title: What areas of physics should a mathematician study to understand TQFT?

text: I am studying topological quantum field theory from the view point of mathematics.(axiomatic treatise) So it has no explanation about physics. I would like to know physic background of TQFT. But I have only taken several basic physics classes when I was undergraduate. Which areas of physics are related to TQFT? (I heard QFT and conformal field theory are closely related. But I don't know how.) If I have graduate level of mathematics background, is it possible to study those related subjects directly? Or should I start studying from the basic physics first, like quantum mechanics or relativity theory? If you can suggest any reference on TQFT that allows people with mathematics background to easily understand the physics motivation or physics origin of TQFT, that would also be helpful. Thank you in advance.


title: Some questions about Ward-Takahashi Identity

text: I'm a learner of Peskin and Schroeder's textbook of quantum field theory. I have proceeded to Ward-Takahashi identity and have one question when I look for Wikipedia for reference. The following is the Ward-Takahashi identity, where $M^{\mu}$ is the correlation function for $n$ inserting electrons and $n$ out-going electrons. $$k_{\mu}M^{\mu}(k;p_1...p_n;q_1...q_n)=-e\sum_i[M_0(k;p_1...p_n;q_1...(q_i-k)...q_n)-M_0(k;p_1...(p_i+k)...p_n;q_1...q_n)].$$ The wiki says that > _Note that if ($M^{\mu}$) has its external electrons on-shell, then the > amplitudes on the right-hand side of this identity each have one external > particle off-shell, and therefore they do not contribute to S-matrix > elements._ Does _on-shell_ means a divergent contribution according to LSZ reduction formula? Besides, can you tell me why the S matrix is zero if all the external electrons in the left hand side are on shell?


title: proper variation of action term

text: I have a term I want to vary by a field, $\phi$. $$ `S' = \frac{-1}{2}\,\sqrt{-g}\,g^{\mu\,\nu}\,\delta\left[h(\phi)\,\partial_{\mu}\phi\,\partial_{\nu}\phi \right]. $$ Is it correct to get this? (I am unsure about the derivatives) let $$a:=\frac{-1}{2}\,\sqrt{-g}\,g^{\mu\,\nu}$$ Basically I want to know how to do this: $$ a\,h(\phi)\,\delta\left[ \partial_{\mu}\phi\,\partial_{\nu}\phi\right] $$ I should also say, that unlike the usual case, I am only interested in varying the field, not the coordinates. So I think $\partial_a\phi \mapsto \partial_a\phi+\partial_a(\delta\,\phi)$.... If I take Taylor series would then the variation be, $$ \left( \partial_{\mu}\phi + \frac{1}{2}\,\partial_{\mu'}\partial_{\mu}\phi\,(\delta\phi) \right)\,\left( \partial_{\nu}\phi + \frac{1}{2}\,\partial_{\nu'}\partial_{\nu}\phi\,(\delta\phi) \right) = $$ $$ \cdots = \partial_{\mu}\phi\,\frac{1}{2}\,\partial_{\nu'}\partial_{\nu}\phi\,(\delta\phi) + \partial_{\nu}\phi\,\frac{1}{2}\,\partial_{\mu'}\partial_{\mu}\phi\,(\delta\phi) $$ and then collect on $\delta\phi$? I have 4 index values... I think $\mu' \neq \nu$ and $\nu'\neq \mu$, as there seems to be no reason why they would be.


title: Which is the most accurate way to model the fundamental atmospheric parameters of the Earth?

text: I need to calculate the fundamental atmospheric parameters, I mean the actual ones, this is not an exercise but a model for a real world application so I need to take account of the humidity of air. I need to calculate the density of the air, and I've solved this by implementing this calculator in MATLAB. But now I need to find a way to calculate the input parameters which are:   * Air Temperature   * Altimeter Settings (Which is the barometric pressure right?)   * Relative Humidity given a certain altitude in meters above the sea level. If it's not possible to calculate all the three parameters, given an altitude, please show me a way to calculate the possible ones. For example I know that for the barometric pressure the best equation is the Laplace equation which is an improved version of the barometric formula right?


We often see a limit $\hbar \rightarrow 0$ in quantum mechanics and sometimes its related with Symmetry breaking. Can someone briefly write the story behind this limit. Thanks in advance


title: When is Fermi golden rule exact?

text: My recent study Nonsmooth and level-resolved dynamics illustrated with a periodically driven tight binding model motivates me to ask this question: Is there any example in which the Fermi golden rule gives a quantitatively exact prediction of the transition rate? Note that the Fermi golden rule is just a first order perturbation result. In a generic problem, it should not be exact. I mean, the transition probability $p(t)$ should be a linear function of time for $t_{c1} <t < t_{c2}$, where $t_{c1}$ and $t_{c2}$ are two characteristic times, but the slope is not that predicted by Fermi golden rule.


title: How the nucleon structure has been identified experimentally?

text: It is known that nucleons (proton, neutron) are composed of partons (quarks, etc.). How was this identified experimentally? In particular, how it has been identified that nucleons comprise of more than one constituent?


title: Penetration versus Frequency

text: I would like to know the relation between penetrating ability and the frequency of a wave. For example, gamma waves have high frequency and high penetrating power: intuitively I imagined this as attacking a target rapidly in quick succession and managing to get through. But the penetrating ability is also a feature of low frequency waves - the usual telecommunications spectrum. What is the intuition behind this? Are there other factors like the field which play a dominating factor here? Edit: The question is in reference to the permeable zone indicated in this figure.


title: Solution to Klein-Gordon equation

text: I have a sound grounding on ODE's, not that much on PDE's, i've read many books on QFT and most if not all come to the conclusion that the solution to the Klein-Gordon equation $$(\partial_{\mu}\partial^{\mu} + m^2)\varphi=0$$ is $$\varphi(\vec x,t)=e^{-ip\cdot x}$$ without derivation where $$p \cdot x=p_{\mu}x^{\mu}=Et-\vec p\cdot \vec x.$$ Which to me means that the characteristic equation $\partial_{\mu}\partial^{\mu} + m^2$ if it should be named like that, has the root $ip_{\mu}x^{\mu}$. Could someone please show me how these covariant PDE's are solved?


title: Can Loop Quantum Gravity connect in any way with string theory?

text: The one difficulty I see with LQG is that it requires an enormous number of degrees of freedom, _e.g._ these spin variables in the net. This is in contrast to stringy holographic theory where the fields in a space are equivalent to fields on a boundary or a horizon of one dimension lower. In this setting entropy of a black hole is the entanglement entropy of states interior and exterior to the black hole. This reduces the amount of data, and thus entropy, required. Are there suggestions, conjectures or maybe serious theory which attempts to describe the spin variables of LQG according to such entanglements in string- brane theory?


title: Massless Thirring Model in 1+1 Dimensions

text: In Coleman's paper, "Quantum sine-Gordon equation as the massive Thirring Model" (link to Phys Rev D article), he pointed out that the massless Thirring Model is exactly scale invariant. More over, the massless part scales as $$H_0(x) \rightarrow \lambda^2 H_0(\lambda x)$$ What does it mean here by scale invariance, and why does it imply that the Hamiltonian scales as this? Note the Thirring Model has Lagrangian $$\cal{L} = i\bar{\psi}\partial_{\mu}\gamma^{\mu}\psi - \frac{g}{2} j_{\mu} j^{\mu}$$


title: Help making a solenoid engine

text: I am currently working on a school project and my aim is to build an electric motor using DC. I am looking at a design similar to this: Solenoid Engine and I have built majority of it however I am having trouble getting the solenoid to pull with enough force. At the moment I am using PVC piping with around 2m of insulated copper wire wrapped around it. I am using 12V of power which according to my multimeter is producing about 0.02m Amps. Also I am using a super magnet as the core which was found in a hard drive (I believe it is neodymium). My question is how can I cause more magnetic force within the pvc piping using the materials I have stated? Also would it be better if I purchased some more wiring to go around the PVC?


title: Electrostatic potential of a proton

text: I have been working on a quantum mechanical problem regarding the ground state of the Hydrogen atom. It appears that the best way to solve the underlying problem is to modify the electrostatic potential that is generated by the proton and felt by the electron. The modification is only required for very small distances r. While the modified potential is not precisely defined, it should have the following general structure: $V(r) = A - Br^2 + Cr^4 - Dr^6 + \dots \quad \text{for} \quad r < R$ $V(r) = 1/r \quad \text{for} \quad r > R$ Here $R$ is some unspecified distance, much smaller than the Bohr radius ($10^{-10} \mathrm{m}$). I suppose $R$ may well related to the proton size. For very small separation between proton and electron the potential diminishes approximately like a Cosine function, a Bessel function [i.e. $\sin(x)/x$], or a Gaussian. For distances $r$ larger than $R$ the usual Coulomb potential of a point charge can be used. The transition between the two regions ar $r=R$ is smooth. My question to the experts is: Is there any evidence or confirmation, theoretical or experimental, for the result described above?


title: A table of Particles and Energies In different satellite orbites(GEO MEO LEO)

text: I have done a bunch of search for information about: which particles with how much energy exist in near space environment of earth in inner and outer Van Allen Belt or satellite orbits like GEO MEO and LEO, and I found some sporadic and sometimes antithetic information. Any help Would be awarding.


title: Weather difference on Mars compared to Earth

text: How the weather on Mars differs from here on Earth? In here you see that weather on Earth is > Hurricanes, typhoons and tornadoes a real problem. Disgustingly interminable > fog in coastal California. Utter lack of rain in parts of Africa. Way too > wet in many other places. I have hard time reading what is said about weather on Mars, because it can't be read on my browser. What about temperature; is it truth that temperature reaches never +23 celcius even on Mars equator? Is it true that weather here on Earth is more complex than on Mars or on any other bigger celestial bodies(moons, planets) with atmosphere in solar system? The reason I ask this is because of the notion that there are many kind of weather phenomena in Earth, so I guess that weather here is more complex that any other body in Solar system.


title: Does a fundamental principle require specific concepts?

text: The angular momentum principle is a fundamental principle. So it can explain a large variety of phenomenon. Doesn't it need concepts like center of mass also for explaining phenomenon? Or just the angular momentum principle can explain these phenomenon?


title: Would it be possible to develop special relativity without knowing about light?

text: My understanding of special relativity is that it is fundamentally based on the constancy of the speed of electromagnetic radiation - that this speed is a physical law (or derivable from physical laws and facts about the vacuum) and not a contingent fact. Does that mean that, if humanity did not know about light (or electromagnetic radiation, generally), would we then be unable to come up with special relativity? To put it another way, imagine a species of intelligent life insensitive to electromagnetic radiation - no eyes etc. Would they still have a reason to produce the theory of relativity, or would they likely have created a physics framework which doesn't involve the speed of light so centrally?


