title: The Z-Torque: how can it be shown intuitively that it does not work?

text: There is a new kickstarter project that claims to increase torque and power compared to a normal crank on a bicycle (Z-Torque on kickstarter). If this patented (US Patent Number 5899119) approach works it would be a revolution for personal transport. ![enter image description here](http://i.stack.imgur.com/TWcjx.jpg) The idea behind this is that a Z-shaped crank should allow somehow better leverage compared to a straight crank. There are quite a few comments that this should not work as intended but as in a lot of cases it sounds plausible at first but it is incompatible with physics. As the inventor and some of the supporters are convinced that this actually works I am looking for a clear and simple argument why this is not possible. Using vectors and cross products ($\tau = \vec{r}\times\vec{F}$) this is easy to show but can it be shown with as few abstractions as possible?


title: Can we make a Maxwell's Demon using Quantum Computers?

text: Although I'm reasonably sure that quantum computing advances will _not_ lead to the ability to construct a machine that globally violates the 2nd law of thermodynamics, it feels like a difficult position to defend when I see things like this: http://www.flickr.com/photos/jurvetson/8054771535 ![Rose's Law](http://i.stack.imgur.com/wXAlH.jpg) (summary: an alternative to Moore's law that predicts basically unbounded growth is computing ability) There's a proviso with this, while quantum computers could solve _problems_ that would take a classical computer almost forever, it can't solve _all_ problems. Wikipedia helped clarify this for me: ![problems quantum computing can solve](http://i.stack.imgur.com/7ljS9.png) (BQP are problems solvable by quantum computers with polynomial time) This image is to say, although quantum computers could solve every computing problem we have now and more, there are things it can't solve. But is THIS the reason we couldn't make a quantum computer into a Maxwell's Demon? My biggest problem with a 10,000 Qubit computer is the internal memory. The Landauer limit dictates that any given memory transition must expend at least $k T \ln 2$ of energy to make the transition, otherwise it then violates the 2nd law. What is the "internal memory" analog to such a massively powerful quantum computer? Would it also be subject to this limit, or would the internal states, never actually existing in a way, circumvent it? So let me narrow the question, looking at the idea of Maxwell' Demon: ![Maxwell's Demon, Wikipedia](http://i.stack.imgur.com/kEuOT.png) Let's formalize this to say that we have some observable vector $\vec{y}$, that we get from sensors in the $A$ gas. We then take that information, process it, and apply the information to a decision vector $\vec{u}$, which in the above image is a single Boolean open/shut decision. What is the reason that we can not build this with a quantum supercomputer? My guesses are:   1. The internal memory switches would use energy, increasing global entropy (seems to violate the claims of quantum computing)   2. The particular type of problem can't be solved by quantum computers with sufficient efficiency (implying there exists a set of problems that could violate the 2nd law if solved with polynomial time)   3. The problem is irrelevant of _both_ memory and processing capability, as the sensors and the control input themselves require too much energy (seems this would trash certain explanations I've heard for why various Maxwell's Demons wouldn't work, in fact, it would seem to flagrantly ignore the principle behind the Landauer limit) As you can see, none of my explanations are consistent. Is the universe big enough for both superpowerful quantum computers and the 2nd law?


title: Symmetries & Lie groups in physics

text: This is not a homework, neither it is any exercise. It is my understanding of $U(1)$ symmetry. I would request if anybody can please correct me on any one of the following understandings:   1. The bottom line of particle physics is Lagrangian density which is a generalization of classical mechanics, $L= V-T$.    2. We come across lot of symmetries in nature which are invariant under any changes made. Like an equilateral triangle is more symmetric than other triangles...... For a symmetry, if the object is rotated or flipped, the appearance will remain unchanged.   3. But when we label a symmetry, we could differentiate it which is something called 'symmetry breaking'.   4. $U(1)$ is a Lie group. Now, typically if a circle is rotated, flipped, it appears the same, called Lie group.   5. There are different type of symmetries like (i) Translational --> Invariance of the laws of physics under any translation as pointed out in Noether's theorem (ii) Rotational -->Whichever direction you rotate it is the same (iii) Time symmetry --> the laws of physics are eternally unchanging (iv) Boost symmetry   6. The rotational and boost symmetry are grouped under Lorentz group. The translational, rotational and boost symmetry together make up the Poincare group.   7. Local symmetry is not a symmetry in physical spacetime.   8. When Einstein applied special relativity to electromagnetism, he found electromagnetic 4 potential-- the four vector (1 time like, and 3 space like, which relates the electric scalar potential and magnetic vector potential). The physicists were happy, as the electromagentic 4 potential appears in the Lagrangian density.   9. But the value of the electromagnetic 4 potential can be changed. The Electric field $E(t,x)$ and the Magnetic field, $B(t,x)$ can be expressed in scalar potential and vector field.The term gauge invariance refers to the property that a whole class of scalar and vector potentials, related by so-called gauge transformations, describe the same electric and magnetic fields. As a consequence, the dynamics of the electromagnetic fields and the dynamics of a charged system in a electromagnetic background do not depend on the choice of the representative $(A_0(t,x),A(t,x))$.   10. $U(1)$ being a circle. When the charged particle move across the $U(1)$ plane, its' mass, kinetic energy does not depend on the position of the particle. It's value depend on the rate at which it circles the plane.   11. This is the $U(1)$ symmetry of the standard model. If we rotate $U(1)$ at any angles, the Lagrangian density will remain unchanged. Please do correct me where I am wrong. Thanks.


title: Diffusion of probability amplitudes

text: Let's say I have a probability amplitude $\psi:\Sigma\rightarrow\mathbb{C}$ for some domain $\Sigma$ (so, $\psi$ satisfies $\int_\Sigma |\psi|^2=1$). **Is there a way to use $\psi$ as initial conditions for diffusion of probability values?** In particular, is there a PDE for computing a function $\psi_t$ with $\psi_0\equiv\psi$ such that the induced probability distribution $\rho_t=|\psi_t|^2:\Sigma\rightarrow\mathbb{R}^+$ satisfies the heat equation $\Delta_\Sigma\rho=\frac{\partial\rho_t}{\partial t}$ for Laplacian $\Delta_\Sigma$ (or any other diffusive equation)? This document seems to think that it might be an open mathematical question, at least for the "Anderson model" of diffusion (see e.g. conjecture (iii) on page 30), but I'm not sure if I am reading it properly. My hope was that it would be as easy as using the Dirac operator $D$ since it looks like the "square root" of the Laplacian in the right way, but apparently things aren't so easy! [This website has been _incredibly_ useful for me to get my bearings in this area of physics despite my total lack of background. I sincerely apologize for posting so many questions and really appreciate everyone's support!]


title: On the double slit experiment with 4 slits

text: I'm not a physicist nor a science savvy person, but I was wondering if this experiment was ever performed in a simultaneous fashion on screens with fixed references(marks) and firing different wavelengths particles. So, to recap, 4 slits, 2 emitters firing at different times (where the $\Delta T$ is known and certain) on two different screens. I hope this question is not too stupid. P.S. I'm sorry, I've been too vague. I ask this because I've recently learned that this interference pattern emerge even firing large atom clusters instead of single particles. This is astonishing and it's clearly stating that there's a limit in mass aggregation where it stops behaving in duality. Cause, you know, firing bricks will hardly produce interference. And, in the end, I was wondering if it's not possible that it's spacetime itself vibrating at a certain $f$ and if there's a limit when mass stop to be affected (relatively) by this vibration. Like pinning a vibrating rubber sheet. I'm so confused.


title: Simple Experiment to Demonstrate Special Relativity

text: I am trying to think of a good experiment that can be done for under $250 or so that would demonstrate some aspect of Special Relativity. Ideally this will be done in a few years with my kids when they were a bit older.


title: What will be the goal of (V)LHC after receiving upgrades?

text: If I understood correctly, the LHC will be shut down at the end of 2012 to prepare for the full-power, 14 TeV collisions in 2014. I also remember reading about a proposed luminosity upgrade some time in 2019 and also about a preliminary plan for VLHC, which should, when fully operational, achieve about 175-200 TeV. My question basically is, what are the goals after these upgrades? I know there's SUSY, but that's supposedly in reach of those 14 TeV collisions, so what experiments are set around the 200 TeV mark? Are we already reaching into the proposed "desert" between the TeV scale and GUT scale?


title: What is the relationship between distinguishability and probability in Quantum mechanics?

text: Firstly I am sorry for any awkward English expressions. Recently I'm reading "Feynman Lectures on Physics - Quantum Mechanics" and come to have a single question. In the book Feynman explains, "You must never add amplitudes for different and distinct final states". For example) in double slit experiment with two holes (hole 1, hole 2), if we call the probability amplitude of an electron through the hole 1 to an electron detector as Y1 and hole 2 as Y2, without any disturbing measurments such as a light, we can say, "the probability of electron to reach the detector is [Y1 + Y2]^2 ." and...... however with some light emitting device to distinguish which hole is taken by the electrons - in this case we can know the choice of electrons by photons - the probability of electron to reach the detector is not just [Y1 + Y2]^2 but [Y1]^2 + [Y2]^2. I do know that the difference between the results depends on the distinguishability of alternatives, but the problem is why distinguishability makes the results different. Why can't the probability amplitudes interfere if we can know which alternative is chosen? (Additionally, Feynman says, the probabilities of passing hole 1 and hole 2 are independent each other, but I cannot find any relationship between this mention and my problem.)


title: pattern of moving electrons in wire under AC

text: when we use a DC battery into a circuit the flow of electrons in wire creates a clear picture as they flow from negative terminal to positive terminal. under AC(Alternating current) we know how energy flows and what does it mean by $I_{rms}$ or average current etc. But what about the pattern in which electrons move?


title: Thermal gravitational radiation and its detection

text: To my poor knowledge on the topic, the gravitational waves that are most likely to be detected by LIGO or other experiments do not have thermal spectrum. But I'm not certain. I know that Hawking's radiation is thermal and it is partially make up of gravitational radiation. However, as far as I know (correct me), its detection is not possible in practice. I think that the gravitational wave background is thermal, but I have no idea about its direct or indirect detection. Will (Advanced) LIGO be able to say anything about this? Maybe the B modes of CMB can tell us something? Any information about possible sources of gravitational radiation with thermal spectrum will be welcome.


title: Can an electric motor force angular momentum not to be conserved in an isolated system?

