Setting of the experiment: Triplets Alice, Bob, and Carla have plenty of entangled electrons when they depart from Earth. Alice stays behind, Bob goes to Zeta Reticuli, and Carla goes to Andromeda. All three continuously make a video of everything around them, assuming they could even see each others clocks. Because of time dilation (including relativistic Doppler-shift) they all see each others clock running slow. However, if Bob returns to Alice she will be older because he accelerated. In Carla her reference frame, she thought that Bob was travelling anti-parallel to the motion of the Milky Way when he was on his way to Zeta Reticuli. The velocity of Alice was greater than Bob's according to Carla, concluding Alice her clock was running slowest. Outside the lightcones of certain events, Carla might even see a different sequence of events than Alice or Bob would. The experiment: The triplets have distributed entangled pairs of electrons among them so that each pair is separated after departure. They have agreed to make a position measurement at the end of every week (7 days of exactly 24 hours on their own clock). The &quot;collapse of the wavefunction&quot; happens instantaneously, while relativity denies the notions of absolute time: there is no &quot;now-moment&quot;. The question is: when does the other electron collapse, &quot;after&quot; the position measurement? Could the triplets carry out this experiment, and see regularities in the wavefunction collapses caused by their siblings? I know it's correlation rather than causation, but what if the triplets agreed to a secret code? Since they might be able to predict each others clocks, they could agree that a postion measurement between 0-30 min of some hour represents 0 while 30-60 min represents 1.
It is often stated, particularly in popular physics articles and videos, that if one measures a particle A that is entangled with some other particle B, then this measurement will immediately affect the state of the entangled partner.  For example, if Alice and Bob share an entangled pair of electrons and Alice measures her spin in the $x$ direction, then Bob's spin will also end up spinning in that direction, and similarly if she measures in the $z$ direction. Moreover, the effect will be instantaneous, regardless of the spatial distance between the two particles, which seems at odds with special relativity.  Can I use a scheme like this to communicate faster than light?
What is known about $\mathcal C^\infty$ functions $\mathbb R\to\mathbb R$ that always take rationals to rationals? Are they all quotients of polynomials? If not, are there any that are bounded yet don't tend to a limit for $x\to +\infty$? If there are, then can we also require them to be analytic?  (This is basically just a random musing after I found myself using trigonometric functions twice in unrelated throwaway counterexamples. It struck me that it was kind of conceptual overkill to whip out a transcendental function for the purpose I needed: basically that it had to keep wiggling forever. I couldn't think of a nice non-trancendental function to do this job, however, and now wonder whether that is because they can't exist). Since  from other SE sites and is not thought to point out a lack of quality or helpfulness, but only to express agreement or disagreement, I'm wondering why downvoted answers here on meta are shown semi-transparent.  Shouldn't they be non-transparent then (like upvoted answers)?  Or am I missing something? How do you mock a Sealed class? can be quite a pain.  I currently favor an  to handle this, but something about just keeps feels weird.    So, What is the best way you mock sealed classes?  Java answers are more than welcome.  In fact, I would anticipate that the Java community has been dealing with this longer and has a great deal to offer.  But here are some of the .NET opinions: Distribution of the ratio of two i.i.d standard normals I am reading an article in which the author states that given two i.i.d random variables $X,Y\sim\mathcal{N}(0,1)$, we have $\mathbb{P}(\frac{X}{Y}\le t)=\mathbb{P}(\frac{X}{|Y|}\le t)$ since the random varaibles $\frac{X}{Y}$ and $\frac{X}{|Y|}$ are identically distributed by the symmetry of the standard normal distribution.  But I don't really understand why the random variables $\frac{X}{Y}$ and $\frac{X}{|Y|}$ are identically distributed. Can you provide a reason for why these two random variables are identically distributed? How do I get my Broadcom BCM4313 working correctly? Last night I was grilling chicken thighs on a barbecue and I was told that if there was any pink inside them, they are not safe to eat. My question is twofold:  (a) Is this true?  (b) Is there a way to tell that doesn't involve cutting the thighs open to have a look at the colour? Isometries of the sphere $\mathbb{S}^{n}$ I have latitude and longitude as 19.0649070739746 and 73.1308670043945 respectively.   In this case both coordinates are 13 decimal places long, but sometimes I also get coordinates which are 6 decimal places long.   