title: What force does bathroom scale measure?

text: When you stand on a bathroom scale, I know that the force displayed is the normal force. Since it is the normal force, then technically the force displayed would actually be Fg= (mass)(acceleration) right? If this is true, then why is it that your normal force changes in an elevator? (i.e. if you travel down an elevator, why would the normal force decrease?) Please explain this to me, as I am really confused! It would be best if you could relate this to the Newton laws. Thanks!


title: Another layman blackhole question, pulling one end of a string out from behind the event horizon

text: No long explanation is needed, What would happen if I were to allow one end of a rope to fall past the event horizon of a black hole while I held the other end? Would I be able to pull it out? Would the rope feel extremely (infinitely?) heavy?


title: Gravitational force exerted by a rod on a point mass

text: I have doubts with the solution of a certain problem. I will give the entire solution below and will lay out my doubts as well.      A point mass $m_1$ is separated by a distance $r$ from a long rod of mass $m_2$ and length $L$.The objective is to find the total gravitational force exerted by the rod on the point mass.      This is how a particular author solved this question in a book.      The total mass of the rod was differentiated with respect to the total length of the rod, and each mass piece was called $dm$ and each length piece was called $dx$. Hence this equation was formulated:      $\large \frac{m_2}{L}\ =\ \frac{dm}{dx}$      Also, the distance between the point mass and each individual $dm$ piece was taken as $x$. Then the gravitational force between the point mass and each mass piece is given by:      $F\ =\ \large \frac{Gm_1dm}{x^2}$      $dm$ was substituted using the first equation, now the new equation becomes:      $F\ =\ \large \frac{Gm_1m_2}{Lx^2}\small dx$      This is then integrated from $x\ =\ r$ to $x\ =\ r + L$.      My question is this: how can we integrate $x$ with respect to $dx$?   $dx$ represents the tiny length pieces of the rod, and $x$ represents the distance from the centre of the point mass to any point along the rod. How can we integrate $x$ with respect to $dx$, it does not make any physical sense to me? I am new to differentiation and integration, but I understand the basics well enough. If there is something wrong with this solution please tell me the right way to solve this problem, otherwise tell me how this solution makes sense.


title: How does carbon dioxide or water vapour absorb thermal infra red radiation from the sun?

text: We are all told at school water vapour and carbon dioxide are the top two greenhouse gases, and that they absorb thermal infra red radiation, trap heat and warm up the Earth. My question is how do they do that? Why can't Oxygen or Nitrogen or any other gas not absorb infra red radiation as well as water vapour or CO2?


title: How to measure declination of sun and moon?

text: I came by some graphs showing the declination for sun and moon (between angles of -30° and +30°). The graphs look very much like sine waves. I googled a bit and read about what the declination is, and I found tools to look up the declination for a certain date. However, what I really haven't understood yet is, how to measure the declination. So if I would like to create such a graph during the next 365 days by hand, what exactly would I measure?


title: Does the electric field change only inside the dielectric, or even after exiting the dielectric?

text: I know that the field inside a dielectric is changed and is $\epsilon$ times less the original field (some books use $K$ for this constant). This is because the induced field inside the dielectric is in opposite direction to the original field. But what happens to the field after it passes the dielectric? **For example:** Assume a point charge $q$ is somewhere on the $z$ axis, above the $x-y$ plane, and that the $x-y$ plane is made out of a dielectric material with $\epsilon>1$, does the field below the $x-y$ plane is still given by $E=\frac{q}{r^{3}}\vec{r}$?


title: Are electromagnetic "plane" waves measurable or just a virtual concept?

text: I find plane waves are uncompatible with light cone. Perhaps plane waves are "virtual" and can never be measured in that case, shouldn't we call plane waves as "virtual plane waves"? (other option could be that plane waves allows waves travel faster than c) I would like to clarify this point through this question. If plane waves would exist(as measurable), then higher than c speed could be reached like this: A wave going from X to Y at a speed c, it will reach Z at higher than c speed, because it will reach at same time, traveling more distance.                                  (X).                         |                            v                          ________________________________________________       plane waves       ________________________________________________       going X to Y      ________________________________________________                        (Y).                                       (Z).      In a real situation the wave will be a circle (or a sphere in 3d) so it will get Z later then that's not a plane wave.


title: Does the Lorentz force change under a boost?

text: I have a question about the Lorentz force on a charge $q$: $$\mathbf{F}=q(\mathbf{E}+\mathbf{v}\times\mathbf{B}).$$ I understand that if one performs a Lorentz boost then the electric field $\mathbf{E}$, magnetic field $\mathbf{B}$ and the velocity of the particle $\mathbf{v}$ will all change. Does the Lorentz force $\mathbf{F}$ change under a Lorentz boost as well? I would have thought that it shouldn't as the force is something that has an observable effect: it can be measured directly using an accelerometer.


title: How to guess the correct fitting function to some data?

text: Imagine we are plotting some date points $\left(x_i,f(x_i)\right)$ that we obtained experimentally, and that we want to know what $f(x)$ is. The way to do this is to use some software and try to fit the data to some guessed function. For example, if the behavior of the data points looks like exponential decay we then choose an exponential decaying function ..etc. My question is: sometimes the data points are perfectly fitted to the exponential decaying trial function only on a certain region, but then the rest of the points show deviation away from the trial function.   1. How to proceed in this case? is there a catalog (something like mathematical tables) for functions and their plots that one can use as a guide?    2. Is there a systematic way to get the best fit instead of that trial and error method?


title: Retrodiction in Quantum Mechanics

text: To focus this question let us consider first classical mechanics (which is time-symmetric). Given a final condition (and sufficient information) one can calculate the system conditions of an earlier time (retrodiction). Given Quantum Mechanics (which is time-symmetric) and a final condition what is the status of retrodiction in that theory? Without choosing between them, here are three options: (1) An earlier condition can be determined probabilistically exactly as a prediction can be. (2) An earlier condition can be determined exactly (with enough accessible information) from a final condition. (3) It is inappropriate to use QM for retrodictions: it is a prediction-only theory. I have seen some thought experiments on all this in Penrose's books, but it remains inconclusive there, and standard QM texts are not interested in retrodiction. **EDIT AFTER 6 ANSWERS** Thanks for the effort on this question, which was challenging. I will continue to investigate it, but some initial thoughts on the Answers. (a) I was expecting to receive comments on decoherence, chaos and something on Interpretations and such are amongst the answers. Perhaps the single most important sentence is Peter Shor: _The time-asymmetry in quantum mechanics beween retrodiction and prediction comes from the asymmetry between state preparation and measurement_. Lubos's introduction of Bayesian probability and response (c) is the most useful, although discussion of entropy does not seem immediately relevant. This response though suggests a different framework for retrodiction, with an apriori set of assumptions introduced for the calculation of initial state. A complication that was not clearly enough addressed was the link with Classical Mechanics retrodiction. Statements that Quantum Retrodiction was "impossible" does not square easily with the fact that some will have corresponding classical systems easily retrodicted. Of course the fact that Quantum Prediction is probabilistic, allows Quantum Retrodiction to be probabilistic too (and thus different from classical retrodiction) was not followed up in some answers. As far as references to Chaos is concerned does not "retrodiction Chaos" result in an _increase_ in ability to classically retrodict given that the trajectories will be converging? On Peter Morgan's points I should say that the question is open to any interpretation of how the experimental apparatus is used - if it is relevant to giving an appropriate answer then so discuss the significance. On Deepak's links I should note that these include references to Applications to this idea in Quantum Communication: ie what was the sent state given a received state? I think Lubos's Probability is relevant here too. Feel free to EDIT your answers if you think of anything else!


title: Fukushima - Isn't the hydrogen presence a proof of meltdown?

text: As I understand, the hydrogen is produced by water thermolysis, which need quite high temperature. This temperature is close to previously observed corium temperatures. So:   1. Is the eutectic temperature of the corium of those type of reactors known and publicly accessible?   2. Isn't the hydrogen presence a proof of meltdown?


title: Mechanical momentum of the EM field in a continuum?

text: Given an uncharged continuum the EM field produces no force on it. Yet in a discrete system we know that atoms are not uncharged locally and momentum can be exchanged due to the electric field(Which Maxwell's equations are suppose to govern). viz., The transfer of momentum between atoms is due to the electric field(although it's not as simple as the 1/r^2 version). Maxwell's equations should describe the motion of the atoms exactly when one includes the Lorentz force and Newton's second law. Yet when one moves up to the continuum these microscopic effects no longer exist and the electric field cannot influence the mechanical motion of density if it is not charged. How can we include this in Maxwell's equations(or probably instead in the Lorentz force)? I'm thinking that we simply use and it's conservation law(on the same page) http://en.wikipedia.org/wiki/Electromagnetic_stress-energy_tensor but there doesn't seem to be a way of controlling how well the EM energy is coupled to the material(Some materials will experience a larger motion due to the EM field it experiences). or even http://en.wikipedia.org/wiki/Maxwell_stress_tensor in both cases though q = 0 for the continuum. I think was thinking that possibly one could temporarily treat the continuum as being charged even though it isn't which will allow the momentum due to the field to propagate and one could compute forces and such. With proper scaling one might get the same effect as if modeling a discrete material. Effectively one is breaking up the material into positive and negative charge, computing the momentum then subtracting... in a continuum this is 0 but for the discrete case it cannot be zero unless there are no particles. What is a better way? How can one model the microscopic collision transfer of momentum that can be applied to the continuous case?


title: Snell's Law of Refraction

text: I was told that "Snell's law of refraction implies that a light ray in an isotropic medium travels from point a to point b in stationary time." Why is this true? Thanks.


title: Molecular rotation - Energy levels for an asymmetric molecule

text: For a molecule with spherical symmetry, the energy level of rotation for quantum number $J$ is: $$E(J)=\frac{J(J+1)\hbar^2}{8\pi^{2}I}$$ "$I$" is the Moment of inertia for the molecule ($I_{x}=I_{y}=I_{z}$ for a molecule with spherical symmetry) For an asymmetric molecule however, $I_x$, $I_y$, $I_z$ are all different. What would then be the expression for energy levels in terms of quantum numbers? Thanks.