text: An ice skater is in a spin, she pulls her arms in and she spins faster, she lets her arms extend outward and then she starts to slow down. She will probably weigh on a weigh scale about the same weight during this spin cycle. Now let us connect an electric motor to her to make her spin faster as she extends her arms outward. Would angular momentum still be conserved? It seems to me that it would not. Also would she still have the same weight? I think she will weigh less as she is being accelerated by the electric motor.


title: Why the breath sometimes warm and sometimes cold? (2 different explanations!)

text: If you blow air against your hand with your mouth open, you feel warm breath. If you do with with your lips closed except for a small opening, you feel cold breath. One explanation from here says "With your mouth open most of the air which reaches your hand has come out of your mouth. With pursed lips lots of cold air is entrained so the air reaching your hand is cold and moving quickly." Another explanation from Paul Hewitt video,(go to min 24:00), is that air comes out cold it because it expands coming out of small opening. So which explanation is right?


title: chirality oscillations in weak interaction

text: As far as I have understood, the mass $m$ of a fermion causes a coupling of the both chiralities $\psi_L$ and $\psi_R$. This coupling would induce an oscillation of the chirality within a time scale determined by $\frac 1 m$. Furthermore, it is known that the weak interaction only couples to the left- handed particles, i.e. only to $\psi_L$. Combining these two statements, one would have to conclude that the weak interaction of a massive fermion is time dependent, i.e. it is stronger when $\psi_L$ dominates and vanishes completely half an oscillation period later. However, I have never heard about such a strange phenomenon and I conjecture that there's a mistake in my reasoning somewhere. I'd be grateful if someone could help me find it.


title: Free 'fall' on an Inclined Plane

text: I guess we can say that two identical balls on the same inclined plane with different heigths reach the ground at the same time. So, who was the first one to observe it? http://www.sketchtoy.com/56474231


title: Conservation of angular momentum across different reference frames?

text: I saw the following problem from the USAPhO: > A uniform pool ball of radius $r$ begins at rest on a pool table. The ball > is given a horizontal impulse $J$ of fixed magnitude at a distance $\beta r$ > above its center, where $−1 \leq \beta \leq 1$. The coefficient of kinetic > friction between the ball and the pool table is $\mu$. Find an expression > for the final speed of the ball as a function of $J$, $m$, and $\beta$. Two solutions are presented. In the first solution, we are told to "consider an axis perpendicular to the initial impulse and coplanar with the table." Then we apply conservation of angular momentum momentum with the initial state immediately after the impulse and the final state after the ball has achieved rolling without slipping (and hence has constant velocity) From my understanding, at any given moment, the axis always passes through the point of contact between the ball and the ground. This is the part the confuses me. Since the axis is not fixed, why is angular momentum $\ell$ conserved between the initial and final states? I noticed that $\ell$ at some time when the ball is still rolling without slipping is not the same as the initial $\ell$. (If the ball has angular velocity $\omega$ at some time, then $\ell = I\omega$, which varies as $\omega$ varies.) I believe this is related to the fact that during the rolling without slipping phase, we are not in an inertial reference frame. (In particular, the problem is is USAPhO 2008 Quarterfinal, problem 2(a). You can find the problem and its solution here: http://www.aapt.org/physicsteam/2012/exams.cfm)


title: Drude theory of electrical conductivity

text: I was just trying to calculate the electrical conductivity for a Fermi-Dirac distribution and a Maxwell-Boltzmann distribution, and I ended up with the same result: $$\sigma=\frac{ne^{2}\tau}{m}$$ My question is, how come this is? Ending up with the same result even though it is different distributions?


title: Any physical example of an "explosive" differential equation $ y' = ky^2$?

text: I was told that in physics (and in chemistry as well) there are processes that may be described by a differential equation of the form $$ y' = ky^2. $$ That is, the variation of a variable depends from the number of **pairs** of the elements. I understand the mathematical meaning of that equation, but I cannot conceive of any physical process which leads to this. Maybe some nuclear reaction could, but I am at a loss. Any hints?


title: How the dielectric rigidity depends on the shape of material?

text: ![enter image description here](http://i.stack.imgur.com/4rJQ7.jpg) A research article says that, "The conical shape improves the dielectric rigidity", but how I am not able to understand.


title: Diodes (Forward biased)

text: Why does the width of the depletion region decrease,when the diode is forward biased?Is it because the ions have moved to p-junction,or n-junction? Please clarify.


title: What is Nanotechnology, basically?

text: Can someone elaborate Nanotechnology? Google has made me confused.


title: Infinite motion on a 3D curve

text: Suppose we had a curve defined by $$\underline{r}(s) = \alpha \cos(s) \underline{i} + \gamma s \underline{j} + \alpha \sin (s) \underline{k}$$ with $\alpha^2 + \gamma ^2 = 1$ and suppose we had a particle which originally was at the point $\alpha \underline{i}$, and the particle had initial speed $U$, I'm trying to figure out what the necessary conditions are for $U$ so that the particle keeps moving forever. I'm having quite a hard time picturing what's going on in 3D, i.e. how the particle moves, but I've made certain calculations such as the three Frenet- Serret formulas, but no idea how to proceed. Could someone please give me a hint on how I'd go about actually picturing the situation and hence solving the problem?


title: difference between battery and capacitor in urdu languege

text: ## Heading   1. List item   2. List item`enter code here` > Blockquote*emphasized text*


title: Electric potential is zero but non zero electric field?

text: What is the physical significance of such a point where electric field is non- zero but electric potential is zero? I mean, how can we understand this concept without mathematics?


title: Why should a holomorphic function be expanded in Laurent series rather than Taylor series?

text: In 2d free conformal field theory, there is an operator equation: $$ \partial\bar\partial\hat{X}^\mu\left(z,\bar z\right)=0 $$ Why can it have Laurent expansion like this below rather than Taylor $$ \partial X^\mu\left(z\right)=-i\left(\frac{\alpha'}{2}\right)^{1/2}\sum_{m=-\infty}^{\infty}\frac{\alpha_m^\mu}{z^{m+1}}, \\\ \bar\partial X^\mu\left(\bar z\right)=-i\left(\frac{\alpha'}{2}\right)^{1/2}\sum_{m=-\infty}^{\infty}\frac{\tilde{\alpha}_m^\mu}{\bar z^{m+1}}. $$


title: Inside a conductor?

text: My textbook says the field inside a conductor must be zero in order for the system to be equilibrium and therefore there must be no excess charge inside. Their proof: 1) Place a gaussian surface inside the conductor. Since the system is at equilibrium, all points on the surface must have an electric field of zero. 2) Therefore the net flux is zero, implying the charge inside is zero. 3) If there is no charge inside, all excess charge must lie on the surface. My problem: "Since the system is at equilibrium, all points on the surface must have an electric field of zero." Why? Consider an conductor with no excess charge. To simplify things, say the conductor consists of a 100 free electrons and a 100 ions of charge 1e+. The conductor is neutral and at equilibrium. Now consider the field on one specific electron. There a total of 99 other electrons and 100 ions. So there _would_ be a net field acting on that specific electron. So even though the system is at equilibrium, the net field on the individual particles is non-zero. So a system can be at equilibrium, even if the net field inside is non-zero. What am I misunderstanding? **Edit:** Another example: Consider a system consisting of one electron and one proton. If nothing is holding them back they will attract each other until they touch. After they touch, the force acting on them is still non-zero, yet they wouldn't accelerate.


title: Charge vs Charge Density in classical electrodynamics

text: What is assumed to be a more fundamental physical quantity in _classical_ electrodynamics. The charge density as a scalar field or the physical entity charge.


title: Non-symmetric Lorentz Matrix

text: I was working out a relatively simple problem, where one has three inertial systems $S_1$, $S_2$ and $S_3$. $S_2$ moves with a velocity $v$ relative to $S_1$ along it's $x$-axis, while $S_3$ moves with a velocity $v'$ along $S_2$s $y$-axis. So I constructed the Lorentz transformation by multiplying the transformation from 1 to 2 with the transformation from 2 to 3, and I obtain the transformation. Now, this is all nice and well, and it is also where the question for which I'm doing this stops. However, it made me think: the resulting Lorentz matrix is not symmetric! Somehow I always thought that they always were (simply because I hadn't encountered one that was not), which I suppose is naive. Is there any information inherent to the fact that the transformation is not symmetric? Does this in some way mean that there is a rotation happening? This is what seemed most plausible to me, as if you boost 'harder' in one direction than in the other, your axis is essentially rotating. Or am I going about this the wrong way?


title: Resources in space, and their distribution

text: I'm making a video game in which the economics of an interstellar civilization is important. What I'm wondering is, how are resources in space distributed? Since everything ultimately comes from stars, and everything past iron comes from supernovas, I assume an area with more stars blowing up would have more precious metals eventually condensing into planets. But do certain areas of the galaxy have more nova-capable stars? Would core-ward systems have more metals on them, since there's more stars closer together? Or would every planet in the galaxy have more or less the same loadout as any other? Would it only be possible to mine metals on planets that have water, since that's what makes metals condense into veins? Furthermore, are there any natural resources that might be found on alien worlds, or in space itself, that cannot be found on Earth? Would it ever be feasible or desirable to "mine" a nebula of its gasses? I've heard supposition of there being pockets of antimatter floating about; though that raises the question of how you're ever going to store the stuff.


title: Calculating Magnetic Field Magnitude and Direction?

text: I am trying to find the equation for calculating the direction and magnitude of $B$ and/or $H$ at a distance from a dipole magnet but my searches are proving impossible. So far I have found the calculation for the magnitude of $B$ of a single wire at distance $r$ and I know the direction is found with the right-hand rule but I cannot find anything to do with permanent magnets, in particular the vector quantity. I know the field will want to travel from the north pole to the south pole but the field doesn't take the shortest route, it has a sort of "trajectory" if you look at pictures? * * * Sod's Law I make this post then I found this: http://en.wikipedia.org/wiki/Dipole#Field_of_a_static_magnetic_dipole One thing I am unclear on is $\bf r$, which is: > $\bf r$ is the vector from the position of the dipole to the position where > the field is being measured What point on the dipole is this vector calculated from? The north pole, the south pole, the center of the dipole?


title: A bird problem and trains

text: So that the problem: > _There are 2 trains at speed of 30km/h in the same trail and opposite > directions and moving for a collision at 60km of distance of each other. One > bird in front of one of the trains fly at 60km/h toward of other train. When > he reaches he flies back to the other train until the trains collide._ I got a question: as the bird travels in all the way to the collision?


title: Quantum Mechanics: Creation and Annihilation operators

text: Is an eigenvector/eigenstate of the creation operator an eigenvector/eigenstate of the annihilation operator too? Why?


title: Photons from stars--how do they fill in such large angular distances?

text: It would seem that far-away stars are at such a distance that I should be able to take a step to the side and not have the star's photons hit my eye. How do stars release so many photons to fill in such great angular distances?