title: Parachute jumping (high altitude)

text: I heard about parachute jumping at an initial altitude of 30km. I want to simulate this flight _numerically_. How could I simulate the air drag (I mean, Which equation gives the air drag)? Normally I use, $$\frac{\text{d}v}{\text{d}t}=a -bv^2$$ where $a$ is the acceleration and $b$ is the drag coefficient. **In this case, how does air drag coefficient variate with altitude?**


title: The origin of femto, atto and zepto SI prefixes

text: Do you know why the SI prefixes: femto, atto, zepto have been accepted by Scientific Community, if this triad of metric units, is neither greek nor latin?


title: Fusion vs. Fission

text: I understand why fission generates large amounts of energy when the nucleus is split, but then why does fusion generate such large amounts of energy. If fission releases energy when some mass is lost as energy, then shouldn't the fusion process absorb energy to fuse nuclei together? I also am curious as to where the energy released from fusion comes from, while fission releases some of the energy of the strong nuclear force.


title: Imaginary time?

text: If we begin with the equation for time dilation: $$ \Delta t^\prime = \frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}} $$ Now, for a particle moving in space with no potential energy, $$ E = \frac{1}{2} mv^2 $$ So $$ v^2 = \frac{2E}{m} $$ Then $$ \Delta t^\prime = \frac{\Delta t}{\sqrt{1-\frac{2E}{mc^2}}} $$ $$ = \frac{\Delta t}{\sqrt{1-2}} $$ $$ = \frac{\Delta t}{\sqrt{-1}} $$ Explain please?


title: Pauli matrices as measurement operators

text: I am trying to understand a paper on the Bell test experiments. I understand that if we wanted to measure the spin of a spin-1/2 particle in state $\psi$ along the z-axis we would apply the operator $$\sigma_z= \begin{pmatrix} 1&0\\\0&-1 \end{pmatrix}$$ and to measure along the x-axis we would use $$ \sigma_x = \begin{pmatrix} 0&1 \\\ 1&0 \end{pmatrix}.$$ But if, given an ensemble of spin-1/2 particles we wanted to measure spin along either the x-axis or z-axis in random alteration, how would we construct the relevant measurement operator? What about if we wanted to measure, again choosing randomly, spin either along the line 45 degrees between the positive x and z axes, or along the line 45 degrees between the negative x and positive z axes? What is the operator in this case? The paper I am reading assumes the reader is already familiar with such details.


title: Why is the Higgs boson created so infrequently at the CERN collider?

text: Although each collision at CERN has the available energy to create a Higgs boson each time, the vast majority of the time it does not create one. I suspect that part of the reason for this is that most of the energy goes into creating mostly lighter, secondary particles which carry a lot of kinetic energy away. As a result, this would leave very little energy left to create more massive Higgs bosons. So I started thinking and realized that there is more that is going on (e.g. cross sections sizes). I have purposely left this question open-ended to just see what people are thinking since I know very little about this. Therefore, as the title of this question puts it: why is the Higgs boson not created more frequently at the CERN collider? Aside: I guess I could of asked this question about some X-particle instead of the Higgs boson. Either way, my question would still be the same.


title: Why do covalent bonds form?

text: why in a covalent bond are "the bonded electrons are in a lower energy state than if the individual atoms held them at the same proximity"? Also is it correct that " I think when you start pushing two molecules together orbitals between the two start overlapping - forming covalent bonds?" Essentially why are covalent bonds made? A QM description would be nice but I don't really know QM so a somewhat reduced-to-classical explanation of the QM explanation would also be nice!


title: Acceleration in $F=ma$

text: I tried to ask this question in Electrical Engineering Stackexchange but was told I was better asking here. Newton's Second Law of Motion states that the vector sum of the forces $\mathbf{F}$ on an object is equal to the mass $m$ of that object multiplied by the acceleration vector $\mathbf{a}$ of the object: $$\mathbf{F}=m\mathbf{a}.$$ By this equation we may associate, among others, the following three properties with any object in newtonian mechanics:   1. A mass $m$.   2. The vector sum of forces $\mathbf{F}$ acting on it.   3. An acceleration vector $\mathbf{a}$.  These properties are related by Newton's second law, as stated earlier. However, they seem to have a different status. We can change the mass of an object (by simply removing parts of the object) independently of the other two properties. We can also change the sum of forces on the object independently of the other two (e.g. by adding a new force). However we are unable to change the acceleration vector of the object directly, we would need to change either $\mathbf{F}$ or $m$ to do that. This difference seems strange to me, because after all the equation treats all of these characteristics the same (we can choose to solve any of them by substituting for the other two). For example, in the model $V=RI$ of a resistor this doesn't happen. We can choose to alter directly any of the three properties of the resistor (the voltage accros it, the current flowing through it or its resistance). Why is $\mathbf{a}$ in $\mathbf{F}=m\mathbf{a}$ different? I know it's pretty common sense to us that we can't change acceleration directly (at least for me it is), but still the mathematical equation wouldn't suggest that. So is there a physical (theoretical) explanation as to why this third property (acceleration) can only be changed indirectly? Why does it seem to have a different status than the other two (in the sense that we humans can't alter it directly, only indirectly)?


title: Charges of quarks and leptons

text: Are there any theoretical restrictions within the framework of QFT that fix the relative sign between charged leptons and up-type quarks? We know that in our universe, they have opposite signs -- but would a Standard Model in which they have the same sign run into any problems?


title: Is there a finite unit of distance that we cannot divide past?

text: If distance could be divided into an infinite no of units or points, then it seems to me that motion would be impossible since a meter for instance, having an infinite no of points within it (and the points having an infinite point within it), would be un-breachable. It seems (intuitively) to me that for a measure of distance to be finite it would have to be made up of a finite unit of points however small those units were. Otherwise, we are all teleporting at some point in the process of motion...


title: Looking backwards in time at yourself

text: If a person on Earth today is looking at a star, say, 10 billion light years away, is it possible that some of the atoms he is looking at will eventually go on to make him?


title: Massless Dirac equation is Weyl covariant

text: Does somebody know how to show that the following equation is Weyl invariant? $$\gamma^ae_a^\mu D_\mu \Psi=0$$ where: $D_\mu \Psi=\partial_\mu\Psi+A_\mu^{ab}\Sigma_{ab}\Psi$ is the spin- covariant derivative. Under a Weyl transformation the metric changes as $g^{'}_{\mu\nu}=\Omega^2g_{\mu\nu}$, with $\Omega$ positive function. In particular is to me not clear how spinors (and $D_\mu \Psi$) transform.


title: Ontic state space from operational structures

text: Operationalism eschews a notion of system state in favour of the empirical behaviours of preparation and measurement. Abramsky has formalized operational structures as Chu spaces. It would be nice to know that there is a mathematical prescription, involving the Chu spaces (or some other model of operational structure), that generates an ontic state space. This could be used to form a foundation for physics. In this model, we build a notion of an ontic state space based on our interaction with a laboratory system. I guess this is in contrast to normal physics and science, where we posit the form of an ontic state space and then prove where it works and does not work. Has anyone seen work that attempts to take operationalist structures and develop an ontic state space?


title: Taking pivot about an accelerating point

text: Given this question: > _A small ball of mass $m$ and radius $r$ rolls without slipping on the > inside surface of a fixed hemispherical bowl of radius $R >r$. What is the > frequency of small oscillations?_ The standard solution is to write Newton's second law for the ball and then take the centre of mass of the ball to be the pivot and write $$\tau = I \alpha.$$ Only the frictional force contributes to the torque in this case. From Newton's second law, I can express the frictional force in terms of the gravitational force and therefore the frictional force can be eliminated in the equation for torque. I then make small angle approximation and get the equation to be of the form $$k\theta=-I\ddot{\theta}$$ from which I can find the frequency. Another approach uses the point of contact of the ball with the sphere as the pivot. It has the advantage that the frictional force adds no torque. Both approaches give the same result. My question is since both pivots that we have chosen are accelerating, why are not fictitious forces considered? In the first place, can the pivots that we choose when writing $$\tau = I \alpha$$ be accelerating?


title: Why is $B(T)\approx b(T-T_C)$ near critical point $T_C$ in Landau theory?

text: In _Peskin &Schroeder_ page $270$ equation $(8.4)$ you see that they approximate the function $B(T)$ near the Curie temperature as $$B(T)\approx b(T-T_C)$$ i.e. they omit $B(T_C)$ in the Taylor expansion of $B(T)$. Similarly for $C(T)$ they just keep $C(T) \approx c.$ How come this is OK? For those without the book in hand: $\partial G/\partial M=H$ where $G=$ Gibbs free energy, $M=$ magnetization, $H= $ external magnetic field. For $T$ near $T_C$, $M\approx 0$ so we expand gibbs: $$G(M) = A(T)+B(T)M^2+C(T)M^4+\cdots$$ with only even powers of $M$ due to symmetry of the system under $M\rightarrow -M$.


title: Neutrinos and anti-neutrinos in the Standard Model

text: In standard model neutrinos and the left handed electron forms SU(2) doublet.   1. What about the anti-neutrinos in the standard model? Do they also form some doublet?    2. If neutrinos have tiny masses will it not imply indirectly and conclusively that right-handed neutrinos must exist in nature? **EDIT :** _Neutrinos will have Majorana mass term if they are Majorana fermion. Is that right? Now, if neutrinos are Majorana fermions, will they have definite handedness? For example, does $\nu_M=\begin{pmatrix}\nu_L\\\ i\sigma^2\nu_L^*\end{pmatrix}$ have definite handedness? Therefore, doesn't it imply that if neutrinos are massive then a right-handed component of it $\begin{pmatrix} 0\\\ i\sigma^2\nu_L^*\end{pmatrix}$ must exist? Although we are not using $\nu_R$ to construct this column, does it imply $\nu_M$ do not have a right handed component? It is the column $\nu_M$ which we should call a neutrino. Then it has both the components. However, one can say that a purely right-handed neutrino need not exist if the neutrino is a Majorana fermion. Therefore, it seems that if neutrinos are massive a right handed component of it must exist (be it a Dirac particle as well as a Majorana particle). Correct me if I am wrong._


title: Hamiltonian in SUSY (SUSY algebra)

text: I was reading the book _Supersymmetry, Theory, Experiment and Cosmology_ by P. Binétruy, and on page 25 the author goes from $$ 1)[Q_r,Q_t]_+ \gamma^{0}_{ts}=2\gamma^{\mu}_{rs}P_{\mu} $$ $$ 2)\mbox{Contracting with $ \gamma^{0}_{sr}$, } \sum_{r,t}[Q_r,Q_r]_{+}(\gamma^{02})_{tr} = 2Tr(\gamma^{0}\gamma^{\mu})P_{\mu} $$ $$ 3) \sum_{r}Q^{2}_{r}=4P^{0}$$ $$ 4) H=\frac{1}{4}\sum_{r}Q^{2}_{r} $$ I don't really understand how to go from stage 1 to 2 or 3 to 4, can anyone help?


title: Do the proton PDFs change much with Q?

