title: Which phenomena is involved in the clothes drying process?

text: There's this question that has been bugging me most of my life: how is it that wet clothes left hanging to dry, get actually dry? If I get it right, the clothes are a mesh of fibers (we could assume synthetic fibers to make it simpler) that capture droplets of water in the mesh. When one hangs the cloth gravity makes some of the droplets fall from the mesh; still if there's a side that's exposed to a heat source it dries faster, so in addition to gravity there's also heat. However, the heat does not boil the droplets. So... \- what is actually going on there ? \- could the drying be optimized, e.g. maximizing surfaces exposed, etc ?


title: Is there some explanation for $y_t=1$

text: The Yukawa coupling of the top quark is Dirac-natural in a too excellent way, it is within one sigma experimentally, and within 99.5% in absolute value, of being equal to one. Without some symmetry, it seems too much for a quantity that is supposed to come down from GUT/Planck scale via the renormalization group. Is there some explanation for this?


title: Gauss's Law :To find the Electric Field for a Non-Conducting Sphere

text: While determining the electric field in a Non-Conducting Sphere using Gauss's law,why the positive charges are considered inside the surface,but in determining the electric field in a conducting Sphere,why the positive charges are considered outside the surface? And,why if any point charge is inside a sphere,the the net electric field is considered zero?


title: What are nuclear isomers? What is isomeric energy?

text: Can someone explain nuclear isomers to me, and in particular what the energy involved is? I understand generally that we're talking about moving from a less to more stable configuration of nuclear particles, but that's about as far as my understanding goes.


title: How is Mechanical advantage of Wedge = length of slope/width

text: Mechanical advantage is defined as Force Output/Force Input For a symmetrical wedge with the length of the slopes being equal and the width being the distance between the end points, articles quote the Mechanical advantage as length/width ![forces in a wedge](http://www.essential- physics.com/samples/Images/SB/28/LR/WedgeForces.png) I will assume that you are splitting wood using a symmetrical wedge (lengths of the slopes are equal) and driving the wedge into the wood with a hammer vertically starting with the center of the wooden block. Let us say the width is $w$ and the slope length is $l$. The Input vertical force is resulting in two sideward forces on the wood. Each of these sideward forces is causing the separation in the wood. If, based on the above diagram, I assume that each of these output forces is $F_{in} sin \theta$ where $\theta$ is the angle between the vertical direction of $F_{in}$ and the slope, I have $$\sin \theta = \left(\frac12 w\right)\cdot\frac{1}{l}, $$ Output force, $$F_{out} = 2 F_{in} \cdot \sin \theta = 2 F_{in} \left(\frac12 w\right)\cdot\frac{1}{l} = F_{in} \cdot \frac{w}{l}$$ or $$\frac{F_{out}}{F_{in}} = \frac{w}{l}$$ This is the inverse of the expected mechanical advantage. When I equate work done, I get $F_{in} \times height = Load moved \times distance$. Assuming Load moved is $2*F_{out}$ and distance moved is the perpendicular from center on the slope (perhaps, this statement is wrong. Each point along the vertical was moved by a different amount), I have $$2*\frac{F_{out}}{F_{in}} = 2\frac{\rm height }{\rm perpendicular\,from\,center\,on\,the\,slope} = 2\sin \theta = 2\left(\frac12 w\right)\cdot\frac{1}{l}= w/l$$ But the mechanical advantage of a wedge is mentioned as $l/w$. Why?


title: Rotational Dynamics

text: In studying rotational dynamics of a rigid body , I can't seem to understand why you can solve the problem correctly only using certain points in a body and not all ? Means angular momentum and torque leads to correct answer only in some cases


title: Electrostatic Potential Energy Derivation

text: How is the boxed step , physically as well as mathematically justified and correct ? Source:Wiki http://en.wikipedia.org/wiki/Electric_potential_energy As work done = $- \Delta U $. for Conservative force and it shouldn't matter whether we take $ds$ or $-dr$ ? And when $dr$ is just a notation to specify the variable and the real thing behind it , is a limit , why is it that $dr$ is so important here . ![enter image description here](http://i.stack.imgur.com/HCWeH.jpg) Image : http://www.artofproblemsolving.com/Forum/download/file.php?id=43358&mode=view What is wrong here ? > $$\newcommand{\newln}{\\\&\quad\quad{}} > \begin{align}&\int^{r_b}_{r_a}\mathbf{\vec{F}}\cdot d\mathbf{\vec{r}}=-(U_a- > U_b) \newln \Rightarrow \int^{r}_{\infty}\mathbf{\vec{F}}\cdot > d\mathbf{\vec{r}}=-(U_r-U_\infty) \newln \Rightarrow > \int^{r}_{\infty}\mathbf{\vec{F}}\cdot d\mathbf{\vec{r}} =-U_r ~~~~~~~ > [U_\infty = 0], \cos\theta=-1 , \vec{A} \cdot \vec{B}=|A||B|\cos\theta\newln > \Rightarrow -\int^{r}_{\infty}k\cdot\frac{q.q_o}{r^2}dr=-U_r ~~~~~~~ > [\textrm{Coulomb's Law}]\newln \Rightarrow kq\cdot > q_o\int^{r}_{\infty}\frac{1}{r^2}dr=U_r\newln \Rightarrow kq\cdot > q_o\left[\frac{-1}{r} \right]^r_\infty=U_r\newln\Rightarrow > \frac{-kq.q_o}{r}=U_r\newln \Rightarrow U_r=-\frac{kq.q_o}{r} \end{align} $$


title: Autocorrelation of sound in liquids vs gas

text: This is just a curiosity and you need to bear with me as my math skills were always sub-par and so is my English academic language. My specialty is Electronics but I have always been a programmer. Years ago I was working on my diploma paper that dealt with locating leaks using auto-correlation.   Basically you have several sound sensors along a pipe which record the sound wave. If a leak appears then you get a peak in the autocorrelation function. Then you perform a 'triangulation' from two or more sound sensors and you can locate the leak pretty accurately. Anyway, my task was mostly to help a PHD student with transposing her algorithms into Matlab.      We have succeeded doing this with air but as soon as we switched to water I could not use any kind of windowing and/or transformation to get relevant peaks. At some point I just hunted blindly for some Matlab functions that would give me a relevant peak somewhere that would correlate with the distance to the leak, but failed.      I cannot to this day understand why we were not able to succeed, though I do assume that is has to do with water's turbulence. The setup was a running tap routed through metal pipes (about 10cm diameter), with about 5 very sensitive sound sensors (going to about 100kHz) placed about 3 meters apart and some taps along the way that simulate leaks. Everything was placed in a phonic- insulated basement, signals were truncated taken to stabilize against footsteps/vibrations so measurements were pretty good.      The multiple question is: what could have been done to achieve the goal or at least get closer to it? Is it really achievable (probably not in real life where you have trucks running above)?   Some variables that could influence but for which I lack the knowledge to explain: pipe diameter, water debit rate, tap/leak rate and diameter, choice of liquid, pipe material, sound spectrum and possible frequency filtering.


title: Why does inelastic X-ray scattering probe the longitudinal dielectric function as opposed to the transverse dielectric function?

text: Light is a transverse wave. Therefore, light in the optical range (i.e. visible light) couples to transverse collective excitations of a material when measuring the optical conductivity for instance. Likewise, X-rays are also transverse waves, but somehow couple to longitudinal collective excitations of a material. I understand that it is because X-ray photons couple to the electron density as detailed in this paper, but what I am looking for is a plausible intuitive explanation with some physical insight as to why this might be so. (Sorry if you can't view the paper from the publisher without incurring a fee, but I couldn't find it anywhere else. I think the question is clear enough without the link, though.)


title: Why do we orbit around the sun instead of one the other stars?

text: I am still very new to many physics theories, however while sat in class today, a thought came to mind that I have not been able to answer from simple googling. What is so specific about our sun that we orbit it? It is by no means the largest star and it's mass is apparently around average for a star. So why, out of all the stars, do we orbit the sun? Is it due to position, pure coincidence or is it something I do not know about with my limited knowledge. Thanks for your help.


title: What is the difference between 'flow' and 'move'?

text: I just met with a very basic question.(Might even sound silly!) My textbook kinda says(not exactly), 'Whatever flows is a fluid'. That got me wondering because we are creating a whole category of matter just because they flow! So there must be some significance to 'flowing'. That further led me to ask why in the first place should we say liquids and gases "flow" and not "move"?! It seems to tell me that there should be a major difference between the physics of flow and movement. What is it? PS:- I don't want the difference in meaning from a dictionary but a scientific difference. Please don't get too mathematical. I haven't acquired good mathematical skills YET. Edit:- Okay. Since a comment below says "Movement is actually seldom defined very rigorously", I suppose I must refine my question here. Consider someone is saying that a box moves on a table as you applied a force on it. Now why is that person saying it 'moved' rather than it 'flowed', here? What is the difference between flow and movement in this case and how can we generalize the idea?


title: Lebesgue integration

text: I know this question is probably not adequate to this SE either, but let me explain my situation: I'm civil engineering's college, so, there isn't a SE for civil engineering, and my doubts about integration in engineering are pratically pure physics. So, as I said, I'm graduating, but I'm from Brazil, education here is the same thing as nothing (belive me, it really sucks, I see people come out of physics's college without knowing who Maxwell was..), and I read my calculus books and see they all use Riemann integrals (of course, they don't say that..); but, in my searchs, I see a lot of Lebesgue integration, especially concerning problems of calculating the center of mass of an object, in continuum mechanics, etc. So, here's my question:   1. Lebesgue integration isn't the most easy thing in the world, I don't have a lot time, and education here sucks, should I spent my time studying Lebesgue integration instead of Riemann's?    2. Which one do you guys use more in physics with applications in engineering?; of course, the last one it's a little trouble, because engineering just "borrow" from physics. But, in general, which compensates more?


title: Are there any exceptions to Newton's laws?

text: So I am studying the laws of Newton and I'm wondering, are there any deficiencies related to the laws? I mean, somewhere where I can't use them or anything?


title: Is the following a simpler viable alternative to Feynman's interpretation of the double slit experiment

text: Feynman suggested that there is an infinity of trajectories for a single electron travelling from the source to the phosphorescent screen. He said that one electron goes through both holes (Fig 4.10, page 110, The Elegant Universe, Brian Greene). Is it possible that there is a simpler explanation? The double slits bear a parallel resemblance to the characteristics of a simple slot antenna equal to a simple dipole antenna. Can the incident electrons induce a charge into the area surrounding the slot and cause an electric field to be created between the slot edges. This would serve to convert the electron from a transverse particle wave to a longitudinal magnetic wave which is then radiated forward. The interference pattern is created as the output of each slot interferers with each other producing the interference pattern on the phosphorus screen. It would also explain why, when a sensor is introduced to monitor what is happening in the slit, it causes the magnetic wave to change back to a particle wave, because it has disturbed the field in the slots.