title: Question about the quantization of lattice vibration (phonons)

text: In my syllabus about solid state physics they state that lattice vibration is quantized, analogous to the harmonic oscillator: $$E = (n+\frac{1}{2})\hbar\omega$$ So the lattice vibration has zero-point energy $\frac{1}{2}\hbar\omega$. I wonder what this actually means: are all possible vibration modes of the lattice quantized in this way? So do all the vibration modes (acoustical/optical and transversal/longitudinal) have nonzero energy for all possible wavevectors $\vec{k}$ in the Brillouin zone? So If I interpret this quantization in this way, it means that the lattice is at all time vibrating in all possible vibration modes. In the syllabus they state though (somewhat earlier (and translated to English)) : _"The vibration modes are purely longitudinal or transversal only in the case of sufficient symmetry, e.g. in some directions of a cubic crystal structure. Otherwise, the waves consist of a mixture of the two." (I thinks that this refers to f.i. the [100] direction in a cubic crystal)_ This seems to be contradicting the idea that longitudinal and transversal modes should have zero point energy. I hope that someone can clarify this.


title: Kinetic energy of a body rotating on another rotating body

text: Consider a body which can freely rotate with respect to the inertial frame, and a rotating disk whose axis is fixed in body frame. When applying the lagrangian method (does that make a difference?), is the kinetic energy of the disk with respect to the body frame (for constant disk rotation rate, the kinetic energy is constant) or with respect to inertial frame (for constant disk rotation rate, the kinetic energy depends on the rate of the parent body)? Parent discussion: Defy gravity torques with gyroscopes?


title: Kinetic energy in Lagrangian formalism

text: In reading Goldstein's Classical Mechanics (2nd edition) I came across a confusing derivation. Goldstein (Eq. 1-71) derives the total kinetic energy of a system of (classical) particles as: $$ T = \sum_i \frac{1}{2}m_iv_i^2 = \sum_i \frac{1}{2}m_i \left( \sum_j \frac{\partial \mathbf{r}_i}{\partial q_j} \dot{q}_j + \frac{\partial \mathbf{r}_i}{\partial t}\right)^2 $$ Where the $q_i$ are the generalized coordinates. He then expands the square to obtain three terms: $$ T = M_0 + \sum_j M_j\dot{q}_j + \frac{1}{2}\sum_{j,k} M_{jk} \dot{q}_j\dot{q}_k $$ Where $M_0$ only carries the time dependency of $\mathbf{r}$ on $t$, $M_i$'s carry linear dependence on $\frac{\partial \mathbf{r}_i}{\partial q_k}$, and $M_{i,k}$ carry the quadratic dependence. Goldstein then claims that if the transformation equations do not contain the time explicitly, then only the last (third) term survives. I don't understand this. The first two terms consist of $\frac{\partial \mathbf{r}_i}{\partial t}$'s, which are not necessarily zero. Nowhere in this definition of $T$ do I see something like $\frac{\partial q_i}{\partial t}$, which would be zero by Goldstein's assumption. How do the first two terms vanish?


title: Does stew lose more liquid if stirred as it cools?

text: Suppose I cook a stew or soup and then take it off of the stove and leave it uncovered to cool. Of course, it will cool faster if I stir it (more surface area), but it will, eventually, cool to room temperature even if I leave it alone. As it cools, it loses liquid to evaporation -- steam rises from it -- until is has cooled a bit. Does it lose more liquid, total, if I stir it as it cools, or if I leave it alone -- or does it lose the same amount either way?


title: degree of freedom in 6 dimensional space

text: Let us assume a cartesian space, where the directions are given by $\hat{i},\hat{j},\hat{k}$. The degree of freedom of a rigid body is $6$. The first three correspond to the position coordinates $\left(x,y,z\right)$, and the next three correspond to the velocity coordinates $\left(\dot{x},\dot{y},\dot{z}\right)$. Suppose I know the angular momentum of this body along $\hat{i},\hat{j},\hat{k}$. I also know the total energy of this body. Can I say that having knowledge of these four quantities reduces the degree of freedom to $2$?


title: Is the symmetry group of two spin 1/2 particles $SU(2) \times SU(2)$ or $SU(4)$?

text: This is a simple question. Please forgive me, as I am a lowly experimentalist. Suppose we have two free spin 1/2 particles, i.e. a 4-fold degenerate system. What is the set of symmetry operations on this system? Is it $SU(2) \times SU(2)$, $SU(4)$, or something else? Or am I misunderstanding all of this group jargon entirely? My current understanding is that $SU(2)$ rotates a single spin 1/2 particle, and $SU(2) \times SU(2)$ rotates both particles (but not necessarily with the same axis and angles). Furthermore, when we do this addition of angular momentum magic, we are taking $SU(2) \times SU(2)$ and decomposing it into irreducible representations of $SO(3)$ because we want to rotate the spins together (with the same axis and angle). Am I wrong about any of this? I ask this because people in the graphene field say that a "fourfold spin–valley degeneracy lead[s] to an approximate SU(4) isospin symmetry." This was confusing to me because I previously thought that two spin 1/2 degrees of freedom led to $SU(2) \times SU(2)$ symmetry. However, now I'm led to believe that $SU(4)$ describes the symmetries of a 4-fold degenerate system, and that $SU(2) \times SU(2) \subset SU(4)$ with some entangled states not represented by rotating two spins (i.e., if I prepare two spin up particles, I can't get every possible state by simply rotating them).


title: Why does the Walecka model not include pions?

text: The Walecka or $\sigma$/$\omega$-model is an effective theory describing nucleon-nucleon interaction by an exchange of $\sigma$/$\omega$-mesons. Why does it not include interactions by pions?


title: Trying to combine red, green and blue to produce white

text: I tried to mimic the mechanism of typical screens to produce white color out of red, green and blue. What I did is displayed the attached image on the screen, and moved far away as to let the diffraction effects take place, so that the three colors appear as if they're coming from the same point. Nonetheless, quite paradoxically, what I have seen was black instead of white. I don't know if this question fits this place, so excuse me. ![enter image description here](http://i.stack.imgur.com/EHzCq.png)


title: Massless particles and the speed of light - New? Theories of existence

text: "The best understanding we have is that it [light] is a disturbance in the electromagnetic fields of charged bodies." http://einstein.stanford.edu/content/relativity/q212.html This is a link to the most recent report I could find for experiments attempting to observe or measure a photon without destroying it. http://www.livescience.com/41465-photons-seen-without-being-destroyed.html "The photon didn't interact with the atom directly, but it did alter the atom's phase — the timing of its resonance with the cavity. The scientists could use the difference between the superposition state — when the atom is in two states at once — and the atom's measured phase to calculate whether or not the photon entered the cavity. In that way they "saw" the photon without destroying it, without touching it." The title is misleading because this 2013 report concludes that the most advanced experiments to observe and measure a photon only observe how the photon interacts with other things, not the photon itself. Measuring and observing and predicting the impact that something has is not the same as measuring and observing and predicting the thing itself, even if your results are consistent and sensible. Special relativity states:   * The speed of light in a vacuum is always $c$, regardless of the velocity of the observer.   * The laws of physics are the same for all observers in uniform motion. These two statements that we know as "special relativity" indicate that $c$ (speed of light) does not follow the same laws of physics as the observer (anything which is not traveling at $c$).   * The laws of physics are the same for all observers in uniform motion.   * The observer is (anything that never travels at the velocity $c$).   * The laws of physics are the same for (anything that never travels at the velocity $c$).   * The laws of physics are not the same for anything that does travel at the velocity $c$. Special Relativity also indicates that any experiments regarding the "speed of light" that are not conducted in a vacuum will not allow for a "proper" velocity of $c$. The laws of physics are the same for anything not traveling $c$, and because they are the same for anything not traveling $c$, we are able to transform the perspective of anything not traveling $c$, into the perspective of any other thing not traveling $c$, regardless of the velocities that each thing not traveling $c$ is traveling. The laws of physics are not the same for any observer as they are for $c$. That is why we are not able to transform the perspective of $c$ to the perspective of anything not traveling $c$, or the other way around. If the laws of physics were the same for us as they are for $c$, we would be able to travel $c$. It is light's different laws of physics, in its different universe, that allow it to travel at $c$, while here in our universe, without the laws that make it possible, we can never travel at $c$. $c$ and "observers", which can never travel in uniform motion, are prevented from traveling in uniform motion by the different laws of physics that apply to each of them. Namely, $c$ exists without time, so the entire concept of "motion" is different if you can't move from moment to moment, as well as from space to space. This is also why it's not possible for $c$ to have an "inertial frame of reference", or for $c$ to have "inertia". Where $c$ exists, there is no time, so there is no change, so there is no resistance to change. The physics concept of inertia is inapplicable to $c$ because $c$ is not governed by time. Philosophically speaking, the two statements of Special Relativity could be said as: $c$ is constantly different from everything else. Everything else is relatively the same. Why is this meaningful? Physicists would say that this only prevents us from applying physics to $c$'s perspective, which is meaningless anyway; and then to understand $c$, physicists applies physics to $c$ that don't govern $c$, the physics of anything not traveling at $c$. Other observer's have a different perspective of the same physics, which allows us to transform our perspective into any other observer's perspective; because we're using the same physics. If $c$ had a different perspective of our physics, then we would be able to transform our perspective into $c$'s perspective using our physics, the way we can with anything else that has a different perspective of our physics. Since $c$ has a different set of physics, our definition of "perspective" can't be applied to $c$, so there can be no transforming between perspectives because only one "perspective" exists. Transforming perspectives between two observers is like two people who speak different languages agreeing on a single word for a color. Applying the perspective (or frame) of an observer to $c$ (or vice versa) is like asking two people who speak different languages to agree on a single word for a color when one of them is blind and mute and the other one is deaf and illiterate. It explains the dual nature of light, being both particle and wave. Distinguishable from one another and yet the same thing. The photon exists outside of time in a parallel universe, while the wave "co-exists" in time, in our universe. More accurately, $c$ is a cause, and $c$ causes a disturbance, and the disturbance is an electromagnetic wave. Assume for a moment that time truly does not exist to the photon ($c$). We can't even say that it's "instantaneous" because an instant is a unit of time, and time doesn't exist. A photon ($c$) isn't created on the surface of the sun, it's created in a parallel universe. In that universe there is no time. If time does not exist in $c$'s universe, when $c$ is created, it must come into existence already existing at every infinite point in space between, and including, its point of origin and its destination. There is no time, so $c$ can't travel from one location to the other, so it will just have to "be there". Strictly speaking, $c$ isn't a "speed", it only appears that way in our universe where there is time. The "passing" of this "particle" ($c$) through space, but not through time, causes a sort of friction between space and time, a disturbance that manifests in our universe as the electromagnetic wave "light" (not "strictly" = $c$), which we measure and predict according to our laws of physics because it exists in our universe, unlike it's photon/particle/$c$ counterpart. This disturbance, the electromagnetic wave "light", (not $c$) which unfolds in our reality, does not unfold according to the physics of $c$, the photon has already existed and is now gone, but according to the physics of our universe. What we observe in our reality is more like time catching up to the passing of the photon (or, catching up to the passing of 'whatever causes the disturbance that we observe as the electromagnetic wave, or, catching up to $c$). After the photon (the cause) is gone, the electromagnetic wave begins to ripple through space but now, this understanding of "light" (which does not strictly travel at $c$) is under the influence of time (because it does not strictly travel at $c$), which means it can't exist at two points simultaneously and instead it has to travel, much unlike it's photon ($c$) counterpart. So it's important to distinguish that when our physics predict "light" (not strictly $c$) it is only predicting "half of the total light phenomena", the half that exists in our universe and which is consistent with our laws of physics, known as the electromagnetic wave "light". Which is not strictly $c$. Trying to understand $c$ by observing electromagnetic wave "light" is similar to trying to understand the cause "lightning" by observing its "disturbance", thunder; where in both cases, $c$ and lightning, energy creates a wave form disturbance in a medium. Lightning creates the disturbance thunder in the medium of atmosphere, photon ($c$) creates electromagnetic wave (not strictly $c$) disturbance in the medium of "space time", or "time", or "our physical universe where time exists". It would then be more accurate to say that $c$ is the "speed" of "time" (or the speed at which one escapes time), and $c$2 is the "speed of light" (or the speed of the pure energy "photon"). Theoretically, there could be one single photon in the photon's universe creating all of the electromagnetic wave disturbance light in all of our existence throughout all of our time. If you want to abandon the "photon theory of light", then this disturbance could also be explained by "quantum tunneling". The electron that is lost from its atom in the sun travels immediately through a wormhole to the atom that would absorb the loose energy. In theory, it wouldn't be necessary to "accelerate" a particle to $c$. In theory, removing a particle's "matter based mass" would achieve the same effect of $c$. "Matter based mass" is not the mass that can be added in the form of stored energy. In theory, time is a property of "matter based mass" that does not apply to pure energy. Time is a necessary force for matter to decay. Time is not necessary if you're not matter. According to Einstein's theory of mass-energy equivalence, if the photon is a particle of pure energy, and if E=mc2, then the photon is theoretically traveling at $c$2; not $c$. This is a lecture by Neil deGrasse Tyson, Special Relativity and Light are talked about, starting at around 10 minutes. Really the whole video and series is great. https://www.youtube.com/watch?v=vUCBxS0_194&list=PLdgNN42xmuhmr7rrFRb8hWNrcd2gGW6Qc


