title: Experimental measurement of volumetric flow rate

text: The other day I with my team had to measure the volumetric flow rate through a pipe only using a 2000 mm$^3$ volumetric flask and a chronometer. The end of the pipe discharged to the atmosphere. As we thought the measurement was very imprecise and we only had 3 measure to do, we wanted to make the measurement the best we could, so I told them "Hey, lets measure the time it takes to make it to 2000 mm$^3$ three times and the take the simple mean of that value, so the flow rate would be $$Q^*=\dfrac{3}{t_1+t_2+t_3} \times 2000 \text{ mm}^3/s.$$ and that's it, we will minimize manipulation errors." But someone said "that is not the best thing to do, something better is to take 3 points $(t_1,V_1), (t_2,V_2), (t_3,V_3)$, make a linear regression and use the slope as the flow rate $Q^*$ My concerns with this method is that if we take the points too separated, then some point will be near cero and therefore the error associated with the manipulation of the flask will be big, but if we take all the points near 2000, then the linear regression will be with 3 points very near each other, and if some measurement went wrong, that would affect very much the final result. _What method do you think is more precise_? Why? I suppose the statistics involved are simple but I can't solve this by myself.


title: $\require{mhchem}$ $\ce{\beta^{+}}$ decay for $\ce{_9^18F}$, computing $\Delta m$

text: For the decay: $$\require{mhchem}\ce{_9^18F\to_8^18O +e+ +{v}}$$ To compute $E$, I need $\Delta m$, the provided answer looks like: $$m_i = 18.000938~u$$ $$m_f = 17.999159~u + 2~(5.49 \times 10^{-4}~u)$$ I believe $m_i$ is mass for $\ce{F}$ and $m_f$ mass for $\ce{O}$? Then where did the numbers $17.999159~u$ and $5.49 \times 10^{-4}~u$ come from?


title: Is there there is another universe which is made up of antimatter, in large amounts like ours is made up of matter?

text: Can it be possible that in the big bang, not one, but two universes were formed, one formed of matter, and the other formed of antimatter? It seems logical to me that since our universe is formed of matter, there must be some universe made of antimatter, so that a sort of an equilibrium is maintained. Can this other antimatter universe be treated like a mirror image to our universe, so as to maintain the equilibrium? Actually, to me it seems a bit strange that the big bang should produce a universe with much matter and little antimatter. So it seems that there must be a universe with greater antimatter and less matter, just the mirrored image of our universe, doesn't it?


title: Can a light beam be used as a wire for telephony?

text: I've heard that Edison (maybe) invented a way to talk over a light beam. Is this true and how do you modulate the light beam?


title: Why does wavelength change as light enters a different medium?

text: When light waves enter a medium of higher refractive index than the previous, why is it that: Its wavelength decreases? The frequency of it has to stay the same?


title: How does wind speed affect the velocity of light?

text: As you know, there is a maximum speed things can go called $c$, the "speed of light." Light in a vacuum goes $c$. Light in the atmosphere, however, goes a little less than $c$. My question is: what effect does wind have on light's velocity? Simply adding the wind's velocity to light's would not even be remotely close, since a 10 mph tail wind would probably push it over $c$.


title: Significant Figures (rules of addition)

text: It is a simple one but different teachers answer this question differently. $$34+1.4+0.2$$ what would be its answer with due regards to significant figures?


title: Transfer Equation between two oscillating pendulum collision

text: How to model the energy transfer equation between two oscilators colliding? For example two pendulum oscilating at frequency $f_1$ and $f_2$ and they transfer energy during colision.


title: Help to find nature of noise gotten from digital oscilloscope

text: I've got strange noise while using digital oscilloscope (Auris B-424). Spectrogram of this signal presented on this image: (X time in seconds, Y frequency in Hertz, in this image case from 0 to 50 MHz) ![enter image description here](http://i.stack.imgur.com/ni3L5.jpg) Zoomed versions: 1, 2 On oscillogram noise looks like impulse interference with amplitude approximately 10 millivolts. Simple scheme (fiber semiconductor detector) is connected to the input of oscilloscope with short 50 Om coaxial cable. Without anything on input channel noise is significantly lower (10-15 times), although still presented. Surge protector and ground used for powering oscilloscope and notebook. (outer conductor of coaxial cable is grounded too) My main guess is impulse interference from notebook and oscilloscope itself, but I can't find way to deal with it. What do you think? What nature has this noise and is there any way to reduce it?


title: If a neutrino has a rest frame, why can't a photon have a rest frame as well?

text: Concerning Rest Frame Wikipedia states: > For example, in the rest frame of a neutrino particle travelling from the > Crab Nebula supernova to Earth the supernova occurred in the 11th Century AD > only a short while before the light reached Earth, but in Earth's rest frame > the event occurred about 6300 years earlier. If a neutrino has a rest frame, why can't a photon have one as well?


title: semiclassical exact expression (in one dimension only)

text: let be $ N(x)= \sum_{n} H(x-E_{n}) $ the eingenvalue 'staircase' function and let be a system so $ V(x)=V(-x)$ and $ V^{-1}(x)=\sqrt \pi \frac{d^{1/2}}{dx^{1/2}} N(x) $ then would it be true that the two function $\sum_{n}exp(-tE_{n})=Z(t)= \int_{0}^{\infty}dN(x)exp(-tx) $ and $ \int_{0}^{\infty}dx\int_{0}^{\infty}dpexp(-tp^{2}-tV(x))=U(t) $ would be equal ?? i have just compared the two results $\int_{0}^{\infty}dnN(x)exp(-tx)=\int_{0}^{\infty}dx\int_{0}^{\infty}dpexp(-tp^{2}-tV(x)) $ i have taken the Laplace transform inside and get the desired result assuming that the potential V(x) is EVEN


title: light ray 'entropy'

text: Is there something like an entropy law for light rays? I came up with the following experiment: A black box has two circular holes in it, a small and a large one. I don't care about there placement. Now I like to build something into the box that any ray entering the large hole will exit the box through the small hole. However, I could not imagine any combination of optical tools like lenses, mirrors and so on that would do that. It seems possible to concentrate a parallel bundle of light to a small spot or hole, but not unordered rays. Is there a law written in ink that forbids such a contraption?


title: How did the energy/entropy/volume/pressure/temperature relationship exist at the Big Bang and how did it evolve thereafter?

text: According to the current Big Bang with inflation cosmological model? I was under the mistaken impression that there was very low volume, very high temperature/pressure, very low entropy and the Big Bang (perhaps prompted by the high pressure) resulted in an expansion of volume where energy didn't change much so temperature went down and entropy went up. Now I've learned about inflation and how there is no conservation of energy at cosmological scales and that the universe gained an exponential amount of energy during the inflationary period. How did this happen with a _decrease_ in temperature? Inflation was a period of supercooled expansion, was it not? Why was positive pressure not enough to cause inflation such that we need a negative pressure in the form of the inflaton field (or later dark energy) to explain the expansion of the universe? Thanks for your time


title: Zero energy universe

text: Regarding this thread: http://www.physicsforums.com/showthread.php?t=506985 Why is the idea that the total energy in the universe "zero" so popular (re: Laurence Krauss) and why is the flatness of the universe used to back this up when, according to that post, an open universe would not conserve energy so the total energy of the universe cannot be "zero", can it? What's the energy being defined as zero and why is that energy used to predict things about the universe when "the" energy (as the term is used in that post) is not zero? Additionally, I found one very good explanation here for this, http://mathoverflow.net/questions/38659/total-energy-of-the- universe/38690#38690 This seems to indicate that in flat space (the sort of space used in these zero energy universe theories) the mass can NOT be positive thus contradicting the notion that mass is positive and gravity negative and the whole thing winds up being zero. Did I interpret that correctly? The MO question is cross-posted to Physics.SE here, Total energy of the Universe


title: Curvature, Omega, the Flatness problem, and the evolving shape of the universe

text: I'm a little confused by this: http://en.wikipedia.org/wiki/Flatness_problem Which seems to imply the universe is more curved now than it was soon after the Big Bang. Look at the graph on the right side. It's not drawn to scale but clearly implies that with continued expansion the mass-energy density to critical density ratio (Omega) will change which should mean a difference in curvature... no? > In other words the term |Ω − 1| is currently less than 0.01, and therefore > must have been less than 10−62 at the Planck era. So while it's still close to flat, it was closer to flat in the early period of the universe than it is now? And this is due to the mass-energy density decreasing quicker (due to expansion) than the curvature?   * And this is a problem because this implies the curvature had to be closer to flat (Omega had to be closer to 1) very early on, and this low level of curvature could not have contributed enough to the expansion of the universe to match the contribution of the mass-energy density? When they should have matched? Implying curvature was being governed by some other factor? (Assuming one didn't go the philosophical route of invoking the anthropic principle)   * OR am I reading the Wiki's language incorrectly and it merely says that curvature and mass-energy density should match but they don't as mass-energy density decreases faster than curvature which implies curvature in the past approaches the necessary value for the critical density? Which then implies that curvature is being affected by more than just mass-energy density? So the inflationary model says there's an inflaton field which drove the sharp exponential inflation during the early period of the universe which quickly flattened out the universe (overriding the effect of mass-energy density?) and then the curvature began to deviate away again slowly as the universe continued to expand? So now the curvature will increase slightly to match our current Omega which is slightly off the critical density? Should this not then mean that the universe is actually not flat but spherical (due to omega slightly greater than one) and soon to be hyperbolic because of the decreasing energy density? (due to expansion driven by dark energy)? Does the expansion from dark energy affect flatness?


title: Textbook on group theory to be able to start QFT

text: I am very enthusiastic about learning QFT. How much group theory would I need to master? Please could you recommend me a textbook on group theory, which would help me to start QFT?


title: Conceptual quantum field theory

text: Often papers and books give some bold(deep physical insight) statements in quantum field theory which are not backed by mathematics, and seldom by citing papers. Being a student I don't grasp the real meaning of those statements, making me think that I don't really understand QFT. I have access to all the standard books in QFT, but is there a book/lecture notes that really aims to explain QFT in a way in which the ideas emerged, it's philosophy with a physical insight at a level of a graduate student ? I am mighty interested in doing theoretical high energy physics, and crave for a better understanding of QFT. Could somebody help me ....


title: Question about uncertainty

text: Are $3.43\pm 0.04$ $\frac{\mathrm{m}}{\mathrm{s}}$ and $3.48$ $\frac{\mathrm{m}}{\mathrm{s}}$ within expected range of values? The answer is yes, but I do not clearly see why this is so. I appreciate if you can give me a hint on this. This is what I could think of: 3.48 could be either $3.47\fbox{5-9}\cdots$ or it could be $3.48\fbox{0-4}\cdots$, 3.43 could be either $3.42\fbox{5-9}\cdots$ or it could be $3.43\fbox{0-4}\cdots$, and 0.04 could be either $0.03\fbox{5-9}\cdots$ or it could be $0.04\fbox{0-4}\cdots$. So if for example, we say that 3.48 was $3.476101$ and 3.43 was $3.43404$ and 0.04 was 0.04304, then $3.43+0.04$ would be 3.47708 and $3.43-0.04$ would be 3.391. So 3.476101 lies between 3.391 and 3.47708. So it could be possible that $3.43\pm 0.04$ and 3.48 be within expected range of values.


