Pardon me for my stubborn classical/semiclassical brain. But I bet I am not the only one finding such description confusing.  If EM force is caused by the exchange of photons, does that mean only when there are photons exchanged shall there be a force? To my knowledge, once charged particles are placed, the electromagnetic force is always there, uninterruptedly. According to such logic, there has to be a stream of infinite photons to build EM force, and there has to be no interval between one "exchange event" to another. A free light source from an EM field? The scenario is really hard to imagine.  For nuclei the scenario becomes even odder. The strong interaction between protons is caused by the exchange of massive pions. It sounds like the protons toss a stream of balls to one another to build an attractive force - and the balls should come from nothing.  Please correct me if I am wrong: the excitations of photons and pions all come from nothing. So there should be EM force and strong force everywhere, no matter what type of particles out there. Say, even electrical neutral, dipole-free particles can build EM force in-between. And I find no reason such exchanges of particles cannot happen in vacuum.   Hope there will be some decent firmware to refresh my classical brain with newer field language codes.
Since Newton's law of gravitation can be gotten out of Einstein's field equatons as an approximation, I was wondering whether the same applies for the electromagnetic force being the exchange of photons. Is there an equation governing the force from the exchange of photons? Are there any links which would show how the Coulomb force comes out of the equations for photon exchange? I know that my question is somewhat similar to the one posted here , but it doesn't really have an answer to my question specifically.
How to stop a script from running if it's not root (and echo "Not running as root! Exiting...") Here's my source:  #!/bin/bash  echo "Running script to free general cached memory!" echo ""; echo "Script must be run as root!"; echo ""; echo "Clearing swap!"; swapoff -a &amp;&amp; swapon -a; echo ""; echo "Clear inodes and page file!"; echo 1 &gt; /proc/sys/vm/drop_caches; echo "";   It clears caches and stuff, and it echoes that it needs to be run as root in the terminal. I basically just want the script to cease running if it detects it's not being executed as root.   Example:  "Running script to free general cached memory!" "Warning: script must be run as root or with elevated privileges!" "Error: script not running as root or with sudo! Exiting..."   If run with elevated privileges, it just runs as normal. Any ideas? Thanks! OneDrive isn't uploading all my photos from my phone I've got an Office 365 (Microsoft 365) Family license. I've set up OneDrive on my Samsung Galaxy S10 phone. I've verified that it is set up by following the . I've got it set up to upload photos using either Wi-Fi or mobile. And I see photos I've taken with my phone, uploaded to OneDrive from as recently as a few days ago. So, it works. But not all the time or for all my photos. I've scrolled through my photos on my phone's Gallery app. I see some photos from as recently as 4 days ago to several months ago, are not uploaded to OneDrive. Why is that? What can be said about the convergence on $|z|=1$? I already found the radius of convergence of the power series $:$ $$\sum_{n=1}^{\infty} \frac {(-1)^n} {n} z^{n(n+1)}.$$ What happens at the boundary of disk of convergence?  I found that the radius of convergence to be $1$ and hence the disk of convergence is $|z|&lt;1$. Now I found at $z=1$ the series converges. Now how can I proceed? Please help me. Thank you in advance. Read a file backwards line by line using fseek Create ArrayList from array I have an array that is initialized like:  Element[] array = {new Element(1), new Element(2), new Element(3)};   I would like to convert this array into an object of the  class.  ArrayList&lt;Element&gt; arraylist = ???; Do file descriptors optimise writing to files? To prove that $(\mathbb{P(N)},d)$ is a metric space To prove that $(\mathbb{P(N)},d)$ is a metric space where $\mathbb{P(N)}$ is the power set of $\mathbb{N}$.  And $d:\mathbb{P(N)}\times \mathbb{P(N)} \mapsto\mathbb{R}$ is defined by $d(A,B)=\begin{cases} 0, &amp; \text{if A} \Delta \text{B=}\emptyset  \\ m^{-1}, &amp; \text{where m is the smallest member of} A\Delta B \end{cases} $.   Attempt: $x \in P\Delta Q=(P-Q)\cup(Q-P) \implies x\in (P-Q) \text{ or } x\in (Q-P) $. But $(P-Q)\cap(Q-P)= \emptyset \implies x \in P \text{ and} \notin Q \text{ or }x \in Q \text{ and} \notin P. \ \ \ $    (*)  To prove the triangle inequality:  Take any three sets $A,B,C \subset \mathbb{P(N)}$ such that none of them are equal to another. Now,  $\min A \Delta B  =m_1, \min B \Delta C  =m_2,  \min A \Delta C  =m_3   $. To prove $d(A,B) \leq d(A,C)+ d(B,C)$. By (*), $m_1 \in A$ or $m_1 \in B$ but not both.   Again,  $m_2 \leq m_1$  or $m_3 \leq m_1$. Either way, we are done. When $A \neq B$ and either $B =C $ or $A=C$ (not both), we have respectively $A=C$ , $B=C$ . Which satisfies the triangle inequality. When $A=B$ it is evident.   