title: Why is it that the cathodic battery symbol in an equivalent battery circuit doesn't point in reverse for an open circuit case?

text: I've been thinking about batteries a whole lot, and I've uncovered why the battery symbol looks like a pair of cap-like things in circuit diagrams: it's modeled as two cap-like things using an equivalent circuit diagram:![enter image description here](http://i.stack.imgur.com/3zCA9.png) We see here that the two sides have a similar assigned voltage. The actual voltage is dependent on the chemical reaction. Here's the problem. I'm having quite an issue looking at the right side, the cathode, as a cap-like thing that has a direction pointing the way it does. My issue is this: all cells want to dissolve. You may disbelieve this, but take a quick look at this link: http://en.wikipedia.org/wiki/Absolute_electrode_potential. The article states that the "zero" hydrogen half-cell reaction does **not** have a voltage equal to zero, but in fact serves as a reference. You may have known this, but since the actual voltage of the oxidation of Hydrogen is 4.44 V, we must add this number to the oxidation reaction for the list of elements' oxidation reactions. Or, given the reduction reaction, we would subtract 4.44 V, because they are each measured in respect to a hydrogen half-reaction. Let us take a look at a table of reduction half-reactions: ![enter image description here](http://i.stack.imgur.com/nWpRB.gif) After realizing that the actual reduction potentials need to have 4.44 V reduced from their total volts, we realize that not a single reaction wants to reduce at all! None of them! So, my question is, given the equivalent circuit diagram, how can we say that any cap-like thing points the way it does? Its not like the positive ions in solution are attempting to form a metal (and get reduced) before the external circuit is closed. The electrons should be trying to escape the cathode just like the anode, you see what I mean? Now let me be clear: I'm not talking about when the circuit is closed as it is in the diagram: I'm talking about before this moment, when the only thing connecting the cathode and anode is the electrolytic fluid. I get that when the circuit is closed the difference in potentials is all that matters (which would explain why two different metals are used for many galvanic cells). From my reasoning above, shouldn't even the metal in the right-hand area want to dissolve? Therefore, shouldn't both cap-like things point inwards? Basically, I'm saying that the direction of the cathodic cap-like thing should reverse.


title: How can we "know" that system interacted with another system or environment in quantum mechanics/decoherence?

text: I might be raising measurement problem in quantum physics in different words, but I will ask the question. Quantum decoherence has been proposed by proponents as a theory that eliminates all weird issues involving quantum mechanics, such as Schrodinger's cats and measurement problem. So in quantum decoherence theory, system (example: a particle) becomes "measurable" when system interacts with another system or environment with certain conditions and consequences. But this seems to raise issues of how systems can ever be interacting "objectively". After all, every system described by wavefunctions that only give probability for possible measurements in general (of course there are cases that when met with proper basis and knowledge of wavefunction, definitive measurement can be guaranteed). This for me seems to suggest even before quantum decoherence, two systems that will interact have been connected by some wavefunction that describes the chance of quantum decoherence. Or we need some kinds of observers to either bring effects of quantum decoherence. If the question seems a bit confusing, the context in which the question is being asked is how quantum decoherence theory affects quantum mechanics's measurement problem.


title: Could airport security possibly distinguish gold and silver coins from other coins?

text: People usually don't carry pure gold and silver coins in their wallets. If I put some in my wallet, would it be likely that airport security would detect some anomaly with my wallet as compared to other wallets? Can physics answer this?


title: Is the Earth's atmosphere a Faraday cage?

text: X-ray telescopes are required to be above the atmosphere as the atmosphere blocks EM waves with wavelengths < UV . Does this mean that the Earth's atmosphere can be thought of as a Faraday cage only allowing low energy light to pass through?


title: Energy of an Electron in a One Dimensional Periodic Potential

text: First, we consider the time independent Schrodinger equation of the form: $$\bigg(-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+u(x) \bigg)\phi_A(x)=E_A\phi_A(x)$$ Where $u(x)$ is a potential created by a single ion (of a one dimensional single ion crystal lattice). Then now we expand the case from a single ion case to a $M$ ion case $(M>>1)$ in which the Schrodinger equation is given by : $$\bigg(-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+U(x) \bigg)\psi(x)=E\psi(x)$$ with boundary conditions: $$\psi(x)=\psi(x+Ma)$$ where $$ U(x)= \sum\limits_{j=1}^M u(x-ja)$$ $$ \psi_k(x)= \sum\limits_{j=1}^M e^{ik(ja)}\phi_A(x-ja)$$ In this problem, I am trying to solve for the Hamiltonian Eigenvalue $E(k)$ for $\psi_k(x)$ through integrating the Schrodinger equation after multiplying it with the complex conjugate $\phi^*_A(x)$ as shown as follows: $$\bigg\langle\phi_A(x)\bigg|-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+U(x)\bigg|\psi_k(x)\bigg\rangle = E\langle\phi_A(x)|\psi_k(x)\rangle$$ $$\sum\limits_{j=1}^M\bigg\langle\phi_A(x)\bigg|-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+U(x)\bigg|e^{ik(ja)}\phi_A(x-ja)\bigg\rangle = E\sum\limits_{j=1}^M\langle\phi_A(x)|e^{ik(ja)}\phi_A(x-ja)\rangle$$ I am stuck here. What would be my next step in solving for the Energy $E(k)$ using the following relationships: $$\langle\phi_A(x-ma)|\phi_A(x-na)\rangle = \delta_{mn}$$ $$\beta=\langle\phi_A(x)|u(x\pm na)|\phi_A(x)\rangle$$ $$\gamma=\langle\phi_A(x)|u(x)|\phi_A(x\pm a)\rangle$$


title: Adaptive Optics Capability in the Visible Range

text: Telescopes with adaptive optics (AO) have been in use for several decades. To my knowledge, the lowest wavelengths utilized are in the near-infrared. It's known that Fried parameters are smaller for visible versus infrared ranges. > Are there any earth-based observatories utlizing AO in the visible range? > What are the technical issues to achieve acceptable AO Strehl ratios in the > visible range?


title: Work done on charged particle by magnetic field in quantum mechanics

text: Classically, we know from $\mathbf{F}=q\mathbf{v}\times \mathbf{B}$ that magnetic field does no work on a charged particle. In quantum mechanics, the Hamiltonian of a charged particle in a magnetic field is given by $$\hat{H}~=~\frac{1}{2m} \left[\frac{\hbar}{i}\vec\nabla - \frac{q}{c}\vec A\right]^2.$$ How can we deduce from this Hamiltonian whether work done is on the particle?


title: Why does motion help you balance on ice skates?

text: It's almost impossible to balance on a single ice skate if you're standing still. But give yourself just a little forward motion—it doesn't take very much—and it suddenly becomes easy. You can stand there on one leg and glide effortlessly half way across the rink. Friction will cause you to gradually slow down, and it's only when you've slowed almost to a complete stop that balancing becomes hard again. Why? This seems suspiciously similar to the question of why it's easier to balance on a moving bicycle. But the standard answer to that involves the angular momentum of the wheels. There's nothing rotating here. In fact, other than the very slight deceleration from friction, moving should make no difference. In both cases, you're standing still in a nearly inertial reference frame. Does that slight deceleration somehow matter? Or does the interaction between the ice and a moving skate somehow help you to balance?


title: Why do we classify states under covering groups instead of the group itself?

text: Why do we always classify states under covering group representations instead of the group itself? For example see the following picture I lifted from 'Symmetry in physics' by Gross ![enter image description here](http://i.stack.imgur.com/JLJMs.jpg) So in the first example, why not classify states under SO(3) instead of SU(2)? EDIT: From a physicists perspective, I know enough that we consider projective representations of groups in quantum mechanics because those are the most general thing that keeps $ |\langle \phi|\psi\rangle|^2 $ invariant. But Gross above seems to indicate that representations of the covering group are a better way to go. Furthermore, covering groups are always simply connected, to where-as groups with projective representations are in general not simply connected - is this property of (universal) covering groups related to why we use them in these sorts of cases?


title: Can you explain Fermat's Principle to me?

text: The textbook(F.A.Jenkins and H.E.White **_Fundamentals of Optics_** ) states that the Fermat's principle is that > _the path taken by a light ray in going from one point to another through > any set of media is such as to render its optical path equal, in the first > approximation, to other paths closely adjacent to the actual one._ To be honest, I can't understand that description. But I know that > _the actual ray path between two points is the one for which the optical > path length is stationary with respect to variations of the path._ Are the two descriptions same?


title: Positive Permutation Tensor

text: I have seen that one can make an operator with $$ L^i=\epsilon^{ijk}x_{j}\partial_{k} $$ But what if I want to make instead items that are sums, instead of differences. For instance $$\mathcal{L}^z=x\partial_y +y\partial_x$$ Is there an object like $|\epsilon_{ijk}|$ that has only 1s (no -1s)? Thanks,


title: What properties define a good resonator?

text: In my question "Resonance in a 1 ft granite box", someone answered that my granite box (a one foot cube) would make a very poor resonator, which makes me ask what characteristics make a good resonator? Is there a difference between a cube or other rectangular box and a ball (like a Helmholtz resonator)? Also, what defines the pitch? Size?


title: What is the physics behind explosion of Stars?

text: ![enter image description here](http://i.stack.imgur.com/mjhTo.jpg) Looking at the above photo, you will soon find it is impossible to explain what actually happens (with today's physics), in one word star is like a nuclear fusion bomb which its pressure is in balance against gravitational force.   1. A supernova (or a black hole) is triggered by an imbalance between them, so isn't supernova a natural pure fusion bomb?    2. Then what equations are able to simulate a virtual supernova explosion?


title: How do I calculate the intensity of a diffraction pattern in a double slit experiment?

text: I'm currently struggling to understand the physics behind this question (purely because our lecture hasn't given us proper grounding in quantum mechanics). In a double slit experiment, you are given $\psi_1= A_1e^{-i(ky- wt)/\sqrt{1+y^2}}$ and $\psi_2 = A_2e^{-i(ky+\pi y-wt)/\sqrt{1+y^2}}$ where $A_1$ and $A_2$ are normalization constants to be determined. These state vectors represent the diffraction pattern that occurs at 2 separate vertical detectors as a light source hits a screen. I'm asked to calculate intensity when: a) 2 slits are opened and a light source is used to detect which slit the electron goes through. b) 2 slits are open with no light source. I found $A_1$ and $A_2$ to both equal $1/\pi$ and to get intensity I know I have to superposition them and square the sum so intensity = $\psi_1^2 + \psi_2^2+2\psi_1\psi_2$. However I don't know what it means by the options a) and b) or if I am to get a single value for the intensity or is it to be in respect of $y$ and $t$. I would really appreciate it if someone could take the time to explain to me what it is I am meant to do.


title: Why are interactions always mediated via bosons (as opposed to fermions)?

text: Weak, Strong and electromagnetic force are mediated via bosons. I've come across the Walecka-model where the exchange particles are $\sigma$ and $\omega$ mesons; bosons again. why are interactions always mediated via bosons (not fermions)?


title: How do spiral arms form?

text: Why aren't all spinning galaxies shaped as discs as my young mind would expect? I understand how the innermost parts of a galaxy spin faster than the outer parts, and that could explain why some galaxies are more spiraled than others based on age. Though, this doesn't explain how the arms came into existence in the first place. Might it have something to do with an imperfect distribution of mass, and therefore an imperfect distribution of gravity, causing a split in the disc from which point gravity, centripetal force, and inertia could take over? Or does something happen earlier in a galaxy's life?


title: Question about Komar integral derivation in Wald

text: I have a question about derivation 11.2.10 in Wald (page 289). Here is a screenshot of the relevant passage: ![Wald p289](http://i.stack.imgur.com/UI69w.png) I don't get the step $$-\frac{1}{4\pi}\int _{\Sigma}R^{d}{}{}_{f}\xi^{f}\epsilon_{deab} = \frac{1}{4\pi}\int _{\Sigma}R_{ab}n^{a}\xi^{b}dV.$$ Could someone explain to me how he gets that equality? Thank you very much in advance.


title: If you throw dynamite into a pool of lava, will it explode or melt?

text: I was playing a table-top rpg with a friend. It was set... well it was pretty weird, so I won't get into it. Suffice it to say the bad guy had a stick of dynamite and we were on a volcano. I hit the dynamite with my slingshot, knocking it into the lava directly behind the villain. My DM said the dynamite melts away. I said it should have blown him up. Needless to say, as a couple nerds (we were, after all, playing a fantasy game and then arguing about the physics of it) we were pretty upset with each other. What would have happened in this... totally realistic scenario? Would the stick of dynamite exploded? Or simply melt away?


title: Dimensional aspects of the imaginary unit $i$ in physics

text: From a real world perspective each dimension in the 3-D Cartesian System can be represented by an axis that is perpendicular to 2 other axes. I read somewhere else that the effect of ${\sqrt {-1}}$ is to reorient data 90 degrees on the "imaginary" axis. I guess my question is this: What role ( if any) does ${\sqrt {-1}}$ serve in everyday or even quantum physics? ${Edit}$ To clarify, I am more concerned with the dimensional aspects of ${\sqrt {-1}}$. If for instance you were to consider a 3-D location to be a "point" with length width and height in a complex graph representation with three additional mutually perpendicular axes? PS. I know this thread is getting a bit hair brained. But in my defense, I did look for a "specualation" tag before I posted this thread here.


title: In classical mechanics, are complex numbers unphysical?

text: > **Possible Duplicate:**   >  Physics math without $\sqrt{-1}$ When I produce a complex final solution to a problem that began without complex coefficients at all, I have so far (with my limited expertise) tended to discard it as unphysical, unless I had to tinker some more, in which case the $i$s may square and real-ity be restored. Is this acceptable? I understand that the Wessel plane is useful in modelling planetary motion, and many other things, but the fact (?) that you could do it all (albeit more awkwardly) without them seems to be indicative that they are a little contrived. In short, is there a counter-example?; a physical theory ( _not_ a particular, neat, mathematical model of a physical theory) in classical mechanics that could not be formulated without complex numbers?


title: Complex variables in classical mechanics

text: In quantum mechanics complex numbers are absolutely essential because of the relation $$[\hat q_i,\hat p_j]=i\hbar\delta_{ij}.$$ But is complex number also essential anywhere in the formalism of classical physics, except for some convenience of mathematical calculations? Is there any example from classical physics where there is no other way out except to introduce complex variables? Is there any strong reason by which I can say that complex number are unavoidable in classical physics too?


title: An astronaut and a vengeful pole

text: Imagine an astronaut floating in free-space with no significant nearby gravitational influences. The astronaut takes an arbitrarily thin pole of uniform density with length $l$ and mass $m$, orients it vertically from his perspective, and then positions it some distance $h$ in front of him. Finally, once the pole is in place, he kicks it with force $F$ at some coordinate in space $p$, at distance $r$ from the pole's center of mass. Under what conditions will another coordinate on the pole's contour pass through coordinate $p$ to collide with the astronaut's foot?


title: Gauge fields in 2d spacetime

text: I believe it is only a technical question. However I cannot realize it. It is said in 2d spacetime the gauge fields $A_\mu$ can be rewritten in lightcone coordinates as $A_+=ig\partial_+g^{-1}$ and $A_-=ih\partial_-h^{-1}$, where $g$ and $h$ are the elements of the gauge group. Anyone could give me a simple and transparent explanation on it? Thanks!


title: How Newton found Gravitational acceleration?

text: How Newton found Gravitational acceleration (g) of The Earth? Can you describe the methods to find and prove it(g value)? (may be describe both classical methods and modern methods)


title: Is the entire Universe the same age?

text: Is all of the visible Universe exactly the same age everywhere? What about the Universe beyond what we can see?


title: What is a quark condensate?

text: 1. What is a quark condensate? is it a bound state between 2 quarks? can we have 3(or more)-quarks condensate?   2. What mediates the interaction between the constituents of the condensate?   3. Are the constituents of the condensate always fermions?


title: Should I cook two pieces of Canadian Bacon twice as long as one in a microwave?

text: It will probably depend on the size of the pieces... but at what point should I stop assuming a linear relationship? I was prompted to ask in a previous question.


title: Calculate acceleration and time given initial speed, final speed, and travelling distance?

text: A motorcycle is known to accelerate from rest to 190km/h in 402m. Considering the rate of acceleration is constant, how should I go about calculating the acceleration rate and the time it took the bike to complete the distance?


title: Gravity stronger than electromagnetic force in a black hole?

text: Well, the question has somewhat been answered before, but there's one part missing, which - I'd think - is in conflict with the physical laws. The earlier reply says that the gravitational pull even at the event horizon is so big, that not even the other forces can overcome this. So far, so good...this part I can accept. However, what makes it possible for the black hole to appear in the first place? In this situation, the gravity between every single atom would have to fight against the electromagnetic force in order to compress the atoms sufficiently to create a singularity. Once the singularity is there, the gravitational pull becomes infinite - but how the he** does the electromagnetic force allow the gravity to create the singularity in the first place? I'd say that since the strength of gravity is directly related to the amount of mass - the more mass, the stronger the gravitational pull...but the same amount of mass generates millions of times stronger electromagnetic resistance between the atoms...or, did I misunderstand something completely here?


title: Why does an infrared thermometer display very low temperature when being directed to the outer air?

text: I'm toying with an infrared thermometer - one which you point onto an object, press the button and it instantly measures the temperature by estimating the infrared radiation from the object. It shows more or less the room temperature when I point it to things in the room. Now I open the window. The temperature outside is 12 degrees Celsius. I point the thermometer to the ground - it shows something near 12 degrees. When I point it horizontally and directed onto a building located several hundred meters away - it shows something like 5 degrees. When I point it onto the sky it shows an error message indicating that the measurement result is below zero Celsius and it can't display it. This doesn't make sense - the ground has the same temperature as the air and there's a thick layer of air above, so wherever I point the thermometer the temperature is more or less the same and so the infrared radiation intensity should be more or less the same. Yet the thermometer displays largely different results. Why does the infrared thermometer display much lower temperatures when directed to the outer air compared to when directed onto nearby solid objects?


title: domestic electric AC wiring - Live and Neutral correct or not?

