments.


In KK theory, is proper time defined using the 5 dimensional or the 4 dimensional line element?

Let's consider five dimensional KK theory. This is Klein's metric $\hat{g}_{AB}= \begin{pmatrix} g_{00}+A_{0}A_{0}&g_{01}+A_{0}A_{1}&g_{02}+A_{0}A_{2}&g_{03}+A_{0}A_{3}&A_ 0\\\ g_{10}+A_{1}A_{0}&g_{11}+A_{1}A_{1}&g_{12}+A_{1}A_{2}&g_{13}+A_{1}A_{3}&A_ 1\\\ g_{20}+A_{2}A_{0}&g_{21}+A_{2}A_{1}&g_{22}+A_{2}A_{2}&g_{23}+A_{2}A_{3}&A_ 2\\\ g_{30}+A_{3}A_{0}&g_{31}+A_{3}A_{1}&g_{32}+A_{3}A_{2}&g_{33}+A_{3}A_{3}&A_3\\\ A_{0}&A_{1}&A_{2}&A_{3}&1 \end{pmatrix}$ my question is the following, is proper time defined using the five dimensional line element? $d\tau^2=\sqrt{-\hat{g}_{AB}dx^{A}dx^{B}}$ or is it defined as usual using the 4 dimensional line element? $d\tau^2=\sqrt{-g_{\mu\nu}dx^{\mu}dx^{\nu}}$ in either case, why?


A paradox with spin: Is spin a physical degree of freedom?

Suppose I want to calculate the state associated with a spin particle under a magnetic field. I suppose the particle interacts via the Zeeman effect, and only through it. Then I want to resolve the Schrödinger equation: $$\mathbf{i}\hbar\dfrac{\partial\Psi}{\partial t}+\dfrac{\hbar^{2}}{2m}\dfrac{\partial^{2}\Psi}{\partial x^{2}}=h_{Z}\sigma_{z}\Psi\left(x,t\right)$$ with $h_{Z}$ the Zeeman term. All other terms are usual. To resolve, I apply the transformation $$\Psi=e^{-\mathbf{i}h_{Z}\sigma_{z}t/\hbar}e^{-\mathbf{i}Et/\hbar}e^{\mathbf{i}kx}\Psi_{0}$$ with $\Psi_{0}$ a constant taken to be real for commodity, and the dispersion relation reads $$E=\dfrac{\left(\hbar k\right)^{2}}{2m}$$ as usual for a **free** particle. There is no mark of the spin splitting we are used to, like the energy doublet $E_{\pm}=E_{0}\pm h_{Z}$ due to the Zeeman term. Of course this is just a redefinition of the energy origin, done in two different ways for spin up and spin down (or something like that). If I calculate observable like the density $\rho\propto\left|\Psi\right|^{2}=\Psi_{0}^{2}$ or the current $j\propto\Im\left\\{ \Psi\partial_{x}\Psi^{\ast}\right\\} =k\Psi_{0}^{2}$ again I find no _measurable_ signature of the spin degree of freedom... So where is the spin degree of freedom gone ? Do we need to discuss only space and/or time dependent spin degree of freedom to make any sense of it ? And then the spin is only a _relative_ degree of freedom (in other word, I know what is a spin _mismatch_ , but not what is a spin, a bit like a phase: only phase difference matters). Or anyone gets a better idea of what a spin is? Thanks in advance.


Existence and uniqueness of solutions for Einstein equations

Now that an equivalence of Navier Stokes and Einstein equations has been established, and it is known solutions to Einstein-Maxwell-Boltzmann exist and are unique, and it is known that Einstein equations in a wave guage with electromagnetic source with a lorentz gauge also have unique solutions that exist, what are the next steps? What are the good references on research for existence and uniqueness for einsten solutions without electromagnetic sources? Also, what does it mean physically that there are unique solutions to Einstein Field equations when electromagnetic sources are included? For those struggling with the concept of existance and uniqueness, I think this post provides some good insight.


Euclidean derivation of the black hole temperature; conical singularities

I am studying the derivation of the black hole temperature by means of the Euclidean approach, i.e. by Wick rotating, compactifying the Euclidean time and identifying the period with the inverse temperature. Consider the Schwarzschild case as an example. The Euclidean Schwarzschild metric is of course $ds^2=\left(1-\frac{2M}{r}\right)d\tau^2+\left(1-\frac{2M}{r}\right)^{-1}dr^2$ where $\tau=it$ the Euclidean time. Here $\tau\in[0,\beta]$ with $\beta=T^{-1}$ the inverse temperature, where the points $\tau=0$ and $\tau=\beta$ are equivalent. (I ignore the 2-sphere part of the metric.) Outside but close to the event horizon $r=2M$, we can (after simple some steps) write this as $ds^2=\frac{\sigma^2}{16M^2}d\tau^2+d\sigma^2$. Here $\sigma^2 \equiv 8M(r-2M) $, though this is not really relevant for my question. Now the next step in all the literature is to require that $\tau/4M$ is periodic with period $2\pi$ to prevent conical singularities. I have trouble understanding this.   * A conical singularity basically means that the point at $\sigma=0$ looks like the tip of a cone, right? So we have a singularity at $\sigma=0$. But don't we still have a singularity there for polar coordinates $(r,\theta)$, since the coordinate chart $\theta$ is not continuous there?    * If so, removing the point $\sigma=0$ would erase the conical singularity, right? Then why do we want to get rid of the conical singularity, why is it any worse than the polar coordinate singularity? Of course polar coordinates just describe flat space without the origin, is this not the case for the conical coordinates? Clearly I have not understood the concept of a conical singularity... Last question: suppose I did understand it, and continued the derivation to get the temperature $T=1/8\pi M$. Apparently this is the temperature as measured by an observer at infinity, how can I see this? I know the temperature gets redshifted, like frequency, but I don't see where the derivation identifies $T$ with the one measured at infinity.


Does thermal energy change within a chamber depending on what's in it, where it is, what it is?

I have noticed that some people will say that, when you put more mass in an oven, it takes longer for both to cook than if just were one. Some others will say that timings are the same. Assume we have an oven that's heated to 350 degrees fahrenheit, and it's 10 cubic feet(it should hold about 340 liters of liquid, volume-wise). If we stick a 1 lb, 6 ounce cake in the oven in a 9x9 aluminum pan, let's say that it cooks until succinct in about 25 minutes. If we were to add the exact same mass, but in another cake and equivalent pan (with the exact same ingredients to the nearest degree possible on the atomic scale), and we place that pan right next to it in the center of the one-rack oven, will cooking times differ? Basically, does thermal energy become affected when you place more mass over an area of heat within a chamber? It takes different cooking times for different things(molecule-wise, etc.), and mass is always a factor(e.g. a chicken drumstick will cook at 350F in less than 15 minutes, but a whole 5 lb chicken, say, will most definitely take quite longer). So my question is, in an enclosure of 10 cubic feet (or the like), if you add more mass/volume to the chamber, will thermal energy change, will cooking times change with varying mass and volume, distributions and placement inside the chamber, and why or why not? PS: I know this is broad, but we can narrow it down by just taking my aforementioned examples _as just examples_ , and provide answers relevant to the idea within any scope of measurements desired.


Path integral formulation understanding

I have done basic quantum mechanics and now I want to do the path integral formulation. I find Feynman's book _Path Integrals in Quantum Mechanics_ difficult. Is there an easier alternative?


Is it possible to restart formal higher education in physics at a later age?

I would begin by apologizing for a soft question. Reading the FAQ, I have tried to formulate my question precisely in the last paragraph and you may skip the following paragraph where I make subjective observations, which I think may be relevant and any comments would be more than helpful. By formal education I mean registering in an academic department in a university as a grad/Phd Student. Subjective belief: I feel I am personally not upto the mark of high-quality physics students. I need to learn a lot more, and do a lot more problems to be any good. I've noticed that Physics particularly is a very selective field dominated by hard-working and primarily young people who accomplish a lot at an early age (olympiads/contests, early phd's from very good places, etc). Even among this bunch a lot get filtered out and wouldn't get faculty positions. Theoretical Physicists tend to be outliers in a field almost entirely composed of outliers. And to learn from such a community, I feel an academic environment is essential, and not just reading books in isolation. So I beleive academia is the only legitimate environment that functions to produce sane physicists who know their field. However, if one has been set- back for some reason but carries the self-beleif that he can be smart enough to do it, would ageing be a parameter. I read a statement in Kleppner's undergrad mechancis book that "by finishing all this at the age of 26, Newton set the trend which follows today, that great advances are made by young physicists". I haven't found a counterexample so I would trust academic departments have the same criterion. Q: Do people who missed out all the action in their 13-20 ages miss out on having a good career? What are the possible reasons to take a hiatus of "self- study" for a 22-year old so that he may be a good candiate for a respectable physics career (Phd/postdoc etc) later.


Aharonov-Bohm Effect and Integer Quantum Hall Effect

What is the relationship between Aharonov-Bohm effect and Integer Quantum Hall effect?


A few questions on passive vs active Lorentz transformations

1.) How do we physically interpret an active Lorentz transformation? The passive transformation seems simple enough: you view a fixed object from the perspective of a new observer. When we actively Lorentz transform a vector are we interpreting this as moving the vector to a new point in spacetime considered from the perspective of a single observer? 2.) I am reading David Tong's QFT notes, and am having a hard time interpreting what he means by active transformations. The notes in question can be found here: http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf The notes in question are on pg 11-12 as labeled by the book or pages 17-18 as labeled by the PDF. In his notes, Tong states that we can transform a scalar field as follows: $$\phi (x) \rightarrow \phi'(x) = \phi \left(\Lambda^{-1} x \right).$$ When he does this, I'm interpreting this as $$\phi (x) \rightarrow \phi'(x') = \phi \left(\Lambda^{-1} x' \right),$$ where $x'=\Lambda x$. From what I understand, the advantage of using the inverse Lorentz transformation on the primed system is that we can use the same functional form of $\phi$. However, when moving to the primed system we have still used $\Lambda$, not its inverse. Can anyone tell me if I'm correct in my understanding up to this point? If my understanding is correct up to this point then I really don't understand the next section in his notes. He states that under this transformation derivatives transform as $$(\partial_\mu \phi) \rightarrow \left( \Lambda^{-1} \right)^\nu_{\phantom{\nu} \mu} (\partial_\nu \phi)(y),$$ where $y=\Lambda^{-1}x$ (where this $x$ is primed, right?). But we've still gone from $x \rightarrow x'$ where $x'=\Lambda x$ (again based on my understanding which may be terribly wrong). Using $\Lambda^{-1}x'$ was simply a mathematical trick to allow us to use the same functional form of $\phi$. If that's the case, why are the derivatives transforming as $\Lambda^{-1}$ instead of just $\Lambda$? I'm sorry -- I know this is a little convoluted, but I'm having a really hard time getting my head around this, especially with his notation. I really wish he would have used primes or something... Am I completely lost? Someone please rescue me.