title: Strong Decay and Parity Conservation?

text: The following decay is possible according to the PDG and according to my notes it is a strong decay: $$\omega(1420) \to \rho^0 + \pi^0$$ The JPC values are: $\omega(1420)$ 1-- $\rho$ 1-- $\pi$ 0-+ So, all three particles have, for themselves, a parity of -1. The combined parity on the right side should then be (-1)*(-1)=1. But the left side has a parity of -1. This violates parity, but parity should not be violated in a strong decay. 1) What's going on and where is the error in my argument? 2) How can I calculate the orbital angular momentum the two decay products have in relation to each other?


title: Are there controversies surrounding the principle of general covariance in GR?

text: I'm a physics graduate now working with computers. I study GR in my spare time to keep the material fresh. In the Wikipedia article about the mathematics of GR, one can read the following: > The term 'general covariance' was used in the early formulation of general > relativity, but is now referred to by many as diffeomorphism covariance. > Although diffeomorphism covariance is not the defining feature of general > relativity, and _controversies remain regarding its present status in GR_ , > the invariance property of physical laws implied in the principle coupled > with the fact that the theory is essentially geometrical in character > (making use of geometries which are not Euclidean) suggested that general > relativity be formulated using the language of tensors. [My italics.] Do anyone know what kind of controversy the author(s) may be aiming at? Isn't general covariance, ehrm ... diffeomorphism covariance, a founding principle of GR? **UPDATE:** Evidently there is no "right" answer to a question like this (unless you happen to be the author of said article and thus could share with the world what you where aminig at). Anyway, it seems as there isn't a widely known, heavily debated controversy regarding general covariance. ~~Even so, I've chosen to accept Ron's answer.~~ **UPDATE 2:** I've retracted the acceptance due to the linked article by prof. Norton. I think that, for all practical purposes, Ron's answer still stands, yet I want to review said article first. However, nobody should hold their breath waiting for me to figure this out. :)


title: Would a thinner atmosphere (such as high altitude) yield better solar panel energy generation?

text: I am curious. If you were to put a solar panel up in high altitude or on the surface of the moon, both of which have much less atmosphere to reflect/refract light, would that solar panel produce more energy? I am curious because an article comments discussion got me thinking about setting up a low Earth orbit solar collection platform as a power plant for a city or nation. Then I got thinking about how to bring it down to the surface (the energy that is). Which had me thinking about using really long cables stretched from the satellite to a high-altitude dirigible platform that would then allow it to more easily bring the energy to our planets surface. From there I started wondering if the high altitude dirigible platform would instead be up high enough to garner any added energy collection benefits. It would certainly help with space saving on the ground and could be rather quickly moved into a disaster area for emergency power purposes. Being a dirigible it would also be relatively easy to keep it aloft. With it far above the clouds it should be able to avoid many weather issues as well (as far as I am aware). So does anyone know if there would be any added benefits from solar collection in a thinner atmosphere environment from a power generation perspective? What pitfalls can you think of? The biggest one I can think of is the efficient transport of the energy.


title: Normalization of Momentum Eigenfunctions: the number of particles

text: After finding the eigenfunctions $u_p(x)=Ce^{ipx/\hbar}$ of the momentum operator just like in this UCSD lecture notes, one seeks to normalize them, so one first tries: $$\int\limits_{-\infty}^{\infty} dx \, |C|^2 e^{-ipx/\hbar} e^{ipx/\hbar} = \int\limits_{-\infty}^{\infty} dx \, |C|^2 \rightarrow \infty $$ which diverges unless $C =0$. Then it is shown that $u_p(x)=\frac{1}{\sqrt{2\pi \hbar}}e^{ipx/\hbar}$ satisfies the normalization condition $\langle p'|p\rangle=\delta(p-p')$ Why does the UCSD page say that the first solutions (the divergent ones) "are not normalizable to one particle"? How does the development that follows relate to many particles? Does this have something to do with $\int\limits_{-\infty}^{\infty}dp \delta(p-p') =1$? Then all the $p'$ are the other particles? I have no source to show for this, but how would $\frac{1}{2\pi \hbar}$ particles per unit of length and unit of momentum relate? Is it correct to say that $2\pi \hbar$ is the expected number of times one repeats the measurement of the momentum? Then where would the 'per unit of length' part come from?


title: How does one pronounce this particle's name?

text: How would you read the following particles' names in a conversation in English? I am looking for some "proper" way of doing it. Say, imagine you are reading a technical description in a semi-formal occasion that you would like to avoid being lousy or overly simplistic. $$\Delta(1750)^0 P_{31}$$ $$\bar\Delta(1910)^0 P_{31}$$ $$\Delta(1910)^- P_{31}$$ [EDIT] One additional question, would you write $\Delta^0(1750) P_{31}$ or $\Delta(1750)^0 P_{31}$ ?


title: Bolzmann entropy

text: The Boltzmann entropy is defined as the logarithm of the phase space volume (E). Is there a reference, book, paper which shows where this definition comes and how it is equal to the phase space volume?


title: Why does cold water weigh more than hot water in a fixed volume?

text: Take a bucket of hot water and the other bucket of cold water. Why does the bucket full of cold water weigh more than bucket full of hot water?


title: Hilbert, Gödel, and "God equations" - a 19th century lesson for 21st century physicists?

text: It seems there are a lot of respected physicists appearing on pop-sci programs (discovery channel, science channel, etc.) these days spreading the gospel of "we can know, we must know." Three examples, quickly: 1) Many programs feature Michio Kaku saying that he is on a quest to find an equation, "perhaps just one inch long," which will "describe the whole universe." 2) Max Tegmark has come out with a new book in which he expresses the gut feeling that "nothing is off-limits" to science. The subtitle of this book is _My Quest for the Ultimate Nature of Reality_. 3) In the series _Through the Wormhole_ there is talk about a search for the "God equation." (A good counter-example would be Feynman, but his self-described "non- axiomatic" or "Babylonian" approach does not seem popular with physicists today.) Is there any sense among physicists that it might be impossible to articulate the "ultimate nature of reality" in equations and formal logic? It seems to me that physicists are following in the footsteps of the 19th century mathematicians (led by Hilbert) who were on a similar quest which was put to rest by Gödel's incompleteness theorems in 1931. Is there any appreciation for how the Incompleteness Theorems might apply to physics? Has any progress been made on Hilbert's 6th problem for the 20th century? Shouldn't this be addressed before getting all worked up about a "God equation?"


title: Atomic mass of Copper-63?

text: This URL lists the mass of Copper-63 as 62.9295975(6) and this other URL lists the mass as 62.939598. These values differ by almost exactly 0.01 which seems hard to explain by experimental error. Why is it that these values differ in a significant digit but have the same less-significant digits? Is one of them a typo of the other? What is the correct value? What is the origin of both of these values? This discrepancy was noted by commentators in this article about a supposed cold-fusion reactor. According to those commentators, this value is relevant to the cold-fusion debate because it makes all the difference as to whether or not the supposed reaction is energetically feasible. The linked article concerns the same cold-fusion claim discussed in this previous physics.SE question. EDIT: user9325, voix, and user3673 have indicated that the correct answer is 62.929... I have started a bounty on the _origin_ of both the correct and incorrect values.


title: Nuclear physics problem, Why do we use high weight atomic elements?

text: So as far as I know, nuclear fission uses high weight atomic elements to manufacture power. If the risk of runaway reactions are a major reason for not expanding this technology, why don't we use elements with lower atomic weight (eg. less energy) or lower amounts of fuel (eg. less total mass)?


title: Question about gravity probe B

text: I have a question about the gravity probe B experiment. According to this site: http://science.nasa.gov/science-news/science-at-nasa/2011/04may_epic/ The measurements they made confirm Einsteins theory. What I'm wondering is:   1. Did they use a control in the experiment? That is did they put gyroscopes in some place where space time was not supposed to be twisted and get a measurement that was not deflected?   2. If they didn't measure a negative result too, how does this the experiment prove the theory correct?


title: Convergence of periodic single fermion operators

text: First, a quick remark: I'm a mathematician, now working on some problems coming from physics (in particular Ising models on quasiperiodic chains). A few things I find rather mysterious. I would appreciate your help. For the purpose of generality, let's consider the following Ising model on a chain of $N$ nodes. $$H_N = - \sum_{i = 1}^N J_i\sigma_i^{(x)}\sigma_{i+1}^{(x)} - \sum_{i = 1}^N\sigma_i^{(z)},$$ with $J_i$ depending on the node $i$ (we assume no particular order for generality), and $\sigma_i^{(x),(z)}$ the Pauli matrices. By Jordan-Wigner, we can consider the corresponding Fermionic operator given by $$\widehat{H}_N = \sum_{i,j}\left[c_i^{\dagger}A_{ij}c_j + \frac{1}{2}\left(c_i^{\dagger}B_{ij}c_j^{\dagger}+ H.c.\right)\right],$$ where $c_i$, $1\leq i \leq N$ are anticommuting Fermionic operators and $\left\\{A_{ij}\right\\},\left\\{B_{ij}\right\\}$, $1\leq i, j \leq N$ are the elements of appropriately chosen matrices $A, B$, which depend on $\left\\{J_i\right\\}_{1\leq i \leq N}$. We use periodic boundary conditions. Now we can extend $\widehat{H}_N$ to a lattice of infinite size, by gluing the unit cell of size $N$ infinitely many times. Let us call this new extension $\tilde{H}_N$. Now the questions: 1) What is $H.c.$? 2) I am interested in the thermodynamic limit $N\rightarrow\infty$. Is it obvious whether the sequence of operators $\left\\{\tilde{H}_N\right\\}$ converges, say in strong operator topology, to some well-defined operator $\tilde{H}$ as $N\rightarrow\infty$? Let me motivate the second question: For a certain sequence $\left\\{J_i\right\\}$, constructed deterministically with certain properties (so-called _quasi-periodic sequence_ ), I believe I can say something about what Physicists call the "energy-spectrum in the thermodynamic limit". I'm interested to know whether this energy spectrum is the spectrum (in the usual functional-analytic sense) of some operator $\tilde{H}$. Thanks for any help!


title: Could a universe with only massless particles develop life/intelligence?

text: Is it impossible for a universe that only contains particles/fields with no rest mass to develop life/intelligence? Assume there is no mechanism to generate a rest mass (Higgs, symmetry breaking, etc.) It seems ridiculous, but I can't think of a good reason why it can't happen since the life/intelligence may not resemble us. Maybe there is an argument using entropy, information theory, etc. that would be persuasive.


title: Gauge invariant but not gauge covariant regularization

text: I'm not sure if someone's already asked this before, but I was wondering, in field theory,   1. when we say that a certain field is gauge invariant but not gauge covariant, what does this mean? In particular, in Wikipedia, the regulator of Pauli-Villars is said to be as such.    2. Moreover, as a consequence of not being gauge covariant, the Wikipedia article says that this regulator can't be used in QCD. How to see the link between not being gauge covariant and QCD here? And, why can one use it in QED then?


title: Moon and the moving train

text: While travelling by train (travelling West to East), it seems the moon is moving in opposite direction when seen from the window, but then it reverses its direction, after a certain amount of time and moves along the train, but then flips back again. And it kept oscillating, as the train kept moving. Can anyone point out the reason?


title: Why less temperature at high altitude

text: Why there is always cold at high altitudes. e.g. at peak of mountains. Also as we go high from see level, temperature starts decreasing, so why is it.


title: Parabolic or Hyperbolic?

text: How can astronomers find the difference between a parabolic and a hyperbolic comet ? What are the criteria that helps them distinguish these ? Can a parabolic comet switch over to become a hyperbolic one and the vice-versa ?


