If we can predict the quantum leap, won't that render quantum computers useless? Recent news from Yale... We can predict the quantum leap before the particle collapses its superposition. We can even change it to whichever position we like in real time. In layman terms, as I understand with my limited knowledge, Schrodinger's cat can be SAVED.  But... Also to my limited knowledge, the core of how a quantum computer works is because of its superposition feature and its uncertainty.  Then put these two paragraphs together... If the superposition is now old news, so would quantum computers. Right? What am I missing here?
Does the new finding on "reversing a quantum jump mid-flight" rule out any interpretations of QM? new finding by Minev et al. seems to suggest that transitions between atomic states are not instantaneous, but continuous processes wherein a superposition smoothly adjusts from favoring one state to another (if I understand it correctly). The authors also claim to be able to catch a system "mid-jump" and reverse it. Popular articles are  and .  I am curious if this finding rules out any interpretations of QM. It seems to generally go against the Copenhagen attitude, which describes measurements as collapsing physical systems into a definite classical state. The popular articles indeed claim that the founders of QM would have been surprised by the new finding.  The link with the asterisk mentions that something called "quantum trajectories theory" predicts what was observed. Is this an interpretation, or a theory? And are they implying that other interpretations/theories don't work?
Let $T: V \rightarrow V$ be a linear operator.  I need to demonstrate that if all nonzero vectors of $V$ are eigenvectors of $T$, then there is one specific $\lambda \in K$ such that $T(v) = \lambda v$, for all $v \in V$.  I understand that, if all nonzero vectors of $V$ are eigenvectors of $T$, then $T$ must be a scaling transformation. It just stretch or shrinks vectors, but doesn't change their  directions.  So, the statement says that if it happens, then, there is a single $\lambda$ such that $T(v) = \lambda v$. In other words, if there is such transformation, then it scales all vectors by the same scalar $\lambda$.  Applying the transformation to our standard basis vectors, we have: $$ T(e_1) = \lambda_1 e_1 \\ T(e_2) = \lambda_2 e_2 \\ \vdots \\ T(e_n) = \lambda_n e_n $$  I understand I need to prove that $\lambda_1 = \lambda_2 = \dots = \lambda_n$, but I can't see how!  EDIT  $$ v = c_1e_1 + c_2e_2 + \dots + c_ne_n \\ T(v) = \mu v = \lambda_1c_1e_1 + \lambda_2c_2e_2 + \dots + \lambda_nc_ne_n \\ $$  Since what's multiplying $v$ coordinates is $\lambda_i$, then all of them must be $\mu$. I'm not sure how to 'mathematize' this. Is this idea correct?  EDIT 2 Extending the left hand side of EDIT 1, we have: $$ \mu v = \lambda_1c_1e_1 + \dots + \lambda_nc_ne_n \\ \mu(c_1e_1 + \dots + c_ne_n) = \lambda_1c_1e_1 + \dots + \lambda_nc_ne_n \\ \mu c_1e_1 + \dots + \mu c_ne_n = \lambda_1c_1e_1 + \dots + \lambda_nc_ne_n \\ $$  And since $e_i$ are linearly independent, $\mu = \lambda_1 = \lambda_2 = \dots = \lambda_n$. Is this proof correct? I have 4 copies of the Hot Questions widgets.  Sometimes, possibly after they reload on their own, I can only tap to open the last widget I added. If I tap on the question of any others nothing happens.  If I refresh each one then tapping works on the one I refreshed. How to wait in a bash script for several subprocesses spawned from that script to finish and return exit code !=0 when any of the subprocesses ends with code !=0 ?  Simple script:  #!/bin/bash for i in `seq 0 9`; do   doCalculations $i &amp; done wait   The above script will wait for all 10 spawned subprocesses, but it will always give exit status 0 (see help wait). How can I modify this script so it will discover exit statuses of spawned subprocesses and return exit code 1 when any of subprocesses ends with code !=0?  Is there any better solution for that than collecting PIDs of the subprocesses, wait for them in order and sum exit statuses? Is “all women who are mothers of daughters” right? Is the expression      All women who are mothers of daughters are here.   correct? I mean every woman who has at least one daughter is here. How do I delete unwanted Apple ID's? I'm going thru a phone swap, and I now realize that I have multiple ID's   "codename" "codename@example.com" "realname@example.com"   I've tested all three, and they all have different login passwords. Not sure how I got here but I'd like to clean the mess up.  Is there any way to delete / remove / erase unwanted ID's so they don't exist anymore?  (Note: their existence creates total havoc with any type of ID edit...)  I see from  that I can't merge the apple ID's, but can I simply delete the unwanted ID's? I am using BusyBox on a small embedded ARM system.  I'm trying to read the "top" output, in particular for the Python process listed.  How much real memory is this process using?  Also what does VSZ stand for?  The system only has 64MB of RAM.   