I am struggling to understand what frame of reference means in relativity. Imagine the twin scenario. Twin A is at rest, while twin B travels somewhere and back at near the speed of light. If one takes as a frame of reference the one where twin A is at rest, then time goes slowly for Twin B, thus making it so that when B returns, A is older.  Now I get really confused, if I take twin B's rest frame as the frame of reference, then he was stationary all the time, and A was moving at close to the speed of light, thus B will be older than A. What am I getting wrong here?
I read a lot about the classical twin paradox recently. What confuses me is that some authors claim that it can be resolved within , others say that you need . Now, what is true (and why)?
I am getting several new computers for my office.  I want to install Microsoft Office and my proprietary software and all updates on a single PC and create a system image that will be copied to every other PC.  How do I deal with Windows/Office product keys to prevent licence violations?  Am I able to do this from the System Image tool in Windows 7?  Note:  The PCs will very likely not be joined to my domain at this point if that makes a difference. What does "very approximate" mean? An approximate answer is one which is close to the correct answer.  Likewise, we can talk of an approximate model, or approximate methods in mathematics.  The etymology is from the Latin ad, "to" and proximus, "closest", see e.g. .  I don't think this can be disputed.  Occasionally proximate is used as a synonym, though that word has a different meaning in legal English.  So if an approximate answer is close, a very approximate answer should be very close.  In practice, "very approximate" or "very approximately" is overwhelmingly used with the opposite meaning of "roughly", indicating that an answer or estimate is not necessarily accurate.  For examples,   Is there any justification for this use? Is there any justification for my suggested use?  Should we avoid the phrase altogether? Quote unquote (or end-quote), unseparated by the actual quotation In spoken English, people often say "quote-unquote" (or "quote-endquote") to indicate that part of what they are saying is a quotation (scare or otherwise). Sometimes the quoted material will go between quote and unquote, and occasionaly it will precede the quote-unquote. Often, though, "quote unquote" introduces the quoted material.  Why does quote unquote precede the quotation?  It would seem that quote opens the quoted text and that unquote closes it, but then why would we close the quotation before actually providing it. It would be the equivalent of writing your quotation marks together, "", rather than around the quoted text.  What are the origins of this construction?  Three years ago ChrisR asked  on whether it is correct to use quote, unquote. The answers did not deal with origins, but one commenter suggested that quote-unquote is a corruption of quote-on-quote, but he provided no evidence, nor any real explanation. Solve $y'-\int_0^xy(t)dt=2$ I have not idea how to approach this differential equation.   $$y'-\int_0^xy(t)dt=2$$.  Basically, I did,  $$F''(t)-F(x)+F(0)=2 \;\;\;\;\;\;\; F'=y$$  I am stuck.  Thank You. When should I use a struct rather than a class in C#? How to carry cologne bottles in hand luggage and prevent losses? GTA V for PC exited unexpectedly I recently ordered the GTA V PC from Steam and when I finished installing and launch the game. It gave me "Grand Theft Auto V has exited unexpectedly". I tried "safe mod" and every option available, but none of them work. I checked some forums and found a lot of people having the same problems. What could be the possible cause? I'm using a laptop with these specs:  CPU: i7 4700m GPU: AMD HD8970M RAM: 8GB  I'm pretty sure my laptop is way beyond the minimum specs. Does someone know how can I enter the game? How can I log into a different Google account? It only shows one of my Google accounts. I want to log into a different one but I don't want them connected in any way. What do I do? List of lists changes reflected across sublists unexpectedly I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it? I read news on the BBC (on its website) this morning. When I was reading the news I noticed the definite article the was missing in a sentence. As per my opinion, the reporter missed the article the. But I also thought that the reporter also had some point as he did not use the article there. So I just wanted to confirm so landed here to get some help on it.     On the website:      It also proclaimed the group's leader, XYZ  (name), as caliph and   "leader for Muslims everywhere".      As per my opinion it should have been:      It also proclaimed the group's leader, XYZ  (name), as the caliph and   "leader for Muslims everywhere".   Source link: I have read the Rules of a competition. The text of the Rules include a sentence as follows:     As per stated in the Rules the entrants will be notified by May 30th 2010.   Does the sentence above mean that May 30th is included in the term of notification or not? sudo error, is mode 0777, should be 0440 Why do the :before and :after pseudo-elements require a 'content' property? I'm looking for the title of an anthology of children's science fiction stories from the 1950s. The best of the bunch involved a Martian who visited earth, and realized we'd blown ourselves up in a nuclear war and had fallen into savagery. The Martian is a vegetarian who subsists on biscuits made by a machine he brought with him, and communicates by using one of his tentacles to feed messages direction to/from the brain of the person he's talking to.  Inadvertently left behind by his expedition, he initially befriended some children, and eventually managed to rebuild civilization. Presently he dies, but when another expedition comes a generation later, they find the civilization he rebuilt.  there were other stories, but that was the best one.   If I can't find the name of the book it was in, I'd be happy to settle for the name of the author and the title of the story. Question. Let $M = \left\{ \begin{bmatrix} a &amp; b \\ -b &amp; a \end{bmatrix} \,\middle\vert\,  a, b \in \mathbb R \right\}$.  Show that $(M,+)$ and $(\mathbb C,+)$ are isomorphic.  Show that $(M^{*},*)$ and $(\mathbb C^{*},*)$ are isomorphic.    (Here, $M^{*}$ is defined as excluding the zero-element) I understand that there exists an isomorphism $\phi:M \rightarrow\mathbb C$ defined by $\begin{bmatrix} \alpha &amp; \beta \\ -\beta &amp; \alpha \end{bmatrix}\mapsto \alpha+i\beta$, ie. I can show that $\phi(M_{1}+M_{2}) = \phi(M_{1})+\phi(M_{2})$ and $\phi(M_{1}*M_{2}) = \phi(M_{1})*\phi(M_{2})$. However, I'm unsure how to go about the two subquestions seperately. How do I install different (upgrade or downgrade) PHP version in still supported Ubuntu release? I have two tensors that i must calculate double dot product. matrix A is rank 2  and matrix B is rank 4. I want to multiply them with Matlab and I know in Matlab it becomes: A : B = trace (A*B) but it has one error and it says: Inner matrix dimensions must agree So how can I solve this problem? anybody help me? Thanks Stack Exchange blog is showing me the mobile site and won't let me exit on Chrome 21. Could someone take a look? Thanks. Edit I noticed it was with the special query string, that I can't exit it. For a Google account, you are allowed to sync Contacts and People details. What is the difference between these two? I've been informed by those who know much more about Harry Potter than I that Hogwarts is protected with a Disillusionment Charm so all muggles will see is ruins with a "Danger: Keep out!" sign around them.  (Apparently this was in one of the first three books, but I'm not sure where it was.)  My first thought was, "Well, a danger sign would encourage some muggles to investigate!"  Which leads to what I think is an obvious question: Will a disillusionment charm on a place like that still work when a person is real close to the location?  Will it work from inside the location?  For example, if a curious muggle made it to the gates of Hogwarts and started walking around inside, would they still see it as abandon and in ruins, or once they entered, would they see it as it is?