text: Specifically, the second moments, do they change much from say 100 to 1000 GeV? Why or why not?


title: Gamma Ray LASER Theory and Technology

text: I am aware that a similar question has been asked by someone else in the past, but in a very general form. Due to the physics interest and technology, in this question I put emphasis on the detail of the physics part and the question becomes **very specific.** We know the power of visible-light-laser and the effects it can have on matter: Industry, Medicine, Military, Entertainment and many other applications. Given the large amount of energy of $\gamma$-photons, one can extrapolate and see the new applications of LASER designed to amplify $\gamma$-light, emitted by nuclear isomers, which might be called “GLASER” (gamma light amplification by stimulated emission of radiation). The trick is to excite nuclei to a metastable state, to achieve “population inversion” and then stimulate them to decay simultaneously. The excitation can be achieved either by soft neutron bombardment or by synchrotron irradiation, in order to excite the nuclei into an angular momentum state that does not match the one of the ground state. These nuclei can remain at that state for sufficiently long time, so population inversion can be achieved. **QUESTION:** How can the nuclei be stimulated to decay and emit their $\gamma$-photon so that to achieve GLASER? This could depend on how the nuclei are excited in their isomeric states to begin with.


title: is a single photon a wave? Is it a wave packet?

text: How could it split and interfere? How could a wave packet, with many frequencies, be a photon with one freq.? Thank you very much.


title: What effects will the heliosheath have on the Voyager spacecraft?

text: I wanted to know what effects the heliosheath will have on the Voyager 1 & 2 craft. I know they used the slingshot method to travel through our solar system; so, with being way out in the heliosheath, how fast are the Voyagers going considering:   * the amount of fuel still available,   * and having no objects to slingshot around anymore?


title: Telescope for 6 year old and dad new to astronomy

text: What's a good telescope for my 6 year old? We're both brand new to telescopes in general, but love space, stars, planets, cosmology, etc. Happy to spend up to $200 to start. Maybe more for a good reason... **_UPDATE_** : Thank you guys for all the really great answers. I'm about to purchase the Celestron AstroMaster 114 EQ. Seems like the best value for the money based on the feedback below.


title: What demonstrations for a five-hour optical and radio astronomy workshop?

text: I volunteer at a group that has restored the oldest German radio telescope. We are now at a point where we want to invite interested amateur astronomers and school children to workshops. I'm currently thinking about the most interesting things to do in a certain timeframe, say, half a day. What would you consider most important phenomena to show in a hands-on workshop with interested, not-too-amateur visitors? Regarding our instruments: We can do continuum and spectroscopical measurements at 1.4 GHz (hydrogen line) on our 25 m dish and have several optical telescopes, up to an 11 inch Cassegrain. Additionally, we are thinking about using our parallactically-mounted 10 m dish (currently with a 10 GHz receiver) and perhaps buying a H-alpha-scope.


title: How can I visualize a gas giant?

text: From wikipedia > Gas giants are commonly said to lack solid surfaces, but it is closer to the > truth to say that they lack surfaces altogether since the gases that make > them up simply become thinner and thinner with increasing distance from the > planets' centers, eventually becoming indistinguishable from the > interplanetary medium. Therefore landing on a gas giant may or may not be > possible, depending on the size and composition of its core. How can I visualize a Gas Giants. E.G I want to land on Jupiter, what will I see? Will I be sucked towards the core since I am solid and planet is mostly made of gas? Could I possibly walk or I would just be floating?


title: Electric Field for a hollow sphere with point charge

text: I think I am over thinking this question: > A point charge of $-2\space\mu C$ is located in the center of a hollow > sphere. The internal and external radius of the sphere is given by $6.5$ and > $9.5\space \text{cm}$, the charge density is $7.35 \times 10^{-4}$.   > Plot electric field vs. distance from the center of the sphere. My thoughts were the region before $r_1$, it would just be $\text{density}\times\text{area}$, for $r_1$ to $r_2$ the value would be zero, and for a radius greater than $r_2$ out of the sphere it would have an inverse $1/r^2$ curve. Am I horribly off? Any help would be greatly appreciated, thanks


title: Using energy from sun magnetic field

text: Knowing               * earth spin and translation movement around sun,     * sun have a big magnetic field,     * a variable flux can generate a induced voltage (and current) into the circuit      Would it be posible to receive in a coil that energy? Perhaps it's just enough to detecting the earth movement relative to magnetic field, or if it were strong enough even for use the energy. It doesn't seem to be so strong because if it where perhaps every coil in earth without a current generated by this flux variation.


title: What is the luminosity per square meter hitting the Earth's surface from the Sun?

text: So I know that the Sun's luminosity is $3.839 \cdot 10^{26}$. What I want is the luminosity per square meter at the Earth's surface. So this is what I have got so far: I know the distance to the Earth from the Sun is $149.60 \cdot 10^9$ m. So imagining the Sun creates a sphere with a radius of $149.60 \cdot 10^9$ m, the surface area of that sphere would be $2.812 \cdot 10^{23} \mathrm{m}^2$. If I divide the luminosity of the Sun by that surface area, I get 1356 W/m$^2$. Assuming this is right (if not, please correct me), is this actually the amount of Watts per square meter that would reach a solar panel on Earth under ideal conditions? I didn't account for the atmosphere of the Earth, and the amount of light it blocks - as far as I understand. So what calculations am I missing here, and how would I go about finding what I want (that is, how many Watts per square meter hit a solar panel on Earth due to the Sun under ideal conditions)? Thanks!


title: It seems that the harmonic (integer multiple) overtones of a sound usually all have the same phase. Is this true, and if so why?

text: And if you were to give each of them different phases, would the sound start to sound "off", or would it sound the same? All the same frequencies would be present, which makes me think it might sound exactly the same. But on the other hand, the way they add up would be different, so could there be some cancellation that wouldn't be present when they all had the same phase? Also, does this same-phase relationship occur as often with non-harmonic overtones/partials as well?


title: Is the conjecture about $E(11)$ and M-theory (West's conjecture) generally accepted?

text: I was reading this paper by West, in which it is argued that: > Eleven dimensional supergravity can be described by a non-linear realisation > based on the group $E\left(11\right)$ From which they conjecture that $ E\left(11\right) $ can be related to M-theory, too. This seems rather weird to me, given that $E\left(11\right) $ is a rather ugly group, given that it has a cartan determinant of $-2$. And the Cartan Matrix looks like: $$\left[ {\begin{array}{*{20}{c}} 2&{ - 1}&{}&{}&{}&{}&{}&{}&{}&{}&{} \\\ { - 1}&2&{ - 1}&{}&{}&{}&{}&{}&{}&{}&{} \\\ {}&{ - 1}&2&{ - 1}&{}&{}&{}&{}&{}&{}&{ - 1} \\\ {}&{}&{ - 1}&2&{ - 1}&{}&{}&{}&{}&{}&{} \\\ {}&{}&{}&{ - 1}&2&{ - 1}&{}&{}&{}&{}&{} \\\ {}&{}&{}&{}&{ - 1}&2&{ - 1}&{}&{}&{}&{} \\\ {}&{}&{}&{}&{}&{ - 1}&2&{ - 1}&{}&{}&{} \\\ {}&{}&{}&{}&{}&{}&{ - 1}&2&{ - 1}&{}&{} \\\ {}&{}&{}&{}&{}&{}&{}&{ - 1}&2&{ - 1}&{} \\\ {}&{}&{}&{}&{}&{}&{}&{}&{ - 1}&2&{} \\\ {}&{}&{ - 1}&{}&{}&{}&{}&{}&{}&{}&2 \end{array}} \right]$$ So, is this paper well-accepted in the string community? .


title: Regarding Bravais lattices

text: There is 'End-Centered' Orthorhombic lattice . Why this type is not in 'Cubic' lattice ? On which basis did Bravais propose his theory ?


title: The formation of shockwave inside pellets in inertial confinement fusion

text: In the explanations i have read on the internet about ICF they all explain that the top layer of the pellet or the ablator is heated till it explodes and this produces a reaction force which compress the D+T fuel. They then say shock waves are formed due to the collapsing fuel which compress it even further and eventually ignite the fuel. My question is why and when are the shock waves formed?


title: What is the entropy of a string?

text: In his _The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics_ (p. 373) Susskind states that > the entropy of a string is [...] proportional to its length. Imagine moving > along the string as it turns and twists. Each turn and twist is a few bits > of information. (The context doesn't reveal to me whether he is talking about open or closed strings. It also seems to go from String Theory strings to yards of yarn, and back again.) The statement seems (almost) true for open strings, but I wonder especially about closed strings. If we follow his imagination and move along the string, we know that sooner or later we somehow need to make our way back to the beginning of the string in order to close it. Therefore, we have less degrees of freedom, less information. So, i) is this something he chose to overlook, or ii) is a correction like the one I am thinking of going to be linear, therefore maintaining the "proportionality", or iii) is something else the matter?


title: How to find focal length of a single convex lens?

text: I need help finding the focal length of a single convex lens. The radius of curvature is 200mm. left side is air and the glass has a index of 1.5. I search on google but there was only formulas for think lens, convex and converge lends. I need the formula for a single convex lens. Any idea? I know the ray transfer matrix. $$\left(\begin{matrix} 1 & 0 \\\ \frac{n-n'}{nR} & \frac{n'}{n} \end{matrix}\right)$$


title: Understanding ket notation and the unitary matrix, what does a/the unitary matrix represent?

text: I am reading over this paper http://www.scottaaronson.com/thesis.pdf, specifically page 24 under "Quantum computing cheat sheet". The author is explaining ket notation and how it relates to probabilities. * * * ![enter image description here](http://i.stack.imgur.com/Ui6Oo.png) * * * My question is what does the Unitary matrix represent? From what I can tell the martix represents an "operation", if this is correct what is an "operation"? I don't think I can ask the next question properly without knowing the answer to the first. But my second question has to do with understand thing sentence. > Applying a “randomizing” operation to a “random” state produces a > deterministic outcome! The only thing I can really ask about it right now, why are randomizing and random in quotes?


title: Symmetry and Algebra

text: I'm trying to get a more concrete idea how symmetry is understood in quantum theories, as broad as possible. Consider a infinitesimal transformation of states in quantum physics of the form: $$ |\phi'\rangle=(1+i\epsilon G)|\phi\rangle, \tag{1}$$ where $G$ is a (not necessarily Hermitian) operator, which may be associated with the transformation of any Hermitian operator $M$: $$M'=M+i\epsilon G^\dagger M-i\epsilon MG, \tag{2}$$ so that the expectation value $$\langle\phi'|M'|\phi'\rangle=\langle\phi|M|\phi\rangle \tag{3}$$ is invariant.   * If we consider the transformation $G$ to be symmetry, then any operator will create a symmetry transformation of the quantum physics. To what extend is this statement true?   * Generally symmetry is considered by group of symmetries. There is a group of finite transformation of $\epsilon G$ if and only if there is a closed algebra containing $G$. Then if we can construct a closed algebra of operators, can we associate it with a particular kind of symmetry?   * Finally, the whole above discussion is considered under quantum framework. How can we relate to the classical one?


