title: Pushing water along is it possible to calculate the angle it forms

text: If I had a static thin (a few mm) film of water lying on a surface and I tried to push a squeegee across the surface in order to move the water. Would the water rise up in front of the squeegee? Would the angle be possible to calculate if the speed were to increase and or the force of gravity were to increase?


title: Why gauge invariance for electromagnetic fields?

text: What is the physical constraint that gauge invariance is a required condition for electromagnetic fields? What would happen if the electromagnetic fields were not gauge invariant?


title: What do the latest FERMI results say about dark matter?

text: There was an announcement at a recent UCLA symposium on dark matter by the FERMI collaboration which hints at some evidence of dark matter. The results aren't yet published, but the symposium news release is here. Most of the news release is just general dark matter fluff, but it says that > One search technique involves using the vast amount of dark matter in our > galaxy. The NASA Fermi Satellite Telescope, an international collaboration > involving NASA, the Goddard Space Flight Center and the SLAC National > Accelerator Laboratory, searches for gamma rays — very high-energy light > particles — from this dark matter. > > There are models of dark matter that would allow a signal in the galactic > dark matter consistent with the claims at the meeting and provide a small > interaction consistent with the "null results" in the direct dark matter > searches all over the world. This obviously doesn't contain much information. Can anyone closer to the field expound on the findings?


title: General Relativity Paradox - Different local times of two frames a constant distance apart

text: * Suppose there is a habitable star with a significantly large mass, and thus a huge gravitation field. It has a clock on it that ticks each local second. And it also has a mirror. This is Star A.   * Suppose there is another habitable star with a much smaller mass, also with a clock, called Star B.    * Finally, suppose that these two stars somehow maintain a fixed distance between them. (Eg: the two stars have perfectly calibrated rocket thrusters pointing toward one another). Please correct me if I'm wrong: An observer on Star A looking through a telescope at clock B would see it ticking quickly. Likewise, an observer on Star B looking at the clock on Star A would see it ticking slowly. Now, suppose a person on A sends a light pulse towards B and starts a clock. They measure it takes 10 seconds for it to come back. Now, a person on B sends a pulse to A, and measures how long it takes to get back. Does it also take 10 seconds? If so, there's a pretty clear paradox. If not, how could it take light different times to travel the same distance? Thanks


title: Does the Photino have mass or is it mass-less like the photon

text: Does the photino in super-symmetry have a mass, Or is this different in different super symmetric models?


title: Realistic interpretations of quantum entanglement: Are there alternatives to the "Transactional Interpretation"?

text: Quantum entanglement bridges space and time: entangled particles show correlations independently of where and when they are measured. This is most evident in "delayed choice quantum eraser" experiments, where the outcome of single measurments _now_ depends on which measurements are done _in the future_ (though there is no retro-causality in the strict sense). I am looking for realistic interpretations which directly address this topic, i.e. discussions of underlying physical mechanisms or basic structures of the universe on which this correlations may be built. So far I found John Cramers "Transactional Interpretation" of 1986; Bohmian mechanics may also be considered. Are there other physical interpretations or philosophical papers on this topic of correlations over spacetime?


title: Flashlights and Capacitors

text: Why capacitors are used in flashlights of cameras instead of attaching the light directly to the battery? How this leads more light?


title: Solar panel maximum efficiency at specific frequency and temperature?

text: I talked to a professor about solar panels and their efficiency. It seemed that the main reason solar panels aren't that efficient is because it can only accept a single energy input size. Anything below is ignored and anything above only gives the energy of that single limit. That is, say the limit is 1W. A photon with 0.999W energy wouldn't give any voltage. A photon with 10W energy would give the same voltage as a 1W photon. Does this mean I can get very high efficiency from a light source with a specific frequency? For example a solar-powered calculator in a room with only sodium lights. How high? How does the efficiency change depending on the amount of light or the temperature of the solar cell? How about an extremely small amount of light, like 1nW, close to 0K? This could be terribly wrong as there was quite a language barrier between us. I want to learn, so please point out any misstakes.


title: Uniformity in a solenoid

text: I know the magnetic field strength increases as the number of turns in the solenoid increases. However, I've learnt the field inside the solenoid is usually nearly uniform. So, does the number of turns in the solenoid effect the uniformity of the field inside the solenoid? Does the field gets closer to uniform as the number of turns increases?


title: Personalized "anthropic principle" and many-worlds divorce between Shroedinger's cats

text: Anthropic principle, at least in laymen explanations that I have encountered so far, sounds something like "the physical universe suits us exceptionally well because among all the possibilities we, the observers, tautologically encounter the one that can support us." I was wondering whether this principle can be applied to specific observers. That is, suppose that Shroedinger performs his thought experiment with himself, rather than his cat. Would the anthropic principle imply **from Shroedinger's viewpoint** that he would always survive, at least according to many-worlds interpretation? How about this setting, assuming many-worlds interpretation: two people decided to divorce by proceeding with their lives as window&widower in separate universes. They create a setup similar with Shroedingers, except that 2 boxes have been created in such a way that a person in exactly one of them would get killed, depending how a certain superposition collapses. Then the unhappy couple enters the chambers. Does the anthropic principle imply that **each** of them would experience the exiting the chamber as the sole surviving spouse?


title: scattering matrix superccurent density of states

text: while studying scattering formula for the supercurrent (Beenakker) I encountered that the density of states for discrete and continuous spectrum can be simultaneously described by taking $\epsilon\ ->\ \epsilon + i\delta $ in the following formula: $\rho(\epsilon) = -\frac{1}{\pi}Im\frac{d}{d\epsilon}\left\\{lnDet\left[1 - S_{A}(\epsilon)S_{N}(\epsilon) \right] - \frac{1}{2}lnDet\left[S_{A}(\epsilon)S_{N}(\epsilon)\right]\right\\}$. I am wondering if one could argument this by referring to scattering theory and Green's function - eg. Laszlo Szunyogh.


title: How to show with Maxwells Equations that nonaccelerating charges dont radiate?

text: How to show with Maxwells Equations that nonaccelerating charges don't radiate?


title: Moving wedge and pulley system

text: A wedge of mass $M$ rests on a rough horizontal surface with coefficient of static friction $\mu$. The face of the wedge is a smooth plane inclined at an angle $ \alpha$ to the horizontal. A mass $m_1$ hangs from a light string which passes over a smooth peg at the upper end of the wedge and attaches to a mass $m_2$ which slides without friction on the face of the wedge. A) Find the accelerations of $ m_1, m_2 $ and the tension in the string when $ \mu $ is very large. B)Find the smallest coefficient of friction such that the wedge will remain at rest. Attempts: No specification on whether or not any of the masses $m_i$ are bigger than the others, so let us assume that $m_1$ goes down and $m_2$ goes up the slope. Then A) is fine. (a minus error in the final answer for A) is introduced if I assume the other orientation) As for B) if we consider the wedge+masses as a system, then to conserve linear momentum if the masses move as above, then the wedge must move rightwards. So the frictional force acts leftwards until the wedge slips. The only other force acting on the wedge is via the normal contact force from $m_2$. A component of this force acts to accelerate the wedge horizontally. Let's write this relative to some fixed inertial frame of reference with $x$ rightwards. Then the above recast into symbols gives $$-\mu (M+m_1+m_2)g - m_2 g \cos \alpha \sin \alpha = 0 $$ at the point of slip of the wedge. However, solving this for $\mu$ gives a negative result. Where did I go wrong? ![enter image description here](http://i.stack.imgur.com/IQBDT.png)


title: What is charge?

text: I know this isn't the right place for asking this question, but in other places the answers are so awfull.. I'm studying eletricity, so, I start seeing things like "charges", "electrons has negative charges",etc. But I didn't quite understand what charge is. I search a little bit on the internet and found it related to electromagnetic fields, then I thought "negative and positive may be associeted with the behaviour of the particle in the field, great!", but the articles about e.m. fields already presuppose "negative" and "positive" charges. In other places, I see answers relating charges to the amount of electrons/protons in an atom, but if that's right, the "negative" electron is an atom without any protons? What about the neutron? So, my questions are (1) What are charges; and (2) How a particle can "be" electrically charged. What does that really mean? Thanks for your time.


title: Origin of electric charge

text: Baryons have charges that are the result of a polynomial calculation of their building blocks (quarks)'s fractional charges. But what gives these quarks electric charges? What interactions do they have with photons? And what about leptons, like muons and electrons? How do they get their -1 charge? And then, how do positrons and anti-muons get +1 charge? Same goes for quarks: how does up-antiquarks get -2/3 charge? Or I may want to formulate my question this way: **How does any elementary particle interact with the EM-Force to get an electric charge?**


title: What is charge actually? How to define it?

text: Is charge of something for (e.g.) an electron related to electromagnetic space if it exists due to energy, due to which it may have mass? I don't know about quantum mechanics or advanced particle models. Can anyone just simply give an intuitive idea? EDIT I want to mean what actually gives electron charge if it is not assumed fundamental but result of some other physical phenomenon or it is just the quantity defined to explain physical interactions?I think now it is clear


title: Particles and their charges

text: It is always known that electrons and protons have opposite charges but what gives electrons or protons the charges they have?


title: What exactly is charge?

text: If gravity is really the bending of space/time causing objects with mass to experience acceleration, is there a similar physical meaning to 'charge' besides 'a property of matter which causes it to experience a force when placed in an electric field.' What exactly is charge?


title: Is there any theory for origination of charge?

text: We have a theory of a Higgs field that describes how a particle gets mass. Since mass and charge both are intrinsic properties of a particle, is there any similar theory for how particles get electric charge?


title: What gives an elementary particle a charge?

text: We know that proton is positive, and electron is negative. But where does come notion of negativity and positivity? Does charge come from some specific particles, or they specific order?


title: Escape velocity of satellites

text: I know that the equation for it is $$v^2 = \frac{2GM}{r},$$ and with that, the rocket should be launched at that speed. But could it go much slower spending much more fuel to escape from gravity right? Wouldn't it be easier to calculate it with energy?


title: Uncertainty relation for a photon

text: Is it possible to derive an uncertainty relation (Karolyhazy Uncertainty: http://dx.doi.org/10.1007/BF02717926) with photons? I brainstormed a bit to get the following: $$ \Delta x_0 \Delta p_0 = \frac{\hbar}2,$$ and then, $$\Delta k_0=\frac{1}{2\Delta x_0}.$$ I need to derive a relation such that $$\Delta x = (c)^a (\Delta x_0)^{1/3},$$ where $c$ is a constant and $a$ is a power term. The other symbols retain their usual meaning. How must I go about this, if it is possible?


