Firstly, General Relativity states that Spacetime is dynamic and is consonant with the distribution of matter/energy. How does String Theory predict gravity, when it is background dependent, that is it starts off with a fixed, and presumably flat space-time?  Secondly, String Theory predicts the existence of a graviton, but seeing we don't have a quantum theory of gravity, how do we even know that this is the correct quantization of gravity? In other words how do we verify that the graviton should have the properties that String theory says it does, that is what grounds do we have for believing in the properties of the graviton?  Thirdly, how do we go from the existence of gravitons to the curvature of space-time? When we talk about gravitons aren't they already existing in some space-time framework?
First, I'll state some background that lead me to the question.  I was thinking about quantization of space-time on and off for a long time but I never really looked into it any deeper (mainly because I am not yet quite fluent in string theory). But the recent discussion about  got me thinking about the topic again. Combined with the fact that it has been more or less decided that , I decided I should give it a go.    So, first some of my (certainly very naive) thoughts.  It's no problem to quantize gravitational waves on a curved background. They don't differ much from any other particles we know. But what if we want the background itself to change in response to movement of the matter and quantize these processes? Then I would imagine that space-time itself is built from tiny particles (call them space-timeons) that interact by means of exchanging gravitons. I drawed this conclusion from an analogy with how solid matter is built from atoms in a lattice and interact by means of exchanging phonons.  Now, I am aware that the above picture is completely naive but I think it must in some sense also be correct. That is, if there exists any reasonable notion of quantum gravity, it has to look something like that (at least on the level of QFT).  So, having come this far I decided I should not stop. So let's move one step further and assume string theory is correct description of the nature. Then all the particles above are actually strings. So I decided that space-time must probably arise as condensation of huge number of strings. Now does this make any sense at all? To make it more precise (and also to ask something in case it doesn't make a sense), I have two questions:        In what way does the classical space-time arise as a limit in the string theory? Try to give a clear, conceptual description of this process. I don't mind some equations, but I want mainly ideas.   Is there a good introduction into this subject? If so, what is it? If not, where else can I learn about this stuff?      Regarding 2., I would prefer something not too advanced. But to give you an idea of what kind of literature might be appropriate for my level: I already now something about classical strings, how to quantize them (in different quantization schemes) and some bits about the role of CFT on the worldsheets. Also I have a qualitative overview of different types of string theories and also a little quantitative knowledge about moduli spaces of Calabi-Yau manifolds and their properties.
How to find and delete identical points? I recently performed  on a merged point feature class in ArcGIS 10.1.  I specified "1 meter" XY tolerance for the Integrate command.  The resulting point feature appears to be what I want except points that were integrated are now stacked on top of each other, which will be problematic in future processing steps.  The attributes for my dataset consist of an OID, Shape, x, y, z.  Where x and y = UTM coordinates and z = buffer distance.  The command  does not appear to work for my dataset (i.e based on Fields: OID, Shape, x, y, z and XY tolerance = 1m) as the output still has stacked points.  I am also working with big data--the integrate output has 37 million points.    There is a related thread, titled , although I would like to open the question up to python solutions too.  What is the best way to find and delete (spatially) duplicate points?  Is there a better solution to integrating such that the output does not contain overlapping points? How to completely remove Notepad++ in Ubuntu 18.04 terminal?  I can't find it in Synaptic package manager, and don't know where is on system, but I can see an icon in Activity. It is probably not completely installed, because I can't open it. Prove that $(a + b + c)^{13}$ is divisible by $abc$ if $b|a^3$, $c|b^3$ and $a|c^3$. Make account merges propagate to chat I need to make a small correction in a video I uploaded to YouTube. Googling shows that this is not possible. However, I remember seeing it done before. I posted a comment on a video saying that a certain part of the video was missing. I got a reply back that it was fixed, and when I went to see the video again, it was changed. How was this done? This is more of a panic question after reading reviews on Istanbul Atatürk Airport. They said it's messy and hard to navigate, therefore I'm asking questions here in name of my girlfriend who will need to transit through this airport.  