title: Dog running after sephard

text: Assume there is a dog `A` on a field and a sephard `B`. `B` moves on straight line with constant $v$ velocity. The dog `A` is running always towards `B` with also constant - magnitude `$u$ velocity. If initially `B`'s velocity vector is perpendicular to `A`'s velocity vector, when will they meet? Is it possible to solve the problem above without the use of calculus? How?


title: Quantum mechanics: How do the atoms in an electronic circuit enter a smaller orbit on the filament of an incandescent light bulb?

text: Bear in mind that this is not a homework question, and I have put together some stuff to work on from below: http://www.doublexscience.org/how-fluorescent-lights-work-quantum-mechanics- in-the-home/ I am quoting from that source, and placing my question in boldface right below. > They light up when an electric current runs through a thin wire made of > tungsten, which heats up. **I thought it was a filament in which the atoms moved through, entered a smaller orbit, and produced black body radiation?** Source: http://en.wikipedia.org/wiki/Black-body_radiation > Light is a form of energy that can be released by an atom. It is made up of > many small particle-like packets that have energy and momentum but no mass. > These particles, called light photons, are the most basic units of light. > (For more information, see How Light Works.) **So light is now "energy"? I thought light was electromagnetic radiation. How can energy of the light have no mass when atoms running through tungsten/filament entered another orbit?**


title: Is there an upper limit on the radius of a rotating wheel?

text: Is there an upper limit on the radius of a real wheel which is rotating at an Angular frequency of $\,\omega \,$ along its axis, such that we just require a finite amount of energy to rotate it? Why/why not? e.g. if a wheel which is rotating at an angular speed of $\omega = 3 \times {10^5}\,{{rad} \over {\sec }}$ could have a radius of $r = 2 \times {10^3}\,meters$?? \-------- I've added this later: There are two different frames: the underlying frame at which $\,\omega \,$ and velocity relations are defined which means any frame that is not accelerated with respect to the point at which center of the wheel is located. And the other frame is the frame which its origin is located on the wheel center and is at a zero deference of "frequency speed" with the center of the wheel. My question is about the difference of limitations in these two frames of reference. If the limitations of these two frames are the same?? * * * This question may have been caused by a misunderstanding.. But it still worth asking.


title: Newton's Second Law

text: Newton's Second Law tells us that $\sum F = ma$. The vector sum of the forces $F$ on an object is equal to the mass $m$ of that object multiplied by the acceleration vector $a$ of the object. So what is the relation between this law, and the law that says that the sum of all the forces on an object is equal to zero? And what happens if the object has zero velocity?


title: Why does the Fermi Surface cross the Brillouin zone boundary at right angles?

text: I'm not sure why the fermi surface crosses the Brillouin zone boundary at right angles. I understand that this is normally the case, but not necessarily always. I'm aware that the fermi surface is a constant energy surface up to the filling point. The Brillouin zone is in reciprocal space.


title: GHz rate single photon counting

text: The fluorescent lifetimes of molecules used in biological applications tend to be in the sub-ns to a few ns timescale (let's say 0.8-4). The most direct methods to measure lifetimes typically involve gating (either explicit or via time correlations). But this is horribly wasteful as information is discarded from those photons that did not come at a selected time. If you have a delicate sample, you can destroy it before you finish your measurement; if you have a rapidly varying process, the state can have changed before you've finished making the measurement. What is the state of the art in sustained photon counting in the visible range (perhaps 450-600 nm), and is it at the level where one could reasonably time every photon without having to drop counting rates drastically below the fluorescence lifetime itself? The photophysics admits measurement of lifetime at a MHz rate (~100 photons at 10 ns intervals), but is it practical to actually do this? Although there are a variety of options available for photon counting (PMTs, APDs, GaAsPs), it has been difficult for me to get an accurate picture of the speeds and limitations of various devices actually available, or of the physical limits to a certain type of detection scheme. For example, do PMTs suffer from blurred readout times due to the distribution of electron path lengths in the cascade? Do thermal effects render APDs useless for sustained high-rate readout even if they are small enough so that the capacitance isn't a major barrier for recharging? (Or is capacitance impossibly bad for GHz rates even with really tiny e.g. 100 um square devices?)


title: Does 'maximum principal stress fracture criteria' only apply in tensile loading?

text: I'm working on 3d simulation of solid fracture, primarily for graphics applications. I have one question about the Rankine fracture criteria, which is widely used in the computer graphics community. The maximum principal stress fracture criteria, aka the Rankine criteria, states that the fracture is initiated when the greatest tensile principal stress in the solid reaches a critical magnitude: $$\sigma{}_{1 max} = \sigma{}_{TS}$$ where the subscript TS stands for tensile strength. My question is: Does this criteria only apply in tensile loading? Is it that this criteria can only model the 'Mode I' fracture? Note: the 'Mode I' fracture means the 'Open' fracture, as can be seen here: Fracture wikipedia.


title: Maximum velocity allowed for motion profile with constant jerk

text: I´m trying to calculate what the maximum allowed velocity for a mechanical axis traveling towards a stop. The maximum velocity must be a secure speed so the axis have is able to stop in time. I have:   * current position   * current distance to stop   * current velocity   * acceleration/deceleration constant   * jerk constant I did found this formula $$\frac{v^2}{2a}+\frac{va}{2j}=d$$ where   * $a$ = acceleration   * $v$ = velocity   * $j$ = jerk   * $d$ = stop distance but I don't know how to calculate the $v$ instead. Is this the correct formula to use and in that case, how should I use it?


title: Is there a theory about kinetic energy "particles"?

text: We have a model of electricity which says electrons flow from one place to another. We have a model of optics which says that photons go from one place to another. As I understand, there is currently research for a similar model to explain gravity (the hypothetical "graviton"). Is there a similar approach to kinetic energy? That is a theory which is based on small information packages traveling from one atom to another to change it's velocity? Background: I'm researching material for a hypothetical space drive for aliens in a SciFi story that I'm writing which is based on direct kinetic energy manipulation (DKEM). The idea is that instead of throwing stuff around, they directly manipulate the kinetic energy of the matter that makes up the space ship.


title: Why is the tunnel effect of solid matter not observable in macroscopic objects?

text: Assume I place a tea cup on a table (say, about a centimetre thick). Quantum mechanics tells us that the wave function for the nuclei and electrons of the cup is not zero below the table (while being terribly small, though). I'm constantly measuring that system. So, with a very small (but not zero) probability, the particles should be tunnelling through the table. Afterwards, measuring them will cause the wave function to collapse and the particles falling to the floor. So, I'd assume that if I leave the cup long enough on the table, it will eventually tunnel through the table. Completely. Obviously, I wouldn't be around to witness it, given the small probability even a single particle has to fall through the table. But I'm wondering if it is truly a matter of (a lot of) time, for this to happen, or if it is truly impossible for the cup to _gradually (!)_ make its way through the table. Assuming the cup, table, floor, building, earth, solar system, galaxy, and universe would survive an arbitrary timespan, what would happen?


title: Can superdeterminism resolve contextuality, entanglement and Shor's algorithm in quantum mechanics?

text: Superdeterminism is the idea that the apparent freedom for the choice of experimental apparatuses and their settings are nothing but an illusion. Contextuality is the dependence of the properties of a system upon the choice of measuring device. However, what if there is no "free" choice of measurement settings, i.e. the measurement settings aren't a freely variable independent degree of freedom? Bell inequalities require counterfactual polarization settings, but what if the polarization setting could only have been one way and not any other? As for the ability of Shor's algorithm to factorize large integers and compute discrete algorithms, maybe the answers gotten at the end retrocausally determine the numbers fed into the quantum computer in the first place so that it couldn't have been any other number? Are there any absolutely fatal objections?


title: Buoyancy Correction for a Kater Pendulum

text: `Question`: > Consider a Kater pendulum: that is, a rod with two cylindrical masses at > both ends, with a knife edge between the two masses and another between one > of the masses and the end of the rod. Write the corrected expression for the > period $T_0$ as $T_0=T(1\pm T_B)$, where $T$ is the uncorrected period > $2\pi/\omega$ and $T_B$ is the correction term for the buoyancy of the > pendulum in air. `Attempt`: Let $\rho$ be the density of the air, $V$ the volume of the pendulum, and $g$ the acceleration due to gravity. I make the postulate that the buoyant force $F_b=\rho V g$ is acting on the center of mass. Therefore, $\vec{\tau}_{net}=\vec{r}_{cm}\times \vec{F_{net}}$, where $\vec{F}_{net}$ is the net force and $\vec{\tau}_{net}$ is the net torque. Simplifying, we have $$\vec{F}_{net}=-mg\hat{z}+\rho g V \hat{z}$$ $$\rightarrow \vec{\tau}_{net}=-mg\hat{r}_{cm}\times \hat{z}+\rho g V \hat{r}_{cm}\times \hat{z}$$ here, $I$ is the moment of inertia of the pendulum and $\theta$ is the angular displacement. $$\mid \vec{\tau}_{net}\mid=-(m-\rho V)g\hat{r}_{cm}\sin\theta=I\ddot{\theta}$$ $$\frac{d^2\theta}{dt^2}+\frac{(m-\rho V)g r_{cm}}{I}\theta=0$$ $$T=2\pi \sqrt{\frac{I}{(m-\rho V)gr_{cm}}}$$ Simplifying again, we have $$T_0=T\sqrt{1-\frac{\rho V}{m}}$$ Performing a Taylor expansion, we now have $$T_0\approx T(1-\frac{\rho V}{2m})$$ $$\rightarrow T_B=\frac{\rho V}{2m}$$ My question is this: is it correct to assume that the net buoyant force acts at the center of mass of the Kater pendulum system? If not, how would I go about finding the resultant buoyant correction? I have no idea how to go about it unless making the above postulate. Thank you in advance.


title: Calculating specific orbital energy, semi-major axis, and orbital period of an orbiting body

text: Is it possible to calculate the specific orbital energy $ϵ$, the semi-major axis $a$, and the orbital period $T$ (or $P$) without any of them being available to you? The values I do have available to me are the velocity of the orbiting body relative to the center of gravity, its current position (also relative to the center of gravity), and the central mass that is providing the source of gravity $M$. I also have the mass of the orbiting body, but it is negligible. So, given all of these things and no outside factors, is it possible to calculate any of the values listed above? According to Kepler's Third Law, the orbital period is given in the proportion $4π^2/T^2 = GM/R^3$ where $T$ is the orbital period, $G$ is Newton's Universal Gravitational Constant, $M$ is the mass of the larger body (given the orbiting body's mass is negligible), and $R$ is the distance between the center of gravity and the orbiting body. This doesn't help very much simply because it is a proportion and cannot be worked around with algebra to get an real value for $T$ (I think?). Anyway, I have scoured the internet and Wikipedia trying to find a way to calculate these values, but I am at a loss. I am trying to see if there is a way to calculate these things for a small programming project/simulator. Otherwise, it would be necessary to simulate the program for a period to determine one of these values to calculate the others.


