If a photon is sent into a box with perfect mirrors aligned in a way that it won’t ever be reflected out, is it possible to hold the photon for extended lengths of time with its quantum properties intact, and measure it when we want by opening a path into the detector?
My question is a little silly I know, but I'm curious to know if a particle of light can be theoretically trapped between two reflective screens.   For example once the particle of light has left it's source, and is reflected against a mirror (assuming there is no loss of energy) and you immediately replace the source of light with another mirror. Would the light beam bounce in between the sheets endlessly?
Show in linked/related questions sidebar whether a question has answers or not Currently, in the linked/related sidebar, without opening the question the user can only distinguish whether the question has an accepted answer (green icon) or not (grey icon).  I often eagerly open an interesting-sounding question with a grey icon, only to find myself disappointed because it has no answer yet.  To avoid this, I suggest adding a third type of icon for questions that have at least one answer, but no accepted one. Probably a darker/lighter icon or some kind of frame or glow. I've made a quick example with Paint (if relevant, the screenshot I used is from ). I'm in no way satisfied with the look of it, but at least it demonstrates the general idea.    What do you think about this proposal? Would it be a useful addition to the StackExchange interface? to infinitive as direct object?! (as in : I promised to get there in time.) I'm a passionate Korean English-learner, and I would like to ask you a question about grammar.   It was 3 years ago when I first started to study the to-infinitive as studying grammar with Grammar In Use series and English Grammar series by Longman, having been exposed to English for 3 years. There wasn't any mention of the author saying that the usage of the to-infinitive is as an (direct) object. And for me also, the times I have encountered sentences in which the usage of the to-infinitive, so to speak, as direct objects were used, I've read them as some kind of obligatory adverbial that shows what the verbs are about, not as objects, which means they are noun phases! 100% of Korean textbooks say the usage is as a direct object, but I doubt it. I think it's some kind of obligatory adverbial that shows what the verbs are about.    I thought it was better for me to ask Americans themselves. Do you read this usage of to-infinitive as a noun phrase or an adverbial? I recently installed an SSD and AFAIK Ubuntu makes a weekly FSTrim on SSD's that support it.  Is there a log file of this trims? Need Help Fixing Grub after Installing Ubuntu 13.04 x64 Alongside Windows 8 on a Lenovo IdeaPad Y400 with UEFI I have a Lenovo IdeaPad Y400 that came pre-installed with Windows 8. I would like to run Ubuntu alongside it in a dual-boot configuration. I've spent the past week fiddling around, re-installing both Windows and Linux in various configurations, and I've come awfully close to success, but seem to have hit a snag with Grub.  For my most recent attempt, I took the following steps:   Disabled Secure Boot Re-imaged Windows 8 from a hidden recovery partition, effectively restoring the machine to factory state Activated an option called Legacy Support in the BIOS (or is it UEFI now?) Booted Ubuntu 13.04 x64 from a USB stick, chose "install alongside Windows" and accepted all default options After a restart, found that I could boot Ubuntu, but could not boot Windows Once into Ubuntu, I ran Boot Repair with recommended settings and accepted all defaults. When Boot Repair finished, I was presented with the following message:      The boot files of [The OS now in use - Ubuntu 13.04] are far from the   start of the disk. Your BIOS may not detect them. You may want to   retry after creating a /boot partition (EXT4, >200MB, start of the   disk). This can be performed via tools such as gParted. Then select   this partition via the [Separate /boot partition:] option of [Boot   Repair]. ()    I followed the instructions at the url in the message, creating a 1GB EXT 4 partition near the start of the drive  when I tried to run Boot Repair again, the "Separate /boot partition" option on the "Grub Location" tab was disabled.  The new partition is /dev/sda11 and has the label GRUB. On restart, I get the following error message:      error: file '/boot/grub/i386-pc/normal.mod' not found.    grub rescue>    However, if I manually choose the boot partition by hitting F12, I can boot into Windows no problems. Selecting Ubuntu from the boot device menu gives me a Grub menu with the following options:      Ubuntu      Advanced options for Ubuntu       Windows UEFI recovery bootmgfw.efi      Windows Boot UEFI recovery       Windows UEFI recovery LrsBootmgr.efi      Windows Boot UEFI recovery bkpbootx64.efi       Windows Recovery Environment (loader) (on /dev/sda3)       Windows 8 (loader) (on /dev/sda5) System setup    Selecting Ubuntu from this menu allows me to get to my Ubuntu desktop. I haven't tried the other options yet for fear of losing the progress that I've made.   