title: What is jet quenching and how far can the hydrodynamic analogy go?

text: I recently heard about jet quenching concerning data taken by the experiments at the LHC. Apparently it is related to the existence to the quark-gluon plasma. As far as I understood this interpretation is an analogy to hydrodynamics (the jet is "blocked" by the plasma). I would like to understand that in more details: why is this analogy a "good" one, how far can it go and how do we detect that experimentaly.


title: Can the magnetic lines of force of two or more magnets intersect each other?

text: Basic property of magnetic lines of force is that, they can never intersect each other. Among the two points given below, which one is correct?   * Magnetic lines of force of same magnet can't intersect each other, but magnetic lines of force of different magnets can intersect each other.    * Magnetic lines of force can't intersect each other irrespective of their origin (i.e whether the lines were of same magnet or different magnets, they can't intersect)  Suppose I have two bar magnets. If I tend to make the repelling poles join together by exerting force (i.e, if I tend to make north pole of two magnets, or south pole of two magnets join together). Would the magnetic lines of force intersect each other?


title: What specifically does the phrase "continuum limit" mean?

text: I'm interested in the meaning of the phrase "continuum limit" specifically as it is often used in expressions relating to the ability of a quantum gravity theory to recover GR in the continuum limit. I believe I understand the meaning but want to make sure I am not missing some important part of the precise definition as my intuition may be off and I have not seen it defined anywhere. Pointers to a place where it is defined in an online resource would be appreciated. A google search just turned up many references to it being used in papers and articles and such. Thank you.


title: Meaning of Lagrange Multiplier in Ou-Yang and Helfrich's Shape equation for Membrane

text: Dear people in Physics Stackexchange, My question is mostly related to the following papers:   * U. Seifert, _Z. Phys. B_ **97** , 299 (1995). "The concept of effective tension for fluctuating vesicles".   * U. Seifert, K. Berndl, and R. Lipowsky, _Phys. Rev. A_ **44** , 1182 (1991). "Shape transformations of vesicles: Phase diagrams for spontaneous-curvature and bilayer-coupling models". In these paper, the Lagrange multipliers $\Sigma$ and $P$ are introduced to take care of effective constraints on area and volume, respectively. If I understood those papers properly, I believe the area constraint and volume constraint originates from the lack of lipid molecules in aqueous solution and osmotic pressure. Hence, I thought that the free energy $F = \kappa G + \Sigma A + PV$ represents "flaccid" vesicle which has much excess area. In other words, I thought that Lagrange multiplier $\Sigma$ and $P$ are not physical surface tension related to the stretching and osmotic pressure difference, respectively. I imagined them just as a mathematical term to take care of area and volume constraint. However, Wikipedia(http://en.wikipedia.org/wiki/Elasticity_of_cell_membranes) and Ou-Yang Zhong-can and Helfrich used the free energy $F = \kappa G + \Sigma A + PV$ to determine the shape of the vesicle, and they said explicitly that $\Sigma$ represents tensile stress and and $P$ represents the osmotic pressure difference between the outer and inner medium. (Actually they used the greek alphabet $\lambda$ instead of $\Sigma$ and $\Delta p$ instead of $P$) [Ref. H. J. Deuling and W. Helfrich, _J. Physique_ **37** , 1335 (1976). "The curvature elasticity of fluid membranes: a catalogue of vesicle shapes", Ou-Yang Zhong- can and W. Helfrich, _Phys. Rev. Lett._ **59** , 2486 (1987). "Instability and deformation of a spherical vesicle by pressure".] Then, are these two quantities($\Sigma$ and $P$) measurable or experimentally observable? I thought that the Lagrange multiplier is determined by which curvature model I chose and the prescribed area and volume for a vesicle. If $\Sigma$ and $P$ represents true physical tensile stress and osmotic pressure difference, then is the phase diagram in above mentioned Seifert et al.'s paper(PRA, 1991) for 'tense' vesicles and not flexible membrane although the membrane has much excess area? I thought that the paper was solely about fluid, flaccid membrane. Which part I am misunderstanding? Are $\Sigma$ and $P$ vanishing if closed membrane is truly flexible and flaccid due to large excess area? In other words, if I want to find shape of truly flaccid membrane without any tension or osmotic pressure, should I set $\Sigma = 0$ and $P = 0$? If so, which part takes care of the area and volume constraint? In addition, the fluctuation is strongly related to the area constraints. I thought that the effective tension (which is different from $\Sigma$ because this new effective tension is related to the excess area rather than whole area of the fluid membrane) can take care of it. This effective tension can be considered as entropic suppression of fluctuation due to area constraints. If so, the Lagrange multiplier related to the excess area seems observable while the Lagrange multiplier related to the total area is not. Am I understanding correctly?


title: What does a nucleus look like?

text: It's a Christmas time and so I hope I'll be pardoned for asking a question which probably doesn't make much sense :-) In standard undergraduate nuclear physics course one learns about models such as Liquid Drop model and Shell model that explain some properties of nucleus. But as I understand it these models are purely empirical and most importantly _incompatible_. Perhaps it's just my weak classical mind but I can't imagine same object being described as a liquid with nucleons being the constituent particles floating freely all around the nucleus and on the other hand a shell model where nucleons occupy discrete energy levels and are separated from each other. Now I wonder whether these empirical models are really all we've got or whether there are some more precise models. I guess one can't really compute the shape of the nucleus from the first principles as one can do with hydrogen atom in QM. Especially since first principles here probably means starting with QCD (or at least nucleons exchanging pions, but that is still QFT). But I hope there has been at least some progress since the old empirical models. So we come to my questions: >   1. Do we have a better model for description of a nucleus than the ones > mentioned? > >   2. How would some nuclei (both small and large) qualitatively look in such > a better model? _Look_ here means that whether enough is known so that I > could imagine nucleus in the same way as I can imagine an atom (i.e. hard > nucleus and electrons orbiting around it on various orbitals). > >   3. What is the current state of first-principles QCD computations of the > nucleus? > >


title: Is there an official name for "Lorentz Pairs" like energy and momentum?

text: In learning about relativity I've noticed that in the construction of Lorentz invariants (specifically four-vectors) two physical quantities that were previously considered distinct are instead treated as a single object. Examples include position and time (spacetime), electric and magnetic fields, electric and magnetic potential, energy and momentum, charge and current density, and so on. I was interested in learning more about this I tried googling my best guess, "Lorentz Pairs", to no avail. My question is whether there is more specific terminology referring to these pairs of physical quantities outside of the general term "Lorentz Invariant". Additionally, why do we so often see two physical quantities being combined instead of, say, three or some other number?


title: Relation of color and frequency for the visible spectrum

text: In this question the OP is looking for a way to see light that is outside of the visible spectrum without using electronic sensors. This got me wondering about the visible spectrum itself. Typically when the visible spectrum is defined it is defined casually both in terms of frequency and wavelength (e.g. here). Obviously this cannot both be true, because the wavelength of light changes depending on the medium according to the refractive index. The story on this page and in the question here explains that color is related to frequency, not wavelength. My question is fairly straightforward: does this mean that the visible spectrum should be defined in terms of frequencies? If this is not the case then that would mean that we can see a different range of colors when, e.g. under water then we can in air, which sounds strange to me.


title: Cases of any known fundamental physical constants changing within our locality?

text: Has there been any cases where the only explanation has been that at least one of the physical constants must have changed to explain an experiment/event/obervation? I am not intrested in large scale obsorvations such Gaolaxies holding together with insufficient obsorvable mass or stars seem to be moving at faster than speed of the light phenomenons. Just simple instances of experiments/events that the only possible logical explenation can be obtained if one had to assume a known fundamental physical constant must have varied. I am trying to have this question to be only for non scale dependent situations. Just to give you an idea, consider that in mathematics the value of constant $\pi$ changes with the geometry.


title: Why or how is cross product used?

text: I do not understand how does the result of two vectors acting on a particle require me to take the cross product to find the resultant. Won't the actual force on the particle be the result of the vectorial addition of the two vectors? How is it that result of two vectors on a charged particle in a magnetic field (the magnetic field vector and the velocity vector of the particle) has the resultant force on the particle in a mutually perpendicular direction?


title: Why do aircraft inner wings lose lift when turning?

text: first question here, so please be gentle! I'm reading an entry-level engineering course book and am currently up to discussion of aircraft design. There's one particular statement that is unclear to me: Turning with the wing level is aerodynamically inefficient and the inner wing loses a lot of lift because it is moving relatively slowly through the air. Does this mean that, for maximum lift efficiency, a wing has to be horizontally level? I understand that the upward pressure beneath the aerofoil is greater than that above it pressing down, so how does the upward pressure change beneath the aerofoil change when an aircraft is turning? Does downward pressure increase?


title: Significance of isolation of radium?

text: This is an extension of my previous question here. Marie Curie isolated radium in 1903, which paved the way for the development of the theory of radioactivity. In regards to the techniques she used however, what was the impact of the establishment of those techniques? Were the techniques used by Curie new? Are they used today? What impact did they have on modern physics? I can find a lot of information online about the actual isolation of radium, but not regarding the significance of the techniques used.


title: Constant volume specific heat

text: * A monatomic ideal gas is confined to move in two dimensions. What is the constant volume specific heat for this gas?    * Consider a system of N independent harmonic oscillators moving in two dimensions. What is $C_v$ for the system. For the first case, I guess this one is $C_v = \frac{3}{2}R$. Am I correct? However for the second case, I was confused a little bit. Any help on this?


title: What does physics study?

text: Wikipedia definition: Physics (from Ancient Greek: φύσις physis "nature") is a natural science that involves the study of matter[1] and its motion through spacetime, along with related concepts such as energy and force. Topics in my physics book:- Electricity and Magnetism Waves and Vibrations Thermodynamics Mechanics and others... Do all of these study motion? It's just weird for me to know that Electricity and Magnetism is a study of motion. Is Electricity and Magnetism only concerned with motion? Also, what is the relation between the matter itself and it's motion (for them to be unified under "physics" instead of each having it's own field)?


title: Why is energy-momentum 4-vector so much easier to explore/observe than spacetime 4-vector

text: I have read that spacetime 4-vector is quite difficult to observe/explore and that energy-momentum 4-vector is much more appropriate for CERN etc. **Why is that?** Could anyone give me a brief explanation of the differences regarding exploration and observation?


title: How do I calculate the probability that the oscillator is in a certain state using partition function?

text: So let's say I have a single ($N=1$) quantum harmonic oscillator and the energy is determined by $E_n = (n + 1/2) \cdot \hbar \omega$ (where $n$ is the quantum number and $n$ = $0, 1, 2, \ldots$) What's the probability that the oscillator is in the state labeled $n$ at temperature $T$? So according to my calculation, $Z$, the partition function, is $Z = 1 / (1 - x)$ where $x = e^{-\beta \hbar \omega} \Rightarrow P = x ^ n (1 - x)$. Is it correct? Also, how do I go about calculating the probability of finding the oscillator in a state with odd quantum number?