title: Handling halogen lamps

text: When consulting manuals, electricians, online sources, etc., they always instruct you to handle halogen light bulbs with gloves. The "explanation" that usually accompanies this statement is that oils and salts from a bare hand can "react" with the surrounding glass/quartz, owing to the fact that halogen bulbs are much hotter than ordinary ones. These reactions would cause weak spots in the quartz (or in some versions of the story, the filament), decreasing the lifetime of the bulb. Is there any merit to this explanation? What are then the precise mechanisms involved in the bulb's degradation when the bulb is touched by a dirty monkey finger?


title: Correct expression for experimental data

text: I am doing practices at the laboratory. I have some doubts about how to express correctly the errors; I read some pdfs in Google but I can't solve these questions:   * Sometimes, it's correct to write two digits in the error. For example, I'm sure that $1.23\pm0.12$ is correct; also $3.82\pm0.24$ is correct; $4.25\pm0.26$ is not correct and should be written as $4.3\pm0.3$. My question is: is $3.82\pm0.19$ correct? My book don't say it clearly. I think that it is correct, but not sure.   * In my data I've found things like this: 1.79568, with error 0.9605. How should I express that? I think is $1.80\pm0.96$, but I'm not sure because it doesn't follow the previous rule. I've been looking for a solution in Google and here in the Physics Stack, but I am not able to find a great answer. I know it's a basic question, but it's important to know it. Thank you very much!


title: Fluid Mechanics Piston Problem

text: ![enter image description here](http://i.stack.imgur.com/OEbe7.png) **The actual problem:** A hydraulic car lift has a reservoir of fluid connected to two cylindrical fluid filled pipes. The pipe directly below the car has a diameter of 1.8 m. the pipe on which the plunger acts has a diameter of 0.045m. the plunger is depressed a distance of 1.5m. How much does the car rise? **My attempt:** Since the piston movess downaward thorugh a displacement Δx1 equals the volume of liquid pushed up on the right as the right piston moves upward through a displacement $\ π (\frac{0.0225m^2}{4}) (1.5m) = π (\frac{0.9m^2}{4})(x)$ x=0.00094m **My thoughts:** My attempt is wrong but I am confused as to why. Since $(A1)(Δx1)=(A2)(Δx2)$ , I thought that if I used the depressed distance of 1.5m for $Δx1$, then I would be able to find the hight of the car. I understand the diameter of the pipe on the left is very small and unrealistic if you ask me (typical text book problem). **My question** Any hints to how I can look at this problem differently? Maybe I am looking at the problem wrong. Any hints would be appreciated!


title: Visualizing Tension in FBD -- Rope With Mass

text: Asked to find the tension of a point that is halfway up a rope (where the rope has mass), given the system: ![enter image description here](http://i.stack.imgur.com/OQWpl.png) The solution of the problem (FBD included) is as follows. In this diagram (Tm = tension at mid-point, and Tt = tension at top). Question(s): (1) Why is Tt incorporated into the FBD? (2) Why does Tm point downward? ![enter image description here](http://i.stack.imgur.com/4OG2i.png) Also if it helps the FBD's for the individual components are given here: ![enter image description here](http://i.stack.imgur.com/ZvJeq.png) Thanks!


title: Simple & intuitive explanation of superfluidity?

text: I know that superfluidity is caused by the fluid having zero viscosity. This only happens at very low temperature, so the fluid (e.g. Helium-4) is a Bose- Einstein condensate. I also know that in a Bose-Einstein condensate all the particles are in the ground state. Now, that said:   1. How can this explain superfluidity? Many websites just say that _the particles behave as one [...],_ but what is this due to?   2. Superconductivity is due to Cooper pairs, which being composed by two fermions are actually bosons. Is a superconductor a Bose-Einstein condensate? If not how come the Cooper pairs move without any electrical resistance?


title: How can there be a voltage when there is no current?

text: I'm told at school that the Electromotive Force (e.m.f) of a battery equals the potential difference between the terminals of the battery when there is no current. How is that possible? How can there be a potential difference with no charge flowing?


title: Gravity and electromagnetism

text: If light bends due to the curved spacetime,would not the act of bending light warp space? How does one describe curved light?


title: Is "atmospheric geostationary satellite" feasible with current technology?

text: Meaning by "atmospheric geostationary satellite" a vehicle capable of hovering 30 km above Earth surface, hence insde atmosphere, for unlimited time, making use of air propellers, solar panels and batteries. How much energy is needed to keep an object steady in air at 30 km above surface? There are two possibilities: a plane-like vehicle, flying in circle, using wings to stay up; an helicopter-like vehicle, hovering.


title: Radiation heat transfer

text: I'm looking at the radiosity equations for heat transfer http://en.wikipedia.org/wiki/Radiosity_(heat_transfer)#Radiosity_method Specifically, I'm hesitant to accept the equation: $$ \dot Q_i = \frac{ A_i \epsilon_i }{ 1 - \epsilon_i } ( \sigma T_i^4 - J_i )$$ My analysis is as follows: power goes out via Stefan-Boltzmann term, which is given by a term like $$ - A_i \epsilon_i \sigma T_i^4 $$ and radiation goes in via absorption of all emissions from nearby surfaces, that is: $$ A_i \epsilon_i H_i = A_i \epsilon_i \sum_j F_{ij} J_j $$ where the radiosity $J_j$ expression is correct on the article, and we are assuming Kirchoff's law of thermal radiation to hold. But the above implies that the actual expression for the net heat transfer is: $$ \dot Q_i = - A_i \epsilon_i ( \sigma T_i^4 - H_i ) = - A_i \epsilon_i ( \sigma T_i^4 - \sum_j F_{ij} J_j ) $$ Thoughts? Is my derivation correct, or is the one on the article?


title: Why don't atoms emit gravitational waves?

text: Atom's do not seem to emit gravitational waves. But they do contain changing mass quadrupoles, though very small ones. Obviously, the probability for emission of such waves is very small, as the gravitational coupling is very small. But why is there no emission at all? We can split the discussion into two cases: (1) The ground state. Atoms in the lowest state do not emit electromagnetic waves because there is no lower state to fall into. Is this also the reason for the lack of gravitational waves? Or is it that the ground state has no changing quadrupole? Or both? (2) Atoms in excited electromagnetic states. Is the lack of gravitational wave emission (instead or in parallel to electromagnetic emission) just a question of low probabilities? Or is there some other reason?


title: Vibrationing molecules/atoms and the effect

text: If the molecules/atoms of a solid object vibrate quickly enough, would the way a human eye perceives that object be changed? Would the object appear to "flicker" or have almost a transparent look to it? I know with a tuning fork there is a change but I am thinking of a faster vibration. Also, would this type of vibration cause any negative effects to the object? What if the object was living? If you took an animals (No, I am not experimenting on any) and somehow caused the molecules in it's body to vibrate at an extremely high rate, assuming it didn't die for one reason or another, would the vibrations cause increased aging or some other noticeable effect(s)?


title: A Sphere of Black Holes

text: Imagine a sphere of black holes surrounding a piece of space. Will this piece be separated from the rest of normal spacetime (at least for some time, till these black holes finally attracted themselves). So, seen from the outside, we have a black hole, but with a non-singular interior. Is this possible?


title: Why is classical physics not valid for a harmonic oscillator in its lowest energy state?

text: I am reading Born's interpretation of wave function in quantum physics by Eisberg & Resnick and I am not able to understand this description about comparison between the classical and quantum validity for an oscillator at lowest energy.![enter image description here](http://i.stack.imgur.com/aDFYf.png) ![enter image description here](http://i.stack.imgur.com/5Hjwt.jpg) ![enter image description here](http://i.stack.imgur.com/z64Pc.jpg)


title: Is the cross product of two vectors always perpendicular to both?

text: Does the cross product of two vectors result in a vector perpendicular to both of the vectors _or_ does the cross product of **only two perpendicular** vectors result in a vector perpendicular to both of the vectors?


title: Is gauge connection unique?

text: In QFT, given a gauge group and matter field, is the form of the gauge field unique? In other words, given a principal G-bundle and its associated vector bundle, is the construction of the principle G-connection unique? This is related to the other question (here: Gauge Field Tensor from Wilson Loop) where the author implies that the gauge field is natural/unique given the matter field. May be it is, but I wanted to confirm (edit: From answer below, the gauge connection is not unique) Because a gauge connection (or a gauge field) can exist independent of the vector matter field (as in pure gauge theories), non-uniqueness of the connection would imply a symmetry on the connection itself.


title: $\dot \omega $ when momentum is conserved

text: > If momentum is conserved when there is no externel force, why is there an > acceleration when a momentum parameter is changed (inertia)? How does it > accelerate with no external force? For example angular momentum is conserved when: ${\tau}=\frac {d(I\omega)}{dt}=0$ But in this case momentum is conserved, so both $ I $ and $\omega $ are changing, so the product rule applies: So it equals: $ I{\dot \omega}+{\dot I}\omega=0$, hence $\dot \omega $ is acceleration, and we also know the object accelerates when the rotational inertia changes.


title: why does a thread/rope have more tensile strength when swirled like this as shown in the figure?

text: Why does a thread/rope swirled like this: ![enter image description here](http://i.stack.imgur.com/xprTt.gif) become more strong than just the group of single threads without swirling? Is it because of more contact between them and therefore more friction? (I don't know the appropriate word for this process, I called it "swirling")


title: Finding the induced EMF on a bar - Faraday's law

text: I have a couple of questions about the following problem: A conducting bar of length L moves with velocity v, in a rectangular region with a uniform and stationary magnetic field B_1. Near the bar, there is a cylindrical region of radius R with another magnetic field B_2 (it may vary on time). Both magentic field are normal to the plane of the picture, and point inwards. ![enter image description here](http://i.stack.imgur.com/JfLQU.png) a)Find the expression of the induce EMF on the bar, indicating its polarity, and the potential difference between the top and botton of the bar. b)Is it equal to the EMF induced in the circuit P1,P2,P3,P4? c)What if the bar was non-conducting? Faraday's law: $\varepsilon=-\frac{d}{dt} \iint_{S(C)}\vec B \vec{ds}=-\iint_{S(C)}\frac{d \vec B}{dt} \vec{ds}+\oint_C \vec v \times \vec B \vec {dl}$ My solution and doubts: a)Integrating over the red curve C and the surface enclosed by it, I get: $\varepsilon=-\iint_{S(C)}\frac{d \vec B}{dt} \vec{ds}+\oint_C \vec v \times \vec B \vec {dl}=\frac{dB_2}{dt}\pi R^2+vB_1L$ I took positive EMF anti-clockwise, I may have messed up with the signs anyway. Is this correct? I'm confused, shouldn't the EMF be the same whichever curve I take? (Note that if I take a curve such that it doesn't include the cylinder, the first term of the expression dissapears) My question is, how do I know which curve to take? It should be one which has all the points of the bar, but there are lots of them. b)I would say definitely not, since there is no magnetic flux variation on that surface so EMF=0. c)If the bar was non-conducting charges wouldn't move inside the bar, and so there would be no EMF there, but the potential difference would be the same?


