title: How photons represent colors that you see?

text: Right now, my understanding is that, a mixture of photons of many different frequencies is perceived as white by your eye. While no photons at all, is perceived as black. And photons with the blue frequency only cause you to see blue, etc. My question is, how is the "brightness" controlled? I think it has to do with how much blue photons are coming at your eye, a low amount will be dark blue, a high amount will be... a lighter blue. But then I think, to get light blue, isn't it a mixture of mostly blue photons with white light (photons of all frequencies) to produce a blueish white or a light blue? Also, when colors combine to produce different colors, is there any photon combining that exists or is it because your eyes see mixtures of photons and not photons themselves?


title: Graphene's Tight Binding Hamiltonian

text: Graphene has two atoms in its primitive unit cell. This makes it intuitive to see that the tight binding Hamiltonian can be constructed as a $ 2 \times 2 $ matrix $H$ acting on a spinor $S$ that consists of the wavefunction from an atom in sublattice A and B. $H_{monolayer}=\gamma \cdot \begin{pmatrix} 0 & k_x-ik_y \\\ k_x+ik_y & 0 \end{pmatrix}$ $S_{monolayer}=\begin{pmatrix} |\psi_A\rangle\\\ |\psi_B\rangle \end{pmatrix}$ Bilayer Graphene has four atoms in a primitive unit cell and its tight binding Hamiltonian is a 4x4 matrix whose matrix elements represent the hopping between said lattice sites (depending on how it is stacked and what hopping parameters you wish to involve in the calculation). An example might be as follows: $H_{bilayer}=\begin{pmatrix} 0 & 0 & 0 & v(k_x-ik_y)\\\ 0 & 0 & v(k_x+ik_y) & 0\\\ 0 & v(k_x-ik_y) & 0 & \gamma'\\\ v(k_x+ik_y) & 0 & \gamma' & 0 \end{pmatrix}$ $S_{bilayer}=\begin{pmatrix} |\psi_{A1}\rangle\\\ |\psi_{B2}\rangle\\\ |\psi_{A2}\rangle\\\ |\psi_{B1}\rangle \end{pmatrix}$ Where the basis is chosen is in an arbitrary order (1 and 2 indices refer to layer number). **How does one write this in a "two-component basis" and what does that mean?** Also, what is this hamiltonian acting on in this case? The bilayer hamiltation in this basis (which I do not know what it represents) is written as follows: $H'_{bilayer}=-\dfrac{\hbar^2}{2m}\begin{pmatrix} 0 & (k_x-ik_y)^2 \\\ (k_x+ik_y)^2 & 0 \end{pmatrix}$


title: Derivation of $a_{j}$ coefficients in the quantum harmonic oscillator

text: In Griffiths' book page 53, when we derive the solution of the quantum harmonic oscillator by using the power series way, we have: $$a_{j+2} = \frac{2j+1-K}{(j+1)(j+2)}\, a_{j} .$$ And for large $j$, we have: $$a_{j+2}\approx\frac{2}{j}\,a_j.$$ Up to this point I totally agree (one just takes the limit). However, the subsequent derivation of solution $a_{j}$ and $h(\xi)$ I attached from the Griffiths' textbook are very confusing.   * How did it go from $a_{j+2}\approx\frac{2}{j}a_j$ to the solution of $a_{j}$?    * Also, how do the second and third approximations work in $h(\xi)$? My questions are mainly mathematical. I very much hope someone can provide a derivation or refer a link where these questions may already be answered. ![enter image description here](http://i.stack.imgur.com/qklld.jpg) ![enter image description here](http://i.stack.imgur.com/wBTkg.jpg)


I'm going mad about the problem. I really don't understand why do electron have 1/2 spin number, why they are not actually spinning. I can accept that the electrons have their own magnetic field, which is certain, but why do they have $\hbar\sqrt3/2$ of angular momentum, and I don't know what the heck is spin number. I've read the definition of spin and spin quantum number more than a hundred times but there is no betterment. I've smashed my head in my desk more than a hundred times either. My question is the title. Why can't I just think the spin as rotating? What I've saw recently, > _electron's hypothetical surface would have to be moving faster than the > speed of light in order for it to rotate quickly enough to produce the > necessary angular momentum._


title: Majorana equation and non-invariance of spinor representation under discrete Lorentz transformations

text: Here I asked about getting an equation for two-component spinor as the alternative for Dirac equation. It was found that it is called Majorana equation. It may be easily derived by using historical Dirac's method of deriving homonymous equation, but with using the requirement of the absence invariance of the Lagrangian under U(1) transformations. But in the linked question I also wrote about the absense of invariance of spinor $\left(\frac{1}{2}, 0 \right)$ representation of the Lorentz group under discrete transformations of the Lorentz group. If these symmetries is absent, why do we need to analyze this equation?


title: Where does the number "380,000 years for electrons to be trapped in orbits around nuclei" come from?

text: How does this number get calculated? > About 380,000 years after the Big Bang the temperature of the universe fell > to the point where nuclei could combine with electrons to create neutral > atoms. http://en.wikipedia.org/wiki/Photon_epoch I've seen it in many places (or something close to that), but there is never a citation or any explanation.


title: Is there a standard resource that lists all understood particle-particle relationships?

text: I am just starting to dig a little deeper into particle interactions, and just have an introductory college physics background (no quantum mechanics). But I am interested in the conditions of the early universe and am looking for a list of all the particles in the standard model, and the relationships between the particles, so you can see which particles turn into other particles under which conditions, and stuff like that. Is there any such a thing? Or if not, it would be really cool to see a list of all the particles in the early universe and the different types of interactions they had with each other. Such as:   * What happens when a quark + antiquark come close together? What if they collide?   * What happens when 2 gluons collide? Come close together?   * What happens when 1 quark and 1 gluon come together?   * What happens when 2 photons collide (can they collide?)?   * What particles radiate photons? Under what conditions?   * ... Does such a resource exist? Or if not, where would you go about finding that?


title: What exactly is meant by "observed" when talking about the wave-particle duality?

text: When talking about the wave-particle duality, teachers and books say that when you send a single photon through a slit, it makes a wave pattern. But if you send that particle through the slit and "you observe it directly", then it appears as a single point (a particle). What is meant by "observe"? Is that like with your eyeballs? Or is that with some measuring device? It's unclear what that word means, it could mean anything haha. One reason I am wondering is because, it seems like the act of trying to measure it directly (if "measure with a device" is what is meant by observe) would mean sending out some sort of radiation or particle itself, so yes, that would mess with the experiment. But maybe I just don't quite understand yet, so looking forward to a bit of clarification.


title: Autocorrelation function for deterministic nonlinear dynamical systems

text: I am quite puzzled with the problem that spectral analysis has been either applied to noisy dynamical systems or to chaotic ones. I was wondering why nobody makes analysis of non-linear dynamical systems based on their autocorrelation? At least for non-linear oscillators which are essentially periodic and seem to suit for such analyses. For example I simulated Van der Pol oscillator for 500 seconds from initial condition $(1.1,0.1)$. The 2D ODE is as follows: $$ \frac{d\textbf{x}}{dt}= \begin{cases} \mu(x_0-1/3 x_0^3-x_1)\\\ \frac{x_0}{\mu} \end{cases} $$ Where I have set the $\mu$ to $5$. The plot of the oscillator and the autocorrelation function as defined by Wiener are as follows: ![enter image description here](http://i.stack.imgur.com/i3AnX.png) ![enter image description here](http://i.stack.imgur.com/ffyf6.png) Sorry for the lack of labels. The $x$-label in the second plot is representing lag in seconds and the $y$ axis is $C(\tau)=\frac{1}{T}\lim\limits_{T\to \infty}\int^T_{-T}x_0(t)x_0(t+\tau)dt$. What would be wrong with such analysis when the autocorrelation function exists? Is this a totally dumb question??


title: Open problem? Square of the wave function $\Psi(x)_{x_o} = \delta(x-x_0)$ of a particle localized at a point $x_0$?

text: Does anybody know the status of the problem to define the wave function (non- relativistic Quantum Mechanics) of a particle localized at a definite point? Landau-Lifshitz says in chapter 1 that this function is $\Psi(x)_{x_o} = \delta(x-x_0)$ and gives an explanation that it produces the correct probability density when it is used to span some other arbitrary wave function $\Psi(x)$. The problem is of course that the wave function given above squares to a non integrable function. As far as I know this problem is unsolved. My question is if anybody knows the status quo of this problem. I am sorry if this question may be duplicated, I could not find it amongst the answered questions.


title: Are Fresnel lenses widely used for solar electricity? If not, why not?

text: I was just wondering why Fresnel Lenses are not widely used in the production of solar electricity. Their use there would mean that you could produce heat within a fraction of a second, up to a few minutes and run a turbine to produce electricity. Though it is used in welding, I am not sure what are the problems in producing electricity, as stated by this Wikipedia article: > New applications have appeared in solar energy, where Fresnel lenses can > concentrate sunlight (with a ratio of almost 500:1) onto solar cells.


title: Why do photons excite electrons?

text: I know that when electrons encounter photons, they become excited and move to an orbit farther away from the nucleus of an atom as a result. What I want to know is exactly why the photons _cause_ the electrons to enter this state. Edit: Sorry, I wasn't being very clear. What I mean is, why do photons interact with electrons?


title: Why does a container with fluid make different sounds at different fluid levels?

text: Have you ever noticed that when you are filling a container with fluid. As it approaches the top, it makes a different sound? You can tell by listening when your about to reach the top. Why is this?


title: Mie Scattering for spheres with constant dipole moment

text: I was wondering whether there exists a theory that describes Mie Scattering for spheres that have a constant dipole moment. Since there are theories that describe Mie scattering in the case of a charge, this might exist too?


title: Find shadow's height

text: Just starting to learn physics. Now reading about constant motion and after this paragraph I have a task: Boy with growth of 1.5 m runs at a speed of 3 m / s in a straight line, passing under a street lamp, hanging at a height of 3 m. Show that the shadow of his head moves uniformly, and find the speed of the movement. How can I know the height of his shadow to solve it?


title: Linearity of Quantum Mechanics?

text: The proof of the No-Cloning Theorem states "By the linearity of quantum mechanics, ..." -- Could someone please give me a rough sketch/outline of what this means. Does it have to do with the Hilbert Space that wave functions live in? I apologize if this question isn't specific enough, I just wanted to fully understand this concept.


title: Can the buoyant force on an object be seen as reduction in weight on a scale?

