When we perform a double slit experiment we receive interference pattern. when we measure in a specific slit the exact location of the photon (or electron) the interference pattern disappears and we receive only 2 light spots with no interference pattern.  Now let's assume that we perform the double slit experiment on two entangled photon (or electrons) far away from each other (Alice &amp; Bob).  If Alice measures the location of the photon in the slits, she doesn't receive interference pattern, but because of entanglement the location of Bob's photon is now known and he also doesn't get an interference pattern. This way he knows instantaneously that Alice performed a measurement even when she is far away.  If she doesn't measure the location of the photon in the slits, they will both receive interference pattern and Bob will know instantaneously that she didn't measure the photons location.  This ideas based on the EPR famous paper enables faster than light communication. What did I miss here?
I understand that faster-than-light communication is impossible when making single measurements, because the outcome of each measurement is random. However, shouldn't measurement on one side collapse the wave function on the other side, such that interference effects would disappear? Making measurements on "bunches" of entangled particles would thus allow FTL communication, by making observed interference effects appear or disappear. How does such an experiment not:  1) Clearly imply that faster-than-light communication is possible?  or  2) (if #1 is rejected) Imply that measurement of one half of an entangled pair does not cause the collapse of the other half's wave function.  Why doesn't this thought experiment clearly show that if we maintain that FTL communication is ruled out, we must also rule out "universal collapse" in the Copenhagen interpretation?  EDIT: Here is an example of an explicit experiment (though I think experts could come up with something better):  You can entangle a photon with an electron such that the angle of the photon is correlated with the electron's position at each slit of a double slit experiment. If the photon is detected (it's outgoing angle measured), then which-path information is known, and there is no interference. If the photon is not detected, the interference remains.   The experiment is designed such that the photon and electron go in roughly opposite directions, apart from the tiny deflection which gives which-path information. You set up a series of photon detectors 100 ly away on one side, and your double slit experiment 100 ly away in the opposite direction. Now you produce the entangled pairs in bunches, say of 100 entangled pairs, each coming every millisecond, with a muon coming between each bunch to serve as a separator.   Then the idea is that someone at the photon detector side can send information to someone watching the double-slit experiment, by selectively detecting all of the photons in some bunches, but not in others. If all of the photons are detected for one bunch, then the corresponding electron bunch 200 ly away should show no interference effects. If all of the photons are not detected for one bunch, then the corresponding electron bunch 200 ly away would show the usual double-slit interference effects (say on a phosphorus screen). (Note that this does not require combining information from the photon-detector-side with the electron-double-slit side in order to get the interference effects. The interference effects would visibly show up as the electron blips populate the phosphorus screen, as is usual in a double-slit experiment when which-path information is not measured.)  In such a way the person at the photon detectors can send '1's and '0's depending on whether they measure the photons in a given bunch. Suppose they send 'SOS' in Morse code. This requires 9 bunches, and so this will take 900 milliseconds, which is less than 200 years. The point is that such an experiment would only work if you assume that the measurement of the photon really does collapse the wave function nonlocally.
How to get hardware specs of Android device? How can I find information on the hardware of my Android device like processor architecture, RAM, etc? After the training phase, is it better to run neural networks on a GPU or CPU? My understanding is that GPUs are more efficient for running neural nets, but someone recently suggested to me that GPUs are only needed for the training phase. Once trained, it's actually more efficient to run them on CPUs.  Is this true? How do I efficiently iterate over each entry in a Java Map? If I have an object implementing the Map interface in Java and I wish to iterate over every pair contained within it,  what is the most efficient way of going through the map?  Will the ordering of elements depend on the specific map implementation that I have for the interface? How do I tell Maven to use the latest version of a dependency? Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$ Evaluate the summation of: $$ \sum_{k=1}^n {n \choose k-1} {n \choose k} $$ I have been trying to solve this problem by translating C(n, k-1) into C(n, k), because I know that: $$ \sum_{k=1}^n {n \choose k}^2={2n \choose n} $$ However, I haven't been having any luck. Am I on the right track? What am I doing wrong? Biblatex: submitting to a journal How to select top 10 records from each category The adverb "quite" has the following meanings :     1: wholly, completely ("not quite   finished")      2: to an extreme : positively "quite   sure" —often used as an intensifier   with a "quite a swell guy" "quite a   beauty"      3: to a considerable extent : rather   ("quite near")   My understanding is that #1 and #2 conflict with #3. For example, when you say "She's quite right", do you mean "She's completely right" or "To a considerable extent, she's right"? Notice that in the latter case you're not saying that she is completely right.  