title: How to sum over final, and average over initial color states?

text: Consider the $s$-channel mediated top quark production process   $$ d + \overline d \rightarrow t + \overline t$$ Using the Feynman rules for QCD, the amplitude contains a color factor $$[c^\dagger _{\overline d} ~t^a ~c_d][c^\dagger _{t} ~t^a ~c_{\overline t}] $$ where $t^a$ are the generators of the $SU(N)$ color group and summation over a is implicit. To evaluate the cross section $\sigma$, one has to sum over final colors and average over initial colors. One gets $$ \sigma \propto {1\over N^2} \sum_{initial} \sum_{final} [c^\dagger _{\overline d} ~t^a ~c_d][c^\dagger _{t} ~t^a ~c_{\overline t}][c^\dagger _{\overline d} ~t^b ~c_d]^*[c^\dagger _{t} ~t^b ~c_{\overline t}]^* $$ My question is, how does one proceed from here? The answer has a term proportional to ${N^2 -1 \over N^2}$, and I can only account for the $N^2$ in the denominator. PS: My understanding is limited to what is discussed in Griffiths' book. I have no background in QFT/QED/QCD. Please mention sources if possible. Edit: Many have suggested that I use $[c^\dagger _{\overline d} ~t^a ~c_d][c^\dagger _{t} ~t_a ~c_{\overline t}] $ (note Einstein's convention) but I have not seen this in Griffith' book. He has used superscripts for both indices. Also, I have correctly changed the color index to latin.


title: Calculating the mass of a wave of water

text: I am assuming it is possible to calculate the mass of water if the volume is known. My assumption is that doing this for stagnant water, in a container perhaps, is easy. However I want calculate, approximately, for a wave of water at sea. What kind of information would I need if I wanted to calculate the mass or volume of a wave of water? For example, if I know the space from one wave crest to the next and the period could I use that information? **So again how would I calculate the mass of a wave of water?**


title: Creation and Annihilation operator

text: In this page  I want to know, why the equation (1.32) introduced creation and annihilation operator. Please elaborate.


title: Why can't we detect redshift of Galaxies/Clusters moving parallel to us?

text: If a moving Galaxy/Cluster doesn't have radially outward motion component from us, we are unable to detect its redshift. The answer may look obvious: There's no wavelength squeezing/expanding ju-ju. But, here's my problem: As universe expands, the gravitational grip becomes weaker because it's inversely proportional to square of the distance. So, technically, when we receive a light (which is actually from past), light has travelled from strong gravitational field to weak gravitational field (I am talking about whole universe here) which is subject to Gravitational Time Dilation. As frequency is inversely proportional to time, there must be redshift of all lights we receive. Then, why are Galaxies/Clusters moving parallel to us not redshifted?


title: Wouldn't angular momentum of a binary star system decrease?

text: Consider a binary star system, as these stars go around one another they would emit gravitational waves. Since, the graviton is a spin 2 particle. Wouldn't the angular momentum of the stars decrease? And would this decrease be observable? Edit: although the angular momentum change was predicted by GR, could there also potentially be an extra angular momentum effect caused by the quantum mechanical spin 2 effect of the gravitons (which could be looked for for a proof of quantum gravity


title: Fractionalization and the structure of spin rotation group?

text: As we know, the phenomena of fractionalizations in condensed matter physics is fantastic, like fractional spin, fractional charge , fractional statistics, .... And one key point is that the quasiparticals must be created or annihilated by _pair_. On the other hand, consider the groups $SU(2)$ and $SO(3)$, they are the rotation groups for _half-integer_ and _integer_ spins, respectively. And we know that $SU(2)/\mathbb{Z}_2=SO(3)$, which means that each element in $SO(3)$ can be viewed as **one pair** $(U,-U)$, where $U\in SU(2)$ (otherwise put: the coset $\left\\{U, -U\right\\} \subset SU(2)$ in the quotient group $SU(2)/\mathbb{Z}_2$ is our element in $SO(3)$). So I wonder that whether is there any underlying connection between the _pair_ nature of quasiparticals in topological phase in physics side and the _pair_ structure relating $SU(2)$ and $SO(3)$ in mathematics side? Thank you very much.


title: Applicability of the concept of voltage in electrodynamic circuits

text: In electrostatics, we have $$\nabla \times \vec{E} = 0$$. Hence, we can define a scalar potential $V$, where $$\vec{E} = -\nabla V$$. We know from Faraday's law that $$\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$$. In situations involving constant currents(D.C.) the rate of change of the magnetic field is zero, so we can continue to use the concept of scalar potential, also known as voltage in circuit theory, for analysis of DC circuits. However,in practice, in the literature, we find the concept of voltage being used to study alternating current circuits as well. Further, it is also used in the study of high frequency alternating current circuits used for generation of electromagnetic waves. In such situations $$ \oint \vec{E}.\vec{dl} \neq 0$$. So strictly speaking, we cannot use the concept of voltage to study alternating current circuits, especially in the high frequency applications. Yet, in practice we find that it continues to be used in the literature. So is it really justified to use this concept outside of its realm of validity, and why or in what way?


title: Functional derivative and units

text: The both sides of below equation don't give the same units, e.g. $$ \frac{\delta}{\delta \phi (\tau)}\int_a^b \phi (\tau') d\tau'=1\;. $$ where $a<\tau<b$. To show this assume that the field $\phi$ has "$j$" unit and $\tau$ has "$s$" unit then $$ [\frac{1}{j} j s] \neq [ 1 ]. $$ What's wrong with my reasoning?


title: Is continuous evolution from one eigenstate of operator $O$ to another $O$-eigenstate possible?

text: Eigenvectors associated with distinct values of an observable are orthogonal, according to quantum mechanics. Does this entail that a quantum system cannot continuously evolve from one eigenstate into another, for ANY observable? At first, that seems strange: it seems like a particle should be able to "travel" in the sense of continuously moving from one eigenstate of position to the next. Another example: can't a particle "speed up" (i.e. go continuously go from one velocity eigenstate to the next)?


title: How to count photons

text: How are photons counted? What is the experimental setup used to count photons from a laser or even a lamp? Of course, in the case of the lamp, I would be able to count only the photons that pass through an area sensor in a particular observation point. If at all possible, a setup that can be done at home is preferred--one that avoids expensive instruments as much as possible (I may be crazy to even think this is possible). The key point is: > We can't count photons like we count sheep. So how do we infer from the > effects of single photons and count from there? I can start with $E = \frac{hc}{\lambda}$, and all other manifestations of energy, like heat or motion.


title: What is the world's biggest Schrodinger cat?

text: How big is it by a truly quantum measurement? I am thinking of comparing Science magazines "Breakthrough of the Year" (BYOT) with the Zeilinger buckyball. The BYOT is a piezoelectric mechanical oscillator (PO) the size of the cross section of a human hair. It is placed in a superposition of its ground state and its first excited state. The well known buckyball experiment is a two slit experiment using buckyballs. (A third candidate might be a macroscopic Josephson junction oscillator conducting both ways at once.) I have made some basic calculations. For instance, the BYOT contains about 10^14 atoms compared to 60 or 72 atoms in the buckyball. By this measure the BYOT is bigger by a factor of about 10^12. On the other hand, the two slits are separated by 50 to 100 nanometers, or 10^-7 meters. In its first excited state, the top of the BYOT PO moves about 10^-15 meters per cycle, according to my calculations. By this measure the buckyball wins by a factor of about 10^8. Calculating energy of the moving parts, I find a much closer horserace, but the buckyball is about 100 times bigger. However, none of these calculations is at all quantum mechanical (QM). ArXiv lists at least five papers proposing truly quantum mechanical measures of the size of a macroscopic Schrodinger cat. The most recent is Lee and Jeong http://arxiv.org/abs/1101.1209 which references the other four. Can someone competent (or expert) in QM apply one or more of these quantum measures to the BYOT and the buckyball and tell me which is larger? TIA. Jim Graber


title: Vertical circular motion followed by projectile motion

text: If you have a stone tied to a string, and it is given a certain velocity at the lower most point such that it completes a quarter circle but then the string becomes slack, and it undergoes projectile motion. The problem is, is it necessary that this parabola will be symmetric about the verticle? If so, is it impossible that the stone passes through the center of this circle during downward motion? Please give a detailed solution Thanks in advance


title: Is it only the Higgs field that stops me from getting to $c$?

text: Is it only the higgs field that stops me from accelerating up to the speed of light or is there other restriction concerning the increase in mass? In other words if I had a Higgs field shield on my spacecraft could I get close to the speed of light without an increase in mass?


title: How far can one look into space while relying on light in the visual spectrum?

text: Put the other way around. From how far does visible light reach the Earth to be observable by a telescope that operates in this spectrum? Gas clouds for instance absorb light. A star behind such a cloud would be not observable, because its visible light does not reach us.


title: Origin of phases in amplitudes in QFT

text: Amplitudes in QFT are typically real. I'd like to understand the physical meaning of an amplitude having a phase. I know of three ways that amplitudes can get a phase:   * If the couplings have an imaginary component   * If there is a trace over the spin matrices, $ \gamma _\mu $ producing a $ i \epsilon _{ \alpha \beta \gamma \delta } $.   * If a particle has a significant decay width we allow its propagator to have an imaginary contribution, $$ \frac{i}{p^2-m^2} \rightarrow \frac{i}{p^2-m^2+i m \Gamma } $$ I have heard many times that phases have to do with CP violation, but I'm not able to make the connection. In particular I'd like to know   1. What is the meaning behind the different sources of phases in the amplitude mentioned above?   2. Are there any other sources of phases that I'm missing?   3. Is it true that if the above sources were gone then all amplitudes to all orders would be real (or is it possible for extra $i$'s to sneak in due to things like Wick rotation)?


title: How to find a vector normal to a cylinder in cylindric coordinates?

text: I'm trying to solve a problem which demands to multiply a vector M and vector normal to a cylinder's surface in cylindric coordinates. Height of the cylinder is infinite and its radius is R. So how do I express normal vector in such coordinates?


title: Spring Damper System : Recoil Reduction

text: I am designing a man-"portable" 30mm sniper rifle. Although it may be classified as a anti-materiel cannon. I have the mass of the round in total, and the mass of the projectile leaving the barrel, as well as the pressure inside the barrel. I have the weapon's weight as well. Here is my source : http://www.pmp.co.za/index.php?page=mediumcalibre6 Now, my problem.   1. How do I calculate the force that this bullet imparts upon the rifle?   2. If I use a spring-damper system to reduce the force on the shooter, how do I actually determine the force on the shooter? If you do not find the need to supply me with a direct answer, which is understandable, could you please redirect me to a website/book that might help me?


title: Difference between steady state and equilibrium?

text: In semiconductor physics, what is the difference between steady state and equilibrium. How analysis of devices varies in these processes?