text: Consider a container with some fluid of density $\rho_l$ and volume $V_l$. This is kept on a measuring device and has weight $\rho_l V_lg$. Now, consider a block of density $\rho_b$ and volume $V_b$. This block is put into the fluid and here, its apparent weight equals $\rho_b V_bg - F_b$ , where $F_b$ equals the buoyant force which equals $V_b\rho_lg$. Therefore, the apparent weight of block equals $gV_b(\rho_b - \rho_l)$. What happens if you take the weight of this whole apparatus? Will it equal $$gV_b(\rho_b - \rho_l) + \rho_lV_lg,$$ or $$\rho_bV_bg + \rho_lV_lg?$$


title: What's the meaning of the general solution and the particular solution in differential equations?

text: Can anybody cast some physical insight into this? I've been studying differential equations on my own and don't understand how you can have a whole host of general solutions. It seems like a rather curious situation which we don't come across in other areas of mathematics. Is there anything more to the discussion that I'm missing?


title: Black hole Cyg X-1 doesn't seem dense enough

text: According to wikipedia, here are the Cygnus X-1 vital stats:               Mass    14-16[7] M☉     Radius  20–22[8] R☉      A radius of 10 R☉ means a volume of 10^3 = 1000 Sols. Divided by 16 M☉ that means that Cyg X-1 is 60 time _less_ dense than Sol. So how could it be a black hole?


title: Motion of a pendulum

text: The equations of motions for a simple pendulum is given by $$\ddot{\theta} ~=~ -\frac{g}{\ell}\sin(\theta),$$ where $g$ is acceleration due to gravity and $\ell$ is the length of the pendulum's string. Notice that the differential equation is of second order, does this mean that if I solve this equation numerically, the numbers that I get refers to the change in the velocity of the pendulum?


title: Learn QM algebraic formulations and interpretations

text: I have a good undergrad knowledge of quantum mechanics, and I'm interesting in reading up more about interpretation and in particular things related to how QM emerges algebraically from some reasonable real world assumptions. However I want to avoid the meticulous maths style and rather read something more meant for physicists (where rigorous proofs aren't needed and things are well- behaved ;) ) I.e. I'd prefer more intuitive resources as opposed to the rigorous texts. Can you recommend some reading to get started?


title: Books on foundations of QM

text: I am seeking for books on foundations of Quantum Mechanics with subjects like the EPR experiment, Bell's theorem, the problem of measurement, entanglement, decoherence, nonlocality, interpretations, QM without observer, different formalisms etc. I prefer modern books, post graduate oriented, with history, formalisms and different approaches for a young researcher specialize himself on the subject. EDIT: the other question marked as "duplicate" do not fit my needs. I prefer books with higher modern mathematics, deep arguments and well-defined positions within the philosophy of science, post graduate oriented, if those exists. I need a book to get plenty knowledge as to do research in that academic area, not an intuitive approach.


title: Good quantum physics textbooks

text: > **Possible Duplicate:**   >  Learn algebra and interpretation of QM I'm a physics student it's my last year and I find my self struggling with usage of quantum mechanics. Now I'm starting to learn nuclear physics, solid state physics and soon quantum field theory and I see that I have holes in my knowledge. It's not that I'm completely ignorant, I've passed the exam in quantum physics I understand the concepts, but it doesn't feel right, I don't have the intuition like I do for example, classical mechanics or electrodynamics.   For example, of course, there are problems that I can't solve in classical mechanics or electrodynamics but I always know where to start I have an intuition about the problem and in most scenarios I have an ideas what solutions should look like. But in quantum physics, usually even for simple problems I can get stuck or don't know where to start.   I want to rebuild my knowledge from a new source.   The literature I've used so far is:   Introduction to Quantum Mechanics by David J.Griffiths,   Quantum physics by Leonard Schiff,   Modern Quantum Mechanics (Revised Edition) by J.J.Sakurai.      First one is an easy read, good introduction, but it doesn't use bra/ket notation.   Second on I just didn't like, it was hard to read, short on examples.   Third one I really like, but I'd like to see more examples and I can't check solutions for problems at the end of the chapters anywhere.      Could you please recommend me couple of more choices? I prefer books with lot of examples of solving problems. Also, while it's fine that book starts with wave functions, solving Schrodinger equations etc, I'd like a book that uses bra/ket notation.


title: How can two seas not mix?

text: How can two seas not mix? I think this is commonly known and the explanation everyone gives is "because they have different densities". ![enter image description here](http://i.stack.imgur.com/KpmVf.jpg) What I get is that they eventually will mix, but this process takes a long time. From what you see in this picture you can see that they have a clear separation line as if you would mix water and oil. Basically what I'm skeptical about is the clear separation line between them. Putting highly salted water and normal water in the same bowl will cause almost instant mixing. Can you get the same effect as shown in the picture in a bowl at home ? I'm looking for a more complete answer than just that they have different densities. Thanks. EDIT: Looking more on the "density" hipothesis I also found this which I found interesting :)


title: Is there a simple explanation for Schwinger's relation $g=2+\frac{\alpha}{\pi}+{\cal O}(\alpha^2)$ for the $g$-factor of the electron?

text: Schwinger has on his grave (it seems) the relation between the g-factor of the electron and the fine structure constant: $$g~=~2+\frac{\alpha}{\pi}+{\cal O}(\alpha^2)$$ Did Schwinger or somebody else ever give a simple explanation for the second term of the right hand side? The 2 appears from Dirac's equation. The second term is due to the emission and absorption of a photon. Is there a simple way to see that this process leads to the expression $\frac{\alpha}{\pi}$?


title: Enthalpy of vaporization

text: I've been thinking about refrigeration technology and am a bit confused about two common answers. Specifically, the part where the expansion valve releases the pressurized fluid and stuff gets real cold. One is that refrigeration works by lower pressure = lower temperature. This makes sense to me because if there is lower pressure, I can imagine it as the opposite of higher pressure = higher temperature. Less pressure means particles are freer to move apart and thus eventually boil and lose energy as they travel further away from each other. The other is the enthalpy of vaporization, which I understand as meaning that some amount of energy is required for a phase change. This also makes sense to me: when the refrigerant enters the low pressure side of the valve, the particles are more free to spread apart, begin to boil, and thus suck up surrounding energy to break apart from each other. Although, it seems a bit more magical than the lower pressure = lower temperature explanation (it seems odd that already hot liquid particles "suck up" more heat). Could someone please help me understand this better? Thanks! NOTE: As you can see, I think of this in very layman terms and am currently reading books like Feynman's lectures. My background is engineering, not physics, so I tend to understand things best in a much more physical- visualization, implementation-details kind of way.


title: How does a Photocell/Photoresistor work?

text: I'm just curious highschooler beginning an interest in electronics and this concept of light detecting resistance component is really intriguing to me. I assume it's an application of the Photoelectric effect but how exactly does a CdS photoresistor (aka LDR) do what it does. ![Common CdS LDR](http://i.stack.imgur.com/yIxZY.jpg) How can two metal wires and and a zig zag of cadmium on silicon create a light sensitive resistor? What is happening here? How does a common Photocell really work? Edit: I've read the wikipedia page and a whole lot of other sources but I wish for a more technical and in depth of the mechanism. Thank you :D My biggest question is why CdS... why not anything else?


title: Wheel locks and spinout

text: Imagine driving in a straight line on a ice lake, when you hit the brakes, if your goal is to stay in straight path with no spinout, which wheels would you choose to have locked: front or rear? Assuming the steering wheel is kept fixed in both cases, I learned that it's better to have front wheels locked in this case. But can someone explain in accurate terms why? Thanks.


title: Physical Interpretation of four velocity in GR

text: I'm confused about the physical interpretation of the four-velocity $U^\mu=\frac{dx^\mu}{d\tau}$ in General Relativity. I know that it is a tangent vector to a particle's "worldline", but what does this mean more physically? For example, I am comfortable with what $U^\mu$ means in Special Relativity. In your inertial frame, you cover a distance $\Delta x^\mu$ and your clock says time $\Delta \tau$ has passed, and by taking the limit as $\Delta \tau \to 0$ this defines your $U^\mu$. But I'm unsure about what $U^\mu$ means in curved space, or even in an accelerated reference frame. In either case the frame is no longer an inertial frame, which makes it confusing to interpret $\tau$, because it's no longer the "proper time in a frame", there is no one frame we are working in.


title: How to calculate error of parallax and sextant based navigation?

text: 1. First of all, why wasn't the sextant ever used for land navigation? The horizon is easier to see at sea, but land based sextants could be used in conjunction with artificial horizons (as at sea when horizon is hidden by fog).   2. Parallax has been used by both the US army and navy to measure distance to targets. The devices that used this principle were called coincidence rangefinders. It seems this system was still used after the introduction of radar. Why was this system eventually phased out?   3. Finally my main question: How can one calculate the error for measurements made by sextants and parallax devices?


title: The use of the renormalisation constant $Z_2$ of the electron self-energy in Peskin & Schroeder

text: The use of renormalisation constants often puzzles me. A good example is the use of $Z_2$ in the equation (7.58) of Peskin Schroeder. $Z_2$ is defined in equation (7.26). as $Z_2^{-1} = 1-\frac{d\Sigma}{dp}$. Later in equation (7.31) it is said: $Z_2-1 = d\Sigma/dp$ although this term is supposed to be infinite. But $d\Sigma/dp$ is treated of being smaller than 1. Okay, in this example the Pauli-Villars renormalisation is used where a rather high $\Lambda$ is needed to make $d\Sigma/dp$ larger than 1. But what would be if $Z_2$ were computed with dimensional regularization ? Shouldn't be at least : $d\Sigma/dp + (d\Sigma/dp)^2 + (d\Sigma/dp)^3 + \dots $ I know that $d\Sigma/dp$ is of order $\alpha$ and there should be counter term to make the sum of both small (to order $\alpha$). On the other hand I am almost sure that when the counter terms of the next order $\alpha^2$ are calculated that it is already forgotten that there was also a term $(d\Sigma/dp)^2$ which also need a counter term and for $\alpha^3$ order again and so on. Could somebody explain it to me ? Thank you.


title: Help explore a self-feedback camera-monitor chaotic system

text: We are trying to emulate the chaotic system Jim Al-Khalili demonstrate (3 min video). In our chaos lab, we are trying to research the chaotic system shown in the video. We are using just a webcam and a regular PC monitor. Our goal is to build a bifurcation tree for this system and to show how by changing the parameters of the system (location and distance of the camera from the monitor, time delay (between capturing and showing what is captured on the screen)) we can see a transition from "order" to chaos. The problem is we are not sure what exactly is the mathematical representation of the system, and what is the thing that is "doubling" and going to chaos (the y axis of a bifurcation tree - like voltage peaks on the diode in a chaotic RLD system). How do we approach this subject (if it's even possible)?