Does the Hilbert space of the universe have to be infinite dimensional to make sense of quantum mechanics? Otherwise, decoherence can never become exact. Does interpreting quantum mechanics require exact decoherence and perfect observers of the sort which can only arise from exact superposition sectors in the asymptotic future limit?


title: Did Felix Baumgartner produce a sonic boom during his jump?

text: I really got to thinking about this. The speed of sound is measured at 761.2 MPH **at sea level**. But how does this number change as air density decreases? The lack of air density is what allowed his terminal velocity to much lower than say a jump at 5k feet high. I am not disputing his maximum velocity (800+ MPH), **but did Felix Baumgartner actually produce a sonic boom in the process**? I mean, I beleive most people subconsioulsy associate "sonic boom" and "faster than the speed of sound".


title: Locating a Comet, how is it done?

text: How are the comet-hunters able to precisely locate/know about the required comets ? How can they distinguish between comets from such a far distance ? How are they able to estimate the exact time period of these comets like Hale- Bopp's and Halley's comets have orbital time periods 2520-2533 yrs and 75.3 yrs respectively ? Do they have to follow the comet throughout its whole orbital path to deduce that or are there any other procedures ? I've heard of using computer generated programs that help in here. Please notify me some of these.


title: Effect of Charged Particles trapped in Magnetic Field on that Field

text: Given a stream of moving charged particles that encounter a uniform magnetic field such that they are trapped in a circular orbit, what effect do these particles have on the net magnetic field over time? Would the magnetic field get stronger or weaker as the number of trapped particles increase?


title: How is electrical energy transmitted?

text: My original question was in an effort to understand the electrical analogy to Markov chains, which is explained in Snell's article. There are some neat parallels that involve taking a Markov chain and considering the edge weights to be wire conductances. Unfortunately, after reading the article, I realize that they specifically say that their analogy is unrealistic. So, how is electrical energy transmitted?


title: Coriolis force and Newton's third law

text: I would like to ask a stupid question here. If a body 'b' moving downward with a velocity v in a rotating frame of reference with angular velocity w, and w and v not being parallel and anti parallel. We all know that the body 'b' experiences a Coriolis force. If it gets deflected in its trajectory then according to newtons third law shouldn't it push some body with equal force? what if the fame of reference was moon where there is no atmosphere? will the body be deflected?


title: How does a pressure suit work?

text: I recently learnt that a suit called pressure suit is worn by fighter plane pilots to prevent red-outs and black-outs. And it seems to be work by - > "..applying pressure to selective portions of the body." How do these suits work; i.e. by what means, selective portions of the body are pressurised? Do astronauts wear these while takeoffs, and also F1 drivers?


title: How to determine phase angle for a sinusoidal motion?

text: If I have an over-damped mechanical system that is excited with a sinusoidal motion. That sinusoidal motion starts with a determined frequency then increases frequency over time. Of course, it is known that there will be a phase shift between the driving force and the motion of the hanging mass. My question is, how to figure out phase lag of mass motion in relation to driving force?


title: Which direction will Coriolis forces deflect a bubble?

text: If I throw a ball straight up, it deflects slightly to the west due to Coriolis forces. If instead I watch a bubble float up in water, is the bubble deflected west, east, or neither? I think the bubble also moves west, but am not sure. My reasoning is that the air in the bubble must feel a Coriolis force to the west because it is rising. Further, as the bubble rises, the water around it moves, and the net motion of the water is down. Water moving down experiences a Coriolis deflection to the east. Bubbles move the opposite direction of water, so if the water is moving east, then the bubble should move west. ~~I don't have any reasonable-sounding counter-arguments, but I'm not completely convinced by my argument, either.~~ **Edit** : One reason I'm a unsure about this problem is that a bubble does not get thrown outward by a centrifugal force. Imagine a plastic ball filled with water and spinning fast. A bubble is sitting in the water in the equatorial place, half way to the edge of the ball. There's centrifugal force out towards the wall, but the bubble does not move that way. The bubble moves up the pressure gradient. The water gets thrown to the wall, and thus there is higher pressure at the wall than at the center. The bubble moves towards the center. If a bubble moves counter to the centrifugal force, I should be careful before claiming it moves with the Coriolis force.


title: Probability of forming mesons vs baryons

text: When a heavy quark hadronizes it has some probability of forming a meson vs forming a baryon. I suspect there is a well known branching ratio for each type of hadron. Does anyone know what the probability is or, even better, a reference that discusses this? An ideal answer (though not necessary) would further give a crude approximation of this probability (though I don't know if this is even possible).


title: Isospin and Energy

text: I would to know if there is a correlation between isospin and energy. Consider for example the $\eta$ meson ($I =0$) and the pions($I=1$). The $\eta$ turns out to be much heavier then the pions ($m_\pi \approx 150 \mbox{MeV}$,$m_\eta\approx 550\mbox{MeV}$). A counterexample is the $\Lambda_b$ ($I=0$) and the $\Sigma_b$ ($I=1$) baryons. Here the $\Sigma_b$, the higher isospin state, has a larger mass. Are there any known trends between isospin and energy?


title: Twin paradox with two intertial frames in general relativity

text: I assume the twin paradox from special relativity is well known. I wish to focus on the apparent symmetry of the problem: both observer seems to move away from each other, and then come back. Yet, the outcome is asymmetrical. That paradox is resolved because the travelling twin has to turn around at some point. Then he has to change inertial frames, or accelerate, and this means that the situation is not symmetric anymore. What now if the "turn around" is not caused by an acceleration, but a "gravitational slingshot". Say, the traveling twin's trajectory passes by the graviational field of a couple of stars, freely falling, such that the twins just happen to end up in the same place after a while again. According to general relativity, both twins then remain in an inertial frame. Both see the other initially disappear with slowly ticking clocks, and later reappear from some other direction. All the while, they stayed at rest in their own reference frame. So the other twin must have aged less than themselves. The situation seems completely symmetric again. Of course, since they meet in the same point again, they cannot consider the other one younger from both perspectives. What is the resolution? I found this other thread which seems related: Symmetrical twin paradox This refers to a paper that claims that this is due to the fact that the topology of the space induces some preferred reference frame. I don't pretend to understand that paper, but I think it refers to a similar paradox obtained by assuming that the large-scale structure of the universe is spherical/cylindrical, or something like that, allowing one twin to travel "around". Surely it is possible to set up my above scenario with only a few local stars. So it seems strange to me that a local paradox should be solved by relying on a global topologically prefered frame.


title: Newton's 3rd law

text: So i read this in some article on the net > Consider a boy is standing at distance of 10 metres from the wall. Boy holds > a rubber ball and cloth ball in his hands. Firstly, the boy throws rubber > ball with force 2N (Newton) on the wall. The rubber ball after striking the > wall rebounds to 10 metres. Thus, action and reaction are equal in this > case. Secondly, the boy throws cloth ball with an equal 2N force on the > wall. The cloth ball rebounds to five metres. Thus action and reaction are > not equal. Is this really right? o.O P.S: i dont have any background in physics and hence this question


title: Maximum pressure of a rubber balloon

text: I've had a question about this topic previously, but the material was inelastic. Forces in a balloon popping? What happens when a material is non-hookian? Say rubber, I've found this pdf on the web: http://www.researchgate.net/publication/245382031_Inflating_a_Rubber_Balloon


title: Relative motion. Setting course of closest approach (Requested resource recommendation as well)

text: Let $r_{P/Q}$ be the position vector of $\overrightarrow P$ relative to vector $\overrightarrow Q$ and $v_{P/Q}$ the velocity vector of $\overrightarrow P$ relative to $\overrightarrow Q$. Suppose $|v_Q| > |v_P|$ and you want to set the direction of $v_P$ such that $|r_{P/Q}|$ becomes minimal at some point in time. According to the text I have, doing so requires that $v_P \cdot v_{P/Q} = 0$ ![enter image description here](http://i.stack.imgur.com/g45Jd.png) Sorry for the horrendous image but I hope the idea is clear. $v_P$ could be any direction and the blue circle represents all possible directions of $v_p$ Anyway, my problem lies in that I do not understand why this is the necessary condition for the closest approach. Could someone enlighten me? If you know of a resource containing information relevant to this question, that would also be great. Edit: I would add more detail but unfortunately there isn't much more that I know. Of course there are two angles where this works and I guess you choose the one depending on the initial positions of the two objects. Edit: I'm really sorry but I didn't label the image properly which resulted in the post being confusing


title: What exactly is heat?

text: Is it energy? Is it energy per unit volume? Is it energy per unit time i.e power? What is it?


title: Trying to understand the EPR paradox

text: So I keep reading all these articles on the EPR paradox, and I follow them pretty easily right up until it gets to the most important matter. Assuming you are trying to measure x and y spin, Wikipedia and others say that when you measure x-spin on the first particle, it suddenly becomes impossible to measure the y-spin on the other particle. But no one really goes on to say what this means in a physical sense. Let's say you have 2 actual detectors. When the first particle hits the x-detector, now x-spin is measured for both particles. When the second particle hits the y-detector, now y-spin is measured for both particles. But all these articles say the second detector is unable to measure y-spin. So what happened? Did the detector just explode or something?!