title: Is the additivity property of the quantum states valid only for countable families of pairwise orthogonal projections?

text: Consider a generic Hilbert spaces and a map $$ \mu:P(H)\longrightarrow [0,1] $$ such that $\mu(I)=1$ and $$ \mu\left(\mbox{s-}\sum_{i\in\mathcal{I}}P_i\right)=\sum_{i\in\mathcal{I}}\mu(P_i) $$ for every family of pairwise orthogonal projections on $H$. The Gleason Theorem proves that all these states are given by $$ \mu=Tr(\rho\ \cdot) $$ for some trace class positive operator $\rho$. In general in non relativistic Quantum Mechanics one deals with $separable$ Hilbert spaces, hence it makes no sense to consider $uncountable$ families of these elements and so the definition of $quantum\ state$ can be given as above. Suppose instead that the Hilbert space is $non-separable$. The Gleason theorem requires the additivity property for generic families of pariwise orthogonal projections, not only countable ones. Is there any problem in taking as definition of state the one above for generic sets $\mathcal{I}$ or its cardinality $must$ be countable for some physical reason?


title: Difference between expectation values of $L^2$, $L_z$ and measuring $L^2$, $L_z$

text: I was given with this hydrogen radial wavefunction $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ and was asked to find **a)** What are the expectation values of the $L^2$, and $L_z$? **b)** If you measured the orbital angular momentum squared $L^2$, what values might you get? Do the same for $L_z$. The problem is I cannot understand the difference between the answer to both **a** & **b** , aren't they referring to the same answer? My answer for $L^2$ is: $$ L^2 \psi = l(l+1)h^2 \psi \\\ = 2h^2 \psi$$ hence the expectation value for $L^2$ is $2h^2$, now what should be my answer for **b** )?


title: Can or does the Casimir effect play a role in solving the electron self-energy problem?

text: The Casimir effect is usually derived for parallel plates, with the pressure going as the inverse fourth power of the separation. It strikes me that this implies that a tiny spherical shell of charge (approximating opposite walls to be parallel) will feel an attractive force that goes roughly as the inverse square of the radius (since the area goes as the square of the radius). This seems like a suggestive coincidence that would hint that the Casimir effect would provide the attractive force necessary to hold the charge of the electron together. Is this idea trivially ruled out or has it been explored? **Edited to add:** I asked a distinct but related question a couple years ago that I think got a nice answer: link.


title: Robertson-Walker metric and stable orbits

text: The RW metric is defined using 4 spatial dimensions, but stable planetary orbits require 3 spatial dimensions. Does this indicate a problem with the assumption of the RW metric to describe the cosmos?


title: Why does soda fizz when it meets ice?

text: I read that the soda's temperature allows it to contain its $\text{CO}_2$: colder means it can retain its bubbles better. So, why does soda fizz when it meets ice? If anything, because the soda is made colder, it should retain its gas better, as per above. The ice is taking away energy from the soda, thus freezing. Won't heating, not freezing, encourage the gas to escape, or is it not an energy matter?


title: How does a spatial covariant derivative act on tensors that are not purely spatial?

text: I have a possibly dumb question on ADM formalism. Starting with a metric in ADM form \begin{equation} ds^2 = -N^2dt^2 + q_{ij}(dx^i + N^idt)(dx^j + N^jdt) \end{equation} where $i,j$ only run over the spatial components. I'm worried that I've misunderstood how to use the spatial covariant derivative $D_i$ compatible with the spatial metric $q_{ij}$. The sources that I read seemed to imply it could be formed entirely from the spatial metric $q_{ij}$ and its inverse $q^{ij}$ using the usual symmetric connection: \begin{equation} ^{(n - 1)}\Gamma^i_{jk} = \frac{1}{2}q^{im}(\partial_jq_{mk} + \partial_kq_{jm} - \partial_mq_{jk}) \end{equation} Then for a spatial covariant derivative acting on a purely spatial vector we would have \begin{equation} D_kV^m = \partial_kV^m + ^{(n-1)}\Gamma^m_{kn}V^n \end{equation} So what happens when a spatial covariant derivative acts on a vector that is not purely spatial? How would it act on the time component? Would it reduce to a partial derivative, such as \begin{equation} D_r\xi^t \rightarrow \partial_r\xi^t \end{equation} Sorry for the probably dumb question but I really want to make sure I understand the formalism.


title: Non Zero correlation function (for large separations) in one particle state?

text: So i computed the following equal time correlation function for a one particle state. The vacuum correlations give the function $$\langle \phi(\vec x)\phi(\vec y)\rangle_0=D(\vec x-\vec y)\\\ =\frac{e^{-m|\vec x-\vec y|}}{4\pi |\vec x-\vec y|}$$ while the one particle correlation function looks like: $$ \langle\vec q| \phi(\vec x)\phi(\vec y)|\vec q\rangle=2\omega_q\langle0|a_q \phi(\vec x)\phi(\vec y)a^{\dagger}_q|0\rangle\\\\\propto 2cos[\vec q\cdot(\vec x-\vec y)]+D(\vec x-\vec y)\\\=2cos[\vec q\cdot(\vec x-\vec y)]+\frac{e^{-m|\vec x-\vec y|}}{4\pi |\vec x-\vec y|}$$ I recognize that since this is a spacelike separation that it can't be observed, the commutator of this type vanishes since the terms are invariant under $\vec x\rightarrow \vec y$. Since there is no elapsed time there is also no valid interpretation as particle propagation. it just seems odd to me that the field has non vanishing correlations for large spatial separations. I was wondering if there is any consequence to this that people know about. Thanks, Selman


title: What is the status of massless photons traveling through a medium?

text: Photons in vacuum have no proper time, and they are not considered as observers and not as reference frame. But what about photons travelling through matter? Their velocity is lower than light speed, thus the proper time formula (multiplication with reciprocal gamma) would yield a proper time, but do we consider that they have a proper time/ that they are observers/ that they may be reference frames?


title: What is a "charged order parameter"?

text: In condensed matter physics, especially in the context of superconductors, if an author uses the phrase "charged order parameter", what does it refer to? Since the superconductor has a close relation with high energy physics, I think it may come from quantum field theory. Could someone give me a hint?


title: Inelastic collision and impulse

text: Suppose I have some cart moving horizontally in a straight line and with a constant velocity, and there is no friction between the surface and the cart. Now, I throw a plasticine on the cart at some angle with the path (not right angle). ![Illustration](http://i.stack.imgur.com/ckPfy.png) The net momentum before the hit was at some angle with the path. After the hit it changed its direction to the direction of the moving cart. So the momentum is not preserved in this case which means there is some external impulse acting on the system which alters the direction of the net momentum as described before. Now, this impulse must be canceling out the vertical component of the net momentum before the collision. Therefore its direction must be upwards. Now, I'm told that this happens because of the normal force acting on the cart: before the collision it was "canceling out" the gravitation, which made equilibrium in the vertical axis possible, but **during the collision** it has grown so the net force has become some non- zero value at that direction, and it was the source of the impulse which "canceled out" the vertical component of the net momentum. My question is - how could it be? Is it because the plasticine, during this short period of time of the collision is pushing harder and harder the cart, so it pushes the ground and the ground pushes the cart with the same force (according to Newton's third law), but somehow the gravitation is not still balancing the normal force, maybe because the cart and the plasticine can't be considered one uniform object at that short period of time? And another related question - in the example described above, how can I tell whether the speed of the cart will increase or decrease (no values, just that) after the collision, knowing the angle, and using only Newton's laws (no momentum considerations)?


title: Anisotropy and demagnetizing field

text: I'm trying to calculate the anisotropy constant of a ferromagnetic material. Then, of course, I need to worry about the demagnetizing field. However, a book I'm reading claims that we can calculate the anisotropy constant without worrying about the demagnetizing field, if the external magnetic field is applied perpendicular to the easy axis. Why is this? Why don't you need to worry about the demagnetizing field if your field is perpendicular to the easy axis? Thanks you very much.


title: Velocity of a viscous fluid through a tube

text: When a viscous liquid flows through a tube in a laminar flow, why is its velocity highest at the center? I understand the concept of shear viscosity and why the liquid in contact with moving plate has highest velocity. That's because of viscosity itself. But, I cannot understand how it explains liquid flow in a tube or whether it explains at all.


title: Tensor contra- and covariance concept

text: Imagine we have $p$-contravariant and $q$-covariant tensor, such that $$ t~=~t^{i_1, \dots, i_p} _{j_1, \dots, j_q} e_{i_1}\otimes \dots \otimes e_{i_p} \otimes e^{j_1} \otimes \dots \otimes e^{j_q}~\in ~T \left( p,q, L\right),$$ where $e_{i_l}$ are basis vectors of $L$ (arbitrary linear space), $e^{j_k}$ its dual basis in $L^{*}$. My question is following: what is the physical meaning of vector and its dual basises? I mean, for example, how do I interpret 2 times contravariant and 1 time covariant tensor in physics.


title: Quantum Cascade Laser

text: I want to learn about quantum cascade laser in a six month time. Can anyone please suggest me any reading materials or video lectures. I have background in calculus and linear algebra. I am learning quantum mechanics now.


title: Infinite Round Square-Well zeroes of Spherical Bessel function

text: Consider a potential well where the potential is zero within a spherical well of radius a centered on the origin. Taking $a$ as our length scale and $\hslash^2/(2ma^2)$ as our energy scale, we gain the dimensionless form $$ -\biggl(\frac{\partial^2}{\partial r'^2}+\frac{2}{r'}\frac{\partial}{\partial r'}+\frac{1}{r'^2}[\frac{1}{sin\theta}\frac{\partial}{\partial\theta}(sin\theta\frac{\partial}{\partial\theta})\frac{\partial^2}{\partial\phi^2}]\biggr)\psi(r',\theta,\phi)=(E'-U')\psi(r',\theta,\phi) $$ Seeking a solution where the dependence on $r'$ factors from the dependence . on angles $$ -\biggl(\frac{\partial^2}{\partial r'^2}+\frac{2}{r'}\frac{\partial}{\partial r'}-\frac{l(l+1)}{r'^2}\biggr)R(r')=(E'-U')R(r') $$ We substitute: $ \rho=\sqrt{E'-U'}r'=k'r' $ where $E'>U'$ Dividing the above equation by $E'-U'$: $$ \biggl(-\frac{\partial^2}{\partial \rho^2}-\frac{2}{\rho}\frac{\partial}{\partial \rho}+\frac{l(l+1)}{\rho^2}\biggr)R(\rho)=R(\rho) $$ The case where U is infinite and so the wavefunction must be zero for $r>a$, i.e., $r'>1$. Thus we must have: $j_l(k'r')=0$ for $r'=1$ That is $k'$ must be a zero of $j_l$. The energy of the wavefunction can then be calculated from: $E'=k'^2$. Here is the overall solution: $$ \psi_{n_rlm}(r',\theta ,\phi)=\frac{\sqrt{2}}{j_{l+1}(k'_{n_r,l})}j_l(k'_{n_r,l}r')Y_{lm}(\theta , \phi) $$ where $j_{l}(k'_{n_r,l})=0$ If i want to plot the radial part of the function I need $k'_{n_r,l}$. should I use `fzero` in $Matlab$ for example to find theme first? Thanks for any help to draw it.               jnu=sqrt(pi./(2*x)).*besselj(nu+1/2,x);


title: Why do electrons move towards regions of lower potential?