My girlfriend (Canadian national) traveling from Toronto (YYZ) to Istanbul (IST) for a couple hours (~4 hrs, so transiting) in order to come to Pristina (PRN). I would like a quick guideline on how to pass through this airport seamlessly without facing any trouble or delay.  Her tickets are both with Turkish Airlines. She purchased it via a third party (Flighthub.ca). It's only one booking and it includes both flights in it.   Once my girlfriend departs, she's obviously required to follow the signs and go to the transit area. Once she's there, will she be required to present a ticket? Where does she get that ticket? Does she get it in YYZ or does she need to visit a counter in IST and get it? After she's got the proper ticket, what does she need to do exactly? Wait in line to have her passport checked? Will they also control her carryon?  After this step, does she simply go to the PRN flight gate and that's it?   We're simply worried about Istanbul Atatürk Airport because of the recent things that happened in Turkey (coup attempt and ISIS attack) and she doesn't wanna somehow end up locked up there. I've read that the airport is a mess lately and a lot of people will be there waiting in line. So, another question: Are 4 hours enough?  I would appreciate a step by step guideline on how she needs to navigate and what she needs to do in that airport to have a smooth experience without facing any delays. Also some misc information on Istanbul Atatürk Airport would be appreciated. Interpretation of interaction term I have a model: $$ \ln({\rm earnings}) = a+b_1{\rm female}+b_2{\rm white}+b_3{\rm female}\times{\rm white} $$ ${\rm female}$ and ${\rm white}$ are dummy variables.  I have interpreted $b_1$ and $b_2$:    $b_1$ = change in female earnings comparing to male given you are non white $b_2$ = change in white earnings comparing to non white given you are male   But I am unable to interpret the coefficient of the interaction term ($b_3$). Please help me with this.  Let me make it more clear what I need out of this regression $$ \ln({\rm earnings}) = 2.618656-.0899657{\rm female}+.382019{\rm white}-.2754126 {\rm female}\times{\rm white} $$ Now i know there is gender pay difference with b1, i also know there is race pay difference with b2. Now with b3 i need to know is their a gender pay gap for whites only. How can i figure that out with regression above and without test. Trash icon and files have disappeared from the desktop after upgrade to Ubuntu 19.04 Yesterday I upgraded my Ubuntu 18.10 to Ubuntu 19.04, and after the restart, the trash icon and my Desktop files have disappeared from the UI. If I go to the Desktop folder from my personal folder, I can see the files, but my Desktop is empty.  How can I show my files in the Desktop again? This question is updated to request additional answers and details in light of information now available in the Dungeon Master's Guide. In the released DM basic rules, Lost Mine of Phandelver, Hoard of the Dragon Queen, and the DMG teaser there are wands, staves, and rings that you can use to cast spells.  Do abilities that trigger from casting a spell activate when casting a spell from an item?  Can the character modify the spell using class abilities when casting a spell from an item?   Examples include:  An abjurer Wizard's arcane ward recovering hit points from a Dispel Magic cast from a Ring of Spell Storing  A sorcerer using Twinned Spell on a ray of enfeeblement from a Staff of Power  An evocation wizard using Sculpt Spell on a fireball from a Wand of Fireballs.   Now that the DMG is out we have some clearer rules on casting spells from items (DMG p. 141):  Some magic items allow you to cast a spell from the item.  The spell is cast at the lowest possible spell level, doesn't expend any spell slots, and requires no components, unless the item's description says otherwise  The spell uses its normal casting time, range and duration, and the user of the item must concentrate if the spell requires concentration. A magic item, such as certain staffs, may require you to use your own spellcasting ability when you cast a spell from the item.  Does whether or not you can apply class abilities to the casting of the spell depend whether the item uses the user's own spellcasting ability (such as the Staff of Fire) versus an item that comes with a fixed spellcasting ability built-in (such as the Wand of Fireballs)? Does it matter if it's something that triggers more or less automatically like Arcane Ward, versus something you have to control, like Careful Spell? What are the options for a non-EU national who wants to extend his stay in Switzerland (totaling less than 90 days)? What's wrong with "I'll open you the door"? When I call the buzzer outside my girlfriend's flat, she sometimes says *"I'll open you the door". I correct this to "I'll open the door for you".  I've never heard a native speaker say it the first way, which is why I think it's wrong. But I can't explain why.  