title: Relating milliampere-hours to watt-hours for batteries

text: I've seen many batteries that are measured in milliampere hours (mAh), while others are measured in watt hours (wh). How can I convert them between each other so that I can actually compare them? It's often the case that computers or smartphones use one or the other and would be great to have a metric.


title: Simulate free fall in a rotating torus?

text: Say I have a rotating torus filled with air at 1 atmospheric pressure at sufficient speed (and inclined along the direction of the force of gravity with respect to Earth). If the rotation speed were sufficient, would I be able to simulate a free fall environment for an object suspended inside the spinning torus, due to the pressure exerted by the air spinning inside the torus counteracting gravity?


title: How do bicycle spokes work?

text: As you know, it is quite obvious that Bicycle spokes attach the hub in the centre to the rim. What else do they do? If you compare the wheels today with the ones from ancient times, there are more spokes now on motor bikes and bicycles than of a wheel of a chariot. Why is that? What effect does it have on the vehicle if there is a higher number of spokes on the wheels?


title: Why does my door shut faster when the window is open?

text: I've noticed that if I shut my door when the window is open in a room, the door will tend to shut faster. If I shut the door when the window is closed with a normal force it will not fully close as if the air is cushioning it. I think when the window is open the door doesn't stop or slow down at all, it just slams. I was wondering if this was to do with the pressure of the room or something. My hypothesis was that there is more room for the air to escape or there is some sort of convection? Just to note it is definitely not wind because I checked. Here is a graphical simulation of the phenomenon: ![enter image description here](http://i.stack.imgur.com/TietV.png) Can somebody explain what is going on?


title: How to determine donor or acceptor impurity

text: I am working on a practice exam for semiconductor physics. Can anyone help me figure out how to determine whether we have donor or acceptor impurity in Gallium Arsenide?               Gallium is column 3 and (I think) it has a valence of 3.     Arsenide is column 5 and (I think) it has a valence of 5.     But it has a valence of 4 when it is GaAs?      Based on the information I believe I will be provided in the exam proper, I will know only the periodic group and/or atomic number, and/or valence. I am given these choices as impurities:               Si <-- Donor impurity --> n-type semiconductor     S  <-- Donor impurity --> n-type semiconductor     P  <-- ??     Zn <-- Acceptor impurity --> p-type semiconductor      So you can see I have the answers, I just don't know how to get there.


title: How would a large a mass be stable at the Earth Sun L4 or L5 point?

text: I've heard about the Trojan asteroids and there is the famous idea of putting a space colony at one of these points, but the explanations I see for how something is stable at those points it they are 'insignificant mass.' What does that mean? Insignificant to Earth could be pretty big, insignificant to the sun could be downright huge. What are we talking about here, the mass of a large asteroid? The moon? The Earth? Surely it couldn't be bigger than one of the two bodies in the system?


title: Static as opposed to Kinetic Friction in Rolling Motion

text: During analysis of rolling motion, why do we consider coefficient of friction as that of _static_ friction and not kinetic friction?


title: Is it possible that a battery goes flat faster in a cold environment?

text: I own an old iPod Classic with original lithium-ion polymer battery and I use it primarily while running. Recently I discovered that when a temperature outside is low, usually below 5 C degrees, the battery goes flat really fast and I mean 10 minutes. It doesn't matter if it is fully charged or not, it always goes down faster than when it is 10 degrees or more outside. I know that the device is 10 years old so it doesn't work as good as when it was new, but I'm curious what is the physical reason of the battery going dead faster when in cold environment. I also noticed similar behavior of my laptop battery. Any idea why is that? **Edit:** Here I found some info: "Cold temperature increases the internal resistance and diminishes the capacity. Batteries that would provide 100 percent capacity at 27°C (80°F) will typically deliver only 50 percent at –18°C (0°F). The capacity decrease is linear with temperature. The capacity decrease is momentary and the level of decline depends on the battery chemistry." "The performance of all battery chemistries drops drastically at low temperatures. At –20°C (–4°F) most nickel-, lead- and lithium-based batteries stop functioning." All wikipedia can say about battery capacity is: "The fraction of the stored charge that a battery can deliver depends on multiple factors, including battery chemistry, the rate at which the charge is delivered (current), the required terminal voltage, the storage period, ambient temperature and other factors." It dosen't say anything about how the capacity depends on the electrolyte's internal resistance.


title: Does universal wave function exist?

text: Does universal wave function exist? What the science tells us?


title: Why can free lithium atoms not take part in an Auger process?

text: Shouldn't it be possible for an incoming photon to excite one of the 1s electrons to a 2p state (or one of even higher energy) and then for the excited electron to drop back to 1s and kick out the 2s electron? Is there some fundamental reason that prohibits this process, or is it just very unlikely, or is it not called "Auger process" because the first electron is excited instead of kicked out?


title: A question on Galilean Relativity

text: In a test I took recently in my beginning Physics class there was a question that really irked me: > _A man is swimming upstream at 10 mph. The water is flowing downstream at 5 > mph._ > > _How fast is the man moving?_ Well, you can actually take this question two ways:   1. Firstly, "a man is swimming upstream at 10 mph" could mean exactly what it sounds like, and therefore the 5 mph down-streaming water is irrelevant and the man was actually using enough force to swim 15 mph in stationary water. That means he was moving at a speed of 10 mph, like it stated.    2. Alternatively, it could be taken to mean "a man is swimming upstream at 10 mph", meaning that that is the amount of force he is using. The man is using enough force to swim 10 mph in stationary water. Then, if the water is moving downstream at 5 mph, then he is moving at a speed of 5 mph.  I chose the first answer, but I want to figure out if I got the question right. Is there a way to tell? As in some sort of order of operation for Physics?


title: Is there a formula for determining the focal point of a sphere?

text: I guess this is the same as for cylinders, when light is shone through parallel to the cross-section, but Google-ing this only turns up lenses like the ones used in glasses. I'm looking for something like what's described in this article: http://spie.org/x34513.xml I hope to determine the veracity of the equation described there.


title: Hydrogen as a fuel in Sun

text: The source of Sun's incessant energy is hydrogen; which is continuously converting to helium through nuclear fusion reaction releasing energy. Why does not all hydrogen convert into helium in one big explosion just like a man-made bomb or cracker explodes?


title: Water droplet evaporation due to humidity and temperature

text: I am conducting an experiment that requires comparison to models for a water droplet's change in size due to evaporation. I've found plenty of papers, but they all seem to require measurement of the drop's radius and/or height. For the purposes of the experiment, I need a rate of change of the drops volume - $ \frac{dV}{dt} $ - related to temperature, humidity, local pressure, and surface tension. The contact angle starts at $ \approx 90 $ and a volume less than 60$\mu L$. Does anyone know of such a paper? If so, please post the citation and/or a link. I suspect that the lack of papers would be due to the great age of the discovery, Thanks


title: What is the current induced in a straight wire when a magnetic field is turned from on to off?

text: > Consider a straight wire which runs along the y-axis. A B-field exists which > is uniform and only in the x-direction: > > $$\vec{B}=(B(t),0,0)$$ > > The B-field at time $t_0$ is 'switched off' in a sharp step, which will be > modelled by the tanh function: > > $$ B(t)= \begin{cases} B_0 & t\leq t_0 \\\ 0 & t>t_0 \end{cases} \approx > \frac{B_0}{2}\left [ \tanh(100(t-t_0)) +1 \right ] $$ > > **What is the current induced in the wire due to the change in magnetic > field as a function of time?** What I have tried is to work out the E-Field y-component using Maxwell's 3rd law (using the notation $\partial_{yz} x \equiv \frac{\partial^2 x}{\partial y \partial z}$): $$\nabla\times\vec{E} = -\partial_t \vec{B}$$ But the B-field only has an x-component, so: $$\begin{align} \partial_y E_z - \partial_z E_y &= -\partial_t B(t)\tag{i} \\\ \partial_z E_x - \partial_x E_z &= 0\tag{ii} \\\ \partial_x E_y - \partial_y E_x &= 0\tag{iii} \end{align}$$ So if you differentiate (i) by x, (ii) by y and (iii) by z: $$\begin{align} \partial_{xy} E_z - \partial_{xz} E_y &= -\partial_{xt} B(t) \\\ \partial_{yz} E_x - \partial_{xy} E_z &= 0 \\\ \partial_{xz} E_y - \partial_{yz} E_x &= 0 \end{align}$$ But then if you sub them all in together you get: $$\partial_{xt} B(t) = 0$$ Which isn't very useful.   * If I want to work out the current induced in the wire which runs along the y-axis do I want to work out: $E_y$? And If so how do I do so?   * Would current be induced in any other direction?


title: Shouldn't the Uncertainty Principle be intuitively obvious, at least when talking about the position and momentum of an object?

text: Please forgive me if I'm wrong, as I have no formal physics training (apart from some in high school and personal reading), but there's something about Heisenberg's Uncertainty Principle that strikes me as quite obvious, and I find it strange that nobody thought about it before quantum mechanics development began, and still most people and texts explain it in quantum mechanics terms (such as citing wave/particle dualism, or the observer effect)... while actually it should appear blatantly obvious in classical mechanics too, at least regarding the position and momentum variables, due to the very definition of speed. As everyone knows, the speed of an object is the variation of its position over an interval of time; in order to measure an object's speed, you need at least two measurements of its position at different times, and as much as you can minimize this time interval, this would always create an uncertainty on the object's position; even if the object was exactly in the same place at both times, and even if the time was a single nanosecond, this still wouldn't guarantee its speed is exactly zero, as it _could_ have moved in the meantime. If you, on the contrary, reduce the time interval to exactly zero and only measure the object's position at a specific time, you will know very precisely where the object is, but you will never be able to know where it came from and where it's going to, thus you will have no information at all about its speed. So, shouldn't the inability to exactly measure the position and speed (and thus the momentum) of an object derive directly from the very definition of speed? * * * This line of reasoning could also be generalized to any couple of variables of which one is defined as a variation of the other over time; thus, the general principle should be: > You can't misure with complete accuracy both $x$ and $\frac{\Delta x}{\Delta > t}$ For _any_ possible two points in time, there will always be a (however small) time interval between them, and during that interval the value of $x$ could have changed in any way that the two consecutive measurements couldn't possibly show. Thus, there will always be a (however low) uncertainty for every physical quantity if you try to misure both its value and its variation over time. This is what should have been obvious from the beginning even in classical mechanics, yet nobody seem to have tought about it until the same conclusion was reached in quantum mechanics, for completely different reasons...


title: Max rocket speed in interstellar space?