Explain the microscopic nature of Electric current?i.e What is is _average current_ and _Instantaneous current_? A microscopic view what really happens?


title: Value of of gravity 9.8m/sec^2 and centrifugal force

text: I had a doubt regarding centrifugal force on earth is not accounted in any equations as object falling towards earth.eg f=ma.i read questions asked by few about the same and got to a conclusion that value of g(9.8m/s^2) is a relative number derieved.but I still cant find it in gravitational force equation.why is that.or is my interpretation wrong.this might be a repetitive question. But please clarify.


title: free energy and entropy

text: my understanding of free energy and entropy is that as entropy of a system increases its free energy decreases. As sun has free energy and this energy is being converted to useful work, and its entropy is increasing. Its entropy will continue to increase till its material is exhausted to cease free energy production. Are permanent magnets source of free energy? Because of permanent dipoles they are magnetic and do they lose their orientation very slowly to become disordered and increase its entropy?


title: Do any other particles get excited(or absorb energy) by photons like electrons?

text: Electrons get excited to different energy levels when photons of specific frequencies fall on them.But, is there other particles which absorb the energy of the photons?


title: Double variation of Schwinger action principle

text: The Schwinger action principle is given by $$\delta_{1}\big\langle b\big|a\big\rangle= i\int_{t_{a}}^{t_{b}}\text{d}t\,\sum_{c,d}\big\langle b\big|c\big\rangle\big\langle c\big|\delta_{1}L(t)\big|d\big\rangle\big\langle d\big|a\big\rangle$$ where the state $|c\big\rangle$ is in time $t_c$ and so on.   Now we perform another variation $\delta_{2}$ which is independent of the first variation $\delta_{1}$ $$\delta_{2}\delta_{1}\big\langle b\big|a\big\rangle= i\int_{t_{a}}^{t_{b}}\text{d}t\,\sum_{c,d}\bigg[\bigg(\delta_{2}\big\langle b\big|c\big\rangle\bigg)\big\langle c\big|\delta_{1}L(t)\big|d\big\rangle\big\langle d\big|a\big\rangle +\big\langle b\big|c\big\rangle\big\langle c\big|\delta_{1}L(t)\big|d\big\rangle\bigg(\delta_{2}\big\langle d\big|a\big\rangle\bigg)\bigg]$$.   Tom D.J. writes (in the book "The Schwinger Action Principle and Effective Action" page: 345.) "Note that since the second variation in the structure of the Lagrangian is independent of the first, there is no term like $\delta_2\big\langle c\big|\delta_{1}L(t)\big|d\big\rangle$ in the above equation."   Could someone elaborate on this and maybe show with an example why this is true?      The closest I could think of was something of the lines "$\delta_{2}\big\langle c\big|\delta_{1}L(t)\big|d\big\rangle=0$ since if $\delta_{2}$ and $\delta_{1}$ are with respect to different functions this term will be zero. If they are variations of the same variables this will be of second order and will be ignored"


title: Why is Planck mass much larger than the smallest mass that we actually know about?

text: The three fundamental constants $h$, $c$ and $G$ are manipulated and rearranged in different ways to get the Planck time, Planck mass etc. The Planck time is said to be the smallest time possible and Planck length the smallest length(If I'm not mistaken). But, why the Planck mass doesn't fit to this list?


title: Which number should I suppose to $a$ (width of well) and $m$ (mass of particle) in potential well problem?

text: I tried to plot a complete of state functions of potential well problem but graph was so weird. I thought a cause was variables `a` and `m` were not consistent with scale of quantum world. For `m` i might be can guess but for `a` i have no idea. The wave function is:               Y(x) = Ax(x-a)      ,where a is width of well       How should i set `a` (width of well) and `m` (mass of particle)?


title: Lorentz transformed Scharwzschild solution

text: A question that has always intrigued me is: "Imagine a star moving as it evolves into a black hole, Ignore the effect of debris from the supernova. Assume also that before the collapse, the star was moving significantly. How precisely does the information that the star is moving propagate out? Especially the information on the change in the gravitational field." Now of course the first point is that once the mass collapses beyond the event horizon, we can no longer know that the mass is moving. However we can observe that the event horizon, and surface phenomena are behaving as though the contained mass is moving. Or maybe not, it could be that the event horizon becomes a static sphere, but that just doesn't feel right intuitively. In any event, the starting point of such an analysis would be to preform a Lorentz, transform on the Schwarzschild solution, and then perhaps study the normal-modes (?) of the resulting solution. Before I begin to do that, does anyone know if that has been done and "published"?


title: How damaging is light?

text: On _Surely You're Joking Mr Feynman_ , when talking about the Trinity test, the author states: > the only thing that could really hurt your eyes (bright light can never hurt > your eyes) is ultraviolet light. I got behind a truck windshield, because > the ultraviolet can't go through glass, so that would be safe, and so I > could see the damn thing. This is also clear in this video, where the glasses are seen as black by the UV camera. If that's the case, why are sunglasses said to `prevent bright sunlight and high-energy visible light from damaging or discomforting the eyes`? _(from Wikipedia)_ Is it for marketing purposes or was Feynman wrong?


title: extreme heat to extreme cold (define the endstate)

text: Contemporary cosmology frequently has space temperatures just after the 'big bang' in the regions of millions of degrees and with inflation and expansion of the universe this is now down to a couple of degrees above absolute zero, if the universe expansion is accelerating should we expect the universe to 'freeze' to a standstill. If not then what?


title: How can one (formally) determine the particle content of a free field theory?

text: Here's my question: Suppose I'm given a free field theory, where my fields are functions $\phi:\mathbb{R}^4 \rightarrow V$, and the equations of motion are a system of linear Lorentz-invariant differential equations (Given an action of Lorentz algebra on $V$). Is there a way of saying formally or abstractly what the 'particle content' of this field theory is? Ie, how many particles are there and what are there spins/masses? I should mention that I understand how to determine this empirically- One can often just 'look at the Lagrangian' and figure out what the kinds of particles there are and what their masses are. I'm looking for a more formal way of saying this.


title: What do you think about teaching Standard Model in school?

text: Here is a scan from an old Soviet textbook for school children: ![http://storage5.static.itmages.ru/i/11/0129/h_1296295703_dda36c65eb.png](http://i.stack.imgur.com/HCdJh.png) It shows the table of quarks and antiquarks of different generations, colours, spins. The book also includes similar tables of gluons and their interactions with quarks and between themselves. They all are coded in this fancy cake- shape code. The standard model table includes Z and W-bosons, gluons as well as graviton and gravitino. What do you think about such manner of teaching physics and in general, what do you think about appropriateness of teaching Standard Model in junior school? Some other images from the book (quark-gluon interactions, hadron decay): ![quarks-gluon interaction](http://i.stack.imgur.com/1NZlv.png)![decay of hadrons](http://i.stack.imgur.com/1OuOp.png) Illustration in a chapter about quantum parity: ![quantum parity](http://i.stack.imgur.com/mXrKX.png) Tha book has chapters about quantum chromodynamics, spontaneous symmetry breaking, quantum parity and so on.


title: Non-linear Schrödinger equation

text: I have read about the existence of a non-linear scrhödinger equation. What is its utility and application? And how can it be derived? Is it in a relativistic or non-relativistic context?


title: Paraxial rays and marginal rays question

text: Paraxial rays are found to focus far away the lens whereas marginal rays focus near to the lens, why? I didn't find satisfactory answer in my academic book..


title: Transmission of waves

text: How do you know if a wave will transmit when it hits a media boundary? Will a portion of the wave always be transmitted when a wave hits a media boundary? My textbook says part of the wave will be transmitted when the media boundary is neither free-end nor fixed-end.   It says a free-end reflection occurs when a wave is going from a slowed medium to a faster medium, and fixed-end reflection occurs when the opposite is true. How can a medium not be free-end or fixed-end? What is considered free-end, and what is considered fixed-end?


title: Does a perfect mirror behave the same as a blackbody radiator?

text: If I put a perfect mirror(i.e. reflects with no attenuation) next to a blackbody radiator its spectra should be the same as the blackbody radiator. Looking only at the spectra - is there any difference between a blackbody radiator and a perfect mirror? For instance, suppose the mirror is accelerating as in the dynamic Casimir effect - does the spectra change in the same way as the blackbody radiator?


title: Smoothness constraint of wave function

text: Is there anything in the physics that enforces the wave function to be $C^2$? Are weak solutions to the Schroedinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't mention anything.


title: Neutrino Nuclei Coherent scattering and the Dark Matter lower wall

text: Suppose that current and new forthcoming dark matter direct detection experiments find no evidence of Dark matter events and exclude interactions of hypothetical DM particles (like LSP or similar) in the cross-section range 10⁻⁴⁴-10⁻⁴⁸ cm². What would it mean for SUSY? What would it mean for "new physics" in the weak sector?


title: What are the limitations of the FLRW metric?

text: I was wondering, given how in any other area of life making an explosion spherically symmetric is more or less impossible is there any reason to expect that the universe is? I appreciate that the FLRW has the advantage of being an exact solution, but is there any reason to suppose its an accurate one? Does WMAP allow a measurement of any inhomogeneity in the rate of expansion, or is it simply able to probe lumpiness. I should probably have learned this in lectures but if I'm honest at the time I found cosmology a homogeneous, spherical cow in a vacuum too far.