title: Where are the harmonics in the radio spectrum?

text: When I strike a string on my guitar and look at the audio spectrum, I can see the fundamental frequency as a large peak. I can also see the harmonic frequencies as a train of little peaks at increasingly higher frequencies. When I tune an oscillator to produce a pure tone and drive a speaker, predictably I don't see any harmonics. Do harmonics occur in the radio spectrum reserved for communications?


title: Double slit experiment with slit material acting as a detector

text: Suppose the classic experimental setup of the double slit experiment. What is the probability that an electron does not pass through the slits? That is, for every single electron that comes from the source what is the probability that it does not pass through the slits vs passing through? Has there been an experiment that shows electrons not passing through relative to those that do make it through? EDIT: altered the question to not be aligned with Does the material of the slits affect the pattern of the electrons in the double-slit experiment? ![enter image description here](http://i.stack.imgur.com/o6P71.png)


title: Life and Death, and Energy Conservation

text: Humans are born and they die. When we are born, is energy created? Or is it just some amount of energy that our mother gives us? Doesnt she take this energy from the surroundings? If so, then when we die, where does this energy go? It can not be destroyed..... Just as an example to make this clear, if there is a fat man in question (like me :) ), when he dies, where does this "potential energy" stored in the fat, go? Please give due thought to it before closing this, or calling it as silly. Does this sort of prove that there HAS to be an afterlife, wherein we start with the energy we had when we died?


title: LHC data and mathematics of QFT

text: I'm reading _Frederic's Paugam Towards the Mathematics of Quantum Field Theory_ , an advanced theoretical physics book. I would like to know how I could apply the theories in this book. For example, could I use LHC data and to confirm the theories in the book? Could I apply LHC data to test the repesentation theory of the standard model ? Are there any other sources of data for confirming/rejecting mathematical models of similar physical principles?


title: Electric heating rod

text: I usually heat my bathing water with electric heating rod, I always thought that the base of rod is an insulator so that it can develop high heat. But when I tried touching water while rod was dipped in it, I got current, damn! Why that happened? I am talking about this type of rod :![enter image description here](http://i.stack.imgur.com/nS3jk.png)


title: Capacitance of two almost-touching hemispheres

text: This capacitor is composed of two half spherical shelled conductors both with radius $r$. There is a very small space between the two parts seeing to that no charge will exchange between them. ![capacitor spherical](http://i.stack.imgur.com/kzzKi.jpg) So far, I only know the capacity of a half spherical shell conductor is $r/2k$ and I can't figure out how to use this. How do I really calculate this capacitance? > For reference, the answer to this problem is $2r/k$.


title: Total Angular Momentum of a Hydrogen Atom

text: Griffiths in his celebrated book named 'Introduction to Quantum Mechanics' discusses about the total angular momentum of a hydrogen atom on page 187. He writes: > _If a hydrogen atom is in the state $\psi_{nlm}$, the net angular momentum > of the electron (spin plus orbital) is $l+1/2$ or $l-1/2$; if you now throw > in the spin of the proton, the atom's total angular momentum quantum number > is $l + 1$, $l$, or $l-1$._ However, while solving for the hydrogen atom Griffith assumes that the nucleus is stationary. My question: does the proton have any $l$? If not, then why?


title: Fine structure parameter $\alpha$ at event horizon

text: As magnetic field lines collect at a black hole event horizont (for no field lines will be present in the black hole) then ratio of electric field to magnetic field will change, so by this change in magnetic/electric ratio can we re-calculate the potency of alpha the fine structure parameter near the event horizon?


title: How to apply Noether's theorem

text: Say I have a point transformation: $$x' ~=~ (1 +\epsilon)x,$$ $$t' ~=~ (1 +\epsilon)^2t,$$ and Lagrangian $$ L ~=~ \frac{1}{2}m\dot{x}^2 - \frac{\alpha}{x^2}.$$ How do I go out about showing that this transformation is a symmetry of the Lagrangian? When I plug in $x'$ and $t'$ I do not get the same Lagrangian at all, it is off by factors of $(1+\epsilon)^2$ in both terms. I am not sure how I to calculate this. What sort of "symmetry" is this?


title: Measuring more accurately the distance of remote galaxies

text: From what I read in Wikipedia, the velocity of a Galaxy has two components: one is due to Hubble's law for cosmic expansion, and the other is the peculiar velocity of the galaxy. Since the peculiar velocity of galaxies can be over 1.ooo km/s in random direction, this causes an error in evaluating their distance using Hubble's law (I am summarizing from Wikipedia). > A more accurate estimate can be made by taking the average velocity of a > group of galaxies: the peculiar velocities, assumed to be essentially > random, will cancel each other, leaving a much more accurate measurement. I assume that "group of galaxies" actually means the cosmic structure by that name, rather than just any collection of galaxies that seem to be in "the same neighborhood", though the Wikipedia text does not explicitly reference that, as it usually would. But I will ignore that issue. The major problem that I see is that the speed of celestial structures with respect to their "surroundings" seems to be in proportion to their size: 30 km/s for Earth, 200 km/s for the Sun, 600 km/s for the Milky Way, and generally up to 1000 km/s and more for galaxies. So I would expect this to go up again for even larger structures, such as groups or clusters of galaxies. Hence, while averaging velocities may give some correction in the measurement, the major source of error should come from the group velocity itself, and would not be corrected by that procedure. This would weaken significantly the Wikipedia assertion that it produces a " _much more accurate_ " measurement. Am I right, or do I make an error in my reasonning?


title: Rays in Symmetric Resonator

text: I'm having some trouble figuring out how to get started on this question: If I have a symmetric resonator with two concave mirrors of radii $R$ separated by a certain distance, after how many round trips through the resonator could I expect the ray to retrace its path? It seems to me that this implies some sort of periodic function should exist that models the behavior of a ray in such circumstances.


title: Driving a solution of optical isomer molecules with the resonant frequency

text: What happens when we drive a solution of optical isomer molecules (enantiomers) with a microwave radiation in resonance with the tunneling frequency of the molecules (the frequency of the transition between the eigenstates of the Hamiltonian)? I expect it will become a racemic mixture. Is that correct? Update: Any reference for an experiment that does that is appreciated.


The temperature at the surface of Sol is apparently well above 5000C; I'm assuming the layers beneath the surface may be even hotter. At school we learnt heating a metal beyond a certain temperature specific to each metal would demagnetize the magnet. How does Sol's magnetic field continue to exist at such high temperatures?


title: What is the general approach to calculating time of impact in 3D?

text: Given two objects **a** and **b** moving at fixed velocities, how would you determine (a) whether they will collide at all, and if so, (b) time of impact? (Let us assume these are spherical bodies each with different radii **ar** and **br** ).


title: Measuring mass by acceleration due to electromagnetic forces in free fall

text: My question is a simple one (I think): How precise will the results be if you attempt to measure the mass of a macroscopic object by measuring it's acceleration when a constant electromagnetic force is applied to it? **edit** This is an entirely hypothetical question. And when I said macroscopic, I actually meant something with a mass around a kilgram (give or take a few orders of magnitude)


title: The lineshape of a 2D photonic crystal dispersion diagram

text: Using simulation software (CST Studio), I calculated the dispersion of the eigenmodes of a photonic crystal, that is frequency vs wavenumber for the desired propagation direction. I wonder what kind of relation there is between these quantities, but sadly I could not find any theoretical descriptions of this relation. The photonic crystal is shown below. It is a rectangular grid of metallic poles in a vacuum. The desired propagation direction is along the z-axis. Also a few of the dispersion lines are shown below, as well as their derivatives (the group velocity). Finding an analytical description of this relationship seems unlikely to me, but I would like to know what function would describe this lineshape, as this would help with my numerical analysis. ![Dispersion diagram](http://i.stack.imgur.com/pWfoa.png) ![The Photonic Crystal](http://i.stack.imgur.com/6pfkv.png)


title: Einstein and the existence of Black Holes

text: I have seen some papers claiming that Einstein said there is no Black Hole in the real world, here is a phrase from Einstein himself, see this arXiv preprint: > The basic result of study is the distinct understanding that there are no > Schwarzschild singularities in the real world. Thought the offered theory > considers only such systems, in which particles move by circle trajectories, > we have to hardly doubt that the investigation of generic case will lead to > the same results. The Schwarzschild singularity is absent, because the > matter cannot concentrated in an arbitrary way;otherwise particles composing > the clump will reach the speed of light. Why did Einstein say the particles composing the clump will reach the speed of light? And why haven't other physicists accepted his argument?


title: Gravitational binding energy of a white dwarf at Chandrasekhar limit?

text: I was trying to calculate the gravitational binding energy of a white dwarf just before it went on a type Ia supernova in order to calculate the kinetic energy of the ejecta, but I wasn't able to get the radius since the radius is zero at the Chandrasekhar limit. So how to calculate the binding energy of a WD just before a type Ia SN ? EDIT : Found this which gives a number for the binding energy of a WD at Chandrasekhar limit, but still I don't know how it was calculated. EDIT 2 : For Rob Jeffries, please take a look at page 5 of this, it clarifies somethings I think. Any knowledge on how this internal energy was calculated ?


title: Derivation of the full generator of the lorentz transformations

text: Let us study the subgroup of the Poincare group that leaves the point $x=0$ invariant, that is the Lorentz group. The action of an infinitesimal Lorentz transformation on a field $\Phi(0)$ is $L_{\mu \nu}\Phi(0) = S_{\mu \nu}\Phi(0)$. By use of the commutation relations of the Poincare group, we translate the generator $L_{\mu \nu}$ to a nonzero value of $x$: $$e^{ix^{\rho}P_{\rho}} L_{\mu \nu} e^{-ix^{\sigma}P_{\sigma}} = S_{\mu \nu} - x_{\mu}P_{\nu} + x_{\nu}P_{\mu}\,\,\,\,\,\,\,\,\,(1),$$ where the RHS is computed using the Baker-Campbell-Hausdorff formula to the second term. Then we can write the action of the generators $$P_{\mu} \Phi(x) = -i\partial_{\mu}\Phi(x) \,\,\,\,\text{and}\,\,\,\,L_{\mu \nu}\Phi(x) = i(x_{\mu}\partial_{\nu} - x_{\nu}\partial_{\mu})\Phi(x) + S_{\mu \nu}\Phi(x)\,\,\,\,\,(2)$$ Could someone explain the contents of Eqn (1) and how (2) is deduced from it? I think there is an unitary transformation on the LHS of Eqn (1), but I don't understand what the equation is doing and why the contents are what they are in the exponents of the exp terms. Many thanks for any clarity.