text: On electric circuits, with $120$ or $230$ AC mains, there are the wires Live and Neutral. The wiring isn't symmetrical : following the circuit, you cannot switch $L$ and $N$. However, in Italy, sockets and plugs don't have a specific orientation : it is a matter of how the user push the plug in the socket. You cannot watch the socket or the plug and guess the N and L, there aren't signs. Also internal building to sockets wiring isn't specific. So, here it is an Italian socket \- you are sure only about the middle one :               |*|   ?     |*|   Earth Gnd     |*|   ?      If the appliance design expects a specific N and L wiring, it is a random 50 % correct / not correct run. If I recollect well, most of radio appliance show sign N and L wires on their power supply electrical schema. I spoke with some electrical engineers, they cannot explain me how to match the circuit requirements (and hazard regulations) with the real common practices. Is the electric schema sufficient to pass the local regulations / certification, even if going in production the appliance is build with a non polarized plug ?


title: What does a $SU(2)$ doublet really mean?

text: What do we really mean when we say that the neutron and proton wavefunctions together form an $SU(2)$ doublet? What is the significance of this? What does this transformation really doing to the wavefunctions (or fields)?


title: Motion with damping involving both $-v^2$ and $-v$ terms

text: I'm trying to solve for the motion of a particle, accounting for both viscous and drag forces. (There is no potential) The total resistance by medium is modeled by: $\vec{F}=-(\mu_1v + \mu_2v^2)\hat{v} $ Where $v$ is the velocity; There is no potential. I need to set up the Lagrangian and describe motion under the following conditions: $\frac{\mu_1}{\mu_2} = 10^{-5}$ $\frac{\mu_1}{\mu_2} = 1$ $\frac{\mu_1}{\mu_2} = 500$ I have set up the Lagrangian as follows: $L = \frac{1}{2}m(\dot{x}^2+\dot{y}^2+\dot{z}^2)$ $\frac{d}{dt} \frac{\partial L}{\partial \dot{x}} -\frac{\partial L}{\partial x} =- (\mu_1 \dot{x} + \mu_2\dot{x}\sqrt{\dot{x}^2+\dot{y}^2+\dot{z}^2})$ and similarly for z and y. Equations of motion turn out to be: $m\ddot{x}= - (\mu_1 \dot{x} + \mu_2\dot{x}\sqrt{\dot{x}^2+\dot{y}^2+\dot{z}^2})$ Similarly for z and y. I'm at a total loss to how these should be solved. Is there even a way of analytically solving such coupled equations? However, If I orient the x axis along initial direction of velocity, I should get: $m\ddot{x}= - (\mu_1 \dot{x} + \mu_2\dot{x}^2)$ $y=0$ $z=0$ I'm stuck at this point. Wolfram Alpha suggests: ![](http://puu.sh/bmj5K/8d1edff9ab.png) Where $\frac{\mu_1}{m}=a$ and $\frac{\mu_2}{m}=b$ I'm not aware of the techniques used to get to this. Would appreciate some help/pointing to resources on that. After this, I'm not really sure of how to apply limits (Since we have the additional constraint of the domain of Log functions), and how to interpret the motion in the 3 regimes mentioned above. Can someone give me some pointers? Also what really happens when there is a potential (Say, gravity)? (which really is the real world scenario)


title: Why does a fluorescent tube-lamp flicker before lighting up?

text: If you turn on a fluorescent tube-lamp, it flickers before lighting up.   If you then turn it off and turn it back on after 2 seconds, this time it doesn't flicker but lights up straight away.   If you wait for some time (say 10 minutes) and switch on the light again, it flickers before lighting-up, again. Why does it flicker before lighting up?   And why doesn't it after a 2 seconds gap in turning it on and off?


title: Why do the terrestrial planets have many of the same gases in their atmospheres?

text: While the gases are present in very different abundances, and the atmospheres have very different pressures, Earth, Mars and Venus all have a similar cast of gases: nitrogen, argon, CO2, others in trace amounts. I've asked an earth scientist friend and his short answer was "volcanoes." I'm afraid I don't know enough about solid earth processes or geochemistry to figure out where to find out more...where could I start?


title: how to find last position given a time

text: I found this formula (I dont know its name) and I'm trying to apply it in order to find the last position given a time and velocity. $ s = s_0 + v_0 \cdot t + \frac{1}{2} \cdot a \cdot t² $ given $ t = 3h $ $ v = 100km/h $ $ a= \frac{v}{t} $ results $ s = 0 + 0 \cdot 3 + \frac{1}{2} \cdot \frac{100}{3} \cdot 3²\\\ s = 150km $ Although I was expecting the same result of $ \Delta_s = \Delta_v \cdot t $ that would be $300km$. That mean if I remove the $\frac{1}{2}$ part of the equation it will give me the expected result. Why is that? Is that formula wrong or what am I missing? Or what is that formula useful for then?


title: TQFT associates a category to a manifold

text: > _Any 3d TQFT (topological-quantum-field-theory) associates a number to a > closed oriented 3-manifold, a vector space to a Riemann surface, a category > to a circle, and a 2-category to a point._ This is properly well-known in category theory. I learned it from here. I wish to have someone **sharing their physical explanation and their best understanding about this statement**. I suppose the higher dim generalization is what Urs Schreiber describes using codimension surface. I have read the Phys.SE post: about-the-atiyah-segal- axioms-on-TQFT, but would not mind someone starts from the basic.


title: Efflux speed of ideal fluid dependent on diameter?

text: I have a cylinder full of water with diameter $D$ with a round opening on the bottom with diameter $d$. The water is friction-free and incompressible. Now I need a relationship for the efflux speed $v$ with which water exits the cylinder and I shouldn't use the approximation $d \ll D$, but formulate a general relationship. Ok. So what I thought is to equate the Bernoulli law on the top of the cylinder with that on the bottom of the cylinder which gives me $v=\sqrt{2gh}$. Solved. How does the speed of efflux depend on the diameter of the efflux hole? I googled quite a lot and all I could find was the above relationship...


title: How do we deal with irrationals in Physics?

text: This question is really very basic: how do we deal with irrationals in Physics? If for instance, in some meaningful calculation we get a length of $\pi$ meters, or a force of $\pi$ Newtons, how should we understand this? One could say: "well, we understand it as a rational approximation", but then there comes another question: which rational approximation? We can approximate $\pi$ by $3,14$ or $3,1415$ and so forth, increasing the precision, but yet never getting really to $\pi$. Another problem is: well, the equations gave us $\pi$, and this is not a physically meaningful thing, so is there something wrong with the equation? Because, in nature I think there really isn't irrationals lurking arround, so that this becomes a little complicated. So: how do we deal with irrationals in Physics?


title: Effect of gas or liquid within a compound lens system

text: Hi my question is if a compound lens system if filled with gas or a liquid how does it affect the system when compared to the lens system being separated by air alone. Does this affect the focal power of the system or the effective power at all.


title: Finding the acceleration at an angle

text: "What's the maximum acceleration you can achieve in a a water-slide at a 34 degree angle (If you can't use your arms and legs)"? This is the free-body-diagram that I drew, assuming $g = 10m/s^2$:![FBD](http://i.stack.imgur.com/XmXqF.png) The maximum acceleration is when there is no friction. So when I set friction to zero, the maximum acceleration is just the value of a: $sin(34^o) = 10/a$ $a = 10 / sin(34^o) = 17.9m/s^2$ However, the book says it's $5.5m/s^2$. What am i doing wrong?


title: How does a star ignite?

text: I remember reading that X-Rays are generated by 'braking' electrons in a Coolidge tube. Is it fundamentally a matter that the extreme gravity immediately before a star ignites is so strong that it affects the hydrogen atoms to the point the velocity of it's components must be let-off in the form of heat & light? How does a star ignite?


title: Direction of the torque

text: > In each one of the following figures there's a pole of length $1.2 \text{m}$ > and there's a force $\vec F = 150 \text{N}$ acting on it. Determine the > torque that is created by the force relative to the axis of rotation $O$. ![Illustration](http://i.stack.imgur.com/qKq0L.png) I had no problem with calculating the magnitude of the torque, but I did have a problem determining its direction in fig. $D$. I used the rule of the right hand and I got that its direction is "outside the monitor" while according to the answers it has the same direction as in all the other figures before (i.e. "inside the monitor"). I'm also wondering whether the vectors directions are important in cross product. For example - is the direction of the displacement vector is important? If it is, then how can I apply the rule of the right hand here when the thumb and the index finger aren't starting from the same position.


title: The earth's magnetic field

text: This might sound like a silly question. Is it possible for the earth's magnetic field to actually destroy or harm earth? (implosion, crushing etc.)


title: How the value of permitivity of free space is determined?

text: when electric charges are placed on the medium then force of interaction between them decreases. We say this factor permitivity of the medium. The force of interaction between the charges is max if the charges are at space or if there is absence of medium. We know the electric permittivity of free space is $8.85 * 10^{-12} F/m$. My question is how this value is determined. Is there any experiment held?


title: Do multiple electrons exist during superposition?

text: Wikipedia says: > _Quantum superposition is a fundamental principle of quantum mechanics that > holds that a physical system—such as an electron—exists partly in all its > particular, theoretically possible states (or, configuration of its > properties) simultaneously;[...]_ What interests me is what happens when location is the state that is superposed. If an electron exists in two locations at once, as a result of quantum superposition, does that mean that the mass of the universe has increased so long as the superposition exists? So in other words, does it follow that effectively two electrons exist during superposition? Why or why not?


title: Critics of Mannheim's Conformal Gravity Theory?

text: I'm looking for more articles/reactions/critiques/support for Philip Mannheim's recent conformal gravity theory. See here: http://arxiv.org/abs/1101.2186v1 Any ideas on where to start?


title: Peak deconvolution

text: I need some help understanding how much information I can pull out of this data. I have a sample made up of two materials. Materials A and material B. Then I took a picture of the sample. The two materials mix quite well, but not perfectly, so on my image I can see that some areas are mostly material A, some are mostly material B, and most of the areas are a mix between. I also took an image of a sample consisting only of material A. On my images material A will look white, and material B will look black. If I make a histogram of the image of material A (and only A) it has the center around 6 [A.U] which fits my theory. The histogram also has a FWHM of 0.55 [A.U.] The same histogram of material A & B is centered around 7 [A.U] which also fit my theory since it's a 50:50 mix of A & B and A is centered at 6 [A.U] and B should be centered at 8 [A.U]. The FWHM of this peak 0.64 [A.U] - thus only slightly larger than the image with pure A. Here's my problem, since the peak with the mix only is slightly wider than the peak for the pure material it means that my resolution i not good enough to distinguish the two materials from each other (if I could see areas with pure material A or B it would be a camel/double-peak, if I could see areas with mostly material A or B I would have a very wide peak - here I only have a slightly wider peak). However, it is still wider, so there must be some kind of information I can subtract. I'm not really sure what - if any. EDIT: If anything is unclear, please ask!


title: How do the molecules of reacting compounds proceed to form "Most Stable" molecule?