Deriving the rocket equation

Recently I decided to brush on the those parts of classical mechanics that always gave me trouble. One of those parts was the rocket equation so I figured that I would try to derive the appropriate equations from scratch. Evidently I ran into trouble somewhere, so I am hoping that someone can point out my errors and steer me in the right direction. Anyway here goes ... Suppose a rocket expels exhaust behind it with constant velocity (relative to the rocket) $\mathbf{u}$. Fix an inertial reference frame and consider the rocket + exhaust system. If $m_R$ denotes the instantaneous mass of the rocket, then the momentum of the rocket can be written as $m_R\mathbf{v}$, where $\mathbf{v}$ is the instantaneous velocity of the rocket. The momentum of the exhaust ought to be given by the integral: $$\int (\mathbf{v}+\mathbf{u})\frac{\mathrm{d}m_E}{\mathrm{d}t} \; \mathrm{d}t$$ where $m_E$ denotes the instantaneous mass of the exhaust. Combining these expressions for the momentum, we arrive at the total momentum for the system: $$\mathbf{p} = m_R\mathbf{v} + \int (\mathbf{v}+\mathbf{u})\frac{\mathrm{d}m_E}{\mathrm{d}t} \; \mathrm{d}t$$ Now according to the 2nd Law of Motion, the force acting on the rocket + exhaust system is obtained from $\mathbf{p}$ by taking time derivatives. In other words: $$\mathbf{F} = \dot{\mathbf{p}} = \frac{\mathrm{d}m_R}{\mathrm{d}t}\mathbf{v}+m_R\frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t}+(\mathbf{v}+\mathbf{u})\frac{\mathrm{d}m_E}{\mathrm{d}t} = m_R\frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t} - \frac{\mathrm{d}m_R}{\mathrm{d}t}\mathbf{u}$$ This expression superficially matches the ones in my college mechanics books, but there is one big difference. In this expression $\mathbf{F}$ is the total force acting on the rocket + exhaust system, while in my texts this $\mathbf{F}$ is just the force acting on the rocket alone. So based on this I have made some fundamental error somewhere in my argument. As I asked before, if anyone could help me identify this error and correct it, I would be much obliged.


Reference for the polar parameterization of quaternions

I would like to find the original reference in which the polar parameterization of quaternions was given (i.e. the relationship between the components of a unit quaternion and the polar angles of an axis and rotation angle of a three-dimensional rotation). I assume it would have been written by Hamilton, but the physics literature from the 60's doesn't really point back any further (See, e.g. Biedenharn LC. J Math Phys 1961;2:433, equation 10). Any suggestions?


Calculation of a Gravity Resonance Keyhole

Can anyone describe the mathematics behind the calculation of a resonance keyhole (for a two-body model)? It seems like the size and position of the keyhole should be a function only of mass and relative velocity, but I'm having difficulty deriving a formulaic solution.


Radio waves and frequency of photon

How radio waves create the current in antenna in terms of photons? If it is Compton scattering then why is not changed the freuency of photons?


Predicting Decay Rates via the Standard Model

Question 7584 illustrated a procedure to forecast the decay rates of isotopes with known long average lifetimes. Lifetimes of the many U isotopes vary from micoseconds to gigayears. F has only one stable isotope while Sn has 10. Can Standard Model principles be used to predict the stability of isotopes and the average lifetimes for unstable isotopes, or can this only be done by measurement?


Is equivalent resistance always lower if we add a resistor to a passive electronic circuit?

How to prove that equivalent resistance of any passive network is always lower if we add a resistor between arbitrary two nodes? Note that this is not necessarily a parallel circuit, 2 nodes that we connect with a resistor are not the same 2 nodes between we want to measure equivalent resistance but completely arbitrary 2 nodes in passive network. So imagine a circuit with 4 access points: A, B, C and D. We want to measure equivalent resistance between A and B. How can you prove that Rab will be less if we add a resistor between C and D? I tried to search the web but didn't have any success.


Why Transmission of electrical energy without wires was not practical even after Tesla's proposal

Why we couldn't transmit Electricity wirelessly even after so many proposals available proposed by Tesla ? > Tesla tried to generate more interest in Wardenclyffe by revealing its > ability to transmit wireless electricity, but Morgan was not interested, and > the 1903 "rich man's panic" on Wall Street dried up any further > investment.[8][9][10] By July 1904, Morgan (and the other investors) finally > decided they would not provide any additional financing. In May 1905, > Tesla's patents on alternating current motors and other methods of power > transmission expired, halting royalty payments and causing a severe > reduction of funding to the Wardenclyffe Tower. In an attempt to find > alternative funding Tesla advertised the services of the Wardenclyffe > facility but he was met with little success. By this time Tesla had also > designed the Tesla turbine at Wardenclyffe and produced Tesla coils for sale > to various businesses. Source > > In 1891 and 1892, Tesla demonstrated the oscillatory transformer that bears > his name in lectures delivered before meetings of the American Institute of > Electrical Engineers (AIEE) in New York City" and the Institute of > Electrical Engineers (IEE) in London, and in a later presentation titled "On > Light and Other High Frequency Phenomena" (Philadelphia/St. Louis; Franklin > Institute in 1893), where he put forward his ideas on the wireless > transmission of electrical energy. Source ![enter image description here](http://i.stack.imgur.com/O4iFF.png) The Tesla coil wireless transmitter


Non-stationary capacitor

A common exercise in non-stationary electromagnetism is to find the electric and the magnetic field generated by a capacitor with round plates, if the potential difference between the plates varies in time (typically $V=V_0 sin( \omega t)$ or $V= \alpha t$). While finding the fields internal to the capacitor is pretty easy, I was struggling with those on the outside. $B$ is given instant per instant by Biot-Savart law and varies in time, so exists an electric field following the third Maxwell equation; However, I couldn't find an expression for $E$ without evident absurdities. I thought that maybe with some approximations (quasi-stationarity?) such fields could be ignored. Some hints?


Does space have to be filled with charged particles to carry electromagnetic waves?

I'm a newbie here so have mercy. I'm studying electromagnetic waves. This is the propagation of energy via the vibration of charged particles, as I understand it. A charged particle could be like a proton, which has a positive charge. So I'm imagining a simplified "universe" that just exists along a two dimensional line, a long string of protons. You can send energy from one end of this space to the other by vibrating this string of charged particles. Maybe this could be done by "lifting" one proton at one end of space, and that would effect the next proton along the string in a similar way, only less so, to create a wave. You can move your end of space up and down as fast as you'd like. If you move it slowly, you create long waves (from crest to crest). If you move your proton at your end quickly, you produce short waves. But no matter how quickly or slowly you lift your proton up and down, the wave you create (either longish or shortish) will always reach the other end of space at the same time. In other words, you can't control how fast your wave travels through space, you can only control the shape of the wave itself. The energy transmitted always travels the same speed (C, the speed of light). Lift your proton up and down slowly, and you produce a radio wave. Lift it up and down really quickly, and you'll produce an x-ray wave. Lift it up and down somewhere in the middle, and you get a light wave. Here's one problem I'm struggling with. If we can see light emitted from stars that are light years away from us, that must mean that every part of space along that line of sight is full of charged particles right? If that's so, what are these charged particles? Is space full of particles in every direction, in every place? They aren't protons and electrons right, maybe more elementary charged particles like quarks? So space isn't empty, it's absolutely jam packed with charged particles. The "fabric" of space time is "made of something," and that something must be charged either positive or negative. Is this a correct line of thinking, or am I missing some fundamental idea here? Thanks for your help.


Atomic Physics - Bohr's model of atom

Well I'm learning about the models that have been proposed for the atom, and the Bohr model came up. My teacher told me that the one of the main postulate of the theory is that when an atom is in ground state, it can neither absorb nor emit energy. This is what gives the atom its stability. However, it can obviously absorb energy to jump to a higher energy level. I don't understand, how can it jump to a higher energy level, from the ground state obviously, without absorbing energy? Some problem here?


What does this question about entanglement and classical geometry mean?

Below is the question from Andy Strominger's presentation at the String 2014 conference. The question was asked by credible physicist Ashoke Sen as an important question. > "What is the precise relation between quantum entanglement and classical > geometry?" Could somebody describe the question and explain why it is an important question and its implications?


current in series resistors and voltage drop in parallel resistors

when we have resistors in series, the current through all the resistors is same and the voltage drop (or simply voltage) at each resistor is different. **Question 1:** it is fine that voltage drop (potential drop) is different because each resistor offers different resistance (suppose). but how is the current through each resistor same? if we have resistors of different resistance, shouldn't the current be different through each resistor? similarly, when we have resistors in parallel, the current through each resistor is different but the voltage drop at each resistor is same. **Question 2:** current is through each resistor is different because resistance of each resistor is different (suppose). but how is the voltage drop at each resistor same here? shouldn't the voltage drop at each resistor be different because each resistor offers different resistor?


Resistance between two points on a conducting surface

Suppose we have a cylindrical resistor, with resistance given by $R=\rho\cdot l/(\pi r^2)$ Let $d$ be the distance between two points in the interior of the resistor and let $r\gg d\gg l$. Ie. it is approximately a 2D-surface (a rather thin disk). What is the resistance between these two points? Let $r,l\gg d$, (ie a 3D volume), is the resistance $0$ ? * * * Clarification: A voltage difference is applied between two points a distance $d$ apart, inside a material with resistivity $\rho$, and the current is measured, the proportionality constant $V/I$ is called $R$. The material is a cylinder of height $l$ and radius $r$, and the two points are situated close to the center, we can write $R$ as a function of $l$, $r$ and $d$, $R(l,r,d)$, for small $d$. The questions are then:   What is $$ \lim_{r \rightarrow \infty} \lim_{l \rightarrow \infty} R(l,r,d) $$   What is $$ \lim_{r \rightarrow \infty} \lim_{l \rightarrow 0} R(l,r,d) $$


Does the real part of the inverse dielectric function have to be negative at some point for Cooper pairs to form?

Electrons naturally repel one another. However, in a superconductor, a phonon- mediated interaction causes the electrons to have a weak attractive interaction. Suppose that the interaction between two electrons is $V(\textbf{q})$ (the bare Coulomb interaction, which is $>0$) and that the effective interaction between two electrons is $V(\textbf{q})/\epsilon(\textbf q, \omega)$. My question is threefold: (1) Is the only way to have an attractive interaction between electrons is for the $\Re[\frac{1}{\epsilon(\textbf{q},\omega)}] $ to become negative at a certain value of $\textbf{q}$ and $\omega$? (2) If so, does $\Re[\frac{1}{\epsilon(\textbf{q},\omega)}] $ have to become negative at the values of $\textbf{q}$ and $\omega$ that correspond to a phonon? (3) (If yes to Question (1)): Since high-temperature superconductors form Cooper pairs, does this mean that in the space of $\textbf{q}$ and $\omega$ such that $\Re[\frac{1}{\epsilon(\textbf{q},\omega)}] < 0 $, there are clues lurking about high-temperature superconductivity yet unbeknownst to us?