Mem: 41444K used, 20572K free, 0K shrd, 0K buff, 18728K cached CPU:   3% usr   3% sys   0% nic  92% idle   0% io   0% irq   0% sirq Load average: 0.00 0.04 0.05 1/112 31667   PID  PPID USER     STAT   VSZ %VSZ %CPU COMMAND   777   775 python   S     146m 241%   3% /usr/bin/python -u -- dpdsrv.py What is syntax highlighting and how does it work? I noticed that sometimes my code gets highlighted in different colors when rendered.   What is syntax highlighting? How does it work? Why isn't my code being highlighted correctly? How do I report a bug or request a new language? How do I use syntax highlighting? What languages are currently available on Stack Exchange? As linguistics student, I have to put more than one thing on a character every now and then. For example, I need to type ā̆. I thought I could simply do that by typing \={\u{a}}, but then the macron is placed above an empty space in front of the character.  How can I solve this? Thanks  P.S. I'm using MiKTeX 2.9, running on Windows 8; in case it might be of use. A reflection question about a complex function Suppose John has 5 sweets. Is there any difference between the following two sentences?     Jack has 3 times as many sweets as John.      Jack has 3 times more sweets than John.   I prefer the first construction and would know unambiguously that Jack has 15 sweets in this case. However in the second construction I would be inclined to think that Jack has 20 sweets, since it seems to suggest 15 sweets in addition to the original 5. I'm facing this frustrating "feature" that I can't seem to remedy; when I duplicate an object (and now, even when I create two completely new objects), their transformations/scaling is synchronized. This is extremely annoying when trying to use any sort of transformation keyboard shortcut.  It should be noted by going to the properties menu (N) and manually setting the properties works just fine.  For instance, here is just the camera selected (trust me, I made sure):   And when I try to transform by clicking+dragging on the X axis OR by hitting G->X, this happens:   They are not grouped (verified by going to the Groups list up in the Scene panel) and they do not have parents (verified by going to Object->Relations).  I have tried the unlink command as well, to no avail.  I have seriously run out of options; what did I change to have my G->X shortcuts transform multiple objects? It seems completely at random, too; certain objects seemed to be "linked" to other random objects, and this "linking" is guaranteed when duplicating even when I do a non-linking duplicate (Shift+D).  What gives? I´d like to enable the ssh root access on Ubuntu 14.04. Editing the /etc/ssh_config (PermitRootLogin yes) didn't affect anything. Suppose there is a message that is encrypted with AES-128-CBC.  The message is as follows, new lines are used to delimit the 16 byte boundary for each block:  Wire funds from: Alice to Bob in   the amount of $ 1   Because this message is encrypted using CBC mode,  any modification of the first block of cipher text would propagate throughout the message.   However, the amount of the fund transfer falls in the last block.  I am under the assumption that an attacker can use the property of  to alter the last block and produce a valid amount that is greater than \$1 in far fewer than $2^{128}$ operations.   Is this a correct assumption?  Is there a name for this attack or do you know of a real world example?    My instinct is that if you just need one byte of the 16 byte block to be of a specific value then it would only require $2^8$ operations because the other 120 bits of the plain text could be any value. For example lets say we wanted the last block of cipher text to decrypt to 9\0 (where \0 denotes a single null byte, and the message would be interpreted as \$9), then it would take only $2^{16}$ operations to find this cipher text block.  Is there something I am missing? $G$ is a finite group such that $|G|=n$. Let $p$ be the smallest prime such that $p|n$. If $H\triangleleft G$ such that $|H|=p$, then prove that $H\subset Z(G)$.  My Work:  Since $|H|$ is a prime $H\cong \mathbb{Z}/(p)$. Hence $H$ is cyclic and abelian. I was stuck afterwards. Can anyone please give me a hint? How do I read the manifest file for a webapp running in apache tomcat? How to run Unix shell script from Java code? It is quite simple to run a Unix command from Java.   Runtime.getRuntime().exec(myCommand);   But is it possible to run a Unix shell script from Java code? If yes, would it be a good practice to run a shell script from within Java code? Multiple entry visa to UK (sponsored visitor) Prove that field of complex numbers cannot be equipped with an order relation Please guide me in this problem. I am confused about whether its asking that having the relation $z&gt;0$ does not satisfy the order axioms.  Any help would be really appreciated.  Thanks! Solving $x^3-y^3=xy+61$ in integers I'm trying to solve the following equation:  $$x^3-y^3=xy+61$$  I got:  $$(x-y)(x^2+xy+y^2)=xy+61$$  But I can't go any further. I am looking for a solution in integers.  I need some hints to proceed, please! If I took a picture of a windmill on the horizon — given that I know the sensor size and the focal length of the lens and other factors to do with the shot — could I calculate how far away an object is from the photographer?