text: Can someone explain why electrons move from high to low potential regions in quantum mechanics? By the way, what is the very definition of this potential? Moreover, how does this generalize to other particles?


title: Weak interaction and the Chirality of anti-particles

text: Consider a weak current of the form $ J^{\mu} = \bar{u}_{\nu}\gamma^{\mu}(1-\gamma^5)u_{e} $ This describes the part of a weak process where a left-handed electron converts into a left-handed neutrino by emitting/absorbing a W boson. Equivalently, it should also describe the same process for a right-handed positron going to a right-handed anti-neutrino. How do you get this second part from the form of $J^{\mu}$, considering that $P_L = 1-\gamma^5$ is by definition the left handed projector? Whatever antiparticle states contained in $u$ and $\bar{u}$ should have eigenvalue $-1$ of $\gamma^5$ in order to be included in $J^{\mu}$, so, aren't they by definition left-handed? (note: this is all in the massless approximation so that I can equate chirality and helicity/handedness)


title: Force on a point charge q inside a cavity in an uncharged conductor

text: This is problem 2.40 from Introduction to Electrodynamics by D. J. Griffiths: > A point charge $q$ is inside a cavity (not necessarily spherical or anything > similarly regular) in an uncharged conductor. Is the force on $q$ > necessarily zero ? What my understanding tells me is that if the charge on the inner surface of the conductor is just enough to cancel the field from the point charge from every direction, then the force from any two opposite pieces on the inner surface will produce equal but opposite forces. Thus, the net force is zero. Is my reasoning correct?


title: How can one know if a theory allow action at a distance effects or not?

text: 1-In general, if a theory has action at a distance effects, where can that appear exactly in the theory? 2-Does it appear in the dynamical law of the theory? (does it appear in Newton's 2nd law? where can it be spotted?) 3-Does it appear in the force law of the interaction? (it is said that Newton's law of gravitation, $\displaystyle F\sim\frac{m_1m_2}{r^2}$, supports action at a distance effects. How can one see that from the form of the law?) 4-Before special relativity, causality roughly means cases always come before effects. Now if the force law allows action at a distance, as in Newtonian gravity in 3, then the interaction is instantaneous. It seems that the words "before" and "after" lose their meaning in this case, then how causality is defined then?


title: Explanation of "thermite vs ice" explosion

text: There are several videos of the reaction, where some amount of burning thermite explodes on a contact with ice.   An "original" video: http://www.youtube.com/watch?v=IuPjlYxUWc8   A Mythbusters confirmation: http://www.youtube.com/watch?v=BnHR4cMXiyM There are several speculative explanations of the phenomenon, summarised in the end of the latter video. And none of them sounds to me satisfactory enough. Is there any detailed investigation and/or explanation of the effect?


title: state vector notation

text: I've never taken a quantum mechanics class, but I find myself now using principles developed in the quantum theory of angular momentum. One particularly confusing aspect that I'm struggling with is the notation. Could someone please explain the meaning of a ket (or bra) with two arguments, i.e.: $\left|j_1m_1\right>$? I'm mainly interested in the mathematical meaning (i.e. is it a vector with two components?, are $j_1$ and $m_1$ multiplied), but a physical explanation would be helpful too. I have seen other similar notation as well which perplexes me. For instance, in the definition of the Clebsch-Gordan coefficients: $C_{j_1m_1j_2m_2}^{jm}=\left<j_1m_1j_2m_2\mid j_1j_2jm\right>=\left<j_1j_2jm\mid j_1m_1j_2m_2\right>$ what does a bra (or ket) with four arguments written adjacent to each other mean? Similarly I've seen $\left|S_x;+\right>$ which, as far as I can tell indicates that the spin component in the x-direction is $+\frac{1}{2}$, but could this be equivalently written simply as $\left|+\right>$? Please any help would be very illuminating, every text and resource seems to use similar but slightly different notation and they all seem to assume you already know the conventions.


title: A question on an assumption of space-time

text: > "A four-dimensional differentiable (Hausdorff and paracompact) manifold $M$ > will be called a space time if it possesses a pseudo-Riemannian metric of > hyperbolic normal signature $(+,-,-,-)$ and a time orientation. There will > be no real loss of generality in physical applications if we assume that $M$ > and its metric are both $\mathcal{C}^{\infty}$ ." The above is an excerpt is taken from this paper. I'd like to know how the assumption that $M$ and its metric are both $\mathcal{C}^{\infty}$ be made with out any real loss of generality in physical applications. Any intuitive answer is also appreciated.


title: What is better than time-dependent perturbation theory if the pointer states aren't energy eigenstates?

text: Time-dependent perturbation theory works excellently if the interaction is weak and the pointer states are approximately energy eigenstates. However, what if the pointer states are not remotely energy eigenstates? Then, the pointer states themselves evolve in time nontrivially by more than just a phase rotation.


title: Identifying unrealistic traits of this exoplanet. There are a few obvious ones, but I cant find them all. Help!

text: I need to find the inaccuracies of this computer generated picture, the picture shows a non existent exoplanet. I need to identify the unrealistic features of the planet and its surroundings and write an essay on some of them. The image is located here: http://i.stack.imgur.com/zXrPy.jpg Could you help point out some of these innacuracies?


title: III-V semiconductor compounds - band gap approximations

text: I'm looking for the most common and accurate approximation functions for III-V semiconductor compounds. So far, I found two (InGaAs as the sample compound):   1. The simplest one: $E(Ga_{1-x}In_xAs)=(1-x)E_{GaAs}+x \cdot E_{InAs}$   2. Binomial: $E(Ga_{1-x}In_xAs)=(1-x)E_{GaAs}+x \cdot E_{InAs} - b \cdot x \cdot (1-x)$ For InGaAs, b=1.44 Are there more? I mean the methods for which the parameters can be found in articles, not measured by myself. When using the first one is sufficient? Do the scientists bother to calculate next corrections? Are they useful?


title: Projectile motion without air resistance

text: Does the mass of projectile affect its trajectory when it is projected in no air resistance environment and why?


title: Contact resistance copper-silver

text: I need to determine the contact resistance of a copper silver interface. The copper wire was soldered to the substrate using an IR-Laser. I was wondering if I can treat the entire system as a series of three resistors (wire, interface, substrate), so I can measure the resistance between wire and substrate using four terminal sensing and then subtract the resistance of the appropriate lengths of wire and substrate alone and be left with the contact resistance.


title: Is there a general H-theorem?

text: In statistical mechanics, Boltzmann showed that for dilute gases the H-function increases. I remember from a lecture that there is no general H-theorem, e.g. for non-dilute gases or in the quantum case but there seem to be also claims to the contrary. So what is the status of the (generalised) H-theorem?


title: Role of physics in the zeta function $\zeta$ and the Riemann hypothesis

text: Hilbert and Polya suggested a physical way to verify the Riemann hypotesis about $\zeta(x)$. If the Riemann hypotesis is true, we can state all eigenvalues of physical problems are real. What is the connection between the eigenvalues and the $\zeta$ function?


title: Recommendations regarding high-energy astrophysical objects (AGNs, jets, etc.)

text: I know basic astronomy and I know a few good textbooks for general astrophysics (eg. "Introduction to Astrophysics" by Carroll and Ostlie). I also have a strong background in theoretical physics and math for that matter. However I need to quickly catch-up with up-to-date models of blazars, accretion discs and jets for summer work. Do you have any recommendations for someone like me?


title: Why do I have spin splitting at 5 and 7 at the quantum hall effect?

text: I just learned something about the quantum hall effect, and was wondering about the spin splitting at a filling factor of 5 and 7, i.e. I have nearly equal sized plateaus for the filling factor of 2, 3 and 4, but I have only a small plateau at 5, and no plateau at 7. I asked my teacher, but he could not give me an explanation for this, he only could tell me that is has something to do with spin splitting. So, why do I get these "small" plateaus, and why is there a spin splitting?


title: regarding vertex function and proton scattering

text: I am currently going through electromagnetic form factor. I came across the fact that since the proton is not an elementary particle its scattering(elastic) with electron can be modeled using general general electromagnetic form factor of form $ \Gamma_{\mu} = \gamma_{\mu}F_1(q^2) + i\sigma_{\mu\lambda}q^{\lambda}F_2(q^2)\\\ $ where we get scattering amplitude and cross section in terms of $ F_1, F_2 $. So there are two questions   1. Is this the general procedure actually followed while present day experiment for calculating the amplitude or is there another (better) method?   2. Can I do the same for scattering of electron with pions (which are spin 0) using corresponding general vertex function(which i think would have only 1 form factor ,i suppose)?


title: Explaining lightyear to non technical people

text: I need to explain the concept of a light-year to a non technical audience. Actually a presentation about planets and galaxies. It is quite difficult (for them) to comprehend the speed of light itself ,leave alone the distance it travels in one year. Has anyone had to do this or can someone please give me a few ideas of how we can describe this ? Or is there another way to describe sizes of galaxies (e.g. some galaxies are 15 lightyears in diameter) and the huge distances between them in some easy to understand way. Thanks Kevin


title: At what expansion rate (H) would virtual particles be ripped apart into real particles, and what might be the density (temperature) of such an event?

text: Is it even possible for a virtual particle-antiparticle pair to be torn apart by cosmological expansion? Virtual particle-antiparticle pairs are ripped apart near black hole event horizons, creating Hawking Radiation, but can this ever be reproduced by the expansion of space due to a cosmological constant? And if so, at what rate of expansion would this occur? Would the rate have to equal c?


title: Why doesn't my house get misty?

text: When there's dense mist/fog outside and I open a window, why doesn't the inside of my house fill with mist?


title: How often can virtual particle/antiparticle pairs form real particles in a space expanding sufficiently fast to do this?

text: And if the rate of expansion of the universe becomes sufficient for virtual particles to be ripped apart into real particles, what effect would the mass of these particles have on the rate of expansion of space? Would it slow the rate down sufficiently to stop the creation of even more particles?


title: Costant volume gas thermometer

text: I have two constant volume gas thermometers, one with an ideal gas $pv=RT$ and the other following the Van der Waals equation $(p+\frac{a}{v^2})(v-b)=RT$. They are calibrated using the freezing point and the boiling point of water. Will they show the same temperatures?