text: Interstellar space propulsion...if a spaceship were to get beyond our Sun's gravitational pull and since there is no atmosphere/wind/friction in space...does that mean, if an engine was constantly thrusting, that the spaceship would continue to accelerate to the speed of light, as long as the engine was propulsing forward? In other words, does speed constantly increase in a vacuum? or are the two ideas (Space/Vacuum) separate ideas?


title: How are the comoving coordinates NOT a prefered reference frame?

text: Physics me this: The **equivalence principle** has rigorous physical definitions that say, for one, that the laws of physics are the same in all inertial reference frames. This is to say that _the behavior of the universe_ is the same for any system regardless of velocity $(\vec{v})$ and position $(\vec{r})$ according to special relativity. General relativity even establishes some sorts of parallels for acceleration $(\vec{a})$ and spacetime curvature, although it still leaves some reference frames with an obviously more complicated geometry of spacetime. The **Copernican principle** is the "notion" or "philosophy" that neither humans or any given group examining the universe has a privileged view. The idea has been generalized to extend from the original intention applying to the Earth to extend inward as far as a human individual, or outward as far as our local group of galaxies. At the largest scale we have found the distribution and characteristic of matter throughout the universe to be roughly homogenous, as sort of the ultimate example of this principle, leaving no location or collection of matter privileged. Hubble's constant correlates $\vec{r}~$ and $\vec{v}$ between any two points in space, which defines the comoving coordinates, which identifies a point within the constantly ballooning and accelerating mesh of matter that fills the universe. Without loss of generality I'll say that $\vec{r}$ is truly independent and non-privileged, but $\vec{v}$ has a clearly preferred value, which is that which matches the average flow of matter around $\vec{r}$. Reflect for a second to note that $\vec{v}$ is a privileged view of the universe _even though_ it is non-privileged regarding the physical laws of the universe. Why why why?! I expect quick dismissals of the "problem" due to the fact that the Copernican principle is not a physical principle and can thus be comfortably wrong. But it still seems like the implications would be non-trivial and would keep physicists up at night. Ultimately if we truly find the "Grant Unified Theory" it should fully allow the Lorentz Invariance AND provide some way for the big bang to create matter that is roughly stationary to other (close-by) matter. If not, why didn't the big bang create matter with $\vec{v}=-c\dots c$ and momentum spanning $\vec{p}=\infty \dots \infty $ for a given $\vec{r}$? That would obviously be nonsensical since collisions would be releasing infinite energy. But wouldn't it be more consistent with the Copernican principle while at the same time being allowable by consistent physical laws to have galaxies flying by at $0.99999c$, allowed by some kind of reduced probability of interaction? Then matter would could uniformly occupy both $\vec{v}$ and $\vec{r}$. I have never heard this even mentioned as an issue. Why did the big bang create matter along the tapestry of the comoving coordinates? Can any physical theories be said to predict or deny this?


title: Absolute Viscosity of Water at certain temperatures

text: I just started my class on fluid mechanics. There's a problem that requires absolute viscosity $u$ of water at 25C. I looked up my table in the book and I only have it for water at 20C and 30C. I figured we had to manually calculate it in this case. The school notes only have Andrade's equation $u = D \times e^{\ B/T}$ So I've got the absolute temperature which is 25C. There is no information of what D and B are(Defined as constants). So how do I figure out the absolute viscosity at any temperature? I've looked up a table online with the value for water at 25C and it gives me the right answer, is it okay to interpolate the values of my table of 20C and 30C to find the value for 25C?


title: entropy in Information theory vs thermodynamic?

text: We Now From Information Theory That Entropy Of Functions Of A Random Variable $X$ Is Less Than Or Equal To The Entropy Of $X$. ![enter image description here](http://i.stack.imgur.com/RNkQo.jpg) Does It Break The Second Law Of Thermodynamic?


title: Dimensional analysis - the argument of functions

text: Suppose we have some function of time and space (1-D for simplicity) $G(x, t)$ which, by considering some equation relating $G$ to other quantities we know to be dimensionless. We now conclude that the argument of $G$ must be dimensionless, else we have a contradiction. So let us suppose that $G(x,t) = G(\zeta)$ for $\zeta$ being some dimensionless combination of $x$ and $t$. My question is, is there, in general, a further restriction on the form of $\zeta$? Does $\zeta$ have to be some particular dimensionless combination of $x$ and $t$, or can we just (judiciously, given what we will then do with $G$) pick any $\zeta$ that works? EDIT silly of me, $\zeta$ contains some constant to make it dimensionless. My question is, basically, is $\zeta = \lambda \frac{x}{t}$ any better than $\zeta' = \mu \frac 1{\sqrt{xt}}$, or any other $\zeta$ of this style?


title: Has anyone ever measured the one way speed of light perpendicular to the Earth at the Earth's surface?

text: 1 - Has anyone ever measured the one way speed of photons traveling perpendicular to the Earth at the Earth's surface? 2 - Given our current understanding of Physics is there any way both the upward and downward speed would not be $c$? 3 - If the measurement were made and the downward speed were found to be considerably faster than $c$, would there be any plausible explanation given our current understanding of Physics? 4 - If it hasn't been done in the past, how would one do so and how difficult would it be to make such a measurement in both the upward and downward directions with less than 1 km/s error bars? EDIT: Someone helped me find my error on another thread. Thanks again for all help.


title: Expanding two-variable function $f(x,y)$ over the complete sets $\{ g_{i}(x) \}$ and $\{ h_{j}(y) \}$

text: Quite often (see, for example, this PDF, 50 KB) when discussing the Born- Oppenheimer approximation the following assertion is made: any well-behaved function of two independent variables $f(x,y)$ can always be expanded over the complete set of functions $\\{ g_{i}(x) \\}$ and $\\{ h_{j}(y) \\}$ in the following way $$ f(x,y) = \sum\limits_{i} \sum\limits_{j} c_{ij} g_{i}(x) h_{j}(y) \, , \quad (1) $$ or by defining $$ c_{j}(x) = \sum\limits_{i} c_{ij} g_{i}(x) \, , $$ as $$ f(x,y) = \sum\limits_{j} c_{j}(x) h_{j}(y) \, . $$ Sometimes an argument in favor of the statement above is that it is equivalent to expanding a function of one variable $f(y)$ over the complete set of functions $\\{ h_{j}(y) \\}$ $$ f(y) = \sum\limits_{j} c_{j} h_{j}(y) \, , $$ with the difference that coefficients $c_{j}$ in the former case carry the $x$-dependence. For me it seems like this argument is a bit far-fetched. So my question is: **how do we know that (1) is true?** Is it a theorem, or an axiom, or something?


title: How does one find the wave velocity and the phase speed?

text: While I was studying **beats** , I tried to find a displacement function of any particle in the most generalized form. I ended up with $$y=2A\sin(\pi(t-x/v)(f_1+f_2))\cos(\pi(t-x/v)(f_1-f_2)).$$ Now, given such a function wherein you cannot compare to a general equation, how do you find the wave speed and the phase speed? And, I think, some clarification on how "group velocity" applies to such a function or phenomenon would be appreciated . PS: Can we first break down this function using Fourier analysis and then maybe simplify things a bit?


title: Will a black hole increase the speed of sound above the speed of light in this medium

text: For the sake of this question we are inside the EH and a sound wave enters from our perspective as the sound moves closer to us at the EH would it speed up. Specifically how would the extreme expansion of physical space lower the frequency of an incomming sound wave?


title: how does heat energy start to speed up a gas molecule?

text: If it was possible to place a single gas molecule in a cell and freeze it to near absolute zero. What would the molecule do as it thawed out? Would it translate the heat energy into it's electrons and nucleus into vibrations and remain where it was? Would these vibrations cause it to start bouncing off the floor until it gets enough speed to convert the heat into kinetic energy? Do gas molecules need convection to start speeding them up ( like the atmosphere), or do they translate heat into kinetic energy straight away all by themselves?


title: Electric field of a flat metal plate and a point particle

text: I'm currently studying electric potential, and I'm having trouble with one of the problems on my homework: > A) A point particle with charge $+q$ is on the x-axis at a distance $d$ from > the origin, and another point particle with charge $-q$ is on the x-axis at > a distance $-d$ from the origin. Assuming the potential is 0 at large > distances from these point particles, show that the potential is also 0 > everywhere on the $x=0$ plane. > > B) If an infinite grounded flat metal plate is on the $x=0$ plane, the > negative charge is removed, and the electric potential is 0 in the same > cases as in part (A), the potential function $V$ and the electric field > $\vec{E}$ for this part is the same as in part (A). Using this result, find > $\vec{E}$ at every point in the $x=0$ plane. For part A, I simply did $V = \frac{kq}{r} + \frac{k(-q)}{r} = 0$, since the distance from the two particles to any point on the $x=0$ plane is the same for both particles. However, this presents a problem with part B. What I found was $E = \frac{kq}{r^2} + \frac{k(-q)}{r^2} = 0$ using the same logic that I did for part A, which disagrees with the book's answer of $\frac{2kdq}{(d^2+r^2)^{3/2}}$. That looks like the formula for the electrical field of a ring, but I don't see the particular relevance here. What am I doing wrong?


title: Newton's Law of Gravitation, Gauss Law and GR

text: From One of My Unpublished Papers $$\frac{d^2 x^{\alpha}}{d\tau^2}=-\Gamma^{\alpha}_{\beta \gamma}\frac{dx^{\beta}}{d\tau}\frac{dx^{\gamma}}{d\tau} \tag{1}$$ For radial motion in Schwarzschild’s Geometry we have, $$\frac{d^2 r}{d \tau^2}=-\frac{M}{r^2}\left(1-\frac{2M}{r}\right)\left(\frac{dt}{d\tau}\right)^2+\frac{M}{r^2}\left(1-\frac{2M}{r}\right)^{-1}\left(\frac{dr}{d\tau}\right)^2\tag{2}$$ Again from radial motion, we have from Schwarzchild’s metric: $$d\tau^2=\left(1-\frac{2M}{r}\right)dt^2-\left(1-\frac{2M}{r}\right)^{-1}dr^2\tag{3}$$ Dividing both sides of (3) by $d\tau^2$ we have, $$1=\left(1-\frac{2M}{r}\right)\left(\frac{dt}{d\tau}\right)^2-\left(1-\frac{2M}{r}\right)^{-1}\left(\frac{dr}{d\tau}\right)^2\tag{4}$$ Using relation (4) in (2), after factoring out $M/r^2$ from the RHS of (2), we obtain: $$ \frac{d^2 r}{d \tau^2}=-\frac{M}{r^2}\tag{5}$$ The inverse square law should hold accurately if proper time is used. Here $r$ represents the coordinate distance along the radius. One may use the relations: $$M ~\rightarrow~ GM/c^2\qquad\text{and}\qquad\tau ~\rightarrow~ c\tau,$$ to obtain the exact "form" of the law of Gravitation. Query: Is equation (5) indicative of the fact that Gauss law may be used in the same classical _"form"_ in GR? [We may introduce a symbol $F=m\frac{d^2 r}{d\tau^2}$.]