Another example is "I'm quite sure". Does it necessarily mean "I'm completely sure"?   Does the word really have conflicting meanings that can possibly cause ambiguity? Or am I missing something? A story about a male protagonist with special eyes that tells him if things are safe or not; green = safe. Can’t remember if it’s a manga or webtoon. It starts with a male protagonist who was dying on a battlefield, the goddess took pity on him, sent his emotions back into his younger self, (not memories). He had eyes that told him what is safe/good and what is dangerous/bad by using colors: green, orange, red. He used this to gamble, his eyes stopped working, borrowed money from his ex-girlfriend (who works in a cafe). Money got stolen while he took a nap by a river, the evil lady who stole his money tried to get him to enter a contract. From his future emotions, he knew he wanted an invitation instead. This leads to a gathering of people in a school gym, their tasks are given. Invited people are given bags with tools. An oni busted out under the floor. People get killed. Stairways with gates, etc. This is considered the tutorial. Points are given after, those points are needed to buy daily necessities. The protagonist had the highest points, given VIP room. Etc. Not every open set in $\mathbb{R}^n$, for $n\geq2$, is a disjoint union of countable open balls. I know that every open set in $\mathbb{R}$ can be decomposed as the union of countably many disjoint open intervals and I'm trying to show that this property no longer holds in higher dimensions. For this I'm trying to show that there is no countable, pairwise disjoint open balls whose union is the open square $(0, 1)^2 ⊂ \mathbb{R}^2$. I know that it is because of the corners, but I don't know how to write this in mathematical terms. Thanks for any help. Use of "though" versus "however" Consider the sentence      E-books are on the rise, but they haven't suppressed paper books though.    This usage seems to be quite common, but when I learned English  I was taught to use "however" where I now read "though". My questions on this use of "though" are:     Is this a new trend? Is it restricted to American English? Is "though"  considered more colloquial than "however" ?    And on a syntactic level: Do you put a comma before "though"? CSS Selector that applies to elements with two classes How long will foods that have "Best by: XX-XX-XX" on the product last past that date?  I have tried looking online, and all I can find is anecdotal evidence, which isn't very assuring for me since there seems to be no specific "x food will expire y weeks after its best by date".  Is there a rule of thumb or some guide out there that can tell me how long a "best by" food will last? Or is it safe to assume that they never expire, since it's not actually labelled on the product? I am writing a WP plugin. I have created a button for the user to click in thw WP dashboard. I need to run a function when a user clicks the button, shown with a red arrow. The code snippet for the button is:&lt;p&gt;&lt;button class="button button-primary"&gt;Update Media Titles and ALT Text&lt;/button&gt;&lt;/p&gt;. I have already created the function in my class like so:  public function kh_update_media_seo() {      //update media files title and alt tags here }   I can handle the code that goes in the function alone, I only need help making the button in the WP dashboard fire off this specific function when clicked.  Pardon me if this sounds dump or straight forward. It's my first time doing this.  My plugin is a one file plugin if that helps. Not only in ortho: top, front, back.  Please don't link this answer   I want a background image like this guy has -> How to combine measurement error with statistic error In point-set topology, one always learns about the : the topology on an infinite product $X = \prod_{i \in I} X_i$ generated by sets of the form $U = \prod_{i \in I} U_i$, where $U_i \subset X_i$ is open.  This seems naively like a "good" topology to use for $X$.  However, one quickly learns that this is not so; that the  is the natural one.  The box topology has many strange properties that make it a good source for counterexamples, but I am not aware of it having any other applications.  So I would like to know:     Are there examples of using the box topology to prove interesting "positive" statements?   Edit: And to pursue a comment of Jim Conant:     Are there "non-artificial" problems where the box topology arises naturally?   Edit: The title is perhaps too flippant.  I don't mean to minimize the obvious significance of the box topology as a counterexample.  However, for the purposes of this question I am interested in positive results.  I'm not looking to be convinced that counterexamples are useful; I know that they are. Looking for a 1000 most frequent english words Is there a free list of 1000 most frequent words used in everyday English? If there is a list with usage examples (as each of those words has multiple meanings for sure, not to cound phrasal verbs), it would be even greater.  Is there something alike, but with phrases? (E.g. 1000 most frequent phrases) Finding the ID of a process and killing it When ever I need to kill a background process I do ps -e | grep &lt;process_name&gt;  Which prints something like this 1766 ? 00:00:13 conky , Then I use the process ID to kill it like so kill 1766 .   Is there any way I can simplify this ? Make it quicker ? reduce the amount of typing ? How to stop creating .DS_Store on Mac?