Background: While trying to understand the Standard Model I stumbled on a paper that explained it in very simple terms. I recognized that I don't even understand the quantum mechanical way of the electric force. The paper pictured electromagnetic repulsion by two people on different boats, exchanging a bowling ball, one throwing, one catching. The bowling ball standing for an exchanged photon. That cannot be the whole of the truth, as it wouldn't, not even as a picture, explain the attracting force between two bodies with opposite charges. Now the question: how is electromagnetic repulsion and attraction really modeled in terms of quantum physics? Edit: the duplicates only address repulsion, or are out of reach for what I understand about quantum theory. So I state the missing part explicitly: How is an electron attracted to a positron by the exchange of a photon?
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.
What documents to show if I'm a US citizen with no US passport to re-enter the US? Suppose I am a naturalized citizen of the US, but also a citizen of another country, "XYZ". I then boarded a plane and left the US to another country (maybe not necessarily to XYZ), without first getting a US passport, but using my old, but valid XYZ passport.   In this case what would be the best documents to have for me to gain entry back into the US as a US Citizen without a passport?  Would I need to contact the US Embassy for help in order to be able return?  If the airline does let me aboard to return to the US, even without the US passport, what are the best documents could I show at the border to prove I am a US citizen but that I just don't have a passport, for whatever reason? Find lines from a file which are not present in another file Java. Splitting a multiple word string into two word strings every space Showing that $e^x > 1+x$ Prove that $(\mathbb{Z}_n , +)$, the integers $\pmod{n}$ under addition, is a group. Prove that $(\mathbb{Z}_n , +)$, the integers  $\pmod{n}$ under addition, is a group.  To show that this is a group, I know I need to show three things (in our text, we do not need to show that addition is closed-- rather, we show these three items):  $(a)$ Associative Law  $(b)$ Existence of Identity  $(c)$ Existence of Inverse  This is what I have been working with so far:     $(a)$ Associative Law:   First, assume that $n$ is a composite number and that $a,b \in \mathbb{Z}$ s.t. $a=nx$ and $b=ny$ for some integers, $x$ and $y$. Then $a+nx+nx=n(x+y)$.     So, this is where I am stuck for the Associative Law. I'm not sure if I am headed down the correct path to show that $\mathbb{Z}_n$ is associative.      $(b)$ Existence of Identity:   Generally, when showing the existence of an identity we can use this information for addition :  $a + 0 = 0 + a =a$.    I am unsure how to insert the modular portion of the definition into the existence of this identity. I realize that for addition, we generally look at $0$ (rather than $1$ for multiplication).     $(c)$ Existence of Inverse: I need to show that for each element $a \in \mathbb{Z}_n$ that $a^{-1}=-a$. Again, I do not know how to insert the modular portion of definition into this aspect of the proof.   My question is how to incorporate this modular information into the proof that this is a group. We have not covered the integers modulo $n$, binary operations, nor groups in my intro to proofs course. I am trying to read my text to figure out how to prove this, but have a difficult time reading and interpreting math speak. Resize (enlarge) an image without resampling (in favor of quality loss)? How to resize an image or selection without resampling the pixels? I have some pixel art that I want to enlarge without losing the hard, non-anti-aliased, pixel edges. In other words, 1px should become 4px of the same color— fake big pixels. Is there any way to achieve this procedurally?  Example (of what I don't want):  before resize:    after resize:    Open to other tools/methods beyond photoshop, thanks in advance. TSA requirements regarding ID If the name on my boarding pass lists Debbie and my Drivers License lists Debra, will this be a problem? On the canonical isomorphism between $V$ and $V^{**}$ Is there a JavaScript equivalent of Java's class.getName()? Adding hyperlinks to pop-up data in qgis2web? Does anyone know if it is possible to add hyperlinks to image fields etc. in the pop-up windows of Qgis2web?  I've had a look in the layers javascript file, but the image source path isn't rendered using html, so I can't simply append &lt;a href" to it.  The image is coming in via the usual method of having a field that contains the path of the image file.  