The phenomenon of the deflection of a moving electron in a magnetic field is related to the electrons spin. From which phenomenon it is concluded, that photons have a spin?
Electrons have spin 1/2, and as they are charged, they also have an associated magnetic moment, which can be measured by an electron beam splitting up in an inhomogeneous magnetic field or through the interaction of the electrons's magnetic moment with an external magnetic field in spectroscopic measurements.   On the other hand, a photon is neutral - how can one measure its spin if there's no magnetic moment? How do we know it has spin 1?
Integral $\int\frac{dy}{(y^2 + ay + b)^{3/2}}$ Need the indefinite integral with $a,b$ constants. This is not a homework question. Need it for a physics problem. TAR 6 GB worth of files into separate 1.9 GB TAR files What is the difference between the GNU Makefile variable assignments =, ?=, := and +=? Can anybody give a clear explanation of how variable assignment really works in Makefiles.   What is the difference between :   VARIABLE = value  VARIABLE ?= value  VARIABLE := value  VARIABLE += value   I have read the  in GNU Make's manual, but it still doesn't make sense to me. This is my first question in /photography. I'm a very amateur photographer, doing things wrong and by eye with lots of trial-and-error all the time.  I currently own a reflex Nikon D70 my uncle gave us after he bought a better one. It has some nice settings, and he bought a a Nikkor 28-80mm F/3.5-5.6 zoom lens for it. It behaves nicely, but it's getting old (it has those old cartridges before SD cards existed) and every new charge takes longer than the last.  I'm planning to upgrade to a better camera, and there are some neat offers on a nearby superstore (MediaMarkt), this one catching my eye:  Sony DSC-H400 63x, Sensor Super HAD 1/2/3 CCD 20.1MP -> for less than 300€ taxes included  I don't have any type of extra information aside from that, all I can get from the official site is clinical data from other cameras that I suspect it's not 100% accurate, and there's no photography expert on the store to ask.  The common things I use my D70 for are: taking pictures of scenery (castles, towns, forests, waves hitting rocks, etc...), nearby (&lt;5m) persons and objects, and well, things where I want to save a memory in digital format, not for professional purposes at all.  Being that my objective is to have a decent, good-zooming (superzoom looks awesome), amateur (but with manual settings) camera, is this Sony a good replacement? Will I miss any features? Is there any better, similarly-priced alternative you know of?  Basically, I want to know whether I will get better quality photos than I currently do, given the examples, with any averagely-priced bridge camera similar to that Sony, and if it's worth it.  examples of current camera results  Full zoom-out of town at night, bad quality I know; notice the pink blur at the left.    Maximum zoom on that pink blur from almost the same spot:    Daylight, cloudy, modified with Adobe Lightroom, scenery:    Same day, same beach, different settings:    Same day, same beach, rocks: In the following question  the notation $c\in ]a,b[$ is used. What does this mean? I have never seen it before. I want to see what nodes exist under a certain domain from within the domain. Short of querying every valid IP address within that domain, is there a way to get all records/map the network? I'm new to LaTeX and I'm trying to figure out how to correctly format a proof. Can someone show me a basic template for how to do this?   The part I am having the most trouble with is creating new columns and customizing alignment... for instance, how do I add a right-aligned annotation (i.e. by distributive property) to a line of this sample proof? Should I use eqnarray* or is there a better option?  \begin{proof}   Let $t,u \in \mathbb{R}$ where $t=xy$ and $u=zw$. So,   \begin{eqnarray*}     4xyzw &amp;=&amp; 2\cdot2tu \\     &amp;\le&amp; 2\cdot(t^2+u^2) \\     &amp;=&amp; 2\cdot((xy)^2+(zw)^2) \\     &amp;=&amp; 2\cdot(x^2y^2+z^2w^2) \\     &amp;=&amp; 2x^2y^2+2z^2w^2 \\     &amp;\le&amp; ((x^2)^2+(y^2)^2)+((z^2)^2)+(w^2)^2) \\     &amp;=&amp; x^4+y^4+z^4+w^4   \end{eqnarray*} \end{proof} How to compute the topological space of fibered product of schemes? Would you take a share in Stack Overflow? Joel Spolsky has just posted  where he talks about seeking venture capital for Stack Overflow.  If instead they opted to seek shareholders from the StackOverflow community along the lines of the , but at a larger scale, would you be interested?  I'm asking this because I suspect there might be enough fanatics willing to invest $500 or so in a product they love to raise a considerable sum. People also often talk about the motivation for high rep users. It seems to me having an actual stake in the product might be a decent incentive (especially if you also get a gold badge for buying shares). Creating queries to select by attribute with arcpy I'm quite new with arcpy and I'm finding selecting by attribute a bit of a nightmare. There's a problem with my query on the script below [query = "\'Location\' = observer"], but I can't tell what it is. 'Location' is a field of the feature class I'm dealing with (fc_copy).  with arcpy.da.UpdateCursor(fc_copy,field_names) as cursor:        for row in cursor:         observer = row[0]         arcpy.MakeFeatureLayer_management(fc_copy, 'fl_copy_OBS')         arcpy.MakeFeatureLayer_management(fc_copy, 'fl_copy_TAR')         query = "\'Location\' = observer"         arcpy.SelectLayerByAttribute_management('fl_copy_OBS', 'NEW_SELECTION', query)         arcpy.SelectLayerByAttribute_management('fl_copy_TAR', 'NEW_SELECTION', query, invert_where_clause = 'INVERT')   This is the error I get => Invalid expression                            Failed to execute (SelectLayerByAttribute).  