title: Relating Energy to Wavelength in curved space

text: Consider a curved space, e.g. Schwarzschild: \begin{align*} ds^2 = -\left(1-\frac{2M}{r}\right)dt^2+\left(1-\frac{2M}{r}\right)^{-1}dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2 \end{align*} Now, the energy of a photon is $E = \hbar \omega$, and $|\mathbf{k}|= \frac{2\pi}{\lambda}$, but am I correct in assuming that $\omega \neq |\mathbf{k}|$? Because if $k^\mu = (\omega,\mathbf{k})$ then $k_\mu k^\mu = 0$ implies that: \begin{align*} g_{tt} \omega^2 + g_{rr}(k^1)^2+g_{\theta\theta}(k^2)^2+g_{\phi\phi}(k^3)^2 =0 \end{align*} So basically, is it correct that the relationship between $\omega$ and $|\mathbf{k}|$ will vary in curved space? (And so relationships like $E = \frac{h}{\lambda}$ no longer hold?)


title: Wilson's Renormalization Group and Lie's Third Theorem

text: If you think of a one-parameter group of transformations along a curve in the plane as a (Lie) group, and the tangent vector to the curve as a generator of the curve we can intuitively understand Lie's Third Theorem on how a local Lie algebra generates a global Lie group. Does this theorem apply for semi-groups? More specifically, does it apply to Wilson's Renormalization group, in other words do the renormalization group equations generate a curve? (It seems as thought they generate the flow of the coupling parameter ![enter image description here](http://i.stack.imgur.com/S9xLD.png) so if so - is that all it is, a mathematical irrelevancy or is there physical meaning?) I ask to understand whether one can give Wilson's renormalization (semi) group, in the context of the statistical-mechanical partition function, any kind of similar interpretation. If it helps, refer to the 1-dimensional Ising model as an example, thank you. References   1. "Renormalization Group Theory", Yale 430b/530b "Statistical Methods and Thermodynamics" Lecture Notes http://xbeams.chem.yale.edu/~batista/vaa/   2. Bluman "Symmetry and Integration Methods for Differential Equations" P. 37   3. Wilson, "Renormalization Group and the Kadanoff Scaling Picture", P. 3177   4. Grossco, "Solid State Physics" 2nd Ed. P. 764 (For the Flow Diagram)


title: free falling object with air resistance?

text: we already know that if we plot speed vs time of free falling object it will be y=gx graph because we know the acceleration is gravity. If it have air-resistance acceleration will be change right?. So how we can plot the speed vs time graph of free falling object with air resistance ? It have some equations or not. because i want to plot it by using python. Thanks. sorry about my english. ![example graph from google](http://i.stack.imgur.com/cvlE5.jpg) This picture i saw from google but i want to make it by coding


title: What is evidence for an irreversible change?

text: Knowing some about thermodynamics and reactions, I do understand how it can be shown that a change is reversible. But irreversible? Why can't it be that a change that was deemed irreversible thousands of years ago via new changes perhaps developed by physicists or changes, processes and reactions from some other part of the world or space, a change that was deemed irreversible in the future can be shown to be reversible? I think that for instance diseases that were deemed irreversible as science progressed, we could make changes that were priorly said to be irreversible, in fact reversible.


title: How does a flywheel generate electricity at a constant voltage?

text: I believe I am missing something simple here. My question concerns flywheel energy storage. Say we have stored some amount of energy in a spinning flywheel. The flywheel is attached to a generator. So the flywheel (and therefore the generator) would be spinning rapidly at first, and then gradually slow down as the rotational energy is converted into electrical energy. It is my understanding that the induced voltage decreases as the angular velocity of the generator coil decreases. So how is it that we can get electricity at a constant voltage from this setup? Am I misunderstanding how the generator works? Thanks in advance.


title: Instrumentation handbook

text: Does anyone have any suggestion on a handbook of instrumentation? In particular NIM instrumentation... I would like an approach which will explain the techniques and how to use NIM modules. In particluar I would like an approach from the point of view of the user, not the developer. For instance, ''what does the "veto" do in a dual timer?'', ''How to use a discriminator for a simple trigger?'' and stuff like that.


title: Metal sphere and charged ring

text: I think this is an interesting question, to which I don't really know the answer to. (Also, not a homework question.) Say you have an uncharged metal sphere constrained to move in the z-axis. There is a charged ring lying in the x-y plane centered at the origin. Two cases: 1) the diameter of the ring is larger than the sphere, so that the sphere can pass through the ring, and 2) the diameter of the ring is smaller than the sphere, so the sphere cannot pass through the ring but can touch it. What are the equilibrium position(s) of the ball? For case 1) it is obvious that the center, by symmetry, is an equilibrium point. But are there more? The complication arises because of the finite size of the sphere. As the sphere starts to pass through the ring, the charge of opposite sign to the ring is induced near the ring, but the angle is very shallow, so there is not much attractive force. On the other hand the induced charge of the same sign gets pushed to the far end of the sphere, which causes a strong repulsive force, so the sphere might get repelled as it enters the ring. I'm not sure whether this is correct though. It might very well turn out that there is only 1 equilibrium point... So aside from solving the system exactly to find the equilibrium points, is there a way to argue how many there are, for the 2 cases, and where they are?


title: Free electron gas in two dimensions

text: Can someone give a qualitative description on why the density of states for a two dimensional free electron gas is independent of energy while it is not in one and three dimensions? In one dimension it goes as $E^{-1/2}$ and in three $E^{1/2}$.


title: Applying the Maxwell–Boltzmann statistics to astrophysical objects

text: Quoting Wikipedia: > In statistical mechanics, Maxwell–Boltzmann statistics describes the > statistical distribution of material particles over various energy states in > thermal equilibrium, when the temperature is high enough and density is low > enough to render quantum effects negligible.   1. Is it possible to apply Maxwell–Boltzmann statistics to objects as large as nebulae; globular clusters or galaxies, _that is, treating stars as Maxwell-Boltzmann particles_ ; or even the universe as as whole, _treating galaxies or clusters of galaxies as Maxwell-Boltzmann particles_?   2. Can the Universe be considered in thermal equilibrium? Or does an expanding Universe imply non-equilibrium?


title: How far would you need to displace your eyes to get meaningful depth perception of the stars?

text: The question follows from xkcd cartoon "Depth Perception (941)". I've isolated the frames that describe the concept here. ![Credit: Randall Munroe, xkcd](http://i.stack.imgur.com/vNeDp.png) In words, one could theoretically point two cameras at the sky, and displace them so that, if viewed as components of a projected 3D image, the starfield of the night sky would have a perceivable depth. That is, Sirius or Alpha Centauri would appear closer than, say, Betelgeuse. The idea _sounds_ interesting, but I was wondering whether it's actually possible. That is, how large would the displacement of the cameras need to be to create a perceivable depth? To quantify, let's say we're trying to reduce the scale from 5 light-years to 100 m. Would this require a displacement of 5 light-years / 100 m$\times$(separation of eyes)$\approx1/400$ light-years $\approx136$ AU or is it more complicated than that? I guess the maximum we could achieve is by taking two images of the same field of stars, one year apart and combining them, to give a separation of the "eyes" of about 2 AU. I don't know enough astrometry myself to be sure.


title: Will Cone standing on its tip, without any other force other than gravity topple?

text: A cone standing on its tip is considered to be in unstable equilibrium as a slightest force could topple it. So, if the cone is stood on its tip with no other force other than gravity (and the corresponding ground reaction force), will it continue to stand without toppling? Has this been attempted experimentally?


title: Curiosity Rover (MSL): specification / dimensions

text: I have been looking all over and I can't find a detailed specification about the Curiosity Rover. The length is about 10 feet but it would be cool to find out the dimensions of the wheels, clearance and so on. Anybody know where I would find this information?


title: Funding opportunities for an independent researcher

text: In one of my questions I asked about the career paths to become a professional astronomer. Now let's consider the next logical step. What if a person has gained his/her PhD in Astronomy and had an opportunity to do a couple of postdoc positions. The time comes for independent work but where can the funding come from? What are the funding possibilities in different countries to continue the career as an independent researcher?   * Please provide links and general advice if there is for each funding agency   * Keep it short and to the point


title: Did Penzias and Wilson use Wein's law (or data based on it) to determine the temperature of CMB?

text: I'm writing a paper and I used them as an example, but then reconsidered . . . maybe I'm not getting it right! thanks!


title: Should entropy have units and temperature in terms of energy?

text: I've been thinking about entropy for a while and why it is a confusing concept and many references are filled with varying descriptions of something that is a statistical probability (arrows of time, disorder, etc.). Could this confusion be in the nature of it's units and how it is scattered around in different equations? When Maxwell published his paper on the molecular distribution of velocities in 1859. This has led to the identification of temperature with the mean kinetic energy of atoms or molecules in the gas. At that point we could have redefined temperature to units with energy which make sense instead of K. This would make the new $T_a=kT$ where $T_a$ is the new absolute temperature in the units with energy. Once temperature is in the units of energy this makes entropy unitless (makes more sense to me): $S = ln(W)$ In addition this makes other equations more clear: Maxwell's gas law identity has the form (for atomic particles of mass m) $\frac{3kT}{2} = \frac{m<ν^2>}{2}$ where T is the absolute temperature and $<ν^2>$ , the average of the squared velocity of the atoms, and k Boltzmann’s constant. But with $T_a$, the relation $\frac{3kT}{2} = \frac{m<ν^2>}{2}$ will become simpler $\frac{3T_a}{2} = \frac{m<ν^2>}{2}$ And the gas constant R in the equation of state for ideal gases would be changed into Avogadro number $N_{AV} = 6.022 × 10^{23}$ and the equation state of one mole of an ideal gas will read: $PV = N_{AV}T_a$, instead of $PV = RT$ **Why bother?** This would make entropy identical conceptually and formally to information by redefining temperature in terms of units of energy. This creates a strong association between entropy and probability and makes the second law (which isn't absolute anyway) less mysterious. Would it make sense to have temperature in units of energy at other levels of physics and entropy unitless say in the case of black holes entropy?