I'd like to achieve linking of the image, like in the example below. Alternatively, I could just populate the 'more info' field with the URL, but if I did that I'd like to avoid just doing it by having a field that contains the entire URL, as some may be quite long (these will only be internal links). How can I get the values of the parameters of a calling method? Question  I'm writing some code that needs to be able to get the values of the parameters from the method that called into the class. I know how to get all the way to the ParameterInfo[] array, but I don't know how to then get the values. Is this even possible?  If it is, I think it has something to do with using the MethodBody property from the MethodInfo object, which allows you to inspect the IL stream, including properties, but I don't know how to do it, and I haven't found applicable code on Google.  Code  // Finds calling method from class that called into this one public class SomeClass {     public static void FindMethod()     {         for (int i = 1; i &lt; frameCount; i++)         {             var frame = new StackFrame(i);             var methodInfo = frame.GetMethod();             if (methodInfo.DeclaringType != this.GetType())             {                 string methodName = frame.GetMethod().Name;                 var paramInfos = methodInfo.GetParameters();                  // Now what?? How do I get the values from the paramInfos                  break;             }             else if (i == frameCount - 1)             {                 throw new TransportException("Couldn't find method name");             }         }     } } What is the limit of:  $$\lim_{n\to \infty} \frac{n^1+\dots+n^n}{1^n+\dots+n^n} = ?$$  I did some computation with big numbers, I guess it is in the interval $\left(\frac{1}{2},1\right)$. Quantum entanglement for faster-than-light (FTL) network communication? Quantum entanglement is 2 atoms that are paired together and when you stop one from spinning the other also stops with the same spin. Can you use these pairs to have faster-than-light (FTL) communication between 2 computers? When you tap a row in a UITableView, the row is highlighted and selected. Is it possible to disable this so tapping a row does nothing? iPhone makes shutter sound when taking photos despite being on mute Failure to download extra data files - ttf-mscorefonts-installer This is an old problem that deserves a bugfix, but it's getting beyond a joke now and I can't seem to work around it.  I keep getting the dreaded failed To download extra data files error in relation to ttf-mscorefonts-installer:    Repeatedly asking it to try again doesn't help, additionally, repeatedly trying-  sudo rm -rf /var/lib/update-notifier/package-data-downloads/partial/* sudo apt-get --purge --reinstall install ttf-mscorefonts-installer   Isn't working either.  I just get at least one 404 error from one of the sourceforge links that stops it working-  Reading package lists... Done Building dependency tree        Reading state information... Done 0 to upgrade, 0 to newly install, 1 reinstalled, 0 to remove and 20 not to upgrade. Need to get 0 B/29.5 kB of archives. After this operation, 0 B of additional disk space will be used. Preconfiguring packages ... (Reading database ... 352049 files and directories currently installed.) Preparing to unpack .../ttf-mscorefonts-installer_3.4+nmu1ubuntu2_all.deb ... mscorefonts-eula license has already been accepted Unpacking ttf-mscorefonts-installer (3.4+nmu1ubuntu2) over (3.4+nmu1ubuntu2) ... Processing triggers for fontconfig (2.11.94-0ubuntu1.1) ... Processing triggers for update-notifier-common (3.168.2) ... ttf-mscorefonts-installer: processing... ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/andale32.exe Get:1 http://downloads.sourceforge.net/corefonts/andale32.exe [198 kB] Fetched 198 kB in 0s (339 kB/s)                                                 W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/andale32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/arial32.exe Get:1 http://downloads.sourceforge.net/corefonts/arial32.exe [554 kB] Fetched 554 kB in 0s (575 kB/s)                                                 W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/arial32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/arialb32.exe Get:1 http://downloads.sourceforge.net/corefonts/arialb32.exe [168 kB] Fetched 168 kB in 0s (306 kB/s)                                                 W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/arialb32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/comic32.exe Err:1 http://downloads.sourceforge.net/corefonts/comic32.exe   404  Not Found W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/comic32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) E: Failed to fetch https://netix.dl.sourceforge.net/project/corefonts/the fonts/final/comic32.exe  404  Not Found  E: Download Failed Setting up ttf-mscorefonts-installer (3.4+nmu1ubuntu2) ...   