title: Watching something fall into a black hole from far away

text: I am observing (theoretically) an object falling into a black hole from a safe distance away. My understanding is that from far away it appears as if the body will asymptotically approach the event horizon, but I will never see it cross it. Although the object will flatten itself and encompass the entire event horizon its center of mass will slow down. I deduce that there is a radially repulsive force to counter act gravity from my point of view. Is there a different way to do $\sum F=m \ddot{r}$ where I do not have this fictitious force, and if not what do we call this force? This is equivalent to a centripetal force needed to keep something in orbit, although in this case it is the opposite. ## Update From the responses I see the free-fall EOM is $$\sum F=ma=\frac{GMm}{r^2}\frac{1}{\sqrt{1-\frac{2GM}{c^2r}}}$$ So the local gravitational acceleration is $$g = \frac{GM}{r^2}\frac{1}{\sqrt{1-\frac{2GM}{c^2r}}}$$ and any motion besides a free fall is $F_{ext} = m (\ddot{r}-g)$ or $$ \ddot{r} = \frac{r_S c^2}{2 r^\frac{3}{2} \sqrt{r-r_S}} $$ with $r_S = \frac{2 G M}{c^2}$. So how can this produce $\ddot{r} \approx 0$ near the event horizon?


title: Distance travelled in spaceship Newton vs Einstein

text: If you get in the canonical 1G windowless spaceship and accelerate for 5 years as determined by your trusty wristwatch, then decelerate for 5 years, then decide its time to see where you are would the Newton way of calculating your distance from earth work? Distance as predicted by Newton $= \frac12 at^2 = 1.22\times 10^{17} ~\mathrm{m}$ during acceleration and another $1.22\times 10^{17} ~\mathrm{m}$ during deceleration. So when you get out of the rocket, and look back at earth, its 25.8 light years away, according to Newton. Max velocity = a*t = 5.15 times the speed of light. Relativistic calculation: T = 5 years --> shows 82.7ly + 82.7ly which is 165 ly - way farther than Newton's calculation. I guess relativity is really different from Newtonian physics, and you can make measurements without another observer to conclude that something non- newtonian happened while on the ship. I guess I answered my own question here. But if I'm wrong, please chime in. I would think that most people (say those that went to first year physics) would assume that the relativistic calculation would show a shorter distance (c is a limiting speed). Some more investigation results in the thought that the time dilation and the gamma factor somehow 'cancel each other out'. But it turns out that relativity makes you go farther on the same tank of gas than Newton would say you need. Leaving this as a question in the extremely likely circumstance that I made an error.


title: Calculating Orbital Vectors in the Future

text: For the 2D space simulator that I am writing (please note, it is not at all homework), I require formulas that will give me the location and velocity of a spaceship, relative to the parent celestial body, at a specific time in the future. There is only one planetary mass that provides a gravitational attraction for the spaceship, and the spaceship's mass is negligible. From the initial $\vec{r}$ and $\vec{v}$ relative to the planet, I already know how to compute many things, such as:   * standard gravitation parameter $\mu = G M$   * eccentricity $e$   * specific angular momentum $h$   * semi-major axis $a = \frac{h^2}{\mu(1 - e^2)}$ (is this even correct?)   * longitude of periapsis $\varpi$   * eccentric anomoly $E$ from true anomaly $\theta$ (an angle the describes an offset from $\varpi$), and vice versa So using all these values, or possible more (or less), what formulas can I use to compute the **position and velocity in $t$ seconds**? I have already tried using the following formulas to compute the position in the future:   * mean anomaly $M(E) = E - e sin E$   * mean anomaly at periapsis $M_0 = M(E = \theta = 0)$   * mean anomaly at a certain time $M(t) = M_0 + t \sqrt{\frac{\mu}{a^3}}$ However, those formulas don't work for certain orbits (such as hyperbolic orbits, where $a < 0$). Also, I may have just programmed the formulas incorrectly, but using mean anomaly, my simulator does not correctly determine position in the future. So, I have already tried several approaches to computing position and velocity in the future, and they didn't work. What are the correct formulas? Thanks!


title: How can I explain this fallacy of conveying information faster than Light?

text: First statement of this question: In superluminal phase velocities, what is it that is traveling faster than light? says that > information cannot be transmitted at a velocity greater than speed of light Also in the comment to my recent question: Is parallel programming a need of future and worth investing time and money? it is said that: > FTL communication between the two ends of our processors is impossible. Now I have conceptual model of communication system as shown below: ![enter image description here](http://i.stack.imgur.com/9xowJ.jpg) In the upper model, a laser is being moved up and down, and is being detected by the photo-detectors A & B. If the laser spot is at A , A's output is 1 else 0, and similarly for B. In the lower model, a simple optical fiber based communication is being shown. In both the cases we are transmitting data (1001 & 0010) from two sources Green and Red. Now if we assume that the distance between laser and photo sensors A & B is very large, it can be proved that the spot (shown in red) can move at speed greater than light. Can somebody explain this fallacy? In my first case information is being conveyed at a speed which is more than the speed of light, and is thus faster way of transmitting information as compared to fiber shown in the lower diagram. How is this possible? **Why information is being conveyed at much faster rate in upper case?** Start from the case when the laser beam is in between the two detectors. Now let us transfer a 1 to A. So I need to move my hand up - let us say I do this at a speed of 1cm/s. Let us say with this velocity, in 1 second the spot reaches the detector A. So I have conveyed the information '1' in 1 second. And this comm took at a speed of spot which s greater that that of light. Now consider the case of usual optical comm. Assume that the distance is sufficiently large, so that light takes more than 1 second to reach the receiver. What is wrong in my calculations? **Also Even If I do not compare upper and lower case,** am I not proving that information is being conveyed at speed more than that of light. this is because the information is carried in spot that is capable of moving at a speed greater than C.


title: Quantum Thrusters and Warp Drives

text: Any reservations about the potential of this (given in the link below/title above)? Does it seem like a helpless attempt or something which might have the potential of developing into something real? http://news.discovery.com/space/quantum-thruster-warp-drive-physics-130823.htm


title: Is there a lens that would invert my vision?

text: Would I be able to invert my vision by mounting a particular lens in front of each eye? I am currently able to achieve this by mounting a right-angled triangular prism across both eyes. The specific rotation can be thought of as follows: ![enter image description here](http://i.stack.imgur.com/KXX41.png) The effect is that things in the "bottom" of my visual field appear at the "top" and "upsidedown". For example, if I stand and move my head to look down, I see my legs apparently "in front of me" and my feet pointing "towards me". The prism arrangement is heavy, uncomfortable (there is an edge with an acute angle against my forehead), and severely restricts my view (which can be fully occluded by an A3 sheet of cardboard held at arms length). This is a problem as the scientific value of this arrangement comes from being able to wear them for extended periods (e.g. a whole day, or 4 hours a day for a month). Is there a lens that would have essentially the same inversion effect, without all of the problems in the previous sentence? Suggested solutions don't have to be inexpensive.


title: Would an object hit the ground faster when it gets launched vertically upwards or downwards?

text: A while ago I had a discussion with someone about the speed of an object when it hits the ground. When does an object hit the ground faster:   * When you launch the object to the sky so it can fall down;   * Or when you launch the object to the ground so it doesn't have to deal with much air resistance. The attraction “The Booster” has an arm that has a constant speed (about 120 km/h) is about 80M high and undergoes full revolutions. ![enter image description here](http://i.stack.imgur.com/iAbtQ.png) In this situation the cart gets disattached at 90 degrees. ![enter image description here](http://i.stack.imgur.com/gLB1j.png) I think that the cart hits the ground with a higher speed when it's launched to the ground because of:   * The air resistance, when you launch it to the sky it has a longer path to travel, so it needs to travel through much more air.    * The cart has the same initial speed, when you travel a shorter path there will be less to slow the cart down;   * Nothing provides the cart with additional energy;   * I guess that the "final gravity" is the same.


title: Is it true that under water human body can sustain higher levels of acceleration?

text: In several sci-fy novels, I've read about humans being submerged in water (or water like substance) to allow for a higher acceleration. Now, I'm really curious. Is this true? Can you accelerate faster without sustaining any sort of harm if you're submerged? Is there any formula which would give me a relation between effects on human body of acceleration when not submerged vs effects when submerged in fluid with different levels of viscosity?


title: Poisson brackets and angular momentum

text: I'm trying to find $[M_i, M_j]$ Poisson brackets. $$\\{M_i, M_j\\}=\sum_l \left(\frac{\partial M_i}{\partial q_l}\frac{\partial M_j}{\partial p_l}-\frac{\partial M_i}{\partial p_l}\frac{\partial M_j}{\partial q_l}\right)$$ I know that: $$M_i=\epsilon _{ijk} q_j p_k$$ $$M_j=\epsilon _{jnm} q_n p_m$$ and so: $$[M_i, M_j]=\sum_l \left(\frac{\partial \epsilon _{ijk} q_j p_k}{\partial q_l}\frac{\partial \epsilon _{jnm} q_n p_m}{\partial p_l}-\frac{\partial \epsilon _{ijk} q_j p_k}{\partial p_l}\frac{\partial \epsilon _{jnm} q_n p_m}{\partial q_l}\right)$$ $$= \sum_l \epsilon _{ijk} p_k \delta_{jl} \cdot \epsilon_{jnm} q_n \delta_{ml}- \sum_l \epsilon_{ijk}q_j \delta_{kl} \cdot \epsilon_{jnm} p_m \delta_{nl}$$ Then I have thought that values that nullify deltas don't add any informations in the summations. And so, $m=l, j=l$ but so I obtain $m=j$. But if $m=l$, the second Levi-Civita symbol in the first summation is zero... And if I go on, I obtain $\\{M_i, M_j\\}=-p_iq_j$ instead of $\\{M_i, M_j\\}=q_ip_j-p_iq_j$ Where am I wrong? Could you give me some hints to continue?


title: Why is the colour of sunlight yellow?

text: I was going through the preliminary papers of other schools and found a question that I did not know. It was "Why sunlight appears yellow?". Can anyone answer it?


title: Shape of wall's deformation wave caused by baseball's impact

text: Clicking through this year's top sports pictures, I stumbled upon this one. I was wondering about the shape the baseball is leaving on the wall. ![diamond shaped pattern](http://i.stack.imgur.com/6rIoPm.jpg) What phenomenon causes this peculiar shape? Why is it not radially symmetric? My intuition also tells me that the shape should be the solution of some special sort of wave equation (that takes into account the wall's material etc.). But, it looks like something substantially different...


title: AQFT and the Standard Model

text: The German physicist Rudolf Haag presented a new approach to QFT that centralizes the role of an algebra of observables in his book "Local Quantum Physics". The mathematical objects known as operator algebras (C* and W*) seem to have a lot of importance from this perspective. I have heard opinions for and against algebraic quantum field theory. A common argument for AQFT that I hear often is that it places QFT in a formal mathematical universe, but I don't really know what that even means. There are other approaches to quantum mechanics (using techniques from microlocal analysis, for example) that emphasize rigor, but do not necessarily deal with an algebra of observables. I have heard more opinions rather than persuasive arguments against AQFT. The one argument that I am aware of is that AQFT does not deal very well with the Standard Model, which is one of the big empirical success of particle physics and plays a central role in mainstream (Lagrangian) Quantum Field Theory. I am wondering how AQFT's treatment of the Standard Model (among other things) creates a problem for physicists.