title: Correspondence principle and quantum computers

text: I just read this article at https://medium.com/the-physics-arxiv- blog/7ef5eea6fd7a about the work of a physicist called Bolotin, that states that P!=NP (from computer science) implies that large quantum mechanical objects are not possible. The author starts by explaining the Schrodingers cat thought experiment. He then says "Nobody knows why we don’t observe these kinds of strange superpositions in the macroscopic world", which I find strange because you cannot observe a superposition, you either see that the cat is alive or dead. But then he writes "For some reason, quantum mechanics just doesn’t work on that scale. And therein lies the mystery, one of the greatest in science." I thought that the correspondence principle actually explains nicely why quantum mechanics works very well on a large scale? The main point of the article is that if you can have a large quantum mechanical system, you would get P=NP, which is believed to be not true by most computer scientists. But isn't that exactly what they try to do with quantum computers?


title: Pseudo-Riemannian Manifolds with multiple temporal dimensions

text: Consider a Pseudo-Riemannian Manifold with signature $$ (\underbrace{+,\cdots,+}_p,\underbrace{-,\cdots,-}_q) $$ For any positive integers $p$ and $q$. Can this kind of manifold contain closed timelike curves (CTCs)? I know that if $p=1$, then we get a Lorentzian Manifold that can't contain CTCs, but I am interested in the cases where $p>1$.


title: How to freeze the Niagara waterfalls?

text: Here is a picture of the usual vigorous Niagara Falls (in the winter). ![enter image description here](http://i.stack.imgur.com/PgwrA.jpg) Here is the picture of Niagara Falls frozen in 1933 (in the very cold winter). ![Niagara Falls frozen in 1933](http://i.stack.imgur.com/FZB1W.jpg) Here is the picture of Niagara Falls frozen in 1911 (in the extremely cold winter). ![enter image description here](http://i.stack.imgur.com/lcaLv.jpg) Background knowledge: The Melting/Freezing point of the static water at 1 atm is 32°F (0.0°C or 273.15 K). $\bullet$ I am curious to know under what conditions of the air pressure(atm), temperature, solute density in the water **would cause the Niagara fall frozen?** Are other conditions like: winds, snowing or not, the strength of Van der Waals force, the moving speed/velocity of water and the pulling force of gravity (acceleration $g$), the height $H$ of waterfalls would be some important factors to predict **the conditions to freeze the waterfalls**? Is there some simple qualitative relations or quantitative formulas describing the freezing point for waterfall? **A $P$(pressure),$T$(temperature), etc, $\dots$ curve for the water-ice phase transition on the phase diagram?** Perhaps the answer is very simple(?), but it is not entirely trivial to me. ps. Happy winter/holiday times for those who reading the post, and especially those residing on the cold side of the north-hemisphere. Thanks for comments/replies!


title: Why are non-horizontal levers not considered to be in equilibrium?

text: Consider a triple-beam balance, like so: ![enter image description here](http://www.microscopesamerica.com/catalog/images/images/Large%20image%20Ohaus%20Triple%20Beam%20Balance%201610-00%20Cup%20Platform.png) An unknown mass is placed on the left pan, and the provided weights are moved on the right until the lever arm comes to rest at an exactly horizontal position, as indicated by a line on the rightmost tip of the lever arm. Often, when I'm using the device and I'm close to the equilibrium point, the lever arm will come to rest slightly higher or lower than horizontal, so I'll adjust the weights accordingly until the lines align perfectly. However, I don't see why the arm must be perfectly horizontal to read an accurate value. Isn't a stationary lever -- no matter what the angle -- an indication that there is no net torque on the system? If so, wouldn't that demonstrate that the masses are balanced in an appropriate way? In other words, why doesn't a lever which is stationary in a non-horizontal position remain stationary when placed horizontally (and vice versa), since the net torque is zero in both cases?


title: What's the difference between the five masses: inertial mass, gravitational mass, rest mass, invariant mass and relativistic mass?

text: I have learned in my physics classes about five different types of masses and I am confused about the differences between them. What's the difference between the five masses:   1. inertial mass,    2. gravitational mass,   3. rest mass,   4. invariant mass,   5. relativistic mass?


title: Questions about gravitational and inertial mass

text: 1. What differences between gravitational mass and inertial mass? I cannot tell the differences between them.    2. In history, which concept was put forward firstly?    3. Are there some experiments to prove they are identical?


title: Understanding the different kinds of mass in gravity

text: On this site, the Phys.SE question Is there a fundamental reason why gravitational mass is the same as inertial mass? has been asked. See also this Phys.SE question. The 'answer' provided on this forum has been that the curvature of spacetime explains both. The answer is still cryptic for me as I am more a concrete thinker. Newton said $F=ma$. I can use this formula to measure inertial mass. Experimentally I can measure the motion of an object while applying a constant force to it. Newton also said $F=\frac{GMm}{r^2}$. In this case, what simple experiment will allow the measurement of gravitational mass?


title: Why time difference is permanent and mass increase is temporary?

text: When a clock is transported here and there into space and then brought to the same place it differs with the other clock. When particles are accelerated with high speeds and then brought to rest their mass again gets back to its original rest mass. Why? Answer allegorically please.


title: Why does string theory have such a huge landscape?

text: I was browsing through _Foundations of Space and Time,_ a compilation of essays on various theories of quantum gravity. The following passage in the introduction intrigued me: > _Each compactification leads to a different vacuum state.... at least one > state should describe our Universe in its entirety.... the enormous number > (~10^500 at last count) of solutions, with no perturbative mechanism to > select mechanism to select among them, leads some critics to question the > predictive power of the theory..Even more worrying is that, while the theory > is perturbatively finite order by order, the perturbation series does not > seem to converge._ I don't know anything about string theory and so I could not make head or tails this. All I know is that ~$10^{500}$ is a very large number.   1. What exactly is a 'solution' in string theory? Is it a spacetime metric of some sort or the terms of a S-matrix of some sort?    2. Why are there so many 'solutions'?    3. I thought string theory was supposed to be finite, why do perturbative series still diverge?   4. Is there any experimental technique to limit the number of 'solutions'?    5. Will experimental techniques be able to pinpoint a solution within present day string theorists' lifetimes too? If not, how long will it take before we can experimentally probe these things?    6. Are string theorists completely relaxed about these issues? Or are they in anguish?


title: Phases of the moon video

text: I am an educator, and I am looking for a specific video. In the video, they ask some middle school students and some college graduates about why the moon has phases. Most of the students in both the groups get the answer wrong, saying that the phases of the moon happen because of the shadow of the Earth. I remember that they also interviewed the teacher of the middle school students, and she was really perplexed that her students didn't know the right answer. Another thing I remember from the video was that the middle school kids were not sure of their answers, but the college graduates (who are at their graduation ceremony) were really sure. I want to use that video for educational purposes, but I can't find it. Can you please help?


title: Need help buying binoculars online for astronomy (10x50)

text: After reading much online I've decided to by a 10x50 porro prism Binoculars. The one I have in mind http://www.letsbuy.com/celestron-upclose-10x50-p-34652 has BK7 prisms. The one I would like to buy is this: Olympus 10x50 DPS I but it is never available and a tad bit more expensive. Is buying binoculars or telescopes online a bad thing as I've read you need to inspect them carefully before buying? Also will the prism difference (BK7 vs BAK4) make much of a difference for the 10x50 range?


title: How are interplanetary trajectories found?

text: How are interplanetary trajectories that involve gravity assist maneuvers found? Examples:   * the MESSENGER spacecraft made flybys of Earth, Venus, and Mercury before getting into orbit   * the Juno spacecraft will flyby Earth (returning after launch) before continuing to Jupiter   * many more... Are these found using a brute force search of virtually all possible paths or is there a more direct method for finding these helpful alignments? If I decided to leave for Neptune today (using gravity assist), how would I find a good route and are such tools available on the desktop?


title: How do I calculate the curve of a parabolic mirror to melt the ice from my street gutter?

text: I want to make a concave parabolic mirror that will have a focal point six inches below where I place it (on the edge of the sidewalk) so that it will melt the ice collecting in the gutter below and clear a path for the water to drain. I will probably be using shiny stainless steel for the reflector, so it won't be a fully reflective mirror. What would be the ideal size, and how do I calculate the curve needed to concentrate the heat to that focal point? Edit: Here's a real life example of someone doing this unintentionally: Reflected light from London skyscraper melts car


title: The formula used to calculate electrical potential energy

text: ![enter image description here](http://i.stack.imgur.com/QoSeL.png) Sorry for the ugly picture but it makes my question more understandable. The $\Delta V$ from $A$ to $B$ is calculated by$$\int_A^B E \, \mathrm{d}r$$ where $r$ is the distance between $A$ and $B$. The curve line is the real path the charge take going from $A$ to $B$. Suppose that the green arrow is the $\vec E$ and the red arrow is $dl$ at some arbitrary point on the path the charge move. From what I learned from class $$\int_A^B E \, \mathrm{d}r = \int_A^B E \, \mathrm{d}l$$ This is the point I don't understand and make me reconsider what I learn about work in physics. Can someone explain why $\int_A^B E \, \mathrm{d}r = \int_A^B E \, \mathrm{d}l$ Does the calculation of the work involve vector and $E\, \mathrm{d}l$ here is the dot product of $\vec E$ and $\vec {\mathrm{d}l}$ or it is calculated by projecting all the force exert to the object to the axis created by start point and end point?


title: Minkowski spacetime: Is there a signature (+,+,+,+)?

text: In history there was an attempt to reach (+, +, +, +) by replacing "ct" with "ict", still employed today in form of the "Wick rotation". Wick rotation supposes that time is imaginary. I wonder if there is another way without need to have recourse to imaginary numbers. Minkowski spacetime is based on the signature (-, +, +, +). In a Minkowski diagram we get the equation: $$ \delta t^2 - \delta x^2 = \tau^2 $$ Tau being the invariant spacetime interval or the proper time. By replacing time with proper time on the y-axis of the Minkowski diagram, the equation would be $$ \delta x^2 + \tau^2 = \delta t^2$$ In my new diagram this equation would describe a right-angled triangle, and the signature of (proper time, space, space, space) would be (+, +, +, +). ![enter image description here](http://i.stack.imgur.com/YVF18.jpg) I am aware of the fact that the signature (-, +, +, +) is necessary for the majority of physical calculations and applications (especially Lorentz transforms), and thus the (+, +, +, +) signature would absolutely not be practicable.( Edit: In contrast to some authors on the website about Euclidian spacetime mentioned in alemi’s comment below) But I wonder if there are some few physical calculations/ applications where this signature is useful in physics (especially when studying the nature of time and of proper time). Edit (drawing added): Both diagrams (time/space and proper time/space) are observer's views, even if, as it has been pointed out by John Rennie, dt is frame dependent and τ is not.


