Is it speed or acceleration that leads to time dilation?
Does velocity or acceleration cause time dilation?
What is the population of the Star Wars Galaxy? Bought in, bought on, bought from, bought at? Order of evaluation in C++ function parameters Copying files from command line to clipboard How can I use a variable in the replacement side of the Perl substitution operator? Convergence of integrals in $L^p$ Stuck with this problem from Zgymund's book.   Suppose that $f_{n} \rightarrow f$ almost everywhere and that $f_{n}, f \in L^{p}$ where $1&lt;p&lt;\infty$. Assume that $\|f_{n}\|_{p} \leq M &lt; \infty$. Prove that:  $\int f_{n}g \rightarrow \int fg$ as $n \rightarrow \infty$ for all $g \in L^{q}$ such that $\dfrac{1}{p} + \dfrac{1}{q} = 1$.  Right, so I estimate the difference of the integrals and using Hölder end up with:  $$\left|\int f_{n} g - \int fg\right| \leq \|g\|_{q} \|f_{n} - f\|_{p}$$  From here I'm stuck because we are not assuming convergence in the seminorm but just pointwise convergence almost everywhere. How to proceed? Do we know why there is a speed limit in our universe? This question is about why we have a universal speed limit (the speed of light in vacuum). Is there a more fundamental law that tells us why this is? I'm not asking why the speed limit is equal to $c$ and not something else, but why there is a limit at all. EDIT: Answers like &quot;if it was not..&quot; and answers explaining the consequences of having or not having a speed limit are not--in my opinion-- giving an answer to whether there is a more fundamental way to derive it from a law to explain this limit. I know that I can create/burn bootable CD/DVD or live USB and can boot/install from it. But suppose I am currently running GNU/Linux and I've ISO file of another GNU/Linux that I want to install on my hard disk, then Can I directly boot from ISO from hard disk and try/install that GNU/Linux operating system? Fourier transform of a radial function Consider a function $f \in L^2(\mathbb{R}^n)$ such that $f$ is radial. My question is, is the Fourier transform $\hat{f}(\xi)$ automatically radial (I can see it is even in each variable $x_i$), or we need some conditions on $f$? Thanks for your help. 3/4 circle with plus in it? After I recently updated my phone about a day ago, this strange sign showed up on the top left that I have never seen before. Does anyone know what it means? Or how to get rid of it? Different mechanics of \hyperlink vs. \hyperref I am fiddling around with the hyperref package to build a hypertext structure into my pdf. At first glance, hyperref provides two similar macros to put links between parts of my document: \hyperlink{target}{text} and \hyperref[target]{text}. You might notice their slightly different syntax. What really interests me is their different working mechanics. I will illustrate this by the following example: \documentclass{article}  \usepackage{pdfpages} \usepackage[]{hyperref} \usepackage{mwe}  \begin{document}  \section{Section Heading} \label{sectionheading}  \includepdf[link=true, linkname=pdfpage]{example-image}   Link to section works with \hyperref[sectionheading]{hyperref} and with \hyperlink{sectionheading}{hyperlink} (but with slightly different targets on the page).  Link to pdf works with \hyperlink{pdfpage.1}{hyperlink} but not with \hyperref[pdfpage.1]{hyperref} (and not this way, either: \hyperref[pdfpage]{hyperref}).  \end{document}  To link to the labeled section heading, I may use both commands. While \hyperref directs my pdf viewer directly to the linked section, \hyperlink directs me somewhere slightly different, so I can see more context. To link to the \includepdf of pdfpages however, I may only use \hyperlink. \hyperref does not work at all. I suspect this is because of a subtle difference in their working mechanisms. While checking the aux file, I found a line \newlabel{sectionheading}{{1}{1}{Section Heading}{section.1}{}} which \hyperref seems to use as a target. However, I did not find any similar target for the included pdf. My question: I suspect, I understand the workings of \label and \ref very well. \hyperref seems to work quite similarly with the added clickability. Could you please explain to me how \hyperlink does work differently and how it is implemented? E.g. what mechanics explain the difference when clicked on the link and where and how are the link targets stored in the first place? "Reality" of length contraction in SR I was in argument with someone who claims that length contraction is not &quot;real&quot; but only &quot;apparent&quot;, that the measurement of a solid rod in its rest reference frame is the &quot;real length&quot; of the rod and all other measurements are somehow just &quot;artificial&quot; and &quot;apparent&quot;. Seemed to me like a bad conversation about poorly defined words and not really relevant to physics, but then some quotes were offered:  ...so that the back appears closer to the front. But of course nothing has happened to the rod itself.  (Rindler)  The effects are apparent (that is, caused by the motion) in the same sense that proper quantities have not changed.  (Resnick &amp; Halliday) At the same time, the  insists that length contraction and time dilation are &quot;real&quot;, with observable consequences:  Time and space dilation are often referred to as ‘perspective effects’ in discussions of STR. Objects and processes are said to ‘look’ shorter or longer when viewed in one inertial frame rather than in another. It is common to regard this effect as a purely ‘conventional’ feature, which merely reflects a conventional choice of reference frame. But this is rather misleading, because time and space dilation are very real physical effects, and they lead to completely different types of physical predictions than classical physics. [...] However, this does not mean that time and space dilation are not real effects. They are displayed in other situations where there is no ambiguity. One example is the twins' paradox, where proper time slows down in an absolute way for a moving twin. And there are equally real physical effects resulting from space dilation. It is just that these effects cannot be used to determine an absolute frame of rest.  