## My question Is there any good reason/argument/heuristic why one can approximate forces by approximating the potentials? (As a concrete example, in Electrostatics.) ## Motivation for the question I am studying for a (non quantum) electrodynamics course (loosely following Landau and Lifshitz). In electrostatics, we assume that the charge distribution is contained in some bounded part around the origin; and we want to calculate (or rather: approximate) the field in a large distance $r$. This is done the following way: Approximate the _potential_ $\phi(r \vec n)=\frac{Q}{r}+\frac{n_i d_i}{r^2}+O(\frac{1}{r^3})$ (here, $Q$ is the total charge and $\vec d$ the dipole moment). So obviously if we stop at the $\frac{1}{r^2}$ term, the resulting $\phi'$ is a "good" approximation to the potential $\phi$. Then it seems to be implicitly assumed that the field $\vec E'$ given by $\phi'$ is a "good" approximation to the "true" $\vec E$ given by $\phi$. This sounds physically rather convincing and natural. But obviously, it is not generally true that $f\approx g$ implies $f'\approx g'$. ## Some musings Maybe the answer is that the forces are not that important anyway: Many properties of the systems can be described "in a continuous way" by the potential. In Electrostatics this is rather obvious; in more general electrodynamics or in settings where there is no clearly preserved total Energy this becomes more and more fuzzy to me. Btw., I am aware that there is a very general answer along the lines of: "in this family of PDEs, the solutiuon depends continuously from the input, so of course a good approximation to the potential will result in very accurate equations of motion". However, this is not terribly satisfying, since the point here seems to be to estimate (at least in some fuzzy way) how good our approximations is. (For example, this general answer would not tell me why in the example above it is reasonable to ignore $O(\frac1{r^3})$ to get the "first order approximation" to some equation of motion; the $O(\frac1{r^3})$ might have more influence than the $\frac1{r^2}$ part).


title: Good books on elasticity

text: Can someone suggest good books/textbooks/treatises/etc on elasticity?


title: Theoretically if you passed the speed of light, would there be a sonic boom equivalent?

text: I know that it is technically impossible to reach the speed of light since the mass of the object traveling would reach infinity. Despite this if it were possible, would there be some sort of theoretical equivalent to a sonic boom that would occur? Since sonic booms are formed when sound waves can't catch up with an object, could the same happen with light waves? Would it look like an immense burst of light in the sky?


title: Path integral as a functional determinant

text: In Peskin and Schroeder on pg. 304, the authors call the fermionic path integral: \begin{equation} \int {\cal D} \bar{\psi} {\cal D} \psi \exp \left[ i \int \,d^4x \bar{\psi} ( i \gamma_\mu D^\mu - m ) \psi \right] \end{equation} a functional determinant, \begin{equation} \det \left( i \gamma_\mu D^\mu - m \right). \end{equation} I've never heard this way of thinking about it. Why would the generating functional be a functional determinant?


title: Did a racer on a "restless" course race at some particular average velocity? (1: Starting blocks, finish line moving uniformly wrt. each o.)

text: Consider two participants, $A$ and $B$ moving uniformly wrt. each other; first having approached each other, then having met and passed each other, and eventually having separated from each other such that their mutual speed wrt. each other is given quantitatively as $\beta ~ c$ with some particular positive real number value $\beta < 1$. (Evidently, therefore, $A$ and $B$ had not been at rest to each other.) After having observed $B$'s passage, $A$ has been preparing starting blocks;   and at duration $\mathop{\Delta}\limits_{\stackrel{\normalsize{\text{until}}}{\small{\text{start}}}} \\! \tau_A$ after having observed $B$'s passage, $A$ issued a starting signal to a racer ($R$) upon which the racer took off from $A$'s starting blocks. After having observed $A$'s passage (i.e. soon enough after that), $B$ has been preparing a finish line;   and at duration $\mathop{\Delta}\limits_{\stackrel{\normalsize{\text{until}}}{\small{\text{finish}}}} \\! \tau_B$ after having observed $A$'s passage, $B$'s finish line ribbon was passed by $R$. The ratio of those durations is given as some particular positive real number value: $r := \mathop{\Delta}\limits_{\stackrel{\normalsize{\text{until}}}{\small{\text{finish}}}} \\! \tau_B ~ / ~ \mathop{\Delta}\limits_{\stackrel{\normalsize{\text{until}}}{\small{\text{start}}}} \\! \tau_A$ which (of course) satisfies $r > \sqrt{\frac{1 + \beta}{1 - \beta}}$. **Question:** Can an "average velocity" of racer $R$ with respect to the race course, as far as it is specified by $A$'s starting blocks and $B$'s finish line be defined,   such that its magnitude could be expressed in terms of the given quantities $\beta ~ c$, $\beta$ and $r$   (and where its direction is obviously "from $A$ to $B$") ?


title: Why doesn't an electron accelerate in a circuit?

text: Why don't electrons accelerate when a voltage is applied between two points in in a circuit? All the textbooks I've referred conveyed the meaning that when an electron traveled from negative potential to positive potential, the velocity of the electron is a constant. Please explain.


title: Naturalness, simplicity and SUSY

text: With the aid of current LHC + (all the known HEP experiments)+ (astrophysical and additional laboratory measurements)... **Is SUSY natural? Is it simple?** More specifically, what reasons people had (or have) in order to argue the "naturalness" of SUSY? Why (despite the fact it doubles the particle spectrum!) some people says that SUSY is "simple" or a simple solution to the "most" important theoretical issues in physics? **Bonus question:** can a non minimal supersymmetric model be both "natural and simple", according to these definitions? I define naturalness in the sense of 't Hooft: a QFT is natural when its coupling constant is of order one (with respect to, e.g., the electroweak -EW- scale). A theory is "simple" when it reduces the number of degrees of freedom of previous "effective" theories. In my (completely subjective) opinion, current data strongly suggest that: i) SUSY is not natural. There is a relatively "large" gap between the electroweak scale and the SUSY breaking scale, if it (SUSY) exists...Then, the coupling constant of SUSY is not of order "one" with respect to the EW scale. The size of the SUSY breaking scale makes it to suppress the production of SUSY particles. ii) SUSY is not simple. People use to argue...And I agree with it...that SUSY provides a natural lightest supersymmetric particle (LSP), and thus there is a natural Dark Matter candidate. It also "unifies" forces in such a way the 3 SM forces and their coupling constants unify at certain large energy. The unification of coupling is "simple" and usually it is given as a "proof" that SUSY is OK. Maybe it is true. However, gravity is not included in that calculation. I mean, I have not seen a calculation of the running of G in the framework of SUSY. Moreover, despite its goodness providing a natural particle/field for the dark matter, SUSY enlarges the number of particles (and the degrees of freedom) without (yet, please, I don't give up the idea of SUSY myself, I am trying to offer a cold criticism of its problems) experimental evidence beyond that dark matter we do not know what it is made of... SUSY is NOT simple because, from the purely mathematical viewpoint, it enlarges the number of free parameters and particles with respect to the SM.


title: Determine the tensor of contraint and deformation of a cube under compression

text: We have a cube under compression with dimension l1*l2*l3, is put between 2 rigid plates in the axis 1 (two plates block the deformation of the cube in thí axis), the cube is also put on a rigid plate, and it has a rigid plate above it; and also this cube is under the force F from above (axis 3). The material of the cube is isotropic, linear elastic. The deformation of the cube is ∆l2 and ∆l3 (since the deformation of the axis 1 is block) The question is: How to write/determine the tensor of constrain and tensor of deformation? Is this below one is correct? $\left( \begin{matrix} {{\sigma }_{11}} & {{\sigma }_{12}} & {{\sigma }_{13}} \\\ {{\sigma }_{21}} & {{\sigma }_{22}} & {{\sigma }_{23}} \\\ {{\sigma }_{31}} & {{\sigma }_{32}} & {{\sigma }_{33}} \\\ \end{matrix} \right)=\left( \begin{matrix} {{\sigma }_{11}} & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & {{\sigma }_{33}} \\\ \end{matrix} \right)$ and $\left( \begin{matrix} 0 & 0 & 0 \\\ 0 & {{\varepsilon }_{22}}={}^{\Delta {{l}_{2}}}\\!\\!\diagup\\!\\!{}_{{{l}_{2}}}\; & 0 \\\ 0 & 0 & {{\varepsilon }_{33}}=-{}^{\Delta {{l}_{3}}}\\!\\!\diagup\\!\\!{}_{{{l}_{3}}}\; \\\ \end{matrix} \right)$


title: Radioactive decay, why such unintuitive formula?

text: When talking of exponential decay, as with radioactive decay, the formula used (e.g. Wikipedia and my textbook) is: $$ N(t) = N_0e^{-\lambda t} $$ This formula, with the decay constant $\lambda$ makes little intuitive sense. It is the ratio between the amount of radioactive material and the decay at any time. It might lead one to believe that after one time unit, the amount of radioactive material has been decreased by a factor $1/\lambda$, but that is not even the case. A much more intuitive form would be like the formula of exponential growth: $$ N_{wrong}(t) = N_0*(1-k)^t, k= 1-e^{-\lambda} $$ One only needs to look at that formula for a second to get an intuitive understanding of the rate of the decay. I got curious about this, and I want to ask why mathematicians or physicists have chosen the first mentioned formula. Did I miss something clever here?


title: branes-collision -> big-bang -> 2nd Universe?

text: If the cosmological model of the Ekpyrotic universe is correct should there not always a 2nd universe be created on the 2nd brane? Pictures and articles I found speak only of one universe. ![branes-collision](http://i.stack.imgur.com/Pzm82.jpg) Why is that? Did I miss something?


title: Pascal law with two connected cylinders filled with water, and 50kg stones at both their ends

text: If I have two connected cylinders filled with water, and 50kg stones at both their ends (pressing both ends of the water) how much weight do I need to add on one side so that one of the stones reach the bottom? ![Image of connected cylinders](http://i.imgur.com/Yl77d.jpg) So lets assume that the water weighs 1kg. And thus if there were no stones at all, adding a 1kg stone would displace all the water on one side and the stone would touch the bottom on the other. Since the 50kg weights cancel one another it seems like I could count as if there were no weights and adding 1 kg would be enough, But my instincts tell me I need to add 50kg. I don't know why. Thank you very much!


title: Are all effects that change color perception examples of redshift/blueshift?