title: How to prove that the generator of proper vertices is the Legendre transform of $W(j) = \log \frac{Z[j]}{Z[0]}$

text: I'm studying QFT from Le Bellac's book, but I can't understand very well his proof for the generator of proper vertices. Can someone give a more readable and/or understandable proof?


title: Examples of exact many-body ground state wavefunction

text: Is there any non-trivial many-body system for which the exact solution to Schrödinger's equation is known? (By non-trivial, I mean a system with particle-particle interactions.) Perhaps something like positronium, or two electrons in a box.


title: Thermodynamics of zinc chloride to zinc

text: I am trying to deposit zinc metal from zinc chloride using chemical vapor deposition. But it is thermodynamically feasible to obtain zinc from zinc chloride?


title: Why is centrifugal 'force' perpendicular to line of inertia

text: I know that centrifugal is labeled a fictitious force only arising in a rotating reference frame, but I still struggle to understand the forces at play intuitively in tethered rotating bodies. I've always been told that the reason a slingshot works is because the ball wants to go in a straight line. "Yeah cool", I've always just nodded my head but never been able to understand it really. **Intuitively why wouldn't that straight line be in the direction of acceleration - which would be the tangent line at the arc segment at release point**. The direction of acceleration is the same direction for the propagation of inertia usually!? The fact that its perpendicular really makes it look like its own force! _It appears as if inertia in one direction is instantly translated to its perpendicular!_ Also, (this might be two questions), if every force has an equal and opposite one, then why is centripetal force considered a legitimate force but its opposite (centrifugal) a fictitious force? Centripetal ALSO only occurs in a rotating reference frame right? Everything I've read about these two "forces" over the years is always included the same old catch phrases, but for some reason I can't understand it intuitively. I've seen the pictures of the boy with the ball on the string and the arrows pointing inwards for centripetal and outwards for centrifugal but to me thats just labelling an observed effect that is occurring. It doesn't explain WHYYYYY :). I've parroted off the mechanics to people many times with zero intuitive understanding as to why its all happening. Is the explanation related to inertial properties?


title: Approximation of the energy for low $T$ in the early universe

text: In Perkins `Particle Physics', to compute the baryon-antibaryon-ratio, he uses that for $Mc^2\gg kT$: $$E= Mc^2 + \frac{p^2c^2}{2m}.$$ I realize that the approximation comes from $E^2=M^2c^4 + p^2c^2$ and that it is perfectly allright in the ground of the dimension... But how can one derive this approximation? (This is example 6.1 p. 149)


title: Coupled mass spring system with damping and initial values

text: After researching through the web, I can't figure out how to express into a differential equation a coupled mass spring system with damping and initial values. Two masses and two springs, no external forces, just gravity because of vertical position. I know that $mx''+cx'+kx=f(t)$ is used for single spring systems, but it's useless on coupled systems. The values are:   * 1st spring: $k=3, c=1, x(0)=.1\text{ m}$ (initial position), $x'(0)=1\text{ m/s}$ (initial velocity)   * 2nd spring: $k=1, c=3, x(0)=-.1\text{ m, } x'(0)=0\text{ m/s}$ Both masses $=1$ I don't need a solution, I just need the differential equation to solve this system through Laplace transform. Hope someone can help this desperate man.


title: What confines atmosphere around earth?

text: Exactly the title. There needs to be a pressure to prevent gases from perpetually expanding, right? Bear with me, I'm not a physicist or studying to be one.


title: Deriving Virasoro algebra question

text: I'm reading a book _Lie groups, Lie algebras, cohomology and some applications in physics_ by Azcarraga and Izquierdo, and on page 347, when deriving the exact form of the central extension term I came to a bit which I don't understand how they got it. The algebra is given by $$[L_m,L_n]=(m-n)L_{m+n}+c_{m,n}$$ And using the Jacobi identity I get $$(m-n)c_{m+n,p}+(n-p)c_{n+p,m}+(p-m)c_{m+p,n}=0$$ If we transform the generators of the algebra, by adding a constant $b(m)$, the algebra itself won't change: $L_m\to L_m'=L_m+b(m)$. After putting that in the first expression I get $$[L_m',L_n']=(m-n)L_{m+n}'+c_{m,n}'$$ where $c_{m,n}'=c_{m,n}+c_{m,n}^{\textrm{cob}}$, and $c_{m,n}^{\textrm{cob}}=-b(m+n)(m-n)$ is the coboundary generated by $b(m)$. Now starts the part that I don't know where they got it from. They say that taking this into the account we see that, with $$b(m)=\frac{1}{m}c_{m,0},\quad m\neq 0$$ $$b(0)=\frac{1}{2}c_{1,-1}$$ we have $$c_{0,n}'=c_{0,n}+\frac{1}{n}c_{n,0}\ n=0,\quad n\neq 0$$ $$c_{1,-1}'=c_{1,-1}-\frac{1}{2}c_{1,-1}2=0$$ I get why the last one is 0 (the factors cancel each other out), but why is the $c_{0,n}'=0$? And from where do they get the relations with $b(m)$ and $b(0)$? Also, how does that come to play when they set $p=0$ in the equation for $c$ in the Jacobi identity, and getting the result $$(n+m)c_{m,n}=0$$ I have the feeling like there are some steps that were ommited. I cannot reproduce this last equation from Jacobi identity one. Any help will be appreciated.


title: How to understand the entanglement in a lattice fermion system?

text: Topological insulator is a fermion system with only _short-ranged entanglement_ , what does the _entanglement_ mean here? For example, the Hilbert space $V_s$ of a lattice $N$ spin-1/2 system is $V_s=V_1\otimes V_2\otimes...\otimes V_N$, where $V_i$ is the Hilbert space of the spin on site $i$. And the meaning of an entanglement state belongs to $V_s$ is clear — a state which can not be written as a direct product of the $N$ single spin states. Now consider a spinless fermion system lives on the same lattice as spin-1/2, in the 2nd quantization framework, the fermion operators $c_i,c_j$ on different lattices $i,j$ do not commute with each other and the Hilbert space $V_f$ of the fermion system can not be written as a direct product of $N$ single fermion Hilbert spaces. **Thus, how to understand the entanglement in this fermion system?** Mathematically, we can make a **natural** linear bijective map between $V_f$ and $V_s$, simply say, just let $\mid 0\rangle=\mid \downarrow\rangle,\mid 1\rangle=\mid \uparrow\rangle$. **Thus, can we understand the entanglement of a fermion state in $V_f$ through its corresponding spin state in $V_s$?**


title: Factors defining interaction between atoms and molecules

text: Let's say we have a stuff that consists only of hydrogen (H), then we add a single atom of oxygen (O) and they interfere - we get a water molecule where atoms are arranged in a particular way. Then we add salt (NaCl) where Na may take some O and Cl may take some H. What was described might be rough or incorrect, but I wonder what are all those factors that determine what elements interact and what molecule shape they form? Do all those factors boil down to something very basic (like atom mass, wave function, electron shells)? Is there a universal way of finding out what will be the shape (angles between atoms) and properties (electronegativity, pH, etc.) of an atom or a molecule?


title: Vacancy Generation / Annihilation Time (Relaxation Time)

text: Vacancy Generation/Annihilation Time, Recombination Time and Relaxation Time ($\tau$) are all synonymously used in atomic physics literatures. They're defined as the time that it takes for vacancies and atoms to position in steady state sites and reach a thermo-mechanical equilibrium concentration. The relaxation time for copper atoms/vacancies used in semiconductor industry is usually reported to be in order of several milliseconds. I am trying to approximate this quantity by studying the diffusion mechanism. I have made a theory (which might be completely wrong as I'm not expert in this area). Please correct me if I'm doing something wrong. Here is my theory: **Theory:** The relaxation time seems to be highly correlated to diffusivity and the lattice geometry. Thus, the vacancy relaxation time can be approximated by the following equation: $$\tau = D_v^{-1} \times A $$ where $D_v$ is the diffusion coefficient and $A$ is the area of the diffusion path that a single vacancy travels along while it diffuses. **Theorem Check:** I testified this for copper at room temperature as follows: $A \approx$ (the spacing between copper atoms) * (copper atom diameter). $A \approx 0.23 nm \times 0.256 nm = 0.2944nm^2$ (This might be very crude). hence $$\tau = D_v^{-1} \times A = \frac{1}{D_0}\exp(\frac{Ea}{kT}) \times A = \frac{1}{5.2e-5[m^2/s]} \times \\\\\exp(\frac{0.77[eV]}{8.617e-5[eV/K] \times 298.15[K]}) \times 2.944e-20 [m^2] = 5.877 ms $$ which makes totally sense [M.E. Sarycheva, Yu.V. Zhitnikova, L. Boruckib, C.-L. Liub, T.M. Makhviladze, "A new, general model for mechanical stress evolution during electromigration", Thin Solid Films Volume 365, Issue 2, 17 April 2000, Pages 211–218]. \-- I'd not be surprised if I'm wrong.


title: Why is the second the SI base unit for time?

text: Specifically, during the moves towards _Le Système international d'unités_ in the 18th and 19th centuries, why didn't anyone attempt to move us away from the definition of there being 24 hours in a day? Wikipedia informed me that the name **second** comes from the _second division_ of an hour. It also claims that the concept of having 24 hours in a day dates back at least 6000 years to the earliest Egyptian civilization. It also says the word second (as a measurement of time) didn't make it into English until the 1500's and couldn't be measured with any accuracy for 100 years. So by one way of looking at things, the base unit of time (or perhaps the grand-pappy unit of time) is the hour. Is there some convenient property of **24 hours = 1 day** that caused it to hold on over other units? I understand the significance of a degree being 1/360th of a circle (360 = 60 * 60 = (3 * 4 * 5)^2), and 24 is closely related to those factors, but that seems a flimsy reason. The math for converting earth's rotation to elapsed time doesn't even work out very conveniently (IMO) with these units. I expected to find a reason in time being one of the basic properties of the universe, being immutable (in 18th century eyes) and therefore used as a pivot point for other unit definitions. But the dependency graph of SI units mostly dispelled me of that: both temperature and mass were found to be as independent as time, and both units were redefined during this period (to Kelvins and kilograms, respectively). ![The seven SI base units and the interdependency of their definitions. Clockwise from top: kelvin \(temperature\), second \(time\), metre \(length\), kilogram \(mass\), candela \(luminous intensity\), mole \(amount of substance\) and ampere \(electric current\).](http://i.stack.imgur.com/jnGwh.png) During the same period, other units were attempted to be re-measured from new standards:   * Length was adopted to use the meter at one ten-millionth from the North Pole to the Equator in 1793   * Mass was adopted to use the gram at the cube of the hundredth part of the metre (at STP) in 1795   * Temperature was adopted to use degrees Celsius, one hundredth of the separation between boiling and freezing of water. And yet, efforts to define the second seem to center on more perfectly measuring the existing definition of 1/86,400th of the Earth's rotation. Given the predilection for base 10 (and the gradual move away from units depending on our earthly frame of reference), why was the second left at such a cumbersome, ancient interval? Why didn't we redefine a new measure of time to be (say) 1/100,000th of a day, put 10 hours in a day, etc. etc.? Did no one think to challenge the convention of 24 hours in a day? Why not? That came out a little more jumbled than it was in my head, so let me sum up: I'm mainly interested in answers addressing attempts to redefine units of time and why they didn't achieve wide adoption in the scientific community.