title: Dispersion of ferromagnetic ($E\propto k^2$) and antiferromagnetic ($E\propto k$) spin wave

text: The dispersion of ferromagnetic spin wave at low energy is $E\propto k^2$, while $E\propto k$ for antiferromagnetic case. Is there a simple/physical argument (such as symmetry) for these results? Moreover, in a generic system with spontaneous continuous symmetry breaking, what determines the value of $n$ in the low energy dispersion $E\propto k^n$ of the Goldstone mode? In the Wikipedia, the last paragraph of theory of spin wave states that the difference between the dispersion relation of phonon ($E\propto k$) and ferromagnetic magnon ($E\propto k^2$) results from the time reversal symmetry breaking of the ferromagnetic state. I'm confused about it since antiferromagnetic state also breaks time reversal symmetry but possesses dispersion $E\propto k$ as phonon. Can someone explain this statement further please?


title: What is Transverse Energy?

text: What is transverse energy? Why we use transverse total energy instead of energy and transverse momentum in place of Total momentum in the particle detectors?


title: Neutron decay and particles

text: ![enter image description here](http://i.stack.imgur.com/JHkOz.png) On this picture you can see that this $d$ quark turns into $u$ quark and makes this $W^-$ boson. $W^-$ then apparently turns the anti-electron neutrino, $\bar{\nu_e}$, into an electron, $e^-$. My question is why can $d$ turn into $u$ and how is this $W^-$ produced? And how does this $W^-$ boson turn into electron? (what I found on Google didn't explain it really clearly to me)


title: Is Tsirelson's Bound the only constraint on these quantum correlations?

text: Alice and Bob are each in possession of one half of a maximally entangled pair of particles. Alice can make either of two observations, $A_1$ or $A_2$. Bob can make either of two observations, $B_1$ or $B_2$. (Observations have values $1$ or $-1$). Write $E(x,y)$ for the expected value of the product $xy$. Then Tsirelson's Bound says that $|E(A1,B2)-E(A1,B1)-E(A2,B1)-E(A2,B2)|$ is bounded above by $2 \sqrt{2}$. Question: Is the converse true? That is, suppose I have four numbers $x,y,z,w$. Suppose they are all bounded by one in absolute value and that they satisfy $|x-y-z-w| < 2 \sqrt{2}$. Does it follow that there are observables $A_1, A_2, B_1, B_2$ such that $x=E(A_1,B_2)$, $y=E(A_1,B_1)$, etc.? If not, what other conditions do I need on $x, y, z, w$ in order for such observables to exist?


title: Integrals of Motion

text: Landau writes in chapter 2 of his Mechanics book "The number of independent integrals of motion for a closed mechanical system with s degrees of freedom is 2s-1". Then he goes on to show how -- "Since the equations of motion for a closed system do not involve time explicitly, the choice of the origin of time is entirely arbitrary, and one of the arbitrary constants in the solution of the equations can always be taken as an additive constant t0 in time. Eliminating t + t0 from the 2s functions, we can express the 2s-1 arbitrary constants as functions of q and q’ (generalized co-ordinates and velocities) and these functions will be the integrals of the motions." Could someone elaborate?


I have a piece of homework, i have to make a pair of models depicting pure metals and alloys. I want it to be as accurate as possible, and so i'm asking this: Is the relative atomic mass directly proportional to the size of an atom? A Hydrogen atom has a relative atomic mass of 1. Lets say that I assign it a Radius of 5cm. What would the size of a carbon atom be? and Why? Is there a general formula? Thanks in advance


title: tracking a satellite

text: The following article says that because the GOCE satellite has a polar orbit, it is impossible to track where it will land. > "The satellite is one of the few satellites in a Polar Orbit. Consequently, > it could land almost anywhere," Mark Hopkins, chair of the National Space > Society's executive committee told FoxNews.com. I was looking for an explanation based on the physics of the orbit, as I am not familiar with orbital mechanics. http://www.foxnews.com/science/2013/11/08/track-europe-falling-2000-pound- satellite-in-real-time/


title: Skin effect and currents

text: Here in this picture ![http://de.wikipedia.org/w/index.php?title=Datei:Skineffect_reason.svg&filetimestamp=20080727190721](http://i.stack.imgur.com/KpHR5.png) you can see I_W which is induced by H. But why I_W is not vice versa? Because of $$rot \, \vec B = \mu_0 \, \left( \varepsilon_0 \frac{\partial E}{\partial t} + \vec j \right)$$ ? Maybe I have to use $$\oint E \, dr = - \int \frac{\partial B}{\partial t} \, dA = U_{induced}$$


title: Light bending by black holes

text: In the center of our milky way, it is assumed that a black hole exists with a mass of $\approx 4\times 10^6$ times our sun's mass. How much light bending (in degrees) would arise for stars that are in perspective near the position of this black hole in the sky? Could the mass of a black holes become so great that it actually distorts the area in the sky we see around it (through telescopes)?


title: Quantum mechanics scattering theory

text: When an electron absorbs energy and jumps to the another excited state by absorbing the photon and why it is always said that the electron will come back to $\hbar\omega/2$? Why doesn't the electron sit in the excited state ? What is the actual reason for it to come back to ground state?


title: What defines the interaction strength of a particle (massless or not) with matter?

text: Generally, talking about photons, the shorter the wavelength, the higher the interaction with matter. I doubt that I really understand why this happens. What about other massless particles? And particles with mass? Can we define a general principle that explains how the momentum and charge of particle defines its interaction strength with matter?


title: EMF induced in a dynamo is by photons of permanent magnets?

text: i know little about the quantum field theory and also that the permanent magnets have there fields because of exchange of virtual photons across or around the ends. so when we take a dynamo and the constantly changing magnetic field and the emf thus produced, is it possible that it is due to the virtual photons of the magnetic field. Please correct me if I am wrong and please explain the QFT also if possible and veeeerrrryyyy simply please.


title: Shaking water inside bowl causes waves but why does the water stabilize?

text: Suppose you shake water inside a container, then at first the waves goes up and down strongly but they gradually dissipate. What makes them dissipate?


title: How can I calculate out the 'specific charge' of an atom?

text: I know that it's charge/mass. But what steps do I take to calculate the specific charge of say, carbon-12? What about ions too?


title: What is the physics of a spinning coin?

text: When we spin a coin on a table, we observe 2 things:   1. It slows down and stops after sometime.   2. It does not stay at just one point on the table but its point of contact with table changes with time. I was trying to explain quantitatively this but I am stuck at how to take frictional torques into account. Any help will be appreciated.


title: Am I making the right assumption about a jump discontinuity in the acceleration?

text: > A train heads from Station A to Station B, 4 km away. If the train begins at > rest and ends at rest, and its maximum acceleration is 1.5 m/s^2 and maximum > deceleration is -6 m/s^2, what's the least time required to complete the > journey? **My attempt at a solution** : I assumed the acceleration function, $a(t)$, has a jump discontinuity at some time, say $t_1$, where it jumps from 1.5 to -6. Under this assumption, it's easy to use the velocity boundary conditions to get the total time $t_f$ is $\frac{5}{4}t_1$, because the velocity $v(t)$ for $t>t_1$ is just $1.5t_1-6(t-t_1)=7.5t_1-6t$. Setting this equal to 0 at $t_f$ gives this result. The position $x(t)$ for $t\leq t_1$ is just $\frac{1}{2}(1.5)t^2$ and for $t>t_1$ it's just $\frac{1}{2}(1.5)t_1^2+(1.5t_1)(t-t_1)-\frac{1}{2}(6)(t-t_1)^2$. Using the fact that $x(t_f)=4000$, and substituting $t_f=\frac{5}{4}t_1$, I find $t_f\approx 86.06$ seconds. But my teacher's solution says the minimum time is $81.65$ seconds. Who's wrong? Is my assumption about the jump discontinuity of $a(t)$ what's wrong?


title: Meaning of subscript in $V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$

text: This is probably a simple question, but what does the subscript $0$ mean in the following expression? $$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$


title: How Lyman transition (to the ground state from higher excited) happens ? The dipole selection rule is +/- 1?

text: How are the lyman series observed when the dipole selection rule is +/-1 in l change for hydrogen atom ?


If a people happen to be fall into the ocean from 50m high, then would the diving pose in the olympiad make less percussion then the leg going first into the water so that the body receive less damage?.


title: Black hole entropy

text: Bekenstein and Hawking derived the expression for black hole entropy as, $$ S_{BH}={c^3 A\over 4 G \hbar}. $$ We know from the hindsight that entropy has statistical interpretation. It is a measure of possible number of microstates that is consistent with a particular macrostate. My question is how far string theory predict this result.


title: Usefullness of an only qualitative understanding of momentum?

text: A few days ago I had a discussion with a friend who wants to become a physics teacher (in Germany). He told me that from a pedagogical/didactial point of view it seems to be a good idea to introduce momentum at a very early stage in school but without mentioning any formulas, I didn't really understand it, in particular this leads me to the following question: Suppose you know that momentum is "something" which can be transferred between bodies, that the total amount of that something is conserved and that a momentum of a body is greater if it is heavier or if it is faster, but you don't even know that $p = mv$. Can one know anything new about nature or solve any problems in every day life, if one has such a vague, only qualitative notion of the concept of momentum in mind?


title: Are Bloch equations empirical?

text: Are Bloch equations (which describe the evolution of macroscopic magnetization) empirical? If so, under what assumptions do they hold? $$\frac {d M_x(t)} {d t} = \gamma (\mathbf{M} (t) \times \mathbf {B} (t) ) _x - \frac {M_x(t)} {T_2}$$ $$\frac {d M_y(t)} {d t} = \gamma (\mathbf{M} (t) \times \mathbf {B} (t) ) _y - \frac {M_y(t)} {T_2}$$ $$\frac {d M_z(t)} {d t} = \gamma (\mathbf{M} (t) \times \mathbf {B} (t) ) _z - \frac {M_z(t) - M_0} {T_1} $$


