I understand that nothing can move faster than light due to time dilation. I want to build upon my understanding of Einstein's theory of Special Relativity, so I came up with this hypothetical problem for myself:  If both particles are moving at 0.9c towards each other (according to an observer on Earth), what speed does each particle have relative to the other?  I'm stumped since I am only familiar with Newtonian classical mechanics to solve this (which would be wrong). I am aware of Lorentz' factor $\gamma =\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ and the time dilation equation $t_m = \frac{t_o}{\sqrt{1 - \frac{v^2}{c^2}}}$, but I'm not sure how to apply it in this instance. I'm just looking for a gentle push in the right direction. Edit: My prior research:  This article, ,  talks about the effect of a baseball thrown at 0.9c would have as it traveled towards a batter. This is not what I'm looking for since it doesn't explain the math behind finding the collision speed between two high velocity entities.  This question on Yahoo, , asks a similar question to mine, but no math is involved to demonstrate the calculations behind the reasoning.  This question on Physics.SE, , does not answer my question either. I have not been able to find a similar Physics.SE question which can provide me to clues to my own hypothetical question.  I have also Googled the following phrases:    i. &quot;collision faster than the speed of light&quot; ii. &quot;collision of high speed particles&quot; iii. &quot;lorentz transformation in a collision&quot; iv. &quot;collision analysis at light speed&quot;
Let's say we have $2$ particles facing each other and each traveling (almost) at speed of light.    Let's say I'm sitting on #$1$ particle so in my point of view #$2$ particle's speed is (almost) $c+c=2c$, double light speed? Please say why I am incorrect :)    EDIT: About sitting me is just example, so in point of view of #1 particle, the second one moves at (almost) $c+c=2c$ speed?
I bought two pieces of land. One from Morthal, and one from Falkreath. Morthal was the first plot of land I purchased. I only finished half of it. I bought the plot of land in falkreath because I liked the nature better. I finished the house completely in Falkreath. Every time I try to adopt a child off the streets it keeps saying "I have a place but no room for you" Even though I have the bedrooms in my Falkreath house. Why can I not adopt a child and have him/her live at my house in Falkreath? Do I need a bus/train/plane ticket out of Thailand in order to get a Visa-on-Arrival? Someone told me I need a ticket out of Thailand in order to enter.  I am traveling to Thailand, on March 18th. I have a Ticket from Bangkok to Sweden booked for June 4th.   I will be staying in Thailand for 2 weeks when I arrive there, then traveling around Cambodia, Laos and Vietnam until June 4th when I leave.   With that ticket out of Thailand, will I be able to get in and get a (30 day) Visa-On-Arrival (or not because the ticket out is not within the first 30 days). Or do I need to show proof that I am leaving within 2 weeks of being there at first? Why rationalize the denominator? There are many times when I curse the autocorrection mechanism for changing what I typed, but overall, much of the corrections are welcome so I don't really want to disable it. I do want to have it do it's work but alert me when it makes each change so I don't have to proofread everything or focus with perfect attention to the screen to see the momentary red and/or blue underlining that alerts me to the machine override.  I would love a way to turn on an audible beep (customizable of course) so that I also get a warning each time my typing gets corrected (and only when autocorrection occurs). How to install and configure Wine? I am looking for a step by step instruction to guide me in the ways of installing, configuring and debugging many of the issues new users have when dealing with Wine in Ubuntu.  What is the recommended way of installing Wine, some of the key issues that it has and how to solve them?  If I have a specific problem with an App in Wine, how do I go about solving it? What are the recommended steps to ensure that I can fix a problem related to an app I wish to use? Does the shape of a containter affect the apparent mass of liquid inside it when measured by a scale? For both containers it is true that:  $p_{bottom}=p_{atm}+\rho gh$ and $F_{bottom}=a*p_{bottom} \iff F_{bottom}=a*p_{atm} + a\rho gh$  I do not know how a scale functions, but I guess that the only force it can count is the force by the liquid on the bottom of each container (the only surface that is in touch with the scale is the bottom of the container). Thus, if we measured the mass of these two masses of water (lets assume that the mass of the containers is negligible) it would appear to be the same in each case. Am I right? How can I evaluate $\int_{-\infty}^{\infty} e^{-x^2} dx$ without using polar coordinates Electromagnetic waves can be shielded by a perfect conductor. What about gravitational fields or waves? How to filter uninteresting questions Electrolytic Capacitor Voltage Rating vs capacitance I have always believed that it was ok to replace a capacitor with a slightly higher voltage rated one. eg 16v with 25v.Going higher than this would risk the capacitance value being out at the working voltage. However I just read the following quote from this       Electrolytic capacitors are non-ferroelectric with a very low dielectric constant. Their capacitance is derived from a very high surface area and nanometer thick dielectric layers. Their capacitance is not a function of applied voltage.