Quantum Field Theory with (2,2) metric

Does someone know some reference which treats QFT in a space with the following non-Lorentzian signature: $g_{\mu\nu}=\text{diag}(-1,-1,1,1)$. I'm interested in basic stuff like the shape of the scalar propagator and Feynman rules in such a space.


Two-state system problem

Given a 2-state system with (complete set) orthonormal eigenstates $u_1, u_2$ with eigenvalues $E_1, E_2$ respectively, where $E_2>E_1$, and there exists a linear operator $\hat{L}$ with eigenvalues $\pm1$,   1. would the normalized eigenfunctions (in terms of the given eigenstates) just be $$u_1\over \sqrt{\int u_1^*u_1}$$ ? Since I am not given an argument/coordinate system for the eigenstates, perhaps I should first project them into one? But I don't have any info on the nature of the quantum system...   2. A second question asks for the expectation values of the energy in the respective states. But isn't that just $E_1$ and $E_2$ respectively?? Grateful for any enlightenment.


Wave / particle duality question for sound and light

Sound is usually referred to as just "sound waves" - we do not talk about a "sound particle" and only as a wave or "matter wave." Could something similar apply to light i.e. that there really is no "light particle" (photon) and that the wave respresentation is what applies both to sound and light? We say light is an electromagnetic movement, could it be that light is an electromagnetic movement with just movement and similarly to sound like there is no "sound particle" (only a movement that makes some sound from vibration and movement of particles that are "ordinary" particles in the air and not in fact any particular "sound particle" so similarly the photon could be just a name or just a concept in fact used to describe what is similar to sound and just a wave and not a special particle? I know this seems controversial like saying that there is no photon and I say it might be not that controversial since there is no particular particle for sound and a waveform only. Thanks for any insight!


View of the Sun from Voyager 1

Today Voyager 1 is approximately 122 AU distance from the Sun. What does the sun look like from this distance? How much brighter does the sun appear to the naked eye compared to other stars in the same field of view? Are any of the other planets from our solar system visible to the naked eye at this distance? Would the sun produce enough light for a normal person to read a book, or would the light be too dark for reading (just trying to get a practical feel of the amount of light)?


Universal central charge in higher dimensional AdS/CFT?

In the $AdS_3/CFT_2$ correspondence, the central charge of the dual CFT2 is universally given by $$ c = \frac{3\ell}{2G} $$ This is independent of the matter in the bulk of AdS3. Is it also universal in the higher dimensional analogues $AdS_d/CFT_{d-1}$ or does it depend on details of the matter in the bulk, etc.? In particular, what is the central charge for $d=4$?


can interaction between a massless fermion and external sourse exist?

For example, let's consider the electromagnetic interaction between a massless fermion and a electromagnetic externel sourse $A^\mu$, then the lagrangian is $$\mathcal{L}=\bar{\psi}\gamma^\mu\partial_\mu\psi+ieA_\mu\bar{\psi}\gamma^\mu\psi$$ and how can we calculate the Feynman diagram and $\mathcal{M}$ of it? But according to relativity, the equation of motion of a particle with charge is $$e F^a\ _bU^b=U^b\partial_bP^a$$ where $F_{ab}$ is the electromagnetic tensor, $U^a$ is the 4-velocity of the particle and $P^a$ is the 4-momentum of the particle. If the particle is massless, then the speed will be $1$ and this equation fails. So can a massless particle have charge and interaction with externel sourse? If could, for example, how can I calculate the force and equation of motion? If couldn't, why?


Is it possible to harness energy from the exothermic reaction of changes of state of matter?

Since a substance emits heat as it transitions from a high energy state (gas) to a lower energy state (solid), is it possible to devise a method to capture this heat and convert it to usable energy? I'm not sure how economical this would be, but consider the exothermic reaction of water freezing. The heat of fusion for water is $3.33 *10^5 J/kg$ So if a 1 cubic meter of water was frozen, there would be: $3.33 * 10^5 J/kg * 1000kg = 3.33 * 10^8 J$ of heat energy produced. The heat value for the vaporization of water is $2.36 * 10^6 J/kg$ which would be even more efficient, though it is more difficult to capture 1000kg of water vapor. I imagine this might be akin to how an air conditioner works, but I cannot imagine how this may be done or if it is already being attempted. So I pose the question here, would it be possible to harness the heat energy from the air and water concentrate it into a usable form of energy--a clean form of energy at that. Why, or why not?


Earthing of conductors

Can anyone please explain me the process of earthing of a spherical conductor in detail. I am aware about the basic idea of earthing but I am not able to understand and visualize it properly.


Spectroscopy and the current state of our ability to determine the composition of extra-solar planets

I was interested in learning more about the status of our scientific understanding and technological instruments regarding extra solar spectroscopy. I am motivated by this almost 3 year old question/answer here at physics SE. Specifically: > The composition of extra solar planet should be taken with a pinch of salt, > the science is very new and uses instruments not designed for the task. Keep > an eye out for new missions such as ECHO which might fly in the next 5 to 10 > years... Since it has been almost 3 years, can someone give an update on our current understanding on this subject? I am curious as to how accurate our measurements of the composition of planets and stars outside our solar system are. Also, what is the impact of our atmosphere? Are we able to tease out the effects of absorption by our own atmosphere in order to get a clean signal?


Mass-Energy Equivalence theory energy or momentum is not conserved?

The famous equation for mass energy equivalence: $E=mc^2$ It cannot conserve energy or momentum without some loss in one way or another. To elaborate further if I take $1kg$ of mass and I also take electromagnetic radiation with same energy as the $1kg$ mass and ensuring its accuracy using the above equation. Then use this radiation and I use it to smash it into a "crash" mat I would get this: $$E=mc^2$$ $$E=1.c^2$$ $$E=89,401,000,000,000,000$$ **Approx.** That being the energy we then use this to calculate the momentum of the electromagnetic radiation transferred onto the "crash" mat which would be: $$p=mv$$ $$p=mc$$ $$p=e/c^2 . c $$ $$p=e/c$$ $$p=89,401,000,000,000,000/c$$ $$p=299,000,000$$ **Approx.** where as if I now take $1kg$ of matter and accelerate it to high velocity (say, 10,000 kilometers per hour ) to measure its momentum we get roughly $10,000 kg.m/sec$ That being said, momentum cannot be conserved, why is that? Next, Energy cannot be conserved. For example if I used the same $1kg$ and I shoot it into space at a $x$ velocity and after say 1000 years I recieve it and measure mass of the object it would weigh exactly the same as 1000 years before therefore I can conclude it has same energy in its mass however if I use the mass-equivalent of electromagnetic radiation and do the same but my conclusion would be vastly different as first due to travelling in long fabric of space it would get slightly or even highly redshifted due to doppler effect. That being said the observer would get different energy reading to that of 1000 years ago. That in mind where did that energy go?


Why doesn't phase space contain acceleration/forces?

I'm watching some Physics lectures on the internet by Leonard Susskind:   http://www.youtube.com/watch?v=pyX8kQ- JzHI&feature=BFa&list=PL189C0DCE90CB6D81&lf=plpp_video In this lecture, and also in Wikipedia and other places phase space is described as the space of all the states we need to know to determine the configuration of the system infinitely into the future. But I don't understand how is position and velocity enough to determine this, what about forces? Let's say we have a particle and we want to know where it will be in 10 seconds, we obviously need it's starting position, it's starting velocity **and also** all the forces acting on it, or it's acceleration. Where is my misunderstanding?


How should the implicit sum $C_{ijkl}u_{i,j}u_{k,l}$ be interpreted?

$C$ is a 3x3x3x3 tensor. How should the expression $C_{ijkl}u_{i,j}u_{k,l}$ be interpreted? This is my guess: $$ \sum_{i=1}^3\sum_{j=1}^3 \sum_{k=1}^3\sum_{l=1}^3 C_{ijkl}u_{i,j}u_{k,l} $$


How to calculate pressure at altitude when there is 0 temperature lapse?

To calculate pressure at a given altitude, the following formula is used: $p = p_0 \cdot \left(1 - \frac{L \cdot h}{T_0} \right)^\frac{g \cdot M}{R \cdot L}$ _(the values can be foundhere)_ This formula is great, but only works completely with the US Standard Atmosphere. I really want to use ISA (International Standard Atmosphere) more, because it accounts for the dynamics of the atmosphere much better. The problem is that the Tropopause has a Lapse rate ($L$) of 0. I don't know how to get that to work in this formula because that would involve dividing by zero. Any ideas?


Transformators (primary and secondary windings)

Consider the following problem: _Robby wants to put a light in the shed so he puts a cable between his house and the shed. In the cable there are 2 wires with a combined resistance of $0,92 \space \Omega$. Robby connects his transformator at his house on an electricity grid of $230 V$. He connects the secondary inductor($14.3V$) to the cable. A $12 \space V$ / $30 \space W$ lamp in the shed works perfectly._ There are a couple of questions about this piece of text, which have been bothering me:   * **Calculate the heat per second which is created in the cable.** My problem with questions like this is that I have an overwhelming amount of data and it is hard for me to distinguish which is needed and which is not. So my initial thought was that I'd calculate $I$ like this: $ I = 230 : 0,92 = 250 \space A$, and then use the formula $P = I^2 \times R$ which would give me a ridiculous amount of $57500 \space J/s$. I knew I did something wrong when I saw this, so I looked at the correction model and found out that they found the $I$ of the lamp, and afterwards used that in he formula I gave in combination with $R= 0,92 \Omega$. Why is it done like this? I first thought that you could you $I_{lamp}$ because this is in series and $I$ is the same everywhere in series, but I have 2 problems with that idea:   * How do we know it is in series?   * Also, if we do $ I = 230 : 0,92 = 250 \space A$ this isn't equal to $I_{lamp}$, so I dismissed that idea and now I am back at square one.. Then we get the following passage which confused me even more: _Robby decides the put the transformator in the shed. The lamp functions perfectly when he puts the loop ratio to 958:50._ What?! Does this mean that he didn't use the transformator in the first passage? But if he didn't why is the secondary inductor mentioned in the first passage then?! The following 2 questions are easier (if you made the first one correctly):   * **Calculate the primary voltage on the transformator** I just did $(958/50) \times 12 \approx 230V$   * **Explain without using calculations that he loses much less now** $I_{secondary}$ is much smaller now, and because of the formula $P=I^2 \times R$ this leads to less loss of energy. So the bulk of my problem lies with 'analyzing' the first text. How can you conclude from that test that the transformator isn't used?


