Nothing can travel faster than the speed of light. Not even an electrical signal. Entanglement seems to violate this. But, does it?  Imagine 100 gears lined up in sequence all the way across a basketball court. As you turn the gear under one hoop, all 100 gears simultaneously spin.  Even the gear across the court would simultaneously spin.  Could you in theory connect gears a longer distance? Even Miles?   Imagine 100 basketballs in a straight line from one hoop to the other hoop with gears around the circumference parallel to the floor. You spin one ball, and they all spin.  Spinning the ball under one hoop, simultaneously spins the other ball.  Imagine, the in-between balls were not visible. Would this be a similar pattern to what we are seeing with entanglement?  Is it possible that it is not empty space between the two particles, yet some gear like matter that is connecting entangled particles?  Gear Theory --THE END--
Is it possible for information (like 1 and 0s) to be transmitted faster than light?   For instance, take a rigid pole of several AU in length. Now say you have a person on each end, and one of them starts pulling and pushing on his/her end.   The person on the opposite end should receive the pushes and pulls instantaneously as no particle is making the full journey.  Would this actually work?
How to force the browser to reload cached CSS and JavaScript files I have noticed that some browsers (in particular, Firefox and ) are very zealous in using cached copies of .css and .js files, even between browser sessions. This leads to a problem when you update one of these files, but the user's browser keeps on using the cached copy. What is the most elegant way of forcing the user's browser to reload the file when it has changed? Ideally, the solution would not force the browser to reload the file on every visit to the page.  I have found  and  suggestion to be useful. It turns out there is a term for this: auto-versioning. I have posted a new answer below which is a combination of my original solution and John's suggestion. Another idea that was suggested by SCdF would be to append a bogus query string to the file. (Some Python code, to automatically use the timestamp as a bogus query string, was .) However, there is some discussion as to whether or not the browser would cache a file with a query string. (Remember, we want the browser to cache the file and use it on future visits. We only want it to fetch the file again when it has changed.) Manually clear saved question drafts I've seen lately that new question editing is stored somewhere for later use if we wander off the new question without posting it and then return back to the page. Which is a good functionality addition in it's own right.  What I'd like to also have is the Discard this draft functionality that would clear form data and forget it. Somehow we find an answer in the meantime and the question isn't valid any more.  So having a Discard saved draft or something similar would be a nice contra-functionality to auto-save to remove stored data. The way it's implemented now seems too hidden hidden and unpredictable to users.  Additional edit  When adding hidden auto functionality usually means creating the opposite as well by either giving the possibility to preference of not having automatism at all or giving the possibility to clear what's been auto saved.  Let's see how GMail doesn't work (and I think we all agree that from UX perspective it does the job as expected:   User clicks Compose message User starts writing a new email message User decides to not send the message and checks their inbox User clicks Compose message again A clean form is presented to user (old one being part of drafts)   I'm not suggesting we should have something like Saved drafts but we surely should have the possibility to clear previous question draft.  Since this new functionality was introduced I should point out that I would use the discard functionality more frequently than the saved one. I do welcome saving messages, but discarding of saved drafts is anything but a rare situation one might want to do. It wouldn't be a problem if this was a 1% against 99%. To me it's more like 50/50.  