title: Whistling on bottle tops

text: It is well known that if you blow horizontally on a bottle top it creates a sound. Pouring water to the bottle changes the pitch. I have been doing experiments on the relation between the sound's main frequency (or rather the corresponding wavelength) and the vertical distance between the bottle top and the water level. My (poor) theoretical thoughts were that by blowing on the top I create a standing wave exactly between the bottle top and the water surface, therefore the wavelength should be equal to the height of the air column. Apparently, I was wrong, but not completely -- it's not $y=x$, but rather a linear relation $y=ax+b$. I have been conducting several experiments with different bottles, and the results are: A 18cm high bottle gave me $a=5.5$ and $b=26.65$. A 21.7cm bottle gave me $a=7.94$ and $b=14.54$. A tall 32.5cm bottle resulted in $a=7.1$ and $b=34.21$. But my biggest surprise was to find a negative $b$, with a glass 19.3cm bottle (the rest were plastic), and $a=9.16$ and $b=-22.43$. Is there a plausible explanation for this phenomenon? (I didn't consider the actual shape of the bottle as I assumed a vertical standing wave will emerge. Most of the bottles are pretty constant in shape, except for the glass bottle which is closer to a cone. Looking at the signal itself one can clearly see a high energy peak at the pitch, and smaller peaks at the pitch's multiples. I noticed that the slopes are close to natural numbers or half thereof.)


title: Regularization of the Casimir effect

text: For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have on the subject is Wikipedia. Nevertheless I suspect this question is appropriate since I don't remember it being addressed in other textbooks Naively, computation of the Casimir pressure leads to infinite sums and therefore requires regularization. Several regulators can be used that yield the same answer: zeta-function, heat kernel, Gaussian, probably other too. The question is: > What is the mathematical reason all regulators yield the same answer? In physical terms it means the effect is insensitive to the detailed physics of the UV cutoff, which in realistic situation is related to the properties of the conductors used. The Wikipedia mentions that for some more complicated geometries the effect _is_ sensitive to the cutoff, so why for the classic parallel planes example it isn't? EDIT: Aaron provided a wonderful Terry Tao ref relevant to this issue. From this text is clear that the divergent sum for vacuum energy can be decomposed into a finite and an infinite part, and that the finite part doesn't depend on the choice of regulator. However, the _infinite_ part does depend on the choice of regulator (see eq 15 in Tao's text). Now, we have another parameter in the problem: the separation between the conductor planes L. What we need to show is that the infinite part doesn't depend on L. This still seams like a miracle since it should happen for all regulators. Moreover, unless I'm confused it doesn't work for the toy example of a massless scalar in 2D. For this example, all terms in the vacuum energy sum are proportional to 1/L hence the infinite part of the sum asymptotics is also proportional to 1/L. So we have a "miracle" that happens only for specific geometries and dimensions


title: How is the orientation of an electromagnetic wave determined?

text: I was looking up for how polarisers work, I understood mostly everything except the part that explains that the polariser filters everything except light that is in a certain orientation. Here are my questions. How do waves have different orientation except being either vertical or horizantal? What determines the orientation and how does that affect in absorption of the wave?


title: Going through a ring of black holes

text: Mathematician here with a speculative physical question -- feel free to boot me if the level isn't right. Suppose one finds, or builds, a constellation of several black holes arranged in a circle. (To get a stable arrangement, presumably one could put a bunch of small positively charged black holes at equal angles around a central positively charged object, or alternatively suspend uncharged black holes gravitationally in a circle surrounded by a quickly rotating ring of heavy matter). Suppose moreover that the event horizons of neighboring holes overlap -- or if there's some reason this is theoretically impossible, suppose they're really, really close to being tangent, while leaving room for light and matter to pass through the middle of this ring. (Is this possible?) My question is whether a trajectory from point A to point B that goes through the middle of the ring is causally related to one that does not. For example say a space explorer measures the spin of an electron, writes down the result and puts it in a box which he leaves at some fixed point in space (we've chosen a reference frame), then goes in a loop through the middle of the ring of black holes and comes back. When he comes back and opens the box again, will the recorded result be the same? I got this question after someone told me about quantum decoherence, and I was curious whether the world can change significantly if you go around a loop that either cannot be contracted or cannot be contracted without at some point becoming ridiculously long (where it's up to you to decide the value of "ridiculously").


title: Preventing a block from sliding on a plane (with friction)

text: Assume a small square block $m$ is sitting on a larger wedge-shaped block of mass $M$ at an upper angle $\theta$ such that the little block will slide on the big block if both are started from rest and no other forces are present. The large block is sitting on a frictionless table. The coefficient of static friction between the large and small blocks is µs. With what range of force $F$ can you push on the large block to the right such that the small block will remain motionless with respect to the large block and neither slide up nor down? This question really is not too complicated without friction acting upon the small block (Preventing a block from sliding on a frictionless inclined plane) But what happens when we add friction to the system? Why is it considered static, if at rest, the mass would slide down the plane?


title: Is the expansion accelerating or decelerating?

text: I have already asked this on Astronomy.SE but I couldn't understand the answer there. > According to Hubble's Law, the farther a galaxy is, the farther it is moving > away. But do we take into account the fact that we are actually looking in > the past? > > For example, there are two galaxies A and B at distance of 5 and 10 billion > light years respectively. Now, when we observe A we are looking at how it > was moving 5 billion years ago. The same applies for B. So, now we conclude > that 5 billion years ago space was expanding at a slower rate while it was > expanding comparatively faster 10 billion years ago. What's wrong with this > conclusion?


title: Convert constant of gravitation to days and AUs

text: I'm working on a problem with celestial bodies and for my purpose days and AUs are more appropriate units than seconds and meters. So I tried to convert the constant of gravitation, $G$, like this: $$ k= \frac{\frac{\text{AU}^3}{\text{kg}\times \text{D}^2}}{\frac{\text{m}^3}{\text{kg}\times \text{s}^2}}=(\frac{\text{AU}}{\text{m}})^3(\frac{s}{D})^2=\frac{(1.496\times 10^{-11})^3}{(24\times 60\times 60)^2}=4.485\times 10^{-43} $$ $$ G=6.673\times10^{-11}\times k = 6.673\times10^{-11}\times4.485\times 10^{-43}=2.993\times 10^{-53} $$ Now I want to do some calculations with this value. First of all, what is the orbital period of a circular orbit around the sun? $$ v_0=\sqrt{\frac{G M_\odot}{r}} $$ $$ t = \frac{2\pi r}{v_0} $$ The initial velocity has been adapted so that the centripetal force equals the force of gravitation, so the orbit will be circular. For $r=1$ I expected that the orbital period would be a couple of hundred days, since it takes about 365 days for the earth to circle the sun and one AU is the distance between the sun and the earth. However, when I do the calculation I get that $t=8.14462\times 10^{11}$. What did I do wrong?


title: What is the name and value of the constant that relates to electrons and that coincidentally has the same exact value as the speed of light?

text: There's some constant relating to electrons that also has the same value as the speed of light. What is it, what is the value, and how are they related? EDIT: Is it the fine-structure constant?? Are there any other similar constants? If you posted that answer before, you shoulda left it (to the person who deleted their answer)!


title: Does anybody know of a source that explains Wick rotation for fermions in 3-dimensional spacetime?

text: I've been looking for a long time and I've not had a lot of luck. I've found sources that **use** fermions in 3d Euclidean space but I can't find any that explain the Wick rotation from Minkowski space. This source provides a nice explanation of the Wick rotation procedure for fermions in 4d. However it leaves the odd dimensional case as an open question.


title: Will a CFL light bulb and an incandescent light bulb produce exactly the same amount of overall temperature increase over time?

text: Will a CFL light bulb and an incandescent light bulb, in separate respective closed systems, produce exactly the same amount of overall temperature increase over time? Assume you have two identical closed systems with gray walls, with a system input of 20 watts of power each. **EDIT added for clarity: (On the packaging of the CFL light bulb the large print equivalent wattage is irrelevant... the input current of both bulbs is a consistent 20 watts of power each. The comparison wattage vs. the actual wattage of the CFL is off subject.)** One has a CFL, one has an ordinary incandescent light bulb. Will both systems increase in heat the exact amount, every hour? Due to conservation of energy it shouldn't matter if one light source is more efficient, right?... it's the same amount of energy input. One light makes more heat one makes more light, but the light when it hits the gray wall is converted to heat, right? There is no such thing as loss of energy... it's just converted to another form of energy... and light is converted to heat, right? The back story of this question is my wondering that if my wife leaves an incandescent light bulb on in the winter time it's not so bad because even though no one is in the room it's still heating up the room. On the other hand if she leaves on a CFL it's more efficient but it should still add heat to our "system," i.e., our home.


title: What is the resolution to Gibb's paradox?

text: This question is essentially a duplicate of Gibbs Paradox - why should the change in entropy be zero?. The question concerns the following situation: I have some gas of identical particles and they are in a box which has been partitioned into two halves by a removable divider. Now the question is " **If I remove the divider, why should the change in entropy be 0?** " The standard answer is given in the above-linked-to question. The main idea of the answer is that the particles are supposed to be considered indistinguishible. If you treat the particles this way, you find that there is no change in entropy when the partition is removed. I understand this answer, and I suppose it should work for identical atoms, but you can easily imagine a situation where you have a collection of objects which are distinguishible, say some nanoparticles with differing numbers of constituent atoms. Furthermore, you should be able to treat a gas of identical particles as classical distinguishable bodies, and still get the right answer from statistical mechanics. I would say this is a good check of understanding of statistical mechanics. If this isn't enough motivation to come up with an alternate resolution to the paradox, consider this paradox, which requires essentially the same resolution that the gibbs paradox does: Imagine two systems initially in thermal contact and in thermal equilibrium. Now suppose they are separated. Here we might think the entropy will decrease in this process because in the initial configuration the energy of both systems were allowed to change as long as their sum remained constant. After separation, the systems' energies are fixed at some value. Clearly the set of final states is a subset of the set of initial states, so the entropy has decreased. This is the analogy of the gibbs paradox where instead of the systems exchanging particle number, they are exchanging energy. I would expect it to have essentially the same resolution. So my question is, " **Why should the change in entropy be zero, even in the particles are distinguishible?** "


title: Difference between current and voltage sources

text: I am confused about the current and voltage. My intuitive example would be that of a pipe of say water. The diameter of the pipe determines the amount of water flowing per second but the pressure is comparable to voltage. Am I right? And what is the difference between voltage source and current source? In what class our electric sockets on the wall do fall?