title: Missing something basic about simple orbital mechanics

text: I seem to be missing something basic. I've been trying to get a simple orbital simulation working, and my two objects are Earth around the Sun. My problem is this. I placed the Earth at 93M miles away from the Sun, or 155M km. As I understand it, the orbital velocity of something at 155M km from the Sun is: $$v = \sqrt{\frac{GM}{r}}$$ Plugging in the numbers for the Sun, I get a velocity of: $$29261 \frac{\mathrm{m}}{\mathrm{s}}$$ However, if I want to get the acceleration that the Sun has upon the earth, I use: $$g = \frac{GM}{r^2}$$ For the Sun, and 155M km, I get an acceleration of: $$0.0055\frac{\mathrm{m}}{\mathrm{s}^2}$$ Now, I start with a simple body at the proper radius out along the X axis and give it a simply vector of 29261 m/s along the Y axis, then I start applying the 0.0055 m/s^2 acceleration to it. And the acceleration of the Sun is simply not enough to hold the Earth. If the Earth starts with a vector of (0, 29261 m/s), and after and I add the acceleration vector of (-0.0055 m/s, 0) to it, you can see that after a single second, it doesn't move a whole lot. If I chunk things to days, 86400 seconds, then the acceleration vector is only, roughly, -477 m/day, but the velocity vector is: $$2,325,974,400 \frac{\mathrm{m}}{\mathrm{day}} = 29,261 \frac{\mathrm{m}}{\mathrm{s}} \times 86,400 \frac{\mathrm{s}}{\mathrm{day}}$$ As you can imagine, the -477 isn't going to move that much towards the Sun. I understand that better simulations use better techniques than simply adding basic vectors together, but that's not what this is. I seem to be missing something fundamental. I had assumed that given the correct velocity, that the pull of the Sun should keep the Earth in orbit, but the "pull" that I'm using doesn't seem to be having the desired effect. So, I'm curious what basic "D'oh" thing I'm missing here. Edit for Luboš Motl answer. Perhaps there's something more fundamental I'm missing here. I understand you point, but .0055 m/s * 86,400 is -477. I was doing that math fine. Simply, I have an object with a velocity vector. Then I apply an acceleration at a right angle. I do that for N seconds to come up with a new, right angle velocity vector. I then add that to the original vector to come up with the objects new vector. I then take that vector, apply to the current position of the object, and arrive at a new position. Clearly there is a granularity issue which makes some amount of seconds a better choice for a model than others, but this is high school level simple mechanics, so there's going to be some stepping. I chose one day so that my little dot of a planet on my screen would move. If I update every 1/10th of a second "real time", and each update is a day, then I should get a rough orbit that's really a 365ish polygon in a little over 30s real time. If I choose a step size of 1 second, then my acceleration (0.0055 m/s^2) * 1 s = a right angle velocity vector that's -0.0055 in magnitude. That vector is added to the original vector of 29261 (at right angles), giving me a new vector of (-0.0055, 29261). That's after one second. That's not much of a bump. It's barely a blip. If I apply one days full of acceleration, "all at once", I am obligated to not only multiply the acceleration by 86,400, but also the original vector (since it's 29261 m/s, and we have 86,400 s), thus giving me, proportionally, the same vector, just longer. And it's still just a bump. So, I'm mis-applying something somewhere here, as I think the numbers are fine. I'm simply "doing it wrong". Trying to figure out what that wrong part is. Edit 2, responding to Platypus Lover Thank you very much for the simple code you posted. It showed me my error. My confusion was conflating updating of the vector with the calculation of the velocity vector. I felt that I had to multiply both the original vector AND the acceleration amount by the time step, which would give me the silly results. It was just confused in my head.


title: Publication Authorship Credits

text: Many physics papers now have dozens of authors per paper. Experimental physics may have multi-organizational and multi-country contributing staffs, but I'd guess that most of the names don't contribute a word or equation to a paper, yet they get individual authorship credit. My question is who determines the author list, does everybody listed have editing privilages, and perhaps most importantly, who decides on their listed order?


title: Is there a simple way to compute some physical constant from Feynman diagram statistics?

text: I've been playing around writing some software to generate Feynman diagrams for QED, respecting the vertex "rules" described here, and avoiding creating isomorphic duplicates. So from a starter fermion arc ![zero order](http://i.stack.imgur.com/o6sMN.png) the only possibility - at least the way I create these things, by adding pairs of vertices by splitting fermion arcs and linking the fresh vertices with boson arcs - is: ![first order](http://i.stack.imgur.com/k6MMU.png) (boson arcs are in red) and from that there are 3 possibilities ![second order](http://i.stack.imgur.com/A3Skb.png) ![second order](http://i.stack.imgur.com/cEqO8.png) ![second order](http://i.stack.imgur.com/4UTsE.png) and then 15 ![enter image description here](http://i.stack.imgur.com/LNFPc.png) and then 105, and then 945 (for 10 interior vertices) and so on (I just killed it after a few hours runtime and it was working it's way through the many thousands of 12 interior vertex possibilities). **My question is: given all these diagrams, is there some simple procedure I can apply and have some fundamental dimensionless constant of the universe (or at least of QED) pop out the other end ?** Background: my interest in this stuff got started with the iconography of these diagrams and their visual aspects (e.g how to layout such things nicely, and how to plot them with some wiggly lines as per the usual convention for the photons will get some attention next), and the original driving idea was to do some nice big poster which gives some visual impression of how the number of possibilities explodes. But it'd be the icing on the cake for the poster to also be able to show that some physical property of the universe follows as a direct consequence of some statistics or whatever of the diagrams (capped with the "Nobody knows how it can be like that" Feynman quote no doubt). Disclaimer: I know mathematics and computing but most of my knowledge of this area of physics is from reading "pop science" books and I'm well aware they grossly simplify things, so maybe I'm hoping for too much from the diagrams alone. **Update:** following helpful input from Vibert below, I'm now generating the below for 2 and 4 vertex diagrams (a grey background indicates "one particle reducible" diagrams); these now include the expected virtual particle loops (missed in my first attempt above). Diagrams which are isomorphic by simple reversal of all the arrows are omitted in the interests of saving space. ![4 vertices](http://i.stack.imgur.com/OyclK.png) ![6 vertices](http://i.stack.imgur.com/IHa8k.png) **Outcome:** Well after digging into this a bit more it seems there's no getting away from Doing The Math, integrals and all. I was originally hoping there might be something as simple and understandable as "well there are N diagrams in this category, M diagrams in that category and so the correction to the 1st order approximation is (N-M)/(N+M), which is more accurate". But material on Lamb Shift corrections gives an idea of what's actually involved (e.g the contribution from the simplest diagrams is ~1058 MHz, most of it from one case), while the next order's contributions sum to on the order of 100kHz.


title: Freedom in the Choice of a Beta Functions in RG

text: Assume we're given a certain statistical model, say the infinite range Ising model \begin{equation} H_{N}\\{\vec\sigma_{N}\\}~=~ - \frac{x_{N}}{2N} \sum_{i,j =1}^{N} \sigma_{i} \sigma_{j} \end{equation} with $N\rightarrow\infty$, where $N$ is the number of spins, $\sigma_{i} \in \\{ \pm 1 \\}$ for all $i\in\\{ 1..N \\}$, $\vec\sigma_{N} = (\sigma_{1}, ... , \sigma_{N})$ and $x_{N}:=\beta J$ with J being the coupling strength between the spins. In addition $\beta := \frac{1}{k_{B}T}$ with $k_{B}$ the Boltzmann constant and T the temperature. In the limit $mx\ll1$ one can implement a renormalization procedure of the form $Z_{N}(x_{N}) = \exp(-f_{N}(x_{N})) \cdot Z_{N-1}(x_{N-1})$ where intuitively one step in the RG process consists of the reduction of one spin site. In the limit as $N\rightarrow\infty$ one can write down the flow of the coupling constants as a differential equation of the form $\frac{dx}{dl} = (-x + x^{2})$ where the vectorfield $\beta(x):=-x + x^{2}$ is usually called the beta-function. I was told that the main "physics" (meaning most likely critical exponents) of the RG is contained entirely in the critical points of the beta function, i.e. the x for which $\beta(x)=0$. In particular I was told that one can change the $\beta$-function "arbitrarily" as long as the critical points are the same. So in principle one could use $\beta'$ instead of $\beta$ where $\beta'$ has the same zeros as $\beta$ and obtain the same physics. In particular I could for example to a rescaling, i.e. choose $\beta' := \lambda \cdot \beta$ for some real number $\lambda$. I don't really understand why this is true? In the case of one coupling constants it's a bit understandable since one only decreases the "speed" so to say as one moves from one critical point to another. But when one has more coupling constants in the RG process (such as a magnetic field) I don't see why this should be the case? Is there a certain general freedom in the choice of a beta-function? I'm looking forward to your responses:)


title: How does capacitance work?

text: I have a circuit whit a AC source a capacitor and a resistance all in series. I find that the difference of potential between the capacitor leads begin to change after some instants as it should. But my question is, if the resistance is very high, say infinite, the capacitor have no tension per se, but it experiences high voltage as a whole in respect to the ground. What i don’t understand is why there is not electric field between the plates. I’m sorry if the question isn’t clear but I really cannot understand the implication of the definition of “potential”.


title: How do we know that black holes evaporate?

text: This has been bugging me for some time. As I understand it, Hawking radiation is the result of the mismatch between the vacuum state of a quantum field as seen by a free falling observer (falling directly toward the black hole) and one that is sitting at a constant radius far away from the black hole. This is perhaps the result of my naive understanding of the subject, but it doesn't make sense to me to say that a black hole radiates, because it's observer-dependent. How do we know that the thermal bath of particles that we see when we sit at a constant radius actually causes the black hole to lose mass? Is it just a simple energy conservation argument, or is there some subtle process here that I'm missing?


title: Does quantum collapse involve a loss of information? Does it require energy as suggested by the Landauer Limit?

text: I read in the context of quantum computing or of the minimal energy required for computation that there has to be a minimum possible amount of energy required to change one bit of information, called the Landauer limit. During collapse of a wave function, for example for one of a pair of entangled particles, it seems one is losing information content (losing one bit as the wave function goes from either possible state to one). If so does this imply that collapse requires energy? Or is the Landuaer limit not relevant to this setting.


title: Why do electrons couple in atoms?

text: In describing electron states in hydrogen, we have a very "simple" picture, at least in intro-quantum. But this only has one electron! As we permit more electrons, we also have things like the exclusion principle, which comes from the spin-statistics theorem, but that relies on the electrons having some kind of coupled wave functions, right? Why do electrons always come in pairs?


title: Calculus used by Gauss to find Ceres' position?

text: With very little data, the great mathematician Gauss was able to predict the exact location of where to find the asteroid Ceres. If possible I would like a reconstruction of his work, from the data that he had at his disposal and the rest of his calculations. Is the data available somewhere?


title: Iron Man repulsor question

text: Ignoring the whole movie situation along with the power demands, what do you think Iron Man's repulsors use to "repulse" his targets? I don't think they are lasers or electric beams, or "reverse magnetism", but I'm guessing its some sort of focused sonic waave or a shock wave generator.


title: Why removing one slab in Michelson-Morley experiment causes an elliptical fringe pattern?

text: I performed Morley experiment using He-Ne laser. Two glass slabs were there and circular fringes were formed but when I removed one slab elliptical fringes were there (and less intense fringes). Why?   In general is there any benefit of using two slabs?


title: Direction of friction in case of a rolling sphere

text: Suppose a ball rolls on a ground .obviously it is friction that helps to develop the required torque.Hence I find the direction of friction by pointing out the direction of rolling of the ball. But is there any intuitive method for predicting the direction of friction?


title: Local EPR-experiments with photons in vacuum?

text: The principle of non-locality states _"that an object is influenced directly only by its immediate surroundings."_ (Wikipedia) ![enter image description here](http://i.stack.imgur.com/UO6OG.jpg) When two entangled particles are measured in an EPR experiment, we consider these events as **non-local**. Generally I agree. But does this also apply to a pair of **photons in vacuum**? (and if so, why?) ![enter image description here](http://i.stack.imgur.com/t7lDE.jpg) From the point of view of any observer's Minkowski diagram, the two spacetime intervals of the lightlike worldlines of the two photons AB and AC are always zero (so- called "empty intervals"), and by consequence, B and C are located in the "immediate surroundings" of A, and the events should not be nonlocal. For more clarity I replaced "B in immediate surroundings of C" by "B&C in the immediate surroundings of A". In spite of the attribution of a bounty, the question is still unanswered. As user 12262 pointed out, some comments have disappeared in the meanwhile. Edit 01/07/14: Up to now, no answer explains why there is the word "interval" in "spacetime interval = 0".


