Hawking radiation is explained by particle-antiparticle creation. A particle with positive energy escapes away from the black hole while the particle with negative energy falls down.  Why isn't that vice versa? A particle with positive mass should fall down due to gravity force, while the negative mass is to be repeled by the gravity force?  Edit: I think was wrong about the gravity repeling the negative mass. Even though the force is directed away from the black hole, a=F/m so the particle still falls down the black hole! Now I see no point why any particles should be escaping more than the other?
I was reading Brian Greene's "Hidden Reality" and came to the part about Hawking Radiation. Quantum jitters that occur near the event horizon of a black hole, which create both positive-energy particles and negative-energy particles, produce the so-called Hawking radiation. However, I do not understand why only the negative-energy particles are being absorbed into the black hole, while the positive-energy particles shoot outward. Shouldn't there be 50/50 chance that each type of particle is being absorbed by the black hole? Also, the book mentions that a negative-energy particle would appear to an observer inside the black hole as positive. Why?
Algebraic Property inherited by a "lift"? Suppose $K$ is a field, and $K\subset E$ is an algebraic extension, and $K\subset F$ is any extension.  Suppose that $L$ is some field which contains both $F$ and $E$ as subfields.  I want to show that $FE$ (the smallest subfield of $L$ containing both $F$ and $E$) is algebraic over $F$.  Lang mentions that the result is true because an element remains algebraic under lifting, but I can't prove the claim with this.  I interpret his comment to mean that if $x\in E$ is algebraic over $K$, then $x\in FE$ is algebraic over $F$.  This is certainly true.    But this doesn't seem enough if I start with any element of $FE$. Why do we multiply the magnetic flux by the winding number? To prove that $(\mathbb{P(N)},d)$ is a metric space To prove that $(\mathbb{P(N)},d)$ is a metric space where $\mathbb{P(N)}$ is the power set of $\mathbb{N}$.  And $d:\mathbb{P(N)}\times \mathbb{P(N)} \mapsto\mathbb{R}$ is defined by $d(A,B)=\begin{cases} 0, &amp; \text{if A} \Delta \text{B=}\emptyset  \\ m^{-1}, &amp; \text{where m is the smallest member of} A\Delta B \end{cases} $.   Attempt: $x \in P\Delta Q=(P-Q)\cup(Q-P) \implies x\in (P-Q) \text{ or } x\in (Q-P) $. But $(P-Q)\cap(Q-P)= \emptyset \implies x \in P \text{ and} \notin Q \text{ or }x \in Q \text{ and} \notin P. \ \ \ $    (*)  To prove the triangle inequality:  Take any three sets $A,B,C \subset \mathbb{P(N)}$ such that none of them are equal to another. Now,  $\min A \Delta B  =m_1, \min B \Delta C  =m_2,  \min A \Delta C  =m_3   $. To prove $d(A,B) \leq d(A,C)+ d(B,C)$. By (*), $m_1 \in A$ or $m_1 \in B$ but not both.   Again,  $m_2 \leq m_1$  or $m_3 \leq m_1$. Either way, we are done. When $A \neq B$ and either $B =C $ or $A=C$ (not both), we have respectively $A=C$ , $B=C$ . Which satisfies the triangle inequality. When $A=B$ it is evident.   Symmetry: We know $A \Delta B =B \Delta A$. $d(A,B)= d(B,A)$  Non-negativity and $0 \iff A=B$:   $d(A,B)=0 \iff A \Delta B= \emptyset \iff A \subset B \text{ and } B \subset A \iff A=B$. By definition $d(A,B) \geq 0$  Is this okay? Please verify. Can Resharper be set to warn if IDisposable not handled correctly? Is there a setting in Resharper 4 (or even Visual Studio itself...) that forces a warning if I forget to wrap code in a using block, or ommit the proper Dispose call in a finally block? Why doesn't the height of a container element increase if it contains floated elements? Conditional sentences not starting with "if" Were I rich, I would live on Long Island.   If I were rich, I would live on Long Island.   Is the first sentence still used, or is used in particular contexts (in example, to give emphasis to the sentence)? In the United States we have a saying, "your mileage may vary", which means "your experience may be different".  In English-speaking countries that don't use Imperial miles, is there an equivalent expression? Submitting a URL to Google using PHP/cUrl I don't know much more about SEO, but it's interesting to learn about it. When I tried to search my website with an associated keyword or you can say with the exact name of the domain, I got some suggestions by Google. Here's .  First of all, I don't want to spamming here, I just want prove my question and want to give a hint about what I am talking here. The above link display the Did You Mean, I know the specific reason why Google shows this, but I want to know the Google's guidelines and some guidance by you experts so that if someone search for the particular keyword then Google hide that Did You Mean and display the result. When casting a spell as a bonus action, you can't cast another spell on the same turn except a 1-action cantrip - can the order be "reversed"? Can you cast a cantrip first as a bonus action, then any other spell? If not, would it be broken to allow it?  