title: How does information about charges propagate through the electromagnetic field

text: I understand how the wave equation works, and therefore how light moves through the EMF; this question is not about that mechanism. But when a charge moves in space, information about its location travels outward at the speed of light, altering the field strength of the EMF. What is the mechanism by which this information moves? Is it _also_ the wave equation? In my classical electromagnetism texts, Maxwell's equations simply state that the information about changes in charge density/location travels through the field at the speed of light, but do not explain the mechanism.


title: Canonical transformation that contains the time as an explicit parameter

text: On the Page 385 of Goldstein's Classical Mechanics book (third edition), it starts to talk a bout the canonical transformation with time as an explicit parameter. But I don't quite under understand the following argument: > Considering a canonical transformation of the form $$\zeta(t) = > \zeta(\eta,t),$$ if the transformation $$\eta \rightarrow \zeta(t)$$ is > canonical, then so obviously is the transformation $$\eta \rightarrow > \zeta(t_0).$$ Why is the transformation $\eta \rightarrow \zeta(t_0)$ obviously a canonical transformation as well?


title: What is difference between white objects and transparent objects as far as photons are concerned?

text: Transparent materials let photons through because the energy gap of electron is so large that the photons cannot be absorbed. If the material absorbs a photon, the photon disappears; does this mean that its appearance is opaque? How about the colour white? In this case, does the material absorb photons?? Because white materials seem opaque most of the time.


title: Falling into a black hole

text: I've heard it mentioned many times that "nothing special" happens for an infalling observer who crosses the event horizon of a black hole, but I've never been completely satisfied with that statement. I've been trying to actually visualize what an infalling observer would see (from various angles), and I'd like to know if I understand things correctly. Suppose we travel near a sufficiently large black hole (say, the one in the center of the Milky Way) so that we could neglect tidal effects near the horizon, and suppose that it's an ideal Schwarzschild black hole. Suppose that I'm falling perfectly radially inward, and you remain at a safe distance (stationary with respect to the black hole). 1) If I'm **looking inward** as I fall, the event horizon will always appear to be "in front" of me, even after I've crossed the event horizon relative to you, and will continue to be "in front" of me right until I'm crushed by the singularity. This makes perfect sense (and correct me if it's wrong), but it's the following case with which I'm having the most difficulty: 2) If I'm **looking back** at you (an outside observer), what effects, if any, would I observe? My reasoning was: as I approach the event horizon, a "cosmological horizon" begins to close in around me, beyond which I can no longer observe the universe. At the point when I cross the event horizon relative to you, my cosmological horizon will have "engulfed" you, since I'm effectively traveling faster than light relative to you. Therefore, for me, the universe would redshift out of observability when I cross the event horizon. Is the above correct? I guess it can't be, if all sources say that "nothing special happens"... but I don't completely understand why. Or is the following more accurate: 2a) If I'm looking back at you, I will continue to observe you even after crossing the event horizon (until my demise at the singularity), since the light emitted by you went into the event horizon along with me, even though I can no longer communicate with you (but I have no way of knowing it). And if this is true, would you appear at all red- or blue-shifted to me? Also, if this is true, do I still have a rapidly-collapsing cosmological horizon around me (even though I can't observe it)?


title: Examining the presence of persistent domain from time series data

text: There are three variables, $X_t$, $Y_t$, and $Z_t$ that are dependent of each other, and I have the time series data of those variables from replicated experiments. The stochastic dynamics look quite persistent and repeat some patterns. Based on my subjective view, it looks like there is some weak attracting force that make the system persist but sometimes a balance is broken and the system will collapse (e.g., one of the variable becomes 0). The duration that a system persists can vary, but if good initial values are selected, they persist quite long. Is there any way to test (i.e., using the time series data) whether there is a weak attractor that allows the system to persist (although I cannot formally define what a weak attractor is)?


title: A way to determine the exact location of the Big Bang?

text: See What is our location relative to the Big Bang?, which contains the following: > _The conclusion is that the Big Bang happened everywhere, all at once._ > Phys.SE users Ali and WernerCD reached this same conclusion. Known: The most distant galaxies seem to be traveling at faster than the speed of light, but Einstein said nothing can travel faster than the speed of light. Question: Do any galaxies travel at exactly the speed of light? If so, it should be possible to determine the exact location of the Big Bang.


title: Surface UV exposure with cooler star

text: If the sun's surface was ~ 4000K (and earth closer to compensate), the UV component of the radiation would be less. However, UV makes ozone via photolysis of oxygen. Also, the stratosphere would probably start up higher (and contain less mass) because UV heating is what's responsible for the inversion. So what is the relationship between surface UV exposure (measured in DNA damage) and star temperature, which effect "wins"?


title: Parity violating Dirac particle

text: We normally write down the Dirac Lagrangian as \begin{equation} {\cal L} _D = \bar{\psi} ( i \partial _\mu \gamma ^\mu - m ) \psi \end{equation} but are the Lagrangian's, \begin{equation} \bar{\psi} ( i \partial _\mu \gamma ^\mu \gamma ^5 - m ) \psi , \quad \bar{\psi} ( i \partial _\mu \gamma ^\mu - m \gamma ^5 ) \psi , \quad {\cal L} _D = \bar{\psi} ( i \partial _\mu \gamma ^\mu \gamma ^5 - m \gamma ^5 ) \psi \end{equation} all equally as good but just don't agree with Nature? Furthermore, how would you check that the propagator is or isn't Parity invariant?


title: The speed limit is with respect to what?

text: As I understand, an object with mass cannot reach the speed of light because its (relativistic) mass increases "exponentially" as it approaches light speed. So there is a relation between mass and speed. But if speed is a relative measurement (it depends on a point of reference) how does that affect the mass?   Is the mass also relative to a point of reference?   Or is there some absolute speed (wrt some fixed point) which affects the mass of an object? **_Follow-up_** :   What I have trouble to understand is... given these two facts (I hope I got the facts right):   1. Light always moves at the same speed (independently of the inertial frame of reference)   2. The speed of a mass object is relative to a frame of reference then if an object is moving at 99.999% of light-speed for a given observer, what will a different observer see?   Will that other observer see the object moving at a different percentage of light speed?   (assuming the observers are moving at different speeds, of course)


For a while I've been trying to write a simple geometric derivation of the Lorentz transformation, based only on the second postulate. Although I'm able to successfully derive the Lorentz transformation, the geometry of that derivation is always a combination of relativistic effects (ie. Lorentz contraction and time dilation) together with observational effects related to observing an event through the medium of light. Is observation a component of the Lorentz transformation? From what I've understood previously, the Lorentz transformation has always been communicated as a transformation of space-time for a single event from one inertial frame to the same event in another inertial frame. So I'm guessing there's something wrong with the geometry that I'm deriving. Here's what it looks like: ![geometry of the Lorentz transformation](http://i.stack.imgur.com/FvGY2.png) In words, given two inertial frames (Amy and Henry), for any given photon emission event $(x_{\small{e}}, t_{\small{e}})$ from a stationary torch in Amy’s inertial frame:   * calculate where the photon from that event, travelling at the speed of light relative to Amy, intercepts Henry’s path,   * calculate where, in Henry’s time-dilated and Lorentz-contracted coordinates, a photon observed at the same point must have originated from the torch if the photon was travelling at the speed of light relative to Henry. The result is the Lorentz transformation. If it helps to find where I'm going wrong, the visualisations that I've included on the geometry of the Lorentz transformation are interactive SVG's so you can test any point you want. Thanks for any help!


title: Melting ice in a tray in space shuttle

text: We have an ice cube in a tray in a space shuttle. As the ice cube melts, the centre of mass shifts downward, so the tray should move downward to maintain the position of the centre of mass. Now, _some_ force is required to move the tray, right? Where is this force coming from? Where does it transfer energy from? And when the tray stops, where does it transfer energy to?


title: What causes the structure visible in first few milliseconds of a nuclear explosion?

text: Following on from this question, here is a high-speed photograph of a nuclear explosion, taken about 1 ms after detonation: (source) As anna v pointed out, several similar images can be seen in a Google image search for "high speed nuclear explosion photos". ![enter image description here](http://i.stack.imgur.com/IOATF.jpg) The spikes at the bottom are know as "rope tricks" - they're caused by cables being heated by the radiation. But what causes that weird-looking structure in the fireball itself? My suspicion is that the explosion at this stage is an expanding ball of air that's being ionised by the radiation coming from the nuclear chain reaction. If some regions of the surrounding air are ionised more easily due to differences in their temperature (or density or moisture content) prior to the explosion then perhaps this would explain the structure. The explosion is probably taking place in a desert, meaning that there could be quite a bit of turbulence in the ambient air due to thermal convection. However, this is just a wild guess, and I'd be interested to know if anyone has any knowledge or insight about this structure.


title: Does fluorescence produce most of the colors we see day-to-day?

text: I read the following on Wikipedia regarding fluorescence, > _Fluorescence is the emission of light by a substance that has absorbed > light or other electromagnetic radiation... The most striking examples of > fluorescence occur when the absorbed radiation is in the ultraviolet region > of the spectrum, and thus invisible to the human eye, and the emitted light > is in the visible region._ Recalling my grade-school knowledge of color perception: The colors I perceive of an object that does not produce light are those that the object does not absorb. Both those notions seem the same to me; however, I suspect that I've missed something. Is there a difference between the way that the colors we perceive of most objects is produced and the way that flourescent color is produced?


title: Why does a helium filled ballon move forward in a car when the car is accelerating?

text: I noticed that when I had a helium filled, latex ballon inside of my car, it moved forward in the cabin as I accelerated forward. The faster I accelerated forward, the faster the ballon went from the back of the car to the front of the car. The balloon didn't have a string. This became a game with my 4 year old as we drove home. We figured out where the balloon would go based on how fast I accelerated, turned corners etc. I expected that it would act a lot like the water in a cup does, but it was the total opposite it seemed. What forces caused this behavior? I assumed it has something to do with the fluid dynamics in the closed cabin, but I can't figure it out. Help?


title: Is the acceleration and deceleration of a wave instantanious?