title: Would the north poles of two magnets repel each other if a weaker south pole was inserted between them?

text: My son asked me this question and I was stumped - my intuition says that is the south pole was strong enough the attraction between the north and south poles would outweigh the repulsion between the two north poles - but how strong would the south pole need to be in this case?


title: Light pollution calculation using camera

text: Is it possible to calculate light pollution values using camera (analyzing camera feed) integrated in new smartphones (8 Mpx camera) but with pretty decent accuracy? Or that is only possible with special equipment? Using google I found something on that subject here : http://www.sciencebuddies.org/science-fair- projects/project_ideas/Astro_p022.shtml. But they are using professional digital cameras. Thank you in advance!


title: Sedna, VP113 and the likelihood of the PX/Tyche/Thelistos hypotheses

text: The recent discoveries in exoplanetary science (specially those findings of planets orbiting far far away from its parent star/stars) raise questions about how much we know about the (true, AIU definition) number of planets in our solar system. Question: does the discovery of VP113 and Sedna increase the odds of some kind of planetary object in the edge of the known solar system (Oort's cloud)? How could we find it if it is very cold and dark? I mean, how many Sedna or VP113 objects we would need in order to guess its position and location? Reading about this topic, I don't know how to quantify the odds of finding   * PX(Planet X): An Earth sized body perturbing the orbits of Sedna, VP113 and other similar objects.    * Thelistos: A super-Earth (about 5-10 Earth masses times a O(1) factor)   * Tyche: (Now disfavoured by WISE data, I think it can not be excluded if it is extremely cold and "dark") Gas giant (Neptune-like, Saturn-like, etc)   * Nemesis: A "dark star"/brown dwarf object.


title: Ideas for high school physics paper, including simulations

text: I have to write, with two friends, a simulation based physics paper at school. The problem is, that will I am quite familiar with the concepts of calculus and algebra, my friends aren't. So, we could find a good topic. The task is, to write a paper about a physical topic, with the use of a selfmade program. The development of the program shouldn't be a problem at all. we have a good programmer. Any suggestions, for a topic that involves only pre-calculus math or only just some calculus?


title: Euclidean black hole extrinsic curvature

text: I have read that the extrinsic curvature at the horizon of a euclidean black hole is zero? Does anybody know how this can be shown?


title: Showing that the variation of an affine connection is a tensor

text: How can i show that $\delta\Gamma_{\mu\nu}^{\rho}$ transforms like a tensor? Metric compatibility is not assumed here. That means 1) First i need to compute $\delta\Gamma$ first. To do that i need an explicit formula for it. But without metric compatibility, I don't which should i use. Like i get one from principle of equivalence : $$ \Gamma_{\mu\nu}^{\lambda}=\frac{\partial^2\zeta^\alpha}{\partial x^\mu \partial x^\nu}\frac{\partial x^\lambda}{\partial\zeta^\alpha} $$ Where $\zeta$'s are local inertial coordinates obeying $$ d\tau^2 = -\eta_{\alpha\beta}\zeta^\alpha\zeta^\beta $$ I'm confused about how to compute $\delta\Gamma$ from this. 2) After computing $\delta\Gamma$ I have to show it transforms like a (1,2) type tensor. Which i think i can manage if i can manage the 1.


title: Number of decays in a chain reaction

text: It is widely known that the probability of $n$ decays from one _system_ to another $A \rightarrow B$ (e.g., electrons decaying from one atomic energy level to another or muons decaying into neutrinos and electrons, etc) in a given period of time is given by a Poisson distribution. However, consider the following simple chain-reaction $$A \xrightarrow{\lambda_A} B\xrightarrow{\lambda_B} C$$ where $\lambda_i$ is the decay rate. At $t=0$ (initial time) there are no particles in $B$ or $C$, all of them are in $A$. **The question is how to compute or estimate the probability of a given number of decays from $A$ to $B$ plus the number of decays from $B$ to $C$ in a given period of time**. In other words, one can assume that in each of the reactions one particle, say one photon, is emitted and one would like to estimate the likelihood of getting certain number of emitted photons over a period of time. The probability of $n$ decays from $A$ to $B$ in a time $\Delta t$ must be given by a Poisson distribution with average number $\lambda_A\, \Delta t$. However, I wonder which the probability of $m$ decays between $B$ and $C$ in a period of time is. I do not think it follows a Poisson distribution given that the probability of getting $n$ decays in a given period of time should depend on time. This must be something well-known since it has applications in nuclear (fission), atomic (spontaneous emission), and particle physics ($\pi^-$ going to $\mu^-$ (emitting $\bar\nu_{\mu}$) followed by muon decay). And also in chemistry. Seems to be something pretty common. References are welcome. _N.B.:_ I am **not** asking about the distribution of particles in $A,\, B,$ and $C$ as a function of time.


title: Are there any models that explain the cause of the dual symmetry-breaking of the in electrodynamics?

text: Source-free Maxwell eqautions a dual symmetry between electric and magnetic fields is obvious. But in the presence of electric charge, such symmetry is broken. Recover it possible by an introduction in the theory of magnetic charge. However, here are some problem with Lagrangian formulation of the theory. Is there in modern literature theories that explain the reasons for the absence of a magnetic charge by some mechanism of symmetry-breaking?


title: Photon "stuck" on the event horizon of a black hole

text: According to what I've read on special relativity, $c$ is the speed limit for every object in the universe, and according to Einstein, an object's speed through the three spatial dimensions plus its speed through the fourth temporal dimension always sums to $c$. I once watched a video demonstrating what it would be like to fall into a black hole. At one point the author stated that if a photon was emitted directly away from the singularity and at a distance equal to the Schwarzschild radius, the photon would hover there for eternity. My question is based on these assumptions so please let me know if either is incorrect. With its motion through the spatial dimensions halted, will the photon in question not experience time at roughly the same rate we do? Will it decay?


title: What gives substances their color?

text: As far as i know (i may be wrong!), substances appear to have a definite color because they reflect/ transmit all the light rays of the given color, and absorb all the lights rays of the remaining colors (of course, we are talking about the visible region only). That means, that if a substance is red in color, it absorbs all the visible region light except red, and reflects red light. When we say light is absorbed, it means that the electrons in the molecules of the substance get excited, right? And, since energy levels are quantized, only certain wavelengths get absorbed. Let's take an apple. It always appears to be red, no matter much light i shine on it. So, that means for how much ever light i shine on it, all wavelengths except those corresponding to red get absorbed, and the electrons are continuously excited. How is that taking place without any deexcitation?(Assuming that if any deexcitation takes place, the energy is released as photons only. If so, all other wavelengths should also be emitted, and the apple should appear white.) How can we definitively say, that the energy gaps are equally spaced? If deexcitation does not take place, all substances, after shining light on them for a sufficient amount of time, should eventually become conductors, but i don't think that happens. Also, if the light source is switched off, the electrons should deexcite, and the apple should appear cyan in color(complementary color of red). But that does not happen. Why?


title: How to calculate the electrostatic force applied on an object that is along the axis of a charged tube's surface?

text: Let's say there is a charged tube(a cylinder with no top and bottom) with radius r and length l, charge q1 which also made out of insulating material. And also if there is an object with charge q2 along the axis of the surface of the tube, how can I calculate the force applied on this object?(the distance between tube and object is d) Here is my calculations: From the Gauss' law: $$ \phi_E= \frac Q{\epsilon_0} $$ I took cylinder as Gaussian surface. $$ E \times 2\pi dl= \frac {\lambda \bullet l}{\epsilon_0} $$ $$ E = \frac {\lambda}{\epsilon_0\times 2\pi d} $$ or $$ E = \frac {q_1}{\epsilon_0\times 2\pi dl} $$ Thus we found the electric field applied to a point d away from the tube.To calculate the force we use $F=qE$. And finally the electrostatic force is: $$ \frac {q_1q_2}{\epsilon_0\times 2\pi dl} $$ However what I found is the force applied to an object d away from the tube but perpendicular to the surface of the tube. Would this calculation be valid for an object which is along the axis of the surface of the tube? P.S: I know I asked that question but I couldn't get any answers so I hope this question won't be closed. Thanks in advance.


title: Assuming that extra dimensions will not be visible at LHC, what motivation will still remain to study them?

text: Many physicists believe that there is little possibility of observing extra dimensions at LHC so that some extra dimension models originally designed to solve hierarchy problem (ADD/Randall-Sundrum) will probably be useless for the original purpose. However some people claim that even if unobserved at LHC, these models will not be forgotten and people will continue to use them for other purposes. I am confused here -- if the proposed model fails to solve the very problem it was supposed to tackle, how can such models still be used? Will these not be inconsistent with nature? Apart from the confusion, I am interested to know what insight such extra dimension models (RS/ADD) have provided which would be impossible unless such models were developed and studied?


title: experimental verification of theory

text: Which equation of physics could we call the best verified one experimentally? Let us define "best verified" in the sense of smallest relative error of the predicted variables. Thank you.


title: Why is it easier to walk diagonally upstairs

text: Try it yourself on a set of wide steps! Work is given by $$\int_C \mathbf{F} \cdot d\mathbf{x}$$ where $C$ is a path integral. In this case I think $\mathbf{F}$ is a rotational vector field because the stairs are essentially a set of discontinuities. This would mean that the integral is path dependent. Here is why this seems like a paradox: if you where to climb the same height over a smooth hill, then the integral is path independent since $\mathbf{F}$ is "smooth" and irrotational. This means that the amount of work done never changes given the path you take, hence if you take a longer (diagonal) path you must exert less force over that distance than if you where to take a straight path. In the case of walking up stairs, you must always cross the same number of stairs no matter the path you take. All other distance you make is along the horizontal parts of the tops of stairs and hence requires much less force. This would seem to suggest to me walking up stairs always requires the same force to scale the vertical parts of each stair. Am I hallucinating that walking diagonally up stairs is easier?


title: How do magnetically levitated trains (maglevs) stay on the tracks?

text: Just went on one yesterday, and had a bit of a thrill. And I was musing on the fact that electromagnetic forces are so strong, that they can keep a whole train up in the air. But then, wouldn't maglevs be awfully unsafe? Like, you wouldn't even be able to turn a corner safely. How do they do it? How do they stay on the tracks?


title: Why do balloons deflate?

text: Title says it all. Every balloon that I have got, from parties, etc, all slowly deflated for no reason at all. Why is that?


title: How to obtain Dirac equation from Schrodinger equation and special relativity?

