How is Einstein's postulate about the invariance of the laws of physics justified? According to one of Einstein's postulates related to special relativity, > "the laws of physics remain invariant in their form and nature in all inertial frames".   But global inertial frames don't exist in this universe, so how is Einstein's postulate justified?
Is there any true inertial reference frame in the universe? Is there any true  in the universe?  Newton's first law states that an object at rest remains at rest, and an object performing uniform motion performs uniform motion, until and unless acted upon by an external force, if viewed from an inertial frame. It is the definition of an inertial frame of reference. And Newton's second law states that the net external force acting on a particle equals its mass times its acceleration. Thus we need to have an inertial frame in order for Newton's 1st and 2nd laws to be applicable.  Scientists claim that Earth is an inertial frame, either the  frame or the  frame.  Why is that? Earth's different parts have different accelerations when it performs rotational motion about its axis. Now you may say that Earth's axis is inertial, but the Earth is also revolving around the Sun. Thus Earth's frame should be non-inertial.  Even supposing that earth's frame is inertial, then it means that rest of the universe is non-inertial, because only a frame that moves with constant velocity with respect to an inertial frame is also an inertial frame and according to various scientific experiments there is no other matter in this universe which satisfies that criterion. Now you may say that earth is an approximate inertial frame, but still, my question is: is there any perfect inertial frame in the universe where Newton's laws are exactly applicable?
Error: invalid environment block. Press any key to continue...   The error message appears immediately after the boot screen on purple background. Ubuntu 12.04.1 LTS. Making a (simple) directory tree Integral of periodic function over the length of the period is the same everywhere Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD? I'm considering the ring $\mathbb{Z}[\sqrt{-n}]$, where $n\ge 3$ and square free. I want to see why it's not a UFD.   I defined a norm for the ring by $|a+b\sqrt{-n}|=a^2+nb^2$. Using this I was able to show that $2$, $\sqrt{-n}$ and $1+\sqrt{-n}$ are all irreducible. Is there someway to conclude that $\mathbb{Z}[\sqrt{-n}]$ is not a UFD based on this? Thanks. The forgetful functor $\mathsf{Groups} \to \mathsf{Sets}$ admits a left adjoint, namely, "forming the free group" functor.  I was wondering if this has a left adjoint.  This seems unlikely, but I don't have a proof.  Is there a functor $\mathsf{Sets} \to \mathsf{Groups}$ that admits a left adjoint at all? How can we prove charge invariance under Lorentz Transformation? I need another LP-E5 type battery for my Canon 450D. Should I buy an original Canon battery or one of the many generic brands available? There are loads of cheapos on , for example.  I should add that the new battery will be added to my existing Canon battery in a battery grip.  Does anyone have any experience (good or bad) of using generic batteries? Are there any universal rules in appropriating “_an,” “_sh,” “_es,” “_ch” for the demonyms of countries? Suffixes indicating people and language of country vary by country:  _an: American, German, Italian, Belgian, Australian, Russian, Ukrainian, Korean,  Mexican, Brazilian, Chilean, Argentinean, Indonesian, Malaysian, Iranian, Egyptian, Somalian, Palestinian  _sh: English, British, Polish, Danish, Swedish, Turkish,    _ch: French, Dutch  _ese: Chinese, Taiwanese, Japanese, Vietnamese, Portuguese  _no: Filipino, Latino  _i: Israeli  _: Thai  Among the above, _an seems to outnumber other suffixes.  Are there any simple rule to govern appropriation of suffix turning a country name into adjective, indicating people and language of countries in the world in terms of say, region, race, or cultural background? Or is it just discretional? Recently I commented on  question   and the text did got bold but the italic word didn't seem to get italic on Android Chrome(Latest Ver.), but when I saw from the PC browser, it rendered as it should...  I've attached a screenshot of my phone ... Understanding how references and labels work I'm trying to understand why I cannot effectively reference figures or equations that I have defined with labels.  For example:  \begin{figure}   \label{fig:area_Treasuries}   \caption{Treasuries as a portion of total financial flows.}   \centering   \includegraphics[width=0.75\textwidth]{graphs/Area_Treasuries.png} \end{figure}  \paragraph{} Figure~\ref{fig:area_Treasuries} presents Treasuries (both flowing into and out of the United States) as a share of total financial flows.  