I went through a lot of Einstein, Minkowski and Lorentz original material, and didn't find anything about what is &quot;real&quot; and what is not. Finally, I know about muons, where the effects of SR seem to be very real (from , but I had seen it in a physics class before):  When a cosmic ray proton impacts atomic nuclei in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (their preferred decay product), and muon neutrinos. The muons from these high energy cosmic rays generally continue in about the same direction as the original proton, at a velocity near the speed of light. Although their lifetime without relativistic effects would allow a half-survival distance of only about 456 m (2,197 µs×ln(2) × 0,9997×c) at most (as seen from Earth) the time dilation effect of special relativity (from the viewpoint of the Earth) allows cosmic ray secondary muons to survive the flight to the Earth's surface, since in the Earth frame, the muons have a longer half life due to their velocity. From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame. Both effects are equally valid ways of explaining the fast muon's unusual survival over distances.  So which is which? Why do Rindler, Resnick &amp; Halliday use the word &quot;apparent&quot;? I have a little question here.  If I have two files, say filea and fileb, mv filea fileb would   delete fileb rename filea to fileb   Then if I have two directories, say dira and dirb, mv dira dirb would   move dira into dirb (it will become dirb/dira)   Noting that in both cases there are no notice or message, then this is pretty inconsistent to me. I think mv dira dirb should just overwrite dirb with the contents of dira (or merge the two directories under a directory named dirb).  I remember reading somewhere that a directory name with a slash (like dira/) is treated like a directory, and name with no slash (like dira) is treated like a file (to certain extents, of course). Anyway now I want to make the shell (zsh and possibly bash) respect my notation of a directory by using a slash. Is there a terminal option which enable me to enforce that?  To clarify, here is my desired behaviour:   mv dira dirb results in dirb being overwritten with the contents of dira mv dira dirb/ results in dira being moved into dirb (in dirb/dira)   Has anyone thought the same way as me? Or am I just weird? How does the secondary effect of the Heat Metal spell work? The  spell description states:  If a creature is holding or wearing the object and takes the damage from it, the creature must succeed on a Constitution saving throw or drop the object if it can. If it doesn't drop the object, it has disadvantage on attack rolls and ability checks until the start of your next turn...  I am unsure how this disadvantage mechanic functions as a whole. When do you suffer from it and in what ways (if any) can you end it? For example: What happens if you fail the save but cannot drop the object? Does dropping the object later, on your turn, do anything? What happens if you succeed on the save?  Does dropping the object later, on your turn, do anything? I would like it to be assumed that ; however, heat metal can still force you to drop the weapon. I would also like it to be assumed that . How to replace forward slash with backward slash Removing and adding permission using numerical notation on the same line How can I get a shapefile from a postgis query? How to set the close-laptop-lid-action? I was using this:    To try and create numbered examples in my document.  However, when I load it and put the example exe in that link in one of the separate Tex files (Introduction.tex) I include in main.tex, I get:  ./Chapters/Introduction.tex:14: TeX capacity exceeded, sorry [parameter stack s ize=10000]. \gb@ifnextchar #1#2#3-&gt;                        \let \reserved@d =#1\def \reserved@a {#2}\def \reserv... l.14 ... and political news \cite{washington_post}                                                   .  More importantly, when ...   Which is not even referring to the exe example I inserted but a couple of blocks of tex above it.  For info, here is my full code before my document begins:  \documentclass{report} % [fontsize=11pt,border=5pt] % standalone for the tree \usepackage{forest} % This overrides warnings like http://tex.stackexchange.com/questions/52576/difference-between-bookmark-levels-greater-than-one-what-does-this-mean \usepackage{bookmark} \usepackage{amsmath} \usepackage{subcaption} \usepackage{standalone} \usepackage[round]{natbib} \usepackage[T1]{fontenc} \usepackage{lmodern} \usepackage[utf8]{inputenc} % This is for hyperlinks \usepackage{hyperref} \hypersetup{     colorlinks=true,     linkcolor=blue,     filecolor=magenta,           urlcolor=cyan, }  \urlstyle{same} % Not sure why I need to use this % \usepackage{graphicx} % \graphicspath{ {images/} } % \usepackage[pdftex]{graphicx} % fontsize=11pt,twoside]{scrartcl} % This is for numbered examples \usepackage{gb4e}   Would appreciate some help as I feel like my Latex is very messy here. Does the 90 days VWP rule expire if you travel from the US to Canada? I'm on a New Zealand passport.  From most US Embassy webpages:     The Visa Waiver Program (VWP) enables nationals of certain countries,   including Australia, New Zealand, and the U.K., to travel to the   United States for tourism or business for stays of 90 days or less   without obtaining a visa, if certain requirements are met. Under the   VWP, time spent in Canada, Mexico, and adjacent islands counts towards   the maximum of 90 days stay allowed under the program.   I'll be there on a 1-year working holiday visa starting when I arrive in Vancouver. I'm spending 3 days in Hawaii en route to Vancouver. This seems to imply that 90 days after landing in Hawaii, my time will be up and I won't be able to get back into the US, as my living in Canada will not reset the clock. What if after this time I want to say, pop across the border to Seattle? How can I restart the 90 days, without having to resort to say, flying to Japan and back just to reset it?