Gravitational waves were theorized a century ago and recently discovered, leading to the awarding of the 2017 Nobel Prize in Physics. According to :     Gravitational waves transport energy as gravitational radiation, a   form of radiant energy similar to electromagnetic radiation.   The comparison to electromagnetic radiation makes me think that gravitational waves must be describable in  as well. It also makes me think that the particle form must be the long-rumored . Yet, about the graviton, Wikipedia has to say:     the graviton is a hypothetical elementary particle   I understand that relativity and quantum mechanics are not well integrated, and that this gravitational wave is a macro-scale phenomenon that, experimentally, doesn't have much to do with particles. But I have basically no understanding of how gravity is interpreted in quantum mechanics (it seems like you can ignore it at such small scales).  Shouldn't the detection of a gravitational wave be evidence in favor of the existence of its corresponding particle? Can gravitational waves be used to 'prove' the existence of the graviton particle?
I studied the theoretical part about the Gravitational waves in General Relativity (linearization of gravity and small perturbations of the metric and so on).  But I was wondering about: since electromagnetic radiation is composed/carried by Photons (or better:the EM force), shall gravitational waves be composed/carried by Gravitons?   In the end:do gravitational waves imply the existence of gravitons? Or it's something unrelated and off topic?
How is it, that $\sqrt{x^2}$ is not $ x$, but $|x|$? As far as I see, $\sqrt{x^2}$ is not $x$, but $|x|$, meaning the "absolute". I totally get this, because $x^2$ is positive, if $x$ is negative, so $\sqrt{y}$, whether $y = 10^2$ or $y = -10^2$: $y$ is positive.  But then I remember that $\sqrt(x)$ is the same as $x^{1/2}$ and thus, $\sqrt{x^2}$ is the same as $x^{1}$.   So, as far as I get it, $\sqrt{x^2} = x^{2/2}$.  But then, I can cancel $\frac{2}{2}$ to $1$. So: $\sqrt{x^2} = x^1 = x$.  Where does the absolute value in this derivation of the calculation come from?  I get it why its there: Because $(-x)^2 = x^2$, so the radicand is always positive. But from $\sqrt{x^n} = x^{n/2}$ I dont understand how it gets there. How do I disable DVD auto eject in Windows 7? I just discovered an incredibly annoying "feature" of Windows 7 tonight.  If you click on your optical drive in Explorer, and there is no disc in the drive, Windows 7 is kind enough to open the tray for you.  I'm finding it hard to contain my rage over this idiotic design decision.  WTF?  According to , this behavior was apparently introduced in Vista.  The author posted a workaround, but I don't want a workaround.  I want it to stop doing this.  Like he, I have a case with a door that covers the drive bays.  If it's closed, and I accidentally click on that optical drive, it knocks on that door 10 or 12 times before giving up.  Can this behavior be turned off in Windows 7? XeTeX: What happened to \mathcal and \mathscr? Recently I switched from pdflatex to xelatex to be able to use OpenType fonts. I like to use variables highlighted using \mathcal for specific variables, while I used to use \mathscr-typeset variables for matrices. But when I compile with XeLaTeX they look exaclty the same.  Old code  \documentclass{standalone} \usepackage{mathrsfs} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        New code  \documentclass{standalone} \usepackage{unicode-math} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        Broken code  I tried to get back the glyphs from mathrsfs, but it failed this way.  \documentclass{standalone} \usepackage{unicode-math} \usepackage{mathrsfs} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        Question: How can I get back the behaviour? In principle I'd like to have the old \mathcal letters from the pdflatex-version of Computer/Latin Modern.    Alternate solutions (Addendum 2016/05/11) How do I completly remove XP from my pc. I currently have a dual boot with XP and Windows 7. Since installing Windows 7, I have never used XP. Can I remove it without causing problems with Windows 7? pm-hibernate freezes and/or fails to resume on Dell XPS 13, 14.04, 3.19 kernel What is the best way to repeatedly execute a function every x seconds? File permissions and saving Let's say you open a file on which you have write permission. Meanwhile you change permissions and remove write permission while you still have the file open in some editor.  What will happen if you edit and save it? If the matrix $A^3 = 0$, is $A$ singular? Why do this() and super() have to be the first statement in a constructor? Throughout Blade Runner we see Gaff (Edward James Olmos) making origami figures at various points in the movie. He makes a chicken, matchstick men and at the end of the film there is a unicorn waiting outside Deckard's apartment.    There is a   of  out there regarding the unicorn in particular, and how it indicates that Deckard is a replicant. I think an answer regarding the use of origami in general will be interesting new ground to cover.  Why origami? What does the origami represent in Blade Runner? How does reflection work? What is AC actually? What is actually alternating current (AC)? And direct current (DC)? I've been reading several books about basic electric circuits analysis and they are contradictory.   