title: QED BRST Symmetry

text: This is a homework problem that I am confused about because I thought I knew how to solve the problem, but I'm not getting the result I should. I'll simply write the problem verbatim: "Consider QED with gauge fixing $\partial _\mu A^\mu=0$ and without dropping the Fadeev-Popov ghost fields. Thus the gauge fixed Lagrangian is $$ \mathcal{L}=-\frac{1}{4}F_{\mu \nu}F^{\mu \nu}+\frac{1}{2}(\partial ^\mu A_\mu )^2+\overline{\psi}(i\gamma ^\mu D_\mu -m)\psi+\overline{c}(-\partial ^\mu \partial _\mu)c $$ Verify that the Lagrangian is invaraint under the BRST transformation $$ \delta A_\mu=\epsilon \partial _\mu c,\delta \psi =0,\delta c=0,\delta \overline{c}=\epsilon \partial _\mu A^\mu" $$ Two questions. First of all, if we are working in the gauge where $\partial _\mu A^\mu =0$, then why has he left this term in the Lagrangian? Does he mean something different by "gauge fixing" than I am thinking? Second of all, I am not getting this Lagrangian to be invariant under the transformation listed. I find that the transformation of the gauge field gives an extra term of the form $$ -\epsilon e\overline{\psi}(\gamma ^\mu \partial _\mu c)\psi $$ that doesn't cancel. This term arises from the $A_\mu$ contained in the covariant derivative. Did I screw up the computation somewhere? What's going on?


title: Does the passage of time effect a photons entanglement with another?

text: I recently read an article about "Delayed-choice entanglement swapping". Here is an excerpt from the article: > Delayed-choice entanglement swapping consists of the following steps. (I use > the same names for the fictional experimenters as in the paper for > convenience, but note that they represent acts of measurement, not literal > people.) > >   1. Two independent sources (labeled I and II) produce pairs photons such > that their polarization states are entangled. One photon from I goes to > Alice, while one photon from II is sent to Bob. The second photon from each > source goes to Victor. (I'm not sure why the third party is named "Victor".) > >   2. Alice and Bob independently perform polarization measurements; no > communication passes between them during the experiment—they set the > orientation of their polarization filters without knowing what the other is > doing. > >   3. At some time after Alice and Bob perform their measurements, Victor > makes a choice (the "delayed choice" in the name). He either allows his two > photons from I and II to travel on without doing anything, or he combines > them so that their polarization states are entangled. A final measurement > determines the polarization state of those two photons. > > > > The results of all four measurements are then compared. If Victor did not > entangle his two photons, the photons received by Alice and Bob are > uncorrelated with each other: the outcome of their measurements are > consistent with random chance. (This is the "entanglement swapping" portion > of the name.) If Victor entangled the photons, then Alice and Bob's photons > have correlated polarizations—even though they were not part of the same > system and never interacted. Question: Does the passage of time (from our perspective) really matter? Each photon itself is traveling at the speed of light, which I believe should make time have very little, if any, affect on it. I would think that measuring a photon at X time and Y time from our perspective would be the same exact time from the photons perspective. Therefore, wouldn't it make sense that "modifying" a photon at Y time would have an affect on a measurement taken at X time? After all, it would seem as if we are looking at the same exact photon...                  0   <-- same time from the photons perspective       / \      X   Y <-- different times from our perspective


title: Problem with calculating the curvature tensor of the $n$ dimensional sphere

text: I am calculating the Riemann curvature tensor, Ricci curvature tensor, and Ricci scalar of the $n$ sphere $$x_0^2 + x_1^2 + ....+x_n^2=R^2,$$ whose metric is $$ds^2=R^2(d\phi_1^2 + \sin{\phi_1}^2 d\phi_1^2+\sin{\phi_2}^2\sin{\phi_1}^2 d\phi_2^2+......).$$ I have done the same exercise for the 2 sphere, and found that the Riemann curvature wih a lowered index is proportional to the product of two $g \cdot g $, and the Ricci tensor to $g$. I am hoping to see the same result for the n dimensional sphere. I am using the following expression which can be found in Schutz. $$R_{\alpha \beta \mu \nu}=\frac{1}{2}(g_{\alpha \nu, \beta \mu}-g_{\alpha \mu, \beta \nu }+ g_{\beta \mu, \alpha \nu}-g_{\beta \nu, \alpha \mu}).$$ It can be seen clearly that only derivatives of the form $g_{\phi_p \phi_p, \phi_m \phi_n}$ where $m,n < p$ are non zero. **How do I show that the Riemann curvature tensor is proportional to the product of the metric tensors**? The Ricci tensor is $R_{ij}=R^l_{ilj}=g^{lm}R_{milj}$, as the metric tensor is diagonal $m=l, and setting first and third index equal in the expression for the RIemann curvature which would cause the first and third term to be zero as the derivatives are zero by the above argument, I get $$R_{ij}=-\frac{1}{2}g^{il}(g_{ll,ij}+g_{ij,ll})=-\frac{1}{2}g^{ll}g_{ll,ij}.$$ I was predicting, that from the 2 sphere case to get a term proportional the the metric tensor. (For the 2-sphere case $R_{ij}=\frac{1}{R^2}R_{ij}$). Where am I going wrong? How do I convert it to a form which reduced to the 2-sphere on substituting, $n =2$. The Ricci scalar expression is much more horrible, $R=g^{im}R_{mi}=g^{ii}R_{ii}$. I moronically expanded this and got a terrrible expression in $\cot{\phi}$ which cant be summed easily, while I need a number inversely proportional to $R$. Any help is appreciated. Also, (maybe this should be posted as a separate question), could I get the same tensors using some other method, e.g. tetrads. I have heard of this but don't know much. So it would be great if somebody could show it specifically for this case.


title: Questions concerning some parts of the section on one-particle states in Weinberg's first volume on QFT

text: Below are the scan copies of some pages of Weinberg which are relevant to my doubts. My doubts basically concern the determination of normalization constant defined in (2.5.5).   1. Isn't (2.5.12) true directly from the fact that $\Psi_{p,\sigma}$ are the eigenstates of a complete set of commuting hermitian operators? Or is it that because of the definition (2.5.5) the states $\Psi_{p,\sigma}$ are no longer orthonormal which doesn't seem to be the case to me as U's are unitary. Moreover, doesn't (2.5.5) imply that N(p) is just a phase factor by the unitarity of U?   2. I can't see why (2.5.13) is an immediate consequence of (2.5.12) but isn't that just a restatement of the fact that U's are unitary? If these are all the usual things already clear, then why has Weinberg got to write it this way? And how do you conclude that (2.5.13) is an immediate consequence of (2.5.12)? Kindly clarify even if it is dumb.   3. Then, he goes on to consider scalar product of states having arbitrary momenta p and p'. He defines $k'=L^{-1}(p)p'$. Now, if p and p' belong to the same class and are not equal, then we would have two standard momenta for the same class which shouldn't be the case. Also, as I vary p' (now p' need not be in same class), k' varies. So, there is no fixed standard momentum for the class in which p' belongs. Please clarify what's going on. You might say that k' has got nothing to do with standard momentum, but I have strong reasons to believe so as you get the second equality in the equation between (2.5.13) and (2.5.14) by setting N(k') (where k' is as defined above in this paragraph) as 1 which should be the case only if k' is the standard momentum for the class. ![enter image description here](http://i.stack.imgur.com/ofKjv.jpg) ![enter image description here](http://i.stack.imgur.com/PHxk5.jpg) ![enter image description here](http://i.stack.imgur.com/3Kwqh.jpg) ![enter image description here](http://i.stack.imgur.com/HixsT.jpg) ![enter image description here](http://i.stack.imgur.com/0E6oX.jpg)


title: Proportion of energy compared to mass in universe

text: In Wikipedia (http://en.wikipedia.org/wiki/Dark_matter), there is a picture that shows us the proportion of matter and energy in the current universe - CMB. It seems to suggest there is nothing that exists as energy form except dark energy - which we are yet to see - and every observable exists as matter forms. Is this correct interpretation? Of course, I know that matter's mass can be converted into energy by Einstein's basic and famous equation. If every observable exists as matter, is energy always converted to matter after being converted into energy from matter? Thanks.


title: General Relativity - Einstein field equation and quantum field theory

text: Einstein field equation has many solutions. Out of them, is there any solution that is incompatible with quantum field theory? Also, what solutions of Einstein field equation would be incompatible with some variants of string theory? (let us restrict the scope of string theory into superstring theory.) Thanks.


title: Can someone explain the science behind MIT's 230% efficient LEDs?

text: I was reading Gizmodo the other day and I didn't quite understand the Physics behind this. Could anybody shed some light on how this effect actually works?


title: Can I calculate the maximum concentration of sucrose that will dissolve in water at STP using physical constants?

text: I am interested in identifying the maximum solubility of sucrose in water. Can this value be estimated based on the physical properties of sucrose? Eventually I will need this in degrees Brix (%w/w). * * * _this question represents is a specific case of myquestion at biology.SE_


title: Enlightening experimental physics books/resources

text: Most book recommendations I've seen are usually geared toward theoretical understanding. It would be nice to know at least one or two classic experimental physics books. e.g. from Carl Brannen's question in Products of Gaussian stochastic process variables : "In the classic experimental physics text "Statistical Theory of Signal Detection" by Carl. W. Helstrom, ..." another e.g. From http://pdg.lbl.gov/2011/reviews/rpp2011-rev-particle- detectors-accel.pdf I can at least find several books in experimental HEP, but they seem to be too specialized. Compare this with Carl Brannen's book, which appears to discuss about the common unifying theme (zeitgeist, sense, or whatever) of experimental physics.


title: What is kappa symmetry?

text: On page 180 David McMohan explains that to obtain a (spacetime) supersymmetric action for a GS superstring one has to add to the bosonic part $$ S_B = -\frac{1}{2\pi}\int d^2 \sigma \sqrt{h}h^{\alpha\beta}\partial_{\alpha}X^{\mu}\partial_{\beta}X_{\mu} $$ the fermionic part $$ S_1 = -\frac{1}{2\pi}\int d^2 \sigma \sqrt{h}h^{\alpha\beta}\Pi_{\alpha}^{\mu}\Pi_{\beta}{\mu} $$ plus a long and unwieldy term $S_2$ due to the so called local **kappa symmetry** which has to be preserved. This $S_2$ term is not further explained or derived. So can somebody at least roughly explain to me what this kappa symmetry is about and what its purpose is from a physics point of view?


