False vacuum is a hypothesis that there exist a state that is a local minimum, but not the lowest energy state.  Why do we think such a state as false vacuum really exist?
I was thinking of the noted 1980 paper by Sidney Coleman and Frank de Luccia--"Gravitational effects of and on vacuum decay"-- about metastable vacuum states that could tunnel to a lower energy "true vacuum" with catastrophic results. I suspect the answer is that if our vacuum is a false one, we wouldn't "see" the true one til it hit us.
Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is:  Let's say I receive two envelopes. Both envelopes have this written on them:     Hello! Open this letter...   If the paper inside is red, then other envelope has blue paper.   If the paper inside is blue, then other envelope has red paper.   So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper.  Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope?  In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct?  Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue?  In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes?  In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? Clocks for multiple timezones in GNOME Shell I looked everywhere but I couldn't find a way to display multiple clocks in GNOME 3. In classic GNOME and Unity, it is possible. Also, for some strange reason, additional timezones cannot be added to the clock using the time-date applet in classic GNOME. Any solutions? Overflow to left instead of right I have a div with overflow:hidden, inside which I show a phone number as the user types it. The text inside the div is aligned to right and incoming characters are added to right as the text grows to left.  But once the text is big enough not to fit in the div, last characters of the number is automatically cropped and the user cannot see the new characters she types.  What I want to do is crop the left characters, like the div is showing the rightmost of its content and overflowing to the left side. How can I create this effect? I'm using Python, and would like to insert a string into a text file without deleting or copying the file. How can I do that? Evaluate trigonometric function I see this often in the build scripts of projects that use autotools (autoconf, automake).  When somebody wants to check the value of a shell variable, they frequently use this idiom:  if test "x$SHELL_VAR" = "xyes"; then ...   What is the advantage to this over simply checking the value like this:  if test $SHELL_VAR = "yes"; then ...   I figure there must be some reason that I see this so often, but I can't figure out what it is. Is there a constraint that restricts my generic method to numeric types? Cannot invoke method or retrieve property from null object. Object returned by the following call stack is null. \"File\r\n\" A No-Nonsense Introduction to Quantum Field Theory I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page .  pdf ), a 24-page overview of the topic, very helpful for beginning study.  It all got me over the hump of learning the meaning of various terms associated with GR, most of which I had heard before without understanding.  It also outlined the most important examples.  Is there a similar document for quantum field theory, which presents the main equations, briefly describes the main ideas, and summarizes the most important applications and results so that the reader can feel the lay of the land before studying in depth? Discrete mathematics - Find all integer solutions of the equation $a^2+ b^2 + c^2=a^2 b^2$. Find all integer solutions of the equation $a^2+ b^2 + c^2=a^2 b^2$.  This is one of the questions we presented in one session to contest preparation PUTNAM. It turns out that I can't get from the problem. Could someone just give me a hint? (Please, don't give me the answer. Simply, an argument that can help me advance in the problem or theorem might suffice.) What is the name of a squircle with three, five, six or more corners? I know that the second shape is a squircle, but what are the other shapes called? Is there an actual name for them?    The shapes do not simply have rounded corners, but the sides have a "circularity". Here is a triangle with rounded corners next to the shape that I do not know the name of:    "Trircle", "Triarcle", and "Pentircle" do not seem to be used for them, at least Google's image search does not provide any results. Why does bash show 'Terminated' after killing a process? Here is the behaviour I want to understand:  $ ps   PID TTY           TIME CMD   392 ttys000    0:00.20 -bash  4268 ttys000    0:00.00 xargs $ kill 4268 $ ps   PID TTY           TIME CMD   392 ttys000    0:00.20 -bash [1]+  Terminated: 15          xargs $ ps   PID TTY           TIME CMD   392 ttys000    0:00.21 -bash   Why does it show the [1]+  Terminated: 15          xargs after I kill a process, instead of just not showing it as it was just killed?  