From 1985 to 2010, Treasuries account for, on average, 53.2\% of total financial flows.   With the above code, I get this warning:      LaTeX Warning: Reference `fig:area_Treasuries' on page 37 undefined on   input line 477.   The result is "Figure ?? presents Treasuries..."  Why is this happening?  Related, I don't understand why I can't reference, say, an equation before (I mean physically above in the text) the actual equation.  Isn't this what compiling multiple times and cross references is supposed to take care of? Books or resources for learning unified view of classical statistics? I did a science PhD doing applied bayesian statistics, and I liked it so much that I decided to shift to statistics.  For the last 2-3 years have been working at a firm that has more of a frequentist focus.  It seems to me that the bayesian approach (at least what I learned) has an underlying theory that was laid out and I could understand.  Now I find this - more classical - field fascinating but I am looking for some resources to get a unified view of the matter.  For example, I am learning and applying anovas, F-tests and chi-squares, thinking about degrees of freedom, etc but part of me is looking for deeper understanding that would make it more than just methods.  Does anyone have any suggestions on books or more resources that provide such a unified, deeper focus? Simple way to understand what derivative is A question was asked in one of my friend's interview. The question was to determine the right form from the below sentences.     Q. Correct form of English:          Samuel was with Susan and I   Samuel was with Susan and me   Samuel was with I and Susan   Samuel was with me and Susan   None of these      Now I vaguely remember a rule of thumb from my school days. That is "2-3-1" i.e. where all the persons are acting in a sentence, second person comes first, then third person and it is followed by first person.  So according to this theory, 1 seems to be correct to me. Is this theory correct? Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite. I have seen another post for this same question but it never got an answer. Since I am fairly new, I can't comment on other's posts, therefore I am creating a new one. The question states:  If a, b, and c are positive integers, prove that if $(a + b + c) | (a*b*c)$, then $a+b+c$ is composite.  I do not really know how to approach this.  The link to the post with the same question is: Good reasons to prohibit inheritance in Java? Let $R$ be commutative ring with no (nonzero) nilpotents. If $f(x) = a_0+a_1x+\cdots+a_nx^n$ is a zero divisor in $R[x]$, how do I show there's an element $b \ne 0$ in $R$ such that $ba_0=ba_1=\cdots=ba_n=0$? Enumeration within self defined environment My self defined environment having a symbol at the beginning and at the end works fine for text without enumeration. When including enumerate the symbols are not there where desired. Is it possible to have the first symbol directly in front of &quot;1.&quot; i. e. in the same line and the ending symbol in the same line as the last line of the enumeration? With \ignorespacesafterend and \unskip I did not succeed. \documentclass{article} \usepackage{amssymb} \newenvironment{myenv}{$\blacktriangleright$}{\hfill$\blacktriangleleft$}  \begin{document} There is a text.  \begin{myenv} And an example \end{myenv}  Here is another text.  \begin{myenv} \begin{enumerate} \item A \item B \end{enumerate} \end{myenv}  \end{document} Deleting polygon defined area from raster layer in ArcGIS Desktop? Which tool do I use in ArcGIS 10.1 for Desktop to exclude areas covered by vector polygon layers from a raster layer?   I want to keep portions of the raster layers that exclude the portions covered by the vector layer. Font characters displayed as squares in Ubuntu 18.04 Recently, on my Ubuntu 18.04 I have noticed that at least on gnome-calculator and chromium browser the fonts are displayed as squares. I have followed instructions  and , the calculator is fixed, but the problem on chromium still exists when I open a dialog to search for a file.  Not sure if this happens on other applications as well, I haven't checked all my apps, but File managers nemo and nautilus are working fine.  Also, before few months ago, I have included some windows fonts for my libre office shown . I used the copy (cp) method, not the link (ln -s). But, was working fine until yesterday. Haven't done any major change or update, at least on my Linux partition (dual boot). But, I don't think that this has anything to do with that.  Any idea how can I fix this issue?  . I'm a bachelor student majoring in math, and pretty interested in physics. I would like a book to study for classical mechanics, that will prepare me to work through . What books would be good for a beginner?