Some books say that AC is the same as the sinusoidal stationary state. That is, a sine or cosine function (actually, they are the same only shifted horizontally). For instance, \$v(t) = A \sin(\omega t + \phi)\$. Acording to these books, DC is totally stationary (static), that is, the voltage and current are not time-dependant (\$v(t) = k\$, where \$k = \mathrm{const.}\$). Currents have the same form as voltages on each of these cases. According to other books, AC is any current that is changing (that is alternating) his sign over time (\$t\$). With maths notation: \$i(t_1) &lt; 0\$ and \$i(t_2) &gt; 0\$ for some \$t_1\$ and \$t_2\$ where \$t_1 \neq t_2\$. It could have any shape as long as it's alternating his sign.   I'm inclined to think that in practice wins the first option but maybe it's better the etymology of the second option.  Some other cuestions have relation to this:   Is AC a voltage that is the sum of a sinusoidal stationary state and a constant voltage? For instance, \$v(t) = A \sin(\omega t + \phi) + k\$. Is AC a shawtooth wave? About two weeks ago I had a problem with my PC that my brother wrote a question about at .  I still haven't solved the problem, so my PC is unusable now.  Now I think that it would be simpler to re-install both Win7 &amp; Ubuntu than repair them, but there're some data on their partitions. I want to recover this data.  These partitions are not mountable for some reason. I don't know why.  sudo fdisk -l about the problematic partitions:     Device    Boot      Start         End      Blocks   Id  System /dev/sda1            2048     147912703    73955328   83 Linux /dev/sdb2            206848   174079999    86936576    7  HPFS/NTFS/exFAT   And in GParted:      And the error of the mount command:  Failed to mount '/dev/sdb2': Invalid argument The device '/dev/sdb2' doesn't seem to have a valid NTFS. Maybe the wrong device is used? Or the whole disk instead of a partition (e.g. /dev/sda, not /dev/sda1)? Or the other way around?   And the exact same message for /dev/sda1  How can I recover my data from those HDDs?  EDIT     I have tried to specify the type of the drive:  $ sudo mount -t ext4 /dev/sda1 /olddisk mount: wrong fs type, bad option, bad superblock on /dev/sda1,        missing codepage or helper program, or other error        In some cases useful info is found in syslog - try        dmesg | tail  or so $ sudo mount -t ntfs /dev/sdb2 /olddisk NTFS signature is missing. Failed to mount '/dev/sdb2': Invalid argument The device '/dev/sdb2' doesn't seem to have a valid NTFS. Maybe the wrong device is used? Or the whole disk instead of a partition (e.g. /dev/sda, not /dev/sda1)? Or the other way around?   EDIT     sudo ntfsfix /dev/sdb2 returns:  Mounting volume... NTFS signature is missing. FAILED Attempting to correct errors... NTFS signature is missing. FAILED Failed to startup volume: Invalid argument NTFS signature is missing. Trying the alternate boot sector Unrecoverable error Volume is corrupt. You should run chkdsk. Low current battery monitoring What kinds of compensation can I get from Deutsche Bahn for canceled and late trains? How do we "restore" notepad after crash? I just bought a new config ( ASUS p8z68-v lx, i5-2500k + ram and new graphic card ). Coming back and installing it in my old computer, I just saw that my DVD player was on IDE (yup…).  So, I needed to install windows 7 64bits from my usb key. Fine, I made my usb key bootable and copy the official DVD on it (the same version that was on my old computer), set BIOS to boot on it first and started the computer up.  It worked fine until it asks me for cd/dvd drivers (which is funny since, I do it via USB because I can't plug in my DVD player :D) I have 3 SATA HDD plugged in and that's it.  I made a small google search and found that it could be SATA or RAID drivers. Fine, I took another USB KEY and put all my motherboard drivers on it (from the CD sold with the MB) and none of those drivers seemed to work. I tried downloading new drivers from ASUS website and same effect.  Any idea but no "buy a new DVD player", I'm now broke for the month :) ? How to grep a specific line _and_ the first line of a file? Assuming a simple grep such as:  $ psa aux | grep someApp 1000     11634 51.2  0.1  32824  9112 pts/1    SN+  13:24   7:49 someApp   This provides much information, but as the first line of the ps command is missing there is no context for the info. I would prefer that the first line of ps be shown as well:  $ psa aux | someMagic someApp USER       PID %CPU %MEM    VSZ   RSS TTY      STAT START   TIME COMMAND 1000     11634 51.2  0.1  32824  9112 pts/1    SN+  13:24   7:49 someApp   Of course, I could add a regex to grep specifically for ps:  $ ps aux | grep -E "COMMAND|someApp"   However, I would prefer a more general solution as there are other cases in which I would like to have the first line as well.  Seems like this would be a good use case for . How to prove the midpoint of a chord is also the midpoint of the line segment defined by the points of intersection of other two chords with it? Is it possible to use "negative sound waves" to "cancel out" a sound to create silence?