title: Producing electricity from all wavelengths of electromagnetic spectrum

text: Is it possible to produce electricity from all wavelengths of electromagnetic spectrum beside visible light ?Like using gamma rays or x-rays .


title: How does Doppler effect differ between EM -waves in Electrodynamics and Sound -waves?

text: I have an electrodynamics -course that contains doupler -effect but unfortunately with little explanations. Is it the same thing as the classical doppler effect for example with sound, more here, or do I need to take into account something such as Quantum-theoretical -corrections or something else? _Griffiths in the "Introduction to Electrodynamics" has something on the page 463, investigating -- other reading?_


title: How is an ideal mirrored box of photons distinguishable from massive particles?

text: Suppose you have an ideal mirrored box that contains enough photons as to have a relativistic mass equivalent to the [rest mass + kinetic energy] of an electron. In other words, the two systems have the same total energy. How would I distinguish these two systems? They have equivalent gravitational pulls and I believe they have equivalent inertia. Are charge and spin the only distinguishing factors (I'm assuming the "box" itself has no properties of interest)?


title: The meaning of 'postulate' in physics?

text: What does postulate mean in physics? What is its role in physical theories? Is it possible to break physical postulates?


title: why nontrivially space-like connected event horizons do not respect unitarity?

text: I want to understand the assertion that the gluing between distant event horizons is forbidden by unitarity. What is exactly the argument that unitarity will necessarily forbid topological nontrivial spacetimes?


title: Diffraction Gratings

text: Is it possible to use the sawtooth shape diffraction grating instead of rectangular grating if yes then which parameters will affect at the output ? Secondly, what is special in blaze grating comparison with rectangular shaped diffraction grating ?


title: representation of SU(2)

text: The question is regarding SU(2) group and SU(2) algebra. The SU(2) group can be generated by exponentiating the generators of SU(2) algebra $X_a$ as $exp(i t_a X_a )$ with $t_a$ being three parameters. Genreally we use half the Pauli matrices as $X_a$ when discussing SU(2) algebra as well as the group. But if we use the spin-1 representation of $X_a$ (which can surely be done at the Lie Alebra level) can they be exponentiated to give another rep. of the SU(2) group (which would be 3 dimensional)?


title: photons in expanding space: how is energy conserved?

text: If a photon (wave package) redshifts (streches) traveling in our expanding universe, is it's energy reduced? If so, where does it go?


title: With redshift, energy is lost. Where does it go?

text: A photon emitted by a distant source billions of light years away arrives here with a lower frequency hence less energy than it started with. What happened to the energy?


title: Ultrafast Lasers

text: The main idea of femtosecond or Attosecond lasers is to achive the high energy or do we have any other parameters achieved by ultra-fast lasers ?


title: Relativity on a moving train

text: I've been given the following scenario: > Observer $B$ is in the center of a train carriage which is moving at > velocity $v$ with respect to an observer $A$. Two light signals are emitted > from sources L at the left end and R at the right end of the carriage, such > that they reach $B$ simultaneously. $B$ observes that the light signals were > emitted at the same time. Show that $A$ doesn't agree. I've no idea how to do this mathematically. I understand the concept; that as the carriage is moving to the right, $A$ will see that the light from the left will have to travel further than light traveling from the right, as $B$ is moving towards the light coming from the right. What I've done so far (which I feel is wrong) is as follows: Let the carriage be of length $2d$ from $A$'s point of view. Then the distance that light has travelled from the left is $d+v\Delta t_L=c\Delta t_L$. Similarly, the distance that light has travelled from the right to B is $d-v\Delta t_R=c\Delta t_R$. Can solve these to get $\Delta t_L=\dfrac{d}{c-v}$ and $\Delta t_R=\dfrac{d}{c+v}$. If this is correct then I'm ok, as if $\Delta t_R \neq \Delta t_L$ then the light can't have been emmitted simultaneously according to $A$. However, I feel like having the denominator $c+v$ is wrong, as in some sense I'm adding velocity $v$ to the speed of light which is not allowed in SR. Secondly, in B's frame of refence, the two times $\Delta t'_L=\Delta t'_R$. Surely two equal time differences will dilate the same and we get that $\gamma \Delta t_L= \gamma \Delta t_R$ and thus $\Delta t_L=\Delta t_R$? Thanks for any replies!


title: Funny recurrence in escape velocity calculation of some planets

text: If we calculate the escape velocity of the not gaseous planets in solar system (mercury, venus, earth, mars...) is it possible to show that the escape velocity measured in Km/h is $E. V. \sim 2 \pi \frac{r}{1 \mathrm{h}} $ where r is the radius of the planet measured in km and $1\mathrm{h}$ is one hour. e,g. the E.V of the earth is 40.320 km/h $\sim \frac{\pi 12 756,27 \mathrm{km}}{1 \mathrm{h}}$ where 12 756,27 km is the diameter of the earth and $1 \mathrm{h}$ is still one hour. Is this funny recurrence depending from how we have choose the definition of meter and second? **Edit** My question is a little bit more subtle of what can look at first sight. Namely the earlier definition of the meter was 1/(4*10^6) part of earth circumference and the second was 1/86400 part of the solar day. So why not 1/(4.1*10^6) part of the earth or 1/86000 part of the day? Then is it conceivable that the definition of seconds or meters were chosen in order the get the e.v. on the earth equal to velocity of it circumference traveled in one hour only for sake of physical elegance?


title: X-ray diffraction from crystals and time-averaging

text: To calculate the elastically scattered intensity of x-rays from crystals, one classically considers scattering from a free electron first and then one sums up the scattered em-fields of all electrons in an atom and eventually in the whole crystals, after which the time-averaged Poynting vector gives an expression for the scattered intensity. For an unpolarized beam with intensity $I_{0}$, the elastically scattered intensity from a free electron in spherical coordinates is given by (Thomson scattering) $$\begin{split}I(R,\phi,2\theta)=&I_{0}\frac{r_{e}^{2}}{R^{2}}(1-\sin^{2}2\theta\left<\cos^{2}\phi\right>)\\\ =&I_{0}\frac{r_{e}^{2}}{R^{2}}\frac{1+\cos^{2}2\theta}{2}\quad\quad\quad\quad\quad\quad\quad (1) \end{split} $$ with $\left<\cdot\right>$ the time-average. Now when expanding this to crystals one writes $$I(R,\phi,2\theta)=I_{0}\frac{r_{e}^{2}}{R^{2}}\frac{1+\cos^{2}2\theta}{2}GG^{\ast}\left<FF^{\ast}\right>\quad\quad (2)$$ with $X^{\ast}$ the complex conjugate of $X$ and $G$ the Laue interference function (wich is zero almost everywhere except for the directions for which Bragg's law holds) and $F$ the structure factor (which depends on time because electrons move in an atom and atoms move in a crystal due to thermal motion). **The point is that the time average of $F$ and $\cos^{2}\phi$ are considered separately!** But why is this valid? Or in other words, how does (2) follow from (3) $$I(R,\phi,2\theta)=I_{0}\frac{r_{e}^{2}}{R^{2}}GG^{\ast}\left<FF^{\ast}(1-\sin^{2}2\theta\cos^{2}\phi)\right>\quad\quad (3)$$


title: How would time duration and space distance change when we move in the speed of light?

text: It is possible to figure out how time duration and space distance change when we are close to the speed of light - but I am not sure what happens to them if we travel in the speed of light.


title: How do I find the force from drop shock using material properties?

text: I am dropping a cylindrical cast iron bar with a know elastic modulus and poisson's ratio, $E_{1}$ and $v_{1}$, onto a flat beam of elastic modulus, $E_{2}$ and $v_{2}$ so there is tangential drop impact. Originally I was going to use the conservation of energy to find the velocity before impact, and then assume the final speed to be 0. And I would also assume an impact time of 0.1 sec so the force would be $$F=m\Delta v/\Delta t$$ I feel like there is a way to find a more precise impact time using the properties of the two objects since there will be elastic deformation between the two. I also want a better way of doing this with the properties because I want to be able to show rubber affects the impact time to reduce the force exerted


title: Space Quantization of Quantum Angular Momentum

text: I am trying to understand what my book is trying to convey. Quantum angular momentum is $L_z = m_l \hbar$ "Choosing arbitrarily a z axis and using an appropriate experimental technique, we measure the z component of $\vec{L}$. We find $L_z = -\hbar,0, \hbar$. Choosing another z axis and repeating the measurement we again find $L_z = -\hbar,0, \hbar$. This behaviour is completely different from classical vectors." The Idea of a classical vector is that it exists independent of the coordinate system used to examine it. Why is this not the case with this quantum system? how does the vector "Know" where the z axis is?


title: What are hidden variables exactly?

text: What are hidden variables in quantum mechanics? I am aware there are many types but what exactly do they mean or even "do" exactly? Do they mean that the quantum indeterminacy becomes hidden but still exists in reality somewhere but is hidden? Or does it mean that it is a hidden mechanism which means the reality underneath really is single world determinism or there abouts? I have done some searching but it really is not clear to me.


title: Is this field redefinition for free scalar field theory non-local?

text: The action of free scalar field theory is as follows: $$ S=\int d^4 x \frac{\dot{\phi}^2}{2}-\frac{\phi(m^2-\nabla^2)\phi}{2}. $$ I have been thinking to redefine field as $\phi'(x)=\sqrt{m^2-\nabla^2}\phi(x)$, where I assume that I can separate the operator $(m^2-\nabla^2)$ as $\sqrt{m^2-\nabla^2}\sqrt{m^2-\nabla^2}$ and integrate one of them by part (by infinite expansion of the square root of Helmholtz operator). The hamiltonian becomes $$ H=\int d^3x\frac{\pi'(m^2-\nabla^2)\pi'}{2}+\frac{\phi'^2}{2} $$ One can check the equation of motion and solutions are consistent to the original free field theory (as it should be), the things I am worried are:   1. Is it fair to do the infinite expansion+integration by part?   2. Since there are infinite series in the field redefinition, is it nonlocal? According to Wavefunction in quantum mechanics and locality and Why are higher order Lagrangians called 'non-local'?, it seems to be nonlocal. However, since there is no time derivatives in the square root, the initial data at every space point should be two, which corresponds to one dof at every point. If the infinite expansion is valid, one can know the field configuration $\phi'(x)$ if we know $\phi(x)$, it's not clear to me that whether we need all those initial data for the infinite series of derivative.  The above simple example might be too trivial, the question I am investigating is whether the following action stable or not, $$ H=\int d^3x \frac{1}{4}\pi \frac{1}{(1+2\beta \nabla^2)}\pi-\phi(\beta\nabla^2\nabla^2+\nabla^2)\phi, $$ where $\beta$ is a constant. I was thinking use the non-local field redefinition $$ \pi':=\frac{1}{\sqrt{1+2\beta\nabla^2}}\pi, \phi':=\sqrt{1+2\beta\nabla^2}\phi $$ to rewrite the hamiltonian as $$ H=\int d^3x \frac{1}{4}\pi'^2 -\phi\frac{(\beta\nabla^2\nabla^2+\nabla^2)}{1+2\beta\nabla^2}\phi, $$ which is guaranteed to be no-ghost. I agree the Hamiltonian I start with is rather unusual but it is a reduced Hamiltonian of a constrained higher derivative theory. It is not obvious to see how to analyze this by usual canonical transformation, is there any good way to analyze this or could anyone tell me what will go wrong with this kind of field redefinition?