‐Design Solutions For DC Bias In Multilayer Ceramic Capacitors (August 2010 Electronic Engineering Times)   So does this rule not apply to aluminum electrolytics? Eg will I have no issues replacing an electrolytic 25v 100uf with a 50v 100uf assuming both are low esr, similar footprint and good quailty? Visa for European countries for US passport holder I'm a US passport holder. What documents do I need when I fly from the U.S. to Germany?  Assume I'm going for a few weeks of vacation.  Obviously I need my passport.  What about a "visa"?  Anything else? How can I install Whatsapp web app on Ubuntu? I found a similar question , but here I am asking for the WhatsApp desktop webapp so that I can directly access the application without opening a browser. How do I show for an ideal transformer $M^2=L_1L_2$? I've been stuck on this problem for about an hour.     In an ideal transformer, the same flux passes through all turns of the primary and of the secondary . Show that in this case $M^2=L_1L_2$, where $M$ is the mutual inductance of the coils, and $L_1$, $L_2$ are their individual self-inductances.   My first instinct was the following: If we isolate the response of each coil to the other one, we get the equations $N_1\Phi_1=MI_2$ and $N_2\Phi_2=MI_1$, where $\Phi$ is magnetic flux going through a single turn of the coil and $I$ is current. Likewise, if we isolate the response of each coil to itself, we get the equations $N_1\Phi_1=L_1I_1$ and $N_2\Phi_2=L_2I_2$. I would now naturally want to say "Now just multiply $N_1\Phi_1$ and $N_2\Phi_2$ both ways, and get the desired result!" i.e.,  $$(N_1\Phi_1)(N_2\Phi_2)=(MI_2)(MI_1)=(L_1I_1)(L_2I_2)\implies M^2=L_1L_2$$  But that's incorrect, because the response of the coils to themselves and to the other coil are different quantities (i.e. not necessarily equal).  Realizing this, I write down the more general equations.  $$N_1\Phi_1=MI_2+L_1I_1$$ $$N_2\Phi_2=MI_1+L_2I_2$$  Now even with the hypothesis that $\Phi_1=\Phi_2=\Phi$, I still can't see how the identity $M^2=L_1L_2$ follows. Could you help clear up my confusion?  *Taken from D. Griffiths Introduction to Electrodynamics (4th ed.), Problem 7.58. Usage of singular or plural SI base units when written in both symbol as well as name I have multiple doubts related to the usage of singular or plural SI base units when written in both symbol as well as name.  I have framed this question under two parts, namely, Part (a) and Part (b). Each part has three sentences which I have written on the basis of my understanding.  Please answer these 6 sentences/questions.   Part (a):   says that while using prefix for e.g., centi as in centimeter, it is   l = 75 cm long.(correct) l = 75 cms long. (wrong)    Does this rule is used for all SI prefixes (having powers of 10)? In this regard, we should be saying, or writing that, "how many cm are there in one metre?" (while saying we should say centimter or centimetres?) Please strike-through the wrong SI unit in the following sentences.  My weight is 70 kg / kgs,  or My weight is 70 kilogram / kilograms.   Part (b):  and the page next to above web link says, we should write:  2.6 m/s, or 2.6 metres per second.   In this regard, we should say, or write:   Its speed is 0.26 metres per second.  This pipe is 0.75 metres long. How many cm are there in 2 metres? I recently installed Ubuntu 18.04 and I'm not keen on the desktop environment. I want the desktop env. I used to have in Ubuntu 14.04. How can I get it?  I've attempted to use , but when I try to install the Unity's 7.2.5 version using the command:  apt install unity=7.2.5   it gives me   E: Version '7.2.5' for 'unity' was not found   For sure I need to add a PPA for this, but which one!? How do I open PDF in Adobe Reader DC without locking the file from being updated by pdflatex? I don't know if this is possible on Adobe Reader DC on Windows, but asking in case someone has managed to do it.   When I am working on a large document in LaTeX (I use TexStudio) I sometimes like to keep a second copy of my PDF on a second screen so that I can easily refer to what I wrote before, while on my main screen I would have TexStudio with its preview window, which is typically automatically in sync with my current editing location.  On Ubuntu (which uses evince as its default PDF viewer) I used to do it quite nicely. It also seems to watch the PDF file for updates, and keeps in sync of any new versions of the PDF file and reloads it (staying on the same page) when I re-run pdflatex from TexStudio.  At the moment I am working on a Windows machine, and I am trying to recreate the same workflow. I would really like to open a second viewer on my second screen so that I can navigate easily to previous chapters without losing my current position in TexStudio's preview window (which will anyway go back to the current editing location when I run pdflatex).  