title: Understanding the diagrams of electromagnetic waves

text: I'm having trouble understanding the diagrams of elctromagnetic waves. I have no problem with any concept in classical mechanics, and I think this can be answered without any relativity (which I don't know yet). I hope for an answer which is as intuitive as possible but any answer will be good. So in the common diagram of an electromagnetic wave: ![Diagram of EM wave](http://i.stack.imgur.com/x2fQa.png) What exactly do the vectors represent? The wave is propagating though an eletromagnetic field. Are the lines just the field created by a particle? We learned in physics that a charged particle creates a field in all of space, Is this a picture of changes in the field when it moves? And if so, how does it move? does it move up and down with the amplitude of this wave? Lastly, It's not clear to me why the E-field part is not in the direction of the motion of the wave, because usually an electric field is depicted as so: ![Electric field of a point charge](http://i.stack.imgur.com/R4nit.png) i.e it is in a direction "outwards" from the source of the charge. This is really running through my mind for some time, so thanx for reading this!


title: Can ship/boat propellers be placed, with adequate protection, alongside the fuselage instead of at the back?

text: On small private aircraft the engine is placed at the front of the fuselage, or on the wings E.g. Stationair, Otter On combat aircraft the engine/s is placed at the end of the fuselage E.g. Raptor, Typhoon On larger aircraft constructed to carry cargo/passengers the engines are placed on the wings E.g. DC3, A380 The positioning probably has to do with the amount of load to be lifted into the air, and manouverability desired... which seems sensible. Yet most water-going craft (boats, power-boats, merchantmen, naval craft) have their propellers/push-pull placed at the back of the fuselage. What is the advantage in placing the driving component for boats in this position in addition to protecting them against damage? Can the propellers on a boat, with adequate protection say- a tubular enclosure, placed alongside the fuselage not drive the watercraft with equal efficiency and power?


title: Way to measure wavelength of infrared radiation?

text: I am wondering if there is a device for measuring wavelengths of things. As semiconductors emit infrared radiation and I would like to know what is the wavelength it is so I can check to see if its going to be interfering with my project.   Thanks in Advance,   Dean


title: Forces: Worth worrying anything?

text: I am a general physics student, I had a question in my text-book and according to it two students having gravitational attraction between them = ($6.67\cdot10^-8\ \mathrm{Nm}^2/\mathrm{kg}^2$) is not worth worrying about. My question is Why? How much force between two objects is worth anything?


title: Is there a simple way to express the 2ⁿ+1 mutually unbiased bases for n qubits?

text: The title says it. An explanation for only 2 qubits would already be interesting, since I already have difficulties to find the 5 MUBs in this simple case.


title: Distributions (e.g., Dirac Delta): confused and unhappy

text: I am sorry that the following set of questions is very fuzzy and ill informed. I am a trained mathematician and now studying an undergraduate theoretical physics course. We use distributions. I have no clue of the How and Why, which makes me unhappy. So far I have some tiny idea about the physical intuition; and I have read the definition (and some properties) in http://en.wikipedia.org/wiki/Distribution_(mathematics) . ## Very fuzzy questions Sorry for the vagueness. If you do not want to be bothered but would kindly be willing to answer more concrete questions please jump to the next section.   1. Distributions make most sense to me in the following mindset: We have a situation A too complicated to calculate, we approximate it as B using step functions or delta distributions or similar stuff, which we can solve. Then we somehow claim that this solution (e.g., equations of motion) of B is close to the solution of the original problem A. **Question:** Is there any good argument for this claim?    2. Continuing the previous question: My (very poor) physical intuition would rather be: a delta distribution is the limit of stuff which has integral 1 and smaller and smaller support. The derivatives have no role in this intuition, which seems incompatible with even the most basic mathematical contents of distributions: The topology of the test function space uses (higher order) derivatives. **Question:** Is the simple intuition just nonsense? Is there a better working intuition?    3. Specific rant: It makes me particularly uneasy that some QM texts (cf.\, for instance, the introduction of Cohen-Tannoudji et al's) often use as an argument in a proof that wave functions have to be continuous, bizarrely arguing that non-continuous things make no physical sense because of measurement precision(!), while in the same proof happily using non-continuous potentials, distributions (and, of course, ignore the fact that the basic operators are non-continuous). **Question:** Is there any valid point in Cohen-Tannoudji et al's argument (that wave functions have to be continuous, even when appearing in solution for artificial problems that where constructed using distributions)? Which one?    4. I am completely lost about which calculus concepts/constructions/arguments are still OK with distributions and which ones are not. Well, obviously you can differentiate, and you can generally not multiply. But this leaves open the vast area of vector calculus, where it is not at all clear to me what is OK and what is not. I see two ways to rectify this: Either study mathematical physics for 5 years and then arrive at a very complicated mathematical understanding of simple stuff that physicists already knew anyway; or just continue to stumble through the horrors of distributions, without a clue, and somehow get used to it and learn simply by example what you can do and what not. Both sounds depressing. **Question:** Is there any better way to learn about the practical use of distributions in a consistent way, including some mathematical justification? ## Slightly less fuzzy questions   1. (Classical) functions that are not locally integrable, such as $\frac{1}{x}$, can not be interpreted as distributions. Is that correct?    2. In particular, the formula $\Delta\frac{f(r)}r=-4 \pi f(0) \delta^{(3)}(\vec x)+\frac{f''(r)}r$ does not seem to make much sense if $\frac{f''(r)}{r}$ is not integrable?   3. Speaking of which: $\Delta\frac{1}r=-4 \pi \delta^{(3)}(\vec x)$. What does this even mean? (It seems that $\frac{1}r$ is not a distribution, how can I differentiate it?) And, once it is clarified what it means: How is it proven? Thank you for your patience.


title: Is this $W_{r} = \frac{1}{2}kx^2 $ procedure correct

text: I have a $0.40 Kg$ of mass that has $v= 0.5 m/s$, and then crashes with a spring with constant $k = 750N/m$ Whats the distance that the spring was compressed? I was using the equation $W_{r} = \frac{1}{2}kx^2 $ so $\frac{1}{2}(0.4)(0.5*0.5) = \frac{1}{2}(750)(x^2)$ so $x = 0.011 m$ Is this correct? what is the solution?


title: Suppose that the position of some object is goiven by the expression: x = 6.8t + 9.0t^2. Determine the object's acceleration

text: x is in meters t is in seconds Answer = 18 m/s/s How do I solve this problem? Thank you for your time.


title: deriving a Lorentz transfomation for velocity vector components

text: If $S'$ and $S$ are two different inertial reference frames and $S$ moves along the $x$ axis of $S$ in a standard configuration, then the Lorentz transformation will be: $$x'=\gamma(v)[x-\beta ct]$$ $$y'= y$$ $$z'= z$$ $$ct'=\gamma(v)[ct-\beta x]$$ Where $\beta=\frac{v}{c}$. But deriving an expression for the velocity from here is a little tricky. Say examining the infinitesimal form, firstly at the $x$ direction: $$dx' = \gamma(v) [dx - vdt]$$ $$cdt = \gamma(v) [cdt - \beta dx]=\gamma(v) [1 - \beta u_x]cdt$$ Then combining should yield the result $$\frac{dx'}{dt'}=\frac{u_x-v}{1-\frac{u_xv}{c^2}}=u'_{x'}$$ But I am getting something confused because I am at $$\frac{dx'}{dt'}=\frac{[dx - vdt]}{[1 - \beta u_x]cdt}=\frac{[u_x - v]}{[1 - \beta u_x]c}$$ and wondering what happens to the $c$ that is kicking about on the denominator.


title: What is the temperature evolution of the conductance of a quantum chaotic system?

text: I read this really nice article by Abanin and Levitov: http://arxiv.org/pdf/0704.3608.pdf They argued that the mixing of the quantum edge channel at the vicinity of a PN junction is described by the physics of a quantum chaotic system. I'm not very familiar with this physics and I was wondering if anybody knows how the conductance of such a system evolve with a temperature. I looked through Internet but I found only shot noise experiments and not low frequency conductance measurement (or prediction).


title: What time scale is used by the JPL HORIZONS system?

text: I'm confused by the ust of the term "UT" in the description of time scales used by the JPL HORIZONS system. Their manual states that > UT is Universal Time This can mean one of two non-uniform time-scales based > on the rotation of the Earth. For this program, prior to 1962, UT means UT1. > After 1962, UT means UTC or "Coordinated Universal Time". and the key attached to the tool's output says > Prior to 1962, times are UT1. Dates thereafter are UTC. My understanding is that UTC has leap seconds, so that there should be an extra second at the end of a day on which a leap second was added, but the intervals reported by HORIZONS lacks these, and look more like UT1:                2012-Jun-30 23:59:58.000 2456109.499976852       2012-Jun-30 23:59:58.667 2456109.499984568       2012-Jun-30 23:59:59.333 2456109.499992284       2012-Jul-01 00:00:00.000 2456109.500000000      2012-Jul-01 00:00:00.667 2456109.500007716       2012-Jul-01 00:00:01.333 2456109.500015432       2012-Jul-01 00:00:02.000 2456109.500023148      Even more confusingly, the data reported do in fact behave as if the times are UTC. For example the reported azimuth of Pluto at Greenwich for the times above changes by 0.0028° for each of the intervals but the third, where it changes by 0.0069°, a factor of 2.5 times the change in each of the other intervals, which is exactly what would be expected ((1 + 2/3)/(2/3)) if there were an extra second between 2012-Jun-30 23:59:59.333 and 2012-Jul-01 00:00:00.000. This, despite the fact that the difference in JD over that interval is the same as each of the other intervals, meaning that one can't expect differences between JD that span any leap seconds to line up with changes in data! If the times and data are UTC, how can the differences between JD be uniform? If they're UT1 how can the data "jump" at the leap second? * * * Note also that the form for entering queries describes "Delta T" as CC-UT ![enter image description here](http://i.stack.imgur.com/7pqj8.png) which means that if "UT" can mean UTC, this means that after 1962, $\Delta T$ is a discontinuous function, but my understanding is that $\Delta T$ is that a continuous function, TT-UT, where UT is _not_ UTC (see note 1 here).


title: Why do some satellites fall to Earth?

text: In another question How does Newtonian mechanics explain why orbiting objects do not fall to the object they are orbiting?, one can read an affirmative answer. They how do you explain satellites falling to Earth? (Here, falling means colliding with the Earth surface or burning out before reaching the surface. For example, fragments of Sky Lab fell on Australia in 1979.)


title: What does "coherent wave function of a macroscopic body" mean?

text: What is meant by the "coherent wave function of a macroscopic body"? I found this phrase in a paper on QM, but am unfamiliar with the terminology.


title: Why do metal surfaces reflect thermal signature?

text: I recently borrowed a thermal camera from a friend and I tried to observe my palm print over a reflective metallic plate. When I looked at it through the camera, it reflected my thermal signature too. Why this happens and how to measure the heat signature for that material?


title: Average of $\sin^2 \omega t$, $\cos^2 \omega t$ for long times

text: I don't understand how the averages mentioned in excerpt below work out. The question is regarding calculating the power spectrum of an oscillating classical dipole. IS averaging over long periods, for example, For $\sin^2 \omega_o t$ given by $$<\sin^2 \omega_o t> = \frac{\int t \sin^2 \omega_o t}{\int \sin^2 \omega_o t} =?? \frac{1}{2}$$ Also, how is the time important in doing this average. What I mean is, how is it justified to replace the function with its average value for times longer than its time period, how does this make sense physically? Thanks ![enter image description here](http://i.stack.imgur.com/kbBqN.jpg)


title: From which side should I solder electrical feedthroughs into a vacuum flange?