title: What is electron hole? Isn't it just an absence of electron?

text: I was reading Wikipedia article about impact ionization and there's something in it's definition that makes me wonder: > Impact ionization is the process in a material by which one energetic charge > carrier can lose energy by the creation of other charge carriers. For > example, in semiconductors, an electron ( **or hole** ) with enough kinetic > energy **can knock a bound electron out of its bound state** (in the valence > band) and promote it to a state in the conduction band, creating an > electron-hole pair. Isn't "electron hole" concept to express lack of electron? I thought it is similar concept to "darkness", which is lack of light. And if it is just a lack of electron, how can "empty space" knock out an electron? If it's "just a hole" (there's nothing there), then it have no mass, no real energy... how can it even affect another electron in such way that it will be pushed away? I would be glad if someone could explain to me what really electron hole really is, and if it's not just an absence of something, then what is it?


title: Can I apply symmetry to this boundary value problem (BVP)?

text: Let's say I have a hollow cylindrical shell with inner radius $a$ and outer radius $b$ and length $L$. The temperature at at z=L is $T_{2}$ and the temperature at z=0 is $T_{1}$. There is also an ambient temperature of $T_{1}$ outside the shell. The inner radius is insulated. Right now the boundary conditions I am working with are $$T(r,L)=T_{2}$$ $$T(r,0)=T_{1}$$ $$-k\left. \frac{\partial T}{\partial r} \right|_{r=b}=h[T(b,L)-T_{1}]$$ $$\left. \frac{\partial T}{\partial r} \right|_{r=a}=0$$ Instead of saying the inner radius is insulated, can I use the problem's symmetry about the radial coordinate to make the last boundary condition as $$\left. \frac{\partial T}{\partial r} \right|_{r=0}=0$$ so that the solution is easier to determine when I apply my boundary conditions? I am not sure if the fact that it is a hollow cylinder means I cannot do that like I normally would apply symmetry. EDIT: The problem states the inner side is well insulated


title: Is kinetic energy a scalar?

text: Is it correct to say that kinetic energy is a scalar?


title: Why isn't steam/cloud blue like liquid and solid water?

text: Most of us here are aware as I think that pure water has a natural quest to absorb visible red colour wavelength slightly due do which liquid water and sometimes even ice appears to have a blue colour tinge. But even gaseous water(water vapour or steam) also absorbs red, rather it absorbs more strongly the red then liquid and solid water due to absence of hydrogen bonding. So why don't clouds/ masses of suspended water vapour appear blue. Why do clouds simply scatter/reflect the white light that falls upon them instead of simultaneously absorbing the red from white llight along with scattering of white light and finally appearing blue jast like water....?????? The proof of gaseous water absorbs red more strongly then liquid and solid water - http://www.webexhibits.org/causesofcolor/5B.html In this link look up in "What is the role of hydrogen bonding" section. Thanks for your kind kind attention.


title: A basic question on the derivation of the wave equation

text: Today I saw the derivation of the wave equation in class, and I did not understand the following step. We are modeling a uniform-density string as being made up of tiny masses spaced a small amount $h$ apart connected by springs obeying Hooke's law. Let $y_i(t)$ be the vertical position of the $i$'th such particle. The mass of this particle is $(h/L) M$ where $L$ is the total length, $M$ is the total mass. On the other hand, the displacement of the string between the $i$'th and the $i+1$st particle can be shown to be approximately proportional to $y_{i+1}(t) - y_i(t)$. It seems to me that this leads to the equation $$ \frac{hM}{L} y_i''(t) = k \left( [y_{i+1}(t) - y_i(t)] + [y_{i-1}(t) - y_i(t)] \right) $$ but that is, in fact, wrong; the derivation by instructor gives sticks a $1/h$ on the right hand side. Can someone explain to me (i) why the right hand side needs a $1/h$ (ii) intuitively, what is happening? My first guess is that the spring constant $k$ should be proportional to the length of the spring, keeping everything else constant? But that seems weird to me; it seems to me like if you have a spring with spring constant $k$, then cutting the same spring into two halves should result in two springs each with half the length but the same spring constant. Can someone unconfuse me? Thanks.


title: Are the known exoplanets representative of the population of exoplanets?

text: An article about the recent release of a large number of confirmed exoplanets states that most of the 715 newly announced exoplanets orbit very close to their host stars. Do the theories predict that this is a representative sample and that most planets are very close to their host stars? Or is it just that our current detection techniques are predisposed to finding only those planets close to their stars (because the sensors look for dimming of the host star for example)?


title: What's the physical meaning of the Fourier transform of magnetic flux density?

text: I have here below the distribution of the magnetic flux density $B$ across a 1 pole pitch in the airgap of a synchronous machine. The horizontal axis represents the distance along the arc length formed by a pole pitch across the airgap. ![plot of flux density distribution](http://i.stack.imgur.com/0NEXq.jpg) If I take the Fourier Transform of this flux density,how should I interpret the results? I am used to taking Fourier Transform with respect to time and not with respect to spatial data that I have here. Thanks a lot... **Update** I think it makes sense instead to use the Fourier Transform on a complete cycle (i.e. not the half cycle shown up) to look at the harmonics that we have in the magnetic flux density. This is what I get: ![enter image description here](http://i.stack.imgur.com/GxmWI.jpg) I guess from the Fourier Transform, this is the only information that is relevant.


title: Why are there Gravitons among the modes of oscillation in String Theory?

text: Why are gravitons present among the modes of oscillation of the 'strings' in String Theory?


title: Why would it be true that people with longer legs walk faster than ones with shorter legs?

text: When a person walks, the only force acting on him is the force of friction between him and the ground (neglecting air resistance and all). The magnitude of acceleration due to this force is independent of the mass of the object (longer legs have more mass). Hence the person should move with with a velocity independent of the length of his legs. But I have heard (also observed) that people with longer legs walk faster than ones with shorter legs. If that is true, then why? One can argue that the torque about the pivot due to friction is more in case of longer legs, But then the torque due to gravity (when one raises his leg to move), which opposes the frictional torque, is also more for longer legs. And why would these torques make a difference anyway, as they have no effect on the acceleration of the center of mass?


title: On an Uncertainty Relation for Angular Variables

text: I'm looking for a proof of the Angular Momentum - Angle uncertainty relation $$\frac{\Delta L \Delta \theta}{1-(3/\pi^2)\Delta \theta^2} \geq \frac{\hbar}{2}$$ which does not involve solving the differential equation for the parabolic cylinder functions (such a derivation was originally given by M. Bouten, N. Maene and P. Van Leuven). Does such a proof even exist?


title: Is Space conserved

text: Can space be created or destroyed? Is space conserved? I am **not asking for matter,energy and time**. Its just a question about **conservation of space** PS: I am asking for **what was there before big bang**. Surely Big bang would require space in the first place...


title: Why does the Sun's (or other stars') nuclear reaction not use up all its "fuel" immediately?

text: The temperature and pressure everywhere inside the Sun reach the critical point to start nuclear reactions - there is no reason for it to take such a long time to complete the reaction process. Just like a nuclear bomb will complete all the reaction within $10^{-6}$seconds. Why does most of the hydrogen of the Sun still not react even though it reaches the critical point, and why take stars billions of years to run out of fuel?


title: The equivalence of two worlds related by T-duality

text: T-duality in string theory relates a world containing open and closed strings with a D$p$-brane with a compact dimension with radius $R$ with a dual world with a D$(p-1)$-brane with a radius $R'=\alpha'/R$, where the D$(p-1)$-brane is located at an certain angle $\theta$ on the dual circle. If you apply the duality a second time on the dual world containing a D$(p-1)$ (and imagine this brane has still a compact dimension), you get a dual dual world with a D$(p-2)$. I'm wondering about two issues:   * By duality I understand an isomorphism relating two different worlds. In the case that all $p$ dimensions of the brane are compact. Is this world containing than isomorphic to one with a D$0$-brane?   * I also suppose that my understanding of a duality as an isomorphic is somehow wrong: if you apply the 'duality-map' you do not get the original D$p$-brane but a D$(p-2)$-brane.


title: Electric field produced by a charged ring

text: I have a question I couldn't find an answer for anywhere. There is a ring of radius $R$ which is charged uniformly with linear density $\lambda$, and I have to find the electric field on any point of the axis of the ring. So far so good, but this $\lambda$ includes both free and polarization charges, and the ring is in a region which is dielectric, with $\varepsilon_r$. I don't know if I can find the electric field just like $\lambda$ didn't include polarization charges. What do you say?


title: Aluminum foil to reflect sunlight from behind a textured glass

text: I'd like to keep room(facing east) cool during mornings. The room covered with textured glass on the east. By how much can I reduce heating by sticking the aluminum foil on the inside behind the glass. I understand that the glass/foil will be heated and radiate inside the room, So lets ignore that for the moment. the total surface area of the window is 108sqFt if it helps. Note: I can't afford to put the foil in from of the glass as this is in the 3rd floor.


title: How does the string worldsheet affect the space-time in which they live?

text: I don't understand much about string theory and never really got much further past the Nambu-Goto action and very basic supersymmetry (SUSY) lectures in my undergraduate courses, but the only thing that stuck is that the string worldsheet _lives_ in space-time. So, if strings are allowed to interact only by string exchange (which amounts just to changing the genus of the worldsheet, that still keeps living in space-time), how do we go from that state of things where we have actions (that is, Polyakov) that depend on the metric properties of the worldsheet, and describe how the worldsheet evolve inside space-time as a fixed background, to strings-exchange-things-that-curve-spacetime-itself, understanding spacetime the very space those strings live within. If strings are allowed to interact only via string exchange, does it mean that...   1. **strings are connected topologically to the space-time via strings?** That would be weird, a two-dimensional surface connected to a four-dimensional one, but I guess it would be logically possible. But that suggests that strings basically live outside space-time and only touch it through its boundaries, so closed strings are out of this picture   2. **space-time is itself made of interacting strings?** that would not make much sense to me. How would that preserve the traditional Lorentz invariance? Besides, string theory assumes the Lorentz invariance is exact   3. **strings have a mass density and just behave as classical general-relativity energy-momentum stress tensor densities?** That would make sense, but then that would be openly cheating, since that would not explain how strings create gravity, since gravity would be added _ad-hoc_   4. I'm out of options. How can strings interact with the space-time manifold? * * * **Edit** Thanks for the existing answers, but what I want, or what I was hoping is, if there is some diagrammatic/visual insight into the connection mentioned in the answers, say, the one from flat spacetime with graviton strings propagating that turns into an equivalent curved spacetime.