text: I'm reading the Wikipedia page for the Dirac equation: > _The Dirac equation is superficially similar to the Schrödinger equation for > a free massive particle:_ > > A) $-\frac{\hbar^2}{2m}\nabla^2\phi = i\hbar\frac{\partial}{\partial > t}\phi.$ > > _The left side represents the square of the momentum operator divided by > twice the mass, which is the non-relativistic kinetic energy. Because > relativity treats space and time as a whole, a relativistic generalization > of this equation requires that space and time derivatives must enter > symmetrically, as they do in the Maxwell equations that govern the behavior > of light — the equations must be differentially of the same order in space > and time. In relativity, the momentum and the energy are the space and time > parts of a space-time vector, the 4-momentum, and they are related by the > relativistically invariant relation_ > > B) $\frac{E^2}{c^2} - p^2 = m^2c^2$ > > _which says that the length of this vector is proportional to the rest mass > m. Substituting the operator equivalents of the energy and momentum from the > Schrödinger theory, we get an equation describing the propagation of waves, > constructed from relativistically invariant objects,_ > > C) $\left(\nabla^2 - \frac{1}{c^2}\frac{\partial^2}{\partial t^2}\right)\phi > = \frac{m^2c^2}{\hbar^2}\phi$ I am not sure how the equation A and B lead to equation C. It seems that it is related to substituting special relativity value into quantum mechanics operators, but I just keep failing to get a result...


title: Vacuum Wavefunctional

text: I am having this problem in understanding the vacuum wavefunctional in QFT. Hence this naive question. I mean, if someone say vacuum wavefunctional, I can think of an element like wavefunction as in Quantum mechanics but now a function of fields. Its easier to solve for it, I think, in Schroedinger representation, as e.g Hatfield does in chapter 10 of his book QFT of point particles and strings. I seemingly understood that. Step by step. easy. But now I see that in path integral formalism, say in Euclidean FT, the vacuum state is defined as path integral over half of the total spacetime with some fixed boundary condition (B.C) $\psi(\tau=0,x,z)\psi_0(x,z)$ obeyed in the boundary of the half space and is given by $\mathbf{\Psi}[\psi_0]=\int_{fixed B.C}\mathcal{D}\psi e^{-W[\psi]}$ with $W$ the action. Isn't it reminiscent of the generating or partition function of an Euclidean field theory? Anyway, I don't understand (may be also because I didn't find a reference, could you suggest one?) why this is and how to see it. An intuitive explanation will be very helpful. Thanks.


title: Is it (theoretically) physically possible to project an image into thin air?

text: Is there some law of physics that strictly prohibits the projection of 2D or 3D images into thin air (such as holograms in movies) or is a solution to achieve this still up for grabs by an eventual discoverer?


title: Reality constraint

text: What is the "definition" of a reality constraint and why is it called that way? (I mean how it is used for example in quantum field theory and string theory)


title: Physical meaning of Impedance

text: So I have been thinking about the way impedance is defined for electrical systems, and the way it is derived. Even after looking through some websites, I cannot seem to grasp something, which every website I visited seemed to skip on. In an ideal resistor, if we take the ratio of the voltage to the current at ANY time, the ratio is a constant. This ratio is then the resistance (also the impedance) of the resistor. I have been interpreting this as the opposition the resistor bears to the current flow through it upon application of a voltage. I thought of it like a constant that relates the otherwise-would-be- infinite current to the applied voltage. Coming to a capacitor, there seems to be some sort of change in the definition of impedance. The impedance for a capacitor is no longer the ratio of voltage to the current, but the ratio of the complex voltage to the complex current. In other words, mathematically it is equivalent to $$\dfrac{1}{i\omega C},$$ and not $$\dfrac{\tan(\omega t)}{\omega C},$$ for a capacitor with capacitance C at a frequency w. I am finding this difficult to interpret because the ratio of the voltage to current is definitely varying in time. How can the analogy of a resistor's impedance be applied to the impedance of a capacitor when the ratio of the voltage across it to the current through it is changing (it's even 0 or undefined sometimes). Why is the magnitude of the quantity $$\dfrac{1}{i\omega C}$$ now the resistance of the capacitor circuit? What happened to the plain old voltage to current ratio? Have books been skipping this subtlety, or I am just not understanding something very simple? Clarification: $$ if \hspace{.5 pc} v(t) = V_m \sin (\omega t), \hspace{0.5 pc} then \dfrac{d V(t)}{dt} = \omega V_m \cos (\omega t) $$ $$ so \hspace{0.5 pc}the\hspace{0.5 pc}ratio\hspace{0.5 pc} \dfrac{v(t)}{i(t)} = \dfrac{V_m \sin (\omega t)}{C\omega V_m \cos (\omega t)} = \dfrac{\tan (\omega t)}{C\omega} $$ $$ In \hspace{0.5 pc}phasor \hspace{0.5 pc}notation, \hspace{0.5 pc}this \hspace{0.5 pc} ratio\hspace{0.5 pc} seems\hspace{0.5 pc} to\hspace{0.5 pc} be\hspace{0.5 pc}different \hspace{0.5 pc}in \hspace{0.5 pc}that: \\\ \dfrac{\mathbf{V_c}}{\mathbf{I_c}} = \dfrac{1}{Cj\omega} = -\dfrac{1}{C \omega }j $$ $$ and \hspace{0.5 pc} \Re\\{-\dfrac{1}{C \omega }j \\} = 0$$ $$but \\\ |\dfrac{\mathbf{V_c}}{\mathbf{I_c}}| = \dfrac{1}{C \omega } $$ So my question is why does the magnitude of the ratio of the complex voltage to the complex current now suddenly carries a physical meaning (if my understanding is correct, it is the resistance which can be measured in ohms, just like in the resistor). Also, why is going from the complex domain to real domain not possible for this ratio, because clearly the real part of the complex impedance is 0 (@Alfred Centauri mentions that the impedance is not itself a phasor). I understand that the math works, but the thing that is not making sense to me is this ratio of two complex quantities and the apparent emergence in its physical meaning.


title: When do I know if energy stored in an object is 0 or nonzero? (Heat transfer)

text: There is uniform internal heat generation at $\dot{q}=5\times10^{7} \frac{W}{m^{3}}$ is occurring in a cylindrical nuclear reactor fuel rod of 50 mm diameter and under steady state conditions the temperature is distribution of the rod is $T(r)=800-4.167\times10^{7}r^{2}$. The fuel rod has a thermal conductivity of $k=30 \frac{W}{mK}$. What is the rate of heat transfer per unit length of the rod at r=0 and r = 25mm (the surface). I did this two different ways. The first way is correct but and the second isn't so I need to understand what isn't correct about it. So to get the rate of heat transfer at r=0 and at the surface I just used Fourier's Law $$q'=-k(2\pi r)\frac{\partial T}{\partial r}$$ I found the derivative of my temperature distribution and then plugged in the number to get.... $$q'(0)=0 \frac{W}{m}$$ $$q'(.025)=9,8182.6 \frac{W}{m}$$ Now when I looked at this question, I realized that I didn't use the internal heat generation of the rod. That made me begin to think that I had to use an energy balance on the cylinder as a whole. $$\dot{E}_{in}-\dot{E}_{out}+\dot{E}_{g}=\dot{E}_{st}$$ I know that $\dot{E}_{in}=0$ and that $\dot{E}_{out}$ is due to conduction but I am not really sure what $\dot{E}_{st}$ would be. I assumed that it would be zero. Is this true? If I were to set it equal to 0 then I wind up with... $$\dot{E}_{out}=q'(.025)=\dot{q}(\pi r^{2})=9,8174 \frac{W}{m}$$ This value does not equal to what I previously calculated above. Can someone tell me why this isnt the same? I assume that the energy storage is nonzero in this case but I dont understand why


title: When a gas expands against an external pressure of 0, must the stopper on the cylinder be massless?

text: Basically, I need to conceptually understand why the work a gas does is the integral $\int p_\mathrm{external}dv$ and is 0 when pressure external is 0. I understand why $\mathrm{d}w = - p_\mathrm{externa } \mathrm{d}v$ and so obviously I understand why the math says the work is 0; I need to conceptually understand it. When you have isothermal expansion in a cylinder where the external volume outside the gas has pressure 0, a.k.a. vacuum, must the movable top of the cylinder be massless? The equations obviously say the work is 0, but I think of the stopper itself as being resistance. Could I think of isothermal expansion in a vacuum as the top basically "disappearing" when the gas is released? This is difficult to phrase for me, so please ask if you don't understand. I also am only a sophomore in high school, so I have a limited understanding of calculus. Like I said, conceptually for the pressure against the gas to be 0, the lid must be frictionless and massless, right? Thank you.


title: For a theoretical (not mathematical) physicist, is there a need to learn pure mathematics?

text: For a theoretical physicist (not a mathematical physicist), is there a need to learn pure mathematics ?


title: How can we represent the motion of a particle in 2D space using Lagrange's equations?

text: Can we represent the motion of a particle in 2D space using Lagrange's equations? This is what I tried. Please tell me what is wrong? Consider a particle on a plane have the co-ordinates $(x,y)$ with a velocity $v$ and mass $m$. Now $v=\dot{x}+\dot{y}$ where $\dot{x}$ and $\dot{y}$ are the derivatives with respect to time. According to Lagrange's equation, $L=\frac{1}{2}m(\dot{x}+\dot{y})^2-mgy$ $\frac{{\partial}{L}}{\partial{y}}=-mg$ ---(1) $\frac{{\partial}{L}}{\partial{\dot{y}}}=m(\dot{x}+\dot{y})$ Therefore $\frac {\mathrm d t}{\mathrm d t}(\frac{{\partial}{L}}{\partial{\dot{y}}})=\frac{{\partial}{L}}{\partial{\dot{y}}}=m(\ddot{x}+\ddot{y})$ Now $\ddot{x}$ and $\ddot{y}$ are the vertical & horizontal components of the acceleration $a$ of the particle. So let $\ddot{x}=a_x$ and $\ddot{y}=a_y$ Hence $\frac {\mathrm d t}{\mathrm d t}(\frac{{\partial}{L}}{\partial{\dot{y}}})=m(a_x+a_y)$ ---(2) From Lagrange's equation, Eq (1)= Eq(2) => $-mg=m(a_x+a_y)$ $-g=a_x+a_y$ Does the above equation make any sense? I tried to apply it to a real problem and it gave me a wrong result. What is wrong with my working? Thanks in advance. ## **Update:** Thanks a lots guys. Yes, the expression for $v$ was wrong. When I calculated with the correct expression I got the result $a_y=-g$ What does it mean? Does it mean that the Y component of the acceleration is always equal to acceleration due to gravity? And can someone explain how Lagrangian mechanics can be used to solve simple mechanical problems? When I tried applying it to problems all I got were few known results & other nonsensical ones (like the one in this question. Probably due to my erroneous application of the Lagrange.) PS: Will someone explain why this question was downvoted?


title: Conditions for heat exchange and evaporation

text: I wonder if there is any law for heat exchange. I have learnt that heat exchange between systems occurs when the temperature of respective systems differ. But in case of **evaporation** , the process _creates a cooling effect even in an **isothermal condition_** ( I mean by isothermal condition to be a isothermal situation between the evaporating liquid and the surrounding). I would like to discuss the cooling effects produced by evaporation under isothermal condition. If I am wrong in saying that, evaporation is possible at isothermal process, please correct me.


title: Is an atom-thick sheet of a material visible and tangible?

text: If one could make a sheet of a material (thickness of an atom), Aluminum for example, would it be visible to naked eyes? What about tangibility? would it be tactile by human finger skin?