title: Solutions to SHMO equation in Feynman's Thesis

text: I'm reading Feynman's Thesis, and have some background in math and physics, but I'm not sure where Feynman gets his solution to his harmonic oscillator equation. He gives three different formulations. The first includes an integral. Is this standard Fourier Analysis stuff? Can you give me some kind of link? One of them is $$ x(t) = x(0) \cos \omega t + \dot{x}(0) \frac {\sin\omega t}{\omega} + \frac {1}{m \omega}\int_o^t \gamma (s) \sin \omega (t-s) ds $$ $$\gamma = I_y + I_z $$. The "I" is a function involving the coordinates of positions y and z. $$ m\ddot{x} + m\omega^2 x = [ I_y + I_z ] $$


title: What is the physical reason a $+5V$ equipotential coutour cannot intersect a $-5V$ equipotential coutour?

text: Now I've been told that equipotential contours with different values can never intersect. That is, if one level is 5V and one is -5V, they can't intersect. This make sense to me mathematically (one contour is above the other), but how do you explain that this is true in terms of energy? In other words, how is energy even related to this problem? Because I don't see the relationship at all.


title: Calabi-Yau condition, moduli and Lichnerowicz equation

text: I have a conceptual confusion about the metric moduli of Calabi-Yau manifolds, when I was reading Calabi-Yau compactification. As I understand, the metric moduli is parametrized by infinitesimal deformation of the metric that preserve Calabi-Yau condition (Ricci-flatness or equivalently, admit one covariantly constant spinor). So we would have the Lichnerowicz equation of the deformation metric: \begin{equation} \nabla^l \nabla_l\ \delta g_{mn} - [\nabla^l,\nabla_m]\ \delta g_{ln} - [\nabla^l, \nabla_n]\ \delta g_{lm} = 0 \end{equation} And moreover, the deformation is a deformation of complex structure: the compensating coordinate transformation is not holomorphic. Or more specifically, the metric can be no longer written in a Hermitian form. But since the deformation preserves Calabi-Yau condition, it should still be Calabi-Yau, so it is still Kahler. Thus, is the deformed metric still Calabi-Yau? If it is, how to understand the emergence of non-Hermitian component in the metric?


title: How can we determine the inbuilt barrierpotential and electric feld for a given band diagram?

text: Suppose I have got two p type silicon materials of different concentrations (the difference in thier concentrations is small but considerable enough that their fermi levels differ by noticeable amounts).Now if I wish to make a junction device using these two p type semiconductors , I would like to know how the built in potential when plotted against length of the junction device looks like ? Also I would like to know is there any general way of finding built in potential from any given band diagram even if it is in terms of energy levels?


title: Gaussian integral of a function with nonzero mean (generalizing Wick theorem)

text: From the wikipedia article, for a Gaussian integral of an analytic function we have that ![enter image description here](http://i.stack.imgur.com/VztzS.png) This is equivalent to the Wick theorem when f(x) is a polynomial. Now I'm trying to obtain a similar formula when there is a linear term in the Gaussian (ie the Gaussian has a nonzero mean). My guess is that $$ \int f(x) \exp \left( - \frac{1}{2} x^T A x + B^T x \right) d^n x = \\\ = \sqrt{\frac{(2 \pi)^n}{\det A}} \exp \left[ \frac{1}{2} \left( B^T + \frac{d}{dx_i} \right) A^{-1} \left( B + \frac{d}{dx_j} \right) \right] f(x) \bigg|_{x=0} $$ but I can't prove it. Is this equation correct? How can I prove it?


title: Calculate transparency from Beer-Lambert Law

text: I want to calculate a transparency parameter for a superposition of several volumes containing media using the Beer-Lambert Law, which states that $$I/I_0=exp(-\tau)$$ where $I$ is the transmitted intensity, $I_0$ is the incident radiation intensity, and $\tau$ is the optical depth of the medium. My question here is: Can I replace $\tau$ with $\tau_1 + \tau_2 + ... + \tau_n$ when dealing with n media of same/different optical depths? Does it matter whether the volumes overlap (assuming that they do not interact with each other)?


title: Should acceleration be included in state vector of a Kalman filter?

text: I'm developing (actually adopting existing solution) a Kalman filter to model motion of a vehicle (UAV or automobile). The state vector will include position, velocity, and, possibly, acceleration. In that existing solution acceleration is included; state transition is something like $(\vec x,\vec v, \vec a) \to (\vec x+\Delta t\cdot \vec v,\vec v+\Delta t \cdot \vec a,\vec a+\xi)$, where $\xi$ is a process noise. I think that such model is good when acceleration is changing somewhat smoothly, but when there are bursts of acceleration, removing $\vec a$ from state and adding noise to velocity should be more suitable: $(\vec x,\vec v)\to(\vec x+\Delta t\cdot\vec v,\vec v+\xi)$. Tests show that there is almost no difference in precision of solution between both models (turns out that the observation data provides more effect on position than the velocity). So the question is, when should I include acceleration in state, and when should not? What things should I consider?


title: Why doesn't a nuclear fuel pool become irradiated?

text: Why doesn't the volume of water in a nuclear fuel pool become irradiated? Why wouldn't the water around the pool become radioactive and circulate around making the whole thing deadly? My question spawned from this cartoon from XKCD. The Spent Fuel Pool


title: How can Doppler Shift be applied to Electromagnetic waves

text: Doppler Shift applies (originally) to mechanical waves. Waves that are propagated in a medium. Can anybody explain to me why EMW can get "Doppler Shifted" when they are self propagating "Vacuum" waves .


title: How does food plastic wrap get positive and negative charges on opposite sides of the plastic?

text: Related: Why two objects get charged by rubbing? After reading the above question’s answer given by Luboš Motl in terms of the triboelectric effect, I believe I have a good grasp on how charge is transferred between two different materials. My question is why does plastic wrap, made of one type of material, when pulled from a roll gets one side negatively charged while the other side gets positively charged? I was unable to understand this question after reading several links on the triboelectric effect and electronegativity. It appears to me that this effect is responsible for two different materials transferring charge but was unclear to me when speaking on how charge is transferred between the same material, as in the case of the plastic wrap. I’d appreciate any help for a correct explanation.


title: How can the product of two real linear operators be not real?

text: I'm puzzled about a statement from Diracs book "The principles of quantum mechanics" (§8, p.28): > As a simple examples of this result, it should be noted that, if $\xi$ and > $\eta$ are real, in general $\xi\eta$ is not real. This is an important > difference from classical mechanics. However, $\xi\eta + \eta\xi$ is real, > and so is $i(\xi\eta - \eta\xi)$. Only when $\xi$ and $\eta$ commute is > $\xi\eta$ itself also real. Here $\xi$ and $\eta$ are linear operators, so (I think) these could be represented as matrices. However how can a product of two real matrices be "not real"? What does Dirac mean when he says "is not real"? Is Dirac maybe talking about eigenvalues? So does Dirac mean, that the product of two matrices with real eigenvalues could have imaginary eigenvalues? And does he want to say, that a real symmetric matrix like $\xi\eta + \eta\xi$ and a purely imaginary antisymmetric matrix like $i(\xi\eta - \eta\xi)$ always have real eigenvalues?


title: Mie theory "upper limit"?

text: I have read most often that objects experimented with in Mie theory are on a scale not much larger than the incident wavelength (usually a fiber of diameter $5$ microns with an incident wavelength of $630$ nm or so). Can Mie theory be used to describe the scattering pattern of an object any size, as long as a sufficient number of terms in the Mie solution can be calculated?


title: Is air resistance affected by both mass and surface area?

text: If so, which has the biggest impact?


title: How does the aluminium foil do the thermal and WiFi isolation?

text: Aluminium foil is widely used for thermal isolation. As far as I know it reflects the thermal infrared radiation. Also I've seen a lot of guides about strengthening WiFi signal by putting the electromagnetic shield at not needed sides of WiFi antenna, so that EM waves are reflected to the useful zone. I'd like to know how exactly it works though. In Wikipedia it is written that usual household aluminium foil has thickness of about 16 microns, and heavy duty foil – 24 microns. The thermal infrared light has wavelength of 3-30 microns. Does it mean that, for example, 16 microns thick foil will reflect only light with wavelength up to 16 microns, and all light with larger wavelength will pass through such foil freely? WiFi has frequency 2.4 GHz which corresponds to wavelength of 12.5 cm. Then such long waves shouldn't be affected my the foil that has thickness 10000 times smaller. Or does it have to do with the fact that aluminium is a conductive material, and any electromagnetic waves, regardless of wavelength, can't pass through the conductive material. If this is the case, then how does the reflection work?


title: Why are there no elementary charged, spin-zero particles?

text: In the spirit of a related inquiry, I would like to know if there's a basis for understanding why there aren't any elementary particles that have non-zero electric charge but zero spin? Can such a quantum theory be written down and self-consistent? Do the current symmetries of our present QFTs not allow such a particle?


title: Notation for differential operators and wave function math

text: I know that $[\frac {d^2}{dx^2}]\psi$ is $\frac {d^2\psi}{dx^2}$ but what about this one $[\frac {d^2\psi}{dx^2}]\psi^*$? Is it this like $\frac {d^2\psi\psi^*}{dx^2}$ or this like $\frac {\psi^*d^2\psi}{dx^2}$? And what about this one $[\frac {d^2\psi}{dx^2}]\phi$?


title: What does a closed time-like curve look like?

text: I want to see a plot of closed time-like curve in $(t,x)$. $t$ - vertical axis   $x$ horizontal axis   (the usual setting just neglect $y$ and $z$ components of $(t,x,y,z)$). What does it look like?


title: How Does Cosmology Constrain the Number of Neutrino Species?

text: I know that based upon theories of structure formation cosmologists can constrain the **sum** of the masses of neutrinos - if neutrinos were too light or too heavy it would simply change the power spectrum of the universe. My question is how exactly is the number of neutrino species constrained by cosmological measurements (i.e. - $N_{eff}$ as measured by WMAP or Planck)? The recent results from the Planck Satellite give us $3.3\pm0.3$, which is consistent with three neutrino species. How is this measured?


title: What's the relationship between concentration and refraction rate in a solution?

text: I am supposed to determine the concentration of a solution of ethyl alcohol and cyclohexane by measuring its refraction rate. Now I have some standard sample of the solution at concentrations 10%, 20%, ... , 100% and I measured their refraction rates respectively. I'm now supposed to perform a non-linear fit to the data, but which fitting model should I use? Someone had suggested exponential, and the data look like an exponential growth, but is there a theoretical equation for this?


title: Impedance Matching

text: When viewing fast pulses on an oscilloscope, why is impedance matching required? I'm not totally clear on why. I'm guessing it is because I don't want 'ringing' and because I want signal integrity.