title: Negative energy/mass bounds on de-Sitter spacetime

text: There exists a Positive Energy theorem for General Relativity in Anti-de Sitter and asymptotically flat spacetimes, but there is no equivalent theorem for de Sitter spacetimes > **Question:** Is there a lower bound theorem on negative mass-energy density > on de Sitter spacetimes? The intuition says that the absence of a positive energy theorem in dS has to do with the fact that for small enough positive energy densities, the cosmological expansion beats the gravitational attraction, which means that positive energy densities need to exceed a threshold in order to behave attractively from far away. Is this intuition correct?


title: What proof techniques have failed for solving the SIC-POVM problem and what new insights have been gleaned from them?

text: The SIC-POVM problem is remarkably easy to state given that it has not yet been solved. It goes like this. With dim($\mathcal H$) $=d$, find states $|\psi_k\rangle\in\mathcal H$, $k=1,\ldots,d^2$ such that $|\langle \psi_k|\psi_j\rangle|=\frac{1}{d+1}$ for all $k\neq j$. The state of the art on the solution I believe is here: http://arxiv.org/abs/0910.5784. Various constructive conjectures have been given but what existence proofs have been tried and why have they failed? What insight has been distilled from these attempts?


title: Virasoro constraints in quantization of the Polyakov action

text: The generators of the Virasoro algebra (actually two copies thereof) appear as constraints in the classical theory of the Polyakov action (after gauge fixing). However, when quantizing only "half" of the constraints are imposed. I understand it's inconsistent to apply all of the constraints. I also understand this choice has mathematical significance in the sense of picking out highest-weight vectors. Nevertheless, on the surface it seems somewhat arbitrary. What is the physical reason it is "ok" to ignore the other constraints while mandatory to impose these? Also, are there simpler (preferably finite dimensional phase space) examples of quantization where some of the constraints must be dropped?


title: Geometric entropy vs entanglement entropy (dependent on curvature coupling parameter)

text: I have a quick question. In hep-th/9506066, Larsen and Wilczek calculated the _geometric entropy_ (which I believe is just another name for _entanglement entropy_ ) for a non-minimally coupled scalar field in Eq. 3.10 of their paper. They basically calculated the Heat Kernel on a cone with a non-zero curvature coupling parameter $\xi$ and then found the corresponding appropriate effective action and from there geometric entropy. They also discussed problems about calling this entropy geometric for its possibility of being negative etc. But still they kind of try to explain why geometric entropy can in fact depend on background curvature and so on (the rest of their section 3.3). But for example Solodukhin (and also other places) in 1104.3712 clearly states the (similar) problems of calling it entanglement entropy near his equation (144). So, my question was whether it is a settled matter that calling this type of entropy (one which depends on non-minimal coupling parameter in general), entanglement entropy is wrong. Please let me know if there are some subtlety involved that I am missing. Thanks in advance.


title: The Paper by Fateev and Zamolodchikov

text: I would like to read the following paper by Fateev and Zamolodchikov. Operator Algebra and Correlation Functions in the Two-Dimensional Wess-Zumino SU(2) x SU(2) Chiral Model. In addition to the fact that I could not find it online, I don't have access to the Journal, Sov.J.Nucl.Phys. It is very unfortunate that such a highly cited paper is not in the accessible situation. Does anybody know how I can reach this paper?


title: From vertex function to anomalous dimension

text: * In a $d$ dimensional space-time, how does one argue that the mass dimension of the $n-$point vertex function is $D = d + n(1-\frac{d}{2})$?    * Why is the following equality assumed or does one prove that a function $f$ will exist such that, $\Gamma^n(tp,m,g,\mu) = f(t)\Gamma^n(p,m(t),g(t),\mu)$? ..in writing the above I guess one is assuming that all the inflowing momentum are equal to $p$ but if that is so then what is the meaning of again specifying the "renormalization scale" of $\mu$?..Does this somehow help fix the values of the functions, $m(t)$ and $g(t)$ at some value of $t$?..If yes, how?.. * * * * * * If the above equality is assumed as a property of the vertex function then it naturally follows that it satisfies the differential equation, $[-t\frac{\partial}{\partial t} + m[\gamma_m(g)-1]\frac{\partial}{\partial m} + \beta(g)\frac{\partial}{\partial g} + [D-n\gamma(g)]]\Gamma^n(tp,m,g,\mu)=0$ where one defines, $\beta(g) = t\frac{\partial g(t)}{\partial t}$ $m[\gamma_m(g)-1] = t\frac{\partial m(t)}{\partial t}$ $D-n\gamma(g) = \frac{t}{f}\frac{\partial f}{\partial t}$ and the last equality integrates to give, $f(t) = t^De^{-n\int_1^t \frac{\gamma(g(t))}{t}dt}$ and $-n\int_1^t \frac{\gamma(g(t))}{t}dt$ is defined as the "anomalous dimension".


title: Defining the ground state energy of a QFT

text: * I would like to hear of some general discussion on how is the ground state and its energy defined in QFT and how does one go about finding it. (..at least in some simple cases I have seen the use of Bogulibov transformation to make the theory look like a free-field theory to be able to identify the vacuum - but does every theory have a generalized Bogulibov transformation?..)  To initiate let me point out one specific formalism which I am confused about. If one takes the Lagrangian as $L = \frac{1}{2}\left(\partial _\mu \phi\right)^2 - V(\phi)$ then in an expansion in powers of $\hbar$ gives the first term of the partition function as, $Z \approx \frac{1}{\sqrt{\mathrm{det}\left[-\partial^2 - V^{\prime\prime}\left(\phi_c\right)\right]}} e^{iS\left[\phi_c\right]}$ where $S$ is the action of the theory and $\phi _c$ is the classical extrema of that action. Then one sees that if $E_0$ is the energy of the classical solution and the action is evaluated for a time interval $T$ then one has the relation $S\left[\phi_c\right] = -T\,E_0$ In the footsteps of the above identity one wants to define $E_G$ as the true quantum groundstate energy as $E_G = \lim_{T\rightarrow \infty} \frac{i \ln Z}{T}$. If one used the above definition to the same order of perturbation as $Z$ is given and one replaces the value of $E_0$ before one takes the limit of $T \rightarrow \infty$ then one one has the relation, $E_G \approx E_0 - \lim_{T \rightarrow \infty} \frac{i}{2T} \ln \left\\{ \det \left[-\partial ^2 - V^{\prime\prime}\left(\phi_c\right)\right]\right\\}$   * Now I am not sure as to how to interprete the second term of the above expression since naively that seems to go to $0$ since the determinant doesn't depend on the time-interval. But I guess I am wrong and I would want to know how at least this way of thinking works out.


title: light penetration in the ocean

text: Is there an equation that describes the percentage of solar energy per wavelength that penetrates the ocean surface? For example, this website states that only 44.5% of the surface light reaches a depth of 1 meter. So, is there an equation that can be used to determine the percentage of solar energy per wavelength?


title: Cause and properties of northern lights

text: If outside on a dark night in the middle to high latitudes, one might be able to see an aurora. It may be several hundred kilometers high and several thousand kilometers long, stretching around Earth in an arc. However, it is less than 1 km thick. What produces this huge display and what makes it so thin?


title: A force's magnitude

text: In this question I asked about gravity and in the answers it came up that the magnitude is equal (of the gravity acting on the Sun and the of the gravity acting on the Earth) Does magnitude simply mean it's strength?


title: Distance and displacement of an object on a straight line

text: I had this homework problem, but don't actually know if what I did is right, or that I even read the problem correctly. Can someone please tell me if this is the right interpretation of the problem and my answer is right or wrong? >   1. at $t=0s$ an object has a position of $-4.0m$ and without changing > direction moves to a position of $+6.0m$ at $t=4.0s$ It then moves in a > straight line and accomplishes a displacement of $-8.0m$ at the $t=8.0s$ > mark. For the $8.0s$ interval: > > a. What was the total distance the object traveled?   >  b. What was the objects overall displacement?   >  c. What has been the object's average speed?   >  d. What has been the objects average velocity?   >  e. At $t=8.0s$, what is the object position?   > > > So what I did is this: _a._ I did $6-(-4)-(-8)$ and got a total distance of $22m$ _b._ It says the displacement of $-8.0$m _c._ Average speed would be $\frac{22m}{8.0s}=2.75m/s$ _d._ Average velocity would be $\frac{-8.0m}{8.0s} = -1.0m/s$ _e._ Would it be $-12.0m$?


title: Quality loss when adding more components to a telescope?

text: I would think this would be inherently true, but I'm curious: (Assuming the highest quality _amateur_ instruments are used.) Is quality lost when, say, adding a T-mount adapter, diagonal or any other instrument between your eyes (or camera) and the primary focus? Maybe not discernible to our eyes, but could this be something to avoid when approaching astrophotography?


title: Names, maps for Milky Way dust clouds?

text: There is a nice image of the Milky Way, labeled with constellations, at 360°x45° panorama with constellations: ![Image of the Milky way - in visible light? Image source: home.arcor.de/axel.mellinger/images/mwpan45_full_c.jpg](http://i.stack.imgur.com/5qLVN.jpg) It leads me to wonder how much we know about the Great Rift, Coalsack and other prominent dust clouds that obscure the stars in the background. Are there names for other clouds that can be distinguished by eye (in dark places)? How far away is the dust? Do we have any 3D maps of these dust clouds? My web searches haven't turned up much along these lines. _Update_ : I know there is a huge variety of information on the brighter nebulae and smaller telescopic Messier objects. I'm looking for information on the dust clouds "visible" to the naked eye.


title: How do I measure the temperature of a tiny water droplet?

text: How do I accurately (+/- 0.1 degrees Celsius or better) measure the temperature of a small (5 to 50 microliter) water droplet without noticeably affecting its temperature? The mass of a thermistor or thermocouple could exceed that of the droplet I'm measuring, and putting it in contact with the droplet would reduce the droplet's temperature and mess up my reading (and experiment). If it helps, the droplet is sitting on three thin metallic-film electrodes on a translucent plastic substrate. I thought about IR, the beam width on the IR thermometers I have is pretty wide so I couldn't target a small droplet.


title: What is the cosmic "Axis of Evil" problem?

text: What is the cosmic "axis of evil" problem? Apparently it is a more modern version of the old cluster mass discrepancy problem, where masses determined by gravitational lensing are always higher than masses determined by X-ray observations. Now Sunyaev-Zeldovich (SZ) masses from Planck seem to make the problem worse. Do the SZ masses disagree with both the lensing masses and the X-ray temperature masses?