What's the big deal with Nd:YAG rods?

I see the prices of Nd:YAG rods for lasers, and could someone explain why they are so expensive? Do they need to be mono-crystalline or something? Will Nd:YAG laser work with amorphous/poly-crystalline rod?


How come the universe is made of matter and not antimatter?

Antimatter is like matter on opposite day: it has the same properties as the stuff that makes up planets, stars and galaxies, but one vital piece is different—its charge. The universe supposedly started off with equal parts matter and antimatter, but somehow, matter won out. Most of both substances annihilated each other shortly after the big bang, and left a small surplus of matter remaining.


Why the magnetic flux is not zero?

If $\vec{\mathbf B}=B\vec{\mathbf a}_z$, compute the magnetic flux passing through a hemisphere of radius $R$ centered at the origin and bounded by the plane $z=0$. ![Figure](http://i.stack.imgur.com/WavK2.png) * * * **Solution** The hemisphere and the circular disc of radius $R$ form a closed surface, as illustrated in the figure; therefore, the flux passing through the hemisphere must be exactly equal to the flux passing through the disc. The flux passing through the disc is $$\Phi=\int_S\vec{\mathbf B}\cdot\mathrm d\vec{\mathbf s}= \int\limits_0^R\int\limits_0^{2\pi}B\rho\,\mathrm d\rho\,\mathrm d\phi =\pi R^2B$$ The reader is encouraged to verify this result by integrating over the surface of the hemisphere. * * * According to Maxwell's equations the magnetic flux over a closed surface must be zero, why in this case does not happen?


Some Dirac notation unclarities

**Q1:** Ok so i have come to a point where i know that $\Psi(r,t)$ which we denote only by $\Psi$ can be represented in a Hilbert space by a vector which we denote $\left|\Psi\right\rangle$. Does this mean $\left| \Psi(r,t) \right\rangle$? **Q2:** I know that equation $\Psi = \psi e^{- iWt/\hbar}$ represents a link between a stationary Schrödinger equation and a time dependant Schrödinger equation (we denote $\Psi(r)$ as $\psi$). I want to know now if we denote $\psi$ in a Dirac notation as $\left|\Psi(r)\right\rangle$ or any differently? **Q3:** How do we write a Schrödinger equation and a time independant Schrödinger equation using a Dirac notation?


Heisenberg uncertainty principle - question

> _A beam of particles each having mass $m$ and velocity $v$ in the incident > on a circular hole of radius $b$ located on a screen. If another screen is > placed at a distance $D$ from the hole, determine the minimum size of the > pattern formed on the screen by the beam._


Is there a depth at which a human body, with lungs full of air, will no longer float?

I was watching a special on divers who dove down hundreds of feet without tanks or gear. The show referred to a depth at which the diver was no longer buoyant and would actually sink, even with lungs full of air. Is there such a point and if so, why? What is happening there?


What to work on?

(I am not exactly sure if this question is supposed to go here, but it seems like the appropriate place for it.) Hello Scientific Community, I am soon graduating from high school and, as everyone does, I am searching for something to study at college. I have always wanted to study straight forward physics, but recently I have been having problems finding the application (possible jobs) of a physicist. My parents are trying to push me towards mechanical engineering, but I am trying to convince them I can get a decent job studying physics. They hate the idea of having me become a teacher, so that is out of question. I know many of the members in the community have studied physics, and I would like all of you out there to please help me making a short description of your job and it`s availability. If you know of any other jobs apart from the one you are on, feel free to list them. Thanks a lot for the help P.S: I live in a country were not many resources are spent on scientific investigation. If you work in some kind of job on applied physics, please answer, at least a short response. Still make an answer if you are some kind of investigator for anyone else that reads the thread in the future.


I was wondering why water freezes from up to bottom and not the other way around. The reason I question this is because in a Video I came across, I discovered water freezes from top but surely with the current knowledge I would say it should be opposite because we know cool air drifts down while hot air drifts up so similarly the heat should fall down and this that the freezing should start from bottom and not up? Unless my knowledge applied is wrong and potentially stupid so I want to ask: Why does water freeze from top to bottom?


Is there an official name for "Lorentz Pairs" like energy and momentum?

In learning about relativity I've noticed that in the construction of Lorentz invariants (specifically four-vectors) two physical quantities that were previously considered distinct are instead treated as a single object. Examples include position and time (spacetime), electric and magnetic fields, electric and magnetic potential, energy and momentum, charge and current density, and so on. I was interested in learning more about this I tried googling my best guess, "Lorentz Pairs", to no avail. My question is whether there is more specific terminology referring to these pairs of physical quantities outside of the general term "Lorentz Invariant". Additionally, why do we so often see two physical quantities being combined instead of, say, three or some other number?


Significance of isolation of radium?

This is an extension of my previous question here. Marie Curie isolated radium in 1903, which paved the way for the development of the theory of radioactivity. In regards to the techniques she used however, what was the impact of the establishment of those techniques? Were the techniques used by Curie new? Are they used today? What impact did they have on modern physics? I can find a lot of information online about the actual isolation of radium, but not regarding the significance of the techniques used.


Constant volume specific heat

* A monatomic ideal gas is confined to move in two dimensions. What is the constant volume specific heat for this gas?    * Consider a system of N independent harmonic oscillators moving in two dimensions. What is $C_v$ for the system. For the first case, I guess this one is $C_v = \frac{3}{2}R$. Am I correct? However for the second case, I was confused a little bit. Any help on this?


Why is energy-momentum 4-vector so much easier to explore/observe than spacetime 4-vector

I have read that spacetime 4-vector is quite difficult to observe/explore and that energy-momentum 4-vector is much more appropriate for CERN etc. **Why is that?** Could anyone give me a brief explanation of the differences regarding exploration and observation?


How do I calculate the probability that the oscillator is in a certain state using partition function?

So let's say I have a single ($N=1$) quantum harmonic oscillator and the energy is determined by $E_n = (n + 1/2) \cdot \hbar \omega$ (where $n$ is the quantum number and $n$ = $0, 1, 2, \ldots$) What's the probability that the oscillator is in the state labeled $n$ at temperature $T$? So according to my calculation, $Z$, the partition function, is $Z = 1 / (1 - x)$ where $x = e^{-\beta \hbar \omega} \Rightarrow P = x ^ n (1 - x)$. Is it correct? Also, how do I go about calculating the probability of finding the oscillator in a state with odd quantum number?


How do bicycle spokes work?

As you know, it is quite obvious that Bicycle spokes attach the hub in the centre to the rim. What else do they do? If you compare the wheels today with the ones from ancient times, there are more spokes now on motor bikes and bicycles than of a wheel of a chariot. Why is that? What effect does it have on the vehicle if there is a higher number of spokes on the wheels?


How would a large a mass be stable at the Earth Sun L4 or L5 point?

I've heard about the Trojan asteroids and there is the famous idea of putting a space colony at one of these points, but the explanations I see for how something is stable at those points it they are 'insignificant mass.' What does that mean? Insignificant to Earth could be pretty big, insignificant to the sun could be downright huge. What are we talking about here, the mass of a large asteroid? The moon? The Earth? Surely it couldn't be bigger than one of the two bodies in the system?


Static as opposed to Kinetic Friction in Rolling Motion

During analysis of rolling motion, why do we consider coefficient of friction as that of _static_ friction and not kinetic friction?


Does universal wave function exist?

Does universal wave function exist? What the science tells us?


Hydrogen as a fuel in Sun

The source of Sun's incessant energy is hydrogen; which is continuously converting to helium through nuclear fusion reaction releasing energy. Why does not all hydrogen convert into helium in one big explosion just like a man-made bomb or cracker explodes?


What is the current induced in a straight wire when a magnetic field is turned from on to off?

> Consider a straight wire which runs along the y-axis. A B-field exists which > is uniform and only in the x-direction: > > $$\vec{B}=(B(t),0,0)$$ > > The B-field at time $t_0$ is 'switched off' in a sharp step, which will be > modelled by the tanh function: > > $$ B(t)= \begin{cases} B_0 & t\leq t_0 \\\ 0 & t>t_0 \end{cases} \approx > \frac{B_0}{2}\left [ \tanh(100(t-t_0)) +1 \right ] $$ > > **What is the current induced in the wire due to the change in magnetic > field as a function of time?** What I have tried is to work out the E-Field y-component using Maxwell's 3rd law (using the notation $\partial_{yz} x \equiv \frac{\partial^2 x}{\partial y \partial z}$): $$\nabla\times\vec{E} = -\partial_t \vec{B}$$ But the B-field only has an x-component, so: $$\begin{align} \partial_y E_z - \partial_z E_y &= -\partial_t B(t)\tag{i} \\\ \partial_z E_x - \partial_x E_z &= 0\tag{ii} \\\ \partial_x E_y - \partial_y E_x &= 0\tag{iii} \end{align}$$ So if you differentiate (i) by x, (ii) by y and (iii) by z: $$\begin{align} \partial_{xy} E_z - \partial_{xz} E_y &= -\partial_{xt} B(t) \\\ \partial_{yz} E_x - \partial_{xy} E_z &= 0 \\\ \partial_{xz} E_y - \partial_{yz} E_x &= 0 \end{align}$$ But then if you sub them all in together you get: $$\partial_{xt} B(t) = 0$$ Which isn't very useful.   * If I want to work out the current induced in the wire which runs along the y-axis do I want to work out: $E_y$? And If so how do I do so?   * Would current be induced in any other direction?


Max rocket speed in interstellar space?

Interstellar space propulsion...if a spaceship were to get beyond our Sun's gravitational pull and since there is no atmosphere/wind/friction in space...does that mean, if an engine was constantly thrusting, that the spaceship would continue to accelerate to the speed of light, as long as the engine was propulsing forward? In other words, does speed constantly increase in a vacuum? or are the two ideas (Space/Vacuum) separate ideas?


Absolute Viscosity of Water at certain temperatures

I just started my class on fluid mechanics. There's a problem that requires absolute viscosity $u$ of water at 25C. I looked up my table in the book and I only have it for water at 20C and 30C. I figured we had to manually calculate it in this case. The school notes only have Andrade's equation $u = D \times e^{\ B/T}$ So I've got the absolute temperature which is 25C. There is no information of what D and B are(Defined as constants). So how do I figure out the absolute viscosity at any temperature? I've looked up a table online with the value for water at 25C and it gives me the right answer, is it okay to interpolate the values of my table of 20C and 30C to find the value for 25C?


Why is the second the SI base unit for time?