title: Is a vacuum needed in photoelectric effect?

text: This question was asked to me. My first thought was that electrons may ionise the air and potential difference that was applied may increase or decrease the current which should have been observed. I'd like to know whether this is the right reason or if there is any other reason which I should take into account. $$hv-w.f=hv'=eV$$ where $V$ is stopping potential , my second question is: if there isn't a vacuum will that stop potential change?


title: What is the ram-facing side of spacecraft?

text: what is the ram-facing side of a satellite? What does it mean and why is it called "ram"-facing? Thanks.


title: Why do some carbonated drinks fizz more than others?

text: Wired magazine ran an article this month on carbonation in soft drinks. If all soft drinks are manufactured effectively identically, why do some types fizz more than others? For example, root beer is always extremely fizzy (and laces well). In similar fashion, lemon-lime drinks like Sprite and Sierra Mist are very fizzy - but do not lace like root beer. Compare those to diet colas, which fizz slowly and/or minimally, and one is left to ponder. What is it about some types of drinks that make them hold and release their carbonation differently?


title: When can the source term of a partition function be put in?

text: More specifically, in quantum field theory books, we usually have this: \begin{equation} Z = \int D(\bar{\psi}, \psi) e^{-S + \int_0^\beta d\tau \sum_l [\bar{\eta}_l (\tau) \psi_l (\tau) + \bar{\psi}_l (\tau) \eta_l (\tau) ]} \hspace{10mm} (1) \end{equation} where $S = \int_0^\beta d\tau \sum_l (\bar{\psi}_l (\tau) \partial_\tau \psi_l (\tau ) +H(\bar{\psi},\psi))$ is the action, and $H$ is the Hamiltonian of the system. Can I instead start off with the Hamiltonian in diagonal form and include the source term in, say, a momentum basis? So that \begin{equation} Z = \int D(\bar{\psi}, \psi) e^{-S + \int_0^\beta d\tau \sum_k [\bar{\eta}_k (\tau) \psi_k (\tau) + \bar{\psi}_k (\tau) \eta_k (\tau) ]} \end{equation} where $S$ is now $\int_0^\beta d\tau \sum_k (\bar{\psi}_k (\tau) [\partial_\tau +\epsilon_k]\psi_k (\tau ))$. Or do I have to start off with equation (1) and apply various transformations to the Hamiltonian and the rest of the exponent until $H$ it is in a diagonal basis? - If this is the case, the resulting source term in the momentum basis could be extremely complicated after the transformations are performed. Thanks!


title: What really is a wave and how it is treated mathematically?

text: First of all, I know there's a much alike question here but this is not duplicate since I couldn't find there the answer I'm seeking. My problem is the following: I know that intuitively we have a wave when we have some quantitiy (that as I see can be anything) oscilating at each point in space. So for instance, electromagnetic waves are composed of electric and magnetic fields oscilating on each point of space. Now, this is vague and imprecise. It is not clear at first how to model this mathematically and what properties this thing should have. However there's the wave equation: $$\nabla^2 \psi = \dfrac{1}{v^2} \dfrac{\partial ^2}{\partial t^2}\psi,$$ but asking some physicists they told me that not every wave obeys that equation. That anything obeying that equation is really a wave, but that there are waves which evolve differently, some that are nonlinear and all of that. In that case it seems everything is totally vague. A wave is something that moves like a wave, some of those things obeys a certain equation and the others can obey equations totally different. In that case it becomes a little bit difficult to grasp what really is a wave and how do we treat waves with precision. So, what is a wave and how waves are preciselly dealt with in some mathematical framework?


title: Lorentz transformation via light clocks in parallel direction

text: In order to derive the Lorentz transformation one can use the picture of a light clock. A Photons bounces back and forth between two mirrors. This is then observed in two different inertial systems. If the relative speed of the inertial systems is perpendicular to the propagation direction of the photon deriving, extracting the Lorentz transformation is easy and there are hundreds of examples on the web: http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/lightclock.swf However, I am trying to calculate this scenario if the relative motion between the Inertial systems is parallel to the direction of the light propagation: ![Depiction of clock moving parallel to light propagation](http://i.stack.imgur.com/XfeMN.png) In this case I simply get for the standing observer: $T_{Periode} = \frac{2 h}{c}$ and for the moving observer: $ T_{Periode} = \frac{h + v_{rel} t}{c} + \frac{h - 2v_{rel} t}{c} = \frac{2h - v_{rel}}{c}$ I can't see how this would lead me to the Lorentz transformation.


title: Proof of centripetal acceleration formula ($a_c = \frac{v^2}{r}$) for non-uniform circular motion

text: The formula for centripetal (radial) acceleration is well known, and there exist many proofs for it: $$||a_c|| = \frac{||v||^2}{r}$$ However, all the proofs I've seen rely on the fact that it is _uniform_ circular motion and the magnitude of the tangential velocity vector does not change. For instance, take the classic proof using similar triangles — the similarity can only be established if the final tangential velocity vector and the initial one are of the same length. In addition, take this calculus based proof from Khan Academy, outlined as follows: ![Image 1](http://i.stack.imgur.com/7ysrf.png) ![Image 2](http://i.stack.imgur.com/lzHw6.png) For this proof to work, $\frac{\text{d$\theta $}}{\text{dt}}$ must be considered a constant, $\omega$, that does not depend on time. In the case of non-uniform circular motion, however, this is not always true as since there exists a tangential acceleration along with a radial one, $\omega$ must depend on time and is not necessarily a constant value. Intuitively I understand that the centripetal/radial acceleration depends only on the difference in orientation between two tangential velocity vectors, and that their magnitudes do not matter -- hence the formula intuitively holds true in the non-uniform case. However, how would you go about modifying either of the proofs presented so that they are still valid in this case? Or alternatively, is there another proof that holds valid even when there exists tangential acceleration? * * * As per the suggestion of one of the answers, I let $\omega$ vary with time and took its derivative as $\alpha(t)$. This is my work so far. Unfortunately, I am stuck after the last step. $$\overset{\rightharpoonup }{p}(t)=r \cos (\theta (t))\cdot\hat{i}+r \sin (\theta (t))\cdot\hat{j}$$ $$\overset{\rightharpoonup }{v}(t)=-r \sin (\theta (t))\cdot\omega(t)\cdot\hat{i}+r \cos (\theta (t))\cdot\omega(t)\cdot\hat{j}$$ $$\overset{\rightharpoonup }{a}(t)=(-rcos(\theta(t))\cdot\omega(t)^2 - rsin(\theta(t))\cdot\alpha(t))\hat{i} + (-rsin(\theta(t))\cdot\omega(t)^2 + rcos(\theta(t))\cdot\alpha(t))\hat{j}$$ > From here on, $\theta(t)$ is represented as just $\theta$ for brevity and > clarity $$\overset{\rightharpoonup }{a}(t)= -\omega(t)^2(rcos\theta\cdot\hat{i} + rsin\theta\cdot\hat{j}) -\alpha(t)(rsin\theta\cdot\hat{i} - rcos\theta\cdot\hat{j})$$


title: Most ideal Black-body!

text: According to the definition of Black-body, it absorbs all of the wavelength irradiates on it. A recent material absorbs 96.4% visible light rays. Therefore , can we say that it is the most closest (ideal) blackbody?


title: Torque And Moment Of Inertia

text: I am reading the two concepts mentioned in the title. According to the definition of torque and moment of inertia, it would appear that if I pushed on a door, with the axis of rotation centered about its hinges, at the door- knob, it would be difficult, relative to me applying a force nearer to the hinges. However, I just experimented with my front door, and it would appear to be the converse, what am I misunderstanding? Definition of torque: $\tau=r\times\vec{F}$, where r is the length of the lever arm (the distance from the axis of rotation to the point of application of the force). EDIT: Also, what does it mean for torque to be perpendicular to the rotation?


title: How do we know that some radioactive materials have a half life of millions or even billions of years?

text: If a radioactive material takes a very long time to decay, how is its half life measured or calculated? Do we have to actually observe the radioactive material for a very long time to extrapolate its half life?


title: Why do some metal containers not conduct heat, while some do?

text: Some metal containers such as the Nissan Thermos ones, even if 100 C water is filled inside, the container is still cold to the touch on the outside. It won't be even warm: ![enter image description here](http://i.stack.imgur.com/E3Cbs.jpg) At the same time, some that look similar are so hot on the outside that holding it for a couple of seconds won't be possible: ![enter image description here](http://i.stack.imgur.com/gg9pq.jpg) Also, some teapot at Chinese restaurant or Vietnamese Restaurant, it can be boiling hot water inside, but the handle is also cold to the touch: ![enter image description here](http://i.stack.imgur.com/mc5il.jpg) The question is, for the Nissan one and the ones at Chinese restaurants, if the metal part is all connected, from where the liquid is, to the part that the hand can touch, why isn't the handle or outside too hot to hold, but can be not much different from room temperature? (the Nissan one is vacuum inside, but the metal container part is all part of a single piece.)


title: Why does my natural whistle have a maximum volume

text: When I whistle, I find that I can vary the volume by pushing more or less air through my mouth at once. However, when I increase volume past a point, I start to hear a blend of rushing air and a faint whistle sound. Why? Is the air just subtly pushing my lips out of shape, or is there some other maximum (such as size/shape of my mouth) that I'm encountering? Is there any adjustment I can make after I cross this point to continue whistling louder? **EDIT** Why is it possible for people to whistle louder with their fingers in their mouth?


title: Does a flame produce free electrons?

text: > **Possible Duplicate:**   >  Does Fire Conduct Electricity? Why?   >  Is fire plasma? Does a flame produce free electrons ? Or is the answer sometimes depending on the chemicals ? Does the answer depend on the exact heat ? Does a (strong) magnet influence a flame ? Can that be seen ?