title: What narrow-linewidth laser system runs at 2100nm with 1W of power?

text: For an experiment at our university we need a laser that runs at about 2.1 μm (about 20nm higher or lower would be fine too. We have found a multitude of lasers that achieve this (typically Thulium- or Holmium-doped solid state or fiber lasers), but they don't meet the requirements that we have. Specifically, we need:   * CW output (pulsed won't work for our application).   * Single-mode emission with a linewidth of about 0.1 nm.   * Polarized output.   * The laser should be single-mode fiber-coupled (or at least have an M^2 below 1.5 or so to allow efficient fiber coupling).   * 1W of power would be perfect (500mW would be the minimum). Many lasers around this wavelength are high power (in the range of tens of Watts), but have bad beam quality, or very broad linewidth. Medical lasers with large fiber outputs won't work for our application (they generally have fibers with hundreds of μm diameters). Tunability of the laser would be a bonus, but isn't strictly required in our application. One option we are considering is using an Optical Parametric Oscillator (OPO) consisting of a periodically-poled crystal (Lithium Niobate or KTP) which is phase-matched such that the frequency of a pump laser running at 1064nm if halved (which would result in a wavelength of 2128 which would still be fine for our application). It isn't trivial using such a laser in a high-power configuration though (since the signal/idler beams would have to produce 1W of power at least the pump laser would need to have several Watts). We would appreciate any ideas or names of companies that would be able to build such a system. Thank you very much. Benjamin


title: If I replace all my lights with LEDs will my heating costs increase?

text: A number of nations are passing bills to phase out incandescent light bulbs. The thinking is that the tungsten filament is an inefficient method of turning electricity into light, the rest of the energy is converted to heat, so LED will save power and lower energy usage, electricity costs. In the UK where the atmosphere is generally cooler than room temperature, except for peak summer weeks when the evenings are light, will the use of LED lights result in my central heating having to work harder, burning gas, to make up the difference?


title: scrap iron for stopping a meltdown

text: Would it be possible in a Fukushima-style meltdown to halt the process (edit: I mean halting the meltdown process, not the actual nuclear processes) by dumping large amounts of iron into the vessel? The iron would melt and mix with the uranium, which would 1) Dilute the fuel to slow the reaction 2) Absorb and transport away heat 3) Encase the fuel in a massive block of metal 3) Iron doesn't contain carbon, as steel would. Carbon moderates the neutrons. Of course, this would render the reactor useless, but if it is already melting down, it is already useless. It would slow the reaction and lower the temperature so you stop building up hydrogen gas in the containment vessel. Other metals might be theoretically better, but iron is cheap, strong, and readily available.


title: Why does increasing the flickering speed of a light have a dimming effect?

text: I'm setting up one of my first circuits. I have a knob to increase the flickering speed of a led. When I increase the flickering speed up to a certain point I am not able anymore to perceive it is flickering. When I increase the flickering speed even more the led dims. Why? Some sort of wave interference effect?


title: Is it possible to excite a semiconductor @ k=0?

text: Let us assume a direct semiconductor with parabolic band structure around the $\Gamma$ point (which is not bad for most semiconductors) in momentum ($k$) space. Now we excite it with light: ![enter image description here](http://i.stack.imgur.com/4vsEL.png) I encircled the start and end state in red. The shaded area resambles the photon energy with momentum $q$. So my question to this kind of situation is, is it possible to have an electron at exactly $k=0$? My concerns are, that this would mean, that the electron would have no kinetic energy when $E=\hbar^2k^2/2m_e$. That means, that the position has maximal uncertainty after Heisenberg. And that would mean that the electrons wave function would be extended into infinity. Since a semiconductor is typically smaller than infinity, this can't be possible.


title: How can sunlight be white , but pictures of the sun be orange?

text: I was thinking about elementary physics today and realised: We learned and proved that sunlight is white. But i don't understand why when you look at a picture of a satellite orbiting the sun , it(the sun) seems yellow-orrange. How could this be? It is like there is a red light bulb in the room but what you see is green.


title: Why does Hauksbee's electrostatic machine produce light?

text: I'm reading on the history of the discovery of electricity and the electron, and I've went from reading about Rutherford's gold leaf experiment all the way back to Francis Hauksbee's spinning glass machine. Hauksbee was essentially the first person to preform scientific study on the effects of electrostatics in vacuum. He observed that when spinning a glass orb evacuated of air (vacuum inside the orb) and while placing his hand on the spinning orb, a charge was created such that blueish glow was seen **inside** the orb, where his hands were placed, and on the opposite side of the orb. As seen in this show, see from 4:30 : http://www.youtube.com/watch?v=uhgo9fAlAQQ I understand the glow of fluorescent tubes due to an electric current driven through a gas -filled tube, i understand the effect of the release of a photon when an electron decreases an energy level, and that gives the glow. What I don't understand is why is the glow **inside of the orb** instead of outside, and **why does the glow "stick" to Hauksbee's hand?** and furthermore, **what does the vacuum have to do with the glowing effect**? Can I preform the same results with an orb that inside is a nearly complete vacuum or no air at all? I'm intrigued because the advancement in our scientifically and technological abilities was due to the "combination" of vacuum and electrostatics (tribo- electric effect) and I want to understand the thought process that brought Hauksbee to build this machine. Thanks in advance! :)


title: Topological insulator vs. topological superconductors in any dimension

text: My question today is simple. What is the difference between a topological insulator and a topological superconductor? How that difference depends on the dimensionality of space(time)? What is the difference in terms of the so- called edge states? PS: I only know that a topological insulator is some material that is conductor on the edge but insulator in the bulk...Is that definition right in ANY dimension?What about topological superconductors?


Why some particles interact with the Higgs field and others don't? Higgs doesn't explain that much: why some particles have mass and others don't? is like why some particles interact with the Higgs field and others don't?


title: Finding the illuminance from a triangular light source

text: Since most light sources in games are point-like, it's pretty difficult to approximate area light sources with point sources. As triangles are a universal form to represent 3D models (thus area light sources too), I stumbled upon a task consisting in finding the total illuminance at some point in 3D space from a uniform triangular source. So I started from the basic formula to compute the illuminance from a point source: $$E = I \frac{\cos(\alpha)}{ r^2}$$ where $I$ being the intensity, $\alpha$ being the angle of incidence & $r$ being the distance from the source to the point. In order to find the angle of incidence, we not only need to know the radius- vector of the point, but also its normal. So the following vectors were defined:               n - normal of the illuminated surface in the given point;     p - position of the point itself;     s - position of the light source;     r = s - p (distance vector).      From the dot product formulae the cosine of the angle of incidence is calculated as: $$\cos(\alpha) = \frac{\vec n·\vec r}{|\vec n||\vec r|} = \frac{\vec n·\vec r}{|\vec r|}$$ as the normal's length is 1. Thus the formula of the illuminance can be calculated as: $$E = I \frac {\cos(\alpha)}{ r^2} = I \frac{\frac{\vec n·\vec r}{ |\vec r|}}{|\vec r|^2} = I \frac{\vec n·\vec r}{(\vec r·\vec r)^{3/2}}$$ Since we've got a triangle, we need to find the illuminance from all points on the triangle. Any point $s$ on the triangle can be defined using barycentric coordinates, thus: $$\vec s = \vec a + (\vec b-\vec a)u + (\vec c-\vec a)v$$ where $a$, $b$ & $c$ are the vertices and $u$ & $v$ are parameters ranging from 0 to 1 & which sum cannot exceed 1. Thus: $$\vec r = \vec s - \vec p = \vec a + (\vec b-\vec a)u + (\vec c-\vec a)v - \vec p$$ Finally, I came up with the double integral & stuck: $$E = I\int\limits_{0}^{1-u} \int\limits_{0}^{1} \frac{\vec n·\vec r}{(\vec r·\vec r)^{3/2}}\, du\, dv $$ where: $$\vec r = \vec a + (\vec b-\vec a)u + (\vec c-\vec a)v - \vec p$$ Can anyone verify my solution & help me solve the integral? (As I've honestly no idea how integrals involving dot products are solved.) And perhaps, there could be simpler solutions for this? Numerical integration is an option, but still I'd like to have the complete formula. P.S. The task can be slightly altered so to calculate the illuminance from the line segment rather than the triangle. One just needs to remove one of the vertices & the $v$-parameter, so the double integral is reduced to the single integral with only one variable.


title: Absorption of radiation due to temperature

text: I was wondering if the temperature of an object affects the amount of radiation it absorbs. For example, if I have a box that is hotter, will it absorb more energy as compared to the same cooler box?


title: What sorts of complications do massive neutrinos bring to the Standard Model?

text: Naively, I'd just think of considering them as any other massive fermions (but without electric charge), including the appropriate chiralities (and neutrino- higgs coupling when necessary). Nevertheless something tells me it is not that simple. People talk about sterile neutrinos and things like that. Would consider massive neutrinos bring extra complications to the SM? Would it require changes in the way we describe the weak interactions? What exactly would it conflict with?


title: The circumference of the Moon's orbit around the sun?

text: I know that it orbits the sun in what looks like a 12 sided polygon with rounded corners. But I can't seem to find the radius/circumference anywhere.


title: Time dilation apeears in the both frame: Where is the problem?

text: Let we consider time in stationary frmae t, and respect the to stationary frame moving frame time $t^ \prime $ . According to lorentz transformation, $$t^\prime= \frac{t-\frac{vx}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}}$$ and according to inverse Lorentz transformation, $$t= \frac{t^\prime +\frac{vx^\prime}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}}$$ If we measure a event we have got,$$ t= t_2 -t_1$$ then, $$t= \frac{t_2^ \prime -t_2^ \prime }{\sqrt{1-\frac{v^2}{c^2}}}$$ $$t= \frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}$$ Therefore t is greather than $t_0$. But if we calculate the time dilation in otherway, we have got, $$t_0 = t_2^\prime -t_1^\prime $$ then, $$t_0= \frac{t_2 -t_2 }{\sqrt{1-\frac{v^2}{c^2}}}$$ $$t_0= \frac{t}{\sqrt{1-\frac{v^2}{c^2}}}$$ Therefore $t_0$ is greather than $t$. I think I am doing wrong somewhere, because I have proven the stationary time longer and after some time I got the opposite. Can you please tell me that where did I get wrong?