title: Statics: particle mechanics versus rigid body mechanics

text: 1. In particle mechanics where the notion of rotation does not apply, particles are said to be in static equilibrium when the sum of the external forces acting on the particle of interest in all directions equals zero.   2. In rigid body mechanics where the notion of rotation applies (or at least the concept of invariant distances between points), rigid bodies are said to be in static equilibrium when (1) the sum of the external forces in all directions equals zero, and (2) the sum of the external moments in all directions equals zero. My question is: in rigid body mechanics, where does the equation on moments come from? Is it a principle similar to Newton's law in particle mechanics or can it be proven from other assumptions (like, for instance, the invariance of distances separating two points)


title: detailed balance in the context of the ising model

text: I am having a very basic problem understanding the idea of detailed balance, particularly in the context of the Ising model. Most references I have found contain the following phrase: "In equilibrium, each elementary process must be equilibrated by its reverse process". What does it mean for one process to equilibrate another? In particular, I am trying to understand the section here: http://en.wikipedia.org/wiki/Ising_model#Algorithm_Specification in which they state that the given form of selection probabilities is required by detailed balance, but I suspect that that will follow once I understand what detailed balance actually means. Thanks!


title: Grounded conductor inside a uniform electric field

text: I am working on a textbook problem of a grounded conductor inside a uniform electric field. The textbook states that "grounded" means potential = 0. In my opinion, "grounded" should mean "same potential as infinity". But in this case we can't set potential at infinity equal zero. So my question is, what is actually the meaning of "grounded". Am I right that it means "equal potential with infinity"? What does it mean by "grounded" in this question when the potential at infinity can't be set to zero?


Where does the energy of a light bulb come from? Is it from the coil of wire, magnet in the generator, mechanical input to the generator or plug where the generator is connected to the wall?


title: How to calculate loss due to Gaussian beam divergence of a laser going through multiple lenses?

text: To better explain my question, I will need to give a brief description of the configuration used in 2D MEMS switches. So, the next figure shows a configuration of a 2D MEMS switch, a light beam arrives from a fiber to the input port, travels inside the switch until it meets a mirror that is in the standing state to reflect the beam to the output port. ![2D MEMS Switch](http://i.stack.imgur.com/bSdBJ.jpg) The output beam from the fiber is wide, therefore, they collimate it using a collimator at the input. This collimator is picked such that the beam waist is minimum at the mirror of the worst case scenario (i.e., longest path). This path is shown in the next figure. ![Analysis of the beam Gaussian divergence](http://i.stack.imgur.com/QVZHy.jpg) During the analysis of the power loss, there is a loss due to the imperfection in the reflection of the mirror, which ranges from 1% to 3%, and there is a loss due to the Gaussian beam divergence and the existence of the mirror 1d in the beam's path. According to the papers, "The optical signal loss due to Gaussian-beam divergence for a mirror of radius R at distance z is": ![loss due to Gaussian beam divergence](http://i.stack.imgur.com/hCE7I.jpg) Usually, they maintain a ratio R/W(z) of 1.5 to 2. Note that the beam propagates in the free space from the input port to the mirror and from the mirror to the output port. This is because mirrors other than the mirror 1d are in the sleeping state (i.e., they are out of the beam's path) My question is: If we assume a case in which the beam propagates in a similar configuration, however, at the positions of the mirrors from 1a to 1c, there are switching elements with the same positions and dimensions made of glass such that the beam propagates through them. What would be the impact of these elements from 1a to 1c on the loss due to the Gaussian beam divergence? Would it be the summation of the losses using the provided equation by at different distances, in other words $L_{Gauss(at\ 1a)}+L_{Gauss(at\ 1b)}+L_{Gauss(at\ 1c)}+L_{Gauss(at\ 1 d)}+...$ If not, then why? and how can I calculate it? Reference: CY Li et al., "Using 2x2 switching modules to build large 2-D MEMS optical switches"


title: Does the reaction force appear without delay?

text: According to Newton's law of action-reaction, there is a reaction force for the action force. He did not say when the reaction appears, whether immediately or with a delay. Could you tell me the truth? If the reaction appear immediately, does it disobey the relativistic principle that the changes must not be faster than the speed of light.


title: If the velocity of particle $A$ exceeds that of $B$, is the acceleration of $A$ greater than $B$?

text: Two particles $A, B$ are travelling along parallel straight paths. At some point, the velocity of $A$ exceeds that of $B$. Does this _necessarily_ mean that the acceleration of $A$ is greater than the acceleration of $B$? If you look at the $v - t$ graph of the two particles, the lines would intersect. Probably, starting off, the velocity of $B$ would be greater, but since the slope of the velocity of $A$ would be greater it would intersect with the graph of $B$ and exceed it. I couldn't think of any other situation. So, my conclusion was that the acceleration has to be greater. But my textbook says otherwise. How come? EDIT: This is question 13 from chapter 2 in Resnick halliday physics. To clarify: the problem does NOT assume that initally A's velocity was lower than B's. (See comments)


title: Superpositions with two observers

text: This is a bit of an odd question. I'm not a physicist, so bear with me if I say something wrong. Lets say you have some sort of quantum event where matter is in a superposition. Standing next to you is another scientist waiting to observe the results (and, in theory, collapse the suposition). You go to get a cup of coffee while your fellow scientist stays in the room. Your fellow scientist observes the result of the experiment while you are out of the room but does not tell you what the result was. There are three possible options here for when you return to the room:   1. The matter is still in a superposition for both you and the other scientist.   2. The matter is no longer in a superposition for either of you (even though you have not observed the event and have no knowledge of what happened).   3. The matter is in a superposition only to you. So which option is it? If the answer is option 2, would that mean that we as humans have some kind of "superpower" forcing quantum superpositions to collapse as soon as we see them?


title: Why aren't there more than three generations of the leptons and quarks?

text: There are three generations of electrons, neutrinos, and quarks. The second and third generations of electrons and quarks are unstable and decay into lighter particles. Why are there exactly three generations? Is it possible that there are more generations of increasingly massive and unstable particles that we aren't able to discover yet (for instance, at higher energy levels that we are capable of), or is there some known reason why it has to be exactly (and can't be more than) three? edit: in addition to the link above, I also found this question helpful: What Do We Get From Having Higher Generations of Particles?


title: How are classical optics phenomena explained in QED (color)?

text: How is the following classical optics phenomenon explained in quantum electrodynamics?   * Color According to Schroedinger's model of the atom, only particular colors are emitted depending on the type of atom and the state of its electrons. Then, how it is possible that the same type of matter changes color in relation to temperature? For example, water is transparent with a light blue tint, but snow is white (which means, pretty much, that photons have no particular color in the visible spectrum). Split by request: See the other part of this question here.


title: Is it safe to use any wireless device during a lightning storm?

text: I need "educated" reasons whether it is safe to use any wireless device during a lightning storm. Most people said don't use it but they cannot explain why.


title: Is temperature in vacuum zero?

text: From Wikipedia entry on Kinetic Theory > The temperature of an ideal monatomic gas is a measure of the average > kinetic energy of its atoms. Now if I remove all the particles from the box shown below will the temperature be zero? ![alt text](http://i.stack.imgur.com/3E0Ak.gif)


title: Is the total energy conserved in a moving reference frame?

text: I have a ball attached to a spring and the spring is attached to a wall. There is no gravity for simplicity. In the rest RF the oscillating ball energy is conserved: T + U = const. In a moving RF it is not conserved. I would like to see the shortest answer to the question "Why?". | <\-- -->   |/\/\/\/\/\/\/ **O**   | =====> $V_{RF}-->$ **Edit:** For those who has doubt - I choose the moving RF velocity equal to the maximum ball velocity, for example. Then the ball with its maximum velocity in the rest RF looks as still and does not have any potential energy in the moving RF (the maximum velocity is attained at the equilibrium position where no force acts). So T = 0 and U = 0. At the farthest right position the ball looks as moving with $-V_{RF}$ and having a potential energy $kx^2/2$, both energy terms are positive ($v^2 > 0, x^2 > 0$). So now the total energy of the ball is positive and thus is not conserved. It oscillates from zero to some maximum value. Why?


title: Radio waves and frequency of photon

text: Is 89MHZ station emitting photons of 89MHZ frequency? (I mean $\nu$ in $E=h\nu$).


title: Redshifted Photon Energy

text: A photon emitted from a receding source (Doppler redshift) has less energy when detected at an observer's location. Please explain the energy loss from the perspective of energy conservation.


title: Qualtitative explanation for the link between low magnitude of high z supernova and accelerated expansion

text: Is there any explanation on a qualitative level why we can see in the observed magnitude vs. redshift z plot that the universe is expanding accelerated? See for example here: http://hyperphysics.phy- astr.gsu.edu/hbase/astro/univacc.html The observed magnitude is, if the absolute magnitude is well know as it is the case for Supernova 1a, a measure for the distance. The redshift z is a measure for how much the object hast moved relative to us., i.e. also some kind of distance indicator. My problem is that I can't get together how we now conclude that we have an accelerated expansion, besides the best fit has $\Omega_{\Lambda}\neq 0$. Any help or link would be awesome.


title: Relativity Question Fireworks explosion

text: A firecracker explodes at the origin of an inertial reference frame. Then, 2.0 microseconds later, a second firecracker explodes 300m away. Astronauts in a passing rocket measure the distance between the explosions to be 200m. According to the astronauts, how much time elapses between the two explosions? Okay. My textbook answers this question using spacetime interval consistency which is simple. I don't understand why the time dilation formula does not work: $$Δt = \frac {Δτ}{ \sqrt{1-\frac{v^2}{c^2}}}$$ Where v is simply the ratio between 300m and 2 microseconds. Δτ=? Δt=2x10^-6 s


title: Matter-antimatter asymmetry problem

text: As we know that matter-antimatter asymmetry is one of unsolved problems in physics. One possible solution to this problem is given as baryogenesis which produce asymmetry in rate of creation between matter and antimatter particles. But doesn't alternate solution like "different regions of space with different type of particles " holds more ground.. Means in one region matter particle dominates (the region we live ) and another region anti matter particle will dominate. When particle-antiparticle pair created from energy (at that energy is so much high that particle- antiparticle pair could be created from energy according to $E=mc^2$) before they meet and annihilate with each other they also has equal chance of meeting with same type of particle in neighborhood, because after some time of big bang the four force were united and gravity was as powerful as remaining three forces. So now in 50% of all pairs destroyed by annihilation and other 50% clumps together with same type of particle means matter with matter and antimatter with antimatter and then inflationary epoch throw these clumps from each other at very large distance so that they can not meet each other and have chance of annihilation. And we now can not see these regions because of accelerated expansion of universe because of dark energy. Doesn't this hypothesis is more or at least equally valid with baryogeneis hypothesis.


