When I read about the expanding universe and inflation I often see pictures like this:    (Source: )   or explanation like this:     For getting an idea of space expansion you have to imagine a cubic grid throughout the whole space where the grid/ the number of cubes does not change, but each cube is increasing in size. It is similar to a sort of "stretching" of the size of the cubes.   (Source: )  My question is this: These descriptions only make sense if you assume a space around the universe which serves a frame of reference for measuring the expansion. In the picture from Wikipedia the expansion takes place with reference to the black background of the image. In the example with the expanding grid there has to be some kind of meta space around the cubes to have a frame of reference for measuring the expansion. An observer within the cubes cannot measure the expansion, as his frame of reference grows at the same time.   To my knowledge at the Big Bang both space and time have been created, so in my understanding there is no meta space which could be used as a frame of reference to measure inflation or an expanding universe.   How can I reconcile the concepts of an expanding universe / inflation without having to assme a meta space within which this expansion takes place?  FYI: I'm not a physicist, so please bear with me if this a noobie question.
If the universe is expanding, what is it expanding into? When the big bang happened where did it occur?  When the big bang happened how did it occur?  Where did the energy come from? Energy can not be created or destroyed does that mean, energy has existed before the universe was here?
How to connect to wifi using just the terminal? Xubuntu Dropbox icon fail Why ; is called semicolon and what is its history? Semi- is a Latin prefix meaning "half" and colon is another punctuation. Should I therefore say that semicolon is a halved colon? How would you prove the following limit?  $$\lim_{(x,y) \to (0,0)} \frac{x^3y}{x^4+y^2} = 0$$  I think the best way is using the squeeze theorem but I can't find left expression.  $$0 \le \frac{x^3y}{x^4 + y^2} \le \frac{x^3y}{x^4} \le \frac{x^3y}{x^3} \le y = 0.$$  But I'm not sure I'm right (especially at $\frac{x^3y}{x^4} \le \frac{x^3y}{x^3}).$  If I'm right - I'd glad if you can accept it.  If I'm wrong - can you please correct me?  Thanks in advance! Tikzexternalize not compatible with Miktex 2.9 abntex2 package Add Virtualbox Shortcut in Unity Launcher to boot to a VM How can I change iTunes country of region when having some credit in my account? I moved to Canada and I want to change my country of region from USA to Canada, but when I try to change it ( by click on my account in the iTunes Store and going to my Account Page) it showed me this error: "You have a store credit balance; you must spend your balance before you can change stores"    I must mention I have redeem 100$ to my account but I don't have any intention to spent it now, what is my option? Are there any known uncountable transfinite increasing sequences of real numbers? The real numbers are uncountable, so assuming the axiom of choice there is at least transfinite sequence of real numbers $r_0, r_1, r_2, ..., r_\omega, r_{\omega + 1}, ..., $ up to (and possibly including) $r_{\omega_1}$ that contains an uncountable number of terms. However, it's not guaranteed that $r_0 &lt; r_1 &lt; ..., r_\omega &lt; ...$  Is there a known transfinite sequence of real numbers that is monotonically increasing and which contains uncountably many real numbers?  Thanks! Can anyone tell me if I should use inspire or inspires in this phrase?     An extraordinary leader whose vision, values, integrity and boundless curiosity inspires all who follow in his footsteps. Dollar Sign corrupts question In  my question () contains a "$" in a quoted section of the question.  Originally I had a second "$" in a second quoted  section of the same question.    However when I did this the second $ seemed to trigger a style that made the text italic and lost spacing between words.  I took out the second "$" and instead emphasized it with the word "dollars" which solved the immediate problem.  However, in the listing of the question, (not the question itself) the same thing happens after the first "$".  The summary shows the text without spaces between words and in italic.  Seems like a bug.  Below is a verbatim copy/paste of the original issue (two dollar signs):    I was able to find a small ESC for about $12 off of ebay.  If you were designing a robot, would you see that and think?       $12 bucks for an ESC that connects to simple pulse-wave interface -   sign me up!   Or would you think:     $12 just to control a motor? I could throw together an H-bridge for   $0.50 and be done with it.   My robot in particular actually has two motors and therefor $24 to control the two of them.  But the interface is really easy (plus has the added advantage of being R/C vs computer controlled with a simple change of connectors.  Which way would you go? Are the tags shown in a particular order? Precision of Coulomb's law Up to which precision has the coulomb law proven to be true? I.e.  if you have two electrons in a vacuum chamber, 5 meters appart, have the third order terms been ruled out? Are there any theoretical limits to measure the precision ( Planck's constant?). Obviously there are practical limitations ( imperfect vacuum, cosmic rays, vacuum fluctuation). Still, does anyone know what was the smallest amount ever correctly predicted by that law?    Edit : Summary  On the high end of the energy spectrum a precision of 10^-16 has been shown ( 42 years ago )  For electron point charges at large distances the law might brake down due to practical reasons.  For moving particles QED gives a correction to the law: How can I make hibernate my desktop in UEFI with Secure boot on.  I used command "sudo pm-hibernate" to make hibernate my desktop but my machine did nothing (my desktop is booted up on UEFI with Secure boot on). But, if I boot my desktop on UEFI with Secure boot off, Hibernation is normal.  Sorry for my English, thanks, What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories?  I'd think that these hypotheses lead to physically "nice" theories in some way, but I've never, even from a computational perspective. really given these assumptions much thought. Real Size Image Printing Universe being flat and why we can't see or access the space "behind" our universe plane? I'm a layman, but i watched some intereting videos about big bang on youtube[michio kaku, hawking this kind of things, not some crackpots :)]   I described everything on my picture:     So is there any possibility to see that inner side, for example, by creating wormhole, or entering new dimension? Or i get something wrong, on the way, and my model is totally wrong?  And another question. I heard that even if you would fly a ship across the universe you would eventually end in the place where you started, because we live in a 3d space that is defined on a surface of big sphere. But why a big sphere? Universe might be a big mobius strip, and the same principle of ending at start will apply. Is it possible?  Thanks in advance, and please don't bash me for silly questions. Im just curious, but i don't have any degree in physics. Im also not an english native speaker. Allow embedded HTML5 YouTube video I am looking for the definition of when I am allowed to do forward declaration of a class in another class's header file:  Am I allowed to do it for a base class, for a class held as a member, for a class passed to member function by reference, etc. ? Query Which Profiles Have Read Access To Specific Object? Since I couldn't think of how to write this query off the top of my head, I thought it might be worth sharing. How can I query which Profiles have Read permission on a specific object? I knew it would have something to do with ObjectPermissions and PermissionSet, but had to look up the documentation for both to piece it together. While writing a proposal at work today I needed to mention a list of things and within that list were multi-part items. It seems like replacing the comma with a semi-colon in this situation would make the sentence easier to understand, but is it correct usage?  With standard punctuation this could get confusing:       Some of my favorite things to do are   camping, playing football and   baseball, watching Laurel and Hardy   Movies, and traveling.   Proposed alternative. Is this acceptable usage?       Some of my favorite things to do are   camping; playing football and   baseball; watching Laurel and Hardy   Movies; and traveling.