title: What causes destruction in car crash?

text: Suppose a car crashes at a speed $v$ against a wall and comes to a stop. Now if the car crashes at $2v$, does that mean it suffers twice as much destruction, if that can be objectively measured? If force is what causes the damage and $F = ma$ and $a = \Delta v/\Delta t$, so $F = m \Delta v/\Delta t$. Assuming $\Delta t$ remains the same, then the force acting upon the car in the crash at $2v$ is just twice the force of the crash at $v$. But by conservation of energy, if the cars come to a stop all the kinetic energy is converted into other forms of energy. So a crash at twice the speed is four times as energetic, since $E = m v^2 / 2$. If that's the case, shouldn't it cause 4 times as much destruction?


title: Mean of a measurement on periodic data: what is the use of the inverse of correlation length?

text: Correlation and autocorrelation is something that in my Bachelor's programme in physics has been somewhat overlooked, so I'm in trouble understanding their use in this paper (The prisoner’s dilemma on co-evolving networks under perfect rationality. C Bielya, K Dragositsa and S Thurnera. _Physica D_ **228** , 40-48, arXiv:physics/0504190 [physics.soc-ph]). Basically, they have a dynamic network which shows periodic behaviour. They try to measure the degree distribution $P(k)$, but of course they have to average over time. So, they present the resulting $\langle P(k)\rangle$, specifying the following: > To improve the accuracy of the plot, degree distributions of networks at > $10^3$ different times have been averaged. The correlation in the time > series has been taken care of by using time intervals of inverse correlation > length. As I understand it, they want to avoid taking samples of the observable of interest at time intervals equal the period of the cyclic evolution of the system, because that would bias the result, based on when in the period you start sampling. If so, then I don't understand why taking the inverse of the correlation length is the preferred option.


title: Is photon emission possible without electrons changing energy levels?

text: Does molecular vibrational transition and consequent emission of infrared radiation involve electrons changing energy level? In wikipedia, about vibronic transitions it says "Most processes leading to the absorption and emission of visible light, are due to vibronic transitions. This may be contrasted to pure electronic transitions which occur in atoms and lead to sharp monochromatic lines (e.g. in a sodium vapor lamp) or pure vibrational transitions which only absorb or emit infrared light.". Does this mean infrared radiation is emitted without electrons playing a direct part? What about changing in molecular rotational energies? Also, I understand reflection is not a radiation absorption-emission phenomena, so can you explain what actually happens to the photons? Same thing for radiation scattering.


title: Determining Water Level

text: Given a cylinder of a constant shape and size, how can the water level be calculated using the inside surface of the container? For instance, could the inside lining of the container be a pressure sensitive foil of some sort, and using that pressure could the water level be calculated?


title: Compton Scattering: Klein-Nishina formula derivation

text: I'm following a derivation of the Klein-Nishina formula from scratch and this is what I have so far: $P_{e,i} = m_0\gamma_u[1,u]$ and $P_{\gamma,i} = [\frac{\hbar\omega_i}{c^2}, \frac{\hbar\omega_i}{c}n_{\gamma,i}]$, where $i=1,2$ is before and after and I'm assuming $n_\gamma$ is the number density. Firstly, four momentum is $[E/c, p]$, so how has $P_{\gamma,i}$ got a $c^2$ and $n_\gamma$ in it? So, if we accept all that. We can conserve the momenta before and after, square it and reduce it to $$P_{e1}.P_{\gamma1} = P_{e2}.P_{\gamma2}$$ Secondly, multiplying by $P_{\gamma2}$ gives $$ P_{e1}.P_{\gamma2} +P_{\gamma1}.P_{\gamma2} = P_{e2}.P_{\gamma2} + P_{\gamma2}.P_{\gamma2}$$. How does that work? Then finally, how do I get $$ P_{e1}.P_{\gamma2} = \gamma_1m_e\hbar\omega_2(1-\frac{v_1.n_{\gamma2}}{c})$$ from the definitions on the second line? So confused!


title: Lagrange multiplier dependent on time

text: At the moment I am following a course on variational methods for mathematicians. Last week we derived the Euler-Lagrange equations for a functional under a constraint. In this derivation we found that the Lagrange multiplier may depend on time. However, I could not remember having ever seen an example of a Lagrange multiplier dependent on time during my physics courses. Does anyone have a nice (mechanical) example?


title: Size of a quantum computer to effectively calculate macroscopic reality from quantum mechanics

text: Assuming the correctness of QM: Would the size of such a computer be smaller than the observable universe? If it were to represent all available information in the universe it seems that it's minimal necessary size would relate to a black hole of a certain mass. Would this lead us to believe this theoretical quantum computer (assuming it didn't represent itself) could be constructed smaller than the universe? Or if the information content of an object is truly expressed in relation to a surface area is the universe the object with the minimal surface required to represent the totality of it's information?


title: Expansion in spherical harmonics in cubic symmetry

text: suppose I have an electrostatic potential which I expand in spherical harmonics via $$\sum_{l,m} A^l_m r^n P_l^{|m|}(\cos \theta) e^{im\varphi}$$ and I know that the field has cubic symmetry. Is there something I can say about the coefficients $A^n_m$? I ask because this would be the case for the crystal field in a cubic crystal, where it is known that the $e_g$ and the $t_{2g}$ orbitals are splitted. I am trying to show that the matrix-element is the same for all $e_g$, and the same for all $t_{2g}$. I tried it using the Wigner-Eckart theorem, but that seems not to be enough; I also need some symmetry relations for the $A^n_m$...


title: Relativistic Conservation laws

text: Conservation of Relativistic mass and thus energy is easily proven by considering an inelastic collision of two bodies while invoking the conservation of momentum. As such the momentum law appears more primitive. Is this somehow an artefact of momentum - space and energy- time as conjugate variables and the implicit necessity to assume causality in constructing such a scenario?


title: Coriolis effect misunderstanding

text: My wife asked me what the Coriolis Effect was, so I did some research. I think I get it now but I'm surprised at the number of "explanations" people have uploaded that actually seem wrong. This one is an example. http://www.classzone.com/books/earth_science/terc/content/visualizations/es1904/es1904page01.cfm This is wrong, right?


title: What are the facts that allow accepting the Oort cloud theory?

text: I admit without any fact that the Oort cloud (comet reservoir) should exist, and it seems to be accepted by far by the large majority of astronomers. But it is still a theory without any direct observation. Except the fact that we guess that comets come from this cloud (a cloud of comets). So what are the facts or indirect observations that may validate this comet cloud theory? Collateral to this question, is it easy to observe these indirect facts, and is there any special way to observe these Oort comets to validate the theory? Is it acceptable to say there is no cloud and just a few solar and most inter- solar objects?


title: Do sound waves bend and/or diffract?

text: Sound waves are normally mechanical wave i want to know whether the sound wave bends if it bends does it undergo diffraction just like light wave?


title: A new idea on unifying sound and light

text: Got a new idea regarding the unification of light wave and sound wave into a single entity , may be probably a wave. Is it possible to proceed in that manner,and has it been done previously,like i have an idea of projecting.The light wave and sound wave and synchronizing their speeds,and let them meet at a point,forming interference, or merging at a point will it create a new wave. If it have been implemented in past can I know the way of unification of sound and light and its applications?


title: Famous physicists' quotations

text: I recently watched Sydney Coleman's 'Quantum Mechanics In Your Face,' and very much enjoyed it. (Highly recommended.) In it, Professor Coleman quotes a very clever comment by a philosopher called Ludwig Wittgenstein. Wittgenstein found it strange that people used to believe in geocentrism (Sun goes around the Earth.) When asked why he felt it strange, he responded: " _well, how would it have have looked if it were the other way around._ " Of course it would look exactly the same. Personally, I loved Wittgenstein's response and thought it showed impressive insight although, clearly, things are always simpler in hindsight than in foresight. This got me thinking. There must be hundreds of equally elegant / beautiful quotes of famous physicists out there. I'm sure almost everyone has a favourite. So, the question, quite simply, is this: **what is your favourite famous-physicist quote, and why??** NB/ For another couple of very interesting _list_ -type questions see: Common false beliefs in Physics and/or Great unsolved physics problems.


title: Basic Field Calculations

text: I'm trying to derive the relation: $\phi(x)\phi(y)=:\phi(x)\phi(y):+\langle 0|\phi(x)\phi(y)|0 \rangle$ but struggling to see the first few steps I need to make. I've made the substitutions $\phi(x)=\phi^+(x)+\phi^-(x)$ and the same for $\phi(y)$, but it hasn't got me very far. I'm then unsure what the it means when it says to compute $\langle 0|\phi(x)\phi(y)|\bf{k_1},\bf{k_2} \rangle$. Any help would be great!


title: What really are some distant astronomical bodies that seems like dust clouds?

text: Looking at pictures like this ![enter image description here](http://i.stack.imgur.com/DzlrB.jpg) I bet it is a picture of a giant cloud of dust, bigger than a galaxy and made of asteroids and planets (instead of stars). But probably I'm wrong. What is that?


title: About muons, taus and the number of generations

text: there! Why cannot consider the muon or the tau just like excited states of the electron (and similarly, with the (u,d) (c,s) (t,b) pairs? I guess that it is related to the absence of decays like muon-> electron+photon and similar stuff. But, is there any other reason?


title: (Why) Can we simply assume a given alignment of VEVs?

text: In GUT theories, one often assumes that Higgs fields take VEVs in given representations, of a given magnitude at a given scale. While I am well aware that this is one of the weak spots in such theories, I suppose there must at least be some work into the possibilities of construcing a Higgs potential with a given VEV structure. What works are there on Higgs potentials in GUT theories w.r.t. VEV structure?


title: Why do we feel a sudden chill?

text: When we are in a room, especially in some old houses, we feel this sudden rush of cold air. How does a strong air current arise and pass away so quickly?(lasts for about a second) I know air-currents are caused by pressure differences. But can pressure difference of the magnitude required to generate an air current be created within a second? If so , please answer with equation that relates the pressure and Temperature with time interval. Thanks..i hope I am now much clearer with my question. (I am inclined to think in the direction of something similar to a weather situation)


title: Why is calcium paramagnetic?

text: As far as I understand, magnetism comes from the 'unpaired electrons' in the subshells of atoms. Atoms with paired electrons are diamagnetic ('not magnetic') while atoms with unpaired electrons are paramagnetic. However, Calcium is said to be paramagnetic, even though it has no free electrons. How come?