text: As defined by Wikipedia: > In physics (especially astrophysics), redshift happens when light seen > coming from an object that is moving away is proportionally increased in > wavelength, or shifted to the red end of the spectrum. I understand the premise of the Doppler effect being attributed to redshift as well as the effects of space expansion and gravitational influence on light when speaking of redshift in astrophysics. I gather the basis of the principle as being - an increase in wavelength = a shift to red in the spectrum where alternatively a decrease = a shift to blue (blueshift). Simple concept, but is this right? If so, my puzzlement now falls upon the seeming similarities in other theories which are used on earth in regard to colour perception, light intensity and the composite structure of photographs. Consider the following resources: Colour Theory (see Intensity), Colour Appearance, Saturation, Bezold–Brücke shift As defined by Wikipedia: > The Bezold–Brücke shift is a change in hue perception as intensity changes. > As intensity increases, spectral colors shift more towards blue (if below > 500 nm) or yellow (if above 500 nm). At lower intensities, the red/green > axis dominates. Can these occurrences, namely Bezold–Brücke shift, also be coined as redshift/blueshift given that the waves emitted by the subject being observed are at varied lengths after absorption and reflection and understanding that the main light source being the sun, can be at variable distances emitting wavelengths (varied after modification by atmosphere) when in contrast to the subject being observed and the observer? Can the term(s) "redshift/blueshift" be used to explain the various changing spectral phases of our "individually perceived" world at any given moment? I know this is dodgy, but if you decide to answer, please cater for a layman with relevant information, because I get the feeling that mis-interpretation runs deep in our quest for truth as a race.


title: Why can't I evaporate water without wind, just heat? (not boiling,evaporating!) Or can I?

text: So here is the thing, I searched all over the internet for this but all the sources say that I need wind because the process of evaporation goes as follow: Water particles at the top layer with highest levels of energy (which they take from lower layers) are trying to break free and jump up. When they meet air particles with enough energy, they take that energy and use it to break the bonds with the other liquid- thus escaping and turning into a gas. Now my question is, what if I got no wind? What if instead I just put a heating coil close to the surface of the liquid which is in a barrel (i.e not touching the water)? Would my liquid just boil? Or maybe the energy from the coil would transfer to top layer first, giving it enough energy to escape (and cool the rest of the liquid)? What if the barrel closed? What if it is open? All of the internet sources say that I have to have air movement, does this mean that my scenario won't work? Also, if it would, does that mean that the energy required to make the water dissapear with evaporation is lower than with boling? Thank you very much!!!!


title: Given moment about a pin and a roller

text: sorry to ask, have not been a able to find a similar question to mine. ![problem](http://i.stack.imgur.com/bj3mN.png) For this problem, given moment $M_2$, distances $a$ and $b$ My reasoning is that we have two support reactions and points _A_ and _B_. Find the moment about each point; taking C-CW moment positive, the arrow for the reaction supports point $+y$ direction positive as well, point _A_ : support reaction $y$ axis at point B = RB_y RB_y*(a+b) - M2 = 0 ==> RB_y = M2 / (a+b) point _B_ : support reaction on y axis at point B = RA_y -RA_y(a+b) - M2 = 0 ==> RA_y = M2/(a+b) let me know if this makes sense, thanks all! Point B: Roller Point: Pin


title: Hermiticity of the quantum field

text: The quantum field resultant from the quantization of a real classical field is hermitian, but why the quantum field corresponding to a complex classical field should be non-hermitian?


title: Origin of elements heavier than Iron (Fe)

text: In all the discussions about how the heavy elements in the universe are forged in the guts of stars and especially during a stars death, I usually hear that once the star begins fusing lighter atoms to produce Iron (Fe) that's the end of the star's life and the whole system collapses onto itself and based on how massive the star was initially it has different outcomes like a white dwarf, a neutron star or a black hole. I have rarely heard a detailed explanation of how the elements heavier than Iron are produced. I would appreciate a convincing explanation of this process.


title: How does the light waves make up to my eye?

text: I was thinking about a situation were there is a group of people in a room. While all those people are observing something(none of them are blind) the light ways need to reach their respective eyes. But, how does the light ways make to one's eyes without being disturbed by the other light waves moving towards the eyes of others? Even there are a million people in a room one can see everything clear. How is it possible?


title: What is the possible potential?

text: The professor asked us to do this one: "..Determine all potentials $V(r,\theta, \phi)$ for which it is possible for find solutions of the time independent Schrodinger equation which are also eigenfunctions of the operator $L_{z}$." I try to solve this problem by assuming separation of variables, and I get $$\Phi(r,\theta,\phi)=R(r)F(\theta)e^{im_{l}\phi}$$ Unfortunately I do not know what to do next for this - should I put it into the formula $H\Phi=E\Phi$ in radial form to see whether it works? The professor give us the hint that the commutator $$[L_{z},V(r,\theta,\phi)]=0$$ I do not know how to use this relationship.


title: Minimum Uncertainty Wavefunction derivation

text: Can anyone point me to a reference (preferably either something online or something a small liberal arts school would be likely to have in its library) that goes through a derivation of the minimum uncertainty wavefunction in more detail than in the Griffiths? **Edit** I've moved the second part of my original question to a separate post: 3D Minimum uncertainty wavepackets


title: How to determine if a optical system is afocal?

text: I have to come up with a method to measure the focal length of a concave lens that's not in my lab guidebook. So I decide that I will build an afocal system with a convex lens and a concave lens and measure the focal length of the convex lens instead. But how can I determine if the foci of the two lens coincide? I will be using reading microscope which can measure length down to an error of 0.001mm, so I guess I should not drag down the accuracy by too much. P.S. we just have a "parallel generator" as the light source. Not sure what that is, but I think it's a point source fixed at a focus of a lens.


title: Forces acting on two balls in a jar

text: Consider the following situation: Two balls are inside a jar with diameter $D$. The balls are uniform in mass and both have the same diameter $d$. ![enter image description here](http://i.stack.imgur.com/14p0A.jpg) Express the forces that acts at the colored dots in the figure. Could any body give me a hint? It seems to me that I can't express one force without using the other.


title: Is a new universe created when dark energy rips open a singularity?

text: Dark energy will tear everything apart, even black holes. Is a new universe created when dark energy rips open the singularity of a black hole ? And does the topology of the universe depend on the type of singularity ?


title: How to uncurve a black hole

text: How can you uncurve a black hole and thereby get at the stuff inside?   1. The Big Rip as dark energy reaches its zenith at the end of the universe.    2. If curvature is a quantum field that is a superposition of all possible values of curvature then some values of the curvature are low enough so that the interior can interfere with the exterior.   3. If two black holes merge then as the event horizons merge the event horizon of the merging object will for a time be non-spherical and more like a snowman which would allow matter inside to get further away from one of the singularities than the radius of its original event horizon which would allow two observers travelling in different black holes to meet each other. Are the above correct ? and in what other ways can black holes be uncurved ?


title: How much work is needed to compress a certain volume of gas?

text: I want to know the formula (and what does the symbols stand for) for how much work is needed to compress a certain volume of gas?


title: Scalar potential in em field task

text: (Sorry for my English) Task. There is a volume with some arbitrary current or voltage source connected to wires. One wire is buried in the ground. ![enter image description here](http://i.stack.imgur.com/ba0ql.jpg) I know values of electric and magnetic fields in many points of volume (cartesian Yee grid) at particular time moments (I use FDTD method and perfectly matched layer so fields go to zero at volume boundary). So fields in the air and in the ground are known. I want to calculate scalar potential in some point at these time moments. Questions.   1. Value of scalar potential depends on choosed gauge (Coulomb or Lorenz)?   2. With any gauge I need to take into account interface between mediums somehow? For example, I want to calculate scalar potential using that from Helmholtz decomposition (as far as I know it coincides with Coulomb gauge) $$ \Phi(\vec r) = \frac{1}{4\pi} \int_V \frac{\nabla ' \cdot \vec{E}(\vec {r} ')}{|\vec r - \vec r'|} dV $$ Do I need to to take into account boundary conditions for elecric field somehow? Or I can simply use known values of elecric field in a volume and don't need to care about where they are (in air or ground)?


title: Who does work while walking?

text: While walking the work done by friction is zero. But who does the work, actually? How someone is getting displaced? This situation also arises when someone climbs without slipping or is climbing a ladder.


title: How to express Allan variance without neglecting clock drift

text: Allan variance, $\sigma^2[ \tau ]$, or its square root (Allan deviation, $\sigma[ \tau ]$) is a quantity (as function of parameter $\tau$) which is said to be a measure of (or related to) "stability of clocks". For a recent example cmp. " _First accuracy evaluation of NIST-F2_ " (T. P. Heavner _et al._ ), especially > " _Figure 1. The Total deviation (TOTDEV) of NIST-F2_ ". Clearly, this quantity is referring to **one** clock **itself** ; e.g. "the _NIST-F2_ " in the article. However, the Wikipedia page points out that for " _practical measurements_ ": > " _All measurements of Allan variance will in effect be the comparison of > two different clocks [...] a reference clock and a device under test (DUT)._ > " Likewise, the article on the _NIST-F2_ states that > " _The measurement was made using a commercial hydrogen maser as a > reference._ " With two clocks being involved, there's necessarily concern about clock drift; indeed: > " _[...] drift will contribute to [the raw] output result. When measuring a > real system, the linear drift or other drift mechanism may need to be > estimated and removed from the time-series prior to calculating the Allan > variance._ " **My question:** Can you please give an expression (as explicitly as reasonably achievable here)   of this mentioned "(raw) **_output result_ before** _post-processing_",   in terms of   * the total phase $\Phi_a[ t ]$ of the " _device under test_ ",    * the total phase $\Phi_b[ t ]$ of the " _reference_ ",    * and other parameters as needed, such as perhaps the nominal angular frequencies, $\omega_a$ and $\omega_b$, of the device under test and of the reference, respectively ?


title: 3-dimensional quasicrystals

text: As is well known, quasicrystals (i.e. their diffraction patterns) show patterns which can be deciphered and understood via the use Penrose tilings (and aperiodic tilings of the plane in general). After reading the following article: "Three-dimensional Penrose tilings and self-similarity" by Eschenburg and Dietl http://www.math.uni-augsburg.de/~eschenbu/Penrose3D.pdf The following question rises: Are there 3-dimensional physical phenomena whose structure may be deciphered using the 3-dimensional Penrose tilings / aperiodic tiling of the space? Do you know some papers referring to this subject? Thank you very much


title: Axioms behind entropy!