text: When an light travels in free space, it has a velocity of propagation equal to the speed of light. However, then the light enters a medium with a refractive index of n, the velocity of propagation changes to $\ v_p = c / n $ Is this change in velocity instant? Or is there a gradual deceleration over distance, such as a ball rolling into a sand box (and acceleration when it exits the medium)?


title: What's Polarization in case of Blazars' emission?

text: It's known that the emission from Blazars is highly polarized. WHat does that mean? Is it simply another way of stating that blazars have highly collimated and beamed emission?


title: Newton's Third Law Of Motion: Earth Falling to an Apple?

text: I 'get' Newton's third law of motion, except for one thing. We know that if we let an apple fall to the Earth, the earth will fall to the apple, because the Earth must experience the same force in the opposite direction (the third law). This I cannot imagine. Is there a possibly intuitive way to explain this?


title: pure compression or pure traction?

text: I know that if we are given a stress tensor that is diagonal, the sign on the diagonal entries tell us whether we have traction or compression. Now, imagine that we are given a non diagonal stress tensor, and we wanna know the only traction and only compression directions. Those are of course the principal directions, that is, the directions given by the eigenvectors, the eigenvalues being the tensions on those directions. But i see a problem here, the eigenvectors don't define a direction because being $\vec{v}$ an eigenvector, $-\vec{v}$ is also an eigenvector. So the sign of the eigenvalues doesn't specify the directions because I don't know whether $\vec{v}$ or $-\vec{v}$ is the positive direction I am meant to take. So, in this case, how to figure out if it is pure traction or pure compression?


title: Derivation of Euler-Lagrange equations for Lagrangian with dependence on second order derivatives

text: Suppose we have a Lagrangian that depends on second-order derivatives: $$L = L(q, \dot{q}, \ddot{q})$$ If we're working on the variational problem for this Lagrangian, then I know that we'll wind up with the following Euler-Lagrange equation: $$\frac{\partial L}{\partial q} - \frac{d}{dt} \frac{\partial L}{\partial \dot{q}} + \frac{d^2}{dt^2} \frac{\partial L}{\partial \ddot{q}} = 0.$$ However, I can't see how to derive this equation. Obviously, the final term is supposed to come from integrating by parts the contribution of the $\ddot{q}$ dependence to the variation in the Lagrangian; doing that yields (writing $T$ for the period of time over which we're extremising the action): $$\int_T \frac{\partial L}{\partial \ddot{q}} \delta \ddot{q} = \left[ \frac{\partial L}{\partial \ddot{q}} \delta \dot{q} - \frac{\partial L}{\partial \ddot{q}} \delta q \right]_{\partial T} + \int_T \frac{d^2}{dt^2} \frac{\partial L}{\partial \ddot{q}}.$$ Now, the term in square brackets presumably has to vanish. The right-hand term will do so, since $\delta q$ vanishes on the boundary of $T$; but why should the left-hand term vanish? Is it just a condition of dealing with the variations for such a Lagrangian that we consider only variations for which $\delta \dot{q}$ vanishes on the boundary of integration as well? Or is there something I'm missing?


title: Coherent States of Coupled Oscillators

text: I am given the following coupled Hamiltonian $$H=\hbar\omega[a_x^\dagger a_x+a_y^\dagger a_y+1+K(a_x^\dagger a_y+a_y^\dagger a_x)]$$ Which I can decouple into two different oscillators $$H_u=\frac 12 \hbar \omega(1+K)(a_u^\dagger a_u+1)$$ $$H_v=\frac 12 \hbar \omega(1-K)(a_v^\dagger a_v+1)$$ I am then given that the system is prepared in a state $|\psi(0)\rangle=|0\rangle_x|\alpha(0)\rangle_y$ is a coherent state such that $$\langle\psi(0)|y|\psi(0)\rangle=y_0$$ $$\langle\psi(0)|p_y|\psi(0)\rangle=0$$ I find that $$\alpha(0)=y_0\sqrt{\frac{m\omega}{2\hbar}}$$ Finally, I am asked to show that each of the oscillators is in a coherent state for all time and that $\langle x(t)\rangle$ and $\langle y(t)\rangle$ act as coupled classical oscillators. I am not sure how to show that they act as coherent states. Showing the expectation values seems simple enough once I can find x and y as functions of time.


title: Relative effects of forces

text: Excuse me for my ignorance but I really couldn't find a solution. According to Einstein, every happening is possible to describe by both of interacted objects.   1. Is there any other way to describe the Big bang than the one that describes the rapid expansion of the universe?   2. I just read that Kepler's laws were proof that geocentrism is not true. But according to Einstein, gravity is reciprocal effect of two curvature of space. It is therefore relative, if we live in a heliocentric or geocentric system? Thank you.


title: Is it probable that planets will stop orbiting in ellipses?

text: I saw this video, but I had the impression that orbiting in an ellipse or a circle is quite a coincidence - it depends on how the planet got into the Solar System. Because I think that either all active forces balance in a circle, or simply all the planets with too much eccentricity burn in the Sun, or to break away from the Sun's gravitational field. Is it true?


title: Data For Quantum Entanglement

text: Is there any publicly accessible data that shows quantum entanglement empirically. I want to see what these researches are seeing that is showing them that indeed this phenomenon is real. Also, any explanation of such data would be greatly appreciated, ie. what instruments are used to measure what aspects, how to interpret the data, and what specific elements prove the phenomenon beyond any doubt or what things would have to be different in the data to falsify the claim of quantum entanglement.


title: Clarification on factors of $c$ in the Lorentz' force

text: I was told that Lorentz' force is given by $${\bf F}= q{\bf v} \times {\bf B}.$$ But I have read that it is given by $${\bf F}= \frac{q}{c}{\bf v} \times {\bf B}.$$ Why have these two relations different forms if they represent the same force? Thanks for any help!


title: Is there an upper limit to wavelength and particle size in the Mie Scattering solution?

text: I figure that Mie scattering is best for finding the scattering when the wavelengths are between 1/10th to 10x the particle diameter. However, is there an upper limit to this? If I send 2.8cm microwaves into a 10cm sphere, will it scatter according to Mie Scattering?


title: Electron in a uniform magnetic field and center of the circumference

text: I have an electron in a 3D space and there is a uniform constant magnetic field $B$, oriented according to z-axes. At $t=0$, we have $z=0$ and $\dot z =0$. I have proved that the trajectory is a circumference and that the motion is uniform. Now I have to find the center of the circumference. I have found the radius: $$R=\frac{mv}{qB}$$ And I have thought that I could find the coordinates of the center considering: $$R_x= \frac{m \dot x}{qB} \rightarrow x-x_c=\frac{m \dot x}{qB} $$ $$R_y= \frac{m \dot y}{qB} \rightarrow y-y_c=\frac{m \dot y}{qB} $$ Is it correct?


title: Homework Question involving Momentum

text: I'm trying to solve a homework problem as review for an exam I have tomorrow and I was wondering if someone could help explain it to me. It is as follows: > You are at Lowe’s shopping for bricks with your best friend. You fill your > cart and put the remaining bricks in your friend's cart. As it turns out, > your cart has twice the mass of your friend’s. In the parking lot you and > your friend do a physics experiment. Ignoring friction (and assuming the > parking lot police are not watching), > > a. if you each start from rest and push your respective carts with equal > force for 3 seconds, what is the ratio of the momentum of your car friend's > cart?   >  b. what is the ratio of the work you do on does on her/his cart during this > race **Approach for a** Let $p_1$ = my cart, $p_2$ = friend cart, where _p_ is a vector denoting momentum $\Delta p = p_f - p_i$ , $p_i$ = 0 since it's at rest $$p_1 = 2m_1v_1,\quad p_2 = m_1v_2$$ $$m_1=\frac{p_1}{2v_1}$$ $$p_2=\frac{p_1}{2v_1}v_2$$ $$\frac{p_2}{p_1} =\frac{v_2}{2v_1}$$ The answer is a 1:1 ratio but I'm not sure where to go from here to prove that answer


title: Transform torque from Euler angles to infinitesimal Cartesian rotations

text: For a certain pair of rigid bodies, I have the gradient of energy in terms of Euler angles. I want to transform this gradient to the gradient of energy in terms of rotations about the $x, y, z$ axes (the very useful gradient known as torque). Performing the analogous transformation between, say, spherical coordinates and Cartesian is easy because both form a full basis. One simply expresses the spherical coordinates in terms of Cartesian and finds the partial derivatives for each $r, \theta, \phi$ with respect to $x, y, z$ (the Jacobian). Then matrix multiplication gives the answer. But the Cartesian rotations are not a basis for full rotations! They are only a basis for infinitesimal rotations. Therefore it is not possible to take this simple chain-rule approach, because one cannot represent an arbitrary Euler angle in terms of fixed-axis $x, y, z$ rotations. I strongly suspect that this Jacobian exists, especially since this Phys.SE post seems to have found it (without stating the Euler convention or any derivation or sources, making it useless). How can I find this Jacobian?


It's possible that this question is too soft or even quite senseless for this forum, but I will ask nevertheless. Everyday (macroscopic) things, like a grandfather's pendulum clock or the grandfather himself have age, which can be determined in several (not independent) ways: 1, **testimony of birth** \- when a child is born or clock made, someone makes a dated record of this event and archives it. This is useless, however, if we are not sure that the examined person is _identical_ with the recorded one (in other words that the birth record or identity card is his). Since electrons (or atoms) are _indistinguishable_ particles, this method cannot be used. 2, **signs of aging** \- as clock or man age, various irreversible changes accumulate, and it is possible at least estimate their age. We can measure state of electron or atom, but it doesn't make sense to speak of how long ago the state (like excitation) has been changed. 3, **historical style period** \- pendulum clocks made in the 18th century look different from those made in 2013 (and there are no pendulum clocks made before Christiaan Huygens). Electron or atom created in glacial period or Triassic are the same as those created a while ago. Does it make a sense to speak about age of electron or atom?


title: Time evolution operator to find expectation value

text: I have a state $\Psi (x,0) = \sum_{n=0}^{\infty} c_{n}u_n(x)$ and want to find the expectation value of any observable A at time t, $\langle \Psi(t)|\hat{A}|\Psi(t)\rangle$. I know that I should apply the time evolution operator to find $\Psi(t)$ but am not sure how to find the expectation value when I'm not dealing with an eigenstate. I'm looking for the answer as a function of matrix elements $A_{mn} = \langle u_{m}|\hat{A}|u_{n}\rangle$. Could anyone give me some guidance? I'm a QM newbie if you haven't noticed!


title: Physical explanation for why total internal reflection occurs

text: I have been trying to understand total internal reflection (and have read several posts on this site already). Mathematically, I feel that I understand how the evanescent wave decays exponentially as it crosses a boundary surface and why there is no transmission. However, I have no intuition as to why it happens. Is there a deeper physical explanation for total internal reflection that explains what the atoms are doing?