There is a pattern in lots of English phrases that would suggest both are correct. A few common examples:   Give the keys to me before you go — Give me the keys before you go I'll buy a coffee for you at the cafe — I'll buy you a coffee at the cafe We sent a text to Martin on his birthday — We sent Martin a text on his birthday   The left-hand side is more formal, and the right-hand side is more common in everyday speech.  What do you call this pattern?  What makes the 'open-the-door' sentence an exception? How to install League of Legends in Ubuntu Calling a function of a module by using its name (a string) Every separable Banach space is isomorphic to $\ell_1/A$ for some closed $A\subset \ell_1$ How to prove the following mind-blowing fact?     Let $X$ be a separable Banach space and let $\ell_1$ be the space of all absolutely summable scalar sequences. Then there exists such closed subspace $A\subset \ell_1$ that factor space $\ell_1/A$ and $X$ are isomorphic as normed spaces.   Edit: So what, this is like a classification up to isomorphism of all separable Banach spaces? Each separable Banach space corresponds to some closed subspace of $\ell_1$? Too much whitespace in "Thanks for the feedback" While attempting to downvote something on a site I don't have an account on, I see this message, which has too much whitespace:    The same thing happens with upvotes (and プラス票が):    (I think it's safe to say that this is a network-wide bug, since I took these all on different sites.)  However, it looks more reasonable when you are not logged into the network at all (e.g. in private browsing):    An earlier version of this issue was reported at , but the difference is that there is no newsletter UI on the right anymore. (The extra space could have been justified before given the height of the newsletter; now it's definitely a bug.)  Also, is newsletter supposed to be gone? I was using , implemented in scikit-learn, for my research work. But I have no good understanding of this.   Can anyone please give a simple, good explanation of one class SVM? Antivirus software is breaking SE web page? (blocking CSS and JS)? Time Traveler steps on a butterfly, changes everything I heard of this in high school, but never learned its title or author- supposedly the aforementioned worm butterfly would have played a part in evolution that caused the extinction of the dinosaurs (instead of that meteor most people blame now). This story might even have been parodied on a certain Simpsons Halloween Special (the one where Homer accidentally makes a time machine trying to fix the toaster). Find probability using distribution function method Let $X_1$ and $X_2$ be two independent random variables with distribution $U(0,1)$. Let $Y=|X_1-X_2|$. Find the distribution function and density of $Y$.   Solution:  f(x1)=1 whenever x1 between 0 and 1          =0 Else where f(x2)=1 whenever x2 between 0 and 1          =0 Else where f(x1,x2)=1 whenever x1,x2 between 0 and 1           =0 Else where G(y)= P[-y &lt;= x1-x2 &lt;= y]       =\int_{-y}^y \int_{x1_y}^{y+x1} 1 dx2 dx1       =\int_{-y}^y -2y dx1       =4y^2 when y between 0 and 1       =0 when y less than 0       =1 when y greater than 1 Thus, g(y)= \diff G(y) =8y  Is it correct? Every ordered field has a subfield isomorphic to $\mathbb Q$? I'm going through the first chapter in a text on real analysis, which contains preliminaries on ordered fields, the real numbers, etc. Supposedly I had learned about such things already, in calculus, but I thought it wouldn't hurt to go over it again.  Up until the paragraph which is the subject of my question, everything is thoroughly proven and examples are provided. However the following excerpt just goes through facts, whose proof I cannot conceive:      Although $\mathbb Q$ is an archimedean field, these properties cannot be used to define $\mathbb Q$ since $\\$ there are many Archimedean ordered fields. What distinguishes $\mathbb Q$ from the other $\\$Archimedean ordered fields is that $(\mathbb Q,&lt;)$ is the $smallest$ ordered field in the following sense: $\\$ if $(X,\prec)$ is an ordered field, then $X$ contains a sub-field which is (field) isomorphic to $\mathbb Q$.$\\$ Furthermore such an isomorphism preserves the order relation.   I've concatenated the paragraph a bit, so the text isn't idem from the book (if anyone wishes to know it's Phillips, An Introduction to Analysis and Integration Theory, Dover Publications). Also $\mathbb Q$ contains no proper subfields, and this can be verified by the apparently easy-to-prove fact that, if a field has characteristic zero, then it contains a subfield isomorphic to $\mathbb Q$. Then it remains to prove the preservation of order.  I'm guessing that some concepts from abstract algebra or field theory would easily suffice, but at the moment such topics are a bit over my head, so all I can think of doing is actually constructing the isomorphism $\phi:\mathbb Q\to\hat{\mathbb Q}$, where $\hat{\mathbb Q}$ is a certain subfield of  $X$ in such a way that field operations are preserved, but I really can't come up with anything. So the question is: how do I construct this isomorphism, or, if there's a better way of proving this, how is it done? Thanks for any help.  Edit: Assume the existence of $(\mathbb Q,&lt;)$ as an archimedean ordered field.