title: Why is the Ritz combination principle incompatible with Classical Mechanics?

text: This is a quote from Dirac's Principles of Quantum Mechanics: > "(...) if an atomic system has its equilibrium disturbed in any way and is > then left alone, it will be set in oscillation and the oscillations will get > impressed on the surrounding electromagnetic field, so that their > frequencies may be observed with a spectroscope. Now whatever the laws of > force governing the equilibrium, one would expect to be able to include the > various frequencies in a scheme comprising certain fundamental frequencies > and their harmonics. This is not observed to be the case. Instead, there is > observed a new and unexpected connexion between the frequencies, called > Ritz's Combination Law of Spectroscopy, according to which all the > frequencies can be expressed as differences between certain terms, the > number of terms being much less than the number of frequencies. This law is > quite unitelligible from the classical standpoint." I'm having trouble understanding this paragraph. Assuming that the atom is a system in equilibrium that emits e-m waves when perturbed and these e-m waves are product of the oscillations of the atom about its equilibrium configuration that result from the perturbation, does it follow that the Ritz's law is in contradiction with classical mechanics? Why? Thanks.


title: If black and white object are in isolated space will the black absorb heat from the white?

text: This question has come to me from my friend in fact: he noted that the heating in the pub is painted black. I replied that it's better for heat emission. I don't know where did I know that from. And he disagreed, asking me: "Why would black emit more heat than white?" I didn't know. We could, however, agree on fact, that black _absorbs_ more heat than white. I quickly created a thought experiment to proof by contradiction that the black must emit more light than white: > Assume that white and black both emit the same amount of light. Put a black > and white object in an area. Assume that any light (or heat) emitted by the > objects can only be absorbed by them. Imagine that the white object emits > light and heat. The black one will absorb considerable amount of it. When > the black object emits the light the light one will reflect a great portion > of it - which can be then absorbed back by the black one. Written like this, it seems that second law of thermodynamics is being broken by this concept. However, my friend has also thought something to oppose me: > If black objects emits more heat than the white one, why the black objects > are hotter when put in the sun? Shouldn't they emit the extra light they > absorbed? I understand that it's not all that simple. There's an article that says I'm right but it doesn't really satisfy me. For start, infrared is no color at all - how could it have to do anything with black, white or any other color? Shouldn't an _"infrared_ " painted stuff reflect most heat? I ask for an answer that sufficiently explains why the black and white things absorb/emit heat as they do. And, if questions post by both mine and my friend's arguments are asked, I will be very happy.


title: Can one construct a new operator in terms of the powers of another operator?

text: Suppose we have a quantum state, well described by its time-independent wave function Psi. And we have a well-defined Hermitian (self-adjoint) operator $A$. We successfully evaluate the expectation value of the operator $A$. Next we derive the general formula for the higher moments of $A$ (i.e. the expectation value of $A^n$ for $n=2,3,4\ldots $). In this situation, is it permitted to regard each of the $A^n$ for $n=1,2,3,\ldots$ as a proper operator by itself? For example, should every $A^n$ have a positive variance and other statistical properties (as long as we restrict ourselves to the state $\Psi$)? Can one make linear combinations of different powers to construct a new operator, e.g. $B = A + A^2$? Is it allowed to construct new operators acting on $\Psi$, that are defined in terms of their series expansion in $A^n$? For example, $D = \exp(CA)$ where $C$ is a constant?


title: So physicist's really do think the Universe could be a holographic Illusion?

text: http://www.nature.com/news/simulations-back-up-theory-that-universe-is-a- hologram-1.14328 http://guardianlv.com/2013/12/compelling-evidence-says-our-universe-is-a- hologram/ I thought the holographic Principle was just a sexy way of referring to the fact that a black hole's maximum entropy is bounded by its surface rather than its volume, and since the surface is a Schwarzschild radius, and that can be said to be 2D, then that's where they got the notion of calling the principle, holographic, since holograms are thought to be 2 dimensional(even though they are not 2 dimensional). But the notion that the holographic principle applies to all the Universe, not just black holes, and that it shows the universe is a holographic illusion, won't go away, as shown by the two links above. So, is there a real possibility that the Universe is a hologram, and that we live in the matrix, and that what we think is real, which is the 3D, material world, is just an illusion?


title: Can a small change in the Earth temperature give rise to large-scale climate changes?

text: Earth's atmosphere is a chaotic system. In such systems arbitrarily small changes the conditions can give rise to very large effects. There are many rumors about the physical and large scale environmental impacts that global warming will cause in the future. (for example, here) After a remark made by one of the users here, I thought to ask this question: **Can a small change in Earth's temperature (that can't be _felt_ ) give rise to large-scale climate changes?**


title: Wave function with a delta potential

text: I have a particle and a potential $V(x)=\frac{\hbar^2}{2m}k\delta(x)$. Where $\delta (x)$ is the Delta function, and I am interested in the solutions of the **stationary** Schroedinger equation. If $\psi_1$ is the solution for $x<0$ and $\psi_2$ for $x>0$, must be that $\psi_1'(0) \neq \psi_2'(0)$, because of the delta function. Now I read that the condition is $$\psi_2'(0) -\psi_1'(0) = -k\psi_2(0).$$ My question is: why? How do I get at this conclusion?


title: periodicity of diffraction gratings

text: Imagine we have a diffraction grating consisting of N slits (being N very large) with a separation of "d" from slit to slit. Now, we could regard this grating as a diffraction grating constructed by a repeated double slit, in which case the periodicity would be 2d. I realize this can't be legitimate since the theoretical positions of the maximums would change and this can't be (since the grating is doesn't change no matter how we regard it). Nonetheless, dealing with examples of defectuous grating exercises I have seen examples that regard gratings as repetitions of double slits or triple slits. So, my question is the following, why is it possible in some cases and not in others? I mean, why can't we regard the typical grating mentioned above as a repetition of double slits (or triples or whatever)? (my guess is that maybe we always have to choose the $\textit{minimum}$ periodicity but I am not sure)


title: Could the Earth have a dark matter core as well as a disk?

text: If it is established that the Earth does have a dark matter disk as this recent discovery suggests. http://www.newscientist.com/article/mg22129503.100-gps-satellites-suggest- earth-is-heavy-with-dark-matter.html Then could the Earth have a dark matter core as well as a disk?


title: Surfaces that refract, but do not reflect

text: I know there exists surfaces that only reflect light (mirrors), but are there surfaces that only refract light? If so, how does that happen?


title: Bound States clarification

text: Our professor hasn't explained what bound states are. Could you give me an idea of what they mean and their importance in quantum-mechanics problems with potential (e.g. a potential described by a delta function)? And why, when a stable bound state exists, the energies of the related stationary wavefunctions are negative? I mean, I figure it out, mathematically, in the case of a potential described by a Delta function, but which is the physics sense of that?


title: Radio antenna producing waves in the visible spectrum

text: If a radio could produce waves in the visible light spectrum, what would the result be? This is a thought experiment that I've pondered for a few years now. I realize there are a few/many real-world constraints, but if we lifted these constraints for the sake of thought, what could we expect? Personally, I don't see why we wouldn't observe visible light emitting from the antenna, disregarding any light from Blackbody Radiation.


title: Lorentzian and Einstein Manifold

text: I am studying for my Bachelor thesis (in Mathematics). I and my advisor agreed on the Penrose-Hawking singularity theorems. My question is: 1) Which mathematical background should I focus on mastering in order to be able to approach the singularity theorems? 2) Is it the Lorentzian (Pseudo-Riemannian) manifolds which is flat (and there isn't very much to say about it) or the Einstein (Riemannian) manifolds (which for what I know now is in a important way different form the nature of space- time? Or both? Perhaps am I missing something important? 3) What is the role of Schwarzschild metric in this? How is it related to the manifolds above? 4) Is the next statement correct? > _Schwarzschild metric is a particular solution of Einstein field equations > (under which hypothesis?) in the sense that it models the space time of a > portion of universe as a manifold with that particular metric. In this > setting the singularity theorems can be proved._ 5) Can anyone give me a complete statement of the singularity theorems so that I can see what mathematical objects are involved? I still haven't looked for them because I taught that studying the math before even reading them could save me some time. But I have been studying Manifolds for two weeks now and I am getting more and more confused and I fear I am wasting time.


title: Where did the energy come from?

text: Suppose there are two slopes. Imagine its just small slope and can be placed on your floor. One slope is made of a very smooth material and another which provides a lot of friction for example made of rubber. Now you place a cubical metal block on each of the slopes. Both the blocks are exactly identical. The metal block on the smooth surface will slide down due to the action of gravity but the one place on the rubber slope will not. Where did the rubber slope get energy from to work against the action of gravity and holding the block in its position?


title: Do physics laws really apply to anything?

text: My professor said that a law was stated and announced as a law because it happens in our everyday life. He gave us an example of Newton's 3 laws. He said that walking possess 3 laws of Newton's. Is it true that all laws really happen in our daily motion?


title: Solving equation of motion of two massive particle exerting the gravitational force each other

text: I'm trying to analyze the motion of the particles which exert the gravitational force each other. Let $M_1$, $M_2$ be the masses of the particles, and the equation of motion of particle $M_1$ $$ F=G\frac{M_1M_2}{r^2}=M_1\ddot{r} \\\ \ddot{r}r^2-GM_2=0 $$ I find it doubtful that the simple motion has difficult equation of motion. Should I just use some form of successive approximation?


title: Has anyone actually "seen" entanglement?

text: I want to know if the following has been done experimentally; after the spin (or any other characteristic with a probability of 50%) of 2 entangled particles has been measured, we change the spin of one and we see the spin of the other changing instantaneously at a distance. For example, entangled particle A is spinning up and entangled particle B is spinning down, we make A spin down and see B start spinning up at the same time. I know entanglement has been proven experimentally but it always seems to imply this "spooky action at a distance" and I wonder if THAT has actually been proven experimentally. Maybe my question should have been has anyone seen spooky action at a distance...


title: Physics of weird "boing" sound in racquetball courts?

text: While playing racquetball, I frequently hear a very prominent "boing" sound (or more formally, a chirp). For example, you can hear it in this video when the ball hits the front wall. Does anyone know what the origin of this sound is, and why the pitch rises? Here is the spectrogram from the above video: ![enter image description here](http://i.stack.imgur.com/G2tdWm.png) A careful examination shows that there are at least four linear chirps, which I've highlighted below. If you really listen carefully, all four of these are audible. (However I can only distinguish between the two high frequency chirps when the audio is played at half speed.) ![enter image description here](http://i.stack.imgur.com/lzyGMm.png)


title: Find values of $x$ such that the probability density $|\Psi(x)|^2$ of a wave function is maximized

text: How do I find the values of $x$ for a given wave function $\Psi(x)$ such that it's probability density function $|\Psi(x)|^2$ will be maximized? My guess is to to constrain the derivative by the conditions $\frac{d\Psi}{dx} = 0$, and then plug those values into $|\Psi(x)|^2$. Is this the right approach?