Do fewer decimal points affect accuracy, and what does every digit after the decimal place signify? In addition to the .tex and .dvi or .pdf files, TeX/LaTeX/ConTeXt produces and uses lots of other files. What do they do? Which ones are used to create the document and which ones are automatically created by the compiler. What files can I safely delete? Constants of integration in integration by parts How to reformulate differential equation problem as OrnsteinUhlenbeckProcess An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$ Someone recently asked me why a negative $\times$ a negative is positive, and why a negative $\times$ a positive is negative, etc.  I went ahead and gave them a proof by contradiction like so:  Assume $(-x) \cdot (-y) = -xy$  Then divide both sides by $(-x)$ and you get $(-y) = y$  Since we have a contradiction, then our first assumption must be incorrect.  I'm guessing I did something wrong here. Since the conclusion of $(-x) \cdot (-y) = (xy)$ is hard to derive from what I wrote.  Is there a better way to explain this?  Is my proof incorrect?  Also, what would be an intuitive way to explain the negation concept, if there is one? I am stuck with the following problem.     Prove that $$\limsup_{n \to \infty} (a_n+b_n) \le \limsup_{n \to \infty} a_n + \limsup_{n \to \infty} b_n$$   I was thinking of using the triangle inequality saying $$|a_n + b_n| \le |a_n| + |b_n|$$ but the problem is not about absolute values of the sequence.  Intuitively it's clear that this is true because $a_n$ and $b_n$ can "reduce each others magnitude" if they have opposite signs, but I cannot express that algebraically...  Can someone help me out ? Electromagnetic wave properties of light vs radio waves How long does it take for police 'presence' to clear when they are alerted? I engaged with some enemy NPCs, and accidentally shot a civilian in the head (though not sure it would've mattered if I hit them somewhere else or not) as they ran across my screen. As a result of this, I was alerted by the game that the NCPD (the police) were automatically en route to 'investigate', and that I could avoid them by leaving the area and &quot;lying low for a while&quot;. How long does it take for the police to stop searching for me, and is there any kind of visual information on the HUD that alerts me to when NCPD is or is no longer looking for me? A comparison between Grade, Mark, Score and Point Let's suppose a teacher wants to punish a student and wants to decrease his / her achieved points on a test paper; he would say something to the student; I would like to know which one of the following self-made examples may work here:        I have to take two marks of you.   I have to take two grades of you.   I have to take two scores of you.   I have to take two points of you.      For me all the first three mean the same and though the last one is not the same, but works here either. I need to get your feedback. How can I force a long string without any blank to be wrapped? We have an instance of SQL Server 2008 installed on a customer server. The customer's IT department is in charge of the various backups of the machine.  The SQL Server log shows there is a full backup every day at 7 PM but we can't find evidence of any plan scheduled in SQL Server.  The technicians we contacted couldn't tell us if there was some sort of automatic backup, all they told is that the entire machine is being backup up.  Using a script I found in  I found out that the physical device name is a GUID and that this means that this is an external backup process:  USE [msdb] GO  SELECT      [bs].[database_name],      [bs].[backup_start_date],      [bs].[backup_finish_date],      [bs].Server_name,     [bs].user_name AS [BackupCreator] ,     [bmf].physical_device_name FROM msdb..backupset bs   INNER JOIN msdb..backupmediafamily bmf ON [bs].[media_set_id] = [bmf].[media_set_id]  ORDER BY [bs].[backup_start_date] DESC   This is a row from the above query:     db_name 2015-09-16 19:01:23.000   2015-09-16 19:01:28.000SERVER_NAME  NT AUTHORITY\SYSTEM{424F084A-F35D-4A66-8FC7-072268A89A77} 5   Moreover the backup start and finish date spans only for 5 seconds, so I guess it's clear it's not a job of sql server.  This is a line from the log:     2015-09-03 19:02:30.71 Backup   Database backed up.   Database: db_name, creation date(time): 2012/10/12(20:52:11), pages dumped: 3290021,   first LSN: 276028:152755:172, last LSN: 276028:152827:1, number of dump devices: 1,   device information:   (FILE=1, TYPE=VIRTUAL_DEVICE: {'{95380B0A-D50B-408F-B95F-1AB8975BA7F8}5'}).   This is an informational message only. No user action is required.   So, since they can't help us what can I do to track down the process responsible of the backups? We need this because we want to coordinate the backup in an ordered manner, and do the transaction log backups too in order to keep the log at a reasonable size (now we do shrink the log every week, and this is not the good way to go). Interaction with the site on the app should count towards Enthusiast/Fanatic If I do any of the below, which would normally constitute "activity" on any Stack Exchange site (including mobile):   View my profile Vote on any question or comment Visit one or more questions   ...then Stack Exchange considers me to have "visited" the site.  If I do any of the below on the mobile app:   Vote on any question or comment Visit one or more questions   ...then Stack Exchange does not consider me to have visited the site.  If one wants the app to have feature parity with the mobile site, then shouldn't my participation within the app also count towards the Enthusiast/Fanatic badge?