title: Apparent paradox in special relativity: transmitting a message and setting off after it

text: I have a question about special relativity, which is set in the context of the science fiction anime Voices of a Distant Star, though it is independent of that context. Mikako goes on a spaceship with a speed of $0.99999c$, heading towards a star system 4 light years away. In her rest frame, the journey takes a few days, but for her friend Noboru on Earth it takes approximately 4 years. Now when Mikako arrives at the star system, she sends Noboru an e-mail at light speed, which takes another 4 years to arrive. So 8 years after Mikako departs, Noboru gets an e-mail, inviting him to meet with Mikako. Suppose that after sending the e-mail, Mikako immediately heads towards earth in her $0.99999c$ spaceship, while Noboru gets a similar spaceship and heads toward the direction of the star system. In a few days' rest frame time for both of them, they meet in deep space. Mikako then gives Noboru an album of pictures of the star system. This seems like a paradox. When Noboru gets the e-mail, he is 2 light years away from Mikako. But a few days later in his reference frame, he obtains the pictures of the star system. Why does this work? Is this not a paradox due to the fact that Noboru must wait 8 years for the e-mail to arrive? Or is it not a paradox due to relativity not working the way I expect it to work? Yet even from Noboru's $0.99999c$ perspective, Mikako's relative speed should never exceed $c$, so why, from Noboru's perspective, do the photos seem to be transmitted superluminally?


title: Killing vectors for 2-sphere as generators of $SO(3)$ symmetry

text: How to get Killing vectors in a form of generators of $SO(3)$ group symmetry? By using Killing equations for metric $ds^{2} = d\theta^{2} + \sin^{2}(\theta^{2}) d\varphi^{2}$ I got $$ \varepsilon_{\theta } = C_{1}\cos (\varphi ) + C_{2}\sin(\varphi ), $$ $$ \varepsilon_{\varphi} = \frac{1}{2}\sin(2 \theta )(C_{1}\cos(\varphi ) - C_{2}\sin(\varphi )) + C_{3}\sin^{2}(\theta ). $$ So, if I set $C_{1,2}$ to zero, I will get $$ \varepsilon^{\mu}_{1} = C_{3}(0, sin^{2}(\theta )), $$ and for another combinations $$ \varepsilon^{\mu}_{2} = \left(C_{2}sin(\varphi ), \frac{C_{2}}{2}cos(\varphi)sin(2 \theta)\right), $$ $$ \varepsilon^{\mu}_{3} = \left(C_{1}cos(\varphi ), -\frac{C_{1}}{2}sin(\varphi)sin(2 \theta)\right). $$ But the correct result refers to $$ \varepsilon^{\mu}_{1} = C_{3}(0, 1), \quad \varepsilon^{\mu}_{2} = \left(C_{2}sin(\varphi ), C_{2}cos(\varphi)ctg(\theta )\right), $$ $$ \varepsilon^{\mu}_{3} = \left(C_{1}sin(\varphi ), -C_{1}sin(\varphi)ctg(\theta )\right). $$ Why do I must multilpy the results for $\varphi $component on $\frac{1}{\sin^{2}(\theta )}$?


title: Can water pressure ever be high enough to trap gas bubbles or keep them from surfacing?

text: Can water pressure ever become high enough to trap gas bubbles and/or keep them from surfacing?


title: A question about biceps and rotational equilibrium

text: I know that as the angle of the elbow increases, the force of the bicep increases. i.e. when angle is 180, arm is fully extended and there is 0 force from bicep. When the elbow angle is smaller there is more force from the bicep. So would shorter forearms be the answer, because the angle would be smaller?


title: System in mechanical but not thermal equilibrium

text: Let's say there are two systems which can interact by a moving wall but cannot exchange heat. Then the system will be in mechanical, but not necessarily in thermal equilibrium. The maximality of entropy in mechanical equilibrium requires only the ratio p/T to be equal. So there is a possible equilibrium state where one system has double pressure and double temperature... Where is my mistake?


title: Is it foolish to distinguish between covariant and contravariant vectors?

text: A vector space is a set whose elements satisfy certain axioms. Now there are physical entities that satisfy these properties, which may not be arrows. A co-ordinate transformation is linear map from a vector to itself with a change of basis. Now the transformation is an abstract concept, it is just a mapping. To calculate it we need basis and matrices and how a transformation ends up looking depends only on the basis we choose, a transformation can look like a diagonal matrix if an eigenbasis is used and so on. It has nothing to do with the vectors it is mapping, only the dimension of the vector spaces is important. So it is foolish to distinguish vectors on the way how their components change under a co-ordinate transformation, since it depends on the basis you used. So there is actually no difference between a contravariant and covariant vector, there is a difference between a contravariant and covariant basis as is shown here http://arxiv.org/abs/1002.3217. An inner product is between elements of the same vector space and not between two vector spaces, it is not how it is defined. Is this approach correct? Along with this approach mentioned, we can view covectors as members of the dual space of the contra-vector space. What advantage does this approach over the former mentioned in my post? _Addendum:_ So now there are contra variant vectors and their duals called covariant vectors. But the duals are defined only once the contravectors are set up because they are the maps from the space of contra vectors to $R$ and thus, it won't make sense of to talk of covectors alone. Then what does it mean that the gradient is a covector ? Now saying because it transforms in a certain way makes no sense.


title: Do I need to take both particles' momentum into account in photoelectric emission?

text: > An aluminum dust particle of mass $m=2.2*10^{-18}$ grams is floating in > space ( initial velocity is zero). The particle emits electron under > influence of a photon whose frequency is $8*10^{17}$ hertz. If the work > function of aluminum is $W=4.08$ electron volts, calculate the speed of the > particle after the emission.. Velocity vectors of particle and photon have > same but respectively negative directions. My attempt: Calculate velocity of electron by using Einstein's photoelectric effect equation. Use conservation of momentum to calculate the speed of the particle. What puzzles me is: Do I need to take both electron and photon momentum into calculations?? Maybe conservation of energy would be a better approach??


title: Diagonal Hamiltonian of 3 Spin 1/2 Particles

text: I have three Spin 1/2 Particles and a Hamiltonian given by $$H=A(S_1\cdot S_2)+B(S_2\cdot S_3+S_1\cdot S_3)$$ In order to find the energy spectrum, I want to diagonalize H in terms of $(S_1+S_2+S_3)^2$ and a coupling of 2 of them (I already have spectrum of $H=A(S_1\cdot S_2)$). However, every combination I have tried if terms of coefficients and couplings have not been successful, so I was hoping someone could give me a hint as to how to couple these guys. Thanks.


title: How exactly is the Poisson bracket of the modes of a classical string defined?

text: In the theory of a classical bosonic string, we have expressions like: $$ \\{\alpha^\mu_m,\alpha^\nu_n \\} = - i m \delta_{m,-n} \eta^{\mu \nu} $$ were $\alpha^\mu_n$ are the Fourier modes of the string. How is this Poisson bracket defined? The definition from analytical mechanics involves partial derivatives with respect to the generalized coordinates and momenta. Since the modes $ \alpha^\mu_n $ are constants, their partial derivatives are zero, so there must be something I'm missing here.


title: Why is static friction called self adjusting force?

text: Explain what is limiting force of static friction.


title: Can temperature affect or change the wavelength or frequency of EMR?

text: If we were to emit Electro Magnetic Radiation(X-rays for example) to a very hot body such as the sun would we still get X-rays if we had a capturing device at the other end or would the high temperatures affect its frequency and wavelength and change it to another kind of Radiation?


title: What is a superfluid in field theoretic terms?

text: I'm wondering how one precisely defines a superfluid in terms of the effective field theory description. In Nicolis's paper http://arxiv.org/abs/1108.2513 there seems to be an extremely simple characterization of the superfluid: it is just a scalar field $\psi$ with a nonlinearly realized $U(1)$ shift symmetry, $\psi\mapsto \psi + a$. Does this mean I can call any theory with such a shift symmetry a relativistic superfluid? E.g., the simplest action you could write for $\psi$ is just $$S=\int d^4x \sqrt{-g}\partial_a\psi \partial^a\psi$$ which is just a massless free scalar field. Is it correct to regard this as a superfluid? Or is there some other feature that is needed as well? For definitiveness, I'm just concerned with zero temperature superfluids, so I'm not worried about including the second fluid that is needed for vortices and the like.


title: hadron jets from quark-antiquark in colliders

text: The observation of hadron jets from electron-positron collisions (LEP) is explained (e.g. Wilczek, The Lightness of Being, p 55) as follows- e,p collide and produce a virtual photon. the photon goes into a quark, antiquark pair, and one jet of hadrons comes out of the quark, and an opposing jet comes out of the anti-quark. Question: How can a quark with fractional electric charge produce a jet of particles that all have integral electric charge? What happens to electric charge conservation in the process?


title: 'Validity' of QED/QCD/Electroweak interaction

text: I am currently attending a course on Quantum Field Theory and I got into thinking how valid these theories are. As the theory attempts to describe reality only far above the Planck (length) scale, this has to be taken into account. Another problem that occurs is, how can we measure the validity of theory? For example the new particle found at LHC in 2012 has been detected with more than 5 sigma. But such a standard deviation can not be given for a whole theory. I remember that one my lecturers once said that QED has been validated more than QCD. As both theories describe the same scope of energies, is that a statement one can make? Is there a way to measure the validity of a theory?


title: Heat transfer speed - affected by difference in relative heat?

text: If I put something at room temperature in an environment that is at roughly half room temperature, does it get colder less quickly than if it were placed into an environment with 1/4 room temperature, assuming all environments are non-liquid and transfer heat mainly through air. Quintessential example: a can of pop at room temperature, placed into fridge or freezer for the same amount of time. Does the can in the freezer really get colder, or is it just an example of expectation bias?


title: Confusion concerning the use of wavenumber in exercise about Fabry-Perot etalon

text: In the exercise we are given that the spectrum of a light source consists of two spectral lines, which both have wavelengths around $500 \text{ nm}$ and the separation between them - given in wavenumbers - is close to $0.1 \text{ cm}^{-1}$. One part asks us to calculate the distance between the mirrors if we want the free spectral range of our Fabry-Perot etalon to satisfy $FSR(\text{in } \overline \nu) = 2.5(\overline \nu_2 - \overline \nu_1)$. Now, I know that the free spectral range ($\theta = 0$, $n_{air} \approx 1$) is given by $$FSR = \frac{c}{2d}$$ where $d$ is the distance between the mirrors and we have $$\Delta\overline \nu = \frac{c}{\lambda_2} - \frac{c}{\lambda_1} = \frac{c}{2\pi}\Delta k $$ So shouldn't then $$d = \frac{c}{2 FSR} = \frac{c}{2 \cdot 2.5c/(2\pi) \Delta k} = \frac{\pi}{2.5\Delta k} \approx 12.566 \text{ cm}$$ According to the solution this is wrong: They get $FSR = 0.25 \text{ cm}^{-1}$ and $d = \frac{1}{2 \cdot FSR} = 20 \text{ mm}$ I seem to be missing something. If they calculate the free spectral range in terms of the wavenumber, shouldn't they convert it to frequency by $$FSR(k) \to FSR(\nu) = \frac{c}{2\pi} FSR(k)$$ instead of $$FSR(k) \to FSR(\nu) = c \cdot FSR(k)$$ Does anybody see what's going on here (maybe the solution is simply wrong, but I'd like to know for sure)?