Specifically, during the moves towards _Le Système international d'unités_ in the 18th and 19th centuries, why didn't anyone attempt to move us away from the definition of there being 24 hours in a day? Wikipedia informed me that the name **second** comes from the _second division_ of an hour. It also claims that the concept of having 24 hours in a day dates back at least 6000 years to the earliest Egyptian civilization. It also says the word second (as a measurement of time) didn't make it into English until the 1500's and couldn't be measured with any accuracy for 100 years. So by one way of looking at things, the base unit of time (or perhaps the grand-pappy unit of time) is the hour. Is there some convenient property of **24 hours = 1 day** that caused it to hold on over other units? I understand the significance of a degree being 1/360th of a circle (360 = 60 * 60 = (3 * 4 * 5)^2), and 24 is closely related to those factors, but that seems a flimsy reason. The math for converting earth's rotation to elapsed time doesn't even work out very conveniently (IMO) with these units. I expected to find a reason in time being one of the basic properties of the universe, being immutable (in 18th century eyes) and therefore used as a pivot point for other unit definitions. But the dependency graph of SI units mostly dispelled me of that: both temperature and mass were found to be as independent as time, and both units were redefined during this period (to Kelvins and kilograms, respectively). ![The seven SI base units and the interdependency of their definitions. Clockwise from top: kelvin \(temperature\), second \(time\), metre \(length\), kilogram \(mass\), candela \(luminous intensity\), mole \(amount of substance\) and ampere \(electric current\).](http://i.stack.imgur.com/jnGwh.png) During the same period, other units were attempted to be re-measured from new standards:   * Length was adopted to use the meter at one ten-millionth from the North Pole to the Equator in 1793   * Mass was adopted to use the gram at the cube of the hundredth part of the metre (at STP) in 1795   * Temperature was adopted to use degrees Celsius, one hundredth of the separation between boiling and freezing of water. And yet, efforts to define the second seem to center on more perfectly measuring the existing definition of 1/86,400th of the Earth's rotation. Given the predilection for base 10 (and the gradual move away from units depending on our earthly frame of reference), why was the second left at such a cumbersome, ancient interval? Why didn't we redefine a new measure of time to be (say) 1/100,000th of a day, put 10 hours in a day, etc. etc.? Did no one think to challenge the convention of 24 hours in a day? Why not? That came out a little more jumbled than it was in my head, so let me sum up: I'm mainly interested in answers addressing attempts to redefine units of time and why they didn't achieve wide adoption in the scientific community.


Surface UV exposure with cooler star

If the sun's surface was ~ 4000K (and earth closer to compensate), the UV component of the radiation would be less. However, UV makes ozone via photolysis of oxygen. Also, the stratosphere would probably start up higher (and contain less mass) because UV heating is what's responsible for the inversion. So what is the relationship between surface UV exposure (measured in DNA damage) and star temperature, which effect "wins"?


Does fluorescence produce most of the colors we see day-to-day?

I read the following on Wikipedia regarding fluorescence, > _Fluorescence is the emission of light by a substance that has absorbed > light or other electromagnetic radiation... The most striking examples of > fluorescence occur when the absorbed radiation is in the ultraviolet region > of the spectrum, and thus invisible to the human eye, and the emitted light > is in the visible region._ Recalling my grade-school knowledge of color perception: The colors I perceive of an object that does not produce light are those that the object does not absorb. Both those notions seem the same to me; however, I suspect that I've missed something. Is there a difference between the way that the colors we perceive of most objects is produced and the way that flourescent color is produced?


Derivation of Euler-Lagrange equations for Lagrangian with dependence on second order derivatives

Suppose we have a Lagrangian that depends on second-order derivatives: $$L = L(q, \dot{q}, \ddot{q})$$ If we're working on the variational problem for this Lagrangian, then I know that we'll wind up with the following Euler-Lagrange equation: $$\frac{\partial L}{\partial q} - \frac{d}{dt} \frac{\partial L}{\partial \dot{q}} + \frac{d^2}{dt^2} \frac{\partial L}{\partial \ddot{q}} = 0.$$ However, I can't see how to derive this equation. Obviously, the final term is supposed to come from integrating by parts the contribution of the $\ddot{q}$ dependence to the variation in the Lagrangian; doing that yields (writing $T$ for the period of time over which we're extremising the action): $$\int_T \frac{\partial L}{\partial \ddot{q}} \delta \ddot{q} = \left[ \frac{\partial L}{\partial \ddot{q}} \delta \dot{q} - \frac{\partial L}{\partial \ddot{q}} \delta q \right]_{\partial T} + \int_T \frac{d^2}{dt^2} \frac{\partial L}{\partial \ddot{q}}.$$ Now, the term in square brackets presumably has to vanish. The right-hand term will do so, since $\delta q$ vanishes on the boundary of $T$; but why should the left-hand term vanish? Is it just a condition of dealing with the variations for such a Lagrangian that we consider only variations for which $\delta \dot{q}$ vanishes on the boundary of integration as well? Or is there something I'm missing?


Data For Quantum Entanglement

Is there any publicly accessible data that shows quantum entanglement empirically. I want to see what these researches are seeing that is showing them that indeed this phenomenon is real. Also, any explanation of such data would be greatly appreciated, ie. what instruments are used to measure what aspects, how to interpret the data, and what specific elements prove the phenomenon beyond any doubt or what things would have to be different in the data to falsify the claim of quantum entanglement.


Phase space in quantum mechanics and Heisenberg uncertainty principle

In my book about quantum mechanics they give a derivation that for one particle an area of $h$ in $2D$ phase space contains exactly one quantum mechanical state. In my book about statistical physics they do exactly the same, but now for $6D$ phase space (now one quantum mechanical state covers a volume of $h^3$). I'm not sure that I interpret this well. Does this mean that in this $6D$ volume of phase space (of $h^3$), the particle can only be in exactly one location with only one possible set of momentum vectors $p_x$, $p_y$, $p_z$ (this is how I interpret "one possible state")? If this interpretation is right, I have the following problem. Both books say that this is conform the uncertainty principle of Heisenberg, but I don't see why. It seems to me that because one can measure (f.i. in $2D$ phase space) $p_x$ and $x$ so that $∆x∆p_x = h$ and because this is exactly the surface of phase space in which there is only one state, that one has now determined exactly the position and momentum of the particle (because there is only one state in this area). Because of this I guess something is wrong with my interpretation (although it seems to match with the derivation).


What is a sudden singularity?

I've seen references to some sort of black hole (or something) referred to as a sudden singularity, but I haven't seen a short clear definition of what this is for the layman.


Unclear how heat interacts with Navier Stokes

I am playing around with an Navier stokes solver and I'm having trouble introducing heat. Am I right in thinking this would be introduced in the ${\bf f}$ term of ${\partial{\bf u}\over\partial t} = -({\bf u}\cdot\nabla){\bf u}+v\nabla^2{\bf u}+{\bf f}$? I find the lack of mass term disturbing. Please reassure me! Also, how do I calculate the force vector, given that I have computed the scalar $dQ\over dt$ from Newton's law of cooling? Or is that the wrong approach?


Why does the alcubierre drive get roasted by hawking radiation?

I read that an alcubierre drive would get destroyed by hawking radiation inside the warp bubble. Where does this hawking radiation come from? And why does it only happen to objects inside the bubble?


Pulsed Spherical Wave

Can somebody help show me how a pulsed spherical wave has a wavefunction of the form U(r,t) = (1/r)a(t-r/c), where a(t) is an arbitrary function, r is the radius of the spherical wave, t is time, and c is the speed of light?


do Higgs Bosons happen in nature all the time? Rarely? Or do they only happen when the Higgs field is excited in a particle accelerator?

I'm trying to reconcile an apparent contradiction between explanations given by Dr. Cox in 2009 and 2012, and those given by a panel of Berkeley professors. I'm not a physicist, and so I realize this contradiction is likely my layman misunderstanding. I appreciate your time in teaching me. Dr. Cox seems to describe, I think, the Higgs Boson as though it were just another gauge boson, i.e. one of the fundamental "force carrier" particles by which force is transmitted to other particles. Except in this case, the H.B. is not transmitting force but imparting mass. He goes on to say explicitly that Higgs Bosons exist in vast numbers all around us and are constantly bombarding all other particles at all times. It is through this bombardment that mass is gained. Is my summary and interpretation correct? If so, is his explanation accurate? My understanding was the H.B. is more or less a byproduct of the Higgs field itself, the result of its excitation, and it is interaction with the field itself, not the H.B., that endows other particles with mass. This slide from the Berkeley lecture lists the H.B. as neither a gauge boson particle, nor a matter particle, but an entirely different, third type of particle. Does the Higgs field exist because there's an abundance of H.B. particles just moving around, themselves giving rise to the Higgs field? Or does the Higgs field simply exist everywhere, and by virtue of its existence, occasionally an H.B. pops out? (Of this last point, I am certain. Several sources have directly stated that what makes the Higgs field unique is that its default energy state is nonzero, i.e. unlike the "electron field", it exists everywhere, even in a vacuum). **Do Higgs Bosons happen on their own in nature all the time?** Rarely? Or do they only happen when the field is excited under deliberate conditions, e.g. within a man-made particle accelerator? Or is my question malformed and running afoul of the wave/particle duality? A final summary of my running understanding: Consider an electron and a positron, some distance apart. They each experience an attractive force to one another, via the electromagnetic field they produce. The actual means by which this force is transmitted, the means by which the electron "knows about" the positron, is by way of a gauge boson, in this case the photon. "The photon is the mediating particle of the EM field". **You quite literally have photons moving back and forth between the electron and positron**. They serve as the actual means of transmission of force/energy/momentum transfer and exchange between the two particles. (I'm referencing some illustration I saw in a video that quite literally had an animation of photons bouncing back and forth from, in their example, nuclear protons and their orbiting electrons). I think I'm just at a loss to explain the relationship between and difference among the Higgs field and the H.B. itself. Explanations in lectures and the media seem to vary from "With respect to endowing mass, the H.B. does it all" to "The Higgs field does it all; the H.B. is just a theoretical consequence of the existence of the Higgs field; finding the H.B. is strong confirmation that the Higgs field itself exists". Thanks!


ADM Hamiltonian formalism and Quantum gravity

is there a Hamiltonian reformultion of gravity ?=? if so if we use the usual Quantization scheme we can not we quantizy the gravity ?? in terms of a Gauge Theory with the potential $ A_{\mu}^{i} $ how can we get the Schroedinguer equation ??


What is this shadow of the Sun on the Moon?

I was reading the article _Moon Phases_ on HowStuffWorks. In the picture, each moon has a dark green area which represents the shadow of the Sun. How is this shadow formed and why is this important?


Energy and Matter

I was watching a show about the big bang theory. They were saying that in the beginning all that existed was energy. After the big bang that energy transformed into matter which then started forming into different elements. How exactly does energy change into matter and at what point does this happen?


What is a photopeak?

I'm currently studying for an exam, where I'm looking into decays and gamma radiation. I then have a diagram where there are stuff like "Compton scattering", "Single Escape Peaks", "Double Escape Peaks" which all are calculated if I know the value of the photopeak. And all these three are actually quite well explained But, nothing in my notes actually tells me what the photopeak is :/ So could anyone explain, just briefly, what the photopeak is/means, at least in this regard. Thanks in advance :)


What does it mean to "wrap" a D-brane around some manifold?