text: This question is a cross post from chemistry. I'm not very convinced with the answer there. So, I'm posting it here. I'm tutoring few students for Chemistry. During the course, I many times use the phrase "Out of these possibilities this one is stable. So it is formed". I get questions like, "How do the molecules know?" Honestly I don't know. How do they proceed to form "Most Stable" compound?


title: Braking distances on a rainy road

text: I am curious to find the braking distance for a car on a road. In attempting to find this out, I found that the braking distance for a car (on a flat road) is $$ d = \frac{v^2}{2\mu g} $$ where $\mu$ is the coefficient of friction between the road and tires (CRF), $g$ is gravity, and $d$ is the distance traveled. However, this book mentioned that $\mu$ increases as velocity increases. Right now, I'm having trouble finding said coefficient of friction. This transportation engineering site gave several examples of CRFs at various speeds on a rainy road, but I'd like to understand if they needed to empirically measure it. (EDIT: Of course $\mu$ increases as $v$ does; there wouldn't be a table if it didn't.) In short, my question is this: Is there a general method of calculating $\mu$, given that the car is on a 0% grade, wet, asphalt-covered road? Or must $\mu$ be measured/calculated using empirical data? (Note: not _really_ a homework question; if it was, I'd just guesstimate the answer based on the data from the second link. I just want to understand the data better, if possible, as opposed to just having the value.)


title: A strange audio phenomenon, could there be a physical interpretation to it?

text: http://mathoverflow.net/q/165038/14414 Motivation : Here is a motivation as to why this problem is so important. Let $f(t)$ be an audio signal. We can safely asume it to be bandlimited to 0-20kHz as we cannot hear anything above that. Capture this signal in digital computer with appropriate sampling frequency and denote it as $f[n]$. Now take Discrete Hilbert transform of $f[n]$ to get $f_h[n]$, (using the code $f_h$ = imag(hilbert(f)); in Matlab). Compute the signal $f_{\theta}[n] = f[n]\cos\theta + f_h[n]\sin\theta$ for any value of $\theta$, then listen to the signal with different values for $\theta$. They all sound **exactly identical**. Similarly our $MI_{\omega_0,\omega_1}(t)$ is same for all $f_{\theta} = f\cos\theta + f_h\sin\theta$, for any value of $\theta$. **Question :** just try it. $<f,f_h> = 0$, they why do they produce same effect in the listner? Is it some quantum mechanical effect gone wrong? **Added :** Also see this metric space : metric space I've recently filed a patent using this metric with a slight change, instead of arccos i used sqrt(2(1-cos(theta))), which makes it a Hilbertian metric. I had then embedded this metric space into an Hilbert space isometrically, to model using vectors. **MATLAB code :** [f,fs] = wavread('audio_file.wav'); fh = imag(hilbert(f)); theta = pi/4; f_tht = f*cos(theta) + fh*sin(theta); wavplay(f,fs); wavplay(f_tht,fs);


title: Quantum to classical mapping: quantum criticality and path integral Monte Carlo

text: I'm trying to understand the connections between quantum models in d dimensions and classical models in (d+1) dimensions within two, possibly related, contexts: (i) in path integral monte carlo, the Trotter-Suzuki decomposition gives an equivalence between a d-dimensional quantum spin model at a given temperature and a d+1 dimensional classical Ising model (e.g: Progress of Theoretical Physics, Vol. 56, No. 5, November 1976), and (ii) in quantum critical systems, where the zero temperature maps to one extra additional infinite dimension of a classical system. Now as Suzuki emphasizes in the above paper, critical properties of a d-dimensional quantum system need not be the same as that of a d+1 dimensional classical system. Therefore, is my understanding correct that the temperature in the mapped classical system need not be the temperature in the original quantum system? If not, what is the temperature in the classical model? Thanks!


title: Since when the term 'mass' is being used in physics?

text: I was wondering who used the term 'mass' in physics and in what context? The Online Etymology Dictionary says it is in use since 1704. According to the Wiki article the year is contemporary to the work of Newton on Principia Mathematica. Had Newton anything to do regarding the first use of 'mass' as a quantitative term for expressing aspects of nature?


title: Fourier transformation, electric field and magnetic field to have a shielding lattice against particles

text: With Fourier-Series Expansion, we can write a function as sum of many non- repating different frequncied different amplituded sine and cosine functions. Lets assume we know electric-field and magnetic-field representation function of Hydrogen atoms or Iron atoms as a periodic-lattice **(If we cannot know, lets take periodic-Dirac-Delta)**. Question: how many sine+cosine wave generators do we need to produce such imitation for at least xy plane with minimal erroer(lets say %0.1 about electron-orbit's uncertainity) ? (ofcourse electromagnetic waves are transverse sinusoidal) Very narrow angled generators targeted at same points so they would make a spot of super-positioned waves acting like Iron lattice or whatever em-field needed maybe (even a shield against big objects, with enough power source and strong generators, like in the Star-Trek realm?). ![enter image description here](http://i.stack.imgur.com/CAxik.png) like ion cores in the lattice as a barrier for nano-particles. Thanks.


title: Why is the summer, in the temperate latitudes, in average, hotter that the spring?

text: It is common knowledge that the transition from the Spring to the Summer season occurs in the Summer Solstice when the "Sun reaches its highest excursion relative to the celestial equator on the celestial sphere" (as stated in Wikipedia). It is also stated in Wikipedia' Summer page: "Days continue to lengthen from equinox to solstice and summer days progressively shorten after the solstice, so meteorological summer encompasses the build-up to the longest day and a diminishing thereafter, with summer having many more hours of daylight than spring." My question is: why is the summer, in the temperate latitudes, in average, hotter that the spring?


title: Is there a reasonable lower bound for free energy per site of the 2D Ising model in the presence of an external field?

text: Given the standard Ising partition function: $$Z(\theta ,h) = \sum\limits_{\bf{x}} {\exp \left\\{ {\theta \sum\limits_{(i,j) \in E} {{x_i}{x_j}} + h\sum\limits_{i \in V} {{x_i}} } \right\\}}, $$ is there a closed form expression for the lower bound of the free-energy (Pressure) per-site, defined as, $$\psi (\theta ,h) = \mathop {\lim }\limits_{n \to \infty } \frac{{\log \left( {Z(\theta ,h)} \right)}}{n}.$$ My hunch is that is $2\theta + h$ based on taking limits of an approximation suggested in this article Any ideas on its suitability as a lower bound?


title: Based on note, how fast is a stringed instrument's string oscillating?

text: to be quite honest, I have no idea where to start on this problem mathematically. However, it struck my curiosity and would love to know how it works on a mathematical level. # the problem You have a guitar. All of the strings start at a resting position. When you play a string, it is now oscillating between two points (as far as I can tell). The speed at which it oscillates is correlating to the frequency, and the distance between the points is how hard the note was struck or the volume of the note. You play the E string, open, and let it ring. Then you play the 7th fret of the same string, and let it ring. Now how does one determine how quickly the string is oscillating between the two points in this scenario, in a unit of measurable distance? All I really have so far is that E and B are a perfect fifth apart, making the ratio of their frequencies 3:2. If one were to play the 12th fret of the same string, that would be a 1:2 relationship. Therefore it follows that the speed they oscillate should follow the same proportions. I, however, am not sure how to get an initial distance. ### Edit for some clarity; the application to put this question in context, I am trying to programmatically work with a three-dimensional model of a guitar as it is played by a guitar player and make it visually convincing. As such, when he plays an open string, it would move more slowly. If he put his finger on a fret on that string and played it, nothing from his finger to the nut would vibrate, but the rest would vibrate FASTER. I'm trying to discern a reasonable level of accuracy of this visual effect. Thank you


title: Is water a gas at critical density, room temperature?

text: I am quoting Chaikin, Lubensky, _Principles of Condensed Matter Physics_ , p. 4. > Now suppose we have a closed container of water vapor at a density of 0.322 > g/cc at room temperature. As the temperature is lowered... It then proceeds to describe condensation, and says it is a continuous process because the system is at the critical density. However, it is definitely not at the critical temperature. How can it condense at a temperature lower than that? Is it a mistake?


title: Alternative derivation for the capacitor energy equation

text: I hope this is the right place for this kind of post. A friend is trying to derive the equation for the energy stored in a capacitor by analysing the change in potential on one plate when the capacitor is shorted, however I don't think this valid. Could anyone explain why this is right or wrong? He says that when the capacitor is shorted the potential at each plate changes by V/2 (from 0 to V/2 on one side and from V to V/2 on the other), so by substituting in V/2 into the equation he gets E = 1/2 QV, the capacitor energy equation. ![Diagram](http://i.imgur.com/Q7H7oXk.png)


title: Why is $F = mg - T$ in this case?

text: The situation is as follows: ![Hello, world!](http://i.stack.imgur.com/UXYod.png) I am told that $F_{net} = mg - T$ in this case, but doesn't that not take into account that $T$ isn't applied to the center of mass? Newton's second law is defined for discrete particles, but this is a continuous body... If a force is applied to the center of mass of the body, it can be treated as a particle. But $T$ isn't applied to the center of mass - does this change anything? If it does, how would you find the translational acceleration in this case (given $r$, $m$, and $T$)?


title: Resolution of identity in interacting QFT

text: $\mathbf{Background:}$ Consider a free scalar field $\phi$ ($\mathcal{L}_0 = \frac{1}{2}\partial_\mu \phi \partial^\mu \phi + \frac{1}{2}m^2 \phi^2$). In the Hamiltonian viewpoint, this system has a Hilbert space $\mathcal{H}_0$ (the Fock space). We can write down a resolution of the identity in $\mathcal{H}_0$ (in the Schrodinger picture): $\begin{align} I = |0 \rangle \langle 0 | + \int dp\ |p \rangle \langle p | + \frac{1}{2!} \int dp_1 dp_2\ |p_1 p_2 \rangle \langle p_1 p_2 | +\ \cdots \end{align}$ $\mathbf{Question:}$ If we add an interaction term to the Lagrangian (such as $\lambda \phi^4$), is $I$ still the identity operator in the new Hilbert space $\mathcal{H}$? (To be clear, I mean exactly the same $I$, with the free vacuum and free particle states.) $\mathbf{Motivation:}$ The analogous thing holds in QM. A non-relativistic particle moving in a potential $V$ has a Hilbert space $L^2({\mathbb{R}})$, so by Fourier transform, $\int dp\ |p \rangle \langle p |$ is a resolution of the identity. (Where $\langle x | p \rangle = \frac{1}{\sqrt{2\pi}} e^{i p x}$ are free particle states.) The Hilbert space is the same regardless of $V$.