title: Phase space in quantum mechanics and Heisenberg uncertainty principle

text: In my book about quantum mechanics they give a derivation that for one particle an area of $h$ in $2D$ phase space contains exactly one quantum mechanical state. In my book about statistical physics they do exactly the same, but now for $6D$ phase space (now one quantum mechanical state covers a volume of $h^3$). I'm not sure that I interpret this well. Does this mean that in this $6D$ volume of phase space (of $h^3$), the particle can only be in exactly one location with only one possible set of momentum vectors $p_x$, $p_y$, $p_z$ (this is how I interpret "one possible state")? If this interpretation is right, I have the following problem. Both books say that this is conform the uncertainty principle of Heisenberg, but I don't see why. It seems to me that because one can measure (f.i. in $2D$ phase space) $p_x$ and $x$ so that $∆x∆p_x = h$ and because this is exactly the surface of phase space in which there is only one state, that one has now determined exactly the position and momentum of the particle (because there is only one state in this area). Because of this I guess something is wrong with my interpretation (although it seems to match with the derivation).


title: What is a sudden singularity?

text: I've seen references to some sort of black hole (or something) referred to as a sudden singularity, but I haven't seen a short clear definition of what this is for the layman.


title: Unclear how heat interacts with Navier Stokes

text: I am playing around with an Navier stokes solver and I'm having trouble introducing heat. Am I right in thinking this would be introduced in the ${\bf f}$ term of ${\partial{\bf u}\over\partial t} = -({\bf u}\cdot\nabla){\bf u}+v\nabla^2{\bf u}+{\bf f}$? I find the lack of mass term disturbing. Please reassure me! Also, how do I calculate the force vector, given that I have computed the scalar $dQ\over dt$ from Newton's law of cooling? Or is that the wrong approach?


title: What is the symbol Å?

text: I saw this symbol like: $$\lambda=3000\overset{\circ}{\text{A}}$$ and I don't know what this means. Is it a frequency? (since $\lambda$ is usually used for frequency)


title: Why does the alcubierre drive get roasted by hawking radiation?

text: I read that an alcubierre drive would get destroyed by hawking radiation inside the warp bubble. Where does this hawking radiation come from? And why does it only happen to objects inside the bubble?


title: Why are there gapless excitations in the anti-ferromagnetic Heisenberg model while the true ground state is a singlet?

text: The true ground state of the anti ferromagnetic quantum Heisenberg Model (nearest neighbor only)is known to be a singlet (I think this is Liebs theorem.) Since a singlet is invariant under rotations, the ground state doesn't break the rotational symmetry of the Hamiltonian (which the classical Neel state does break) So Goldstone's theorem should not apply as we have not spontaneously broken any continuous symmetry in the ground state. Yet we do have anti-ferromagnetic magnons which are gapless excitations. Why do we have the gapless excitations without breaking any symmetry?


title: Clebsch-Gordan Coefficients for two spin-1 particles - Why is there a ∣0⟩∣0⟩ ket?

text: I have used the rules for addition of angular momenta to work out the Clebsch- Gordan coefficients, which all seem right except for state $\lvert0,0\rangle$: **For n = 1** \begin{align} \lvert1,1\rangle & = \frac{1}{\sqrt 2} \left( \lvert0\rangle\lvert1\rangle - \lvert1\rangle\lvert0\rangle \right) \\\ \lvert1,0\rangle & = \frac{1}{\sqrt 2} \left( \lvert-1\rangle\lvert1\rangle - \lvert1\rangle\lvert-1\rangle \right) \\\ \lvert1,-1\rangle & = \frac{1}{\sqrt 2} \left( \lvert0\rangle\lvert-1\rangle - \lvert-1\rangle\lvert0\rangle\right) \end{align} Now the state $\lvert0,0\rangle$ must be perpendicular to $\lvert1,0\rangle$ and is a linear combination of the basis kets of $\lvert1,0\rangle$: $$\lvert0,0\rangle = \frac{1}{\sqrt 2} \left(\lvert-1\rangle\lvert1\rangle + \lvert1\rangle\lvert-1\rangle\right)$$. But in the table, there is an extra ket $\lvert0\rangle\lvert0\rangle$; Why is this so? (From the table): $$\lvert0,0\rangle = \frac{1}{\sqrt 3} \left(\lvert-1\rangle\lvert1\rangle + \lvert1\rangle\lvert-1\rangle - \lvert0\rangle\lvert0\rangle\right).$$ My intuition tells me that you need to include the $\lvert0\rangle\lvert0\rangle$ state in order for the entire set of basis to be complete. But how do I show this?


title: Photoelectric Effect Problem

text: Say in a photoelectric experiment, we find a stopping potential of 1.85V for $\lambda=3000\overset{\circ}{A}$ and of 0.82V for $\lambda = 4000 \overset{\circ}{A}$.   1. How can I get the Planck's constant from the above information?   2. Determine the work function of the sodium in electron-volts.   3. Determine the threshold wavelength for sodium. For 1, I converted the wavelengths to meters, and got $3\times10^{-7}m$ and $4\times10^{-7}m$. I know these formulas: $\lambda\times c = v$, $E=hv$. How do I get the energy, is there a formula that I miss? For 2, I have no idea about how to get the work function, my professor didn't teach anything about it. Are there any good references? (And for 3 as well). Thanks for any hint and help!


title: simple explanation of chiral anomaly?

text: Can somebody provide a fairly brief explanation of what the chiral anomaly is? I have been unable to find a concise reference for this. I know QFT at the P&S level so don't be afraid to use math.


title: Pulsed Spherical Wave

text: Can somebody help show me how a pulsed spherical wave has a wavefunction of the form U(r,t) = (1/r)a(t-r/c), where a(t) is an arbitrary function, r is the radius of the spherical wave, t is time, and c is the speed of light?


title: do Higgs Bosons happen in nature all the time? Rarely? Or do they only happen when the Higgs field is excited in a particle accelerator?

text: I'm trying to reconcile an apparent contradiction between explanations given by Dr. Cox in 2009 and 2012, and those given by a panel of Berkeley professors. I'm not a physicist, and so I realize this contradiction is likely my layman misunderstanding. I appreciate your time in teaching me. Dr. Cox seems to describe, I think, the Higgs Boson as though it were just another gauge boson, i.e. one of the fundamental "force carrier" particles by which force is transmitted to other particles. Except in this case, the H.B. is not transmitting force but imparting mass. He goes on to say explicitly that Higgs Bosons exist in vast numbers all around us and are constantly bombarding all other particles at all times. It is through this bombardment that mass is gained. Is my summary and interpretation correct? If so, is his explanation accurate? My understanding was the H.B. is more or less a byproduct of the Higgs field itself, the result of its excitation, and it is interaction with the field itself, not the H.B., that endows other particles with mass. This slide from the Berkeley lecture lists the H.B. as neither a gauge boson particle, nor a matter particle, but an entirely different, third type of particle. Does the Higgs field exist because there's an abundance of H.B. particles just moving around, themselves giving rise to the Higgs field? Or does the Higgs field simply exist everywhere, and by virtue of its existence, occasionally an H.B. pops out? (Of this last point, I am certain. Several sources have directly stated that what makes the Higgs field unique is that its default energy state is nonzero, i.e. unlike the "electron field", it exists everywhere, even in a vacuum). **Do Higgs Bosons happen on their own in nature all the time?** Rarely? Or do they only happen when the field is excited under deliberate conditions, e.g. within a man-made particle accelerator? Or is my question malformed and running afoul of the wave/particle duality? A final summary of my running understanding: Consider an electron and a positron, some distance apart. They each experience an attractive force to one another, via the electromagnetic field they produce. The actual means by which this force is transmitted, the means by which the electron "knows about" the positron, is by way of a gauge boson, in this case the photon. "The photon is the mediating particle of the EM field". **You quite literally have photons moving back and forth between the electron and positron**. They serve as the actual means of transmission of force/energy/momentum transfer and exchange between the two particles. (I'm referencing some illustration I saw in a video that quite literally had an animation of photons bouncing back and forth from, in their example, nuclear protons and their orbiting electrons). I think I'm just at a loss to explain the relationship between and difference among the Higgs field and the H.B. itself. Explanations in lectures and the media seem to vary from "With respect to endowing mass, the H.B. does it all" to "The Higgs field does it all; the H.B. is just a theoretical consequence of the existence of the Higgs field; finding the H.B. is strong confirmation that the Higgs field itself exists". Thanks!


title: What is the essence of BCFW recursion techniques?

text: I have recently briefly read about new methods as the Britto-Cachazo-Feng- Witten (BCFW) on-shell recursion method.   1. Can anybody please tell me about the essence of it?    2. What does it mean for the recursion to be on-shell?    3. What happens to the vacuum?    4. What is the relation to gravity?


title: Thermal noise from capacitor; circuit analysis

text: I'm trying to model the thermal noise from a capacitor. The capacitor is connected directly into an amplifier with resistance $R_{A}$ and capacitance $C_{A}$. A noisy capacitor is modelled as a thermal noise source $V_{J}$ due to a frequency-dependent resistor $R_{J}= 1/\omega C_{J} \tan \delta$ ($\tan \delta$ is the loss tangent) in parallel with a perfect capacitor $C_{J}$. The circuit is: ![Circuit](http://i.stack.imgur.com/tivmK.png) I want to calculate $|V_{A}/V_{J}|$. First, I can combine $C_{J}$ and $C_{A}$ in parallel to get $C_{\text{eq}} = C_{A} + C_{J}$. Then I can combine the impedance of $C_{\text{eq}}$ in parallel with the impedance of $R_{A}$. Then the circuit is a voltage divider between $R_{J}$ and $R_{A}$, so the transfer function should be: $$ \left|V_{A} \right|=\frac{|V_{J}|}{\sqrt{\left(1+\frac{R_{J}}{R_{A}}\right)^2 + (C_{\text{eq}}R_{J}\omega)^2}} $$ with $V_{J} = \sqrt{4k_{B} T R_{J} \Delta f}$ at a temperature $T$. Is that right? It doesn't really agree with my data but maybe some of the measurements are wrong.