title: Energy of an EM Wave and its temperature and amplitude

text: I'm trying to understand why classical physics fails to explain black body radiation. I'm confused. According to Boltzmann, energy calculation for em wave is based on temperature. According to Maxwell, energy calculation for em wave is based on amplitude. Are those different kinds of energies? How can we determine the energy of an em wave just taking temperature as a parameter, but not amplitude or frequency??


title: Orbital plot to explain bonding and anti-bonding molecular orbitals

text: Related is this question: https://chemistry.stackexchange.com/questions/2586/molecular-and-atomic- orbitals-and-antibonding. In my textbook on organic chemistry they represent an orbital as a 2d wave function to explain the formation of bonding and anti-bonding molecular orbitals (I displayed it here as a simple $\sin x$ function, just for illustration. I understand real wave function may be quite different). ![Example wave function, sin x](http://i.stack.imgur.com/ktOWh.png) They say the bonding atomic orbitals can either combine in phase, resulting in a bonding molecular orbital (the electron density becomes larges between the molecules, creating an electrostatic astringent force exerted by the electron in the center on the nuclei of the combining atoms), here represented as $2\sin x$ ![Example bonding molecular orbital wave function, 2sin x](http://i.stack.imgur.com/ctM61.png) or combine out of phase resulting in a nodal plane between the nuclei: an anti-bonding molecular orbital. Here represented as $\sin x + \sin (x+\pi)$ ![Example anti-bonding molecular orbital wave function, sin x + sin \(x + pi\)](http://i.stack.imgur.com/DMLtU.png) Now the question: how can a single orbital, that is either in phase or out of phase with the orbital of the bonding atom (i.e. the other atom) form both a bonding molecular orbital and an anti-bonding molecular orbital, while it is clear that an orbital is either in one phase or an other and not both? Related is, what this 2d diagram actually represents (related question, but not quite the same: https://chemistry.stackexchange.com/questions/12397/meaning-of-depiction-of- atomic-orbitals). Please ask if anything is unclear. Your help is appreciated!


title: Standing wave velocity

text: My question is simple: How is it that a standing wave has velocity? I mean, it's not travelling... A lot of equations depend on this concept, for example: $f_n = \frac{nv}{2L}$ Here we're finding the frequency of the nth harmonic given the velocity of the wave on a string.


title: Is escape velocity the same for all objects?

text: Would a lighter-than-air craft in the mid atmosphere at 80,000 feet altitude need to achieve the same velocity to escape earth gravity as the space shuttle?


title: Problem in Grandfather paradox

text: I am very confused about a paradox and a recent research on Quantum particles. I have read an article which states that time travel is possible for quantum particles. If it is possible then why does it violate the Grandfather paradox? As far as I know that f we can go to the past we can not change our past. They why a photon interacts with a past versions of photons?


title: Do divergent parts cancel out between the 1-loop contribution to the vertex and the self-energy on the electron legs of the vertex diagram?

text: I regret I don't know how to draw Feynman diagrams here, so I refer to the standard book Peskin-Schroeder. At the beginning of section 7.5 on page 244 of this book several Feynman diagrams are shown, I will refer to the second block of diagrams. There is shown the electromagnetic vertex diagram with one loop (generated by the photon "short-cutting between the electron legs") and two further diagrams with EM-vertex without loop, but each with one electron self- energy part on the in-coming electron leg respectively on the out-coming electron leg.   Is it true that (apart from the electron mass renormalization) taking these 3 diagrams into account, their respective divergent parts would cancel out mutually by virtue of the Ward identity ? One might argue that each single diagram is made finite at the end by the use of counter-terms, but my question refers to cancellation of their divergent parts without use of counter-terms.   Furthermore, could it be even concluded that the divergent part for any kind of complicated EM-vertex would cancel out against corresponding electron self- energy parts on the in-coming and out-coming leg of the graph for each order of $\alpha$ in perturbation theory by virtue of the Ward identity ? If it is not like this, which diagrams should be possibly added to achieve this or am I wrong with my understanding ? Thank you for any help.


title: How does a flat wedge lens work?

text: I've been seeing this lens in a lot of places especially microsoft: http://www.youtube.com/watch?feature=player_detailpage&v=rJ1p5SD3sOM#t=45s http://blog.seattlepi.com/microsoft/2010/07/08/on-tap-at- microsoft-a-3d-display-without-glasses-and-multiple-programs-at- once/?from=blog_last3 It is a flat lens that bends light at 90 degrees. This allows all sorts of neat tricks like using the screen as a camera. For the life of me I can't understand how it's being done. Can anyone here explain?


title: How do I describe the energy an electron gains (and loses) in a circuit?

text: I am looking at the simple circumstance of an electron traveling through a long wire by a potential. I see how one would be motivated to use the usual formula, W=F*d, to describe the electron's net energy imposed by the E field with F=E*m(e) and d= length of wire, but I feel that I have a problem with that. Shouldn't the energy gain be greater than this formula describes since the energy from the electric field is applied for so long? It's not like there is a net force on the electrons, so it almost seems the concept of impulse needs to be invoked. Granted, I am very confused in general so maybe there is some obvious answer here. I know the voltage actually describes the same thing but how do I calculate it from the electric field and wire length? This seems like a simple kinematics question and let me describe the dance between extremes my mind suggests for this situation: On the one hand, if I have a field and an object, and the object moves completely from the point where it initially is and where the source of the field is, with no resistance, it will absorb energy all the way along the distance for a fixed quantity of energy (the potential energy), which can be measured as F*d. On the other hand, if along the path energy is taken away from the object, exactly enough to balance the accelerational energy (making for a constant velocity), then if the object starts with zero initial velocity it will constantly absorb energy. If I vary the initial velocity from zero on up, the fixed amount of energy absorbed from points a to b will vary from infinity down to ever smaller quantities. So, since an electron has a very small net velocity, shouldn't its actual amount of absorbed energy be greater than the energy predicted by the equation F*d (ie W=E*e(m)*l)?


Is there a difference between correlation processing and matched filter processing? To me, they look same.


title: How to understand the curvature of this metric?

text: Suppose we have the metric $ ds^2 = dr^2 + \alpha^2 d\phi^2$, where $\alpha$ is a constant, $0 \leq r \leq \infty$, $ 0 \leq \phi \leq 2 \pi$ and we identify points $\phi = 0$ with points $\phi = 2\pi$. Now since we have a constant metric the Christoffel symbols are zero and thus so to is the curvature tensor. So this should be flat space. When I try to find the length along radial paths from $0$ to $R$ I find the length to be $R$, but when I find the length of fixed radius paths from $0$ to $2\pi$ I find them to be of length $2\pi \alpha$. So regardless of the position in the $r$ direction we have fixed circumference, thus it seems like this space can be embedded in 3D cylindrical coordinates as a cylinder. Question 1: Is the above correct? If it is, why are cylinders flat but not spheres or saddle points? Intuitively is it because flattening a cylinder only introduces folds where as a sphere would have complex deformations? Question 2: If you draw a sphere in spherical coordinates where $r$, $\theta$ and $\phi$ are all draw at right angles a sphere would look like a rectangle with relevant sides of $\theta$ and $\phi$ identified. Since a rectangle looks flat to me, how can you be sure that you are embedding in such a way as to visualise the curvature? Is it that any coordinates where the sides are identified will reveal the curvature?


title: A Subtle Connection Between Time Dilation in SR and GR - Why is this so?

text: I've been reading a book on General Relativity lately (Gravitation and Cosmology, Weinberg), and I was reading about the weak field approximation. It derived the time dilation in a weak gravitational field (spherically symmetric so that $\phi=-GM/R$) as $$\frac{dt}{d\tau}=(-g_{00})^{-1/2}=(1+2\phi)^{-1/2}=\left(1-\frac{2GM}{Rc^2}\right)^{-1/2}.$$ The term itself reminded me a lot of time dilation in Special Relativity. Namely, $$\frac{dt}{d\tau}=\left(1-v^2/c^2\right)^{-1/2}.$$ And then I noticed that if you were to somehow equate these (which I know can't really be done, but just for analogy), then a particle travelling at exactly the escape velocity of the spherical body in question would experience the same dilation as a particle sitting on the surface. My question pertains as to why this is true. Better put: Is there some symmetry of nature (possibly a consequence of the equivalence principle or something else) that I'm just not noticing, or is this just a coincidence of math (I see this possibility as unlikely)? Please note that I'm quite the beginner in GR, so if there's something well known that I just haven't learned (read) yet, please let me know.


title: Finding instantaneous speed in MPH given acceleration, RPM and gear ratio

text: I am still trying to figure out how to (semi) accurately model instantaneous speed after having found acceleration. I have found that at higher RPMs, the resultant acceleration will be lower. I was told that the boost in speed comes from changing the gear ratio due to a changing gears at higher RPMs. Is this true? If so, what is the algebraic relationship between these independent variables?


title: How did ancient physicists around 500 BC decide that the earth is spherical?

text: One of the standard stories that is given for this (and is mentioned in Aristotle) is that the hull of a ship disappears first as it sails towards the horizon on a calm sunny day. Is this a myth, or is it possible? After all, at the time no telescopes were available. Scenario: Assume, for instance the hull of the ship rides 1 metre above the surface of the sea, with a sail whose height is 3 metres (I am going by 'Min of the Desert', a replica of a 3800 years old oceangoing Egyptian ship, so about the right time period.)   1. How far must it travel before the curvature of the earth completely hides the hull?    2. How far must it travel (assuming a flat earth) before visual acuity of a normal naked eye can no longer discern it? I get an answer for question 1 of around 120km, this seems too distant (by my unaided intuition) for the naked eye to resolve. Also it seems wrong from general observation of the horizon from the coast, as one of the commenters has pointed out it looks like only a few kilometers. And surely at that kind of distance atmospheric efects begin to kick in, especially in the mediterrean where its generally warm. Its been a very long time since I've done geometrical optics, so the answer to question 2 is beyond me. Can someone help. Also a verification of 1 would be nice (I've used a radius of the earth as 6000km).


title: Minkowski spacetime vs Euclidian space

text: Two questions marked in bold: **What is the _magnitude_ of a Minkowski spacetime four velocity?** I'm deducing that it is c for all observers, but I'd like it confirmed. In Euclidian space, a velocity vector integrates over time to an absolute position. **Does a four velocity integrate over time to a four dimensional displacement, and is it used in physics?** Eventually; why not?