title: Equation to estimate droplet volume falling from a needle of a known orifice diameter at a given flow rate

text: I am doing some research to see if there is a simple equation (or an equation that can be simplified) to estimate the volume of a drop of liquid falling due to gravity based upon the approximate flow rate, and perhaps the viscosity/surface tension of the fluid. Basically this is a drip chamber fluid set for delivering medications. Clinicians routinely calculate fluid flow based upon the number of drops per minute assuming a fixed drop size. However since drop size varies with flow rate. Using a fixed volume size has some amount of inaccuracy. I would like to see if I can be more accurate in determining actual flow rate.


title: Questions about deduction the dual form of Frobenius's Theorem

text: I am reading Page 435, _General Relativity_ by Wald. Let $T^*\subset V^*$ be a subspace of the dual tangent space of a manifold, $W\subset V$ be the subspace of the tangent space annihilated by $T^*$, i.e. for every $\omega\in T^*$ and every $Y\in W$ we have $\omega_aY^a=0$. Now the author says the Frobenius's theorem implies $$ 2Y^aZ^b\nabla_{[b}\omega_{a]}=0 $$ for every $Y,Z\in W$ and every $\omega\in T^*$. Then the author claims it holds if and only if > $$ \nabla_{[b}\omega_{a]}=\sum_{\alpha=1}^{n-m}\mu^\alpha_{[a} v^\alpha_{b]} > $$ where each $v^\alpha$ is an arbitrary one-form and each $\mu^\alpha\in > T^*$ Can anyone explain to me why? * * * Also, the author later says > $\nabla_{[a}\xi_{b]}=\xi_{[a}v_{b]}$ for some one-form $v$ if and only if > $\xi_{[a}\nabla_b\xi_{c]}=0$. I can work out the "=>" part, but don't know why "<=" holds. Could anyone help?


title: How do I see things of the bright room, being in the dark room?

text: Visible light emitted or reflected from the objects around us provides information about the world. If I sit in a dark room, and see the bright room outside, I am able to see all the objects of that bright room. In other words, it mean light emitted or reflected from those objects of the bright room are entering into the dark room. Shouldn't that make my room bright? But, my room is dark and I am able to see those objects of bright room, both are contrary? Edit: If we consider another situation like the one in the picture below, lets assume that we move as far from the street light, that even in the presence of street light the place remains as dark as it was before. I believe even then we can see the street light, won't we? If we agree that we still can see the lamp, it mean that we are able to see the lamp, without the ray from lamp hitting our eye? Won't it be contrary? ![enter image description here](http://i.stack.imgur.com/ChAQ6.jpg) Edit: Lets consider a laser beam in the dark room (in the picture room is not totally dark, but assume a dark room). Look the laser in the same angle as shown in the picture, as laser remains narrow over long distance, I hope we can assume light is not spreading in other directions. But I hope we can see it even though light is not spreading and reaching me, how is it possible?, I hope this made my question more clearer. Sorry, I am unable to understand the concept, if this question is silly, pardon me. ![enter image description here](http://i.stack.imgur.com/uHxJx.jpg) Sometimes I might have misunderstood the concept, if so, pardon me and explain.


title: The source of gravitation in a spacetime without matter

text: In a discussion concerning: Physical meaning of non-trivial solutions of vacuum Einstein's field equations there were a number of answers claiming that the flatness of the Ricci space (Rµv=0) does not necessarily entail the flatness of the Riemannian spacetime. This is explained by the fact that besides the Ricci tensor, the Riemann curvature tensor depends also on the Weyl tensor said to govern the propagation of gravitational radiation. And although Rµv=0, the Weyl tensor can still be non-zero. That being so, it seems that there are some gravitational forces not included in Einstein's field equations, as the Ricci tensor (Rµv) and the Einstein's tensor (Gµv) are said to be trace-reversed (meaning that when one of them vanishes, the other does too). So, if Rµv=0 does not exclude the presence of gravitation - gravitational radiation can still be found through Weyl tensor - then (since Gµv=0) Einstein's gravitational field equations must be incomplete? Yet there immediately arises another - and in my opinion, more important - question: **What is the source of this gravitational radiation, since Rµv=0 means the whole universe is void of matter?**


title: How do Permanent Magnet Generators Work?

text: Why we don't use this in our houses to generate the electricity? Isn't the electricity generated by the magnets strong enough? Why do we have to pay for electricity if we can just create it by pushing the magnets attached to a rotor of the generator?


title: First Postulate of Special Relativity: What does it mean?

text: Wikipedia has this quote: > _Special principle of relativity:_ If a system of coordinates K is chosen so > that, in relation to it, physical laws hold good in their simplest form, the > same laws hold good in relation to any other system of coordinates K' moving > in uniform translation relatively to K. — Albert Einstein: The Foundation of > the General Theory of Relativity, Part A, §1 Does this simply mean that any sound theory expressed in K, should be able to withstand a transfer to another system Z and still hold "true"? Or is there more to "uniform translation relatively to K"?


title: Intuitive explanation of the inverse square power $\frac{1}{r^2}$ in Newton's law of gravity

text: Is there an _intuitive_ explanation why it is _plausible_ that the gravitational force which acts between two point masses is proportional to the _inverse square_ of the distance $r$ between the masses (and not only to the inverse of $r$)?


title: Gravity force strength in 1D, 2D, 3D and higher spatial dimensions

text: Let's say that we want to measure the gravity force in 1D, 2D, 3D and higher spatial dimensions. Will we get the same force strength in the first 3 dimensions and then it will go up? How about if we do this with Electromagnetic force? I've include the Electromagnetic force just to see if I can find an analogy to the gravity force behavior.


title: Newtonian gravity equation in a 2 dimensional world

text: I am wondering if my line of thought is correct - and thus the resulting answer to the problem above would be correct. As we know the gravitational force (of two point masses) is given by $$F = G\frac{m_1m_2}{r^2}.$$ So the gravitational force/vector field reduces with the distance squared. Now this is the formula in 3 spatial dimensions - and I always picture it as a point with gravitational field lines moving outward. Then the "strength" of the field would be the density of the lines. And hence the density drops with the distance squared (as it is inversely proportional to the area of the sphere at that distance). Now taking this line of thought to other situations we can think of course about a hypothetical 2 dimensional world. Here gravity would also be. And here we can also see the density of the "gravitational field lines". However as they propagate only in 2 spatial dimensions the density would be inversely proportional to the circumference of the circle at a distance $r$. And hence the formula would lose the square and become like: $$F = G\frac{m_1m_2}{r}$$ (With change $G$, and obviously we can't talk about mass in 2d). Is this line of thought correct?


title: Ambiguous points in spontaneous symmetry breaking of discrete symmetry

text: For a discrete symmetry: At the minimum value of the potential, $V$, in the Lagrangian density, why do we take $\phi= \langle v\rangle + \eta$? Aren't we deliberately breaking the symmetry? If we don't do this, the symmetry is intact. On the other hand, if we replace $\phi$ by $\phi= \langle v\rangle + \eta$, even when not in a ground state, then also the symmetry will be broken in $\eta$ field. Please explain.


title: Is there a possibility of hydrogen ignition when filling a weather balloon?

text: There's a guide here on how to seal a weather balloon after filling: http://ukhas.org.uk/guides:sealing_the_balloon http://ukhas.org.uk/_media/guides:neck8.jpg Won't the static electricity from the duct tape cause the hydrogen gas to ignite (there's always a little air (oxygen) in the balloon before filling, plus, a very little amount can leak from the filler)?


title: Conservative Vector Fields

text: I was always told that to find whether or not a vector field is conservative, see if the curl is zero. I have now been told that just because the curl is zero does not necessarily mean it is conservative. However, if it is non-zero it is definitely not- conservative. IE: $\vec{F}=\frac{K}{r^3}\hat{r}$ (Spherical coordinates, $K$ is constant) To show this is conservative I would go ahead and take the curl. It will be zero - but that is not definitive proof it is conservative? How would I show it is?


title: Asymptotics of the Wigner 6j Symbol

text: So, in doing some numerical computations in QFT, I've run into the following Wigner 6j-Symbol: $ \left\\{ \begin{array}{ccc} x & J_1 & J_2 \\\ \frac{N}{2} & \frac{N}{2} & \frac{N}{2} \\\ \end{array} \right\\} $ In the regime where $x \ll J_1,J_2,N$ and $J_1 \approx J_2 \approx N$, and $N$ is large. I would like to know if there is an asymptotic formula for such a symbol, or if one can be derived. Using symmetries we can get $ \left\\{ \begin{array}{ccc} x & \frac{1}{2} \left(J_1+J_2\right) & \frac{1}{2} \left(J_1+J_2\right) \\\ \frac{N}{2} & \frac{1}{2} \left(N+J_1-J_2\right) & \frac{1}{2} \left(N-J_1+J_2\right) \\\ \end{array} \right\\} $ Perhaps this could help, I'm really not sure.


title: Helmholtz free energy from a relation for entropy

text: The Legendre transformation defines the helmholtz free energy (at least according to my lectures) as: $F(T,V,N)=E-TS$ It also says to start with $E(S,V,N)$ and $T=\frac{\partial{E}}{\partial{S}}$ My question is I have a relation for entropy (I won't give it because I want this to be more of a concept based question), in terms of the standard $S(U,N,V)$ where U is the energy, I can re-arrange for energy easily. Obviously the E and T to put into the equation are pretty standard it quite clearly states to use the function for each but the ENTROPY, do I just write the variable S next to the partial of E wrt S or do I use the relation I have for Entropy?


title: Solving the equation of relativistic motion

text: How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge $e$ and mass $m$, with 4-momentum $p^a$ and electromagnetic field tensor $F_{ab}$ of a constant magetic field $\vec B$ perpendicular to the plane of motion. $$\frac{dp^a}{d\tau}=\frac{e}{m}F^a{}_bp^b$$ ? Let the the initial condition be $$p^a=(E_0 ,\vec 0)$$ I can see that the differential equation resembles that of a SHM equation or a cosh, sinh one if it's a scalar equation. However, I don't know how to deal with a tensor equation. Could anyone please explain? Thank you.