text: I work on an experiment that requires electrical connections to a vacuum vessel, which is submerged in liquid helium (LHe). For sending the signals into the vessel, we use a feedthrough flange. I am currently redesigning this flange, but there is one important point about the existing design that I do not understand. **The existing design** of the feedthrough flange is shown in the sketch below. The feedthroughs (single pin, weldable type feedthroughs made by Ceramtec) are not shown. They are installed into the holes that are highlighted in DETAIL C. The flange seperates the 1E-11 mbar extremely high vacuum (XHV) region from the outside, which is at ambient pressure. During the important stages of the experiment, the vacuum vessel is submerged in LHe to cool it down to 4 K, which improves the vacuum to 1E-17 mbar and better. The thermal cycling is very demanding on the feedthroughs. (This is one of several reasons why commercial feedthrough flanges don't work for our purposes.) ![Sketch of existing feedthrough design](http://i.stack.imgur.com/ZZrlB.png) **The problem** is: Does this design create virtual leaks? For reasons which might best be investigated in another question, we are soldering (not welding) the feedthroughs into the flange. When the feedthroughs are inserted into the holes, they sit quite snugly in the medium diameter hole. But because the solder is applied on the ambient-pressure side (marked as "LHe" in the diagram below), I fear that we are creating hard-to- pump pockets in the snugly-fitting "problematic" region. ![Soldering of feedthroughs into the existing design](http://i.stack.imgur.com/emIJl.png) The very first flange that was produced had the feedthroughs installed by silver-soldering them in a vacuum induction furnace at 800°C. This destroyed some of the feedthroughs, because they are not rated for 800°C. The destroyed (leaky!) feedthroughs were sealed using indium, but ultimately thermal cycling led to the leaks reopening, and the flange had to be discarded. However, for the 1-2 years that it worked, we had really great vacuum conditions below 1E-17mbar. The current flange, which has the feedthrough soft-soldered (under standard atmospheric conditions), has no leaks to the outside. But judging from the limited lifetime of C$^{4+}$ ions, the best vacuum we get is only 1E-15mbar - 1E-16mbar. After eliminating many other possible culprits, virtual leaks from the hard-to-pump "problematic" region are the most likely explanation. **The possible workaround** would be to reverse the direction of the holes in the design (smallest diameter on LHe, biggest on XHV side) and to apply the soft-solder on the XHV side. But I noticed that similiar experiments use the same design as we did, i.e. they apply the solder on the LHe side. The few people that I talked to about this could not recall why. For welding, the rule of thumb is to always weld on the vacuum side. Is there any such rule for soldering?


What does superposition mean in quantum mechanics? When I say $A+B=C$ (forces). I can mean push something with force $A$ + force $B$ together, and that is same as I push it with force $C$. But when I say wavefunction $A$ + $B$ is also a solution of Schrodinger equation, what do I mean? The physics between them obviously is not same. Is it just something pure mathematical?


title: Can electromagnetic fields be used to deconstruct and reconstruct atoms?

text: I was thinking one day and came up with a theory after reading about how scientists were studying anti-matter by using electro magnetic fields to separate matter from the anti-matter they made. It got me thinking would it be possible to use very powerful electromagnetic fields to break down the atomic structure of objects or build things in this way? Is this atomic reconstruction with electromagnetic fields theoretically possible? That is, is it theoretically possible to use electromagnetic fields generated by a machine to separate the parts of an atom thereby deconstructing an object on the atomic/subatomic level? I'm not asking about breaking molecular bonds but rather actual atoms apart. If it's possible to break atoms apart with electromagnetic fields, is it also possible to use a similar process to assemble them?


title: Schrödinger function: Separable wave function with even potential function of x

text: I have done the Problem 2.1 in Griffiths' quantum mechanics, and it seems not making sense to me. What if the wave function isn't symmetric at all? Then obviously the proof doesn't work. The solution confuses me. > If $V(x)=V(-x)$ then the "position" wave function can always be taken to be > either even or odd.


title: Is there any law that prevents an object with mass to become massless?

text: I got into a discussion with my physics teacher about the speed of light and I asked > _What if an object with mass was to lose mass as it gained speed-- would > that allow for an object to eventually reach the speed of light or surpass > it if possible through that thinking?_ My teacher didn't really have an answer to that and I was wondering if there was any law of science that prevented an object with mass to become mass-less. Because I know this may be simple minded in thinking but if an object with mass must have infinite energy to reach the speed of light and at that point will have infinite mass, what if an object was to reduce its mass until it had none? Would it then not need infinite energy and be able to move at or past the speed of light in theory?


title: Torque required to turn the inside of a drum (Honey extractor)

text: I need to mount a motor with a variable speed drive(VSD) onto a honey extractor but need to know how much torque I need to start the extractor to start turning. The diameter is 700mm and the max weight at this diameter will be 50kg. I believe a 1,1kW motor will do the job, but not sure if the configuration with the VSD will produce enough power for it to start turning automatically. Could somebody please help me in solving this challenge?


There is some confusion in the definition of Sommerfeld radiation conditions for an electromagnetic field, which are related to the asymptotic behaviour of the field for a distance $r \to \infty$ (from the origin of a spherical coordinates system) in order to assure the unicity of the field itself as a solution of the Maxwell equations. These are known also as Silver-Muller conditions and they may be presented as $$\displaystyle \lim_{r \to \infty} r|\mathbf{E}| < q_1$$ $$\displaystyle \lim_{r \to \infty} r|\mathbf{H}| < q_2$$ $$\displaystyle \lim_{r \to \infty} r(\mathbf{E} - \eta \mathbf{H} \times \mathbf{\hat{u}}_r) = 0$$ $$\displaystyle \lim_{r \to \infty} r \left( \mathbf{H} - \frac{\mathbf{\hat{u}}_r \times \mathbf{E}}{\eta} \right) = 0$$ where $\mathbf{\hat{u}}_r$ is the radial unit vector in a spherical coordinate system with center in the origin (where are the sources of the field) and $q_1, q_2$ are two arbitrary real constants. (The sources of the fields can be considered all "near" the origin, if their distances to the origin is finite, because now $r \to \infty$). In this form the first conditions state that the asymptotic behaviour of the fields (with any sources) is like $1 / r$ for $r \to \infty$. This is consistent with the field of an electrical (hertzian) dipole, whose _far field_ components are proportional to $1 / r$. But sometimes the conditions are presented like the following ones: $$\displaystyle \lim_{r \to \infty} r|\mathbf{E}| = 0$$ $$\displaystyle \lim_{r \to \infty} r|\mathbf{H}| = 0$$ Does it makes sense? It would not be compatible with the field of a hertzian dipole as before. However, if these latter conditions were the true ones, it would be simpler to prove the unicity of the solution of an electromagnetic field: if we considered an infinite spherical volume of radius $r \to \infty$ and its spherical boundary surface $S$, the Poynting vector would always be zero in all the points of this surface. This question deals with the unicity of the solution. So, which are the correct conditions? Those with $q_1, q_2$ or those with $0$? Thank you anyway!


title: What restricts the value of weak hypercharge from being 5/3?

text: The quarks and leptons chiral states have hypercharges of $0,\pm 1/3,\pm 2/3, \pm 3/3, \pm 4/3, \pm 6/3$. The value of $\pm 5/3$ is prominently missing. Is there a theoretical principle which picks out these values? In looking for papers on arXiv with hypercharge 5/3, I've found only a handful of papers. One is a preprint from December 2010 (See page 16 "KK (Kaluza- Klein) towers") : Giuliano Panico, Mahmoud Safari, Marco Serone, (2010) _Simple and Realistic Composite Higgs Models in Flat Extra Dimensions_   http://arxiv.org/abs/1012.2875 And then they come up as a vector diquark here and in a few similar papers: Journal of High Energy Physics 2002, 024, (2002), Engin Arik, Serkant A. Çetin, Orhan Çakir, and Saleh Sultansoy, _A Search for Vector Diquarks at the CERN LHC_   http://arxiv.org/abs/hep-ph/0109011v3 So is there a theoretical principle that picks out which weak hypercharge values might be observed in nature?


title: Why is the Poynting Vector Symmetric in E and H?

text: Why is the Poynting Vector symmetric in E and H? I always thought that E and B were the analogous fields, so I would think that any equation using magnetic and electric fields should be symmetric in E/B or D/H. I've seen the derivation, but I have yet to find the point where my want for symmetry is being broken.


title: Visibility of moon-based laser from Earth

text: If someone (or some robot) on the moon were to point a laser at the Earth, how many watts would the laser need, to be easily seen with the un-aided eye from Earth? Obviously this depends on a number of factors. Assume the beam is made divergent enough to cover latitudes 60S to 60N, wavelength 532nm, and the beam originates from a fully lit area of the moon, and the observing is done in full darkness. I can work out watts/meter-square from the laser, but don't know how to work out the watts/meter-square from the moon, and don't have a clue about how the eye would perceive the contrast.


title: Time evolution in quantum mechanics

text: We know that an operator A in quantum mechanics has time evolution given by Heisenberg equation: $$ \frac{i}{\hbar}[H,A]+\frac{\partial A}{\partial t}=\frac{d A}{d t} $$ Can we derive from this that $$ A(t)=e^{\frac{i}{\hbar}Ht}A(0)e^{-\frac{i}{\hbar}Ht} \qquad ? $$ L.M.: I added $i/\hbar$ in front of $[H,A]$.


title: Having hard time with Angular Momentum and Parallel axis theorem

text: I'm having hard time with Angular Momentum and Parallel axis theorem. Please explain these 2 formulas. Is one formula derived from the other? $$J = J_{cm} + R_{cm} \times P_{cm}$$ $$I = I_{cm} + MD^2$$ The first formula is for Angular Momentum and the second one is for the mass moment of inertia. However, I think that the first formula only applies in a specific case. Is this true?


title: Distinguishing identical particles

text: I've been going through Shankar's Principles of Quantum Mechanics. In the section of the system of identical particles, he uses an example of billiards to illustrate the difference between identical particles in classical vs. quantum mechanics. He argues that in classical mechanics, we can track the history of a particle (a billiard ball) to distinguish it from another particle with no intrinsic differences. In quantum mechanics, however, he argues since continual observation is not possible, we can't use the same method to distinguish identical particles. A potential counter-example I thought was...suppose we have two non- interacting particles in a same square well. And at the end of some measurement, we find that one particle 1 is in a stationary state $\psi_1$, and particle 2 in $\psi_2$. We measure the system again after some time t, then we know whichever particle that's in $\psi_1$ must be particle 1 from the previous measurement. And the same goes for particle 2. Thus we can distinguish the two "identical" particles. What conceptual mistakes am I making here?