I'm thinking a Sorcerer casting a Quickened true strike, then casting a leveled spell requiring a touch attack. Seems like a great use of the cantrip + Metamagic feature, but it seems like it is not allowed. Can Muggles publicly establish the existence of a magical community? I have added the png transparent image with the setting and its not showing transparent black background is seen. I have the base color aluminum and i want to add that logo of png on to it. The image is black letter with transparent background why its showing in white letters and black background. May i know where im going wrong any suggestion or help. I've seen lately that new question editing is stored somewhere for later use if we wander off the new question without posting it and then return back to the page. Which is a good functionality addition in it's own right.  What I'd like to also have is the Discard this draft functionality that would clear form data and forget it. Somehow we find an answer in the meantime and the question isn't valid any more.  So having a Discard saved draft or something similar would be a nice contra-functionality to auto-save to remove stored data. The way it's implemented now seems too hidden hidden and unpredictable to users.  Additional edit  When adding hidden auto functionality usually means creating the opposite as well by either giving the possibility to preference of not having automatism at all or giving the possibility to clear what's been auto saved.  Let's see how GMail doesn't work (and I think we all agree that from UX perspective it does the job as expected:   User clicks Compose message User starts writing a new email message User decides to not send the message and checks their inbox User clicks Compose message again A clean form is presented to user (old one being part of drafts)   I'm not suggesting we should have something like Saved drafts but we surely should have the possibility to clear previous question draft.  Since this new functionality was introduced I should point out that I would use the discard functionality more frequently than the saved one. I do welcome saving messages, but discarding of saved drafts is anything but a rare situation one might want to do. It wouldn't be a problem if this was a 1% against 99%. To me it's more like 50/50.  Best possible solution  When providing saved drafts there should (from the UX perspective) be the opposite functionality as well. Namely discarding of it. But first thing we should be asking ourselves is:    do users more frequently need pre-filled saved question draft or do users more frequently need empty form with the possibility to populate it with a saved draft   User testing should provide the usage frequency between the two and the one that's more likely to happen (my guess is that there would be a big difference between the two) should be implemented. So one of these:   Pre-populate question fields with saved draft on question form load, while also providing a button to clear the draft and start writing anew without the need to manually clear all the fields (which would be the optimal solution in case of a single field form) Question form should always load empty while also having a button that would pre-populate it with a saved draft.   I think this would be the best consensus related to saved question drafts and their usage. But as we've seen this issue has been swept under the rug for an indefinite time. Creating Users on secondary server in log shipping I have a production Server say ServerA I have setup log shipping to ServerB which is left in read-only mode. The purpose of this log shipping is to lower the load on production server for some expensive queries (painful reports).   Now if I have to create some logins using our domain accounts. I cannot do this because the secondary database is in standby mode.   I thought if I create these logins on Primary server it will be copied over to secondary server then the logs are restored there but this isnt the case.   I have done a lot of research online finding a way around to this. I found the following resources for this. I tried every method suggested in this articles but none of them seems to work.   1)   2)   3)   Has someone experienced the same issue? what did you do? Is there any way around for this issue? Any suggestions any pointer please. Joined pipelines Considering a routine such as this one:  alpha() { echo a b c |tr ' ' '\n'; }   which outputs a stream, I would like to take the output stream, transform it, and paste it with the original output stream.  