So it looks like I have successfully dual-booted the machine, but that Grub is broken for some reason or another.   My current partition scheme can be seen at:   Thanks in advance - Jonathan Let $S = \{1,2,\dots,n\}$. Then $i \in S$ is said to be a fixed point of a permutation $p$ or $S$ if $p(i) = i$. Let $P_n(k) $ be the number of permutations of $S$ which have $k$ fixed point. Prove that $\sum_{k=0}^nk\cdot P_{n}(k) = n!$. Do hit points reset upon each use of wild shape even if the same form's assumed? Let's say I've used wild shape to assume the form of a mammoth that has 126 hit points. I take 26 points of damage, putting me at 100 hit points. If I use my next turn to take a bonus action to exit wild shape then an action to use wild shape to assume the form of a mammoth again, do I now have 126 hit points or 100 hit points? $g\in G$ maximal order in $G$ abelian then $G=\left\oplus H$ If $g\in G$ is an element of maximal order in a finite abelian group $G$ then exists $H\leq G$ such that $G=\left&lt;g\right&gt;\oplus H$  Attempt: Using fundamental theorem I know that $G=C_{n_1}\times\cdots\times C_{n_k}$ where $n_i|n_{i+1}$. With some work I proved $|\left&lt;g\right&gt;|=n_k$, so $C_{n_k}\cong \left&lt;g\right&gt;$. Then $G\cong H\times \left&lt;g\right&gt;$, but this is not an equality. Why didn't Palpatine publicly change his name once he became Emperor? Anakin Skywalker was known as Darth Vader (this was already his Sith name) after the creation of the Galactic Empire.  So why did Palpatine remain "Emperor Palpatine"? Why didn't he embrace his persona as Darth Sidious?  I started wondering after reading one of the answers to Prove that the derivative of an even differentiable function is odd, and the derivative of an odd is even. How do I find diamonds? The durability of iron tools is really starting to annoy me, but in all my hours of playing I've only stumbled across one deposit of diamond ore that provided around 7 Diamonds. What's the best way to locate more in Survival mode? Where is it most commonly found? Why is my command throwing a 'data tag parsing failed' error? I am trying to lock some boxes in a map of mine, and I used this command:   /blockdata 10 4 9 {Lock:Elyiana's Mage Key}   At first it worked, but then when I logged back on the next day it gave me this error message:    Data tag parsing failed: Expected '}' but ''' at: {Lock:Elyiana'&lt;--[HERE]     I don't know why it doesn't like the apostrophe in the key's name. I would change it, but it already worked and locked some other items. My version is 1.12, does anyone have an answer to my problem? What does high credit utilization really mean? Is "from where" grammatically equivalent to "from which"? I am taking a course in Mathematical Methods for physicsPhysics (Junior Level).   We are working from   > Mathematical Methods for physicists, George B.Arfken .    I just need online resources covering ( Matrices, Determinants, Vector Analysis, Tensors and differential forms and Vector spaces...etc) to study and understand from. dpkg-divert: error: rename involves overwriting `/usr/lib/xorg/protocol.txt' with different file `/usr/lib/xorg/protocol-precise.txt', not allowed I want to compute the Galois group of some polynomials, but I want to see some examples first. For example this proposition could be helpful. I don't know how to prove it &lt;.&lt;  Let's consider a polynomial $f(x)= x^4+ax^2+b \in \mathbb{Z} $. Let $ \pm\alpha , \pm\beta$ denote the roots of $f(x)$. Note that $f$ is irreducible iff $\alpha^2, \alpha\pm\beta \notin \mathbb{Q}$. So let's suppose that $f(x)$ is irreducible. Let's denote $G$ the galois group of $f$ (the Galois group of the splitting field $\mathbb{Q}(\alpha,\beta)/\mathbb{Q}$)  $i)$ $G\cong V$ the Klein 4-group iff $\alpha\beta \in \mathbb{Q}$  $ii)$ $G\cong \mathbb{Z}_4$ iff $\mathbb{Q}(\alpha\beta)=\mathbb{Q}(\alpha^2)$  $iii)$ $G\cong D_8$ the dihedral group of order 8, iff $\alpha\beta \notin \mathbb{Q}(\alpha^2)$  I need help with the proofs of this propositions... Well I'm very lost with the computation of Galois group, some care must be exercised, I don't have it. For example I know that Galois group acts transitively, in the sense that $u\in K/F$ a galois extension, the other roots of the minimal polynomial of $m_u(x)\in F[x]$ are precisely the elements $ \sigma(u)$ , where $\sigma \in Gal(K/F)$. And clearly any automorphism, is determined by only the value of a basis. In this case we are working on $\mathbb{Q}(\alpha,\beta)$, so I have to know the values of both. But I have to respect the algebraic relations involving $\alpha , \beta$ I proved that in $i),ii)$ $\mathbb{Q}(\alpha,\beta) = \mathbb{Q}(\alpha) $ So I have to know the values on $\alpha$.   