title: Redshifted from what?

text: We need to know two of the following three to calculate the third: redshifted color, baseline color, and velocity. The velocity is related to the difference between the redshifted color and the objects baseline color. How do we know the baseline color of distant objects to know the amount of redshifting?


title: What happens to the energy not absorbed by a radio?

text: If a radio tunes to a specific frequency, where does the excess energy go? If one continues to hit the resonant frequency, shouldn't the wire begin to melt at some point from too much energy?


title: Magnetic Field versus Line Charge

text: Isn't a magnetic field basically an electric field originating from a line charge, but as seen in a boosted frame? I mean, that's where the relativistic explanation comes from right?


title: can gapped systems have gravitational anomalies?

text: The question is in the title. If it is possible, what are some examples of gapped systems--either quantum field theories or condensed matter systems--which exhibit some kind of anomaly when coupled to a metric with curvature or placed on a spacetime with non- trivial topology?


title: Neutral shell(with a charge inside) in an electric field

text: > A positive point charge $Q$ is kept eccentrically inside a neutral > conducting shell. An external uniform field E is applied. Then: > > a) Force on Q due to E is zero > > b) Net force on Q is zero > > c) Net force acting on Q and conducting shell considered as a system is zero > > d) Net force on the shell due to E is zero My try: Since the shell is neutral, thus net force on it by E must also be zero. Also since Q is electrostatically shielded(by placing it inside a shell), thus net force on it must also be zero. But the answer I'm getting(as you might have guessed) is wrong(that's why I've asked this question). Please point out the flaw in my reasoning.


title: Is a Perfect/Lossless Mirror possible?

text: In traditional mirrors, some of the input light is absorbed by atoms in the mirrors surface and are 'lost' as heat, degrading the quality of the reflected image. Could this loss be compensated by an array of "powered elements" arranged to reflect nearby photons repelling them with some sort of electo-magnetic force, to completely prevent loss? _This would realize theperfect mirror, reflecting all light back._ ![enter image description here](http://i.stack.imgur.com/OD5FI.png)


title: What is the Levi--Civita connection of a Wick rotated metric?

text: A Wick rotation is a transformation that allows to change from a Lorentzian manifold to a Riemaniann manifold. In the cases when this is possible, is the Levi-Civita connection of the Riemaniann manifold the same connection as the initial Lorentzian manifold?


title: Does the uncertainty principle apply to photons?

text: Wikipedia claims the following: > _More generally, the normal concept of a Schrödinger probability wave > function cannot be applied to photons. Being massless, they cannot be > localized without being destroyed; technically, photons cannot have a > position eigenstate and, thus, the normal Heisenberg uncertainty principle > does not pertain to photons._ Edit: We can localize electrons to arbitrarily high precision, but can we do the same for photons? Several sources say "no." See eq. 3.49 for an argument that says, in so many words, that if we could localize photons then we could define a current density which doesn't exist. (Or something like that, I'll admit I don't fully understand.) It's the above question that I'd like clarification on.


title: What is the significance of action?

text: What is the physical interpretation of $$ \int_{t_1}^{t_2} (T -V) dt $$ where, $T$ is Kinetic Energy and $V$ is potential energy.   How does it give trajectory?


title: Angular momentum of a rotating black hole

text: Is there an upper limit to the angular momentum of a rotating (Kerr) black hole?


title: Is it possible to change the path of a single photon?

text: In other words, if a photon is emitted from source, is it possible to change its course en route either by introducing a gravitational lensing or some sort to change the road it travels (spacetime) before it reaches it's source?


title: Lorentz Invariant Integration Measure

text: When we canonically quantize the scalar field in QFT, we use a Lorentz invariant integration measure given by $$\widetilde{dk} \equiv \frac{d^3k}{(2\pi)^3 2\omega(\textbf{k})}.$$ How can I show that it is Lorentz invariant?


title: What is the mean ionospheric height?

text: I am reading some articles about the ionosphere and I am a little bit confused about the terms _mean ionospheric height_ and _effective height of the ionosphere_. Are these the same thing? * * * I would refer to two texts: Variations of yearly mean values of effective heights for the ionospheric sporadic E-layer by V.F.Petrukhin, E.A.Ponomarev, V.D.Kokourov, and N.A.Sutyrin > Each type was analysed separately by calculating the yearly mean values of > effective heights h’Es. It was found that the effective heights of the > sporadic EsC, EsL and EsF vary within 105 - 132 km region with a typical > period of a ... > > ...During 1967-1969 the average height for this sporadic layer type > decreased relative to the mean level by about 20 km; for a long time > afterwards (about 17 years) these values remained low, and it was not until > 1985-1987 that they returned to the long-term mean level. and Klobuchar, J. A. (1975). Klobuchar - First-Order Time delay Degrees (pp. 1–24). Massachusetts: Air Force Cambridge Research Laboratories. > ... The TEC must be found at the geographic point where the ray path > intersects the mean ionospheric height, rather than at the user location. > This point is taken here at a mean height of 350 kilometers. ... * * * I know that the mean height is used when one would like to express at which height a signal would pierce the ionosphere if we would approximate the ionosphere with one thin layer. And I also know that this is not the height of the electron density maximum. **The question is then, how it is (how are they) calculated?**


title: Explain reflection laws at the atomic level

text: The "equal angles" law of refection on a flat mirror is a macroscopic phenomenon. To put it in anthropomorphic terms, how do individual photons know the orientation of the mirror so as to bounce off in the correct direction?


title: How does reflection work?

text: In Newton's model of light as being composed of particles, it's easy to imagine reflection as being the rebounding of individual corpuscles off a surface. However, since light can also behave like a wave, it poses a challenge in visualizing reflection. How does a wave reflect off of a surface, whether it be specular reflection or diffuse reflection? Must the wave be first absorbed, and then re-emitted? Or is there a different mechanism?


title: Relection of light

text: If I recall my physics correctly, and it was a long time ago, when a photon strikes a reflecting surface that specific photon is not what is reflected-- rather the photon excites an electron which ejects a new photon. My question is how does the new photon know it has to come out at the angle of incidence?


title: What IS reflection?

text: How does quantum electrodynamics actually explain HOW reflection occurs on a microscopic scale? Note that Feynman's QED lecture series/book is not sufficient, as he only assumes that light DOES reflect ('turn around and go back') in order to expound his path integral theory. My question is why does light have the propensity to turn around in the first place. Is it just the absorption and re-emission of photons, and if so, why does it happen so uniformly (i.e. on a shiny thing, entire scenes are reflected near- perfectly). In essence, why are flat things shiny? Are all the molecules arranged at exactly the same angle?


title: How do mirrors work?

text: Apparently, light is just a certain wavelength, or "the visible spectrum" of electromagnetic waves. If I recall correctly, my physics teacher explained to me that electromagnetic waves are basically consisted of two, interchanging parts. The "electric" and the "magnetic" parts of the wave are somehow manifesting each other in synchronized intervals, or they are (more probably) causing each other and canceling themselves out in the process. I checked wikipedia and the transition seems to be somehow interpolated (but then again, many things in nature are). So, which part of the mirror actually reflects the wave? Which of these two parts? Both? How come the wave doesn't get heavily distorted in the process? I guess the actual electrons of atoms of silver play a role, but why isn't every material reflective, then? Because is isn't "perfectly" flat? If I lined up atoms of a non-metal element in a perfect plane (maybe several rows, actually), would it reflect light just as mirrors do?


title: What really is reflection?

text: What really is reflection? Is it just the reemission of EMR? I asked my teacher, he said in quantum sense, it is true. But when I read something about emissivity in Stefan Boltzmann's equation, it states that if an object reflects most light, then it absorbs and reemits less. So what it said means reflection and absorption and reemission are different concepts.


title: What exactly is the connection between the Jacobi and Bianchi identities

text: While reviewing some basic field theory, I once again encountered the Bianchi identity (in the context of electromagnetism). It can be written as $$\partial_{[\lambda}\partial_{[\mu}A_{\nu]]}=0$$ Here, $A_\nu$ is of course the electromagnetic potential. This formula is immediately reminiscent of the Jacobi identity: $$[A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0$$ This is even clearer in general relativity, where we have $$\nabla_{[\lambda}R_{\rho\sigma]\mu\nu}$$ which we can rewrite, remembering the definition of the Riemann tensor in terms of the commutator of covariant derivatives, as $$[[\nabla_\lambda,\nabla_\rho],\nabla_\sigma]+[[\nabla_\rho,\nabla_\sigma],\nabla_\lambda]+[[\nabla_\sigma,\nabla_\lambda],\nabla_\rho]=0 $$ This all looks like there should be some profound connection here, but I'm incapable of pinpointing it. Maybe one of the experts here can make this more precise? I'd love to get to know more about this. Any comments are much appreciated. I'd also be grateful if someone could suggest (more) appropriate tags to use.


title: Initial velocity of an orbiting object that lands on the planet with zero speed w.r.t the surface

text: How would you determine what initial velocity $v(r)$ of an object would have to be at some arbitrary point in the vicinity of a planet such that the object will end up on the surface of the planet with a zero velocity with respect to the point on the surface of the planet where it lands? Assume the planet is rotating and the object is traveling by the planet and one could somehow alter it's velocity at a point with an impulse. Hence what kind of initial velocity does the object need to be given so that it will eventually be "drug" to the surface of the planet in a way that it lands. One way to think of it, is to imagine it spiraling in and when it reaches the surface it's velocity is equal to the rotational velocity of the surface and it's verical velocity w.r.t the surface is zero as well. (Assuming no atmosphere on the planet)


title: Heat flow in a hollow cylinder

text: Consider a hollow cylinder of different outer radius and inner radius and two different temperatures are maintained at the outer and inner surfaces such that inner temperature is higher. Because of this heat will flow radially outward. Now I don't understand why we need to use integration to find rate of heat flow that is, why isn't the temperature gradient constant? Why can't we directly apply heat conduction formula?


title: Why does $8\pi/3$ appear in the equations describing cosmological expansion?

text: What is the significance of $8\pi/3$ in the first Friedmann Equation, and in the question concerning the time independence of the Hubble Constant? Is it the 'same' $8\pi/3$ that appears in the total cross section formula of Thomson Scattering ?


title: Where does the principle of superposition come from in newtonian mechanics?