I am getting quite confused with this terminology when I read the papers. Like while constructing the near horizon $AdS_3$ in the $D1-D5$ system one considers $IIB$ on $R^{1,4}\times M^4 \times S^1$ and one "wraps" $N_1$ D1 branes on the $S^1$ and $N_5$ D5-branes on $M^4 \times S^1$. What does it exactly mean? Coming from reading how D-branes were introduced in Polchinksi's book I would think that in a $9+1$ spacetime Dp branes are some planar streched out stuff with a $p+1$ worldvolume and whose $p$ spatial dimensions are transverse to the $9-p$ spatial dimensions which have been compactified and T-dualized. So are we now saying that its possible that instead of imagining the Dp branes as some set of periodically arranged planes on the T-dual torus we can also think of their spatial world being compactified on some arbitrary p-manifold? If "wrapping" is really a choice of topology for the p-spatial dimensions of the Dp-brane then what determines this choice? Is this something put in by hand or does this happen naturally?


The force arrow for centripetal force points in the opposite direction of my calculation?

I need someone to clarify a conceptual problem I can't seem to surpass. Image there is a rollercoaster loop and a rollerbcoaster car enters the loop at high speed. Once the car completes the full loop and is then at the last point at the bottom of the loop, I am trying to understanding the forces at play. I can see that there is gravitational force: $F_g$ = $mg$ and centripetal force: $F_c = $ $v^2/r$, and then there is the normal force $F_N$. Let's say $F_g = 10$ ,and $F_c = 25$, wouldn't $F_N = 35$? And if so, I am very confused about the force diagram. We have $F_N$ pointing up and $F_g$ pointing down, but what about $F_c$? My calculation has it pointing down, but in reality I thought centripetal force always points to the center of a circle? Thanks for the help!


How do you measure neutron energy?

I think you can detect a neutron event with a scintillator (neutron to photon), photomultiplier tube (photon to electric signal) system, but how would a fusion neutron's energy (2.45 MeV) be typically measured?


Outflow for fluid simulation based on "Stable Fluids"

I've implemented a fluid simulation based on the paper Stable Fluids. It works quite well, except I would like to have the velocity at the "upper" edge just to outflow and not to re-enter on the lower(opposite) edge. Apparently that's a side-effect of the periodic boundaries. Is there an easy method to still achieve this? How would I need to modify the velocity? **Edit:** The fluid may just exit, since I'm just interested in how the velocity evolves (and since I'm adding new tracing particles all the time anyway). Actually I use an (3d-)extended version of the CUDA fluid example. I guess it's mesh-full and yes, it involves the FFT.


How do I split a vector into components parallel and perpendicular to a known line?

> Given $\mathbf{F}=\langle 7.20,−12.0,28.2\rangle\text{ Newtons}$, find the > component of $\mathbf{F}$ that acts perpendicular to member DA such that the > vector addition of the perpendicular and parallel components of $\mathbf{F}$ > ($\mathbf{F}=\mathbf{F}_\perp + \mathbf{F}_\parallel$) with respect to DA > equals $\mathbf{F}$. Express your answer in component form. $\mathbf{A} = (−5.60,3.68,5.76)$ and $\mathbf{D} = (0,2.72,3.00)$ By finding the position vector of DA, which was $\langle -5.6,0.96,2.76\rangle$, then getting the unit vector of DA, which was $\langle -0.886,0.152,0.437\rangle$ and dotting it with the force vector I got the magnitude of the force along DA, which was $4.11\text{ Newtons}$. Now I am not sure how to continue this problem. I know that the magnitude of $\mathbf{F}$ minus the magnitude of the force along DA equals the magnitude of $\mathbf{F}_\perp$, but how do I get it in components? ![Diagram](http://i.stack.imgur.com/cAY6w.jpg)


Flux increase due to velocity?

I have a book question I'm trying to understand: ![http://i.imgur.com/IqmS9OB.png](http://i.stack.imgur.com/LJCeE.png) The first bit is easy enough. The second part I was confused so I checked the solution: > B is into the page. The flux increases as the bar moves to the right, so the > magnetic field of the induced current is out of the page inside the circuit. > To produce magnetic field in this direction the induced current must be > counterclockwise, so from b to a in the rod. I thought I had a pretty good grip on increasing/decreasing magnetic field inducing negative/positive current(respectively). Maybe I'm missing something real trivial but I don't understand how flux increases as the bar moves. Why?


Why there is no operator for time in QM?

Is there one central reason why there is no "Time" operator in QM? I know this question has been asked before, but I thought I would try to stimulate some fresh thinking.


Is there an observable of time?

In Quantum Mechanics, position is an observable, but time may be not. I think that time is simply a classical parameter associated with the act of measurement, but is there an observable of time? And if the observable will exist, what is an operator of time?


Time as a Hermitian operator in QM?

In non-relativistic QM, on one hand we have the following relations: $$\langle x | P | \psi \rangle ~=~ -i \hbar \frac{\partial}{\partial x} \psi(x),$$ $$\langle p | X | \psi \rangle ~=~ i \hbar \frac{\partial}{\partial p} \psi(p).$$ On the other hand, despite the similarities, the relations cannot be directly applied to energy and time: $$\langle t | H | \psi \rangle ~=~ i \hbar \frac{\partial}{\partial t} \psi(t),$$ $$\langle E | T | \psi \rangle ~=~ -i \hbar \frac{\partial}{\partial E} \psi(E).$$ Just wondering, how can one mathematically prove that the "classical time" (which means no QFT or relativity involved), unlike its close relative "position", is not a Hermitian operator? I ask your pardon if you feel the question clumsy or scattered. But to be honest, if I can clearly point out where the core issue of the problem is, I may have already answered it by myself :/


How can we detect X-rays?

I know that X-rays can be detected by various ways, like ionizing of air particles. Is there a way to detect X-rays,which are photons, by detecting? Can something absorb the energy of the X-rays and detect if it is there?


How to measure the arbitrariness of a quantum state?

An arbitrary qubit is represented as $\alpha|0\rangle+\beta|1\rangle$ with $|\alpha|^2+|\beta|^2=1$. If we know either $\alpha$ or $\beta$, the state can be completely identified. The 'arbitrariness' of an arbitrary qubit thus can be said to be '1'. For a known state this is '0'. Now if we consider an arbitrary two qubit state, the total number of variables are 3 (actually 4 but 1 less due to normalization). If any two of these variables are equal or one of them is known, the state is still arbitrary but from a given restricted class. We can say that the 'arbitrariness' of this quantum state is something between 0 and 1. Can anyone suggest a measure for the arbitrariness of this quantum state? I want to extend this measure to higher order states. Can anyone suggest any reference for this?


How does the Planck length hold true?

If there is a length which no object can breach in terms of the smallest of size, how can that length hold true? Our earth is undoubtedly considered the Planck length to some monolithic planet out there (relatively speaking of course), yet a number was derived stating the smallest possible space occupied? I'm not saying this theory is wrong, I would just like it explained to me.


Which is smallest distance measurement which makes sense talking about

This might seem a silly question, but here it goes: Of all possible values for a measure of distance, which is the smallest that makes sense talking about? I mean, I could talk about $10^{-100000}$ meters but in real life this value is smaller than anything we know (i think), so it wouldn't make any sense talking about this value, now would it? Initially I thought about Planck length, but I'm not sure. Please not I'm not referring to mathematics, any number can be of use in mathematics. But in real life, small values like $10^{-100000}$ meters don't make sense. So, what is smallest distance value that makes sense talking about? Thanks.


Why is the Planck length the shortest measurable length?

I quote from the Wikipedia article on Planck length: > _According to the generalized uncertainty principle, the Planck length is in > principle, within a factor of order unity, the shortest measurable length – > and no improvements in measurement instruments could change that._ I also link to an answer provided to this Phys.SE question: > _The reason there is only a finite number of ways is that we assume > separations smaller than the Planck length can't be distinguished._ I have hear this claimed every once in a while, but I never learned this formally at university. Can it be proven using quantum mechanics/uncertainty principle that the Planck length is the smallest measurable quantity, or is this still an area of debate and opinion in modern physics? If you have a simple proof, could you please provide.


Need help understanding dynamic and static contact angles

I've run into a conceptual road block. I'm coming to you guys because I think my adviser is getting annoyed with me. The concept involves a meniscus being pulled up a cylinder. I understand that the main force "pulling" on the meniscus at the contact line is due to the difference between the static and dynamic contact angles. This force per unit length takes the form: $F=\gamma (Cos(\theta_{static})-Cos(\theta_{dynamic}))$ The concept that describes determining the static and dynamic contact angles have been given to me in terms of minimizing the interface between the liquid and air when the meniscus has reached a known height. In the words of someone much more knowledgable than me: "The fluid interface only knows about the equilibrium contact angle as a boundary condition. For any circle and any height there is a minimum energy configuration of the fluid surface. All of these solutions have a different angle. You find the equilibrium by finding the minimum energy solution that also intersects the solid at the contact angle." For some reason, I am unable to see where I can explore these concepts to determine a relationship between the dynamic and contact angles. Can anyone offer elucidation as to these concepts? Thanks


A basic question on AdS/CFT

Previously I asked a question Question on dimensions of CFT operators (ref: MAGOO, hep-th/9905111) here and it was (correctly of course) answered by Motl. I realized I didn't understand a part of it even though I thought I did. It was about dimensionlessness of bulk scalars from the perpective of boundary conformal transformation. If we have a bulk scalar $\phi$ it is dimensionless from the point of boundary transformations as (as answered by Motl) ``it is an actual field in the AdS space (the bulk), unlike $\phi_0$ that is defined on the boundary. They mean that it is dimensionless under the conformal transformations of the boundary - and that's true because the conformal transformations are realized as simple isometries in the bulk, so they can't rescale the AdS field $\phi$ - at most, they move it to another point. '' But the way we talk about conformal dimension of a boundary operator is through it's transformation under the diffeomorphism $x\to\lambda x$ and then if a boundary field $f(x)\to f^\prime(x)=\lambda^hf(\lambda x)$ (or the relation written later by Motl in that answer), then $h$ is it's conformal dimension. I hope what I said so far is right. But, isn't conformal transformation at the boundary also act as a diffeomorphism in the bulk (at least for boundary part of the coordinates of the bulk field). Then why will it not transform in such a way that it has a dimension? I believe, e.g. spin-1 gauge field in the bulk has (confomal/scaling/mass) dimension 1. So, how does it have a dimension? Sorry for the novice question and thanks in advance!