title: Book Recommendation- Classical Relativistic Fields

text: My bare bookshelves are crying out for the addition of a new family member, more specifically a book:   1. Discussing the classical Klein-Gordon field, spinor fields, gauge fields and all other matter fields in a generally co-variant fashion.   2. Discussing of the Schrodinger (non-relativistic scalar) field.   3. Detailing the application of fields to things like inflation, dark matter, condensed matter etc.    4. Possessing nice, thorough derivations (like the single-particle, relativistic Lagrangians from the complex scalar field) and other such items of interest which show how single-particle mechanics follow from classical fields. Discussion of conformal symmetries, first class and second class constraints are also desired.    5. With some discussion of field quantization. I have possession of some papers covering these topics and some books (like Landau's Classical Theory of Fields), but they are outdated, restricted to EM fields and very often bypass all discussion of classical fields to quantize them right away. Since I asked for a generally co-variant approach, there should be extensive co-ordinate free representations.


title: Characteristics of bloch electron in a priodic potential

text: Effective mass of a Bloch electron in a periodic potential is negative why ?


title: Can you measure the speed of water coming out of a hose by its arc?

text: Water comes out of a horizontally stationed hose and creates an arc as it heads towards the ground. Can I determine the speed the water was traveling in when it exited the hose by the measuring the arc which is created? For example, let's say that I measure that the water has dropped 2 inches vertically when measuring 1 foot horizontally away from the nozzle - at what speed did it exit the nozzle?


title: Can two single particles interfere with each other?

text: Groups of particles can interfere with one another; In the double slit experiment when measuring single photons at the screen each one arrives at the screen in a random manner and they only show the interference pattern once several particles are detected. Obviously two waves can obviously interfere with one another, but can two single particles interfere with one another? Cohen-Tannoudji writes that > light simultaneously behaves like a wave and like a flux of particles But do two particles constitute a flux of particles? I doubt that this could be tested experimentally but if it were so would this constitute a measurement for each particle? **Here was my thought** (Disclaimer:I do not have a good idea of what the interference of two single particle states is): To have interference of two single particles you would have to know something about there position to be able to describe their interference pattern hence the measurement.


title: Order of magnetic phase transitions

text: Is there any phase transition occur in paramagnetism to diamagnetism transitions state. What should be the order and how will I calculate the order?


title: Definition of quantum anharmonicity

text: I have been reading research papers in mathematical physics for some months now, and I've seen the the term "anharmonic oscillator" quite frequently. At first I assumed that given a Schrodinger equation $$\frac{d^2u}{dx^2}+(E-V(x))u=0$$ where $E$ is the energy, and $V(x)$ is the potential function. If $V(x) = x^2 +$ higher order polynomial terms, then this gives rise to the anharmonic oscillator since the higher order terms ensure that the potential will deviate from the "harmonic path". However, I've recently seen potentials of the form $$V(x) = \frac{1}{x^3}+\frac{1}{x^4}+\frac{1}{x^5}$$ described anharmonic oscillator as well. I just wish to know what is a good definition of anharmonic oscillators and anharmonicity?


title: Self Inductance and Mutual Inductance

text: Systems have mutual inductance and self inductance-however won't the effects of these two effect each other as well? Do systems undergo current and magnetic field behavior that are, in this way, dictated by differential equations?


title: Something about things going in black hole?

text: Don't hit me if the question is too lame but here it goes 1) We all know that to see something light must get reflected from it's surface and then reach our eye's 2) Any thing which goes in black holes get incinerated and destroyed completely 3) For a observer outside the event horizon he will see that the falling object slows down and eventually stops moving and seems like it is stuck there. So my question is if to see something light must get reflected from it's surface and then reach our eyes, and something going in black hole gets completely destroyed then how a person outside the even horizon is able to see it -- I mean it is completely destroyed then what is reflecting the light so that we can see it (sorry if not clear in language)


title: Atomic nearest neighbor notation

text: I recently got a correction to a paper that I am writing. The correction references a section in which I talk about nearest neighbors. The comment says: > Do you mean NN, NNN, etc., or NN, 2NN, 3NN? It's different. To clarify: here is the (111) face of an FCC crystal with nearest neighbors numbered (sorry about the horrible mouse-written numbers): ![FCC\(111\) Nearest neighbors](http://i.stack.imgur.com/yGKy1.gif) Starting from the center, I would denote the nearest neighbors as NN, 2NN, 3NN, etc. just as they are numbered. I think it would be the same to call them NN, NNN, NNNN, etc. Does anyone here know what this reviewer could be talking about? Because this seems like a simple concept to me and I have never encountered any confusion with the notation before.


title: Four-gauge-boson vertex in non-Abelian gauge theories

text: In Peskin & Schroeder's book page 524, the following diagram is calculated for the gauge boson self-energy in order $g^2$: ![enter image description here](http://i.stack.imgur.com/i7pTt.png) In dimensional regularization, its contribution is given by $$-g^2C_2(G)\delta^{ab}\int\frac{d^dp}{(2\pi)^d}\frac{1}{p^2}\cdot g^{\mu\nu}(d-1)$$ At this point, Peskin & Schroeder say that "we could simply discard this diagram". It is clear that the integral over $p$ does not give a pole as $d\rightarrow 4$, but it is also divergent. Why can we simply discard this diagram? (Just because it is not logarithmically divergent?) Many thanks in advance!


title: Is time speeding up due to the expansion of space?

text: If we just look at our local galactic cluster, if all of the galaxies that are a part of it are moving away from each other, and so the overall 'density' of the strength of gravity in the cluster is decreasing over time, does that mean that time itself is also speeding up? If this is the case, would it be on a noticeable scale, and if so, would there be any way would could measure it happening (seeing as we'd still be experiencing everything at exactly the same rate since the things/people around us would be just as affected by the weakening strength of gravity)? Let me know if it isn't clear what I'm asking and I'll try to make it more concise, also, be gentle, I'm a layman ;)


title: Can endergonic reactions occur outside of living organisms?

text: If the Gibbs free energy equation is defined as: `∆G = ∆H - T∆S` And the amount of energy/work released from a reaction is: `-∆G = w_max` Living organisms use exergonic reactions to metabolize fuel where the Gibbs free energy is negative and they (can) occur spontaneously in non-living structures. `Exergonic: ∆G<0` Also in living organisms the energy that is released from the exergonic reactions can be coupled with the endergonic reactions. These do not occur unless work is applied to the reagents. `Endergonic: ∆G>0` Given that, is it possible for an endergonic reaction to happen anywhere outside of a living creature or man-made creation?


title: Pfund's method for refractive index

text: I wish to obtain the refractive index of a smooth surface using only a laser of given wavelength and a light sensor. I thought of using the Pfund method (attached), but I can't understand how the light sensor would fit in instead of the paper. I _must_ use the sensor by the way. Can this be done on a horizontal table and then detected using a sensor? http://www.lehigh.edu/imi/docs_edu/RefractiveIndexPfundsMethod.pdf


title: What's the physical significance of using fourier transform for diffraction?

text: I am studying some basic idea of diffraction and there mention in far field, the diffraction pattern could be understood by Fourier transform. But I just don't understand what's the physical fact for that. And why cannot use Fourier transform for the the near-field case? Also, when I am trying to understand the theory of diffraction, it ends up with some complicate math (integrals). I want to learn that but the books I am reading are not easy to understand. Anyone recommends some good books or video lectures (more theoretical but to explain most of the math in plain way)?


title: Eigenvalues of a quantum field?

text: Fields in classical mechanics are observables. For example, I can measure the value of the electric field at some (x,t). In quantum field theory, the classical field is promoted to an operator-valued function of space-time. But no one talks about eigenvectors of the quantum field! If I try to measure the field at one point in spacetime, I should get a real value which should be an eigenvalue of the quantum field, right? I guess the eigenvectors of the quantum field also live in Fock space?


title: How do I find constraints on the Nambu-Goto Action?

text: Let $X^\mu (t,\sigma ^1,\ldots ,\sigma ^p)$ be a $p$-brane in space-time and let $g$ be the metric on $X^\mu$ induced from the ambient space-time metric. Then, the Nambu-Goto action on $X^\mu$ is defined to be $$ S:=-T\int dt\, d\sigma \sqrt{-\det (g)}. $$ (We use the convention of space-time signature $(-,+,+,+)$. Let us try to compute the Hamiltonian for this theory. The first step is to calculate the conjugate momenta: $$ P_\mu :=\frac{\partial L}{\partial (\partial _tX^\mu)}, $$ where of course $L:=-T\sqrt{-\det (g)}$. It turns out that you are unable to invert this map to write $\partial _tX^\mu$ as a function of $X^\mu$, $P^\mu$, and $\partial _{\sigma ^i}X^\mu$, which means that the image of the Legendre transformation $(X^\mu ,\partial _{\sigma ^i}X^\mu ,\partial _tX^\mu )\mapsto \left( X^\mu ,\partial _{\sigma ^i}X^\mu ,\frac{\partial L}{\partial (\partial _tX^\mu )}\right)$ is not surjective, but instead the image of this map is a proper sub-manifold (of course, in general the image of a manifold under a smooth map will not in general be a manifold, but in our particular case, that should not be a problem) of $T^pT^*M$, and so (locally anyways) will be specified by $N$ constraints $\phi _j(X,\partial _{\sigma ^i}X,P)=0$, where $N$ is the dimension of the kernel of the derivative of the Ledgendre transformation. In the case of the Nambu-Goto Lagrangian, I have found that $N=1+p$. I found this by calculating the multiplicity of $0$ as an eigenvalue of $\frac{\partial ^2L}{\partial (\partial _tX^\mu )\partial (\partial _tX^\nu )}$. The question is: now that I know how many constraints there should be, how do I systematically find what those constraints actually are? For what it's worth, I know that one constraint is $$ P^2+T^2\det (k)=0, $$ where $k$ (I have suppressed the time-dependence of $k(t)$ in the notation) is the metric on the space-like sub-manifold $X_t^\mu (\sigma ^1,\ldots ,\sigma ^p):=X^\mu (t,\sigma ^1,\ldots ,\sigma ^p)$ induced from the metric $g$ on $X^\mu$, and that the other $p$ constraints are $$ \partial _{\sigma ^i}X\cdot P=0 $$ for $1\leq i\leq p$. I even know how to verify that these are in fact constraints. What I don't know, however, is how to come up with these constraints without simply pulling them out of my ass. Is there a systematic, yet computationally feasible way of determining what these $1+p$ constraints should be? Furthermore, I have a hunch that each of these constraints arises from a corresponding re-parameterization invariance, so if that is indeed the case, it would be wonderful if someone could elucidate this connection for me. (Is there a re-parameterization invaraince-$\Rightarrow$-constraint theorem analogous to Noether's Theorem for symmetries and conserved quantities?)


