The gravity field is determined by the metric $\eta_{\mu \nu}$ we impose on a flat (Minkowskian) spacetime, for which the metric has diagonal elements only: $(1,-1,-1,-1)$. Solving the Einstein equation gives you the space- and time components of the metric if a stress-energy tensor $T_{\mu \nu}$ is present. Time variations in the metric represent gravitational waves. So we can say that the gravity field is a metric field defined on a flat (Minkowskian) spacetime and from this we can calculate what the real (non-Minkowskian) spacetime looks like (if a stress-energy tensor is present). How can we say that locally this curved spacetime is Minkowskian if a Minkowskian metric is only there in Minkowskian spacetime? Isn't it Minkowskian everywhere if it's locally so? Of course, by looking close enough, you can say the curved spacetime looks flat (like a function can be approximated by a linear function for small values of its argument). If curved spacetime looks flat locally, then why will mass move in curved paths?
I imagine a point-like particle can only experience the local properties of spacetime. But locally there is no curvature and no gravity, as it is often stated that     Locally, as expressed in the equivalence principle, spacetime is Minkowskian, and the laws of physics exhibit local Lorentz invariance. ()   But if this is the case how does a point-like particle know, which direction it should follow in a gravitational field?   Can this be a seen as a hint that point-like particles cannot be used as underlying concept for a field theory like general relativity?
Is there a way to make Git mark a file as conflicted? What is the best introductory Bayesian statistics textbook? Which is the best introductory textbook for Bayesian statistics?  One book per answer, please. Add additional sub-groups to the new Badge page & related Feedback On the  (A+), there are sub-groups under the major groups.  For example, the Participation Badges group has related badges Commentator and Pundit sub-grouped, and Quorum and Convention sub-grouped.  I am of the opinion at least 1 of the following additional sub-groupings should be made:  Question Group   Student &amp; Scholar Investor &amp; Altruist Promoter &amp; Benefactor   Alternately, one sub-group of Investor, Altruist, Promoter &amp; Benefactor    Answer Group   Teacher, Enlightened, Guru Consider moving Generalist to Tag Badges Group or the bottom of the Answer Group if Tag Badges is moved immediately below Answer Group.   Participation Group   Talkative &amp; Outspoken Caucus &amp; Constituent Precognitive &amp; Beta   Tag Badges  Move this group to either the bottom of all groups or below the Answer Group. Its current placement here creates a weird artificial barrier, especially with users who have no Tag Badges.  Moderation Group   Informed &amp; Analytical Taxonomist &amp; Synonymizer Critic &amp; Supporter Disciplined &amp; Peer Pressure Suffrage, Vox Populi &amp; Civic Duty   Alternately, one sub-group of Critic, Supporter, Suffrage, Vox Populi &amp; Civic Duty  add Cleanup and Organizer to the Editor sub-group add Citizen Patrol to the Deputy sub-group   NOTE: Since this is now status-completed, but only a select portion was completed, the rest of the request has been broken into 2 additional questions: Why is $2\pi i \neq 0?$ We know that $e^{\pi i} = -1$ because of de Moivre's formula. ($e^{\pi i} = \cos \pi + i\sin \pi = -1).$  Suppose we square both sides and get $e^{2\pi i} = 1$(which you also get from de Moivre's formula), then shouldn't $2\pi i=0$? What am I missing here? Can I visit the USA as a VWP tourist immediately prior to entry on non-tourist visa? Here's my situation: I'm a UK citizen. I have an H-1B visa to work in the US as of 1 August. I also have a valid ESTA.  I would like to go to the US in July for a holiday, immediately prior to beginning my work. The holiday would be at the other end of the country from my work.  I can't enter with the H-1B as I can only enter the US on that visa 10 days prior to starting work.  Specific question: Would it be possible to visit the US in early July on the VWP, visit Canada/Mexico for a few days in late July, and re-enter the US with my H-1B visa?  General question: Is it possible to visit the US on the VWP, leave briefly, and re-enter on a different status (e.g. H, F, J, K, etc), without ever returning to one's home country?  I have posted this in Travel rather than Expatriates because, although in my specific case I have an H-1B visa, my question is more generally about VWP and travel, and I believe that it is applicable to travellers with non-immigrant visas.  