How does a shadow appear to break the speed of light?
Is it really possible to break the speed of light by flicking your wrist with a laser pointer?
How do I set environment variables from Java? Qt signaling across threads, one is GUI thread? Errors "*ERROR* UVD not responding, trying to reset the VCPU!!!" Select list of node titles for a view exposed filter If a black body is a perfect absorber, why does it emit anything? I'm trying to start understanding quantum mechanics, and the first thing I've come across that needs to be understood are black bodies. But I've hit a roadblock at the very first paragraphs. :( According to :     A black body (also, blackbody) is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.   OK, that's nice. It's an object that absorbs (takes in itself and stores/annihilates forever) any electromagnetic radiation that happens to hit it. An object that always looks totally black, no matter under what light you view it. Good. But then it follows with:     A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic radiation called black-body radiation.   Say what? Which part of "absorbs" does this go with? How can it absorb anything if it just spits it right back out, even if modified? That's not a black body, that's a pretty white body if you ask me. Or a colored one, depending on how it transforms the incoming waves.  What am I missing here? How can it be that, if like charges repel, they don't repel themselves? In other words, why don't charges break apart?  About the possible duplicate: I want to know about charges in general, not just that of an electron. My response to :  Thank you very much for the extensive explanation. Unfortunately it's a bit above my level (I'm a first year electrical engineering bachelor student). This is how I understand it: If the charge is the sum of multiple separate charges, there has to be an external force that keeps this charges together. However we most often think of electrons and protons as point charges. In other words, we don't think of them as if they are made up from different (smaller) parts. But the idea of electrons and protons as point charges has its own problems. I didn't know that the electric field has a mass. From the formula, I understand that $m\propto \frac{1}{r}$. This would mean that $m\rightarrow \infty$ as $r \rightarrow 0$ (or $r = 0$), which of course is physically not possible. But there is a way to calculate the radius of an electron based on the mass, the speed of light and the constant of Planck. (Unfortunately I don't know why.) You can get around this by a technique called called renormalization, which causes the integral to converge. Unfortunately, I don't understand the rest of the answer due to my level in physics. Nevertheless I am grateful for you answer. It would be awesome if you could confirm or correct my understanding. Subset of a countable set is itself countable How is it proved that if $$A \subset B\ \text{with}\ B\ \text{countable} $$ then $A$ is either countable, finite, or empty? I think the proof involves a $1-1$ correspondence between $\mathbb{N}$ and $A$ but other than that I do not know how to proceed.  EDIT: I have checked the solution and it advises me to proceed as follows. " As a start to a definition of $$g: \mathbb{N} \rightarrow A$$ set $$g(1)=f(n_1) $$ Then show how to inductively continue this process to produce a $1-1$ function $g$ from $\mathbb{N}$ onto $A$."  So the proof according to my book involves induction. How to adjust the gap between figure and caption within the same subfloat Evaluating $\int_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}\, \mathrm{d}x$ Infinite Series $\sum\limits_{n=1}^\infty\frac{x^{3n}}{(3n-1)!}$ How can we prove that? $$\sum_{n=1}^\infty\frac{x^{3n}}{(3n-1)!}=\frac{1}{3}e^{\frac{-x}{2}}x\left(e^{\frac{3x}{2}}-2\sin\left(\frac{\pi+3\sqrt{3}x}{6}\right)\right).$$  I think if we write the taylor expansion of $\sin(u)$ and $e^u$, we can arrive from RHS to LHS, but I am looking for a way to prove it from LHS. Book recommendation for Atomic & Molecular physics What are some interesting books for a sophomore undergrad about Atomic &amp; Molecular Physics? Input impedance of Arduino Uno analog pins? I'm using the  on some small robotic arm motors, and reading in the analog voltage with an Arduino Uno.  I've had reasonably good results, but only after putting in an RC filter on the output.  However, in the application note on the datasheet, it says not to do that:  "the addition of an RC filter to the output of a sensor IC can result in undesirable device output attenuation — even for DC signals."  Then it gives a formula to calculate attenuation, but it depends on knowing the input impedance of whatever is reading the signal, so that's what I'm after here. Are C-style macro names subject to the same naming rules as identifiers?  After a compiler upgrade, it is now emitting this warning for a legacy application:  warning #3649-D: white space is required between the macro name "CHAR_" and its replacement text   #define         CHAR_&amp;        38   This line of code is defining an ASCII value constant for an ampersand.  #define   DOL_SN        36 #define   PERCENT       37 #define   CHAR_&amp;        38 #define   RT_SING       39 #define   LF_PAR        40   I assume that this definition (not actually referenced by any code, as far as I can tell) is buggy and should be changed to something like "CHAR_AMPERSAND"? We know that $2^4 = 4^2$ and $(-2)^{-4} = (-4)^{-2}$. Is there another pair of integers $x, y$ ($x\neq y$) which satisfies the equality $x^y = y^x$? i keep getting the script error problem every time i try using polygon to raster tool in ArcGIS 10.1. Please help me how I can solve this?  screenshot embedded Is an HTTPS query string secure? I am creating a secure web based API that uses HTTPS; however, if I allow the users to configure it (include sending password) using a query string will this also be secure or should I force it to be done via a POST? Is it possible that using jQuery, I cancel/abort an Ajax request that I have not yet received the response from? I'm very new to GIS concepts. Is there a way or procedure of finding out whether the co-ordinate system is in UTM, latitude/longitude or in stateplane using .prj file?   My .prj file contains the following text:      GEOGCS["WGS 84",DATUM["WGS_1984",SPHEROID["WGS   84",6378137,298.257223563,AUTHORITY["EPSG","7030"]],AUTHORITY["EPSG","6326"]],PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],UNIT["degree",0.01745329251994328,AUTHORITY["EPSG","9122"]],AUTHORITY["EPSG","4326"]] How would one write object-oriented code in C? Orthogonality and linear independence [Theorem] Let $V$ be an inner product space, and let $S$ be an orthogonal subset of $V$ consisting of nonzero vectors. Then $S$ is linearly independent.     Also, orthogonal set and linearly independent set both generate the same subspace.  (Is that right?)    Then orthogonal $\rightarrow$ linearly independent but orthogonal $\nleftarrow$ linearly independent is that right?    One more question. For T/F, Every orthogonal set is linearly independent (F) Every orthonormal set is linearly independent (T) Why?