title: Regarding the 'Arrow of Time'

text: I read according to 'Newtonian' Mechanics any set of physical activity of particles can be reversed ( I think) so a set of complicated dynamic systems of particles and matter can reverse their 'behaviour'. Yet a Star collapsing towards a 'Black Hole' will probably not 'stop' and reverse it's behaviour. So could Gravity be considered part of the 'Arrow of Time'? Since entropy is part of this 'Arrow' could entropy have 'qualities similar to the qualities of Gravity?


title: Poisson brackets: prove that they are canonical invariants

text: **EDIT** : I haven't forgotten to accept answer, the question is still open.. * * * I need a clarification about Poisson brackets. I'm studying on Goldstein's Classical Mechanics (1 ed.). Goldstein proves that Poisson brackets are canonical invariants for any functions F and G. But there is a step that I can't understand. After some steps, he says that: $$ \tag{1} [F, G]_q,_p = \sum_k ( \frac { \partial G}{\partial Q_k} [F,Q_k]_q, _p +\frac {\partial G}{\partial P_k}[F, P_k]_q, _p)$$ After other steps, he writes: $$ \tag{2}[F,Q_k]= - \frac {\partial F}{\partial P_k}$$. and $$ \tag{3}[P_k, F]_q, _p = \sum_j \frac {\partial F}{\partial Q_j} [P_k, Q_j] + \sum_j \frac {\partial F}{\partial P_j}[P_k, P_j]$$ -> $$ \tag {4} [F,P_k]=\frac {\partial F}{\partial Q_k}$$ and now he replaces these relations in the first expression I have written, obtaining: $$\tag {5}[F, G]_q, _p=[F, G]_Q, _P$$ Why does he obtain in the second last step $\frac {\partial F}{\partial Q_k}$ and not $-\frac {\partial F}{\partial Q_k}$? $[P_k, F]=-[F, P_k]$ isn't it? **EDIT** : Golstein starts from (1) and substituites $Q_k$ to $F$ and $F$ to $G$ and so he obtains (2). Then he substitutes $P_k$ to $F$ and $F$ to $G$ and obtains (3). Immediately after he writes (4), that according to me is opposite to (3). And so I have thought to a printing error. I have tried to substitute $-P_k$ to $F$ and I have obtained $$[-P_k, F]=\frac {\partial F}{\partial Q_k}$$ Then, as $[-P_k, F]=[F,P_k]$, I can say that $$ [F,P_k]=\frac {\partial F}{\partial Q_k}$$. And so I can obtain (5). Could you confirm that my argumentation is correct? Many thanks


title: Derivation of the self gravitational potential energy of a sphere

text: I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 nested integrals (3 for each particle $dm$ and 3 for integrating the potential energy for all other particles).


title: Thermal Velocity

text: What is thermal velocity? What is it's physical significance? Wikipedia says: > The thermal velocity or thermal speed is a typical velocity of the thermal > motion of particles which make up a gas, liquid, etc. Thus, indirectly, > thermal velocity is a measure of temperature. But I cannot understand and comprehend it.


title: Can exhaust gases be diverted to other cylinders during engine operation?

text: Here's a description of new combustion engine improvement by Mazda, called SkyActive-G. They claim that in a "generic" engine... > when the exhaust manifold is short, the high pressure wave from the gas > emerging immediately after cylinder No. 3’s exhaust valves open, for > example, arrives at cylinder No.1 as it finishes its exhaust stroke and > enters its intake stroke. As a result, exhaust gas which has just moved out > of the cylinder is forced back inside the combustion chamber, increasing the > amount of hot residual gas I always though, that exhaust manifold and intake manifold are separated, so exhaust gases just can't possibly enter other cylinders combustion chambers as described in the above quoted text. Can exhaust gases be diverted into other cylinders as claimed in that text?


title: Meaning of instantaneous probability densities in time dependent wavefunctions

text: For a time dependent wavefunction, are the instantaneous probability densities meaningful? (The question applies for instances or more generally short lengths of time that are not multiples of the period.) What experiment could demonstrate the existence of a time dependent probability density? Can an isolated system be described by a time dependent wavefunction? How would this not violate conservation of energy? I see the meaning of the time averaged probability density. Is the time dependence just a statistical construct?


title: Effect of incoming force on linear vs. angular velocity

text: First of all, I should note that I'm a programmer and have only an extremely basic understanding of physics; I only know how to explain my question in layman's terms and I apologize if I'm unclear or unnecessarily verbose. If there's a rigid square object of size 1x1 and mass 1 on a two-dimensional frictionless plane, and while stationery it is struck by a force of strength 1 at exactly halfway along one of its sides from directly perpendicular to said side, like so: ![a picture of a square being struck by a force perpendicular to one of its sides](http://i.stack.imgur.com/f8Pp0.png) then my intuitive understanding is that it will begin traveling at a speed of 1 in the direction of the force. Similarly, if it is struck exactly on a corner by a force of strength 1 that is exactly perpendicular to the square's diagonal (at a 45* angle to its side), like so: ![a picture of a square being struck by a force hitting it on the corner](http://i.stack.imgur.com/bQF8O.png) then my intuitive understanding is that it will begin spinning (I don't know how fast) but remain stationery. What I don't know is how to work out what will happen if it is struck at any other point or from any other angle. For example, if struck three-quarters of the way down a side at an angle perpendicular to the side, like so: ![a picture of  a square being struck by a force partway down one of its sides](http://i.stack.imgur.com/4qvUk.png) It seems as though it should cause it to begin moving (in some direction, at some speed) and spinning (at some speed), and the less perpendicular to the square's center of gravity the force is, the more it will spin and the less it will move. Is there a formula that, given the magnitude, angle, and impact point of the force, exactly how fast it will spin vs. how fast and in what direction it will move? More generally, how does one work out the answer to this sort of problem when applied to objects of other shapes/sizes/masses when impacted by other forces? Does it make a difference if the object is already moving or spinning? (Also, are any of my intuitive understandings actually entirely incorrect?)


title: How does relativity lead to multi particles in Dirac and QFT, exactly

text: I have asked this question before on other forums, but only got the classical answer of the impossibility of the probability interpretation for single particle in QFT. Now, there seems to be also doubt in multi particle interpretation of the Dirac "sea". while in QFT the multi particle seems to be the result of promoting the wavefunction to an operator. And some people claimed it is a multi picture of a single particle. So, is there any clearer explanation?


title: Is the structural similarity between atoms ( smallest) and universe (biggest) a conincidence. Or there can a reason for this beyond imaginations

text: Is the structural similarity between atoms ( smallest) and universe (biggest) a coincidence? Or there can a reason for this beyond imaginations? It seems like, if one starts travelling out from atoms... and grows bigger and bigger, one ends in a similar structure somewhere in the universe. Kind of a circular ring. PS: By structural similarity I mean : single nucleus and electrons revolving around in an atom, is structurally similar to planets revolving around the sun.


title: In MSSM, are the higgs fields eaten by Z,W scalars or pseudoscalars?

text: I am very puzzled by the quintet of Higgs bosons in the MSSM: two charged, two scalars and a pseudoscalar. I wonder if they could be understood better if they were considered jointly with the three "bosons" that are "eaten" by the Higgs mechanism. For instance, if they were two charged bosons and a pseudoscalar one, then the whole set should be four charged, two pseudoscalars and two scalars, which seems more sensible if you wish, for instance, reorder them into chiral and dirac supermultiplets jointly with the higgsinos. I have been reminded of this question because it seems that now LHC is trying to guess if the discovered Higgs boson is a pseudoscalar or an scalar, and they are doing this by looking how it couples to ZZ, if it is to transversal or to longitudinal modes.


title: Computational Science involve programming?

text: I read what is computational science in Wikipedia but the explanation and understanding are not very clear. So, I could you please give a simple example computational science project and what all basic skills a person should have? Also,   1. Does computational science involves programming?   2. How different are computational science and computational materials science?   3. I am from Electrical and Computer Science (basically programming) background. I was assigned a computational materials science project. So, is it in my scope? Probably, the prof assigned based on what individual subjects I studied (Engineering Math, Engineering Physics, Engineering Chemistry, Probability, Programming).


title: Yang Mills Hamiltonian: why do we use the Weyl's temporal gauge?

text: Do you know why in the quantization of SU(2) Yang Mills Gauge Theory, it is always chosen the Weyl (temporal) gauge to derive the Hamiltonian? Is it possible to fix another gauge?


title: Tensor Product of two doublets

text: What will be the tensor product of two doublets $$ (x_1,x_2) ~\text{and}~ (y_1,y_2)? $$ I am very much confused in determining this.


title: Electron-hole symmetry in H and He

text: I'm contemplating particle-hole symmetry, and as an example I am looking at either an electron moving along a hypothetical lattice of hydrogen ions, or a hole moving along a hypothetical lattice of helium atoms. According to some lecture notes I found, the hopping integral I get when I treat this in a tight-binding ansatz is positive for holes and negative for electrons, and now I want to see why this is so. For electrons, I can understand the result: The atomic wavefunctions are just the 1s hydrogen wavefunctions, and they are positive everywhere, so the matrix element with the kinetic energy operator gives something negative. Now, for holes I am not sure how I would have to proceed. Can I just say that the relevant Hamiltonian for holes is the negative of the Hamiltonian for electrons because, after all, a hole with energy $E$ would be an electron with energy $-E$ missing? Of, if that's wrong, how would I come to the conclusion that the hopping integral for electrons is negative and for holes it's positive?


title: Software for simulating supersonic aerodynamics

text: Could you please suggest the software, where I can load my 3D model and see how it behave on various conditions (speed - preferably including supersonic, temperature, pressure)? Both free & commercial variants are interesting.


title: Direction vector of a physical quantity matrix

text: A physical quantity can be represented by the following form: $A = a_1\sigma_1 + a_2\sigma_2 + a_3\sigma_3$ where $\sigma$ matrices are Pauli matrices. Also suppose that there is $B = b_1\Sigma_1 + b_2\Sigma_2 + b_3\Sigma_3$. A. I read that $a_1,a_2,a_3$ are direction vectors, and when the sum of A's representing real quantity and B's is zero, as each quantity can only be 1 or -1, probability $AB$ being 1 or -1 depend on the value of $-a_1b_1 - a_2b_2 - a_3b_3$. The question would be: isn't $a_1,a_2.., b_1,b_2,..$ only direction vectors? If so, how can probability of finding $AB$ being 1 change? I do get this mathematically, but I am unable to picture the situation with $a,b$ being direction vectors. B. I read that when the sum of A's representing real quantity and B's is zero, determining a value on one direction of $A$ set the value of the whole $A$. Is this true? Can anyone explain this?