title: Question on the Hagedorn tower in Type I string theory

text: In a previous question (Mass spectrum of Type I string theory), I had asked about the mass spectrum of Type I string theory. I got a response saying that it is a Hagedorn tower. However, my source does not discuss much about Type I string theory (it only discusses Type IIA and Type IIB) so I searched for more sources. Yet, all the sources (all some lecture notes) I got, for some reason stopped at Type IIA and Type IIB string theories. So my question is, what is really the mass spectrum defining the Hagedorn tower? Is it something analogous to the Type II Mass Spectrums? $ m= \sqrt{\frac{2\pi T}{c_0}\left(N+\tilde N -a-\tilde a\right)}$ Thanks!


title: Why do I get different colours in scratched holograms?

text: ![if we zoom this image we will see different colours in it](http://i.stack.imgur.com/3qRSg.jpg) I was making a scratched holograms and in result got different colours instead of white hologram


title: Find radius of curvature, given a velocity vector and acceleration magnitude?

text: The particle P moves along a space curve. At one instant it has velocity $v = (4i-2j-k)$ $m/s$. The magnitude of the acceleration is 8 $m/s^2$. The angle between the acceleration and the velocity vector is 20 degrees, so one can calculate that the acceleration in the direction of the velocity is 7.52. How can I calculate the radius of curvature from this information? I am clueless... no formulas have been introduced, as I have seen there are throughout the Internet. The chapter that I'm working on is about three dimensional coordinate systems. One of my attempts has been to try to imagine an infinitesimal change in velocity, v = r$\theta$. This implies $\frac{dv}{dt} = r\frac{d\theta}{dt}$. Could I perhaps know somehow what $\frac{d\theta}{dt}$ is?


title: About symmetry, and about electron density in crystals in particular

text: The book Introduction to Solid State Physics by Kittel says: "We have seen that a crystal is invariant under any translation of the form T [...]. Any local physical property of the crystal, such as the charge concentration, electron number density, or magnetic moment density is invariant under T. [...] n(r+T) = n(r)" Why is this the case? Even though the underlying atoms are invariant under translations in T, why should the electron density also be invariant under the same transformation? Couldn't for example if you have this 1D crystal:               o   o   o   o   o      This is invariant under transformations $T = {...,-1,0,1,2,3,...}$. Why couldn't the electron densities be like this:               o h o l o h o l o h o      Where h is a high density and l is a low density. So they would only be invariant under $T = {...,-2,0,2,4,...}$. This is just an example: why do the local physical properties have to be invariant under T? I suppose this question could be phrased even more generally: if the causes of some phenomenon have a symmetry, does the phenomenon also always have the same symmetry? If yes, why, and if no, what are the conditions under which the phenomenon does have the same symmetry?


title: Vertex for quartic interaction of complex scalar multiplet

text: Since I'm new to QFT and I tend to do a lot of errors during calculations, I would like you to tell me if I got the four-point vertex of the quartic interaction with a multiplet of complex scalar fields right: $$ L = (\partial_\mu \Phi)^\dagger (\partial^\mu\Phi) - m^2\Phi^\dagger\Phi-\lambda(\Phi^\dagger\Phi)(\Phi^\dagger\Phi),$$ where $\Phi= (\phi_1,\ldots,\phi_N)$ and $\phi_i$ are complex scalar fields. I have $$-2i\lambda ( \delta^{ik}\delta^{jh} + \delta^{ih}\delta^{jk}),$$ where $i,j$ are the indices of the two $\Phi^\dagger$, while $k,h$ are the indices of the two $\Phi$. Is it correct?


title: Is there a "covariant derivative" for conformal transformation?

text: A primary field is defined by its behavior under a conformal transformation $x\rightarrow x'(x)$: $$\phi(x)\rightarrow\phi'(x')=\left|\frac{\partial x'}{\partial x}\right|^{-h}\phi(x)$$ It's fairly easy to see that the gradient of the field doesn't have this nice property under the same transformation, it gets a non homogeneous term. Still, is it possible to construct a derivative that would behave nicely under conformal mappings and give the usual derivative for Lorentz transformations? By adding a "connection" similarly as what is done in general relativity or gauge theories. And if not, why?


title: Why Planck scale is so important?

text: I know that Planck scale is the scale where both, gravity and quantum effects are relevant simultaneously. Are there more reasons?


title: Air pressure in balloon

text: I have to calculate the air pressure inside of an hot air balloon. After some searching I found out that I can use the ideal gas law: PV = nRT (from Wikipedia) So to get the pressure in the balloon I would have to know n, which is the amount of gas in moles. For that amount I'm currently using the pressure (kg/m3) * the volume. So for the pressure I need the pressure which of course doesn't work. Is there a way to calculate this? Right now I do know the normal air pressure (outside of the balloon) volume of the balloon etc. etc., but I can't know the weight of the amount of air in the balloon, because I use the pressure to calculate it. One thing to note is that it isn't an actual hot air balloon. It's just one made up from physics formulas in a program that calculates them every 0.1 seconds (for example) for me. Is there some thing I'm missing?


title: Properties of Lorentz transformation generator?

text: In chapter 2 of Srednicki, the author defines: $$ U(1+\delta \omega) = I +\frac{i}{2h}\delta \omega_{\mu \nu} M^{\mu \nu} $$ where the $M^{\mu\nu}$s are hermitian operators and are the generators of the Lorentz group. Starting with the assumption that $$ U(\Lambda)^{-1} U(\Lambda') U(\Lambda) = U(\Lambda^{-1} \Lambda' \Lambda) $$ and letting $$ \Lambda' = 1 + \delta \omega', $$ the author is able to conclude (in his solutions) that: $$ U(\Lambda)^{-1} (I + \frac{i}{2h}\delta \omega_{\mu \nu} M^{\mu \nu})U(\Lambda) = I + \frac{i}{2h}\delta \omega_{\mu \nu} U(\Lambda)^{-1} M^{\mu \nu} U(\Lambda) $$ and $$U(\Lambda^{-1}( 1 + \delta \omega') \Lambda) = I + \frac{i}{2h}\Lambda^{-1}\delta \omega_{\mu \nu} \Lambda M^{\mu \nu}.$$ Can someone explain how he came to this conclusion? What properties of $\omega$ and $M$ allow the $\omega$ to move to the left of the $U(\Lambda)$?


title: Killing vector argument gone awry?

text: What has gone wrong with this argument?! The original question > A space-time such that $$ds^2=-dt^2+t^2dx^2$$ has Killing vectors > $(0,1),(-\exp(x),\frac{\exp(x)}{t}), (\exp(-x),\frac{\exp(-x)}{t})$. > > Given that $$\dot x^b\frac{\partial}{\partial x^b}(\dot x^a\xi_a)=0 > \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(*)$$ where $x^a=(t,x)$, $\dot x^a$ is the > tangent vector to a geodesic and $\xi^a$ is a Killing vector, then > $$a\exp(x)+b\exp(-x)+c\frac{1}{t}=0$$ where $a,b,c$ are constants. So I tried directly using $(*)$. What I got are $$t\dot t\dot x=0\\\ \exp(x)(2\dot t\dot x+t\dot x^2)=0\\\ \exp(-x)(2\dot t\dot x-t\dot x^2)=0$$ for each of the Killing vectors given. (Right so far?) Then multiplying the last 2 equations by $t$ and using the first equation, I get $$\exp(x)t^2\dot x^2=0\\\ -\exp(-x)t^2\dot x^2=0$$ So any linear combination of the 2 LHS's must vanish, giving $$\alpha\exp(x)t^2\dot x^2+\beta\exp(-x)t^2\dot x^2=0$$ for arbitrary constants $\alpha,\beta$. Either I have gone wrong somewhere, or somehow we must have $$t^2\dot x^2=1+\frac{\gamma}{t}$$ Unfortunately, I can't see why it is so. Any insight? Thanks.


title: Is it 11% hotter today than it was yesterday?

text: Yesterday the temperature outside was **0.5 °C**. Today, the temperature is **30 °C**. 30 is **5300%** more than 0.5, but today is obviously _not_ 5300% hotter than yesterday. In Fahrenheit, the temperatures are **33 °F** and **86 °F** , respectively. **160%** hotter sounds more reasonable, but this argument uses the same logic as Celsius, just on a different scale. Converting these temperatures to Kelvin, we get **273.70 K** and **303.15 K** , respectively. Since Kelvin is an _absolute_ scale of temperature, can we correctly say that today is **11%** hotter than yesterday? Since temperature is relative, can we also claim that there is _11% more heat today_?


title: Viscous force in a conductor

text: I was told that in a conductor there is a dissipative force and if Ohm's Law is valid for a component, the component has to be dissipative. I'm trying to prove it, but I have some problems. I know that for a viscous force: $$\tag{1}\mathbf {F}=m\mathbf {a}=-\gamma \mathbf {v}$$ so $$\tag{2}\mathbf {a}=\frac{-\gamma \mathbf {v}}{m}$$ and in a conductor (considering the motion of electrons): $$\tag{3}-e\mathbf {E}=m\mathbf {a}$$ so $$\tag{4}\mathbf {a}=\frac{-e \mathbf {E}}{m} $$ Considering the drift velociy given by $$\tag{5}\mathbf {v_d}=\frac {-e \tau}{m}\mathbf {E}$$ I could find $\mathbf {E}$, put it in (4) and obtain an acceleration in function of $\mathbf {v}$. So I could say that I'm treating a viscous force. But I'm not sure that this is a correct way... How could I verify that if Ohm's Law is valid for a component, the component has to be dissipative?


title: How does time dilate in a gravitational field having a relative velocity of v with the field?

text: Consider a Mass on earth. The time dilation on the surface of Earth is $$T' = T \sqrt{1 - \frac{2GM}{rc^2}}$$ Now if the mass is moving around the earth at velocity of v w.r.t Earth, what will be the time dilation within the mass as seen from the Earth? The object could be in free fall, orbit or in an escape velocity orbit away from the earth Is it $$T'' = T' \sqrt{1 - \frac{v^2}{c^2}}\space - (2)$$ or $$T'' = T \sqrt{1 - \frac{v^2}{c^2}}\space - (3)$$ if answer is (2) equation is $$ T'' = T\sqrt{(1 - \frac{v^2}{c^2})({1 - \frac{2GM}{rc^2}})}$$


title: Forward-scattering off a potential well

text: In his book, James Binney writes the following: ![James Binney, David Skinner - The Physics of Quantum Mechanics](http://i.stack.imgur.com/Szr8S.png) My question is what is the meaning of this expansion as $1+T$? I say this because you don't tend to consider the possible "paths" that a particle takes when solving simple eigenstate problems like this. The only other place where we talk about such a thing I can think of is Feynman path integral kind of things. Is this interpretation related to that?


title: Collision of a heavy charged particle with an electron at rest - Deduction

text: When I was studying Nuclear Physics I saw this formula about interaction of radiation with matter. The book mentioned that when considering a elastic collision of a heavy charged particle of mass $M$ with an electron (initially at rest) of mass $m$ the kinetic energy loss for the charged particle is given by: $$ ∆T = T \frac{4m}{M} $$ I tried to understand where this expression came from using simple knowledge of collision mechanics (kinetic energy and linear momentum conservation), but I can't. Can someone help me finding where this expression came from? Thanks in advance. Note: I found this formula on "Introductory Nuclear Physics" by Kenneth S. Krane


title: $\Delta T$, temperature units. How to use fahrenheit in this formula

text: To calculate the power in a fluid with a flow, the following formula is applied: $$P = \Delta T \rho c_p \times flow$$ $\Delta T$ can be entered as both Kelvin and Celsius. But what if I want to use Fahrenheit? Is there any formula for this? Reason is I'm making a web application that calculate some stuff. I have full unit support. I live in Europe so we always use Celsius or Kelvin. But, are americans using fahrenheit for calculations in general? If not, then maybe I can skip it all together.