text: Part of the definition of the concept of force is that if particle $1$ exerts a force $F_1$ on particle $3$ and particle $2$ exerts a force $F_2$ on particle $3$, the total force on particle $3$ is $F_1+F_2$. But, is the principle of superposition deducible from Newton's laws or is it an additional assumption? If so, is it always valid? Is this fact linked to the non-existence of three-body forces (or do such forces exist?) or to some kind of linearity in the laws of mechanics or to some kind of fundamental symmetry?


title: Chemical potential of particles with zero mass

text: Why massless particles have zero chemical potential?


title: Why the chemical potential of massless boson is zero?

text: In Bose-Einstein condensation, the chemical potential is less than the ground state energy of the system($\mu<\epsilon_g$). But why does the massless boson such as photon have zero chemichal potential($\mu=0$)?


title: What are the state functions telling me or how are they related to total energy?

text: I am quite new to thermodynamics and statistical mechanics so this might be an easy question: In thermodynamics you get a bunch of thermodynamics potentials, so as for example enthalpy, internal energy, gibbs energy, helmholtz energy and so on. Now my idea was, that you use them if the natural variables related to this quantity are constant. But I do have a question of interpretation: It is always true that if you have some process that the difference of the thermodynamic potentials, whose natural variables are left unchanged is equal to the difference in total energy?


title: Constant of motion

text: An exercise from Goldstein (9.31-3rd Ed) asks to show that for a one- dimensional harmonic oscillator $u(q,p,t)$ is a constant of motion where $$ u(q,p,t)=\ln(p+im\omega q)-i\omega t $$ and $\omega=(k/m)^{1/2}$. The demonstration is easy but the physical significance of the constant of motion is not so clear to me. Indeed I can show that $u$ can be rewritten like: $$ u(q,p,t)=i\phi+\ln(m\omega A) $$ where $\phi$ is the phase and $A$ the amplitude of the vibration of the oscillator. I can also demonstrate that $m\omega A=\sqrt{2mE}$, where $E$ is the total energy of the oscillator. But there is any further significance of $u$ that I'm missing?


Quite a few of the questions given on this site mention a photon in vacuum having a rest frame such as it having a zero mass in its rest frame. I find this contradictory since photons must travel at the p of light in all frames according to special relativity. Does a photon in vacuum have a rest frame?


title: Surface Tension of a Liquid - When a liquid body is acclerating

text: As far as I understand it (which admittedly isn't very far), surface tension forces are made up by the tension-attractive forces of molecules at the liquid-gas/vacuum interface, such as those between hydrogen-bond-capable molecules in water. But what happens when this liquid surface is in motion? I would assume that, given that there is no acceleration at, the surface tension doesn't really change much since they would be in some sort of "stasis", and the movement would only be that of all the molecules acting in concert. But say, if the molecules were not moving uniformly (but in a single direction), say the molecules in one part of the liquid body accelerates away from the other part, in some "pulling" motion. What happens to the surface tension here?


title: observing Quantum Mechanics

text: When you observe or measure a process in classical physics it almost never really alters the experiment. For example, if you have an Carnot engine and measure the volume and pressure of a gas in some a cylinder while the process is running you can do it without disturbing the process, meaning that if you "ran the laws of physics backwards" or ran the process backwards in time for the same amount of time you ran it forwards it will end up at the same place it started at. However, in Quantum Mechanics if you in any way observe a particle during an experiment it can ruin the whole experiment. For example: If you sent a particle through a ring and then stopped the process and ran it backwards without ever observing it, the particle would go back to where it came from but if you observed the particle in any way, (even after the experiment) it would not matter whether or not you looks at it forward or backward in time, because the probability that particle's path might fluctuate to the left is the same for either case. How does this work?


title: Energy operator

text: Does the Hamiltonian always translate to the energy of a system? What about in QM? So by the Schrodinger equation, is it true then that $i\hbar{\partial\over\partial t}|\psi\rangle=H|\psi\rangle$ means that $i\hbar{\partial\over\partial t}$ is also an energy operator? How can we interpret this? Thanks.


title: Phase space of a discrete dynamical system

text: Suppose a dynamical system of one variable $x$ with discrete time-steps. I've seen in some papers a type of graph in which $x(n+1)$ is plotted versus $x(n)$. My questions are : 1/ Can this be considered as the phase portrait of the system ? 2/ Does this method has a specific name ? 3/ Has there been any studies with regard to the topology of this space ? Thanks for your help!


title: Why does blowing on someone who is wet feel colder than on someone who is dry?

text: The title says it all. If I'm standing in the wind and I'm wet, I feel much colder than when I'm dry. This is true no matter how warm or cold the water. Why is this?


title: How to accurately explain evaporative cooling?

text: I am trying to clearly express in one or two sentences how increased evapotranspiration could cool a region. The audience is educated but non- scientific. Is it accurate to say that the water vapor has removed latent heat? Is there a more clear explanation?


title: Why I will feel colder when I get out from a swimming pool?

text: A friend of mine told me that because water heat capacity is higher. He also mentioned that it was similar to alcohol on skin effect. Assume that there are 3 situations. 1\. I did not get wet 2\. I got wet by water 3\. I got wet by pure alcohol I believe the cold order is 3>2>1 Base on the heat capacity order is water>alcohol>air. This does not match with the cold order. I also think about whether it would be due to the burning point of the material. At the burning point, the material may need more energy because change from liquid to gas. But the burning point of alcohol is still much higher (78.2C) than outdoor temperature (25C). Why?


title: Why does a breeze of wind make us feel cooler?

text: In my Astronomy class, I learned that temperature results from the speed of air molecules colliding into your skin. Thus, if the air molecules in the room have a high kinetic energy and thus collide with you at high speeds, your temperature will increase. So how does a breeze of wind, in which I imagine air molecules would be moving very fast (or if they're not moving fast, YOU are moving fast relative to them), result in feeling cooler?


title: Central charge in a $d=2$ CFT

text: I've always been confused by this very VERY basic and important fact about two-dimensional CFTs. I hope I can get a satisfactory explanation here. In a classical CFT, the generators of the conformal transformation satisfy the Witt algebra $$[ \ell_m, \ell_n ] = (m-n)\ell_{m+n}.$$ In the quantum theory, the same generators satisfy a different algebra $$[ \hat{\ell}_m, \hat{\ell}_n ] = (m-n) \hat{\ell}_{m+n} + \frac{\hbar c}{12} (m^3-m)\delta_{n+m,0}.$$ Why is this? How come we don't see similar things for other algebras? For example, why isn't the Poincare algebra modified when going from a classical to quantum theory? Please, try to be as descriptive as possible in your answer.


title: Is mid-water bouyancy a classic example of a balanced but unstable system?

text: I came to this thought experiment as I was pondering good teaching examples of stable and unstable systems. It occurred to me that stable systems are really quite abundant. For a shoot-from-the-hip example, the speed of a car is stable about a given speed given a constant rate of fuel injection, since any perturbation will disappear over time. To be perfectly illustrative, here is a ball on a hill. Note that the forces are _balanced_ in both these cases, but _stability_ is different. ![ball on a hill](http://i.stack.imgur.com/u8ss8.png) Now, the above illustrates the concepts well enough, but I like to present something that's slightly more non-trivial and try to get people to exercise real physical understanding. Consider: A submersible with a compressible cavity. A model sufficient for this will be that of a weight attached to a balloon. Saying it's an airtight bag instead of a balloon might be more straightforward, as it avoids the contribution to pressure from the balloon elasticity itself. ![submarine](http://i.stack.imgur.com/kdZAS.png) I want to make the _qualitative_ argument that given the buoyancy and gravitational forces are balanced at some underwater point (obviously below the surface and above the ocean floor), this point is unstable. The logic is that the balloon will increase in volume and decrease in density as it gets closer to the surface, where the pressure is lesser. Correspondingly, increasing depth and pressure contracts the balloon. That means that upward movement causes a net upward force and moving down causes a net downward force. Unstable. ![buoyancy water](http://i.stack.imgur.com/i4wzs.png) **Several questions**   * Does this imply that any submersible (below the surface and above the floor) must actively maintain its depth level? Is the condition associated with this claim that the submersible be more compressible than the liquid? What about a compressible atmosphere?   * Are there passive control systems that could maintain a depth setpoint?   * Would anyone like to address the problem and questions with equations, derivatives, and all that good stuff?


title: Which cosmological models support the Boltzmann Brain Paradox?

text: In this article, they mention that the Boltzmann Brain paradox is supported by 'the best cosmological models.' However, it gives no references, and I haven't found any by a Google search. I was wondering if someone here might have some links to where I can read more about this?


title: Characteristic of a common emitter transistor

text: How is Base emitter junction and collector emitter junction biased? How do we determine the value of potential difference between emitter and collector required to be maintained in order to determine input characteristic of transistor? Explanations covering nitty gritty are most welcome.


title: Maxwell's Equations: Induction

text: What is the reason for some writing Faraday's Induction Law as $$ \nabla \times E= -\frac{1}{c}\frac{\partial B}{\partial t} $$ versus $$ \nabla \times E= -\frac{\partial B}{\partial t} ?$$


title: What is the pure energy in matter antimatter annihilation made of?

text: I used to read the term "pure energy" in the context of matter antimatter annihilation. Is the "pure energy" spoken of photons? Is it some form of heat? Some kind of particles with mass ? Basically, what does "pure energy" in the context of matter-antimatter annihilation refer to?


title: Charge Analog of the Higgs Boson?

text: Since mass can be given to particles via the interaction with the Higgs Field could there be a "Charger Field" that supplies particles with charge? Possibly this would require two different "charger bosons" one for + and one for -.


title: Phase diagram for oxygen

text: Do you know where can I find simple diagram (solid, liquid, gas) for for oxygen? EDIT: I made a mistake. I wanted oxygen instead of water. sorry.


title: Quantum mechanics and observation

text: I have read several times by different supposedly knowledgeable authors that conscious observation affects quantum experiments. I think these authors are confused, by which I mean they forget that "observing" is not passive. To take the double slit experiment for example, observing means that there is at least one photon (used for measuring) interacting with the photon(s) passing thru the slit(s). My understanding is that this interaction between the photons traveling thru the slits and the photons used for measuring cause the change in the experiment, ie. whether someone is there "observing" the experiment is irrelevant. Is my understanding correct?


title: Why do electron and proton have the same but opposite electric charge?

text: What is the explanation between equality of proton and electron charges (up to a sign)? This is connected to the gauge invariance and renormalization of charge is connected to the renormalization of photon field, but is this explanation enough? Do we have some experimental evidence that quarks have 2/3 and -1/3 charges? By the way I think about bare charge of electron and proton. And I am also wondering if this can be explained by Standard Model.