title: Running chargino/neutralino masses in MSSM

text: Consider the plot below, showing the running of different masses due to renormalization for a certain point of the (c)MSSM. I am able to exactly reproduce the plot, including the running of M1, M2, M3. However, I can't get the running values of the actual particle masses (e.g. $m(\chi^0_1)$) from the generators. I tried SoftSusy and SPheno, and in both cases the parameters shown below are calculated at the supplied scale, given in the MSOFT block of the SLHA output. The particle masses are given in the MASS block, and are independent of the scale. This is a bit confusing. I was under the impression that M1, M2, M3, ... are high-scale parameters - variables that you put into the theory at the GUT scale, and only make sense there. After all, you don't have the photino, wino, etc. as real physical mass eigenstates, you only have the mixtures. OTOH, particle masses should make sense at many scales. If you probe e.g. the $\chi^\pm_2$ at different scales of momentum transfer $Q$, you should get different masses. This plot, and the output of the spectrum generators, seem to imply the opposite: That the particle masses don't run, but that a running $M_i$ is meaningful. What's the truth? Is there a generator that can give me the running values of $m(\chi^0_1)$ etc.? Can I easily calculate them myself from the running $M_i$ and the mixing angles? What I'd like to make is a plot that shows the actual particle masses run, and eventually unify at the GUT scale to $m_{1/2}$ (or $M_i^\mathrm{GUT}$ in the non-universal case).                     ![enter image description here](http://i.stack.imgur.com/h2YuZ.png) mSUGRA: $m_0=100, m_{12}=250, \tan\beta=10, A_0=-100, \,\mathrm{sign}\,\mu=+1$,   Taken from https://softsusy.hepforge.org/


title: Physical -> Chemical -> Nuclear -> (what comes next)

text: If a splitting atoms / fusing isotopes (fission bomb, fusion bomb) yields more energy than chemical changes (TNT, et al) yields more energy than physical change (hydrogen bonds forming during water condensation), then why doesn't the trend continue BELOW the atomic level, or do physicists have no clue about that stuff yet? I know we cannot examine things more elementary than atoms, but are there any models or theories yet?


title: Consequences of destroying a space elevator

text: Suppose there is a fully functional space elevator built on Earth. The base is attached to coordinates $ (\lambda, \varphi) = (0,0) $ e.g., on the equator on the zero-meridian. What would happen if we were to suddenly remove the counterweight? At what speed would the tip hit the Earth, and at what coordinates (all approximate)? I might be missing something, but I found this scenario exceptionally difficult to model properly. I was trying to get general equations, so for arbitrary material, planet, etc. I suspect the equations involved will be quite messy, so please use abbreviations/substitutions/references to standard transformations etc. where possible. Ignore the atmosphere and any carts/stations/other masses attached to the elevator, assume spherical Earth, etc. For completeness: it is a scenario described in the Mars Trilogy, by Kim Stanley Robinson. So this is purely a pet project :)


title: ADM Hamiltonian formalism and Quantum gravity

text: is there a Hamiltonian reformultion of gravity ?=? if so if we use the usual Quantization scheme we can not we quantizy the gravity ?? in terms of a Gauge Theory with the potential $ A_{\mu}^{i} $ how can we get the Schroedinguer equation ??


title: Optical brightener in plastics?

text: Is there any way to add some type of 'optical brightener' to a PC+ABS molded part? I'm looking for something that will not affect the color / gloss. Ideally it will be a material that can be added during the molding process and only be seen by a camera with a UV light source + UV Pass filter. Does something like this exist? ![enter image description here](http://i.stack.imgur.com/MD0TQ.png)


title: Non linear QM and wave function collapse

text: I heard that there have been some propositions about describing the collapse of the wave-function by adding non-linear terms, but I couldn't anything in any any textbooks or even articles (probably those propositions never reached a good level of consistency). However, I'd like to read about it. Could someone send me a reference?


title: Optical waveguide that can displace a 4D light field

text: Has anyone invented an optical waveguide that can "pipe" a scene from one place to another unaltered? More precisely, I want to displace (and/or rotate) a 4D light field. An optical waveguide is an EM waveguide engineered to operate at visible wavelengths. A light field is a computer graphics concept that represents the RGB intensities and directions of photons in a given linear span of a 3D room. All the light in a room can be described as a 5D light field: the RGB value at each sample along 5 dimensions:   1. theta (compass bearing)   2. phi (inclination)   3. x (+x = right)   4. y (+y = down)   5. z (+z = into scene) A 5D light field sampled along a 3D linear span comes out as still a 5D light field. But a 5D light field sampled along a 2D linear span (such as the aperture of a camera, eye, or display) comes out as a 4D light field. Thus, this hypothetical "light field waveguide" could also be summarized as "the perfect periscope" or "fiber optics for images". You would be able to use one of these to, e.g. create a window between any two rooms, even if they are miles apart. Any ideas on how to make one of these? Don't say light-field-camera -> video- streaming -> light-field-display, because I'm already working on that. ;)


title: What is the advantage of AdS/CFT in studying strong coupled system comparing with the lattice method

text: I often heard AdS/CFT correspondence provides a powerful framework to study strong coupled system, which perturbation is not applicable. However, lattice method still works in non-perturbative domain. My question is, what is the advantage of AdS/CFT? Is there any example impoosible to access by lattice method (I don't mind lattice get numerical than analytic results)?


title: Can extraterrestials detect our messages?

text: We transmitted several messages to the space and listening to space for signs of intelligent life for years (SETI). Assuming they have at least the same technology we have, could they detect these messages we sent out? If not, how powerful transmitter is needed to make our word heard, let's say, from 1000 light years? Which wavelength we should use to transmit? ps: Apparently not so many ET related questions on this site, maybe I asked on the wrong site?


title: What is this shadow of the Sun on the Moon?

text: I was reading the article _Moon Phases_ on HowStuffWorks. In the picture, each moon has a dark green area which represents the shadow of the Sun. How is this shadow formed and why is this important?


title: Energy and Matter

text: I was watching a show about the big bang theory. They were saying that in the beginning all that existed was energy. After the big bang that energy transformed into matter which then started forming into different elements. How exactly does energy change into matter and at what point does this happen?


title: Canonical momentum density vs. energy-momentum tensor

text: Suppose we have a scalar field $\varphi$ with Lagrangian $$ \mathcal{L} = \frac{1}{2} \kappa \left( \frac{\partial \varphi}{\partial x} \right)^2 + \frac{1}{2} \rho \left( \frac{\partial \varphi}{\partial t} \right)^2 \,. $$ Then the canonical momentum density is $$ \pi = \frac{\partial \mathcal{L}}{\partial \dot{\varphi}} = \rho \dot{\varphi} \,.$$ Whereas the energy-momentum tensor: $$ T^\mu{}_\nu =\frac{ \partial \mathcal{L}}{\partial (\partial_\mu \varphi)} \partial_\nu \varphi - \delta^\mu_\nu \mathcal{L} $$ Has a 01 component whose interpretation (I believe) is momentum density, $$T^0{}_1 = -\rho \dot{\varphi}\varphi' \,.$$ These two quantities don't correspond; what is going on here? Thank you.


Vertical takeoff requires disposable rockets (would it a satellite rocket), which is a money loss, and also a lot of fuel, because initial velocity is zero. Also vertical takeoff seems risky, involves huge pieces of equipments, launch pads, to diminish risk. Horizontal takeoff are done with a reusable aircraft, like a modified 747. Initial velocity not being zero, there are much less risk, and the fuel spent in a 747 is much less expensive than a disposable rocket. So, Why are there more vertical takeoff than horizontal for spacecrafts?


title: Does fire create air resistance?

text: Does fire create air resistance/drag? So, for example, would it be harder to swing a flaming sword than a normal one?


title: Finding the wavelength of acoustic source underwater

text: I am currently working on a data fit assignment for my class and ran into some confusion. I will post the entire question here so you can get some background but the only question I have is with what's given. As you can see we are given a frequency (120kHz) and the diamter of the source (6cm). What I need to continue with my project is a(Radius of the source) and lambda(wavelength of the acoustic field. For a I am assuming its 3cm from what is given and for lambda I used lambda = v/f where v is 1600m/s underwater and f is 120 which resulted in lambda = 0.0133. Is this correct? ![enter image description here](http://i.stack.imgur.com/G9ddO.png)


title: Does quantum gravity entail that spacetime is emergent?

text: It is being said by some people, that quantum gravity entails that spacetime is an emergent phenomenon, and thus that the immaterial gives rise to the material. Is this what quantum graivty entails, or is this a bastardization of quantum gravity? Further, is it true what Lee Smolin says that in order to unify General Relativity and Quantum Mechanics, we are going to have to give up the notion that spacetime is the framework in which things occur. And also, Dr. Donald Hoffman says that even if Loop Quantum Gravity is wrong and String theory is wrong, spacetime is still discrete, and that means it's pixelized. Does discrete space mean something is pixelized?


title: Classical black holes?

text: * How big should the black hole be so we can consider it to be classical?    * When they claim that we can not probe shorter distances than the Planck length, can it be true?  The argument says that, doing experiments with higher energies we would create even bigger black hole. But if Quantum Mechanics is valid up to the shortest distances (don't see the reason why it shouldn't be), then, by creating the black holes the informations about interactions would be conserved on the horizon.   * Would this return us to observe larger distances again, or could there be some new things going on even at trans-planckian lengths?


title: What is the cause of noise generation at my bike helmet

text: I am looking for anexplanation of this phenomenon: ![sorry for bad drawing](http://i.stack.imgur.com/kCrBP.jpg) I was riding my bike, (not driving it, was sitting on the back seat) with the helmet on. While the glass of the helmet was intact, I could hear the sound of air striking my helmet's outer surface, but when I just opened the glass of the helmet,(just opening implies opening it by a very small measure, like few degrees), all the noise of the air was gone, and then I closed the glass the noise came back. A Few Details   1. I was sitting on the back seat, so the wind was striking my helmet on its lateral sides   2. My helmet is a very simple one--it doesn't bear the golfball-like craters, to counter friction   3. The noise was coming from all the sides of the helmet, even the back,(or it was just the sides). It was like a 3-d experience,


title: Why can't two or more objects exist at the same place at the same time?

text: Two objects with half spin would consist of the elementary particles (i.e. quarks, fermions etc.) which are waves. Therefore all objects consist of several waves. Waves can exist at the same place at the same time. Depending on whether the wave is at a trough or a crest and the amplitude, the waves either cancel each other out or amplify each other. Therefore why can't objects exist at the same place at the same time, and just cancel or amplify each other depending on whether they are at a crescent or a trough?


title: Summing over topologies

text: Sometimes in quantum cosmology, when we are thinking about 'wave functions of the universe' we have in mind some sort of formal path integral, where we include not just the variations in the dynamical fields (metric and so forth), but also possibly some sort of prescription for summing over all possible topologies. At least, that seems to be some sort of heurestic guess often encountered in the literature (Hawking et al). Now, in String theory, admittedly a different context but there is a rather well defined notion of how this works (basically as a generalization of Feynman graphs over Riemann surfaces). However I don't understand exactly how this is supposed to work in quantum cosmology exactly (say in the Wheeler-De Witt context). First of all there seems to be a massive amount of overcounting already at the metric level (where presumably one needs to mod out by all the diffeomorphisms), but how exactly does one deal with the topologies? Do they only include connected topologies? Is there even a mathematical formalism on how to even approach this problem? Any good papers that deal with this in a comprehensive way?