title: How cold would a bowling ball near absolute zero make a room?

text: If a bowling ball at absolute zero suddenly appeared in my room, how cold would the room get? Would I die? My initial estimation is that it one bowling ball at 0K (i.e., 300K below room temperature) would have about the same effect as 10 bowling balls at 270K (i.e., just below freezing, 30K below room temperature).


title: Applying $\nabla\times\mathbf{B} = \mu_0\mathbf{J}$ in the presence of magnetic shielding

text: **2012-06-13 - Revised question in experimental format** (This is a thought experiment for which RF experts may have an immediate answer.) I'll assume (I could be wrong) the possibility of creating a strongly insulating material with low permittivity and very high permeability. From this material fabricate two identical 30 cm tubes with inside diameters of 1 cm, and wall thicknesses sufficient to provide robust blocking of magnetic fields. A silver wire 30 cm in length and 1 cm in diameter is inserted into one of the tubes. Call this one the silver wire. The other cylinder is placed inside within a vacuum chamber with an electron gun at one end and a conductive target at the other end. The electron gun is designed to fill the 1 cm interior with an even flow of electrons, so that it can simulate the flow of electrons in the wire as closely as possible. Call this one the vacuum wire. Now for the experiment. Identical currents $\begin{align}\mathbf{I}=\frac{d\mathbf{Q}}{d\mathbf{t}}\end{align}$ are sent through both wires. An experimenter then looks for induced magnetic fields around both wires. Will these magnetic fields be: > (a) Identical, > > (b) Greater around the vacuum wire, or > > (c) Greater around the silver wire? My bet is (b). Anyone? (See below for the history of this question. Again, it may turn out to be easy for RF experts who have to deal with weird combinations of permittivity, permeability, and conductivity on a daily basis.) * * * **2012-06-10: Original version of question** Original title: _Where are the electric field gradients in coil-generated magnetic fields?_ **Background** I tried to apply Feynman's SR-focused explanation of the relationship between electric and magnetic fields in wires to this, but in the end concluded he was addressing a rather different set of issues -- and even that only incompletely, since his purposes were for instructive purposes (his Lectures) than a complete analysis. My question is not about the mathematics of Maxwell's equations, but how such equations may be applied a bit to casually to situations that are actually quite different physically. **Case 1: Magnetic field induction in CRTs** In an old-style cathode ray tube (CRT) or television screen, the electrons that cross the vacuum of the CRT create a detectable electric field gradient between the electrons and the surrounding tube. This field can be roughly imagined by picturing the tube as a large capacitor (which it is; I know someone with the scar on his shoulder that proves just how large) in which the central vacuum area carries most of the negative charge and the sounding tube interior the positive charge. In the case of the CRT, the interior negative charges are also in rapid motion towards the screen. Any accurate assessment of the above model requires explicit use of the modern version vector based version of Maxwell's equations. However, Maxwell was also fascinated by and made extensive conceptual use of hydrodynamic-inspired models of electric and magnetic fields. For example, Maxwell originated or at least popularized the term "flux lines," meaning flow lines, to describe both electric and magnetic field structure. The phrase "field lines" is more common these days, but means the same thing. The flux line model is still used in beginning courses on electromagnetics, where experiments using magnetic and non-conductive powders can make such lines starkly easy to visualize and comprehend. The flux line model can be defined with mathematical precision for classical velocities. For the CRT example, electrons are surrounded by flux lines that extend out to the interior of the tube, and the orthogonal motion of those flux lines in turn generates a strong magnetic field with flux lines orthogonal both to the electric flux lines and to the direction of motion of the electric flux lines. So, this is all quite straightforward: The component of electric flux perpendicular to the direction of travel generates a magnetic flux line that is perpendicular to both that electric flux and its direction of motion. The electric flux lines are in turn defined by a field gradient -- a voltage -- that extends from the electron to the interior of the tube. That electric gradient is quite real and easily measured. The resulting magnetic fields is equally real and measurable, and is in fact what is used to steer the electron beam and paint the screen with an image. **Case 2: Magnetic field induction in wires** Now as it turns out, you can also generate an very similar magnetic field using a rather different method. That method is to embed (in the ideal case) the same number of electrons as in the CRT case, moving at the same average velocity, within a conductive wire. The conductive wire would extend along the same path as the vacuum electrons, and electrons of similar number and velocity and moving along inside the wire can generate a field that, with careful physical adjustments, can be made identical in appearance and strength to that of the CRT case of the electrons moving through a region of vacuum. **Comparing the two cases** So, two cases give very similar magnetic field results: Electrons moving through a vacuum, and electrons moving through a wire. Both give strong circular magnetic fields that surround the path of the moving electrons, and both results can be estimated easily using Maxwell's equations. One reflex reaction at this point may be (should be) "so what?" After all, moving electrons give magnetic fields, so why in the world _shouldn't_ similar motions give the same magnetic fields? The interesting point is that if you look at the two cases carefully, they are _not_ the same experimentally, and here's why: One case (the CRT) has a large- scale set of electric field lines that are very explicitly associated with the corresponding magnetic field structure. For example, if you use a tight, wire- like beam of electrons reaching from the back of the CRT to the center of its screen, then at 20 cm out from the path of the electrons there will be a noticeable electric field gradient that in terms of the flux line model is "moving" and thereby generating the magnetic field that can be measured at the same location. In the wire case, _no such electric gradient exists_. Because the charge of the electrons is cancelled out within the positively charged atomic background of the wire, the electric field makes no appreciable showing outside of the wire. Yet if you measure 20 cm out from the wire, you still see essentially the _same_ magnetic field result, even though there are no longer any "moving electric flux lines" to generate the magnetic field locally. **The actual question** So, after all that preparation, my question is really quite simple: > Why do moving electrons seem to generate approximately the same long-range > magnetic field regardless of whether their field gradients (electric flux > lines) are cancelled nearby or very far away? As often is the case in trying to ask questions like this, working through it has helped my look at my own question differently, so I now think I have some inkling of how to answer my own question. (And no, it's not SR based, since in this question is about why remote electric fields differ given the same "moving electron parts.") **So, is induction being taught accurately?** I'm asking anyway, in part because I'm not sure of my answer, but even more so because I think there needs to be some updating of how such situations are taught. Specifically, the moving-flux-line model (which I believe is still used instructively and is certainly seductive) flatly does _not_ give correct results. If it were really accurate, there would be no such things as electromagnets and electric motors. That's because the field gradients of the moving electrons in such devices all cancel out very quickly and very locally, on the scale of atoms, leaving _no_ appreciable external electric fields at the ranges of the stable magnetic fields they generate. **References** Possibly related past Physics.SE questions have been asked by: (1) The equivalent electric field of a magnetic field by Hans de Vries; asked 2012-04-19, answered 2012-04-19. A typically insightful question by Hans de Vries about the SR relationships of electric and magnetic. (2) Mechanism by which electric and magnetic fields interrelate by Nitin Nizhawan; asked 2012-02-02, no final answer. Another interesting and mostly SR question. (3) Moving conductors in magnetic fields: is there electric field or not? by Giuseppe Negro; asked 2011-05-14, answered 2011-05-14. A similar title, but not quite the same topic, I think.


title: How is the direction of Magnetic/Electric Lines of Force Known?

text: It is shown that the direction of magnetic line is from north to the south and that of the electric line is from positive to negative. How do we/scientists know that the imaginary lines of force or the field goes from this to that, what is the meaning of this direction? Do not give me mathematical definitions which I already know; I want the fundamental meaning of this.


title: Why/how does an electron emit a photon when decelerating?

text: I've had two special relativity courses so far but none really gave me a clear description of the process.


How do particle scattering cross sections scale with energy in colliders? Particularly photons, electrons, protons, and gold or lead nucleii? (If necessary, break this into four separate questions.) It is stated that due to the Heisenberg uncertainty principle, it takes more energy to measure a smaller distance and the inverse wavelength energy- wavelength relationship for photons is well known.   Therefore, I would conclude that the (total scattering) cross section for photons at least would vary as the inverse square of the energy. On the other hand, general relativity says the the longitudinal dimension shrinks with increasing velocity, but the transverse dimensions do not.   Therefore, I would conclude that the cross section of say a gold atom in RHIC or a lead atom in the LHC would basically remain constant as the energy increased. But how about the electron, supposedly a point particle?   Due to PEP and LEP, we should have good data on this. Looking at PDG figure 41.6,   http://pdg.lbl.gov/2011/reviews/rpp2011-rev-cross-section-plots.pdf   I see lots of big spikes for resonant particles, but the underlying bacground is clearly a falling powerlaw that I think looks like it could be an inverse square law. The proton cross sections in the next few figures, e.g. 41.7 and 41.11, show a falling elastic scattering cross section, but they also show an approximately constant total cross section. What little i've found for RHIC supports the approximately constant cross section. Therefore I conclude that the cross sections of photons and electrons (neglecting resonances) scale as the inverse square of the energy, but the cross sections of protons and nucleii are roughly constant with energy. Comments or corrections? So is it true that the photons and electrons are different from the protons and nucleii? And why don't the protons scatter as three or six point particles (quarks and gluons) instead of one big blob?


title: What is the nature of electric field? is it quantized? is it a wave?

text: What I seek here is to understand whether the electric field in its pure form as in between the electron and the proton is uniform or does it have some kind of wave/particle nature or both, does it have frequency or wavelength, or is it quantized?. I do not want any explanations of the effects of electric field or thereof, I want to understand the field itself. Please tell me something I all ready do not know from my engineering education.


title: What exactly happens to an exposed human body in space?