title: Space-time Topologies?

text: When it comes to questions of existence of bounds for PDE's and such, one must often make some assumptions regarding the topology of the space-time to use well known theorems. My question is two-pronged: i) I've often read, on Wikipedia (http://en.wikipedia.org/wiki/Spacetime) for example, that space-time is paracompact. I am aware of the mathematical definition and this seems counter-intuitive to me. Since the form of the stress-energy tensor entering Einstein's equations need only satisfy the conservation of energy $\nabla_{\mu} T^{\mu \nu} = 0$ condition from the Bianchi identities, how does one show this result? Can someone give me a reference for a proof? ii) In (electro)-vacuum, what other topologies are permitted globally? I have seen some papers finding solutions that resemble black holes (in the sense they have singularities, event horizons...) but are topologically not 2-spheres at their cross section (seemingly in violation of Hawking's theorem, see e.g, http://arxiv.org/abs/hep-th/9808032, but perhaps the fact the space- time is asymptotically anti de-Sitter is why there is no violation). What space-times are compact? The spheres $S^{n}$ are all compact, but presumably even the Schwarzschild space-time is not globally? I think one can only have a compact space-time if its Euler characteristic $\chi = 0$, can this be translated into a demand on $T^{\mu \nu}$? I am particularly interested in compact space-times, for one can then apply the Yamabe problem. Thanks!


title: Calculating Ground State Energy in 1D Potential

text: Given potential $V(x) = Asec(x)$ for $x > 0$. I want to calculate the ground- state energy $E_0$ via the Schrödinger equation. I'm completely stuck on this one. I've set up the time-independent Schrödinger equation, but it can't be solved without using special functions. I don't see how I can calculate the energy without solving the schrodinger equation. Any hints?


title: Topological phase in Laguerre-Gaussian transverse mode

text: Why is the topological phase in a Laguerre-Gaussian transverse mode is the sum of orbital angular momenta per photon, and why is it quantized?


title: What's the motion of this yoyo under external force will be?

text: A yoyo on a horizontal table is being pulled by a string to the right, the table is not frictionless. If we only know that the object doesn't slip, how do we know if the string is winding up or unwinding? My reasoning is initially the friction is not ever effect so the force pulling the yoyo to the right will act a torque to the object such that the string is unwinding. But someone else said it should be winding up. I don't know why.


title: If electromagnetic fields give charge to particles, do photons carry charge?

text: As I understand these two statements:   1. An electromagnetic field gives particles charge   2. A photon is a quantum of electromagnetic field It must mean that a photon carries charge. But I guess it isn't true. Why not?


title: Does quark color contribute to "spin degeneracy" for QGP calculations?

text: Like the title say, does quark color matter in counting contributions in a early universe plasma (QGP), as when adding up the total plasma energy density, or is it just spin? The book I have (Pathria) only does one example and doesn't really firmly say one way or the other. I kind of thought it was to account for all degeneracy but the table in the book only has "spin degeneracy". E.g.: $u_{total}(T) = X\,u_{\gamma}(T) = \left(2 + 8 + 7/2 \right)\,\frac{u_{\gamma}(T)}{2}$ where the terms are for, photons, gluons, and charm/strange quarks. (I know these together do not make sense, but it is just an example).


title: What could this very dark planet be made of?

text: I was reading about the planet TrES-2b which is less reflective than charcoal. What could possibly be its composition?


title: Is it possible to look into the beginning of the Universe?

text: If we currently can look into some of the furthest stars, actually seeing the past   Isn't it conceivable that given enough distance we should be able to see   Parts of the Big Bang? If the Universe is endless, it means we should be able to see into its beginning.   Has this theory ever been presented ? Is there anyone looking in to this possibility ?


So tonight's Quatrantids shower got me thinking. Why does the debris from comets and former comets hang around so long? Each year the earth sweeps through the region of space that the comet went through. However, the comet doesn't come by each year, so the earth must be going through the same cloud numerous times. And each time we get a meteor shower as a result. I suspect an answer, but I'd rather hear from professionals.


title: What is the correct way to handle significant figures when calculating compound uncertainties?

text: When processing experimental data, and calculating an uncertainty value in multiple steps, should intermediary uncertainties be used to a certain number of significant figures or kept to the full precision allowed by the calculator/computer? I have a number of measured values and their associated uncertainties, and I have processed this data to give me a final value and uncertainty without ever limiting significant figures in either the values or uncertainties at each step. Is this the correct way to go about this?


title: Electric Field due to a charged sphere

text: Suppose we have a spherical surface with a surface charge density varying as $cos(\theta)$. Apparently one can find the electric field both outside and inside such a spherical surface by superposing the fields of two slightly offset charged spheres with uniform volume charge density. Tips regarding how one goes about doing such a thing would be greatly appreciated.


title: Gyroscope bombardment

text: Let's say I have a spinning steel ball that I have somehow managed to be completely free in all axes of movement. If I fire a BB at it with enough force on a north-south (to the ball) angle, what will happen. Will it start to wobble by a certain amount? Will it change it's orientation and then stay there? I welcome complex answers, but please summarize them in laymen's terms as well. When I say north-south, I'm referring to the earth so that means it would be fired along a plane of the axis of the spin at about 45 degrees (or whatever) to the axis if that makes any sense. In other words, not with or opposing the spin, just perpendicular to it at an angle.


title: Time inside a Black hole

text: If time stops inside a black hole, due to gravitational time dilation, how can it's life end after a very long time? If time doesn't pass inside a black hole, then an event to occur inside a black hole needs infinite time relative to the outside. Thus, it will never age. Please keep it simple..


title: Sandstone getting soaked with water

text: I have seen someone putting a sandstone in water. With only about 10% of the stone sitting in the water. One could see the stone getting soaked with water. So there must be a force, which lets the water climb up through the stone against gravity. What is that force? Or is there some other effect present?


title: How do photons decay in superconductors?

text: If $A$ is the vector potential, the London equations imply that: $$(\nabla^{2}-\mu^{2})A=0$$ if there is no external current. This can be interpreted as an effective photon mass and so, light cannot propagate indefinitely within a superconductor. Let $\lambda = 1/\mu$ be the London penetration depth. As a thought experiment, assume we had a thin (< $\lambda$) slab of superconducting material and shined high frequency light on it. Some of the energy would be lost as heat (photons hitting atoms, etc.). The rest would ``decay" exponentially but manage to get to other side of the slab. My thoughts and chain of questions: How would the light emerge? Would the exiting light have lower frequency but proportionally higher intensity? Would it have the same frequency and just be the surviving fraction of photons? Then, what did the photons which didn't survive decay into? Or, does the decay just mean absorption of the photons e.g. heat generation? The $U(1)$ gauge symmetry of quantum electrodynamics is broken/hidden. How do the Feynman diagrams look inside a superconductor?


title: Why isn't resistance proportional to distance squared

text: Here we have a wire. At both ends there is an equal and opposite field caused by a chemical reaction. So, if we decrease or increase the distance between the two points, the strength of the field increases/decreases with the square of distance. Why then is resistance linearly proportional to distance then?


title: Cooper instability

text: I have a question about the mechanism of Cooper instability. I know the naive picture with two interacting electrons and noninteracting fermi sea wchich leads to the bound state formation. However, if you take all electrons into acount and introduce these effective attractive interaction coming from phonon exchange the Cooper pair will also form. My question is the following: do the Cooper pairs form only in the vicinity of the Fermi level (magic $2\hbar\omega_{D}$ interval) or is the whole Fermi sea composed of Cooper pairs like the BCS ground state? Which situtation is the correct one? Is the BCS ground state just an approximation?


title: A question about the Thomson experiment

text: Recently, I was studying about Thomson's experiment with cathode rays. My textbook shows it like this. ![enter image description here](http://i.stack.imgur.com/GrPY3.jpg) It says: > When only electric field is applied, the electrons deviate from their path > and hit the cathode ray tube at point A. Similarly when only magnetic field > is applied, electron strikes the cathode ray tube at point C. But if we apply Fleming's Right Hand Rule, then we get the direction of force in the upward direction, so the rays should deviate towards A but they deviate towards C. I think it is because Fleming's Left Hand Rule is defined for conventional current(flow of positive charges) and what we are dealing with are negative charges. Is that correct?


title: Why is my ballpoint pen spatially temperamental?

text: I'm trying to write with a ball-point ink pen on a plastic[1] sandwich bag. When I try to write on some parts of the bag, no ink transfers to the bag: I can continue trying for quite a while in vain. I move to another part of the bag, and the ink transfers just fine. Then in other parts of the bag again, the ink will not transfer, and in yet others it will. Why? * * * [1] I don't know what kind of plastic it is. The box only says "Ingredients: Plastic and Dye. SCJ Formula # 35*12700". (SCJ is S.C. Johnson & Son, Inc., the manufacturer.)


title: How large can planets or moons appear?

text: In many artistic impressions or movies there are pictures or scenes where the sky is filled with an enormous moon (as seen from a planet) or vice versa. I wonder if there is an upper limit to the apparent size when viewed with the naked eye (no tele lens). Since the Roche Limit forbids celestial bodies coming too close to each other, there certainly is a limit to the apparent size. ![Artistic image of a large planet seen from a moon](http://i.stack.imgur.com/B3mEm.jpg)


title: Is speed of light and sound rational or irrational in nature?

text: Just as circumference of circle will remain $\pi$ for unit diameter, no matter what standard unit we take, are the speeds of light and sound irrational or rational in nature ? I'm talking about theoretical speeds and not empirical, which of course are rational numbers.