title: What's the difference between arc length and signed distance?

text: Suppose I give you a position function $x(t)$ where t is time and x is position. Then i ask you to find the total distance travelled from $t = 0$ to $t = t_f$. Which formula would give you that distance? $$\int_{0}^{t_f} \sqrt{1 + [x'(t)]^2} dt$$ $$\int_{0}^{t_f} |x(t)| dt$$ I know the first one gives you the arc length of the path (which is the total length of the path) and the second one gives me the signed distance, but why are they fundamentally different again?


title: Are quantum effects significant in lens design?

text: Over on Photography, a question was asked as to why (camera) lenses are always cylindrical. Paraphrasing slightly, one of the answers and follow-up comments asserted that quantum effects are significant and that you need to understand QED in order to understand lens design. My intuition tells me that this probably isn't the case, and that modern lens design can be handled via classical optical theory. Is my intuition correct, or are quantum effects really significant in modern lenses?


title: Would it be possible to build a Solar Panel Etalon?

text: Since, on average, 1/3 of all sunlight that hits a solar panel is reflected, wouldn't it be possible to set up some kind of etalon system where the reflected light is then absorbed by another solar panel, and then the reflected light from that panel is further absorbed by the first panel, and so forth? So basically, the amount of sunlight present in the etalon would decrease by 2/3 each time it hits one of the two panels. Is this feasible and practical?


title: Inverting an anisotropic distribution

text: I have come across a research problem where I need to solve an integral equation of the form $\int A^{-1}(x,y) \nabla_z\cdot\left[\nabla_y\cdot\left(v(y) G(y-z) \right) v(z)\right]dy = \delta(x-z)$, where $v:\mathbb{R}^d\to\mathbb{R}^d$. What I need is an understanding of how the distribution $A^{-1}(x,y)$ changes with respect to $v$. Specifically, I need to evaluate integrals like $$\int \frac{\partial A^{-1}(x,y)}{\partial v(x)}f(y)dy\quad\text{ and }\iint f(x) \frac{\partial A^{-1}(x,y)}{\partial v(x)\partial v(y)} f(y)dxdy.$$ Has anybody come across anything similar?


title: Is the statistical interpretation of Quantum Mechanics dead?

text: I'm sure this question is a bit gauche for this site, but I'm just a mathematician trying to piece together some physical intuition. > * _Question:_ *Is the statistical interpretation of Quantum Mechanics still, > in any sense, viable? Namely, is it completely ridiculous to regard the > theory as follows: Every system corresponds to a Hilbert space, to each > class of _preparations_ of a system corresponds to a state functional and to > every class of measurement procedure there is a self-adjoint operator, and > finally, a state functional evaluated at one of these self-adjoint operators > yields the expected value of numerical outcomes of measurements from the > class of measurement procedures, taken over the preparations represented by > the state? I am aware of Bell's inequalities and the fact that the statistical interpretation can survive in the absence of locality, and I am aware of the recent work (2012) which establishes that the psi-epistemic picture of quantum mechanics is inconsistent with quantum predictions (so the quantum state must describe an actual underlying physical state and not just information about nature). Nevertheless, I would really like a short summary of the state of the art with regard to the statistical interpretation of QM, against the agnostic (Copenhagen interpretation) of QM, at present. Is the statistical interpretation dead, and if it isn't...where precisely does it stand? An expert word on this from a physicist would be very, very much appreciated. Thanks, in advance. EDIT: I have changed the word "mean" to "expected" above, and have linked to the papers that spurred this question. Note, in particular, that the basic thing in question here is whether the statistical properties prescribed by QM can be applied to an individual quantum state, or necessarily to an ensemble of preparations. As an outsider, it seems silly to attach statistical properties to an individual state, as is discussed in my first link. Does the physics community share this opinion? EDIT: Emilio has further suggested that I replace the word "statistical" by "operational" in this question. Feel free to answer this question with such a substitution assumed (please indicate that you have done this, though).


title: how does international space station change its orientation?

text: * In what way does the rotating gyroscope help in changing the orientation of the international space station in space ?   * Is there any other way to change the the orientation of ISS ?


title: Fork and Sheet Lightning

text: I've noticed that during British lightning storms, I have only ever seen sheet lightning ![sheet lightning photo](http://i.stack.imgur.com/dlTHL.jpg) However, on holiday in other countries, I frequently see Forked Lightning ![forked lightning photo](http://i.stack.imgur.com/Ijudu.jpg) **Q)** Is this just caused by cloud, or is it two distinct forms of lightning? **Q)** Is there a reason Britain only seems to get the sheet kind?


title: Weighing head by angular momentum

text: A popular Phys.S.E question asks how can I measure the weight of my head. One of the answers suggests measuring the moment of inertia. My suggestion was to construct an apparatus that places the subject on a translatable carrier located on top of a rotating table. Sensors would allow the change of angular velocity to be measured as the carrier is translated relative to the centre of rotation. The subject would begin with their head at the centre of rotation and end with their feet there, many measurements being taken in between. It would (equivalently) rotate at constant speed and measure the forces necessary to hold the translating carrier in place. I hoped that this (with x & y translation, if desired) would give enough information to computationally determine a mass density map of the subject. **Q)** Are these two approaches basically equivalent? **Q)** Would these approaches actually work? A comment on the moment of inertia answer states: > "Isn't the moment of inertia of a rigid body a tensor? More specifically, > it's a 3×3 matrix, so all your measurements above can be calculated knowing > just nine numbers." Is this the case, and does this mean that a density image could not be generated?


title: Commercial large scale production of graphene

text: I am a third year undergraduate Physics student, and for my solid state physics course I am asked to give a short (10 minute) qualitative presentation on the current standings of graphene production, about what can be done right now, what is expected to be doable in the near future, what the current problems are that have to be solved, etcetera. However, I am having quite some trouble in finding suitable sources. It is of course such a hot topic that new papers come out basically every day, and it is hard to find 'objective' sources that don't just talk about how a specific company has found the new, best way to do it. I suppose this is a bit of a non-traditional question to ask, but I was wondering if someone could help me out by pointing me towards some reliable, recent sources. A review article would be optimal, but of course as it is such a swiftly changing field this might be difficult. What I plan on doing at this point is structuring my presentation along these rough lines To start with, talk about how the 'first' graphene was made, using the scotch tape. Everyone I will talk to knows this, but it is still nice to see, especially with good pictures. I will then move on to what can already be done: several techniques that exist and that are being implemented as we speak, and what exactly they produce (multilayer graphene instead of monolayer, for example), and what the problems are that 'we' are currently facing in producing good graphene. Then I would like to talk about what is on the horizon, and on what timescales we expect what. If anyone has any comments on this (improvements or things I should definitely include) I would also be very happy to read them.


title: Why is the solar noon time different every day?

text: If you check the local time for solar noon is different every day. Why is it so? Is it because Earth doesn't make a complete rotation in exactly 24 hours?


title: Is antumbra part of shadow darker than penumbra part of shadow?

text: I'm exploring different types of shadows casted by objects.   I want to know if antumbra part of a shadow is darker than penumbra part. I've found two misleading pictures on Wikipedia:   First: ![Antumbra light](http://i.stack.imgur.com/c5pTC.png) Second: ![Antumbra darker](http://i.stack.imgur.com/ApN9C.jpg) Which one is correct? This example outside astronomy shows that antumbra is lighter than penumbra part of the shadow: ![Antumbra outside astronomy](http://i.stack.imgur.com/wABFH.jpg) btw. Are there any reliable online references on that topic?


title: Neglecting second order differentials

text: I am currently doing some Lorentz invariance exercises considering infinitesimal Lorentz transformations, and have been told to neglect second order differentials. It's not the first time I have come across seeing something like this, and I wonder which is the justification behind this, I mean, is this a justifiable exact procedure or just an approximation?


title: Electromagnetic Field Tensor via Tensor Products?

text: Can the electromagnetic field tensor be thought of as the tensor product of two physically reasonable vectors? Are the vectors arbitrarily constructed so that their components simply give the values in the electromagnetic field tensor matrix? I'm not very comfortable with thinking of thinking about things like second rank tensors as anything other than tensor products of vectors, so showing how second rank tensor transformations like the e-m field tensor act under things like Lorentz transformations is like a game without any meaning to me at this point unfortunately, I'm thinking trying to interpret it in terms of tensor products of vectors makes things more intuitive (i.e. operators on simple vectors)


title: Why is acceleration constant in this example?

text: I was shown this video by our professor: https://www.youtube.com/watch?v=8A7DiGzJUvg&feature=youtu.be And I do not understand why the acceleration is constant. Our professor told us that a freely falling object has constant acceleration of 9.8 meters per second squared. My first question is if an object is considered freely falling when it is thrown upwards, or if it only becomes "freely falling" when it..actually is falling? Secondly, if acceleration measures the rate of change of the velocity, then from looking at the example in the video, the velocity goes down to 0 when it reaches maximum height. Shouldn't changing from an non- zero velocity to a zero velocity be considered a change in acceleration, since it is slowing down at that time? If I understood this correctly, why is the acceleration constant throughout the video? At this point I re-watched the video and realized it says "straight line motion" which I'm not sure if they mean a horizontal line [kinda confusing since it is vertical so I feel like it makes more sense to think of it as it being thrown so I guess the question of freely falling doesn't apply, but either way at one point the velocity reaches 0 so why doesn't the acceleration change at all?


title: Can someone show me how Green's function would apply for this simple case?

text: I'm reading up on some stuff on basic electrostatic here: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/laplace.html ![enter image description here](http://i.stack.imgur.com/WJh1K.png) Can someone use Green's function to show me the form of $V$? **Update:** I have made an attempt to solve for $V$ but I can't understand why it takes the form $$V = \frac{\rho}{4\pi\epsilon_o} \int \frac{1}{|r-r'|}dr^3$$ (can someone check my solution) I can't recall this solution from anything I've previously encountered. What is the meaning of this $V$. What is the underlying geometry I'm working with? Is anyone familiar with this form of $V$? Also, how would you derive $E$ from $V$ given the above expression? I think if I see $E$ then it would make more sense.


title: Why is there a static frictional force on an object that rolls without slipping?

text: It is clear that if a frictional force must exist on an object that rolls without slipping, it must a static frictional force because the contact point of the object with the ground does not move. I know that if a ball rolls on a flat surface, once it begins rolling without slipping, the frictional force is 0. I am confused, however, about the case when a ball rolls down a ramp. For the condition of rolling without slipping to hold, there must be a frictional force on the ball up the ramp. I am confused about where this frictional force comes from if the part of the ball touching the ramp isn't actually moving. It doesn't seem to make physical sense because from the ramp's perspective, it is touching a stationary object and thus there shouldn't be a frictional force. Help??