title: What is the Correlation Between Solar Wind Velocity/Density and Sunspot Count?

text: We have the Advanced Composition Exporer (ACE), which orbits in the L1 libration point as a source for solar wind velocity and density (particles/cm^3) data. Typically, at a velocity in the range of 400 km/s, it takes about 4 days for solar wind changes to reach ACE. Measured solar wind velocities and densities tend to change from moment to moment. Official sunspot counts are obtained from Earth-based telescopes and change much more slowly. > From casual observation, there appears to be a positive correlation between > solar wind velocity and density with sunspot count. Can anyone please gve me > a reference that addresses this topic?


title: What is the orbital path of Omega Centauri?

text: I was under the impression the only objects relatively close to our Milky Way but not _yet_ a part of it were the Sagittarius Dwarf and Large and Small Magellanic Clouds and then much further out, but otherwise relatively close, the rest of the Local Group. I was reading _Florin Andrei's answer to Do all the individual stars that we can see in the night sky belong to Milky Way?_ and was confused about the facts of Omega Centauri. Upon researching more, I became more confused:   * The Wikipedia article _Local group_ is helpful. Although it is very basic, it may answer my question, as I don't see Omega Centauri (NGC 5139). I'm thinking it is a part of the Milky Way and not the Local Group. It only lies 16,000 light years away.   * Wikipedia article _Omega Centauri_ says _" **Orbiting** the Milky Way, [Omega Centauri] is..."_   * _Astronomy Picture of the Day, 2002-04-16, Millions of Stars in Omega Centauri_ states _"[Omega Centauri] is the largest ball of stars **in** our Galaxy."_ I hope that outlines my confusion... My **question** , then: What is the orbital path of Omega Centauri (illustrations or animations would be appreciated)? Is it in or a part of our galaxy or orbiting externally more like the Magellanic Clouds? EDIT: As seen in the comments below; I see how the second part to the question may be ambiguous. So, please focus on the first part of the question (What is the orbital path). No speculation please, only fact; especially when talking about what Omega Centauri may have been in the past.


title: What type of Radiation hits Europa

text: I was recently reading the Wikipedia Page for Europa as I am interested in terra-formation. In one of the sentences, it says that: > The radiation level at the surface of Europa is equivalent to a dose of > about 5400mSv (540 rem) per day,[32] an amount of radiation that would cause > severe illness or death in human beings exposed for a single day.[33] I know that there are different types of radiation (gamma rays, visible light, infrared, etc.) and was wondering, _what is the makeup of the radiation which hits Europa?_


title: Voyager 1 cosmic ray strips

text: In the last months Voyager 1 has experienced a dramatic drop in the cosmic ray radiation, which was been exceptionally uniform for the last 10 years, except for the past july 28 and august 14 events, when the radiation suddenly had big drops. After each of those events, the radiation temporarily went back to normal, until we reach september, when the radiation seems to drop for good to the real galactic background Astrophysicists think this suggests a ribbon-like structure distribution. Is it conceivable that there is a first order phase transition in the magneto- plasma medium, in which we are seeing the Voyager crossing in and out of the interface boundary? What else could keep the two separate regions of different order so well-differentiated from each other?


title: What are fields?

text: I'm following my first course in field theory and the professor began, like many books do, by introducing the scalar field. However, I am a bit hesitant about the physical idea of fields. My question is: what is the physical meaning of the fields? Why they are introduced? I read the introduction of the books of Peskin and Weinberg but I'm not satisfied.


title: Forces: why are the theta's equal?

text: I found this figure in my physics book, the task says that the incline got a angle of theta. How do figure out that the gravity and the y-axis got the same angle as the incline? There is no explanation of this in the chapter of the book. ![Theta](http://i.stack.imgur.com/ZVa9Y.jpg)


title: Definition and difference between the R-symmetry and the $U(1)_R$ internal symmetry

text: * For a general ${\cal N}$ the R-symmetry group is $U({\cal N})$ but for the ${\cal N}=2$ case why is it $SU(2)$ ? I guess it is again different for ${\cal N}=4$. How does one understand this? One denotes the generators of the R-symmetry group by $B^i$ and let $\alpha$ be the spinor index and let $a,b$ be the R-charge indices in a ${\cal N}=2$ theory. Then one writes the defining equations as, $[Q_{\alpha a}, B^i] = -\frac{1}{2} (\tau ^i)_a ^b Q_{\alpha b}$ and $[\bar{Q}_{\dot{\alpha}}^a, B^i] = \frac{1}{2} \bar{Q}_{\dot{\alpha}}^b (\tau ^i)_b ^a$   * But it is not clear to me as to why over and above the aforementioned equations there should be yet another charge $R$ (called the $U(1)_R$ charge) with the defining equations, $[Q_{\alpha a},R] = Q_{\alpha a}$ and $[\bar{Q}_{\dot{\alpha} a}, R] = - \bar{Q}_{\dot{\alpha} a}$ I would like to know why the above charge should exist in ${\cal N}=2$ supersymetry separate from the R-symmetry. Is there an analogue for this $R$ for other values of ${\cal N}$ ?   * Typically this R-charge as defined above is anomalous. How does one see that? Also what is the analogous statement for R-symmetry?


title: Light waves and Schrödinger probability waves

text: Ok, bearing in mind that I only have a brief understanding of quantum mechanics (no formal education, only from reading about concepts in books), so I could be way off here, I have a question regarding probability wave functions and light waves. From my understanding, every particle of matter has a probability wave which fills the entire universe, that's to say the only reason a particle in my fingernail is in my fingernail is because that's where the highest probability of it being is (with the chance that it's anywhere else in the universe being infinitesimally small), so my question is what is a light wave? Also from my understanding, a light wave is simply a probability wave for the location of a photon, and only upon observation does that wave collapse and does the photon 'take on' a definite position in space, so if I compare a particle of matter to a particle of energy (a photon in this case), how come the particle of matter has a probability wave that fills the entire universe, and the photon have only a small defined wave which virtually makes up a straight line in space? Is the light wave just an area (straight line?) of space where the probability is magnitudes higher than everywhere else and the photon's probability wave is still permeating the rest of the universe, or is the photon's location _definitely_ somewhere in the area of space defined by the light wave? For example, could a photon that's part of a laser beam ever interact with a photon from a laser beam travelling parallel to the first beam? (Disregarding any other physical theories that could cause the two beams to converge through other means, I'm wanting to stay on the topic of Schroedinger probability waves) I might well be completely misunderstanding/mixing concepts here, so that might be the reason for my confusion, if so, please enlighten me!


title: How to calculate fuel consumption of car (mpg) from speed and accleration knowing mass, drag coeff and rolling resistance?

text: How can I calculate the current (instantaneous) mpg of my car if I know the speed and acceleration of the car? From reading various answers for the "car going level or up/down hill" question asked earlier by someone, I understand there are 4-5 factors to consider:   1. Rolling resistance (how do I get or calculate this value for my make/model?)    2. Engine resistance (how do I get or calculate this value for my make/model?)    3. Air drag coefficient (assume I know this)    4. Mass of car (assume I know this)    5. "Power curve" of car? What is power curve? Do I need to know this? How do I get or calculate this?    6. Slope of road (assume level for simplification)


title: The Interactions of Light and Matter

text: So basically, I was trying to find a good answer to the question of how light interacts matter. Namely on the quantum level what causes matter to appear transparent, reflective, opaque, etc I came upon the answer with respect to transparency here, but I feel that the concept isn't fully explored here and that something is missing (particularly in the coloured light talk). The jist is that light passes through some matter because the energy gap between the matter's electron's low and excited state exceeds the energy of the photon, and thus the light is not absorbed and the photon passes through the matter. Could someone provide more detailed information about transparency, and information about reflection etc. So I guess for the purposes of forming this into a question I'll simply ask why some materials reflect light and look like mirrors while other materials reflect light with less precision? (thought I get the feeling it has similarly to do with basic mechanics and the regularity of the electron distribution)


title: How efficient is the human body?

text: This question sort of comes to mind when hearing how efficient an internal combustion engine is turning chemical energy in mechanical energy (something like 20-40%) with lots of excess heat. As an analog, how efficient is (or potentially) the human body at turning food into energy? Please bare with me, I realise there LOTS of different variables (how much the person weighs vs mass, metabolism, diet, etc). But I would imagine that there shouldn't be much margin of error given that most people maintain the same constant temperature (98 F +/- 1 degree).


title: WKB method of approximation

text: Would it be legitimate to use the WKB approximation for a particle in a spherically symmetric Gaussian potential? $$V(r)~=~V_0(1-e^{-r^2/a^2}).$$ I'm not sure when to use which approximation method. Variational, perturbation, or WKB. Can anyone enlighten me? What are the "rules" to using WKB? I'm given the particles $n$ and $\ell$ quantum numbers and I'm trying to approximate its energy.


title: Wavelength comparison of two waves

text: Is there any non-digital (naturally existing) mechanism to compare two or more waves in such a way:               Input 1           Input 2          ....            Output     -------           --------         ....          ------------     Lower             Higher           ....          Lower/Higher     Wavelength        Wavelength       ....          Wavelength      ... some kind of selectively permeable membrane which allows one wave to pass- through? Pardon my poor physics knowledge. I don't have a clue; would it be related to wave theory, applied physics or applied optics?


title: Can an Electromagnetic Gauge Transformation be Imaginary?

text: The Hamiltonian of a non-relativistic charged particle in a magnetic field is $$\hat{H}~=~\frac{1}{2m} \left[\frac{\hbar}{i}\vec\nabla - \frac{q}{c}\vec A\right]^2$$. Under a gauge transformation of the magnetic potential: $$\vec A ~\rightarrow~ \vec A + \vec\nabla \chi,$$ the wavefunction of the particle transforms as $$\Psi~\rightarrow~ \Psi\exp(\frac{iq\chi}{\hbar c}).$$ When $\chi$ is real, the wavefunction simply gains an extra phase factor. However, when $\chi$ is imaginary, there is a measurable change to the wavefunction. This seems to contradict the fact that the magnetic field is invariant under the gauge transformation. How do I resolve this?


title: In a Sterling Engine, does heat from the hot side transfer to the cold side?

text: A Sterling Engine is a closed system. The "hot" side oscillates between higher temperature with higher pressure and lower temperature with lower pressure. Does Nature switch back and forth between one temperature/pressure combination and another temperature/pressure combination without loss of energy within the closed system? The International Sterling Engine Society says they can get 60 Watts from a 50 degree temperature differential. Is there the equivalent of 60 Watts of power pulled from the hot tank? If not, where does the 60 Watts come from?


title: Have red shifted photons lost energy and where did it go?

text: I think the title says it. Did expansion of the universe steal the energy somehow?