Symmetry: We know $A \Delta B =B \Delta A$. $d(A,B)= d(B,A)$  Non-negativity and $0 \iff A=B$:   $d(A,B)=0 \iff A \Delta B= \emptyset \iff A \subset B \text{ and } B \subset A \iff A=B$. By definition $d(A,B) \geq 0$  Is this okay? Please verify. Installing File Geodatabase (*.gdb) support in QGIS? I have spent around 2 days to find the way to open GDB (Esri geodatabase) in QGIS (or any other open source software) but still without success.  I have downloaded the newest OSGeo4W installer and tried the setup - express desktop install - all packages, as well as advanced install incl gdal-filegdb.  Can you describe a more detailed procedure, including installation and how to open .gdb in QGIS (OSGeo4W installation)? Detecting the onload event of a window opened with window.open Partition a set into subsets of size $k$ I tried Libreoffice, but its Import option while pasting in the cell is very  annoying.I also tried Gnumeric but I am not able to paste using middle button.Parcellite to make copy paste faster and middle button pasting is not working with Gnumeric. Is there any simple table maker app available that can accept only simple unformatted text? All these software are very complicated for this simple work. Can I boot memtest86+ if I'm using UEFI? Downloaded the Ubuntu 16.04.2 .iso install disk and flashed it onto a USB stick.  Booting on the USB stick, there is no memtest86+ option (along with "Try Ubuntu").  Is there a way to add it to the install options?  (it's for a UEFI boot PC running normally Windows, its owner does not want to install Ubuntu. "memtest86+" is completely free (unlike "memtest86"), but is quite old, and does not offer a UEFI boot - this is why having it within the Ubuntu options makes things easier) Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$ Suppose $(M,d)$ a metric space. I want to show that      If every continuous real-valued function on $M$ attains a maximum, then $(M, d)$ is compact.   I was trying to do this by assuming $M$ non-compact and showing explicitly a function which does not attain a maximum. If $M$ is not bounded it's enough to take the distance from a fixed point as we can always find a sequence which "exits" every compact and pushes the distance at infinity. But what if $M$ is bounded? How to set the default format in text_format and hide the select? /**  * Implements hook_form_alter().  */ function MODULE_NAME_form_alter(   &amp;$form,   \Drupal\Core\Form\FormStateInterface $form_state,   $form_id ) {    if ($form_id == 'node_article_form') {     $form["body"]["widget"][0]['#allowed_formats'] = ['full_html']; // Your default format     $form["body"]["widget"][0]['#after_build'][] = 'MODULE_NAME_hide_format';   } }  function MODULE_NAME_hide_format(   &amp;$element,   FormStateInterface $form_state ) {   if (isset($element["format"]["format"])) {     $element["format"]["format"]["#access"] = FALSE;   }    return $element; } Check if url has domain name and not an ip How to draw a return arrow from node-3 to node-1 Using ReplaceAll on SparseArray How to use multiple HDRIs My question is, how would I make the visible HDRI/Enviroment Map be image 1 and then have reflections as Image 2? If someone can post a node setup, or a .py file that would be great &lt;3 I was thinking maybe using the Is Camera Ray node but I'm not confident it would work, and have no idea where to start. If $a_k\geq0$ is a decreasing sequence converging to $0$, do we have $\lim_{n\to\infty}\frac{\sum_{k=1}^n a_k}n = 0$? Let $a_k\geq 0$ be a non-increasing sequence satisfying $\lim_{k\to\infty} a_k = 0$. Is it always true that $$\lim_{n\to\infty} \frac{\sum_{k=1}^n a_k}n=0$$ ?  I tried proving with "brute force" but failed: Let $\varepsilon&gt;0$. Then there exists a $K\in\mathbb N$ such that $a_k\le\varepsilon$ for all $k\geq K$. Let $C=\sum_{k=1}^K a_k$. We have $$\frac{\sum_{k=1}^{\left\lceil\frac C\varepsilon\right\rceil}a_k}{\left\lceil\frac C\varepsilon\right\rceil}=\frac{C}{\left\lceil\frac C\varepsilon\right\rceil}+\sum_{k=K+1}^{\left\lceil\frac C\varepsilon\right\rceil} a_k\le \varepsilon +\varepsilon\cdot\left( \left\lceil\frac C\varepsilon\right\rceil-K\right).$$  However, this is not good, as the right-hand side depends on $C$, which can get large for small $\varepsilon$.   Also, numerical computations for example with $a_k=\frac1{\log\log k}$ seem to confirm the statement though...  (Additionally, note that I didn't use the non-increasing fact, but I am not sure if it is needed.) If $G$ is cyclic, then $G/H$ is cyclic?   The proof I got goes like this: $G$ is cyclic, so $G=&lt;g&gt;$ for some $g\in G$. So any coset in $G/H$ would be of the form $Hg'=Hg^n$ for some $n$. So $Hg$ is an generator of $G/H$. Thus, $G/H$ is cyclic.  I might just be confusing myself, but we have only shown that $Hg'$ is in form of $(Hg)^n$. But what if we are missing some $n\in\mathbb{N}$? That is, there is no quotient group of the form $Hg^2$, for example.  To make myself a little bit clearer, I think what the above proof has done was showing that $\forall Hg'\in G/H, Hg'\in &lt;Hg&gt;$, thus $G/H \subset &lt;Hg&gt;$. I feel that this is not a complete proof.