title: Area covered by particle between it's path and horizontal lines

text: > **Question:** The maximum range of projectile is $R$ and the maximum height > attained by the particle is _H_. > > If the area covered by the particle between its path and horizontal line is > $A$, then $A$ = > >   1. $\frac{2}{5}$ > >   2. $\frac{2}{3}$ > >   3. $\frac{4}{5}$ > >   4. $\frac{1}{3}$ > > I know the formula for maximum range $R$ and maximum height $H$ $R=\frac{U^2}{g}$, $U$ is initial veocity and $g$ is acceleration due to gravity $$H=\frac{U^2 \sin^2\theta}{2g}$$ I can't find the way to realte this formula with the question.


title: How to weigh your nephew

text: My nephew is 3 and weighs around 30 pounds I am guessing. However, I would like to weigh him at home. I have kitchen scales, one flat one that goes up 1kg and one that looks like this picture that goes up to 5kg. ![enter image description here](http://i.stack.imgur.com/u3rsam.jpg) What is a safe and practical way I can weigh my nephew at home?


title: Microscopic understanding of Brewster angle

text: The textbook explanation is that, at Brewster's angle, the electric dipoles excited by the incident light can't reradiate to the reflection direction since it's aligned with the dipole moments. Is there a deeper understanding of the microscopic physics picture? For example, is there an actual calculation of these electric dipoles induced by the near field?


title: Does dark energy annihilate energy?

text: Antimatter and matter particles annihilate. But does dark energy annihilate energy? We consider energy to be photons, and such, correct? So when we say energy, we're actually talking about some bosons, right? So photons and anti-photons would annihilate, gluons and anti-gluons. I am not sure if anti-bosons are hypothesized so please forgive. I am amateur to this.


title: Bound states in 1D & 2D

text: Why does Mother Nature allow bound states in arbitrarily weak attractive potential in 2D but not in 3D? See, for example, this article: http://scitation.aip.org/content/aip/journal/jmp/44/2/10.1063/1.1532538


title: Is there any way to distinguish experimentally gauge mediation from gravity mediation in an unambiguous way?

text: There are lots of models of gravity mediated SUSY breaking with various spectra as well as various general gauge mediation models. Are there any "smoking gun" experimental singnatures that could definitely distinguish between the two scenarios? Would this be possible to do at the LHC or would we need an ILC-type machine to do that?


title: Why is high temperature superconductivity so hard to solve?

text: The phenomenon of high temperature superconductivity has been known for decades, particularly layered cuprate superconductors. We know the precise lattice structure of the materials. We know the band theory of electrons and how electronic orbitals mix. But yet, theoreticians still haven't solved high Tc superconductivity yet. What is the obstacle to solving it? What are we missing?


title: Is string theory over a time varying background a conformal field theory to all orders in perturbation theory?

text: When computing the first order perturbative corrections to string theory over a curved background, we find the background has to be Ricci-flat if the dilaton is constant and we have no fluxes. Such is the case for Calabi-Yau compactifications. However, to fourth order in perturbation theory, we find nonzero contributions to the beta function. But this can be resolved by perturbative modifications to the background metric which cancels the beta function order by order in perturbation theory. Does this procedure work for a generic time-varying background which is Ricci- flat to first order in perturbation theory? If not, does that tell us we can't apply first quantized string theory to such backgrounds?


title: Are there string backgrounds which can't be described by first quantized string theory?

text: In the strong coupling limit of type IIA and heterotic E8 string theory, we get 11 dimensional M-theory in which we have no strings. Instead, we have M2 branes. Are there any other backgrounds in string theory which can't be described by first quantized string theory?


title: Effects of EMP in superconductor-based devices/equipment?

text: What are possible effects of electromagnetic pulse / EMP on superconductor- based devices/equimpent/transportation? Are they resilient or more sensitive to EMP?


title: Friction between atoms in spring

text: if i doing experiment on spring-mass system in vaccum,if i pull the to some extent (within elastic limit of spring) & let it go,will the system oscillate indefinitely? (neglect contact frictions at support of wall,spring-mass connections),if not tell the reason? hint :there is no posiibility to loss of sound because there is no medium(vaccum) is there any friction between atoms/molecules of spring during continuous extension & contraction of spring, if it so tell the answer in atomic perspective..please help me


title: Acceleration of table tennis racket

text: I can't find any numbers about table tennis. What accelerations occur during a forehand smash for example? Thanks in advance & kind regards, Hans


title: picture of newtonian gravity and black hole

text: ![Picture of gravity](http://i.stack.imgur.com/Vl3a6.jpg) We assume that the earth planet is a black hole. When a light beam is fired. The only way that even light can move is A and B which means this is impossible that light move on other ways C, D, E Isn't it true?


title: How much energy is consumed by a aircraft to maintain a speed of sound?

text: Let's assume that the aircraft is 1000kg and it is flying in a air density of 1.225kg/m^3 at the speed of sound in air. Just how much energy does it require per second to maintain flying at this speed.(Please make other necessary assumptions.) Thank you.


title: Force-Weight Pinewood Derby Car

text: Force-Weight Pinewood Derby Car. I'm trying to make a fast derby car. I was wondering if I could make a car that can drop/eject weight once it comes off of the incline. Would that increase speed or would it make it slower?


title: Conservation Vs Non-conservation Forms of conservation Equations

text: I understand mathematically how one can obtain the conservation equations in both the conservative $${\partial\rho\over\partial t}+\nabla\cdot(\rho \textbf{u})=0$$ $${\partial\rho{\textbf{u}}\over\partial t}+\nabla\cdot(\rho \textbf{u})\textbf{u}+\nabla p=0$$ $${\partial E\over\partial t}+\nabla\cdot(\textbf{u}(E+p))=0$$ and non-conservative forms. However, I am still confused, why do we call them conservative and non-conservative forms? can any one explain from a physical and mathematical point of view? Many off-site threads deal with this question (here and here), but none of them provides a good enough answer for me! If any one can provide some hints, I will be very grateful.


title: Liquid analog of the Black Hole (Part 2)

text: Similar question has been asked but did no get good answers. We know that black hole can confine light, but can we create an ocean black hole - which can confine surface water waves or sound waves in water? Definition:   * What is a static water flow which can CONFINE water waves?   * Is there a configuration confining only surface waves?   * Is there a configuration confining volume waves? Description: Inside a confined region any water density perturbations can not propagate outside. PS:   * Overall volume of water in the "tank" can not change so the solution when the water is removed faster then the waves travel is ruled out.   * There possibly can be additional objects presented in the water "tank".   * It can be some unsual liquid or gas, whith additional "new" properties. Thanks for your answers.


title: Nonlinear waves superposition

text: Non-linear waves do not superimpose to each other, but why? What characteristics give this property?


title: 2 Nucleon Potential

text: I am looking at a 2 Nucleon potential of the form $$V(r)=V_0(r)[a+bI_1\cdot I_2]$$ Where a and b are constants. $I_1,I_2$ are isospins. $V_0(r)$ is of the square well form. My goal is to find an equality for a and b, given that deuteron exists, and that diproton and dineutrons do not. My approach has been the following: 2 nucleons can either be in an isosinglet or an isotriplet. The Isosinglet has I=0 and is the following: $$|00\rangle=\frac{1}{\sqrt2}(pn-np),I_1\cdot I_2=-\frac34$$ The isotriplet has I=1 and $$|11\rangle=pp,I_1\cdot I_2=\frac12$$ $$|10\rangle=\frac{1}{\sqrt2}(pn+np),I_1\cdot I_2=\frac12$$ $$|1-1\rangle=nn,I_1\cdot I_2=\frac12$$ So I get the following equations based on V $$\text{Isosinglet: }\frac{V(r)}{V_0(r)}=a-\frac34 b$$ $$\text{Isotriplet: }\frac{V(r)}{V_0(r)}=a+\frac12 b$$ Now I am supposed to use the fact that $V_0(r)$ is of the square well form to create inequalities, but I am unsure of where the inequalities come from.


title: Is light slower when traveling inside a gravity field?

text: This question is not about phase velocity changed which causes refraction, but about the real time itself being slower by the gravity of any object (from general relativity). If so, would this mean any light traveling inside a glass would be slower than in the air because it is directly affected by gravity of glass? Does this effect also contribute to refraction? How much this effect cause the light to slow down?


title: Two problems with free body diagrams. Contradictions (solutions are provided)

text: This problem is similar, but also different question from my previous question. They are both unfortunately long. **Problem/Solution #1** ![](http://img215.imageshack.us/img215/6696/problem2f.jpg)! ![](http://img59.imageshack.us/img59/4281/sol2pp.jpg)! **Quick Concept Check** a) Could someone briefly explain to me why the block on top can accelerate, but the one hanging on the pulley does not? **Problem/Solution #2** Consider the set up below. What is the minimum force required so that the 3kg block remains on the 8kg block? Given that the coefficient of static friction between the blocks is 0.8 and the coefficient of kinetic friction between the 8kg block and the surface is 0.4. ![](http://img714.imageshack.us/img714/1299/contr.jpg)! ![](http://img163.imageshack.us/img163/5941/contrd.jpg)! $\sum F_x' = F - (N' + \mu_k n) = 8a$ $\sum F_y' = n = (8g + \mu_ s N)$ $\sum F_x = N' = 3a$ $\sum F_y = \mu_s N = 3g$ Solving the systems of equations above, you should get that $F_{min} = 11g(\mu_k + \frac{1}{\mu_s}) = 177.87N$ **Point of the question and why the heck is this so long** Notice how the 3kg block is actually "attached" tot he 8kg block, yet the solution here didn't include it in its free-body diagram and they even included the reaction force from the 3kg on the 8kg. Compared with the cart problem where the hanging mass is also touching the cart, no reaction force was drawn and they even treated the three mass as a single mass. David explained this to me last night and I thought I got it, but I went to bed and started thinking about it and it became even more confusing! Could you have solved the first problem with the cart WITHOUT taking all three mass into the cart's free body diagram? Is there another way of applying Newton's Second Law to the cart problem?


title: How will you measure speed in km/hr in space?

text: How is the speed of an object in space measured? Also more importantly how do you measure your own speed in space? On the road we use a speedometer which tells us the speed easily. How is it done in space?


title: When was the earliest understanding that the stars were similar to the Sun?

