Let $O$ and $\overline{O}$ be inertial frames, $A$ and $B$ be events, the interval between $A$ and $B$ be $(\Delta t, \Delta x, \Delta y, \Delta z)$ in $O$ and $(\overline{\Delta t}, \overline{\Delta x}, \overline{\Delta y}, \overline{\Delta z)}$ in $\overline{O}$.  Is the linearity of the correspondence between $(\Delta t, \Delta x, \Delta y, \Delta z)$ and $(\overline{\Delta t}, \overline{\Delta x}, \overline{\Delta y}, \overline{\Delta z)}$ a postulate in the special relativity theory?
In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity:  Prove that any spacetime transformation $\left(y^0,y^1,y^2,y^3\right)\leftrightarrow \left(x^0,x^1,x^2,x^3\right)$ that preserves intervals, that is, such that  $$\left(dy^0\right)^2-\left(dy^1\right)^2-\left(dy^2\right)^2-\left(dy^3\right)^2=\left(dx^0\right)^2-\left(dx^1\right)^2-\left(dx^2\right)^2-\left(dx^3\right)^2$$  is linear (assuming that the origins of both coordinates coincide). That is, show that $\frac{\partial y^i}{\partial x^j}=L_j^i$ is constant throughout spacetime (that is, show that $\frac{\partial L_j^i}{\partial x^k}=0$).  Thus far all I've been able to prove is that $g_{ij}L_p^iL_q^j=g_{pq}$ (where $g_{ij}$ is the metric tensor of special relativity) and that $\frac{\partial L_j^i}{\partial x^k}=\frac{\partial L_k^i}{\partial x^j}$. Any further ideas?
Is ¬¬(¬¬P → P) provable in intuitionistic logic? Do any (non-hardware) RNGs exist which could be used to create an OTP for crypto purposes? Does Two-Face die at the end of The Dark Knight? If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$ Did not find this from this website...  If $$ \gcd(a,b)=1,$$ then there exists integers $x$ and $y$ such that $$xa+yb=1.$$  Now, the tip is to use particular corollary, that states:  The class $[m]_{n}$ generates $\mathbb{Z}/n\mathbb{Z}\Leftrightarrow \gcd(m,n)=1.$  I am totally lost with the corollary.  Let's assume that $\gcd(m,n)=1$. Then, $[m]_{n}$ generates $\mathbb{Z}/n\mathbb{Z}$.  OK! Then what?  There is also follow up, where I have to prove the converse. I am familiar with Bezout's lemma. What race (species?) is Star Lord's dad? At the end of the new Guardians of the Galaxy Vol. 2 Trailer we meet Star Lord's father:                                  Dad appears to be human. But Peter Quill's mother said in the first film that his father was a      "being made of pure light".    What race (species?) is Star Lord's father in the MCU? How to back up my entire system? If I want to make a backup of my entire OS (including but not just my home directory), how do I go about this?    Is it as simple as backing up everything in / and then when if I suffer a crash, just copying the files back over? Will this cover grub, and how do I actually do this when the system is inoperable? Change MySQL default character set to UTF-8 in my.cnf? $\require{enclose}\enclose{horizontalstrike}{\rm Greatest}\!$ Least prime factor of $n$ is less than square root of $n$, proof I remember reading this somewhere but I cannot locate the proof. Divergence of $\frac{ \hat {\bf r}}{r^2} \equiv \frac{{\bf r}}{r^3}$, what is the 'paradox'? What is this mark over the question When I open a site I see a mark over a question.See screen shot.  When I open the question mark is not remove.It still appear.    is this bug or? I recently upgraded from Ubuntu 11.10 to 12.04. If it makes any difference, my system is a Dell Inspiron 1520.   I encounter a problem whenever I shutdown or restart; it kills all running processes (as far as I can tell), but once I get past the shutdown text screen and the screen goes black,  my computer doesn't power off. The fans still run and the screen is still on, etc. I have to hold down the power button in order to complety shut down.   Does anyone know how to resolve this problem? When voting to migrate an off-topic question, why is the list of sites limited? Earlier, I voted to close  as off-topic.  The question has since been closed.  There is an , but it didn't show up in the list when I selected "off-topic".  The options were:   Meta Stack Overflow Server Fault Super User Webmasters Programmers   Questions:   Should Wordpress appear in this list? Are there any other sites that should appear in the list?   Should all non-beta sites appear in that list by default? How to open Nautilus at current command line directory? I was wondering if anybody knew a command that would allow me to open a Nautilus (if that's the right name for the Ubuntu graphic/window explorer) window from the command line at the current directory that the user is at.  So, if I open a command line, and type:  cd /home/myUser/some/long/path/to/a/directory   Then, I'd like to be able to issue some command:  nautilus open-sesame   And have a graphic window opened to /home/myUser/some/long/path/to/a/directory. Is this even possible? If there is one noble left in line and you play "fled to England" to discard it (thus, ending the day) do you collect a noble from the new day? Assume that $X$ and $Y$ are two random variables such that $Y=E[X|Y]$ almost surely and $X= E[Y|X]$ almost surely. Prove that $X=Y$ almost surely.   The hint I was given is to evaluate: $$E[X-Y;X&gt;a,Y\leq a] + E[X-Y;X\leq a,Y\leq a]$$  which I can write as: $$\int_A(X-Y)dP +\int_B(X-Y)dP$$ where $A=\{X&gt;a, Y\leq a\}$ and $B=\{X\leq a,Y\leq a\}$.  But I need some more hints. How to prove that $\lim\limits_{x\to\infty} f(x)/x=L$ Let $f\colon(0,\infty)\to\mathbb R$ be differentiable on $(0,\infty)$ and suppose that $\lim\limits_{x\to\infty} f'(x)=L$.         a. Show that for any $h&gt;0$, $\lim\limits_{x\to\infty} \frac{f(x+h)-f(x)}h=L$.      b. Show that $\lim\limits_{x\to\infty} \frac{f(x)} {x} =L$.   this is a differentiation question.  i don't know how to solve this question  Because it is Korean, it is difficult to deal with this cite. So for me, it is not easy to write.  thank you Threshold Secret sharing - How to create a shared secret from pre existing secret parts? In usual $(t, n)$ secret sharing schemes, a secret $S$ is split into $n$ parts so that any $t$ out of $n$ parts reconstruct the original secret. So, suppose that there is a group of $n$ participants each one has a secret $x_i$ ($x_i$ may be its private key). My question is, is it possible to create a secret $S$ using the prexisting secrets $x_i$ ($i=1...n$) so that with any $t$ out of $n$ from these secrets ($x_i$) we can find the secret $S$? I am  with the Google login for Pokemon Go. Is there any way, be it contacting support or through Trainer Club, to either link my Google account to a new Trainer Club account or transfer my account to a Trainer Club account?  It seems like a better idea to have a Trainer Club account, so if there are Google login problems it won't matter.  Does anyone know if something like this is possible? Why does a Ball bounce back if Forces are Equal and Opposite? When a ball is thrown onto a wall, the ball exerts a force onto the wall. According to Newton's Third Law, the wall will exert an equal and opposite force to the ball. Thus, how would the ball be able to bounce back? Shouldn't it just slide down the wall? After reading of:  I wonder if the  also applies to flagging of old questions.  I have the subjective feeling the longer the time between the question and the flagging is, the longer it takes to become reviewed.   Is flagging of old posts a waste of moderator time? Should I avoid that?