There's a similar question , although that's about going to the US and before having the H-1B visa. How to show this function's discontinuity?  $ f(n) = \left\{     \begin{array}{l l}      \frac{xy}{x^2+y^2} &amp; \quad , \quad(x,y)\neq(0,0)\\      0 &amp; \quad , \quad(x,y)=(0,0)    \end{array} \right.$ Bounded sequence with divergent Cesaro means Is there a bounded real-valued sequence with divergent Cesaro means (i.e. not Cesaro summable)?  More specifically, is there a bounded sequence $\{w_k\}\in l^\infty$ such that $$\lim_{M\rightarrow\infty} \frac{\sum_{k=1}^M w_k}{M}$$ does not exist?  I encountered this problem while studying the limit of average payoffs criterion for ranking payoff sequences in infinitely repeated games. How to find the real user home directory using python? How can I determine if a C++ object has been deallocated? What is the correct way to install proprietary ATI Catalyst Video Drivers (fglrx) directly from AMD? How to set a font for math mode? I would like to have something like Segoe UI of something similar. Thank you  \documentclass{article} \usepackage{fontspec} \usepackage{firamath-otf} \begin{document} \begin{equation} x+y=45 \end{equation}  \end{document}   Error: I can't really remember how long ago it was, but I think the book was marketed towards children/teens.  All I remember is the basic premise of the story.  Some story about these unusual little blue electric critters that only certain people could see, and these kids took it upon themselves to go about destroying them since they fed off energy or something like that.  Not sure whether they fed off people or off electricity... or both maybe?  I think the dominant method of destroying them was an electric baton that was taken from law enforcement.  I wanna call them buzz batons, but that's probably thanks to Artemis Fowl. Preventing itemize environment to insert initial vertical space I'm using itemize and tables like the following  \begin{tabularx}{\textwidth}{&gt;{\ttfamily}llX}  \toprule  \textbf{\rmfamily Operator} &amp; \textbf{Typen} &amp; \textbf{Regel} \\  \midrule  = &amp; Alle Typen &amp;   \begin{itemize}    \item This is how we roll    \item Maybe we can talk?   \end{itemize} \\  \bottomrule \end{tabularx}   But it keeps inserting a vertical space before the itemized list. How can I prevent it from doing so? why is the output of the following code coming to be zero? How do I write a correct micro-benchmark in Java? I used the OzTeX implementation of TeX, also I used to typeset my docs in plain TeX, not LaTeX for me, so I had no problem to insert an image using the OzTeX, now I'm back to TeX docs, am using the TeXWorks frontend, but I can't insert an .eps image file, it seems the \includegraphics macro its only for LaTeX, so I can't use it, any idea on how to insert an image when using plain TeX? Proving Cauchy condensation test I have to prove the  by tomorrow and I am really unconfident about what I did:  $$\sum_{n=1}^\infty a_n\text{ converges } \iff \sum_{n=1}^\infty 2^n a_{2^n}\text{ converges}$$  I did the following:  Let $(b_n)$ be a sequence as follow: $b_{2^k+m}:=a_{2^k}$ with $k\in\mathbb N_0$ and $0\leq m&lt;2^k$.  It's $a_{n+1}\leq a_n$ and so $0\leq a_{n+p}\leq a_n$ for all $n,p\in\mathbb N$.  So $\sum\limits_{n=1}^\infty b_n$ converges by the majorizing series $\sum\limits_{n=1}^\infty a_n$. And it's $\sum\limits_{n=0}^\infty b_n=\sum\limits_{n=0}^\infty\sum\limits_{m=0}^{2^n-1}a_{2^{n+1}}=\sum\limits_{n=1}^\infty 2^{n-1}a_{2^n}$ so $\Rightarrow$ is done.  For $\Leftarrow$ consider $c_{2^k+m}:=a_{2^k}$ with $k\in\mathbb N_0$ and $0\leq m&lt;2^k$.  It's $|a_n|\leq c_n$ and $\sum\limits_{n=0}^\infty c_n=\sum\limits_{n=0}^\infty\sum\limits_{m=0}^{2^n-1}a_{2^{n}}=\sum\limits_{n=1}^\infty 2^{n}a_{2^n}$ and so $\sum\limits_{n=1}^\infty a_n$ converges by the majorizing series $\sum\limits_{n=0}^\infty c_n$.  Is this in form and content correct? Maybe the concept, why it's used, and an example. How can I get multiple stacked plots (ybar stacked, stack plots=y) in one diagram, such that there are multiple stacked bars for the same x-coordinate, each slightly shifted? Is there a way to reset pgfplot's zero levels after an \addplot command, such that the next \addplot[xhshift=...] doesn't add something to the current stack, but rather starts a fresh stack?  FWIW, overlaying two plots with scale only axis won't help; I need this to work with groupplot How to find and return a duplicate value in array