Best possible solution  When providing saved drafts there should (from the UX perspective) be the opposite functionality as well. Namely discarding of it. But first thing we should be asking ourselves is:    do users more frequently need pre-filled saved question draft or do users more frequently need empty form with the possibility to populate it with a saved draft   User testing should provide the usage frequency between the two and the one that's more likely to happen (my guess is that there would be a big difference between the two) should be implemented. So one of these:   Pre-populate question fields with saved draft on question form load, while also providing a button to clear the draft and start writing anew without the need to manually clear all the fields (which would be the optimal solution in case of a single field form) Question form should always load empty while also having a button that would pre-populate it with a saved draft.   I think this would be the best consensus related to saved question drafts and their usage. But as we've seen this issue has been swept under the rug for an indefinite time. What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu f_i - \eta^{\mu\nu}\mathcal{L}$$ (the four conserved Noether currents corresponding to four possible spacetime translations)  where $\{f_i\}_{i=1}^N$ are the $N$ matter fields in the theory, and we assume $f_i\mapsto\alpha^\nu\partial_\nu f_i$ for translations,  and stress-energy tensor from the Einstein-Hilbert action, which is: $$ T_{\mu\nu}\equiv-\frac{2}{\sqrt{-g}}\frac{\delta\mathcal{L}_{Matter}}{\delta g^{\mu\nu}} $$   In particular, how do you get that the two are equal (are they?) for Minkowski space, for which there is no variation in the metric? I've been looking at  $$\int\limits_0^\infty  {\frac{{{x^n}}}{{1 + {x^m}}}dx }$$  It seems that it always evaluates in terms of $\sin X$ and $\pi$, where $X$ is to be determined. For example:  $$\displaystyle \int\limits_0^\infty  {\frac{{{x^1}}}{{1 + {x^3}}}dx = } \frac{\pi }{3}\frac{1}{{\sin \frac{\pi }{3}}} = \frac{{2\pi }}{{3\sqrt 3 }}$$  $$\int\limits_0^\infty  {\frac{{{x^1}}}{{1 + {x^4}}}dx = } \frac{\pi }{4}$$  $$\int\limits_0^\infty  {\frac{{{x^2}}}{{1 + {x^5}}}dx = } \frac{\pi }{5}\frac{1}{{\sin \frac{{2\pi }}{5}}}$$  So I guess there must be a closed form - the use of $\Gamma(x)\Gamma(1-x)$ first comess to my mind because of the $\dfrac{{\pi x}}{{\sin \pi x}}$ appearing. Note that the arguments are always the ratio of the exponents, like $\dfrac{1}{4}$, $\dfrac{1}{3}$ and $\dfrac{2}{5}$. Is there any way of finding it? I'll work on it and update with any ideas.    UPDATE:  The integral reduces to finding   $$\int\limits_{ - \infty }^\infty  {\frac{{{e^{a t}}}}{{{e^t} + 1}}dt} $$  With $a =\dfrac{n+1}{m}$ which converges only if   $$0 &lt; a &lt; 1$$  Using series I find the solution is     $$\sum\limits_{k =  - \infty }^\infty  {\frac{{{{\left( { - 1} \right)}^k}}}{{a + k}}} $$ How do I use RSolve to solve a system of recurrence relations? Drawing different tikz shapes parameterized by data from a file I have a file with three columns of data, x, y, r.  # x y r 1 1 0.1 2 2 0.5 3 3 1.2   and so on. I'd like to loop over the rows, and draw a circle at x,y with radius r for each row.  I first thought I'd use pgfplots with customized marks, but I couldn't figure out how to pass the radius parameter into the pgfplot mark handler. Then I thought I'd use tikz and pgf directly, but I couldn't figure out how to reference the values for r inside a draw command sequence.   Any thoughts ? I'd be very grateful for some help. How do I know when to use "the" versus "a" versus "∅" as an article on a noun? With proper nouns, we don't use the except for river names, newspaper names, etc.  I want to know why we use the with White House. I mean, under which rule can we categorize it? What could other similar examples for that rule be? How do I calculate areas of an area shapefile in square meters (m²) or in acres (ha)? I didn't find that functionality in the Vector Tools. Ok... so this is embarrassing.  I typed in "boobs" on EncyclopediaDramatica's search because, well, it's a really funny page.  But now I've got a problem... EVERY TIME I click a search field in Chrome now, it shows "boobs" as the first suggestion in the drop down!  This is not really socially acceptable as this laptop goes with me everywhere and Chrome is my primary browser.  Is there a way I can isolate and remove just that one entry? How to measure supply currents ranging from 1μA to 10mA? How can I represent an 'Enum' in Python? I'm mainly a C# developer, but I'm currently working on a project in Python.  