title: On the naturalness problem

text: I know that there are several questions about the naturalness (or hierarchy or fine-tunning) problem of scalars masses in physics.stackexcange.com, but I have not found answers to any of the following questions. Suppose that we add to the SM Lagrangian the following piece: $(\partial b)^2-M^2 \, b^2-g\, b^2 \, h^2+ \, ....$ where $b$ is a real scalar field (that is not contained in the SM) and $h$ is the Higgs real field. Then the physical mass $m_P$ of the Higgs is given by the pole of its propagator (I am omitting numerical factors): $m^2_P=m^2_R (\mu)+I_{SM}(\mu)-g\, M^2\, ln(M/\mu)$ where $m_R(\mu)$ is the renormalized Higgs mass, $I_{SM}(\mu)$ (which also depends on the SM couplings and masses) is the radiative contribution of the SM fields (with the Higgs included) to the two point function of the Higgs fields (note that is cut-off independent because we have subtracted an unphysical "divergent" part) and the last term is the one-loop contribution of the new field $b$ (where we have also subtracted the divergent part). I have two independent questions:   1. The contribution of the $b$ particle (the last term) is cut-off independent (as it has to be) so the correction to Higgs mass is independent of the limit of validity of the theory, contrary to what is usually claimed. However, it does depend on the mass of the new particle. Therefore, if there were no new particles with masses much higher than the Higgs mass, the naturalness problem would not arise. It could be new physics at higher energies (let's say beyond 126 GeV) as long as the new particles were not much heavier than the Higgs (note that I'm not discussing the plausibility of this scenario). Since this is not what people usually claim, I must be wrong. Can you tell me why?   2. Let's set aside the previous point. The naturalness problem is usually stated as the fine-tunning required to have a Higgs mass much lighter than the highest energy scale of the theory $\Lambda$, which is often taken as GUT scale or the Planck scale. And people write formulas like this: $\delta m^2 \sim \Lambda^2$ that I would write like that: $m^2_P=m^2 (\Lambda) + g\, \Lambda^2$. People think it is a problem to have to fine-tune $m^2 (\Lambda)$ with $\Lambda^2$ in order to get a value for $m^2_P$ much lower than $\Lambda^2$. And I would also think that it is a problem if $m^2 (\Lambda)$ were an observable quantity. But it is not, the observable quantity is $m^2_P$ (the pole of the propagator). I think that the misunderstanding can come from the fact that "interacting couplings" (coefficients of interacting terms instead of quadratic terms) are observables at different energies, but this is not the case, in my opinion, of masses. For example, one talks about the value of the fine structure constant at different energies, but the mass of the electron is energy independent. In other words, the renormalized mass is only observable at the energy at which it coincides with the physical mass (the specific value of the energy depends on the renormalization procedure but it is usually of the order of the very physical mass), while one can measure (i.e. observe) interacting couplings at different energies and thus many different renormalized couplings (one for every energy) are observables. Do you agree? *(Footnote: since free quarks cannot be observed the definition of their masses is different and one has to give the value of their renormalized mass at some energy and renormalization scheme.) Thank you in advance.


title: Uncertainty Principle on System of particles

text: I am new to Quantum Mechanics. I read the uncertainty principle - it says there are pairs of physical quantities which can't both be determined with certainty for a particle. My question is does the same apply to a system of particles - the nucleus for example ? Can we determine both the position and momentum of a nucleus (containing more than one protons) with certainty? Any help would be appreciated.


title: Is the 125 GeV Higgs boson some kind of a "almost-commutative graviton" at the electroweak scale?

text: The clumsy "almost-commutative graviton" is provocative. I use it on purpose, to ask two questions in one :   * **Is the observation of only one Higgs and no supersymmetric particle below 8 TeV (up to now) a sufficient evidence to substantiate the almost commutative spectral model?**   * **Can physicists consider now this kind of models pioneered by Connes and Chamseddine to be an _effective_ (physical) and not only _formal_ tentative unification of gravitation and Yang-Mill-Higgs interactions?** Recent developments of the almost-commutative spectral model regarding the Higgs boson and its mass:   * Grand Symmetry, Spectral Action, and the Higgs mass /Devastato, Lizzi and Martinetti 2013;   * Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models /Estrada and Marcolli 2012;   * Noncommutative Geometry in the LHC-Era /Stephan 2013. Last comments: (motives for "graviton" as a metaphore and "almost commutative" as a pedagogical reminder)   * I know that _graviton_ is a spin 2 gauge boson associated to the gravitational field in a tentative quantification of general relativity. _In the framework of Quantum Field Theory_ it is thus an object independant a priori from the _Higgs_ that is a scalar boson responsible for masses of elementary particles from the Standard Model. Nevertheless I remind that Higgs interaction can be considered as _derivated from gravitation in the noncommutative geometric setting_ (following Thomas Schücker).    * The adjective **almost-commutative** has a precise technical meaning but I use it also in my question to underline the fact that in any theoretical framework non-commutativity is a necessary but not sufficient tool to describe quantum phenomena, therefore it is clear that gravitation has not been quantized yet!


title: How to find the resultant of two forces?

text: I got this question in a assignment and haven't been able to figure out how to get to the correct result. > _A force of 6 newtons and a force of 10 newtons can be combine to form a > resultant of what magnitude?_ > > _Ans ( 8 newtons )_ I though this would simply be the sum of these forces, but it wasn't.


title: Difference between weak and strong interactions?

text: This was a statement given in my class: "Strangeness is conserved in the strong and electromagnetic interactions, but not in a weak interaction " But could someone please tell me how we differentiate between a weak and a strong interaction? An example would be helpful.


title: Copper coils for nMRI

text: Given the lack of financial efficacy in the medical industry, I was wondering if nuclear magnetic resonance imaging would be possible with a copper/silver coil if the use is short 10 second imaging bursts. Or is the resistance simply too disruptive for any imaging to occur? What I had in mind is a very small machine you could stick an arm or leg through for home scanning. Either completely uncooled or a very inexpensive cooling technique like simply running faucet water through it for the brief duration in a bathroom.


title: Throwing ball against oily/slippery wall

text: I would like to know whether a ball bounces back normally if you throw it against an oily wall. Like a wall watered down with oil. Basically I want to know if it will actually slip before bouncing back or not?


title: Spacetime line elements and proper time (specific problem)

text: Sometimes, when we have a certain line element and we are given a worldline parametrised by a path parameter that is not necessarily proper time I don't completely understand some of the standard manipulations done. A specific example: Godel spacetime has the line element $ ds^2=a^2(dt^2-dr^2 + f(r)d\phi^2 + 2g(r)d\phi dt- dz^2)$. I came across the following question: > A spaceship travels n a closed timelike worldline given by $$t(\lambda)=0,\, > r(\lambda)=R, \, \phi(\lambda)=w\lambda, \, > z(\lambda)=0,$$ where $w>0$ > and $\lambda$ is a suitable path parameter. Calculate the proper time to go > around the loop once. The normal thing to do is to use $ds^2=c^2\ d\tau^2$. But then I don't understand if when we say that $d\tau=1/c\cdot \sqrt(f(R))d\phi$ we mean that we take $\lambda=\tau$ (are we allowed to do this?) or if we simply divide both sides by the infinitesimal $d\lambda$ then use the expressions for the worldline given and then "cancel out" the infinitesimal again. Both approaches seem a bit suspicious for me.


title: Estimation of polarization perturbative term

text: I'm studying a diagrammatic approach to degenerate electron gas. Now I need to prove that the energy contribution, with an arbitrary potential, of polarization at first perturbative order given by the diagram: ![Diagramma](http://i.imgur.com/pECT8IX.png) is null. I expanded it as an integral: $$ \Pi_{(1)b}^*(q)=\lim_{p^o\to 0^+}\lambda\int d^4k\int d^4p\text{ }(G^{(0)}(k))^2e^{ip^0\eta}G^{(0)}(p)U_0(k-p)G^{(0)}(k-q) $$ $$ E^{(1)}_b\propto\int d^4q\text{ }U_0(q)\Pi^*_{(1)b}(q) $$ I've made several tries, but I can't prove it. Have you got any ideas? Thanks in advance.


title: How to specify BRDF measurement

text: As a person who will be using the scattering measurement results (in Zemax), I was asked to prepare the specs for the BRDF measurement. However I've never done it until now, so help would be greatly appreciated. I have a few questions:   1. What is a realistic range of illumination / detection angles for BRDF measurement?   2. What angular step is typical for elevation and azimuthal angles?   3. What dynamic range should we expect?   4. How do we take polarization into account? Is there a standard procedure? I could find it neither in the Zemax explanation of BRDF, nor anywhere online. The measurements will be executed at 10.6 um and possibly other IR wavelengths. **UPDATE:** For common interest, I will put here some information I already have. Zemax cannot measure at 10 um (350...1050 nm only) and usually perform measurement at 5 incident angles in the range of 0...75°. They do not perform polarization-sensitive measurement. Information is available at their web- site.


title: Change of quark flavour?

text: what do they mean by "in a weak interaction, quark flavor can change" I know that in a weak interaction strangeness is conserved... so is this what the statement is referring to.


title: The effect of Quantum Decoherence on density operators

text: Suppose we have a qubit in state $| \Psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$ Suppose we expose this to decoherence, which we will express as the state $| R \rangle$ such that $$| 0 \rangle| R \rangle \rightarrow | 0 \rangle| R_0 \rangle$$ $$| 1 \rangle| R \rangle \rightarrow | 1 \rangle| R_1 \rangle$$ Where $| R \rangle, | R_0 \rangle$ and $| R_1 \rangle$ are all normalised states. I'm trying to work how the density operator of the qubit changes when we apply $R$. If we consider the density operator for $|\Psi \rangle$ $$\rho=|\Psi \rangle \langle\Psi |= \Big( \begin{matrix} \alpha^2 & \alpha \beta \\\ \alpha \beta & \beta^2 \end{matrix} \Big)$$ Assuming alpha and beta are real. Next, we apply $|R\rangle$ to out qubit, $$\rho=|\Psi \rangle \langle\Psi | \rightarrow |\Psi \rangle |R\rangle \langle\Psi | \langle R|$$ $$=\alpha^2 |0 \rangle |R_0\rangle \langle 0 | \langle R_0|+\alpha\beta( |0 \rangle |R_0\rangle \langle 1 | \langle R_1|+ |1 \rangle |R_1\rangle \langle 0 | \langle R_0| )+\beta^2 |1 \rangle |R_1\rangle \langle 1 | \langle R_1|$$ Next would we take the reduced density operator of $|\Psi \rangle$ to find it's density operator? This would produce a $2 \times 2$ density operator, which I'm hoping to express in terms of $\rho=|\Psi \rangle \langle\Psi |$ Is this the correct way to think about the relation between density operators and reduced density operators for entangled states? What about unentangled states? Also would anyone be able to briefly explain what decoherence is and why we can describe it as such a operator $|R \rangle$? Any help would be greatly appreciated.


title: Electric potential at a point outside a charged sphere

text: The question asked me to find the potential at a distance $r$ from the center of a charged sphere, where $r>r_0$ of the sphere. Actually, the question is answered, but what is confusing me is that the author took 2 points out of the sphere ($a$ & $b$) and calculated the potential difference between them, and getting the result that $$V= \frac{Q}{4\pi \epsilon_0 r} $$ at any point outside the sphere? Why did he take these 2 points ?