text: The concept of entropy is very ubiquitous, we learn about its uses starting from Information Theory (Shannon entropy) up to its basic definition in statistical mechanics in terms of number of micro-states. Limiting the discussion to physics, when studying a physical system, can be a box filled with an ideal gas, a melt of polymers or the state of rods/molecules in a liquid crystalline system, in all such scenarios, there are specific entropic terms that we define in describing the evolution of the system (by including it in the free energy expression). From a statistical mechanics point of view, we use Boltzmann's definition of: $$S=k_B \ln\Omega$$ where $\Omega$, can be the partition function in an ensemble, or simply the number of microstates within a given macrostate. But of course we almost never use this exact form of entropy in studying real systems, as it is impossible to count the microstates by any means. Instead we define entropic terms based on macroscopic variables of a system, like the followings (examples among the usual ones):   * For a perfect gas one can write the entropy per atom of N atoms in volume V as: $$S_{\rm ideal}=k_B \ln\left(a\frac{V}{N}\right)$$ with $a$ a constant.    * In soft condensed matter, studying liquid crystallinity, often we define an orientational entropy, describing the entropy lost when molecules are oriented. In its most general form defined as: $$S_{\rm orient}=-k_B \int f(\theta)\ln f(\theta)d\Omega$$ where $f(\theta)$ is an orientation distribution function and $d\Omega$ a small solid angle.   * In polymers physics, often there are entropic terms attributed to homogeneity in number density distribution of monomers $n(i)$ along the chains (often called Lifshitz entropy), described as $$S_{\rm homogeneity}\propto -\left(\nabla \sqrt{n(i)}\right)^2$$ which is just the gradient of a density distribution. In all such cases, it is relatively straightforward to see as to why we refer to such state functions as "entropic", as they all boil down to describing a certain kind of disorder in the system, and how their inclusion would effect the equilibrium state of a system. But the underlying question is about, how we give physical and mathematical bounds to these entropic terms must be consistent, hence there must be a set of axioms that a function must fulfill in order to qualify as an entropic term. **To elaborate on the question:** On the one hand, from a physical point of view, the entropy is always set to reach its maximum at the most disordered state, and a minimum for the most ordered case (i.e. 1 possible micro-state, complete certainty over its state). For example in liquid crystals again, we want $S_{\rm orient}$ to be at maximum in the orientationally disordered state, the isotropic, and for it to be at minimum in the completely ordered states, like the smectic. On the other hand, mathematically we require that:   1. $S$ to be continuous at every $\Omega$   2. To be extensive with system size   3. Differentiable (does it have to be always?)   4. Path independent: state function   5. ...what else? Clearly if we don't know how to bound such functions based on a set of axioms, we cannot know if they will make sense physically and mathematically. (Helpful thought scenario: Imagine studying a system of particles in suspension, where their positional distribution comes with a certain periodicity, if we are to attribute an entropic term to the state of periodicity of the system, what conditions should such state function satisfy.)   * What are the axioms to be satisfied by a state function for it to qualify as entropy?


title: In a gauge theory, are two states related by a global phase transformation identified?

text: In a gauge theory (non-abelian for this question), I am told that two states $|\psi\rangle$ and $|\phi\rangle$ are to be identified if they are related by a gauge transformation $U(x)$ $$|\psi\rangle\equiv|\phi\rangle\enspace\enspace\text{if}\enspace\enspace|\psi\rangle=U(x)|\phi\rangle.$$ But means that two states are to be identified when the gauge transformation is homogenous, _i.e._ independent of $x$. Does this formally mean that for the _one-particle_ quark state, the red quark $|1_\text{Red}\rangle$, green quark $|1_\text{Green}\rangle$, and blue quark $|1_\text{Blue}\rangle$ are all identified as a single state, as they are all related by gauge transformations? I would say yes... So then I ask, does this mean we are overcounting the number of color states when we calculate the color-averaged scattering amplitude? I want to say, _no_ because there are many quarks in this world, and the color orientation of the incoming and outgoing quarks with respect to some other colored quark elsewhere is gauge-invariant.... Is this correct reasoning or poor thinking?


title: Dipole moment of the electron

text: I've read that there are some restrictions on the value of a possible intrinsic electric dipole possessed by the electron, but isn't the dipole value dependent on the electron's wavefunction? Assuming you can associate a dipole moment to every electronic state, shouldn't the dipole moment roughly be $e<\bar{r}>$?


title: What is necessary for a causal set to be manifold-like?

text: A causal set is a poset which is reflexive, antisymmetric, transitive and locally finite. As a motivation, there is a programme to model spacetime as fundamentally discrete, with causal sets providing the underlying structure. Typically this is constructed by sprinkling (a poisson process) existing spacetime with elements, endowing these elements with an ordering given by causal cones, and removing spacetime. Volume is then given by a counting metric, which with the causal structure is enough to build a geometry. By the poisson nature of this process, the distribution is Lorentz-invariant. This only makes sense in nature if the causal set is manifold-like, by which we mean it can be faithfully embedded into a manifold, such that the element count gives volume. Precisely when is a causal set manifold-like: what are the necessary conditions for the existence of such an embedding? (Are there interesting sufficient conditions?) Do they have natural interpretations? _[This should be tagged quantum-gravity I think.]_


title: intensity of electromagnetic waves

text: I have a trouble understanding intensity of electromagnetic waves, I already looked at this article and this question but didn't understand completely $Intensity = \frac{\epsilon_0}{2} |\vec E|_{RMS}^2 V + \frac{1}{2\mu_0} |\vec B|_{RMS}^2 V = \epsilon_0 E_\textrm{peak}^2 V$ is it the right formula ?!


title: Example for bias in experiments due to "social pressure"

text: I remember the example for the bias in experiments: A famous physicist got a wrong result for a constant. Due to his fame, the published results of other experimenters only slowly reached the correct value after many years. (Presumably, results that were too far from the "known" value were just not published.) However, I do not remember the name of the measured quantity and would be grateful for a pointer. Answer to comments (I cannot comment): Yes, Millikan is the one I was looking for. Reading wikipedia makes it clear that I must have read it in the Feynman book. Thank you.


title: Mass diffusion: is $D_{AB} \neq D_{BA}$ at high pressures? If so, why?

text: From [Takahashi][2], I validated some models I have for estimating diffusion coefficients (methods of Fuller modified by Riazi for high-pressures, all pulled from [Poling][3]). Here is the figure mixing experimental data and the models I was looking at. ![Mass diffusion in the CO2/C2H4 system](http://i.stack.imgur.com/lmEDX.png) The experimental data was measuring diffusion coefficients between CO2 and C2H4 over a range of pressure. As expected, at low pressures, does not matter if we are looking at how a trace of CO2 diffuses into C2H4 or if a trace of C2H4 diffuses in CO2, the mass is being diffused at the same speed and thus the diffusion coefficients are the same. However, at high pressures, it is not the case. I've seen complex mathematical expressions modeling it however, and clearly, even my crude model picks up at least the trend, but I'm not sure I understand exactly why it happens. Is it the diffusion matrix that becomes non-symmetric? Or the diffusion process can no longer be modeled just by this diffusion coefficient and other terms appear? Either way, from a molecular point of view, what explains this change of behavior? [2]: S. Takahashi and M. Hongo. Diffusion coefficients of gases at high pressures in the CO2-C2H4 system. Journal of Chemical Engineering Japan, 15:57–59, 1982. [3]: B. E. Poling, J. M. Prausnitz, and J. P. O’Connell. The Properties of Gases and Liquids, Fifth Edition. McGraw-Hill, 2001.


title: Why basements stay cold even during summer?

text: Why a room below the surface (such as basements) can stay cold all the time? How is it able to avoid the high increase of temperature and heat in hot days and periods?


title: Uncertainty writing

text: This will sound like a silly question, but I don't recall that my professors ever though me what this means. For example: X=1.2345(6) units This is uncertainty, that much I do know, but does it mean: X=(1.2345+-0.0006) units or?? We only did the second notation, and recently (mostly in particle physics papers) I'm finding this notation, and I have problems with it :\ Sorry if it's a silly question...


title: How to prove that a spacetime is maximally symmetric?

text: In Carroll's book on general relativity, I found the following remark: > In two dimensions, finding that $R$ is a constant suffices to prove that the > space is maximally symmetric [...] In higher dimensions you have to work > harder Here, $R$ is the Ricci scalar. This begs the following questions:   * How _does_ ones prove that a $d$-dimensional spacetime is maximally symmetric?    * If the general case is very complicated, then is there a simpler way to obtain the result in four dimensions?


title: Why is tape so hard to rip when it is not broken, but so easy once there is the tiniest cut in it?

text: Question says it all. Ripping a piece of tape along the width is tough, stretches the tape, messes it up, etc, but if you put the tiniest nick at the top, it rips without any problems. Why is that?


title: Why do clouds form in lumps?

text: What forces drive the water vapor to form the shapes every child draws? Why isn't water vapor forming an uniform mist layer consistently (which it some times does)? I have two general ideas how this process can self-sustain itself \- the shade of a forming cloud reduces sunlight to raising and condensing vapor \- the shade of the forming cloud causes varying speeds for vapor raising from the shade and from outside the shade on the ground, causing varying rate of condensation . Neither of these, however, can tell me how the formation of a lump happened in the first place


title: Why does the event horizon of a black hole not look like a bright sphere?

text: All infalling matter-energy appears to an external observer as frozen in time at the event horizon. Why then is this horizon not extremely bright due to radiation that is able to escape radially? So should all black holes not appear as a bright sphere?


title: Identify the weight of operator under conformal transformation

text: I have a stupid (homework tag may be suitable =_=) question about the problem 2.7 in Polchinski's string theory volume 1. Why the weight of operator $:e^{ik\cdot X}:$ is $(\frac{\alpha'k^2}{4}, \frac{\alpha' k^2}{4})$? From the solution manual http://arxiv.org/abs/0812.4408 and a similar procedure in the answers of this post Identity of Operator Product Expansion (OPE), $$ T(z):e^{ik\cdot X}: \sim \frac{ \alpha' k^2}{4z^2} :e^{ik\cdot X(0,0)}: +\frac{1}{z} i k_{\mu} : \partial X^{\mu} (0) e^{ik\cdot X(0,0)}: (1)$$ (skip the antiholomorphic part.) How Eq.(1) is related to the weight $(\frac{\alpha'k^2}{4}, \frac{\alpha' k^2}{4})$ without the contribution of $1/z^2$? For my understanding, consider $T(z) :\mathrm{operator}:$ is to use the Ward identity (2.3.11) in Polchinski's string theory $$\mathrm{Res}_{z \rightarrow z_0} j(z)A(z_0, \bar z_0) + \overline{\mathrm{Res}}_{\bar z \rightarrow \bar z_0} \tilde{j}(z)A(z_0, \bar z_0) = \frac{1}{i \epsilon} \delta A(z_0, \bar z_0)$$ with $j(z)=iv(z)T(z)$ and $\tilde{j}(z)=iv(z)\tilde{T}(z)$ thus we relate $T(z) :\mathrm{operator}:$ to $\delta :\mathrm{operator}:$ For example, the operator $X^{\mu}$, we got $\sim \frac{1}{z} \partial X^{\mu}(0)$. For conformal transformation $z \rightarrow \zeta z$, $\partial$ increase weight 1, $1/z$ decrease 1, thus the weight is (0,0). However, how Eq. (1) is related to $(\frac{\alpha'k^2}{4}, \frac{\alpha' k^2}{4})$ without the contribution of $1/z^2$?


title: Why are some galaxies flat?

text: What is the explanation for the flatness of some galaxies? (If it's due to their rotation then why they are rotating, why some other galaxies are not flat etc., I would like to hear a nice and complete answer :) )


title: Why do solar panels not have focusing mirrors?

text: Most of the solar panels that I have seen do not have any mirrors, etc., but usually solar cookers have mirrors. What is the reason for solar panels not having focusing mirrors?


title: Why is quantum entanglement so important?