text: When did astronomers realise that the stars were similar to the Sun? I'm not asking for when this was established, but when also the hypothesis was first proposed.


title: wavefunction collapse and uncertainty principle

text: 1. We all know that wavefunction collapse when it is observed. Uncertainty principle states that $\sigma_x \sigma_p \geq \frac {\hbar}{2}$. When wavefunction collapse, doesn't $\sigma_x$ become $0$?, as we will know the location of the particle. Or does standard deviation just become smaller?   2. After collapse occurs, what happens to the particle? Does the particle resurrect into a wavefunction form?   3. What can be an observer that triggers wavefunction collapse? (electron wavefunction does not collapse when meeting with electrons; but some macroscopic objects seem to become observers....)   4. What happens to the energy of a particle/wave packet after the collapse?


title: Centrifugal force for non uniform circular motion

text: If a body is under non-uniform circular motion, will it experience or will there be any impact of centrifugal force on the body upon eliminating the centripetal force? update-sorry.the title of question was incorrect.


title: how to determine direction of gyroscopic couple on car?

text: How can I determine the direction of the force acting due to gyroscopic couple on a car's wheels when it is taking a turn to it's left side?


title: The stability of D-Brane

text: In "String Theory and M-Theory: a modern introduction" by K.Becker, M. Becker and J.H.Schwarz, they say that BPS D-brane is stable as it preserves half of the Supersymmetry. I really want to understand more about this statement and see detail calculations. What is the mechanism of D-brane stability? Is there any derivation for the instability of space-filling D-brane (so that open string tachyon will be eliminated from the theory)? Thank you.


title: Temperature of rod if end points are different temperature

text: How does the temperature vary along the length of the rod if its both ends are at different temperature. As an example, consider the problem: > 20 cm long rod has rod at one end 100 ºC and another end at 0 ºC. Find the > temperature at the center of the rod when it's in thermal steady state.


title: What causes light to move through a vacuum

text: I was looking at rockets and stuff and thought about how they move through a vacuum using newtons 3rd law, and then I started thinking of any other ways you could move through a vacuum without using this and then I thought about the photon. I then thought how does the photon move through a vacuum? So I searched it online and couldn't find an answer. So my question is simply how does a photon move through a vacuum? Is it because its massless? Is it because it is thrown from an electron or whatever like a rock from a slingshot? Or is it something completely different? I'm very curious!


title: Question Based On Galileo's Law Of Falling Bodies

text: Galileo discovered that the distance fallen is proportional to the square of the time it has been falling.Why is it proportional to the square of the time and not just time? i.e $d \propto t^2$ why not just $d \propto t$ I know this question involves some common sense which i'am not able to use for some reason!


title: can we calculate velocity of a spinning apparatus by just analysing the frequency of sound emitted by it

text: I have used a new term spinning apparatus as I was unable to name it. I have tied a thread to a stone and was spinning it and I heard a sound something like that of a rotating propellor of a helicopter and then this idea stuck my mind can i calculate it? if yes then how can any one suggest me something and also if any extra information any one needs regarding that apparatus feel free to comment


title: Is the electrostatic field inside of any closed, uniformly charged surface zero?

text: We know that a simple application of Gauss's law tells us that the field inside of a uniformly charged spherical shell is zero. Does this hold for all uniformly charged closed surfaces? If so, how could we prove this? Or does it hold only for certain shapes?


title: How do you levitate a foam rock? ('Endless Second' artwork)

text: I saw this in an art museum: ![Floating Rock](http://i.stack.imgur.com/LLO24.jpg) How is this possible? The materials used to make this were foam, wood, stone dust, paint, electromagnets, and metal. I would like to know how this was make and how I could make something similar. Thank You.


title: non-exotic traversable wormholes and string theory

text: In this article it is claimed that certain type of string theory called EGBd allows for traversable wormhole solutions that do not require exotic matter. What is this EGBd model and how it fits in the grand scheme of things of string theory? is this fringe science or is serious? (i know that there might be fringe authors in ArXiv). But my main concern is how general or realistic is this result?


title: This Expansion-of-the-Universe-Diagram Confuses Me

text: The following blue-cone Wikipedia diagram confuses me. ![](http://upload.wikimedia.org/wikipedia/commons/3/32/Embedded_LambdaCDM_geometry.png) At any point of cosmological time the encircling horizontal lines in the diagram are of finite circumference. That is indicative of a closed model of the universe. Queries: 1\. Why does the author use a closed model of the universe to explain his point? 2.Can we conclude "It is also possible for a distance to exceed the speed of light times the age of the universe, which means that light from one part of space generated near the beginning of the Universe........." if we draw the same diagram on a flat sheet of paper[instead of using the cone we take a flat surface],remembering that the null geodesics are always straight lines in the flat spacetime context?


title: That 10km/day error predicted if GPS satellite clocks not corrected for relativity

text: Some authorities have stated publicly and without explanation that if the theories of Special and General Relativity were not taken into account in the design of the GPS (by building the satellite clocks to run 38us/day slower than GPS time before launch aka 'the factory offset), the position indicated by an earthbound GPS user device would drift by about 11km/day. I've considered this for various GPS models but can only predict much smaller effects. That multiplying the 38us/day uncorrected difference from GPS time by the speed of light yields 11.6km/day, does not for me seem to relate to GPS receiver function. Please reply with references if possible. I'd be very glad for any pointers.


title: Why isn't water running faster hotter?

text: I was running the washing up water this morning, and started to think about why the cold tap isn't hot, and why the water doesn't get hotter the faster it is flowing (if anything, the cold tap gets colder the faster it flows). From my understanding $K.E = \frac{mv^2}{2}$ and temperature is directly proportional to kinetic energy. I know that the $v$ in the above equation is really the mean speed of the particles and therefore some are moving backwards and some moving forwards, it is the speed that is used. But surely the particles of water in the tap are all moving faster, therefore they should all be hotter. Perhaps the particles in the stream are moving at a much higher mean speed than the water is flowing, so the temperature increase is negligible... Am I correct in thinking this? or otherwise, why doesn't the cold tap get hot the more you turn it on?


title: Is the spring constant k changed when you divide a spring into parts?

text: I've always been taught that the spring constant $k$ is a _constant_ -- that is, for a given spring, $k$ will always be the same, regardless of what you do to the spring. My friend's physics professor gave a practice problem in which a spring of length $L$ was cut into four parts of length $L/4$. He claimed that the spring constant in each of the new springs cut from the old spring ($k_\text{new}$) was therefore equal to $k_\text{orig}/4$. Is this true? Every person I've asked seems to think that this is false, and that $k$ will be the same even if you cut the spring into parts. Is there a good explanation of whether $k$ will be the same after cutting the spring or not? It seems like if it's an inherent property of the spring it shouldn't change, so if it does, why?


title: Question on ladder operators

text: Suppose we have a finite , discrete set of orthonormal states $|k\rangle $ We can construct raising and lowering operators intuitively, for example $$a_+ =\sum_{k=1}^nC_{k+1}|k+1\rangle \langle k|$$ However most textbooks begin by defining ladders in terms of the linear combinations of hermitian operators. How do we get from the above construction to showing that such ladder operators have the form $$a_\pm = \frac{\alpha\pm i\beta}{\sqrt{2}}$$ where $\alpha,\beta$ are hermitian?


title: How does cooling scale with volume?

text: What equation would give me the answer to the question, "If i have a cup of water at a tempature of say boiling, how long would that cup of water take to cool off compared to say half that size of a cup of water." So the volume is in half. Its a general question I am just looking for where to start.


title: The signature of the metric and the definition of the electromagnetic tensor

text: I've read the definition of the electromagnetic field tensor to be \begin{equation}F^{\mu\nu}\equiv\begin{pmatrix}0&E_x&E_y&E_z\\\\-E_x&0&B_z&-B_y\\\\-E_y&-B_z&0&B_x\\\\-E_z&B_y&-B_x&0\end{pmatrix}\hspace{0.5in}(\dagger)\end{equation} in _Introduction to Electrodynamics_ by David Griffiths, or as $$F_{\mu\nu}\equiv\begin{pmatrix}0&-E_x&-E_y&-E_z\\\E_x&0&B_z&-B_y\\\E_y&-B_z&0&B_x\\\E_z&B_y&-B_x&0\end{pmatrix}$$ on the _Lecture Notes on GR_ by Sean Carroll, which I know to be consistent via ${F_{\mu\nu}=\eta_{\mu\alpha}F^{\alpha\beta}\eta_{\beta\nu}}$ where the metric $\eta_{\rho\sigma}$ has a (-+++) signature. However on Wikipedia and other sources (sorry I can't remember) they use a (+---) signature and they define the EM tensor to be the negative of ${(\dagger)}$. These are my thoughts about it: The antisymmetry $F^{\mu\nu}=-F^{\nu\mu}$ may point out that it's just an unfortunate mix of index letters and that for the sources notation to be consistent, either the first two or Wikipedia should change $\mu\nu$ to $\nu\mu$. If not the case, the properties seem to be the same; at first I thought the inner product would pop out a minus sign of difference, but it of course didn't happen, and as for other entities I've worked with, e. g. the 4-velocity, though the metric signature can change, the contravariant vector is the same in either case. However again, I've read the stress-energy tensor does change sign depending on the signature. So is the signature of the metric involved in the definition of ${F^{\mu\nu}}$ or any tensor whatsoever? If so, how can I know what signature is involved? or if not, what's the matter with the minus sign difference on the definitions?


title: Differences between probability density and expectation value of position

text: The expression $\int | \Psi\left(x\right)|^2dx$ gives the probability of finding a particle at a given position. If wave function gives the probabilities of positions, why do we calculate "expectation value of position"? I don't understand the conceptual difference, we already have a wave function of a position. Expectation value is related to probabilities. So what is the differences between them? And why do we calculate expectation value for position, although we have a function for probability of finding a particle at a given position?


title: Cosmic Background Radiation: How did planets form before the CBR could reach us?

text: I've understood that the Cosmic Background Radiation(CBR) is an electromagnetic wave that originated from the big bang. However, we now live on a planet which that is also originating from the big bang. Why does that Cosmic Background Radiation reaches us now? Why does CBR reaches us now, and not a couple of billion years earlier?


title: What's the amount of deviation of cellestial orbits from perfect ellipses

text: It's well known that the planets don't orbit the sun in perfect circles and the characteristics of the elliptical orbits which serve as better approximations to their motion have been calculated fairly accurately. How accurately do elliptical orbits model their actual paths?