Difference between $\partial$ and $\nabla$ in general relativity

I read a lot in _Road to Reality_ , so I think I might use some general relativity terms where I should only special ones. In our lectures we just had $\partial_\mu$ which would have the plain partial differentials. On a problem set, the Bianchi identity for the Maxwell field tensor is given as: $$ \partial^\alpha F^{\beta\gamma} + \partial^\beta F^{\gamma\beta} + \partial^\gamma F^{\alpha\beta} = 0. $$ In Penrose's book, this identity is given as $\nabla_{[a} R_{bc]d}{}^e = 0$ where the square brackets denote the antisymmetrisation like in the previous form. **Are those square brackets standard notation in Physics?** Since $\partial_\mu$ is basically the $(\partial_t, \nabla)$ it is a covector or covariant vector. Penrose calls this $\nabla_a$ the covariant derivative (something with a connection and curved manifolds as far as I understood). If I am in a non-curved $\mathbb M$ Minkowski $(1, 3)$ space where I have no curvature (since $\eta_{\mu\nu}$ is $\mathop{diag}(1, -1, -1, -1)$?), I was thingking that $\partial_\mu = \nabla_\mu$. **Can I write $\nabla_\mu$ instead of my partial derivatives or do they mean something different?**


Spinning spheres colliding

In an ideal environment with no friction, in a vacuum, what happens to the velocity of the spin of two spheres spinning in perfect parity at two different velocities when they come into contact?


Why a star commonly exhibits 6 rays?

Have you realized, that often the photo of a star shows 6 rays spreaded symmetrically around it, independently of the camera chosen? Do you have idea of what kind of optical phenomena is behind it?


Oscillating Dipole: Principle of Receiving and Transmitting Electromagnetic wave?

I am practising to Tfy-0.1064 -elementary-physics-exam and doing this practise -exam here. The problem in Finnish goes like this: > _"Selosta lyhyesti sähkömagneettisen säteilyn lähettämisen ja > vastaanottamisen periaate."_ and its translation is: > **"Outline the principle of transmitting and receiving Electromagnetic > wave."**


A question for the generalization of gauge transformation with two antisymmetric indices

I have a question about the generalization of gauge transformation with two antisymmetric indices. Starting from Eq. (3.7.6) in Polchinski's string theory book p. 108. $$S_{\sigma} = \frac{1}{4 \pi \alpha'} \int_M d^2 \sigma g^{1/2} \left[ \left( g^{ab} G_{\mu \nu}(X) + i \epsilon^{ab} B_{\mu \nu} (X) \right) \partial_a X^{\mu} \partial_b X^{\nu} + \alpha' R \Phi(X) \right] \tag{3.7.6} $$ where $B_{\mu \nu}(X)$ is the antisymmetric tensor. It is said variation $$ \delta B_{\mu \nu} (X) = \partial_{\mu} \zeta_{\nu}(X) - \partial_{\nu} \zeta_{\mu}(X) \tag{3.7.7} $$ can add a total derivative to the Lagrangian density. I tried to do some integration by part for $\partial_{\mu}$, $\partial_{\nu}$, $\partial_a$, and/or $\partial_b$ in (3.7.7), miserably I didn't get a total derivative. My question is, how to see Eq. (3.7.7) gives a total derivative?


Possible to calculate carrier lifetime with doping concentrations?

I'm working on a problem involving a silicon semiconductor. A PN junction is created with $N_a = 5\cdot10^{14}$ throughout the entire semiconductor, and is doped with $N_d = 2\cdot10^{15}$ on the N side. I'm asked to calculate the Diffusion Constant $D$, carrier mobility, and carrier lifetime for both sides of the semiconductor. I think I've properly calculated the carrier mobility and the diffusion constant, but I can't figure out how to get the carrier lifetime (or recombination time).


Is it circular reasoning to derive Newton's laws from action minimization?

Usually, a typical example of the use of the action principle that I've read a lot is the derivation of Newton's equation (generalized to coordinate $q(t)$). However, in the classical mechanics interpretation, isn't this like tripping oneself up? Because we've already identified $T$ and $U$ as the kinetic energy and the potential energy, respectively which are derived, in fact, from Newton's equations.


Quantum master equation in the Batalin-Vilkovisky formalism

I am reading the Section 15.9 of Weinberg's book "The Quantum Theory of Fields, vol. 2". Under a shift $\delta\Psi[\chi]$ in $\Psi[\chi]$, we have $$ \begin{split} \delta Z&=i\int[d\chi]\,\exp\big(iI_{\Psi}[\chi]\big) \left(\frac{\delta_RS[\chi,\chi^{\ddagger}]}{\delta\chi_n^{\ddagger}} \right)_{\chi^{\ddagger}=\delta\Psi/\delta\chi}\left( \frac{\delta(\delta\Psi[\chi])}{\delta\chi^n}\right) \\\ &=i\int[d\chi]\,\exp\big(iI_{\Psi}[\chi]\big)\left\\{\frac{\delta_L} {\delta\chi^n}\left(\frac{\delta_RS}{\delta\chi_n^{\ddagger}} \delta\Psi\right)-\frac{\delta_R}{\delta\chi_n^{\ddagger}} \frac{\delta_LS}{\delta\chi^n}\delta\Psi\right\\}_{\chi^{\ddagger} =\delta\Psi/\delta\chi} \\\ &=\int[d\chi]\,\exp\big(iI_{\Psi}[\chi]\big)\left\\{ \frac{\delta_RS[\chi,\chi^{\ddagger}]}{\delta\chi_n^{\ddagger}} \frac{\delta_LI_{\Psi}[\chi]}{\delta\chi^n}-i\Delta S[\chi,\chi^{\ddagger}]\right\\}_{\chi^{\ddagger}=\delta\Psi/ \delta\chi}\delta\Psi[\chi] \end{split} $$ The last line is exactly the same to Eq. (15.9.33). Referring to the definition of antibracket $$ (F,G)=\frac{\delta_RF}{\delta\chi^n}\frac{\delta_LG}{\delta\chi_n^{\ddagger}}- \frac{\delta_RF}{\delta\chi_n^{\ddagger}}\frac{\delta_LG}{\delta\chi^n} $$ we can see that the quantum master equation reads $$ -(S,S)-2i\Delta S=0 $$ which has an extra minus sign. I are not sure whether this is a typo or not. Could someone help me to check this derivation? Besides, I am also confused by $\delta_L$ and $\delta_R$. Any clarifications will be appreciated. Many thanks in advance!


Heisenberg picture of QM as a result of Hamilton formalism

Let's have formula of full time-derivative of physical value in Poisson's formalism: $$\tag{1} \frac{df}{dt} = -[H, f]_{P. br.} + \frac{\partial f}{\partial t}, $$ where $[A, B]_{P. br.}$ is Poisson's bracket, and $H$ the Hamiltonian. By using quantum mechanics the equation can be rewritten in form $$\tag{2} \hat {\frac{d f}{d t}} = \hat {\dot {f}} = \frac{i}{\hbar }[H, f] + \hat {\frac{\partial f}{\partial t}}. $$ It is a bit like Heisenberg picture, but in $(2)$ in the left side there is operator of full time-derivative of function (also, in the right side - operator of partial time-derivative). In Heisenberg picture in the left side is full time-derivative of operator, which represents function. So my question is: can I get Heisenberg formalism from $(1)$?


Voltage and parallel-plate capacitors

Suppose we have two parallel plates (each of area $A$) spaced with distance $d_1$ acting as a parallel-plate capacitor within a circuit. If the capacitor is connected to a power source with constant voltage $V_s$, positive charge will accumulate on the parallel plate connected to the positive terminal and negative charge will accumulate on the plate connected to the negative terminal. This will create an electrical potential between the two plates. Does this process continue until the voltage $V_t$ between the plates is equal to $V_s$, and if not, how can we calculate the terminal voltage? Suppose we move the plates closer to distance $d_2$. Will the terminal voltage be identical to that of $d_1$?


Energy of a damped oscillator

$$ E=\frac{1}{2}m\left(\frac{dx}{dt}\right)^2+\frac{1}{2}m\omega_0^2x^2. $$ This is the equation for the energy of a oscillator. The second term is the potential energy. Now, my question is, will this second term remain the same if we are to consider the oscillator as a damped oscillator. Because doesn't the second term arise from the consideration of a conservative force field? And when talking of damped oscillator, isn't the force field non- conservative?


Is there a physical reason steel balls are not suitable to play billiards with?

Steel is an elastic matter and is often used when demonstrating elastic collisions. We also make springs from it. Due to these properties and for its relative low price, it seems obvious to me to use them to play billiards. But I don't find any information on the internet about this. Maybe I miss something very obvious?


A partial differential equation for kinetic energy

The kinetic energy of a point particle of mass $m$ and speed $v$ is $K = \frac{1}{2}mv^2$. An elementary mathematics textbook I saw asked one to show that $$ \frac{\partial K}{\partial m}\frac{\partial^2 K}{\partial v^2} = K.$$ While this is a straightforward exercise in partial differentiation, is there supposed to be any physical meaning behind this formula? For example, is there a significance to quantities that satisfy this nonlinear PDE?


multiple frequency trapped power signal

is there any possibility to generate a waveform that consists of multiple power signals with different frequencies such that these signals travel together like they constitute [to form a knot(waveform) from a group of threads(signals)] without losing any power while propagation?


Am I missing a trick to solving this differential equation?

I was playing around with a 3-D potential $V$ such that $V_{(r)} = 0$ for $r<a$, and $V_{(r)} = V_0$ otherwise. By using the Schrödinger Equation, I showed that: $$\frac{-\hbar}{2m}\frac{1}{r^2}\frac{d}{dr}\bigl( r^2\frac{d}{dr}\bigr)\psi = E\psi$$ I then used the substitution $\psi_{(r)}=f_{(r)}/r$ and $k=\sqrt{2mE}/\hbar$ to get: $$\frac{1}{r}\frac{d^2f_{(r)}}{dr^2}=-\frac{k^2}{r}f_{(r)} \tag{I}$$ which describes the wavefunction $\psi_{(r)}=f_{(r)}/r$ inside the sphere. Hence, the differential equation has the domain $0\leq r<a$, and I cannot multiply both sides by $r$. This is unfortunate, because there is a similar equation for the outside of the sphere: $$\frac{1}{r}\frac{d^2f_{(r)}}{dr^2}=\frac{k'^2}{r}f_{(r)}$$ As this is outside the sphere, I can multiply both sides by $r$ to get a familiar differential equation that can be solved easily: $$\frac{d^2f_{(r)}}{dr^2}=k'^2f_{(r)}$$ If I do the same thing to $(I)$, I obtain the equation for simple harmonic motion, but substituting the solution back into $(I)$ as a sanity check gives a division by zero when evalutating for $r=0$. After that, I tried a number of substitutions to make $(I)$ have a more recognisable form - to no avail. Then I had the idea of multiplying my trial solution by some other function of $r$ so that upon substitution into $(I)$, the evaluation of $r=0$ doesn't give an infinity... but I don't know quite how to do that... Long story short..... my question is: what trick do I need to get a meaningful solution to $(I)$?