Is there any documentation to learn the rules to follow to build queries for arcpy? What exactly is 'Dark Matter'? List creation/manipulation Motivation for Kolmogorov distance between distributions There are many ways to measure how similar two probability distributions are.  Among methods which are popular (in different circles) are:   the Kolmogorov distance: the sup-distance between the distribution functions; the Kantorovich-Rubinstein distance: the maximum difference between the expectations w.r.t. the two distributions of functions with Lipschitz constant $1$, which also turns out to be the $L^1$ distance between the distribution functions; the bounded-Lipschitz distance: like the K-R distance but the functions are also required to have absolute value at most $1$.   These have different advantages and disadvantages.  Only convergence in the sense of 3. actually corresponds precisely to convergence in distribution; convergence in the sense of 1. or 2. is slightly stronger in general.  (In particular, if $X_n=\frac{1}{n}$ with probability $1$, then $X_n$ converges to $0$ in distribution, but not in the Kolmogorov distance. However, if the limit distribution is continuous then this pathology doesn't occur.)   From the perspective of elementary probability or measure theory, 1. is very natural because it compares the probabilities of being in some set. A more sophisticated probabilistic perspective, on the other hand, tends to focus more on expectations than probabilities. Also, from the perspective of functional analysis, distances like 2. or 3. based on duality with some function space are very appealing, because there is a large set of mathematical tools for working with such things.  However, my impression (correct me if I'm wrong!) is that in statistics, the Kolmogorov distance is the usually preferred way of measuring similarity of distributions.  I can guess one reason: if one of the distributions is discrete with finite support -- in particular, if it is the distribution of some real-world data -- then the Kolmogorov distance to a model distribution is easy to compute.  (The K-R distance would be slightly harder to compute, and the B-L distance would probably be impossible in practical terms.)  So my question (finally) is, are there other reasons, either practical or theoretical, to favor the Kolmogorov distance (or some other distance) for statistical purposes? Problem writing aux file Sending a message to nil in Objective-C As a Java developer who is reading Apple's Objective-C 2.0 documentation: I wonder what "sending a message to nil" means - let alone how it is actually useful.  Taking an excerpt from the documentation:     There are several patterns in Cocoa   that take advantage of this fact. The   value returned from a message to nil   may also be valid:         If the method returns an object, any pointer type, any integer scalar   of size less than or equal to   sizeof(void*), a float, a double, a   long double, or a long long, then a   message sent to nil returns 0.   If the method returns a struct, as defined by the Mac OS X ABI Function   Call Guide to be returned in   registers, then a message sent to nil   returns 0.0 for every field in the   data structure. Other struct data   types will not be filled with zeros.   If the method returns anything other than the aforementioned value   types the return value of a message   sent to nil is undefined.      Has Java rendered my brain incapable of grokking the explanation above?  Or is there something that I am missing that would make this as clear as glass?  I do get the idea of messages/receivers in Objective-C, I am simply confused about a receiver that happens to be nil. How to make ttf-mscorefonts-installer package download fonts, after it says it installed? When I install "Installer for Microsoft TrueType core fonts" (ttf-mscorefonts-installer) from the Software Center on 14.04, it gives a positive response--but after this I get a download error. It seems that the files actually providing the fonts are never retrieved. Is there any way to resolve this? Function whose image of every open interval is $(-\infty,\infty)$ How to find a function from reals to reals such that the image of every open interval is the whole of R?  Is there one which maps rationals to rationals? Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$ Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$  I have expanded it this far:  $$\frac{k \cdot n!}{k!(n-k)!} = \frac{n \cdot (n-1)!}{(k-1)!(n-k)!} $$  but then I am stuck from where to go from there. $\DeclareMathOperator{\card}{card}$From Problem-Solvers Topology  Prove the following: CANTOR'S THEOREM If $A$ is a set, then $$\card A &lt; \card \mathcal{P}(A)$$ where $\card A$ stands for the cardinality of set $A$.  My Answer If $A = \emptyset$, then $\card A =0$ and $\card \mathcal{P}(A)=1$. If $A = \{a\}$, then $\card A=1$ and $\card \mathcal{P}(A)=2$. So suppose that $A$ has at least two elements. Define a function $f: A \rightarrow \mathcal{P}(A)$ such that $f(x) = \{x\}$ for all $x \in A$. Then $f$ is injective. But it cannot be surjective, because for any two distinct elements $a,b \in A$, there is no element in $A$ that is sent to the set $\{a,b\}$ in $\mathcal{P}(A)$. Therefore, there is no bijection, and $\card A &lt; \card\mathcal{P}(A)$. Do you think my answer is correct? Thanks in advance ASP.NET MVC: Weird characters in error page