If I take use upcasing as a sample transformation, I can achieve what I want with:  $ mkfifo p1 p2 $ alpha | tee p1 &gt;( tr a-z A-Z &gt; p2) &gt;/dev/null &amp; $ paste p1 p2 a       A b       B c       C   My question is, is there a better way to do this, preferably one not involving named pipes? I can run faster than _____. (1) him (2) he? Consider the sentence &quot;I can run faster than 15 miles per hour.&quot; Its meaning is clear and to my eyes obviously grammatically correct. Now let me present some variations that have given me trouble for a long time.  I am faster than 15 miles per hour. – To me this is clearly incorrect. Directly comparing me to a speed doesn't seem right. We need to compare my speed to a speed, or me to another person.  I can run faster than him. – Compared to the base sentence, there is a distinct shift in meaning of the comparison. While before I named a speed faster than which I can run, now I am naming a person. It doesn't seem quite right. I realize the parts of speech can change, but my initial objection is that &quot;him&quot; is not a speed.  I can run faster than he. – This seems most correct to me, but still somehow feels objectionable. Is this in fact the correct way to say it? And if so, is it proper as is or need I say &quot;... faster than he can&quot; or even &quot;... faster than he can run?&quot;  I am faster than him. – With &quot;am&quot; instead of &quot;can run&quot; it now seems slightly more correct. But is it?  I am faster than he. – I'm in doubt here. It doesn't seem wrong to me to say, &quot;I am faster than he is&quot; or even &quot;I am faster than he is fast.&quot; (Though I suppose that is a given since I could hardly properly compare to some other category as in &quot;I am faster than he is smart.&quot;)  My speed is faster than his. – Hmm. This seems more proper as &quot;my speed is greater than his.&quot;   So which of these constructions is correct and which is incorrect? Is there a general rule that I can follow? UPDATE The scholarly article  may be of great interest to some readers!  Once we accept that the elided constituent and its antecedent can differ in form, it becomes reasonable to ask how large this difference can be. The answer in Rooth (1992), Fiengo and May (1994), Chung et al. (1995) and subsequent work is that the wiggle room is actually quite small: the elided constituent and its antecedent are allowed to differ only in the realization of inﬂectional morphology. Other than that, both constituents have to be syntactically and lexically isomorphic. How to prove this statement: $\binom{r}{r}+\binom{r+1}{r}+\cdots+\binom{n}{r}=\binom{n+1}{r+1}$ Let $n$ and $r$ be positive integers with $n \ge r$. Prove that   Still a beginner here. Need to learn formatting.  I am guessing by induction? Not sure what or how to go forward with this.  Need help with the proof. Browning Avocados - What Helps? Years ago  asked "Oxidized Avocado: What's Going on &amp; How to Prevent It?" That question has been merged with this one because it's dealing with the same issue.  Recently, we had this question: . Now I'm just curious, I want an answer.  After Logophobe's answer to the acidity question, and my own research backing up that answer, I feel like I know less than I did before!  Lemon contains more ascorbic acid (Vitamin C) and citric acid than limes, yet limes are more acidic overall. Distilled vinegar is more acidic than lemons and almost as acidic as limes,  is an extremely highly concentrated mixture of ascorbic acid and citric acid specifically developed to prevent browning in fruits.  So what works to keep avocados pretty and green?  Perhaps some experimentation is in order. I think I'll start with acids, since the common wisdom is that acid helps keep avocados green.  EDIT As of 1/8/15, I have added a new answer, as the highly upvoted one really only says what doesn't help. The accepted answer  shows the results of further experimentation, and what does help. Lost reputation after answering my own question with bounty Timeline:  Asked a question, no (interesting) answers for two weeks  Set bounty on it this morning  Found the answer to my question two hours later. Answered my own question.  Bounty reputation is lost. It was not awarded to me, it was not returned to me (the 100 I invested).   Right now, I feel really stupid for answering my own bounty question.   If this is accepted behavior, then user should be warned - you are answering your own bounty question, your bounty reputation will be LOST. Do you know any open source tool to automatically align images, similar to the auto align feature in Photoshop?