title: Why do three dimensional gauge theories flow to conformal theories in the infrared?

text: What is meant with the fact that Super Yang-Mills flows to a conformal field theory in the infrared? Also, is this a general fact or does this depend on the fact of considering a certain class of theories (such as $N=4$, $d=3$ for example)? I have seen this statement numerous times in various articles such as http://arxiv.org/abs/hep-th/0207074 http://arxiv.org/abs/hep-th/0206054 Every time this fact is stated by some author it is given as a known thing, and it is not explained. With an online research I could not make sense of this. Could someone please explain?


title: Calculating the Uncertainty for an Average Value

text: How would I calculate the uncertainty for the average of this set? $32.5 \pm 0.1$ $32.0 \pm 0.1$ $32.3 \pm 0.1$


title: What's the difference between eternal inflation and chaotic inflation?

text: Is there a real difference between eternal inflation and "chaotic inflation" theories?


title: Paramagnetism Spin-1/2 Particles - Partition Function

text: I'm trying to come up with an expression for the partition function of a system of spin-1/2 ideal gas particles on a line of length $L$. The total number of particles $N$ is fixed, with $N = N_\uparrow + N_\downarrow$. Here, $N_\uparrow$ is the number of spin-up particles and $N_\downarrow$ is the number of spin-down particles in a particular microstate. I have the following Hamiltonian for the particles of mass $m$. $$H = \sum_{i=1}^{N}{\frac{(p_i + \beta s_i)^2}{2m} -b s_i} $$ Here, $s_i = 1$ for the spin-up $N_\uparrow$ particles and $s_i = -1$ for the spin-down $N_\uparrow$ particles. $\beta$ and $b$ are constants. I'm trying to use the Hamiltonian to write down the energy for the spin-up and spin-down particles so I can write down the partition function. If I expand the Hamiltonian, I get: $$H = \sum_{i=1}^{N}{\frac{p_i^2}{2m} + \frac{p_i \beta s_i}{m} - b s_i + \beta^2} $$ How do I find the energy of the two sets of spin particles from this and use it to come up with the partition function? Is the energy of the particles just? $$E_\uparrow = \frac{p_i^2}{2m} + \frac{p_i \beta}{m} - b + \beta^2$$ $$E_\downarrow = \frac{p_i^2}{2m} + \frac{-p_i \beta}{m} + b + \beta^2$$ How would one evaluate this in the canonical partition function: $$Z = \sum_{\mu_s}e^{-\beta H}$$ where $\mu_s$ is the summing over all microstates. I'm not sure how to evaluate this.


title: Planatary motion of newtonian force

text: According to the Newtons gravity we can write, $$\vec F = \frac{\hat r_{12} G m_1 m_2 }{r_{12}^2}$$ and we are well known that this law satisfies the planetary motions. What changes will we see if we rewrite the law in this way, $$\vec F = \frac{\hat r_{12} G m_1 m_2 }{r_{12}^{2+p}}$$ where p is a positive number. I mean shape of the arbit, angular and linear momentum etc.


title: Would time freeze if you can travel at the speed of light?

text: I read with interest about Einstein's `Theory of Relativity` and his proposition about the speed of light being the speed limit for anything with mass. So, if I were to travel in a spacecraft at the speed of light, would I freeze and stop moving? Would the universe around me freeze and stop moving? Who would the time stop for?


title: How does a particle of light reach the max speed of light?

text: > **Possible Duplicate:**   >  How can a photon have no mass and still travel at the speed of light? First of all I am not a professional physicist. I was curious as to how a particle of light can reach the maximum speed of light c given that particles experience an increase in mass as they approach c ?


title: If photons have no mass, how can they have momentum?

text: As an explanation of why a large gravitational field (such as a black hole) can bend light, I have heard that light has momentum. This is given as a solution to the problem of only massive objects being affected by gravity. However, momentum is the product of mass and velocity, so, by this definition, massless photons cannot have momentum. How can photons have momentum? How is this momentum defined (equations)?


title: How can a photon have no mass and still travel at the speed of light?

text: I've read a number of the helpful Q&As on photons that mention the mass/mass- less issue. Do I understand correctly that the idea of mass-less (a rest mass of 0) may be just a convention to make the equations work? From a layperson's view, it's difficult to understand how a particle of light (photon) can be mass-less. A physical object (everyday world-large or quantum- small) must have a mass. Yet, if my understanding is correct, the mass of a moving object/particle increases in proportion to its speed/velocity...so that at the speed of light, its mass would be infinite. A photon travels at the speed of light, but it obviously doesn't have infinite mass, right? Can someone formulate a practical explanation that can be understood by middle- school to high school kids? Much thanks for the help. * * * Wow--your answers to my original Q below clear up much of my confusion. I now have the daunting task of going over these nuggets and working up an equation- less (hopefully) explanation of the mass-less photon for non-physicist types. Yes, _from a layperson's view_ , it does seem remarkable that an existing piece of _matter_ \-- which has to be made of _physical substance_ \--could have zero mass at rest (though a photon is never at rest). It would be almost understandable if a piece of matter made of _nothing_ had zero mass, but that seems to be an oxymoron, and "nothing" would equate to nonexistent, right? In case you might find it interesting: I'm working on a writing project that posits we inhabit a universe that consists of matter (physical stuff) only, and that the NON-physical (aka supernatural) does not (and cannot) exist. For instance, if a purported supernatural phenomenon is found to actually exist, then by definition, its existence is proof that it is mundane/natural. All it would take to disprove this premise is reliable proof that ONE supernatural event has occurred. Despite thousands of such claims, that's never yet happened. Who else better than physicists to confirm my premise? However, I do wish the TV physicists would explain the terms they throw about, some of which mislead/confuse their lay viewers. Case in point: "The universe is made up of matter and energy" (without properly defining the term "energy" as a property of matter). The result is that laypersons are left with the impression that energy must therefore be something apart from or independent of matter (ie, nonphysical). Their use of the term "pure energy" without specifying exactly what that means adds to the confusion. (Thanks to your replies on this forum, I now understand that "pure energy" refers to photon particles.) However, "psychics" and other charlatans take advantage of such confusion by hijacking terms like energy (as in "psychic energy"), frequencies, vibrations, etc to give perceived scientific legitimacy to their claims that a supernatural spirit world, etc., exists. As you may realize, the majority of people in the US (per 2009 Harris Poll) and around the world believe in the existence of nonphysical/supernatural stuff such as ghosts and spirits. My purpose is to give laypersons the information they need to distinguish what's real from what's not. Thanks so much for help...And, PLEASE, add any further comments you think might be helpful/insightful to better inform laypersons.


title: How does the solar sailing concept work?

text: Wikipedia describes solar sailing as > a form of spacecraft propulsion using a combination of light and high speed > ejected gasses from a star to push large ultra-thin mirrors to high speeds. I understand the part where ejected gasses bump into the sail pushing the spacecraft. On the other hand, I don't understand how light can do this, since light has no mass. How does that work? Does this mean that if I have a mirror balancing on a needle I would be able to push it over with my flashlight?


title: Clocks tick steadily, so why is there no photon time?

text: Consider a photon bouncing left and right between two mirrors in a photon clock. Seen from inside the clock, the photon bounces at a constant frequency. Time ticks regularly. No matter whether the clock begins moving relative to some outside observer, the clock continues to tick regularly. Light always moves at the same speed relative to the observer in the clock. If the clock is moving forwards relative to an outside observer, we know that _to that outside observer_ , the photon clock appears to tick more slowly. This happens because the speed of light relative to that observer is constant, and, since the photon is moving diagonally relative to the outside observer, the distance traveled by the photon in the clock between ticks is greater, so the photon must take longer to pass between the mirrors and the clock must tick more slowly. But notice how, if you are inside the clock, it continues to tick at the normal speed. This brings me to my question. It is widely reported (including on this very QA site) that a photon traveling uninhibited in a vacuum experiences no time. This seems to be because all the speed of the photon in the clock is now taken up keeping up with the forwards movement of the clock, so there is no speed left to deal with left/right bouncing and ticking. The clock stops ticking. Well, this is the thing. Surely the clock only stops ticking _from the perspective of the outside observer_. If you're inside the light-speed clock, time continues to tick normally. The photon continues to bounce. So why do we say a photon experiences no time? Surely we mean it _appears to us_ as stationary observers to experience no time? If you're a photon, time is just the same as it is to the rest of us, right? Fair enough, your average photon might well feel that it got from A to B in no time at all, because distance was compressed to zero and all the other clocks appeared to have zipped along beyond the end of days in less than an instant, but its own clock, if the photon could observe it, is just ticking normally. This leaves my brain mushed, because now the photon has seen the entirety of an infinity of time in no time at all, yet its clock is still ticking. So what does that mean? What happens the moment after the infinity of external time has completely passed? Surely there is nothing left to happen?


title: Does distance really exist at least for observer which moves at the speed of light?

text: To our time a light year is the distance that light travels in a vacuum but if we consider time of observer which moves at speed of light we found for light time and distance doesn't really exist. Does distance really exist? ($d\tau=dt\gamma^{-1}$ where the at speed of light $\gamma^{-1}=0$) isn't universe just a point for observer at light speed? * * * it is not duplicate guys!.


title: Frame of reference of the photon?

text: In the frame of photon does time stop in the meaning that past future and present all happen together? If we have something with multiple outcomes which is realized viewed from such frame? Are all happening together or just one is possible? How the communication between two such frame s work meaning is there time delay for the information as $c$ is limited? If there is time delay does it mean that time does not stop? My question does not concern matter at that speed rather how it looks viewed from the photon reference. Thanks Alfred! I think I understand it now.


title: Speed of light and lorentzian factors

text: > **Possible Duplicate:**   >  How can a photon have no mass and still travel at the speed of light? If light travels at the speed of light, and anything with rest mass will experience relativistic effects based on the Lorentzian equations, why doesn't light experience these kinds of effects? For example, relativistic mass and rest mass are related via $$m = \frac{m_0}{\sqrt{1-\dfrac{v^2}{c^2}}}$$ Shouldn't light therefore have no rest mass (since the Lorentzian is $0$)?


title: Why does Lorentz factor not hold for relativistic mass when we apply it to photons?