title: kinetic energy in collisions

text: We were hoping you could help us understand collision energy. Vehicle $ A $ is driving West at $35\space mph$ and weighs $ 1437 \space kg$. Vehicle $ B $ is driving North at $35\space mph$ and weighs $1882 \space kg$.   Vehicle $ B $ crashes into the side (frontal) of vehicle $A$. What is the amount of energy absorbed into Vehicle $ A $? What is the difference in kinetic energy if vehicle $ A $ is stopped? Any help you could give us in understanding the physics of collisions would be wonderful. What effect does it pose upon the engine compartment and components?


title: An analogy for resonance?

text: I learned that the phenomena of resonance occurs when the frequency of the applied force is equal to the natural frequency of an object. At this point, an object vibrates with maximum amplitude.   1. How can a force have a frequency? My teacher used the analogy of pushing a child on a swing. The person who pushes should apply a force of the same frequency of the swing (I didn't really get that).   2. Following the analogy, what if the person pushes harder, wouldn't the "amplitude" of the swing be larger... I mean is there any such thing a "maximum amplitude" for a vibrating object as I can always increase the magnitude of the force.   3. Do all objects always vibrate with some kind of frequency? I mean if I put a speaker in front of a goblet and produce a sound having a frequency equal to the "natural frequency", it will just start vibrating with maximum amplitude? I know I asked a lot of questions at once but I am really confused about this phenomena and just cannot get the intuition behind it.


title: electrostatic potential, analytic properties

text: An electrostatic potential associated with some delocalized charge $\int \rho(\mathbf{r}) d{\mathbf{r}}$ is given by: $$v_H(\mathbf{r}) = \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}d\mathbf{r'}$$ This potential is finite at $\mathbf{r}=0$. Since $\frac{1}{|\mathbf{r}-\mathbf{r'}|}$ is a solution to a singular Poisson's equation, we can show that: $$\nabla^2v_H(\mathbf{r})=-4\pi\rho(\mathbf{r})$$ where $\rho$ is a smooth function being finite everywhere. Would a function $$v(\mathbf{r}) = \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|^n}d\mathbf{r'}$$ (where $n$ is some nonnegative integer) be also finite at $\mathbf{r}=0$? In this case, $\frac{1}{|\mathbf{r}-\mathbf{r'}|^n}$ does not represent a solution to Poisson's equation ($\mathbf{r} \in \mathbb{R}^3$) and the above analysis is not valid.


title: How to be sure that a He-Ne laser light is monochromatic

text: How can I be sure that the emission of a He-Ne laser contains only one single mode of laser cavity? The only thing that I know is that if I use a diffraction grating and the light isn't monochromatic, I'll see maximums of the same order $m$ at different angles, but I also know that if wavelengths are very close I may not see them. I have to mind the resolutive power of the grating ($R=mN$). If N1=1000 lines/mm and N2=500 lines/mm and the grating paces are D1=10^-6 m and D2=2*10^-6 m, will I see different maximums if the light isn'tmonochromatic? Do you know other ways to know if the light of a He-Ne is monochromatic?


title: Potential of a charged disc brought above the z=0 plane at an arbitrary point

text: Potential of a charged disc can be obtained easily. If we want to calculate the potential at an arbitrary point we should just write: $$ \phi(z_0)=\frac{\sigma z_0}{2\epsilon_0}\biggl(\sqrt{1+(\frac{R}{z_0})^2}-1\biggr) $$ $$ \phi(r)=\frac{[\sigma r]}{2\epsilon_0}\sum_{0}^{\infty}(-1)^n\frac{(2n-3)!!}{(2n)!!}(\frac{R}{r})^nP_n(cos\theta) $$ Now we have a charged disc with uniform charge density $\sigma$ and radius $R$ that is brought upward with $b$ along the $z$ axis. I want the potential of this system at an arbitrary point not necessarily on $z$ axis. ![enter image description here](http://i.stack.imgur.com/tL9IR.png) Jackson 3th Ed Page 63 Jackson has an example for a ring above the $xy$ plane. Can we use ring and integrate from it to have a disc. I tried but it was not straightforward. Any help would be appreciated.


title: Stress analysis of a cantilever beam using FDM

text: I am a CSE researcher with a not so in depth background of physics. As a part of my research in object modelling, I am trying to computationally figure out the stress for various objects by using Finite Difference Method (not FEM which is the defacto standard for stress analysis). The reason for this has to do with the other part of my research. Anyhow I have written and solved the 3D elastostatic Lame equations and calculated the Von Mises stress. This is the problem I am facing : When I am doing this for a 2D beam, the stress is calculated correctly. The Stress gradually decreases from the hinge point to the other parts. But in 3D the calculations are not correct as I am seeing the maximum Von Mises stress only in the middle portion of the beam instead of at the starting. I am only considering the weight of the grid cell at each grid point for the external force. (in the Z direction). The displacements at the hinge points are all 0. My question is : What changes in the stress computation of a cantilever beam between a 2D and a 3D formulation. Or am I ignoring some reactive forces which are of importance in 3D that is likely causing the maximum mises stress to shift to the center of the beam. (Of course it is entirely possible that my code is wrong but in that case it should have given haywire results for 2D case also). If my question is not clear, I can supply as many details as required. Any inputs will be greatly appreciated.


title: I reached a result concerning displacement with quantized time intervals. Am I on to something?

text: A few days ago, I realized a similarity between distance with constant acceleration, $d = v_i t + 1/2 a t^2$, and the sum of integers up to n, $(n^2 + n)/2$. This came up again today when I decided to work out some formulas for distance and velocity with constant acceleration updated at discrete intervals, as happens in physics simulations I've programmed. > Discretely incremented $v$ and $x$ with constant acceleration, $v_i = 0$ > >   * Add $a\mathrm{d}t$ to $v$ every tick >   * Add $v\mathrm{d}t$ to $x$ every tick > > > $$\begin{align} v_f &= a\mathrm{d}t + a\mathrm{d}t + a\mathrm{d}t + \cdots > \\\ x_f &= v_1\mathrm{d}t + v_2\mathrm{d}t + v_3\mathrm{d}t + \cdots \\\ v_2 > &= (a\mathrm{d}t) + (a\mathrm{d}t) = 2(a\mathrm{d}t) \\\ v_n &= > n(a\mathrm{d}t) \\\ x_f &= (a\mathrm{d}t)\mathrm{d}t + > 2(a\mathrm{d}t)\mathrm{d}t + 3(a\mathrm{d}t)\mathrm{d}t + \cdots \\\ x_n &= > \sum_{i=0}^{n}i(a\mathrm{d}t)\mathrm{d}t = \frac{n^2 + > n}{2}(a\mathrm{d}t)\mathrm{d}t \\\ n &= > \left\lfloor\frac{t_\text{total}}{\mathrm{d}t}\right\rfloor \\\ x_f &= > \frac{1}{2}\Biggl[\biggl(\frac{t_\text{total}}{\mathrm{d}t}\biggr)^2 + > \frac{t_\text{total}}{\mathrm{d}t}\Biggr](a\mathrm{d}t^2) = > \biggl(\frac{t_\text{total}^2}{2\mathrm{d}t^2} + > \frac{t_\text{total}}{2\mathrm{d}t}\biggr)(a\mathrm{d}t^2) \\\ x_f &= > a\mathrm{d}t^2\times\frac{1}{2}\times\frac{t_\text{total}^2}{\mathrm{d}t^2} > + \frac{1}{2}a\mathrm{d}t\frac{t_\text{total}}{\mathrm{d}t} \\\ x_f &= > \frac{1}{2}at_\text{total}^2 + a\mathrm{d}t\frac{t_\text{total}}{2} \\\ > \lim_{\mathrm{d}t\to 0} &= \frac{1}{2}at^2 = \text{normal $v_f$ equation > where $v_i = 0$ and $\Delta a = 0$} \end{align}$$ I'd like to know what relations to theory this or an idea like it has if any, and if it touches on anything else.


title: How do I know the position of some mass in space (starting at rest) over time when applying earth's gravitational force to it?

text: I know how to use Newton's law of universal gravitation. But I'm not sure where to go from there. This is for my understanding while working on a game. I'm not trying to do anything fancy here.


title: plotting an sRGB gamut Chromaticity Diagram starting with xy coordinates

text: Starting with `xy` coordinates I would like to plot a chromaticity diagram displaying just the sRGB gamut portion of the CIE xy chromaticity diagram. For each `xy` coordinate of my diagram I need to determine the corresponding `Y` value to obtain the complete `xyY` representation, from which `XYZ` tristimulus values can be calculated and finally `sRGB` values derived. By starting with the known sRGB `Red`, `Green`, `Blue` and `white` values: `#FF0000`, `#00FF00`, `#0000FF`, `#FFFFFF` respectively I can use the Bradford matrix to deduce their `XYZ` tristimulus values and thus their `xyY` representations. But starting with `xy` coordinates is there a method for determining the `Y` component? ps. If you are able to add new tags, could you possibly add some tags like 'colorimetry', 'chromaticity-diagram' and 'color-models'?


title: What are the optimal conditions to fuel your car?

text: I was filling my car earlier today, and noticed a sticker posted on the pump. > This pump dispenses fuel at a volumetric amount measured in standard gallons > (231 cubic inches). It does not adjust for temperature, or other factors > that may affect the energy content of each gallon. This got me thinking.   1. What would be the optimal conditions to fuel your car so that you can get the most energy per gallon? Let's assume we measure this in miles per gallon achieved traveling at 60mph in a standard car that advertises 30mpg; a Honda Civic, perhaps.   2. Why would temperature affect the energy of each gallon?


title: Could the chemical potential of a Bose gas be zero?

text: Could the chemical potential of a Bose gas be zero ? If it was the case, we will have an infinite number of particles in the ground state ! No ? But I've heard that for $T < T_c$, $\mu = 0$, so I don't understand...


title: Meissner Effect for Type-II Superconductors

text: I was wondering whether the breakdown field strength for the Meissner effect may be attributed to the Zeeman effect? I can see the latter (along with the Stark effect) to be more analogous to electron screening but would the effect on the density of states due to the reduction of degeneracy have any correlation to the critical field strength that puts a type II superconductor into the phase with quantized vortices?


title: Why does the spotlight reflected off of a rectangular mirror tend to become circular?

text: **Background and setup** When I was 12 I used to like a girl, we were almost neighbors and it was essential that our parents don't find out. So whenever one of us wanted to call the other they'd signal the other person with a mirror so they get ready near the phone to answer before anyone else in the house. Here's the setup:   * I lived in A, she lived in B.   * I used a rectangular-shaped mirror. ![Setup](http://i.stack.imgur.com/XNwoa.png) **The observation**   * Case A: When I reflected the light to a close surface, like the small wall in front of me on building A, I saw a spot light that looked like this: ![Spotlight_A](http://i.stack.imgur.com/pqtu1.png) Which was exactly what I'd expect.   * Case B: When I reflected the light to a further target, building B, the spotlight was also rectangular but with much smoother corners: ![Spotlight_B](http://i.stack.imgur.com/VV2Tx.png)   * Case C: This is when I thought it's interesting. When I reflected the light to an even further target, building C, the spotlight looked almost like a circle: ![Spotlight_C](http://i.stack.imgur.com/cYFMk.png) **Question** Why did that happen? shouldn't it stay a rectangle? and even if it had to change, why a circle?