I'm using bash on Mac OS X 10.7.5. Explanation of Spikes in training loss vs. iterations with Adam Optimizer I am training a neural network using i) SGD and ii) Adam Optimizer. When using normal SGD, I get a smooth training loss vs. iteration curve as seen below (the red one). However, when I used the Adam Optimizer, the training loss curve has some spikes. What's the explanation of these spikes?   Model Details:  14 input nodes -> 2 hidden layers (100 -> 40 units) -> 4 output units  I am using default parameters for Adam beta_1 = 0.9, beta_2 = 0.999, epsilon = 1e-8 and a batch_size = 32.  i) With SGD  ii) With Adam OpenVPN restriction Ive set up an OpenVPN server at my place and handed out a certificate to a client who has an openvpn client at his place.  I need require that he should be able to connect to the vpn server only from one IP address (his current one).  How can I do this? Automorphism of rational numbers Let $\mathbb Q$ be group of rational numbers under addition.  Then I want to find out the automorphism group of $\mathbb Q$. In a book it is given that Aut($\mathbb Q$) is isomorphic to $\mathbb Q^*$, the  multiplicative group of rational numbers. I stuck in this. Trig integral $\int ( \cos{x} + \sin{x}\cos{x}) \, dx $ Assume we have:  $$ \int (\cos{x} + \sin{x}\cos{x}) \, dx$$  Two ways to do it:  Use $$\sin{x}\cos{x} = \frac{ \sin{2x} }{2} $$ Then $$ \int \left(\cos{x} + \frac{\sin{2x}}{2} \right) \, dx = \sin{x} - \frac{ \cos{2x} }{ 4 } + C. $$ The other way, just see that $ u = \sin(x), du = \cos(x)dx $, $$ \int ( \cos{x} + \sin{x}\cos{x}) \, dx = \sin{x} + \frac{\sin^2{x}}{2} + C. $$  Now the part I don't see fully is, why aren't these results completely equal?  Taking the 2nd result, \begin{align} \sin{x} + \frac{\sin^2{x}}{2} &amp;= \sin{x} + \frac{1}{2} \, \left( \frac{1 - \cos{2x}}{2} \right) \\ &amp;= \sin{x} + \frac{1}{4} - \frac{\cos{2x}}{4}. \end{align}  So you have to absorb $\frac{1}{4}$ into $C$ for them to be equal.  Shouldn't they be equal straight away? Pure verbal nouns/deverbal nouns vs. gerunds This is a follow-up to a previous question which I am still trying to understand. I think I'm making progress in my understanding, but I would appreciate feedback to help me refine my thinking.  Here is the sentence:     Good writing requires hard work.   Originally, I thought that "writing" was acting as a gerund in this phrase.  After reading through the replies to that question along with back posts related to gerunds, I've since concluded that "writing" in this sentence is a , also termed a deverbal noun.  My reasoning?  —In the sentence above "writing" is modified by "good" and is thus acting more like a noun than a verb. —It has no direct object.  Is my thinking correct here?  If not, could someone politely help me to refine it?  However, what if I had written the following?     Writing well requires hard work.     or   To write well requires hard work.   In these examples, I'm thinking that "writing" would be a different kind of verbal noun—a non-finite verb acting as a gerund or infinitive, which is one piece of a larger complement noun clause.  The last bit is muddy for me, but I will leave it at that. Thank you in advance for your patience and insight. What file sizes and formats are most appropriate for enlarging and projecting an image onto a large wallspace for painting? What is duplicate content and how can I avoid being penalized for it on my site? Why do you cast downvotes on answers? This is a question which started off with a , then turned into an , and now it's a question in its own right (as suggested by Jeff). I'm not sure where it could go from here :)  It's obvious that different people cast downvotes for different reasons. (Upvotes are less controversial, generally.) Here are some possible reasons:   Answer is wrong Answer is misleading (may be technically accurate, but will lead to readers making mistakes) Answer doesn't match the question (e.g. a C# answer to a question about Java) Answer doesn't really address the question, e.g. suggesting a completely different solution, even if the question specifies that there are good reasons why the current approach has to be followed Answer is okay, but not as good as another one which currently has fewer votes Answer appears to be plagiarised from existing answers. Answer is by someone I don't like. Answer is abusive (profanity, spam etc). No reason, I just felt like it. I'm a , and prefer down to up. Have you considered down? Ideological grounds: answer suggests a technology I don't like, or expresses a negative opinion of a technology I do like   Personally I go with 1, 2 and 8 - although I'll add comments suggesting changes in various other situations.  Have I missed anything? What do you do, and why? What are the net benefits (to you, the world in general, and the answerer) from your approach?