text: We know that the photon itself is massless particle $m_0=0$. But we also know, that the mass of the objects does increase with their energy. And we know that under certain circumstances (gravity, collision with objects) the light does behave like a beam of particles that do have a mass. Now, this is the equation to get the (relativistic) mass of the object with certain speed: $$m=\frac{m_0}{\sqrt{1-v^2/c^2}}$$ We already do know some things: $m_0 = 0$, $v = c$. $$m=\frac{0}{\sqrt{1-c^2/c^2}}$$ $$m=\frac{0}{0}$$ Expression $\frac{0}{0}$ is **not** equal to 0. So what is this?   I'll remind you of those weird clock that are run by light - I failed to find any images, but the clock principle was similar to windmill. And it works.   Also there was an idea to make long-distance autonomic spaceships that are pushed by light rays from stars.


title: how photons are said to be in momentum if they are considered to have no mass and no charge?

text: According to quantum theory,Einstein said that light waves have small packets called photons and they are said to have no mass and charge but having energy E=hv and they behave has both particle and wave character. And they travel with certain velocity. How photons have momentum and energy if they said to have no mass? Momentum = p=mv ,where m= mass v=velocity.


title: How can light travel at speed of light?

text: I am well aware that the speed of light is a universal constant at which nothing but light can travel. But why? Why can even light travel at such a speed? Our maths tell us that anything with rest mass takes infinite energy to reach speed of light, so do we just mean that light is the lightest of all things and it can reach speed of light with negligible energy? Why isn't the speed constant which appears not only as speed of light, but various other places like GR etc something even more than speed of light? Why can light reach the speed of light? I think my question was highly misinterpreted, my question has nothing to do with mass of light. My question is why is the speed limit that appears universally equal to speed of light, why isn't even light allowed to reach the universal speed limit? Yes after that I did ask, the reason for light reaching the highest possible speed. Whether it is it's unusually less mass(mass-less) or something else. So to summarize my question is : 1\. Why anything at all can reach the top speed limit, why is even light permitted to reach the top speed limit? 2\. Why light can reach the top speed? (Only this part is related to the question whose duplicate my question is marked)


title: Does $p=mc$ hold for photons?

text: Known that $E=hf$, $p=hf/c=h/\lambda$, then if $p=mc$, where $m$ is the (relativistic) mass, then $E=mc^2$ follows directly as an algebraic fact. Is this the case?


title: Masses of all the particles in the Standard Theory

text: > **Possible Duplicate:**   >  If photons have no mass, how can they have momentum? I'm sure this question has been asked here before but I wasn't able to find it clearly answered in one q/a session. I'm a newb, yes. In the standard model (which I understand is well experimentally supported except for the absent Higgs Boson), all the elementary particles must carry some mass, correct? For E=MC2 to be true, you can't have energy without mass. And energy has been carried away in collisions of sub-atomic particles that can't be accounted for (the Higgs). So EVERY elementary particle in the Standard Model must have mass, correct?


title: How does light travel at the speed of light?

text: If it is impossible for matter to accelerate to $c$ (because doing so would take infinite energy), and if light can be deemed matter (because of wave- particle duality, photons are matter, right? And photons clearly have mass per solar radiation pressure), how does light manage to travel at $c$?


title: What happens with time at the speed of light?

text: Say that by some means you could become massless, and therefore travel at the speed of light. I understand that the closer you get to the speed of light, the slower time appears to the person traveling. Like say you were traveling a 99.999 % of the speed of light, ever year for you would be 200 or so years for people not traveling. So I suppose at the speed of light, time stops for the traveler. Would that mean you'd be frozen in time and an infinite amount of time would have passed for the rest of the world while you were travelling at the speed of light?


title: If photons don't have mass, how can they accelerate objects?

text: As far as I know photons don't have mass but they do have momentum ($p=mv$). Scientists say that if we put a shiny (reflective) shield of large radius in the vacuum of space, then light from sun will will start moving the shield. How can these two facts be commensurate?


title: attaining the speed of light??

text: WHY our time would run slow if we move with the speed close or equal to the speed of light, and is that time dilation restricted to only just '' time' ' or it affects our biological time also (does it stops or slows down our ageing process) ??


title: Are photons travelling in future? Are they lifespan 0 (or close to 0)?

text: We know that if we are going closer to speed of light, we are travelling in future. Since the photons are travelling at the speed of light, that means that they are travelling into future? Also, if we could possible attach a clock to a photon and measure how much time passed for 1 earth year(we put the clock to be 0, then we wait 1 year, then we look at the clock), would that clock show 0?


title: Do photons have mass?

text: As a student in a highschool physics class, my teacher has repeatedly told me that photons are massless. Yet, I have also heard from other sources that photons have momentum. If photons were to have momementum, that would mean that they have mass as according to p = mv. Do photons really have mass? Also, how would this mass be calculated?


> **Possible Duplicate:**   >  Would travelling at relativistic speeds have any impact on human biology? I am asking myself this question for a few day. What is the answer on: Does the increase of (relativistic) mass, while flying near speed of light, has any impact on astronauts? I mean let's pretend a spaceship will be able to travel in space with nearly the speed of light. Does the astronaut on this ship, while its (relativistic) mass increases, feel any difference on gravity or anything else? Or is the increase simultaneous to his own?


title: Why doesn't light travel instantly?

text: I've read that the faster you travel in space, the slower you travel in time. And when you reach the speed of light (which we won't be able to) time will stand still. So when light travels at the speed of light, it doesn't move in time, so no time will have past when the light arrives at it's "destination". Right?


1. What is the mass of a photon moving at the speed of light?    2. And if it does not have mass, how is it affected by gravity?   3. Also why does Einstein's general relativity support that a gravitational wave must travel at the speed of light? I'm just an A-level student. So, I would appreciate it if you could explain it as idiotically as possible.


title: Photons have no mass. So, why does $E = pc$ hold?

text: It's a somewhat theoretical question. In special relativity, The energy of a photon is given by $E = pc$. But, my argument is that, since photons have no mass, how can they have a momentum $p$? The energy $E$ turns out to be 0 always. So, why does this equation hold?


title: How to get the accurate relativistic momentum form for photons?

text: I have studied from Griffiths, the relativistic form of momentum is $$p = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} m_0v$$ Now when I evaluate the momentum for photon, I just insert $v=c$ and $m_0=0$ and I get $p= 0/0$. How does it make sense? Can you tell me that where I am wrong?


title: Would travelling at relativistic speeds have any impact on human biology?

text: If a person was sitting on a craft that has accelerated to near light speed speed from Earth (e.g. 99.999% of light speed) would there be any impact on his or her human biology due to relativistic effects on mass, time and distance? For example, would the heart still be able to pump blood effectively if the relativistic mass of the blood has increased? Or would accelerating the blood a bit further towards light speed requires more energy than when stationary on earth?


title: How do I show that there exists variational/action principle for a given classical system?

text: We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler- Lagrange equations), Optics (in the form of Fermat's principle) and even General Relativity (we get Einstein's equation from the Einstein-Hilbert action). However, how do we explain this very principle, i.e., more mathematically, I want to ask the following:   > _If I am given a set of generalized positions and velocities, say, > $\\{q_{i}, \dot{q}_{i}\\}$, which describes a classical system with known > dynamics (equations of motion), then, how do I rigorously show that there > always _ **exists**_ an action functional $A$, where_ $$A ~=~ \int L(q_{i}, > \dot{q}_{i})dt,$$ _such that $\delta A = 0$ gives the correct equations of > motion and trajectory of the system?_   > I presume historically, the motivation came from Optics: i.e., light rays travel along a path where $S = \int_{A}^{B} n ds$ is minimized (or at least stationary). (Here, $ds$ is the differential element along the path). I don't mind some symplectic geometry talk if that is needed at all.


title: With Newton's third law, why are things capable of moving?

text: I've got a rather humiliating question considering newton's third law "If an object A exterts a force on object B, then object B exerts an equal but opposite force on object A" -> $F_1=-F_2$ Considering that, why is there motion at all? Should not all forces even themselves out, so nothing moves at all? When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposing direction, nothing happens except that I feel the opposing force. But why can I push a box on a table by applying force ($F=ma$) on one side, obviously outbalancing the force the box has on my finger and at the same time outbalancing the friction the box has on the table? I obviously have the greater mass and acceleration as for example the matchbox on the table and thusly I can move it, but shouldn't the third law prevent that from even happening? Shouldn't the matchbox just accommodate to said force and applying same force to me in opposing direction? I've found a lot of answers considering that question but none was satisfying to an extend that I had an epiphany solving my fundamental problem I've got understanding it.


title: Why does the cart move?

text: A while ago someone proposed the following thought experiment to me: A horse attached to a cart is resting on a horizontal road. If the horse attempts to move by pulling the cart, according to the 3rd Newton's Law, the cart will exert a force equal in magnitude and opposite in direction, cancelling each other out and thus the horse and the cart _should_ not move. And yet it moves (pun intended ;) Why? I never got a satisfactory answer, my guess is that the answer lies in the frames of reference involved: horse-cart and horse-road. Any ideas?


title: According to Newton's third law, why don't Action and Reaction make equilibrium?

text: According to Newton's third law, Action and Reaction are equal and in opposite direction. If both forces are equal and in opposite direction then why they don't make equilibrium and void the effect of force?


title: Clarification regarding Newton's Third Law of Motion and why movement is possible

text: Newton's third law states that to every action, there is an equal and opposite reaction. If that's the case, then how do things move at all? Shouldn't all applied forces be canceled by the equal and opposite force it experiences from the object they were applied to?


title: Why body starts moving when force is applied?

text: The recent question by m.buettner regarding self-inductance and its resistance to EMF Faraday's law - does the induced current's magnetic field affect the change in flux?, recalled me the great question that I always wanted to ask. The 3rd law of Newton says _To every action there is always an equal and opposite reaction_. This immediately means that action is exactly balanced by reaction force and, because of zero net force, no speed increase should be observed. How do you explain why our concerns with m.buettner are unfounded?


title: Topolgical insulators order parameter

text: _For topological insulators_ **Is there any way to defineorder parameter for topological phase transitions?**


title: Why are totally antisymmetric tensors more useful than totally symmetric tensors?

text: In an arbitrary number of dimensions, one can naturally define two tensors, Kronecker delta and Levi-Civita epsilon tensor. However, why isn't it advantageous to define some totally symmetric tensor as well? Is there an intuitive reason for that or is it basically related to differential forms?