The specific point at which it fails to download changed - it seems to be a sourceforge reliability problem, but this has now been going on weeks and results in annoying popups as above all the time.  How do we get this fixed and/or how can I work around it for now. Gamma Distribution out of sum of exponential random variables I have a sequence $T_1,T_2,\ldots$ of independent exponential random variables with paramter $\lambda$. I take the sum $S=\sum_{i=1}^n T_i$ and now I would like to calculate the probability density function.  Well, I know that $P(T_i&gt;t)=e^{-\lambda t}$ and therefore $f_{T_i}(t)=\lambda e^{-\lambda t}$ so I need to find $P(T_1+\cdots+T_n&gt;t)$ and take the derivative. But I cannot expand the probability term, you have any ideas? Removing file / folder link after using "Save As..." then "Web Page, complete" When you right-click save-as a web page in FF, the page is saved along with a folder containing any associated media that page needs (images, js, etc).  My problem is that I want to reorganise the associated media folder, but wherever I move this folder, the saved .html file is moved as well. ARGH!   I can rename each folder, which breaks the "link" between html file and media folder, but there must be a cleaner way to do it. Does anyone else know? ensurepip is disabled in Debian/Ubuntu for the system python I am trying to make a virtual environment for the development of my Django application. The commando's which I am using:   vagrant@vagrant:/var/www/djangogirls$ python3 -m venv myvenv The virtual environment was not created successfully because ensurepip is not available.  On Debian/Ubuntu systems, you need to install the python3-venv package using the following command.      apt-get install python3-venv  You may need to use sudo with that command.  After installing the python3-venv package, recreate your virtual environment.  Failing command: ['/var/www/djangogirls/myvenv/bin/python3', '-Im', 'ensurepip', '--upgrade', '--default-pip']   vagrant@vagrant:/var/www/djangogirls$ sudo apt-get install python3-venv Reading package lists... Done Building dependency tree        Reading state information... Done python3-venv is already the newest version (3.5.1-3). The following packages were automatically installed and are no longer required:   javascript-common libjs-jquery libjs-sphinxdoc libjs-underscore python-pbr python-pkg-resources   python-six python-stevedore python3-virtualenv virtualenv virtualenv-clone Use 'sudo apt autoremove' to remove them. 0 upgraded, 0 newly installed, 0 to remove and 108 not upgraded.  vagrant@vagrant:/var/www/djangogirls$ python3 -m ensurepip ensurepip is disabled in Debian/Ubuntu for the system python.  Python modules for the system python are usually handled by dpkg and apt-get.      apt-get install python-&lt;module name&gt;  Install the python-pip package to use pip itself.  Using pip together with the system python might have unexpected results for any system installed module, so use it on your own risk, or make sure to only use it in virtual environments.   vagrant@vagrant:/var/www/djangogirls$ rm -r myvenv/   vagrant@vagrant:/var/www/djangogirls$ python3 -m venv myvenv The virtual environment was not created successfully because ensurepip is not available.  On Debian/Ubuntu systems, you need to install the python3-venv package using the following command.      apt-get install python3-venv  You may need to use sudo with that command.  After installing the python3-venv package, recreate your virtual environment.  Failing command: ['/var/www/djangogirls/myvenv/bin/python3', '-Im', 'ensurepip', '--upgrade', '--default-pip']   As you can see, I am trying to make a myvenv, which cannot be created due to the python3-venv missing. I have already installed this, but the ensure pip is missing. After searching it seems that the system (Ubuntu 16.04) discourages the usage of the package. Could someone help me work around this problem? How to select html nodes by ID with jquery when the id contains a dot? If my html looked like this:  &lt;td class="controlCell"&gt;     &lt;input class="inputText" id="SearchBag.CompanyName" name="SearchBag.CompanyName" type="text" value="" /&gt; &lt;/td&gt;   How could I select #SearchBag.CompanyName with JQuery? I can't get it to work and I fear it's the dot that's breaking it all. The annoying thing is that renaming all my id's would be a lot of work, not to mention the loss in readability.  Note: Please let's not start talking about how tables are not made for lay-outing. I'm very aware of the  and try hard to use it as much as possible.