title: The Heisenberg uncertainty principle: Interpreting $\Delta p$, $\Delta t$, etc

text: (1) I have a textbook question that states the following: An electron has a speed of 500 m/s with an accuracy of 0.004%. Calculate the certainty with which we can locate the position of the electron. The solution starts with $$\frac{\Delta p}{p}=\frac{0.004}{100}$$ I don't understand how the question is being interpreted to give the above expression. (2) The very next question says: The average lifetime of an excited atomic state is $10^{-9}$s. If the spectral line associated with the decay of this state is 6000 Angstrom, estimate the width of the line. The solution begins with $\Delta t = 10^{-9}$s. Again, I don't understand how this is arrived at. I'd expect it to be $t=10^{-9}$s. * * * Can somebody give me an intuitive understanding of uncertainty (perhaps in words) that I can apply to these two problems? I know the statistical definition, but I haven't found it very helpful in this context.


title: Wilsonian vs 1PI

text: As a follow up to Difference between 1PI effective action and Wilsonian effective action, where can I find pedagogical material that highlights the similarities and differences between the 1PI and Wilsonian effective action? Are there any good articles that that have a good exposition on implications to non-renormalization theorems in SUSY and to anomalies/instantons in Yang- Mills theories, as well as implications to gauge-invariance of renormalization group equations for the parameters in the two effective actions?


title: Range Finder Question - Optical Filter For An Apd

text: I am working in a range finder project. I have encountered a problem with an Avalanche Photodiode. I am trying to use a pulsed laser on 980 nm(infrared) but I receive a lot of noise from the APD. I want to ask you if in the APD must be totally dark and no other light must enter in the APD box? Do I need to use a infrared optic filter? What kind of optical filter do I need to use? I use a lens with 10 cm diameter . Thank you, I am not physicist, I am programmer and electronist


title: Can anyons emerge from momentum-space other than spatial dimensions?

text: So far in condensed matter physics, I only know anyons(abelian or nonabelian) can emerge as quasiparticles in 2D _real-space_. But is there any possibility to construct anyons in _momentum-space_ ? And what about the braiding, fusion rules in _momentum-space_ ? I mean do anyons always live in _real-space_ rather than in _momentum-space_ ? Maybe this is a trivial question, thank you very much.


title: Conservation of energy in a non-linear oscillator

text: I have a homework question about a "non-linear oscillator". I actually have an answer to this question, but the answer I get is stronger than what is needed according to the question. The question says ". . . the potential energy of a non-linear oscillator is given by $U(x) = \frac{1}{2}kx^2 - \frac{1}{3} \alpha x^3$. Using conservation of energy, show that the motion is oscillatory if the initial position $x_0$ satisfies $0 < x_0 < \frac{k}{\alpha}$ and the initial velocity satisfies $v_0 < \frac{k}{\alpha}\sqrt{\frac{k}{m}}$". If the motion is oscillatory, then the velocity will be zero at exactly two different positions. So the potential energy must be confined to the region where it reaches its local max/min value twice. In other words, the initial position $x_0$ must lie between the critical points of $U(x)$. Setting $dU/dx = 0$, I get that the critical points are $x = 0$ and $x = \frac{k}{\alpha}$, so that the initial position must satisfy $0 < x_0 < \frac{k}{\alpha}$ as required. For the initial velocity, I reasoned that the initial kinetic energy must be less than the local max of the potential energy. The local max occurs at $x = \frac{k}{\alpha}$ and is equal to $U(\frac{k}{\alpha}) = \frac{1}{6}\frac{k^3}{\alpha^2}$. So the initial kinetic energy cannot exceed this value; i.e. $$\frac{1}{2}mv_0^2 < \frac{1}{6}\frac{k^3}{\alpha^2}.$$ Rearranging, this gives $$v_0 < \frac{1}{\sqrt{3}}\frac{k}{\alpha}\sqrt{\frac{k}{m}}.$$ This condition is stronger than the one in the question: in other words, if my condition holds, then so does the one in the question. So in that sense I technically have answered the question, but I'm unsure if my reasoning is correct. Is what I have done correct, or should I actually be getting the weaker inequality given in the question?


title: What is the energy of interaction between two infinite charged wires?

text: This is related to my previous question. I assume that the two wires have the same charge density with the same sign ($\lambda_1 = \lambda_2 = \lambda$) If I want to take the same approach, the potential is still the same, $V = k\lambda \log(1/r)$. The energy is, I think, the integral over the (second) wire, since this is the direction where I add charges. Since the wires are paralleled, $r$ is constant in the integral $U = \int_{-\infty}^{\infty} l\lambda^2 \log(1/r) dx$ Which explodes. I actually expect this, since I keep adding charges at a finite distance from the other wire. On the other hand though, I think there are well defined solutions for the energy of infinite area capacitors which are worse. Or is it only the fields?


title: Appearing To Reverse Object's Rotation

text: Can it be done, and if so, how does one you explain **mathematically** the ability to cause a rotating object to appear to change the direction of rotation? I believe it has something to do with angular momentum. The thought experiment: I have a satellite rotating around the earth in geosynchronous orbit. If the satellite approaches the planet will the earth appear to change its direction of rotation from the perspective of the satellite? At what point in its distance or angular velocity? Second thought experiment: In a similar illusion to the tires of a car in a movie, at what frame rate would a camera need to be filming the earth from a static position in order to have the earth appear to have a rotation from east to west?


title: Average speed of seismic waves towards the center of Earth

text: I'm looking at an approximation of the average speed of seismic wave _towards_ the center of Earth.   The horizontal path of the waves that affects us directly is well documented, but there is not much about the vertical propagation of such waves. Of course that speed depends upon many factors like   * depth of the earthquake hypocenter    * magnitude of the earthquake   * Earth strata at the hypocenter   * specific topology of the many layers up to the center of Earth at this location and this is a complex area, but a rough approximation would be appreciated.   Something like               (speed, validSpeedForThatKilometers) = speedAtDepth(hypoDepth,mag,desiredDepth)      or even better a more complex function that would directly give the rough time to reach depth desiredDepth based on some parameters               time = getTimeToReachDepth(hypoDepth, mag, desiredDepth)


title: Measuring nucleons using electron beams

text: sorry if the question is too elementary. From: The Britannica Guide to Particle Physics: > The sizes of atoms, nuclei, and nucleons are measured by firing a beam of > electrons at an appropriate target. The higher the energy of the electrons, > the farther they penetrate before being deflected by the electric charges > within the atom. For example, a beam with an energy of a few hundred > electron volts (eV) scatters from the electrons in a target atom. The way in > which the beam is scattered (electron scattering) can then be studied to > determine the general distribution of the atomic electrons. > At energies of a few hundred megaelectron volts (MeV; 106 eV), electrons in > the beam are little affected by atomic electrons. Instead, they penetrate > the atom and are scattered by the positive nucleus. Therefore, if such a > beam is fired at liquid hydrogen, whose atoms contain only single protons in > their nuclei, the pattern of scattered electrons reveals the size of the > proton. At energies greater than a gigaelectron volt (GeV; 109 eV), the > electrons penetrate within the protons and neutrons, and their scattering > patterns reveal an inner structure. Thus, protons and neutrons are no more > indivisible than atoms are. Indeed, they contain still smaller particles, > which are called quarks. I'm confused by this. I understand that the increasing velocity of the electron particles in the beam can overcome repulsive force of the electron cloud in an atom. Thus detecting size of the atom and even particular electrons. But what happens to beam particles in MeV range? At higher velocities, when they do reach nucleus, doesn't the positive charge then attract beam particles? How does it repel them? Is it that they have so much speed that they on near miss of a proton deflect or is something else happening here? What happens on GeV range? Do electron beam particles pass through proton to allow detection of quarks? Or is there happening something completely differentTM, like total annihilation of collided particles and recreation of particles from energy. Thanks for your time...


title: Will a relativistic rocket be destroyed by incident photons?

text: I have read, that as a rocket approaches light speed, objects in front of it become blue shifted and also intensity of light increases. Does this mean that at some point any rocket will be destroyed, just because the blue-shift will cause impacting photons to become gamma rays of arbitrary high energy - so high in fact that no material could withstand it?


title: What is the best path for a given initial and final state?

text: I am trying to calculate an efficient acceleration curve given starting and final positions and velocities. I'm assuming no friction, and that the acceleration can be applied in any direction at any time. Given:   * $p_0$ = starting position    * $v_0$ = starting velocity    * $p_f$ = final position    * $v_f$ = final velocity    * $T$= total time I want to find a nice $a(t)$ function that will produce final conditions. So far I have the following solution that works, but produces an incredibly inefficient $a(t)$ curve: First I calculate the constant acceleration required to get from $v_{0}$ to $v_{f}$ : $$ a_v = \cfrac{v_f - v_{0}}{T} $$ Then I calculate the change in position this acceleration will create over $T$ : $$ p_v = \cfrac{1}{2} a_v T^2 $$ Next I calculate the average velocity required to get from $p_{0}$ to $p_f$ and to counteract $p_v$ : $$ v_p = \cfrac{p_f - (v_{0} + p_f ) }{ T } $$ Next I calculate the acceleration needed to produce this average velocity over the total time: $$ a_p= \cfrac{2 v_p}{ T} $$ Finally, I add twice that acceleration to the first half of my acceleration function, and subtract twice that acceleration from the second half. This produces the net position change that I want, but has a net $0$ velocity/acceleration change so $v_f$ stays correct: $$ a(t) = \begin{cases} a_v + 2 a_p & t \leq \frac T 2 \\\ a_v - 2 a_p & t > \frac T 2 \end{cases} $$ While this solution provides a result, it can cause the simulated objects I'm working with to move backward before moving toward their final goal, along with other weird behavior. I think the ideal solution would minimize total acceleration applied over time (and thus force, since the mass of the object will stay constant over this time). I know that the constraints on this problem are that the integral of $a(t)$ must equal $v_f - v_{0} $, and that the integral of that integral must equal $p_f - p_0$ . I just don't know how to setup the problem to solve for those constraints. I don't even really know what I should Google for to try and solve this problem. Any help would be greatly appreciated.


title: HEPA vs. water filter in vacuum cleaning

text: What is the difference between air being filtered with HEPA or water? Which one performs better within a non-allergic home environment? Does water filter have a meaning still when common vacuum cleaners usually have HEPA filters nowadays? I am asking because I want to buy a new vacuum cleaner and need to decide between traditional paper bag with HEPA filter and one with water filter (like Zelmer 829.0 SP Aquos or Zelmer 819.0 SP Aquario).


title: Would a high-explosive in a vacuum be less harmful?

text: Putting aside shrapnel effects, I believe that high-explosives cause damage by producing a shockwave. How do shockwaves work in space? I've managed to convince myself that a high-explosive shockwave would work "about the same" by producing a shell of high-speed gas that would arrive at the surface with pretty much the same amount of energy that you'd get in air. Is that right?