text: I know that space is a vacuum, has no air and is very, very cold. from what i have seen in movies and TV shows when a space suit is exposed the oxygen will escape will escape like a visible gas and the person would explode. In the movie Event Horizon one of the characters is blow out of an airlock and one of his comrades tells him to expel all the air in his lungs and to curl up, as he does he seems to be bleeding a lot. In The Hitchhikers Guide to the Galaxy movie it says you can hold your breath for a little while before anything happens. Ofcause all these examples are science fiction so they may or may not be accurate. I am wondering what would happen is a human body was exposed in space? would it blow up like so many shows seems to hint it? would the person be frozen to death because of the temperature in space? NOTE: i ask this as in a fan fiction i am writing, in one scene the main character's daughter is suck out through a hall breach of the ship before her friend willing jumps out and hold her as she teleport the 2 through space to the nearest planet, i want to explain how the adverse affects of an exposed human body is negated but i can't do that if i don't know what i am negating


title: A question once confused Confucius

text: A well known story "Two Children arguing about the sun" (From _Lie Zi_ , ca. 500BC): > On the way traveling to the east, Confucius saw two children were arguing. > One child thought that the sun is nearer to us at daybreak and far away from > us at noon, because in the morning it is as big as the canopy of a carriage, > but at noon only the size of a plate or a bowl. The other contended that the > sun was far away at dawn and nearby at midday, because when the sun comes > out, it is very cool, but at midday it is as hot as putting your hand in > boiling water. Confucius was unable to settle the matter for them. The > children laughed at him, saying, "Who decided that you were a wise man?" I think the second kid should be correct. the question is: what is wrong with the first kid's argument or why the Sun in the morning looks bigger?


title: How would I calculate the work function of a metal?

text: In the photoelectric effect, the work function is the minimum amount of energy (per photon) needed to eject an electron from the surface of a metal. Is it possible to calculate this energy from the atomic properties of the metal (atomic number, atomic mass, electron configuration, etc.), and the properties of the lattice structure, in a way that doesn't require a complex computational model? (If so, how?) Or, if not, is there a simple formula in terms of the metal's atomic/lattice properties that can approximate it to within a few percent?


title: Could there be a planet just as the Earth, but bigger?

text: Could there be a planet twice or thrice the size of Earth but while being the same? and by the same I mean, hosting the same life as Earth, having a day last 24 hours and a year 365 days. Basically, could there be a bigger Earth? What would be needed to replicate Earth but in a bigger planet?


title: Which is more efficient Water heating method : Electric heating coil OR Induction stove?

text: Which is more efficient Water heating method : Electric heating coil Vs Induction stove


title: Can we apply $pV^\gamma$=const only for quasistatic adiabatic process?

text: But If this is so, I have often seen people applying this formula for quick processes where no heat exchange is possible. Here is an example from where I am quoting the following: > _we will assume this happens quickly enough that no heat can enter or leave > the gas [...]_ It may be to make $\Delta Q$=0, But does not that "quick" word limit the applicability of the formula $$pV^\gamma=\text{const }?$$


title: Why isn't pressure a measure of energy?

text: Hey guys, I'm having a problem in understanding the 1st Law of Thermodynamics. If i would increase the pressure of a closed system by compressing a gas in a cylinder isothermal, the 1.Law states, that all the work i put in to the system, i get out by heat. So my 2.state would be the gas at the same temperature (same internal energy), but compressed (at a higher pressure). But isn't this compressed gas able to do more work, than the not compressed?   If i drilled a hole in the cylinder my high pressure gas could do some work. Where does this energy come from, since all my input energy i put in by work, came out in form of heat?


title: How to determine real part of optical conductivity by reflectivity measurements?

text: In figure 3 of this document, there is data relating $\Re(\sigma(\omega))$ to the Fermi energy. It is claimed that $\Re(\sigma(\omega))$ is determined via reflectivity measurements. How is this done? What is the formula relating the two?


title: Types of electrostatic force

text: In some references, electrostatic force is said to have 3 types: Coulombic force, image force, and gradient force. I really would feel grateful if anybody can explain to me the difference between them, because I really can't find any good reference detailing about them.


title: Concrete example of divergence of a vector field

text: I'm studying vector analysis and it is hard for me to understand what divergence of a vector field really is. I know that $divF=\nabla\cdot F$ but I don't understand what kind of quantity it gives and what it is used for. Could anyone give me a good example of what it is used for (in real physics)?


title: infinite grid of planets with newtonian gravity

text: Assuming only Newtonian gravity, suppose that the universe consists of an infinite number of uniform planets, uniformly distributed in a two-dimensional grid infinite in both directions and not moving relative to each other. Is there any reason to believe that this is not an equilibrium state? A friend of mine who knows much more applied maths than me assures me that this system is not in equilibrium, but I'm unable to find any evidence for this. I want to be able to say that the net force on each planet in the grid is zero. We approach this by summing the forces exerted on a planet _P_ by each other planet over the whole space, but note that we can pair off the other planets that exert equal and opposite forces on _P_ to show that the total sums to zero. Am I going mad? For bonus points, presumably the same result holds for any number of dimensions to the grid.


title: What happens when light moves perpendicular to a moving object?

text: Imagine the folllowing situation: A coherent light source is attached to a car such that the emitted light beam path is "being crossed over" by the car i.e. the long parallel light beams are struck by the moving car such that their path wrt exach other is a 'X'. Say the car is going at a speed of 3000m//s and the coherent light source is attached to the car. do the light particles experience doppler shift? do they photon get absored by th car body? does the path of the photons change in any velcoity due to a gain in momentum? what about the angle of being hit - does it influence any of the above properties of light particles?


title: Nuclear decay rate affected by sun and quantum randomness

text: If nuclear decay rate were affected by sun, then emission probabilities would be subject to sun state and its influence, so quantum randomness would depend on it, Would it still be truly random? One could argue that randomness would keep intact when consider the whole system.. But what about a non-isolable effect? what if there is no way to "define a system" without a sun/star influence? If a variation source were found (for example neutrino emission) then perhaps it could be generated intentionally to control decay rates. Could we be sure that emission probabilities would never could be controled to reach 0 or 1? Thanks for reading


title: Will we need to update Electrodynamics?

text: A contradiction to the Electrodynamics by the experiment. The author has said that, accordning to the experiment, photon is no more gauge invariant? Why is that? An important thing is that Although the assumption contradicts the gauge invariance but the predicted correction has a reasonable agreement with the experimental observations from Supernova 1987a. If he is true then will we need to update Electrodynamics?


title: Do the various frequencies of light within sunlight have the same coherence length?

text: I'm aware that the coherence length of sunlight can be observed with a Michelson-Morley interferometer. I haven't seen any experiment that separated the different colors within sunlight to determine if the coherence length varied with frequency. My thoughts are that the sun is emitting bursts of electromagnetic radiation that vary in frequency, polarization, and phase. The only way I can see fringes forming is if a single burst is split by the mirrors producing two waves that are perfectly correlated in frequency, phase, and polarization. Once one arm of the interferometer is lengthened so that the two paths exceed the length of the EM bursts then fringes would be impossible. How could selecting specific frequencies cause the EM bursts to be correlated, especially in polarization?


title: How can one make sure that one had understood the material studied?

text: I do not fully understand the process of understanding of a material one reads. Suppose someone reads a chapter from a physics book. How does one make sure that one had really understood what she/he had read? I must confess that at times I read from text and I even feel that I had understood the content but later (may be at the time of exams or solving assignments or when somebody raises a question from that topic), I realize that the feeling was illusory and I feel so stupid. At times I feel that my understanding is incomplete even at basic levels. I am eager to know from experienced people in this forum if there is any method to test whether one had really understood the content of what one had read. I am talking of advanced level physics courses. May be one can also suggest useful skills one can develop for better grasp of items one studies. Thanks. I have some other related thoughts. Perhaps this is not just a problem with me but with many others, including even researchers. I have seen during one seminar given by an well-known faculty member of an institute, another well- known researcher from audience started asking questions and making comments which revealed lack of understanding of the speaker and he was almost in tears! Not that the speaker was dishonest but this shows that even experts like him can have "illusory" sense of understanding of a topic (not only what he/she had read but done some research work). So may be there is nothing like full understanding of a topic but deeper and deeper understanding of topics. So the question now becomes, how can one attempt to understand a topic deeply and keep going deeper? And for students, how can they be sure their understanding of a topic is good enough?


title: Speed of Light, Photons or WaveSpeed?

text: The speed of light is almost 300 000 km/s. The photons have a speed along the wave, and the wave have a speed straight forwards. What is the speed of light? Is it the speed the photons have along the waveline, or is it the speed the wave travels in a straight line?


title: Sparticles: Relationship to supersymmetry and dark matter?

text: I was attempting to read this paper after watching a show with Brian Greene. As I understand it, sparticles are a prediction of supersymetry, so I was wondering:   * Wouldn't the discovery of supersymmetry lend validity to string theory? Isn't this a testable result, or is this type of supersymmetry predicted by most models?   * As I understand it, sparticles require very high energies to detect. Are they candidates for non-baryonic particles?


title: Figuring out the force using Newton's 2nd Law

text: Here's a problem on my test review: > A 12 kg crate resta on a horizontal surface and a boy pulls on it with a > force that is 30° below the horizontal. If the coefficient of static > friction is 0.40, the minimum magnitude force he needs to start the crate > moving is: Okay, so I found the equation for the forces in the Y direction: $$\sum F_{Y} = F_{N} - mg - F\sin\theta = 0$$ $$F_{N} = mg + F\sin\theta$$ And the X direction: $$\sum F_{X} = F\cos(\theta) - F_{f} = 0$$ $$F\cos\theta = F_{f}$$ Solving for the force: $$F\cos\theta = u_{s}F_N$$ $$F\cos\theta = u_s (mg + F\sin\theta)$$ $$F\cos{-30°} = 0.40 \left[(12 kg)(9.8 \frac{m}{s^2}) + F\sin{-30°} \right]$$ $$F \left[\cos{-30°} - (.4)(\sin{-30°} \right] = 47.04 N$$ $$ F=44N $$ However, it looks like the correct answer was `71`. Any ideas where I went wrong here?


title: Is there a simple layman way to explain the incompatibilities between quantum mechanics and (general) relativity to high school students?

text: Is there a simple layman way that I can use to explain the incompatibilities between quantum mechanics and (general) relativity to high school students (people with not much knowledge of the intricate math of quantum mechanics and (general) relativity)?


title: Simple Harmonic Motion Question

text: I have two formulae: Displacement = Amplitude * Cos(Angular Frequency * Time) Velocity = - Amplitude * Angular Frequency * Sin(Angular Frequency * Time) OR $x = Acos(wt)$ $v = -A.w.sin(wt)$ And the question is using these two formulae show $v = \pm W\sqrt{A^2 - x^2}$ Thanks for your help in advance!


Is there the smallest particle that can be guaranteed to be unable to be broken down into smaller particles?