title: Does a FTS work on the same principle as a michelson (amplitude division) interferometer?

text: As far as I can tell within an Fourier Transform Spectrometer the spectral information is gained from changing the path length along one arm, this sounds very similar to a michelson interferometer but using two apertures instead of one. So are there any underlying differences between the two?


title: What is the approximate electrical conductivity $\sigma$ of graphene in S/m or S/cm?

text: I am trying to find an approximate value of the electrical conductivity $\sigma$ of graphene in units of S/m or S/cm. This table on Wikipedia gives $\sigma$ values for a variety of materials (including references), but I do not see graphene. In the classic 2004 paper on graphene by Novoselov and Geim (Novoselov et al., _Science_ **2004** , _306_ , 666: available here), I see a plot of $\sigma \text{ (m} \Omega^{-1})$ versus $V_g \text{ (V)}$, where $V_g$ is the gate voltage: ![Electrical conductivity](http://i.stack.imgur.com/0H2pT.gif) Based on that plot, what can we say about the electrical conductivity $\sigma$? One confusing thing about the above plot is that it is in $\text{m} \Omega^{-1}$. But $1 \text{ S} = 1 \text{ } \Omega^{-1}$, so in the plot is given in units proportional to S, not S/m. Why is this?


title: how to stop water reaching up inside an under water structure (see video)

text: in this video at arround 0:47 they deliver the 'dry pots' to the under water lab, bellow the water and they seem to swim up into an opening where it is completly dry.. how is this dry, surly the water would fill into that void seeing as its under water ? Sorry if this is such a basic quesiton ! http://www.youtube.com/watch?v=kuI7KFsKrBY&feature=player_embedded#!


title: Question on the Electroweak vacuum decay

text: Is there any current estimate of the electroweak vacuum lifetime based on the recent measurement of the Higgs boson and the top quark masses?


title: Why is an exciton only observed when we excite to the conduction band and not to other electronic level inside the bandgap?

text: Excitons can be observed when we excite electrons to the conduction band. I don't know about excitons being observed when we excite the electrons to an electronic level that would eventually be in the middle of the bandgap. Why? Is it related with the binding energy, density of states of the level, or is it a fundamental aspect that I am not aware of?


title: Which BICEP2 r value should be compared to Planck's r<0.11?

text: The BICEP2 paper reports a tensor/scalar ratio $r = 0.20_{-0.05}^{+0.07}$, but then says: Subtracting the various dust models and re-deriving the r constraint still results in high significance of detection. For the model which is perhaps the most likely to be close to reality (DDM2 cross) the maximum likelihood value shifts to $r = 0.16_{-0.05}^{+0.06}$ Which value is proper to compare with Planck's $r<0.11$?


title: How does the tester screwdriver work?

text: How does the tester screwdriver work? If I put the tester screwdriver inside a "phase" hole of an electric socket, it lits up. If I press my finger against the metal cap on top of the screwdriver. This happens also if I stand on a surface of isolating material, such as wood. I read elsewhere that this happens due to stray capacitance formed by the "phase" and the ground. One has $$z=r+1/jwc$$ for the impedance, so if $C$ is high enough, the impedance should be close to $r$, the "effective resistance" of the formed circuit. Here I get lost; why $r$ is small enough to cause a current in the range of $mA$ even if I stand on an isolating surface? But even supposing that the majority of effective resistance is inside the screwdriver and I form a capacitor by pressing my finger on the metal cap (the capacitor "plates" being the metal cap and the ground, for whatever ground means), then why the capacity increases when I press my finger against the cap? Even supposing the human body has a MUCH greater dielectric constant at 50Hz than air, aren't also the dielectric constants of the surface on which one stands etc involved here?


title: Addition of Angular Momentum

text: I am tring to find the eigenvectors of a two spin system, with $j_1=3/2$ and $j_2=1/2$. To start, $$m_1 =-3/2,-1/2,1/2,3/2$$ $$m_2=-1/2,1/2$$ For $j_1$, there are 4 possible states, and 2 possible states for $j_2$. $(2j+1)$. Now, I get confused. I am looking for $$|S,m\rangle=\sum_{m_1+m_2=m}CG|s_1m_1\rangle|s_2m_2\rangle$$ I presume that these are the eigenvectors for total angular momentum and its z component. From here, I am not sure what to do. I write out all of the states, but then I am unsure of how to find the CG coefficients (we are not given a table). Any help would be appreciated.


title: Increasing Earth's albedo

text: How much of a difference would it make if every roof, road and vehicle were painted white? This would certainly reduce the urban heat island effect but how much of a difference would it make to total scattered insolation? Apologies in advance for this the bizarre question.


title: Another question about wormhole traversability in General Relativity

text: It is well known that stable, traversable wormholes require exotic matter that violate the dominant energy conditions. For the purpose of the question, let's assume enough exotic matter can be created for a brief period of time, where the wormhole mouths are stable and traversable. Additionally, suppose that during that time, a strong beam or wire is introduced across the throats. Now the question is: > **Question:** What happens if exotic matter is removed from the wormhole > mouths? Are the tidal forces always enough to break any material crossing > the throats and disconnect the mouths?


title: Calculate integral of motion condition with Poisson brackets

text: **Problem statement** : The Hamiltonian of a system is given by the formula: \begin{equation*} H = \frac{p_r^2}{2m} + \frac{p_\theta^2}{2mr^2} + V(r,\theta). \end{equation*} Under what condition is $f=p_\theta^2$ an integral of motion? * * * **Attempted solution** : In order for $f$ to be an integral of motion, according to Poisson theorem, is that: \begin{equation*} [f, H] =0, \end{equation*} where $[,]$ is the Poisson bracket. Therefore: \begin{align*} \left[\frac{p_r^2}{2m} + \frac{p_\theta^2}{2mr^2} + V(r,\theta), p_\theta^2\right] &= 0 \Leftrightarrow \\\ \left[\frac{p_r^2}{2m}, p_\theta^2\right] + \left[\frac{p_\theta^2}{2mr^2}, p_\theta^2\right] + \left[V(r,\theta), p_\theta^2\right] &= 0. \end{align*} But how do I proceed from here on? **EDIT1** : Regarding the first term: \begin{align*} \left[\frac{p_r^2}{2m},p_\theta^2\right]&=\frac{1}{2m}\left[p_r^2,p_\theta^2\right]=\frac{1}{2m}[p_r p_r, p_\theta^2]=\frac{1}{2m}\left(p_r[p_r,p_\theta^2]+p_r[p_r,p_\theta^2]\right)\\\ &=\frac{1}{m}[p_r,p_\theta^2]= \frac{1}{m}\left(p_\theta[p_r, p_\theta]+p_\theta[p_r,p_\theta]\right) = \frac{2p_\theta[p_r,p_\theta]}{m} \end{align*} So it boils down to what is $[p_r, p_\theta]$ equal to ? I'm not sure whether it can be answered directly without resorting to the definition of Poisson bracket. The coordinates in our problem are $q_i = \\{r, \theta\\}, p_i = \\{p_r, p_\theta\\}$. Therefore: \begin{align*} [p_r, p_\theta] &= \sum_{i=1}^2 \left(\frac{\partial p_r}{\partial q_i}\frac{\partial p_\theta}{\partial p_i} - \frac{\partial p_r}{\partial p_i}\frac{\partial p_\theta}{\partial q_i}\right)\\\ &= \left(\frac{\partial p_r}{\partial r}\frac{\partial p_\theta}{\partial p_r} - \frac{\partial p_r}{\partial p_r}\frac{\partial p_\theta}{\partial r}\right) + \left(\frac{\partial p_r}{\partial \theta}\frac{\partial p_\theta}{\partial p_\theta} - \frac{\partial p_r}{\partial p_\theta}\frac{\partial p_\theta}{\partial \theta}\right)\\\ \end{align*} And now I'm stuck again. The way I understand it $p_r, p_\theta$ are two components of momentum along $r, \theta$ respectively. **Does that imply that $p_r$ does not depend on $\theta$ and that it only depends on $r$** ? If the answer is yes, then the result for the first term is zero. **EDIT 2** : Based on the answers in Hamiltonian formalism all the canonical variables are taken independent to each other, therefore $[p_r, p_\theta]=0$. Similarly it may be shown that the 2nd term is also zero.


title: Is there evidence of a larger universe?

text: While mapping out the position, distance and movement of galaxies and quasars at the limits of the observable universe, have astronomers ever observed the motion of these object due to gravitational sources that may reside outside the limits of the observable universe? If so, would this break the principle of information travelling faster than the speed of light? If not, are these objects in fact the furthest objects there are?


title: How is the shape of the universe measured by scientists?

text: I would like to learn how scientists go about measuring the large-scale curvature of the universe to determine if the universe is closed 'i.e. spherical', flat, or open 'i.e. saddle shaped'. My simplistic thought is that you could measure the corner angles of a really large triangle and see if they add up to <180, 180, or >180 degrees. However I can't imagine how you would do that in practice, (not without owning a Ningi anyway). > _Ref. Hitchhiker's Guide to the Galaxy: The 'Triganic Pu' is a Monetary > unit. Its exchange rate of eight Ningis to one Pu is simple enough, but > since a Ningi is a triangular rubber coin six thousand eight hundred miles > along each side, no one has ever collected enough to own one Pu. Ningis are > not negotiable currency, because the Galactibanks refuse to deal in fiddling > small change._


title: What does the optical zoom in telescopes do?

text: How does the optical zoom works..   1. Does it brings the light closer to the object... Or   2. Does it just enlarges the picture of the object. In other words... Suppose I have telescope with 1 light-year zoom capacity, could I see stars 1 year ahead of its light reaching earth... Ps : I'm not physics graduate, but interested in physics. I joined here, to learn more... Please excuse me if my question is trivial or stupid.


title: How can we be sure that liquid iron/titanium droplets can form around particulates on hot Jupiters - just as they do on Earth and Venus?

text: I know that we have some solar system analogs. But is there a limit to it?


title: How to define the dilatation rate (strain) between two particles knowing the instantaneous positions and velocities?

text: Provided that I have the instantaneous positions and velocities of two particles that can separate in 3D with respect to time. I would like to characterize the change in length. What could be a good formulation for that? Thanks.


title: Double image in binoculars

text: How can I reduce the double image seen when looking through binoculars? I recently got a new pair, but have been having troubles using them because I am seeing double...