My first question is: If in both cases $i),ii)$, I have an extension of degree 4 (so $|G|=4$) I have to map $\alpha$ to determine the automorphism, but I have also to map $\alpha$ to all of it's four roots. Why the galois group in this case are different?  My second question is about $iii)$ I have no idea How to attack it. Taking a spin off of this question:  in a new direction for 2014.  Taking into account a basic Windows infrastructure:   domain controllers Exchange 2007/2010/2013 Sharepoint SQL File Servers / Print Servers AD Integrated DNS AD authenticated 3rd party devices (let's say 802.1X for networking and maybe some content-filtering, etc.) AD/LDAP authenticated "administrative" functions on IT apps/hardware/etc. perhaps some KMS stuff throw in a CA if you'd like home grown apps 3rd party in-house apps   Now, let's rip it all out and decide we are going to the cloud.  We've contracted to move Exchange/Sharepoint/File Services to Office 365.  SQL will now be hosted as well on  something like Azure.  We've gotten away from the need for AD-DNS and simply run everything via a simple Windows DNS server.  We still need 802.1X and would like SSO if possible to our various cloud apps.  Home grown and 3rd party in-house apps would likely stay, but have the ability to use internal user databases instead of AD authentication  The question is...do we really need Active Directory at all?  Or more to the point, AD on-premise or even hosted via Azure or similar (ADFS) or running ADDS on a hosted VM through Azure or similar.  Could/Should we look to something else like a 3rd party SSO option such as  or similar that can provide SSO functionality even if it is as simple as LastPass or similar for each user?  What kind of legitimate needs does AD fulfill if everything else in the cloud?  Could a MS-centric infrastructure get away with not having AD at all if they move everything that previously relied on AD to SaaS offerings that didn't rely on AD authentication? Objective-C for Windows What would be the best way to write Objective-C on the Windows platform?  Cygwin and gcc? Is there a way I can somehow integrate this into Visual Studio?  Along those lines - are there any suggestions as to how to link in and use the Windows SDK for something like this. Its a different beast but I know I can write assembly and link in the Windows DLLs giving me accessibility to those calls but I don't know how to do this without googling and getting piecemeal directions.  Is anyone aware of a good online or book resource to do or explain these kinds of things? Show that $n-m$ is a multiple of 9 when $n$ and $m$ have same digits component.set not working for picklist field I have a number of lightning:inputField that i'm setting based on certain criteria, these all work except for picklist field types. The code below shows how i am setting the fields. The country field is the picklist and the 2 alerts have the correct value in them, however the value is not getting set on country. Is there a different method for setting picklist fields?  var address = res.getReturnValue(); var country = component.find('Country__c'); var pcodeFld = component.find('Postcode__c');  if(country != undefined){  alert(country);  alert(address.Country);  country.set('v.value', address.Country); } if(pcodeFld != undefined){  pcodeFld.set('v.value', address.Postcode); }   EDIT: I can set a default value whilst using $A.createComponents using .set("v.value", "United Kingdom");  it just seems that i can't set it after the component has rendered based on some user action.  Reproduceable Example:  I just can't seem to set the value of any picklist fields when using lightning:inputField.  Component  &lt;aura:component implements="flexipage:availableForRecordHome, force:hasRecordId"&gt; &lt;div class="slds-p-bottom_large slds-p-left_large" style="width:500px"&gt;     &lt;lightning:recordEditForm aura:id="recordViewForm"                                   recordId="{!v.recordId}"                                  objectApiName="Contact"&gt;         &lt;lightning:messages /&gt;         &lt;lightning:inputField fieldName="FirstName" /&gt;         &lt;lightning:inputField fieldName="LastName" aura:id="lastname"/&gt;         &lt;lightning:inputField fieldName="Birthdate" /&gt;         &lt;lightning:inputField fieldName="Phone" /&gt;         &lt;!--Picklist--&gt;         &lt;lightning:inputField fieldName="Country__c" aura:id="Country__c"/&gt;         &lt;lightning:button label="Update" variant="brand" onclick="{!c.update}"/&gt;     &lt;/lightning:recordEditForm&gt; &lt;/div&gt;     &lt;/aura:component&gt;   Controller  ({         update: function(component, event, helper) {         //alert(component.find("Country__c"));        component.find("Country__c").set("v.value", "Ireland");     },  })