Chaos theory and determinism

My professor in class went a little over chaos theory, and basically said that Newtonian determinism no longer applies, since as time goes to infinity, no matter how close together two initial points are, the distance between them will increase greatly. But why isn't this merely a matter of the imprecision of our measuring instruments? If we can somehow know our initial conditions _exactly_ , wouldn't we still be able to calculate what the system will be like at some time _t_ in the future?


Calculate time to go from one point to another point

in a 2D football game I want to calculate cycle(time) until ball go from one point to another point. in this link exist all fomulas that we need for my problem but anyone does not have any parameter that shows the effect of decay on ball speed.


A real gas with gravitation-like interaction

Consider a system (a gas) of point-like particles with a gravitation-like interaction (potential) $V(r) \sim \frac{1}{r}$ between pairs of them. One can rule out statistically that two particles will approach each other exactly along their line, so two particles will never collide directly - thus giving rise to infinite (kinetic) energies. So the particles will always whirl around each other in one way or the other. What can be said about such a system in the framework of statistical mechanics? How does its partition function look like? What are its thermodynamical equilibrium states? What happens when cooling such a system down (e.g. from very high temperatures)?


Calculating Mass for a Reduced Trajectory while Keeping Projectile Force Constant

Apologies if this is not a research-specific question, but applied mechanics. A firefighter has to pass a test in which he is to throw a medicine ball a certain distance. The ball is thrown at a 45 degree angle (Fig. 1) and has to travel a ground distance of 7.5 meters. For the test, a medicine ball is a rough sphere with a mass of 4 kg and ~250 mm in diameter. In preparing for the test, however, the firefighter has only access to a dumbbell, which he does not intend to throw. Given that a certain force is needed to throw the medicine ball with a preparation phase of 1 m and then released for a 7.5 meter throw, how heavy should the training substitute dumbbell be in order to achieve the equivalent force? Assume that the dumbbell only covers a 1 m distance at 45 degrees and that the firefighter intends to train at a 1 m/s velocity. * * * Figure 1 (Source: http://www.bochum.de/C125708500379A31/vwContentByKey/W27LXNMW860BOLDDE#par4)


An Electromagnetic Paradox?

![Two masses](http://i.stack.imgur.com/VfRrV.jpg) The above diagram represents an isolated system with two masses $M$, at position $X$, and $m$, at position $x$, connected together by an extended spring. Each mass is connected by rigid rods to charges $Q$ and $q$ (of negligible mass) separated by a vertical distance $r$. The masses and charges are constrained to move in a horizontal direction so only horizontal forces affect the dynamics of the system. The system is released and the two masses are pulled together by the spring. As there is no external force, $F_{ext}$, acting on the system then we have $$F_{ext} = M_{tot} \ddot{X}_{com} = 0,$$ where $M_{tot}=M+m$ is the total mass of the system and $X_{com}=(MX+mx)/(M+m)$ is the center of mass of the system. Thus we have: $$M \ddot{X} + m \ddot{x} = 0.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)$$ But let us now consider the masses $M$ and $m$ separately together with the internal forces acting on them. The force on $M$ consists of the force $F$ from the spring together with a horizontal electromagnetic radiation force on charge $Q$ due to the acceleration of charge $q$. Therefore we have: $$M \ddot{X} = F - \frac{qQ}{4\pi\epsilon_0 c^2 r}\ddot{x}.$$ Similarly the force on $m$ consists of the force $-F$ from the spring together with a radiation force on charge $q$ due to the acceleration of charge $Q$. $$m \ddot{x} = -F - \frac{qQ}{4\pi\epsilon_0 c^2 r}\ddot{X}.$$ Adding these two equations together we obtain: $$M \ddot{X} + m \ddot{x} = -\frac{qQ}{4\pi\epsilon_0 c^2 r}(\ddot{X} + \ddot{x}).\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)$$ Equation (2) is not consistent with Equation (1). There seems to be a paradox here. One could answer that I have not taken into account the electromagnetic reaction force on the charges due to their emission of electromagnetic radiation. In fact the electromagnetic reaction force on a moving charge $q$ is given by $$F_{reaction} = -\frac{2}{3}\frac{q^2}{4\pi\epsilon_0 c^3}\dot{a}.$$ Therefore $F_{reaction}$ depends on the rate of change of the acceleration, $\dot{a}$, rather than $a$ itself. As the reaction force term has an extra factor of $c$ in the denominator and the rate of change of acceleration is small (the length of the spring doesn't change very fast if the masses are reasonably large) then we can ignore the possibility of the emission of electromagnetic radiation and the subsequent reaction forces on the charges. Therefore this is not an answer to the paradox.


Difference between dielectric constant and dielectric function

I'm confused by the definition of dielectric constant. We all know that dielectric is function of wavelength, because materials respond in different ways depending on the energy of the light. But what does it mean when it says > _Dielectric constant of a material is = 5._ ?


Does relativistic mass have weight?

If an object was sliding on an infinitely long friction-less floor on Earth with relativistic speeds (ignoring air resistance), would it exert more vertical weight force on the floor than when it's at rest?


Relation between quarks and strings

In string theory(s), are quarks just individual strings, or are they made of multiple strings? Are the heavier quarks made of heavier or longer strings? Are there red, blue, and green strings corresponding to the color charges of qcd?


> **Possible Duplicate:**   >  Measurement of Tangential Momentum Accomodation?   * I am using atomic force microscopy (AFM) for characterizing pores of the size of nanometers for application in gas flow. For this, knowing the value of Tangential Momentum Accommodation (TMA) coefficient is an important task. Following is a formalism that describes measurements done by AFM and the formula to compute TMA: Sneddon demonstrated that for any axisymmetric tip of an AFM, the relation between indentation force and displacement can be written as: > $F=\mathrm{TMA} (Zp-Zc)^n$ Where, > TMA = Tangential Momentum Accommodation for a spherical tip, $\mathrm{TMA} = \frac43 E_r R_t^{\frac12}$ > $E_r$ = reduced elastic modulus = $\frac{E}{1-\nu^2}$ > > $n$ = constant between 1 and 2 that depends on the shape of the tip > > $Z_p$ = piezoelectric displacement of the chip during indentation > > $Z_c$ = cantilever deflection > > $R_t$ = tip radius > > $E$ = Young's elastic modulus > > $\nu$ = Poisson ratio of the sample (for rock minerals it lies between 0.1 > and 0.3) AFM can be used to measure $F$, $Z_p$, $Z_c$ and **Bulk modulus of elasticity of materials**. To obtain the exponent $n$, a log-log plot of $F$ versus $(Zp- Zc)$ is plotted, although TMA is not calculated from this plot because doing so would require accurate knowledge of $(Zp-Zc)$ and, thus, the contact point.   * Based on the above information, I would like to know how we can get TMA from force measurement of molecule and pore wall. **ABOUT THE EXPERIMENT:**   1. The goal is to measure TMA by AFM. We measure interactive forces between AFM tip (hemisphere) and planar surface. Using the models for hemisphere and plane surface we can extract necessary data. We extract coefficients that are independent of the shapes to be able to use it in a pore.   2. The tip measures interactive forces.   3. In addition to hydrodynamic forces, electrostatic and van der Waals forces are additional forces.


the causality and the anti-particles

How can I quantitatively and qualitatively understand the fact that there is a relevence between the existence of anti-particles and the causality?


Motion is relative, right? And most pop sci relativity explanations are somewhat incorrect?

On page 20 of _A Brief History of Time_ : > . . . all observers should measure the same speed of light, no matter how > fast they are moving. But in an observer's frame of reference, they're actually not moving at all. So the sentence "should" read, ". . . they are moving, _relative to each other_." BTW, I do realize that this kind of writing is intended to be easy to read and thus omits the obligatory caveats to every claim. I'm just trying to deeply, intuitively understand the material. From a UVA lecture, Conserving Momentum: the Relativistic Mass Increase: > Mass Really _Does_ Increase with Speed . . . particles become heavier and > heavier as the speed of light is approached . . . And here, isn't ". . . heavier and heavier _relative to an observer_ . . ." actually correct?


How to tell whether photons are entangled?

Suppose you have some sort of a "black box" system - you know nothing of its inner workings. The system has two outputs, let's call them A and B, and it occasionally emits photons - one photon from each output, with both the A photon and B photon emitted simultaneously. You observe the system for a while, and notice that when you measure the polarization of the two photons, they always have the opposite polarization - if one is horizontal, the other is vertical, and vice versa. Now, is there any experiment you can do which will show you whether the photons are truly entangled in the quantum sense, or whether it is some purely classical process within the box that's causing the polarization to be opposite? If so, what is that experiment? An answer that won't assume any more than undergrad knowledge of physics would be appreciated!


Modified gravity and dark energy

Is there a model of _modified gravity_ that either was close to or have succeeded in modelling the problem of dark energy, and suffers from no instabilities and explains the observational data. Also has the approach to use modified gravity to explain the problem of dark energy been abandoned? Needed to write a review about the challenges facing modified gravity, Any insight would be great. Cheers


The formation of ice from water properties?

> The formation of ice from water is accompanied by: > > A. absorption of energy as heat > > B. temperature increase > > C. decrease in volume > > D. an evolution of heat > > E. temperature decrease For the first one I think it's correct but I don't know the explanation For second one it is wrong since ice is cold For the third one it is wrong since ice has more volume than water for same quantity For the fourth one I'm confused what is heat? It is colder but doesn't mean heat evolute? For fifth one I think it is correct since ice is cold


Why does separating plastic from a cough drop create flashes?

I was tearing open individually-wrapped cough drops in the dark, and noticed that when I pulled apart two adhesive-joined pieces of silvery plastic film, small flashes of light were produced. It was not a reflection--it was pitch dark. What causes this? The product is Bee M.D. Organic Honey Throat Drops--kind of gooey, old ones (laugh). They contain menthol and eucalyptus oil. I did some more experimenting and think the the flash could actually be separating the plastic from the cough drop itself rather than pulling apart the adhesive. The item is small, the room is dark, my finger has a wound, and all in all it's hard to tell for sure. I don't know if this is a physics or chemistry question--it depends on the answer.


What is the reason behind why a quantum particle cannot be at rest?

So I've seen different reasonings for this; which is correct, or are they both corollaries of each other? 1) For a particle to be at rest, we would know its momentum and therefore by Heisenberg's uncertainty principle, the uncertainty in its position would be infinite. Is this acceptable? 2) $\lambda = h / p = h / 0 \implies \lambda \rightarrow \infty$ which is not possible. EDIT: Another reason: 3) Due to the zero-point energy, even in its ground state there will always be non-zero kinetic energy.