How can I represent the equivalent of an Enum in Python? Isomorphism involving Eilenberg-Maclane space, Tors. Let $\pi$ be a group and let $K(\pi, 1)$ be a connected CW complex such that $\pi_1(K(\pi, 1)) = \pi$ and $\pi_q(K(\pi, 1)) = 0$ for $q \neq 1$. Does there exist an isomorphism between $H_*(K(\pi, 1); A)$ and $\text{Tor}_*^{\mathbb{Z}[\pi]}(A, \mathbb{Z})$? How do you search through flags in the manpages? Whenever I search the manpages, I'm almost always trying to find out what's going on with a specific flag. For example, when searching the man pages for  I was searching the for -f flag. I'm not sure how to say, quickly get to the flag which is here:  OPTIONS    General options        -f FORMAT, -r FORMAT, --from=FORMAT, --read=FORMAT   and filter out stuff like:  iconv -t utf-8 input.txt | pandoc | iconv -f utf-8              or  pandoc -f markdown -t latex hello.txt   I've tried searching for /-f, and I've looked at  and tried (^|\s)-f($|\s\) but it was invalid. So I'm wondering how do you quickly search less for "only the flag -f"?  Would love your thoughts or some other tool that you use to quickly go through documentation Attribute Table Default Order in QGIS I'm having an issue with QGIS version 3.2 Bonn. For my class, a question asks, "What city corresponds to row number 1713 for the Colleges and Universities shapefile?". I'm having issues answering this, because each time I load the shapefile into QGIS, the attribute table order is randomized, giving me a different city each time.   How can I open the "default" version of the attribute table for this layer, so that the order of rows is not randomized each time? Could Muggles enter Diagon Alley from Leaky Cauldron? Courtesy of , I found the a bit of  (currently un-cited):  The Leaky Cauldron The pub serves as a way of entering into Diagon Alley from the Muggle world for Muggle-borns and their parents (both of whom, until the first letter from Hogwarts, have no magical knowledge or means of entering). The rear of The Leaky Cauldron opens onto a chilly little courtyard, in which a particular brick must be tapped three times to open a path to Diagon Alley.  But from what I can see, Muggleborns and their parents wouldn't be able to enter from Leaky Cauldron, because - based on what I can tell - that requires one to use a wand:  He {{Hagrid}} tapped the wall three times with the point of his umbrella. The brick he had touched quivered – it wriggled – in the middle, a small hole appeared – it grew wider and wider – a second later they were facing an archway large enough even for Hagrid, an archway on to a cobbled street which twisted and turned out of sight.  Is there some canon information confirming the Wikipedia assertion that Muggle parents and not-yet-wand-owning Muggleborns could enter Diagon Alley from the courtyard behind Leaky Cauldron? If $G/Z(G)$ is cyclic, then $G$ is abelian Continuing my work through Dummit &amp; Foote's "Abstract Algebra", 3.1.36 asks the following (which is exactly the same as exercise 5 in ):     Prove that if $G/Z(G)$ is cyclic, then $G$ is abelian. [If $G/Z(G)$ is cyclic with generator $xZ(G)$, show that every element of $G$ can be written in the form $x^az$ for some $a \in \mathbb{Z}$ and some element $z \in Z(G)$]      The hint is actually the hardest part for me, as the quotient groups are somewhat abstract. But once I have the hint, I can write:  $g, h \in G$ implies that $g = x^{a_1}z_1$ and $h = x^{a_2}z_2$, so \begin{align*}gh &amp;= (x^{a_1}z_1)(x^{a_2}z_2)\\\  &amp;= x^{a_1}x^{a_2}z_1z_2\\\ &amp; = x^{a_1 + a_2}z_2z_1\\\ &amp;= \ldots = (x^{a_2}z_2)(x^{a_1}z_1) = hg. \end{align*} Therefore, $G$ is abelian.  1) Is this right so far?  2) How can I prove the "hint"? I don't really understand regular expressions.  Can you explain them to me in an easy-to-follow manner?  If there are any online tools or books, could you also link to them? let a,b be real  numbers and $\varepsilon&gt;0$. prove the above inequality. I dont know how to even start. please, I need your help. Maximum Champion Growth size I was reading about Lulu (new champion) and saw this:     Wild Growth (Ultimate) - Lulu enlarges an ally, knocking enemies away   from them and granting them a large amount of bonus health. For the   next few seconds, that ally gains an aura that slows nearby enemies.   Then I start wondering: what is the max size that a champion reach ? Is there a Maximum size ?  Example: Cho'Gath's Feast +  +  + Wild Growth + Something that make champions grow in size. Cho'Gath will grow every time ? or it will stop at some point ? Logical or operator not behaving as expected