title: Type II Superconductors

text: While the microscopic mechanism leading to type II superconductivity is still debated, do scientists at least have a handle on the phenomonology? Specifically, are the experimental properties of type II superconductivity understood well enough that it is possible in principle for the properties of a newly discovered material to lead to declaring a type III superconductor? Or is type II so poorly understood, that it is best described as "not type I" superconductivity, and thus leaving no room for a type III superconductor?


title: Change in time period of a simple pendulum

text: There's a question in my book which goes as: A pendulum has a bob of a hollow sphere filled with a liquid and having a hole at the base. If the liquid is allowed to flow out, what would happen to the time period of the pendulum? My thought: Since the time period is independent of the mass of the bob, the time period would remain unchanged. What my books says: The time period would initially decrease, and then gets restored. This is because as the liquid gets lowered, the center of gravity of the bob gets lowered, which increases the effective length of the pendulum string slightly. When the liquid is completely drained out, the center of gravity again comes to the center of the sphere, restoring the time period. I don't understand why the 'effective length' would increase due to the shift of cog. And would the change in time period would be so significant?


title: Time period of simple pendulum with varying mass

text: How do you find time period as a function of time for a simple pendulum that is in the form of a hollow sphere that is filled with mercury and there is a hole in the bottom through which the mercury is constantly falling at a fixed rate? I tried creating a function for the time period to check how it varies with the mass of mercury, but I had too many variables. EDIT: This question was a concept based multiple choice question in my homework book. The option were time period becomes erratic, time period increases, time period decreases, time period first increases then decreases.


title: Angular momentum in string theory

text: Since strings are extended objects, is all angular momentum in string theory essentially "orbital" angular momentum? Or is there still a kind of intrinsic angular momentum assigned to a string? Either way, is there anything that prevents the "intrinsic spin" of a particle represented by a string from being arbitrarily large?


title: How far away are we from resolving high temperature superconductivity?

text: What are the major recent findings and their corresponding contributions to an overall picture? How well explained are the various regions of the dome, is there any thing that is pretty well understood? What is left and how are people trying to figure it out?


title: Gravity in spacetime

text: Can the effect of gravity in spacetime be thought of as if nearby particles have a tendency to "align" their four velocity direction? I.e. "to point in the same direction".


title: How do spacecraft cameras work?

text: When I look at pictures taken by a modern spacecraft (like that one showing the surface of Titan: ![Titan](http://upload.wikimedia.org/wikipedia/commons/b/bc/Huygens_surface_color.jpg) and taken by Cassini) I kinda understand how they might be produced. There might be some kind of CCD sensor installed and the data is later transmitted to Earth. But then I think about it I start to wonder how cameras worked on older spacecrafts like Mariner, for example this one taken by Viking 1 ![Mars](http://upload.wikimedia.org/wikipedia/commons/a/ae/Mars_Viking_12a001.png). As far as I know there were no digital cameras back then. How did they get around it and were able to produce photos and more importantly sent imaging data back to Earth? I can imagine that there was an analog camera installed along with some scanning facility but that sounds _sooo_ unlikely as it would require a rather complex machinery which isn't feasible for an operation in space. But other than that I'm out of ideas. Wikipedia is surprisingly silent about it, too. * * * **EDIT** : Thanks, everybody, for your great answers! I upvoted everything I could and accepted Georg's answer for a great Wiki link.


title: Relativity and volume of black hole

text: Does Einstein's theory of special or general relativity incorporate volume? In a particle accelerator two particles smash together at relativistic speeds and "create" new particles (quarks etc) due to $E=mc^2$. In our space-time, the volume needed for these new clumps of mass already exists in local space- time. What happens in the super-dense core of a galaxy where stars and black holes are all sucked together into a super-dense object? Presumably, all the matter has been compressed to its theoretical limit. When another super-dense object (another black hole) strikes it at relativistic speeds, where does the volume come from to accommodate the creation of these new particles? If space-time of a black hole is infinitely curved, how can new volume be created for these particles to occupy?


title: In Jackson's expression for the electrostatic Green function, why is the Laplacian taken with respect to the primed coordinates?

text: Jackson writes, > The function $1/|\mathbf{x} - \mathbf{x}'|$ is only one of a class of > functions depending on the variables $\mathbf{x}$ and $\mathbf{x}'$, and > called _Green functions_ , which satisfy (1.31). In general, > > $\nabla'^2 G(\mathbf{x}, \mathbf{x}') = -4\pi \delta(\mathbf{x} - > \mathbf{x}')$ A bit further down, ... > $$ \Phi(\mathbf{x}) = \frac{1}{4\pi \epsilon_0} \int_V \rho(\mathbf{x}') > G(\mathbf{x}, \mathbf{x}') \, d^3x' + \frac{1}{4\pi}\oint_S > \left[G(\mathbf{x}, \mathbf{x}') \frac{\partial \Phi}{\partial n'} - > \Phi(\mathbf{x}') \frac{\partial G(\mathbf{x}, \mathbf{x}')}{\partial > n'}\right] \, da' $$ Since the integration is performed over the primed coordinates, it would seem that $G$, as a function of $\mathbf{x}$, represents the field due to a point source at $\mathbf{x}'$. Shouldn't it then satisfy the equation $\nabla^2 G(\mathbf{x}, \mathbf{x}') = -4\pi \delta(\mathbf{x} - \mathbf{x}')$, that is, with the Laplacian taken over the _unprimed_ coordinates? Taking the Laplacian over the primed coordinates would seem to depend on the variation in the field at a fixed point while the point source is moved, which does not seem meaningful.


title: Where to find experimental/theoretical value of (charge) radius of particles?

text: Where to find experimental/theoretical value of (charge) radius of particles like proton, neutron, $pi^+$, etc. ?


title: Question regarding escape velocity

text: Haliday-Resnick-Walker state that the escape velocity will cause a projectile to move upward forever, theoretically coming to rest only at infinity. I was wondering what the forces forcing the body to come to rest at infinity are when the authors are using the word"theoretically".Your help is appreciated.


title: Resources for current thought on time/spacetime?

text: Are any of the big-name physicists associated with the time in the same way that Hawking and Penrose are associated with black holes? I'm interested in some good books that focus on the topic.


title: Red shift and time distortion

text: Superman throws a light emitting object away from himself fast enough to notice a red-shift. The object passes through a region in which time runs more slowly. From Superman's perspective, does the red-shift change as the object slows or is the light's appearance unaffected?


title: Is the force between solitons with same charge always repulsive?

text: I know the one-dimensional case in which the force is proportional to $e^{-R}$ and the force is attractive for solitons with opposite charge and repulsive for solitons with same charge. I was calculating in an approximated model in 3+1 dimensions the force between solitons and I obtain repulsive for different charge and attractive for same charge. This result seems strange. Is there some law or theorem that doesnt allow this? Do you know any model where this happens?


title: At what temperature does air become liquid at a pressure of X bar?

text: ... with X = 6 in my particular case. I was trying to get a phase diagram for air, only got one for nitrogen and was slightly puzzled. Here's why: I was wondering about a particular detail in industrial air liquification. The original Linde process used 200 bar pressure and cycled the air though several cycles to condense it, as one decompression only gives around 40 K reduction in temperature. This process was replaced rather early by a modified process (called the Linde-Fränkle process) that compresses the air to only 6 bar and then runs it through a pre-cooled regenerator, where it liquifies in the first pass, proceeding to the distillation column immediately. That process was in use until the 1990s, so it probably had decent performance. Now, I was wondering to what temperature the regenerator has been precooled. From the phase diagram of nitrogen, I'm estimating to somewhere not abive 150 K, most probably lower. Since the pre cooling is done with the gaseous $N_2$ and $O_2$ boiling off the distillation column, it sounds like quite close to the liquification temperature at atmospheric pressure. This puzzles me because it makes me wonder why such little compression is sufficient to make the whole process economic. Also, I can't quite see at what point the Joule-Thompson effect comes into play here. The air is liquefied entirely without decompression, so where dies the cooling come from? I was also wondering if I might be confusing liquid and supercritical here, since I'm told pressurized gases in typical containers at room temperature are really supercritical already, even though laymen like me still call them liquid.


title: Generating Pink Noise

text: I've generated some white noise in Excel by using the formula $$2*\mathrm{Math.RAND}()-1$$ I would now like to create some pink noise. I believe this is done by applying some sort of filter to the white noise, but I can't figure out how to do this. P.S. White noise has a flat spectral density, but in pink noise frequency spectrum falls off as $\frac{1}{frequency}$. Any help is much appreciated!


title: A physical understanding of fractionalization

text: all! Is there a physical understanding of fractionalization in condensed matter physics? The textbook approach is theoretical, not physical. I'm thinking of spin-charge separation for electrons, the fractional quantum hall effect, and things like that. The theoretical approach is to introduce an auxiliary gauge field with no kinetic term at the bare level so that it is apparently confining and nondynamical at the bare level, but somehow, dynamics intervenes, and it becomes deconfining, and somehow, there's some mixture between the emergent gauge symmetry and the original symmetries, and somehow, fractionalization comes in in the diagonalization. What is the physical interpretation without introducing theoretical auxiliary gauge symmetries right from the onset?


title: What exactly is a mole?

text: I have some trouble understanding exactly what a mole represents. As I understand, one unit mole is 1/12 of the mass of an atom of carbon-12 (thus it is the mass of one nucleon?). What is a mole, then?


title: Spring system - 3 DoF system and its properties while changing stiffness

text: I was given the attached 3 degree of freedom spring system with the purpose of analyzing it. ![system](http://i.imgur.com/pK0p9kG.jpg) I came up with the following equation of motion ![equation](http://i.imgur.com/vr2QWQr.jpg) and then I ran Matlab to calculate the corresponding natural frequencies and mode shapes using eigenvalues and eigenvectors; I was asked to see what happens when value of stiffness $k_{12}$ is changed. This is the plot of the value $k_{12}$ against the natural frequencies. ![plot](http://i.imgur.com/fdwweRr.jpg) The problem is that I do not know WHY values of natural frequencies are insensitive at low values of $k_{12}$ and why both the 1st and 2nd natural frequencies are insensitive to changes in $k_{12}$ when values are large (first two level off and the third one seems to go to infinity). I assume it has something to do with the equation for force due to a spring between 2 masses but I cannot figure it out. That is why I ask for your help - thanks in advance.