text: > _Entanglement also allows multiple states to be acted on simultaneously, > unlike classical bits that can only have one value at a time. Entanglement > is a necessary ingredient of any quantum computation that cannot be done > efficiently on a classical computer._ -Wikipedia I thought this was the definition of superposition. Why is quantum entanglement so important in quantum computing, to the point where advances are also measured in number of qubits entangled?


title: How does scattering work?

text: Why is the sky blue? I was always taught in high school that light with wavelength $\lambda$ acts like a little particle that wiggles up and down through space (in proportion to its magnitude). I was under the impression for quite some time that higher energies yield higher frequencies which yield more "jiggling" and thus more scattering in the atmosphere. However, after learning quantum physics and relativity, it seems like this is very wrong. From relativity it seems like light can't be "vibrating" or "jiggling" along its path. Light must travel in a perfectly straight line: if it didn't, then either violet photons would travel faster than red photons, or violet light would appear to propagate slower than red light (because the violet light must travel a wavier path). Further, quantum physics treats the quantum amplitude of a photon (as far as I can tell) as a sort of internal property. It certainly doesn't seem to be physically realized as displacement in space. So my question is, how does light scatter? Intuitively, it seems like light with higher frequency jiggles more and thus scatters broader and easier, but this intuition seems to be incorrect. If amplitude really is a property internal to the photon, how does it affect how the photon scatters?


title: How can one localize the massless fermions in Dirac materials?

text: I noticed that finite electric potential cannot localize the low energy excitations in a graphene sheet. Is it possible to localize the massless fermions in the surface band of topological insulators with a magnetic field? ![magnetic layer on surface](http://i.stack.imgur.com/TeG8M.jpg) * * * I found a paper dealing with a similar problem: http://apl.aip.org/resource/1/applab/v98/i16/p162101_s1


title: Schottky and shot noise

text: I am looking for a little history on shot noise: when was it first predicted and first measured? In particular, what was the role of Schottky? His 1918 paper "Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern" ( _Annalen der Physik_ , Vol. 362, No. 23. (1918)) is sometimes cited as the original observation of the effect. Can anyone point me to an English translation of this article? Sometimes it is even said that the "shot" in shot noise is short for Schottky (in addition to conjuring the obvious metaphor)--is there any truth to this is or is it sort of a backronym?


title: Derivation of Ohm's Law

text: Is it possible to derive Ohm's law (perhaps in some appropriate limit) from Maxwell's Equations?


title: Formula for polarized "light" transmission through close filters?

text: I'm still trying to understand photons (or polarized electromagnetic radiation).   This question is similar to one of my previous questions, but different:   Consider the famous demonstration of crossed polarizers.   Two polarizers at right angles block all light. Insert a polarizer at 45 degree angle between the two crossed polarizers, and 25% of the light is transmitted (neglecting absorption). Now perform the experiment with "light" of wavelength on the order of centimeters to meters, ie radar or radio band.   (Let's just choose 10 centimeters to be specific.)   Use parallel wire filters as the polarizing filters.   Now place the two crossed filters a meter apart, say at postions 0 and 100 centimeters.   Consider inserting the 45 degree filter in the middle at position 50 centimeters.   We should get 25% transmission. What happens if we move the 45 degree filter from position 0 to position 100?   I expect zero percent transmission at positions 0 and 100.   I expect 25% transmission at all positions between 10 and 90, but I can't prove it.   I expect transmission intermediate betwween 0% and 25% as the filter moves from position 0 to position 10, and the mirror image as the filter moves from position 90 to position 100.   What formula describes this transition?   More generally what formula describes the transmission as a function of position all the way from 0 to 100?


title: What is a quantum simulator?

text: What is the idea behind of quantum simulator aimed to study properties of matter, such as using quantum dots to study the exotic quantum states?


title: right hand rule using left hand?

text: im kind of confused, the right hand rule is used to know where the direction the magnetic field created by the current is going . is there any particular reason why the right hand is used to determine the direction of the Magnetic field?


1. Why do we treat time as parameter in non relativistic QM instead of treating position as parameter?   2. What is actually a parameter?    3. I have read this Wikipedia page, but could not understand why should we take only time as parameter?


title: What is the mass in $\vec{\nabla}\cdot \vec{B}_g=\text{something}$ called if it could be non-zero?

text: 1. Maxwell's equation for gravity has $$\vec{\nabla}\cdot \vec{B}_g~=~0,$$ see Gravitoelectromagnetism in analogy with the electrodynamics. What is the mass called that needs to make these equations symmetric in $\vec{\nabla}\cdot \vec{B}_g=\text{something}$? There are no magnetic monopoles so far but the electric charge is quantized anyway.   2. My other question is: What is preventing the quantization of mass or is it considered quantized as built from elementary particles?


title: Odd number of second class constraints (!)

text: For my thesis, I have calculated the constraints for a system using Dirac method of constraint analysis. The problem is I got odd number of second class constraints (!), which gives me unusual numbers of degrees of freedom in phase space. I might have made some mistakes. Is there any other method beside Dirac, to analyze the constraints of the system?


title: What would a length contracted object look like?

text: I have multiple sub-questions but they are related.   * What would the object look like if in were passing by?    * What would a star look like if we were traveling near $c$? Would the perspective be a a large blue-shifted disk??


title: How does a supersymmetry transformatio relates bosons to fermions?

text: A superfield is defined as a function of of a spacetime coordinate and two spinor coordinates, $\Phi (x, \theta, \theta^*)$. A supersymmetric transformation is then generated by the operator $\partial_{a}+i\sigma^{\mu}_{a\dot{c}}\theta^{\dot{c}}\partial_{\mu}$. What does it mean when we say this transformation relates fermionic to bosonic fields? Does the parameter $\theta$ measure the 'bosonic' content of a superfield?


title: The Role of Active and Passive Diffeomorphism Invariance in GR

text: I'd like some clarification regarding the roles of active and passive diffeomorphism invariance in GR between these possibly conflicting sources. 1) Wald writes, after explaining that passive diffeomorphisms are equivalent to changes in coordinates, "This 'passive' point of view on diffeomorphisms is, philosophically, drastically different from the above 'active' viewpoint, but, in practice, these viewpoints are really equivalent since the components of the tensor $\phi*T$ at $\phi(p)$ in the coordinate system $\\{y^\mu\\}$ in the active viewpoint are precisely the components of $T$ at $p$ in the coordinate system $\\{x'^\mu\\}$ in the passive viewpoint." (Wald, General Relativity, Appendix C.1) 2) Gaul and Rovelli write, "General relativity is distinguished from other dynamical field theories by its invariance under _active_ diffeomorphisms. Any theory can be made invariant under _passive_ diffeomorphisms. Passive diffeomorphism invariance is a property of the _formulation_ of a dynamical theory, while active diffeomorphism invariance is a property of the dynamical theory _itself_." (Gaul and Rovelli, http://arxiv.org/abs/gr-qc/9910079, Section 4.1) It seems that Wald is saying that there is no mathematical difference between the two, and that both imply the same physical consequences. It seems that Gaul and Rovelli, however, are saying that only _active_ diffeomorphism invariance has physical meaning that may influence the dynamics of the theory. Can anyone explain?


title: Minimum number of atoms in star

text: I am trying to follow a derivation on this site to derive the minimum number of (hydrogen) atoms I need so that the gravitational force dominates over internal electrostatic forces. The derivation begins by introducing the ratio of the two forces for _two_ protons: $$\frac{1}{4 \pi \epsilon_0} \frac{e^2}{d^2} : G \frac{m^2}{d^2} = 1.24\cdot 10^{36}$$ It then considers a sphere of radius $R$, homogeneously filled with hydrogen, to which we add protons at the border. The gravitational energy per proton mass then is $$\frac{W}{m} = G \frac{M}{R}$$ This can be expressed in terms of the number of atoms, $\frac{W}{m} \sim N^{2/3}$. So far, so good. The next argument is that gravity is not shielded, and long range. Sure, otherwise we wouldn't have used the formula above. And the electrostatic forces are shielded by the electrons in hydrogen, so they are short range only. I understand that. But then, the final step is just the claim that $$N > (1.24\cdot 10^{36})^{3/2}$$ and I don't see how this step can be made... I would have expected some discussion of the electrostatic energy per proton


title: References for real life applications on advanced EM

text: For EM (freshman level physics) and advanced EM (Junior/Senior level) to help students appreciate the material, I am looking for books/websites that contain: 1-applications of electricity and magnetism in real life. That is almost nonexistent in Griffiths, e.g. no bubble jet printers or magnetic tape in magnetism. 2-home experiments


title: Treatment of sbottoms in prospino

text: Could someone please explain the details of the following "propaganda plot" from the prospino website? There is one curve for stop pair production $\tilde t \bar {\tilde t}$, and one for general squark pair production $\tilde q \bar {\tilde q}$. Is the pair production of sbottoms lumped together with the other squarks, or is it missing here? If it is included in the $\tilde q \bar {\tilde q}$ curve, are the cross sections for the non-stop squarks nearly identical, or is this just the inclusive cross section for the production of any heavy squark pair? And finally what model/constraints are assumed in this plot? ![Prospino propaganda plot for LHC](http://i.stack.imgur.com/PEacs.png)


title: Difference between Steam and Fog / Mist

text: From a physics perspective, is there a difference between fog and steam? What is it and how does is manifest in properties of fog vs properties of steam?


title: When Eigenfunctions/Wavefunctions are real?

text: 1. When the Hamiltonian is Hermitian(i,e. beyond the effective mass approximation), generally under which conditions the eigenfunctions/wavefunctions are real?   2. What happens in 1D case like the finite quantum well symmetric with respect to the origin might be an example. any general rule? further generalization into 2D case?


title: Tying knots in power cables to prevent power surge from lightning strikes

text: There are plenty of references to this claim on the internet that tying knots in power cables will prevent a piece of equipment e.g. television or computer from a power surge. How can this be debunked (or proven) using mathematics? I stumbled across this which seems reasonable to me, but is there some way this can be proved? > The surge impedance of any line is the square root of its inductance divided > by its capacitance, and electromagnetic waves travel most readily down a > line where that surge impedance doesn't change. A point of changing > impedance is a discontinuity that causes a partial reflection of the wave > back towards its source. As an example, the end of the line is a surge > impedance jump to infinity and the whole wave is reflected back (which means > the wave voltage at the open end doubles!) This is also the reason why you > want to use terminators on the ends of coaxial cables. Open-ended cables > will reflect back the signal causing poorer picture quality and ghosting > (and similar things happen for poorly made connections that have higher > impedances than the surge impedance of the coax). > > Knotting the line gives that part of it a higher inductance (think of the > knot as a coil with a couple of turns). That means two surge impedance > discontinuities (from line to knot, and from knot back to line). It seems to > me (too lazy to resort to doing the math) that this is bound to reduce the > magnitude (voltage and current) of a surge passing through the knot because > some will be reflected back. However, I'd guess that the reduction would be > small.