title: Aspherical lenses

text: It's known that single spherical lens cannot focus parallel beam of monochromatic light into single point. Could you suggest how should aspherical lens look like to be able to focus in single point (again, light is monochromatic)? Do we need conic factor, or higher components? Could you suggest any decent books on aspherical optics & it's manufacturing?


title: Does 'electricity' have mass? Is 'electricity' tangible?

text: **Background:** I'm in a legal academic discussion about the status of electronic 'goods' and whether they qualify as 'goods' in the same way a chair and a pen do. In this context (and specifically at the exact circumstance under discussion), it matters if electricity is 'tangible'. So far, most authors have blindly assumed electricity to be a flow of electrons, making a literal analogy with water, making statements such as:   * Information is stored in capacitors in the form of electrons. When a capacitor is filled more than 50% with electrons, it's considered to be 'on' (a bit with value '1').   * The information represented by a certain current (or rather, a series of on/off currents) has mass, because it consists of the electrons that flow through the wire.   * A virtual object is tangible because it exists in memory in the form of electrons that are there (or not) in a certain pattern. Now I have a background in informatics but only a basic knowledge of electricity, and as good as none on the fundamental (physics) level. However I still feel this representation is wrong, and that you can't just say that information in a RAM chip has mass because it consists of electrons that are or are not in the capacitors on that chip. I have found hints in that direction on sites such as http://amasci.com/miscon/eleca.html#made, but I can't quite make out what 'electricity' _is_ and how it relates to _current_ and _potential_ and other words that are used interchangeably in these discussions but which are, I think, different things. So my questions are (all just different angles of looking at the same underlying concept):   * What is 'electricity', really, on a fundamental level; but explained in terms a layman can understand? Is there an analogy with other things that is accurate, unlike the 'flowing water' analogy, which is sufficient for high school level but is a simplification? (at least, I think...)   * Do 'electricity', an 'electrical current' and an 'electrical charge' have mass, apart from the object they are embodies in? Does the mass of a copper wire change when you put a current through it, because of the electrons coming in and going out?   * How do electrons fit into this? Is electricity composed of a bunch of electrons that flow through a mass? I think not, reading the link I gave before, but I don't quite understand what their role is.   * Most authors blindly assume that electricity is merely a flow of electrons through mass. In how far and under what assumptions is this correct?


title: Would it be possible to measure the change of entropy of a system? why?

text: To be more specific, what I mean is to measure it in a experiment. And if the answer is no, I want to know if it is principally impossible, or just impossible due to the technic limitation of our time. I am sorry I wan't clear enough at first. For most of the times, in the progress of experiment, the system does not have enough time to get an equilibrium state. unless you are aiming to do a thermal dynamics experiment. (in which the entropy of the system could be measured as $$\Delta S = \int_{T_1}^{T_2} \frac{C(T)}{T} \, \mathrm{d}T$$) What I want to ask is, could we develop a normal way to measure the entropy in all kinds of experiments? Thank you for your time:-P


title: B-mode and circular polarization in BICEP2

text: In the case of the B-mode detected in BICEP2, at first they assumed there was no circular polarization and then the Q and U stocks parameter of the CMB is given by E-mode and B mode. If we have circular polarization too, what is relation between the B-mode and circular polarization? Does this B- mode include the contribution of circular polarization or Not not?


title: To what extent is the "minimal substitution" or "minimal coupling" for the EM vector potential valid?

text: In all text books (and papers for that matter) about QFT and the classical limit of relativistic equations, one comes across the "minimal substitution" to introduce the magnetic potential into the equation (Schrödinger/Dirac/Klein-Gordon) through: $$ \hat{p}^2 \rightarrow (\hat{p} - e \hat{A})^2$$ The wording suggests that this is an approximation for small? electromagnetic fields (or at least not strongly coupled). I understand this was chosen such that the "classical" Lorentz force is retrieved from the Hamiltonian, but not why exactly this form and not another that leads to the same result.   1. To what extent is this "approximation" valid?   2. How can one improve this "minimal substitution"? Is there a more general expression, intuitively something like a series of the vector potential?


title: Getting position from an accelerometer on an Android phone

text: I know that integrating acceleration twice will give me position (acceleration-->velocity-->position) but how can I do all this when I all I have are a set of data points (ex: 1 second = some # m/s^2); how can I take these data points and integrate them? Does this have something to do with numerical integration?


title: Why is E85 less efficient than straight gasoline?

text: Why is straight gasoline (or whetever the mixture was before the introduction of ethanol) more efficient (ie, more miles/gallon) than E85? I've known since it's introduction that E85 was less efficient, but why is it?


title: Possibility of making dark energy equivalent with dark matter

text: I was curious whether it is possible to make dark energy equivalent to dark matter. Can this unification be done? If it can, why do scientists prefer to separate dark energy from dark matter?


title: Literature Request: Introduction to d-wave superconductivity

text: I'm looking for a pedagogic introduction to d-wave superconductivity. Ideally, this would involve a derivation of d-wave superconductivity and the form of the gap parameter from some fundamental Hamiltonian (if such a derivation is even possible). Books and papers are welcome.


title: Sensible heat question (solving for temperature)

text: > If $55 034.175 \rm{kJ }$ of heat are transferred to $150 \rm{kg}$ of ice at > a temperature of $-12.15 ^\circ \rm{C}$, calculate the temperature of the > resulting water. Using $Q = mc(t_2-t_1)$ or $t_2 = \frac{Q}{mc}+t_1$, $$t2 = \frac{55034.175}{150 \times 2.135} + (-12.15)$$ My answer is $178.6 ^\circ \rm{C}$ However, this does not seem possible to me because the boiling point of water is $100^\circ\rm{C}$ so therefore it would no longer be water. I feel my answer should be below $100^\circ\rm{C}$ if they are asking for the temperature of the resulting water. Can someone please explain?


title: Classical scattering of two particles by a Yukawa potential

text: A point-like particle $A$, coming from minus spatial infinity, heads at another one, $B$, with an impact parameter of $b$. Initial momenta are $p_A$ and $p_B=0$. They repel each other via a Yukawa potential $$\ \ V(r_A,r_B)= +g^2\frac{e^{-\frac{|r_A-r_B|}{\lambda}}}{|r_A-r_B|} \ge 0.$$ > How does the angle of the incoming particle $A$ change, relative to how it > was before?


title: What do people actually mean by "rolling without slipping"?

text: I have never understood what's the meaning of the sentence "rolling without slipping". Let me explain. I'll give an example. Yesterday my mechanics professor introduced some concepts of rotational dynamics. When he came to talk about spinning wheels he said something like: > "If the wheel is rolling without slipping, what's the velocity of the point > at the base of the wheel?? It is... zero! Convince yourself that the > velocity must be zero. Since if it wasn't zero, the wheel wouldn't be > rolling without slipping. So the wheel is rolling without slipping if and > only if the point at the base has velocity zero, i.e. if and only if the > tangential speed equals the speed of the center of mass." Well, what I really don't understand is this: is the "rolling without slipping" condition _defined as_ "Point at the base has zero speed"? If not, what's the proper definition for that kind of motion? Looking across the internet, I have found more or less the same ideas expressed in the quotation. Furthermore, if it was a definition, then it would be totally unnecessary to say "convince yourself" and improper to talk about necessary and sufficient conditions. I'd like to point out that I'm not really confused about the mathematics behind this or with the meaning of the condition above. What puzzles me is why are those explanations always phrased as if the condition $v'=0$ (where $v'$ is the relative velocity beetween the point at base and the surface) is some necessary and sufficient condition to be "rolling without slipping". Seems to me that this _is_ exactly the definition of "rolling without slipping" and not an "iff". Any help is appreciated, thanks.


title: What does it mean to divide space and time?

text: Goldstein's mechanics book, on the chapter on relativistic mechanics says that "We cannot assume that all observers make the same division into time and space in the same way." What does it mean to "divide" spacetime?


title: Table of matrix elements of powers of r for radial functions in H atom

text: Im looking for some references here. I hope it is the right place to ask. I need to find a table of (or a formula from which to extrapolate) the matrix elements of the radial functions of the hydrogen atom evaluated in powers of $r$ for both diagonal and off-diagonal elements. That is, I need this guys: $<R_{nl}|r^k|R_{n'l'}>$ I found this article http://iopscience.iop.org/0953-4075/28/3/007 which is great, but Im looking for something more textbook-like, say suited for undergrad. I especially need positive powers until k=4. Any help is very appreciated.


title: Gauging discrete symmetries

text: I read somewhere what performing an orbifolding (i.e. imposing a discrete symmetry on what would otherwise be a compactification torus) is equivalent to "gauging the discrete symmetry". Can anybody clarify this statement in any way? In particular what does it mean to gauge a discrete symmetry if no gauge bosons and no covariant derivatives are introduced?


title: What is the minimum non-integer dimension for which the XY model shows a phase transition? (if well-defined)

text: I know that XY statistical model for $d=2$ doesn't show a regular phase transition , while the $3d$ has, I was wondering what is the behaviour for $2< d < 3$. If it is simpler one could consider another model in its class of universality, like it's done for the $2+\epsilon$ expansion. The simplest hypothesis is that exist a $d_{min}$ between 2 and 3 such that for values of dimension greater than $d_{min}$ there is phase transition. Assuming this number has a meaning for every statistical model, I would like to ask if it is universal with respect to the simmetries of the order parameter. Going further, what is the behaviour of the critical temperature around $d_{min}$, is that universal?


title: Newton's Ring: interference problem

text: Newton's ring apparatus consists of a Plano-spherical glass which rests on its vertex on top if a horizontal surface. Reflection-interference occurs along the air wedge, and is seen as a series of concentric rings from above. You may assume the radius of convergence is much larger than the thickness of the wedge. Now, to the actual problem. When a liquid is introduced into the air between the glass and table, the radius of the tenth bright fring changes from $1.50$ cm to $1.31$ cm from the center of the pattern. Calculate the index of refraction of the liquid.


If we want to transform to another inertial frame of reference using Galilean transformation in 4-dimensional space-time, what is the Jacobian matrix of Galilean transformation?


title: What is our estimated running speed on Moon's surface?

text: I was wondering if we have the chance to run on the Moon's surface, how would you expect it look like? I expect our velocity will increase for the same work we do on Earth, but not sure if this will be multiples in term of gravity variations. How do you think our maximum speed would reach?


title: Photons emitted by radioactive source

text: Can we calculate the number of photons emitted per second by a radioactive source (gamma) ? we can take 100g of barium-133 as an example


title: Since there are gravitational lenses, are there gravitational mirrors?

text: Gravitational lensing is an observed phenomenon. Can one have a gravitational mirror? A slightly unrelated question: Can gravitational waves be reflected?