The only problem however is that when I open the PDF in Adobe Reader DC to put it on the second screen and then I try to recompile the PDF I get the error "I can't write to file". I presume that for some stupid reason Adobe Reader DC maintains some write lock on the file, probably keeping it open while the PDF is visible on screen.  Is there a way to disable this stupid file-locking behaviour from Adobe Reader DC?  UPDATE  After some valuable comments, a workaround is possible using a different viewer. One could either use  or  (the default PDF viewer on Ubuntu, but also available for Windows). They are not so feature rich, and maybe do not look so nice, but in this case do the job.  A similar question was posted  for reference. I have written code like below and all works fine, but while submitting the form I get the error below. I am trying to filter the second dropdown based on the first drop down selection.     An illegal choice has been detected. Please contact the site administrator.   How do I overcome that error?       function dynamic_location_dropdown_form_alter(&amp;$form, $form_state, $form_id) {   if($form_id == 'product_node_form') {    $location_options = array();    if(isset($form['field_destination']['und']['#default_value'][0])) {     $destination = $form['field_destination']['und']['#default_value'][0];   }   else {     $destination = 0;   }    $location_options = dynamic_location_dropdown_locations($destination);    $form['field_destination']['und']['#ajax'] = array(     'event' =&gt; 'change',     'wrapper' =&gt; 'squadron-wrapper',     'callback' =&gt; 'dynamic_location_dropdown_ajax_callback',     'method' =&gt; 'replace',   );   $form['field_product_location']['#validated'] = true;   $form['field_product_location']['und']['#prefix'] = '&lt;div id="squadron-wrapper"&gt;';   $form['field_product_location']['und']['#suffix'] = '&lt;/div&gt;';   $form['field_product_location']['und']['#options'] = $location_options;   } }  function dynamic_location_dropdown_ajax_callback($form, $form_state) {   $country_id = $form['field_destination']['und']['#value'];   $form['field_product_location']['#validated'] = true;   $form['field_product_location']['und']['#options'] =  dynamic_location_dropdown_locations($country_id);    return $form['field_product_location']; }  function dynamic_location_dropdown_locations($destination_id) {   $nodes = array();   $nodes[''] = '- None -';   if($destination_id != '') {     $select = db_query("       SELECT node.title AS node_title, node.nid AS nid, node.created AS node_created       FROM {node} node       LEFT JOIN {field_data_field_location_country} field_data_field_location_country        ON node.nid = field_data_field_location_country.entity_id        AND (field_data_field_location_country.entity_type = 'node'        AND field_data_field_location_country.deleted = '0')       WHERE (( (node.status = '1')        AND (node.type IN  ('location'))        AND (field_data_field_location_country.field_location_country_nid = $destination_id)))       ORDER BY node_title ASC     ");     $nodes[''] = '- None -';     foreach ($select as $node) {       $nodes[$node-&gt;nid] = $node-&gt;node_title;     }   }    return $nodes; } Can the Surface Area of a Sphere be found without using Integration? When we were in school they told us that the Surface Area of a sphere = $4\pi r^2$  Now, when I try to derive it using only high school level mathematics, I am unable to do so. Please help. Is there any true inertial reference frame in the universe? Is there any true  in the universe?  Newton's first law states that an object at rest remains at rest, and an object performing uniform motion performs uniform motion, until and unless acted upon by an external force, if viewed from an inertial frame. It is the definition of an inertial frame of reference. And Newton's second law states that the net external force acting on a particle equals its mass times its acceleration. Thus we need to have an inertial frame in order for Newton's 1st and 2nd laws to be applicable.  Scientists claim that Earth is an inertial frame, either the  frame or the  frame.  Why is that? Earth's different parts have different accelerations when it performs rotational motion about its axis. Now you may say that Earth's axis is inertial, but the Earth is also revolving around the Sun. Thus Earth's frame should be non-inertial.  Even supposing that earth's frame is inertial, then it means that rest of the universe is non-inertial, because only a frame that moves with constant velocity with respect to an inertial frame is also an inertial frame and according to various scientific experiments there is no other matter in this universe which satisfies that criterion. Now you may say that earth is an approximate inertial frame, but still, my question is: is there any perfect inertial frame in the universe where Newton's laws are exactly applicable? Below you find the design for our business cards. The triangles are yellow, as you can see outside of the canvas. However, inside the canvas, only when I set the Color Mode to CMYK, they appear pink. When I switch the Color Mode back to RGB, they appear yellow as expected. However, when I print them, in both cases they turn out pink...   I would just like to know what is going on here and how I can change them back to the right colors?  CMYK Colors: