What would the result of a vertical variation of the Michelson-Morley experiment be?  I.e., if one were to compare light traveling along a horizontal arm with light traveling along a vertical arm (perpendicular to the surface of the Earth), what would the result be?  My understanding is that light traveling along each arm will both travel at c and consequently the result of such a variation of the experiment will be exactly as all of the previous (fully horizontal) versions of the experiment.  Namely, that there is no directional dependence in the speed of light.  Is this understanding correct?
For almost a year now, I have been in the uncomfortable position of having an idea.  However, there is one nice thing about this idea.  It makes a concrete, exact and relatively easy to test physical prediction.  The idea predicts that there is a 11,187 m/s (Earth’s escape velocity) aethereal wind directly into the surface of the Earth at its surface.  I believe it would be possible to test this by performing a vertical variation of modern versions of the Michelson-Morley experiment (MMX) with one arm pointed in the vertical direction. ()  In 2003, Müller et al. performed a normal (2 horizontal orthogonal arms) modern MMX using cryogenic optical resonators that found a “possible anisotropy of the speed of light c, (of) 2.6 +/- 1.7 parts in 10^15” (  )  In a brief conversation with Holger Müller a Professor at Berkeley and the lead author of that paper, he stated that to this knowledge no one had ever performed a variation of the experiment using a vertical arm.  He also mentioned that such an experiment would be complicated by the fact that gravity would slightly compress the length of the vertical bar making two equal length bars no longer equal in length.  “They haven't been done as far as i know. The problem is that any interesting physics signal would be hard to tell from a large signal from stretching of the arms under their own weight.” - H. Müller  I am interested in attempting to run this experiment myself.  To that end, I have the following questions:   Given current Physics understanding, is there any reason to expect that such a vertical variation of the MMX wouldn’t return the exact same results as all other MMXs, namely that there is no anisotropy in the speed of light? Given the complications mentioned by Professor Müller, are there reasonable methods available to overcome them?  Especially considering the size of the effect (c + 11,187m/s vs c) is substantially larger than the accuracy obtained in his and similar modern MMXs. What is the order of magnitude cost of such an experiment?  If I am to fund this personally, would such a project cost \$10,000?  \$100,000? \$1,000,000? more?   Any insight offered on this topic will be greatly appreciated.  EDIT: For what its worth, for people looking at this years later.  As I originally alluded to in a comment to [WetSavannaAnimal aka Rod Vance]'s much appreciated and comprehensive answer.  While, I've become increasingly comfortable with the idea that there is a flow of aether or spacetime or whatever you want to call it into the Earth at 11km/s; I strongly believe that a vertical MMX would return the same null result as the horizontal one.  And I believe it will do so because of length contraction; that length contraction exactly masks any anisotropy of the speed of light by ensuring that the roundtrip time of light in any direction is a constant; that length contraction ensures Lorentz co-variance.
How to illuminate the darkness inside glass objects in Cycles? My model has a clear plastic (or glass) dome with objects inside.  The objects appear dark.  I've tried the glass shader with color 100% RGB, with very small IOR, and using just a refraction shader.    I know Cycles has problems with caustics, but I just want broad illumination to fall clean through the glass.  The light-to-column path can ignore refraction, but is blocked or tremendously attenuated. The camera-column path needs refraction, and seems to work fine anyway.  This demo image offers all optical paths of interest:   light upon object, seen directly light upon object, seen through glass (looks okay) light through glass onto object, seen directly. This is the shadow on the lit side of the column just below the glass tubing.  I expect full illumination, but there is shadow.  There is some light, but it's diffuse light from the floor. light through glass onto object, seen through glass. This     I did at one point try non-progressive rendering, and find extremely coarse light where there shouldn't be shadow, but this is not a practical way to make nice images. I've even tried cranking up certain sampling settings to many thousands, but still get bad noise though less, at the cost of long render times. I  would like to finish my creations sometime before "Star Trek, the Generation After the Next" becomes real life, if you know what I mean.  The next image is an example. I think Transmission in Sampling was 5000, but not sure.    I'm using Cycles in Blender 2.67 on a quad core Linux machine, 16GB RAM. Machine limits have never been a problem for 3D rendering.  Possibly, I screwed up some setting when I made my startup file, and just need to fix it. OTOH maybe this is just a limitation of path tracing, or of the way Cycles does it. If that's the case, what to real-world Blender artists do when they need to produce images on a budget and schedule?  What is the practical real-world fix? Lightning-Web-Components Select Option prepopulate value Let's say I have a Lightning-Web-Component with a select list with dynamic options where the value is a user Id and the label is the user's name:  &lt;select class="slds-select" onchange={handleSelectChange} disabled={isDisabled}                           data-value={step.selectedUser} &gt;                                 &lt;option value=""&gt;--None--&lt;/option&gt;                                 &lt;template for:each={step.approvalTemplateStep.Approval_Step_Users__r} for:item="user"&gt;                                     &lt;option key={user.key} value={user.User__c}&gt;                                         {user.User__r.Name}&lt;/option&gt;                                 &lt;/template&gt;                             &lt;/select&gt;    How do I prepopulate the select option with a value? I have the value I want to be prepopulated in the variable called step.selectedUser.  Here's what I see on page load:   Here's what I should see: Why does an conditionally convergent infinite series, when deranged, have a different limit? $\sum u_n = 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\dots$ conditionally converges to $\log 2$; and, when deranged to $\sum u'_n = 1-\frac{1}{2}-\frac{1}{4}+\frac{1}{3}-\frac{1}{6}-\frac{1}{8}+\dots,$ converges to $\frac{1}{2}\log 2$. Why does a deranged conditionally convergent series have a different limit? First Course in Math Anal, p.93, by Burkill, explains that the sums $s_n, t_n$ of the first n terms of the two series are different functions of $n$. This reasoning is incomplete, because different functions of $n$ can converge to the same limit; for example, let $r_n$ be the first $2n$ terms of $\sum u_n$, then $s_n$ and $r_n$ are different functions; besides, by differently defining terms, i.e. clustering pieces of a series, e.g. \begin{align*} 1-\tfrac{1}{2}-\tfrac{1}{4}+\tfrac{1}{3}-\tfrac{1}{6}-\tfrac{1}{8}+\dots = \left(1-\tfrac{1}{2}-\tfrac{1}{4}\right)+\left(\tfrac{1}{3}-\tfrac{1}{6}-\tfrac{1}{8}\right)+\dots \\ = \left(1-\tfrac{1}{2}-\tfrac{1}{4}+\tfrac{1}{3}-\tfrac{1}{6}-\tfrac{1}{8}\right)+\dots,\\ 1-1+1-1+\dots = (1-1)+(1-1)+\dots \\ =(1-1+1-1)+\dots,\\ 1+1+1+1+\dots = (1+1)+(1+1)+\dots \\ = (1+1+1+1)+\dots, \end{align*} one gets the sum of first n terms as different functions, but the series's limit remains. One could view a changed limit from the perspective of the changed number of terms, Denote 'countably many', the size of natural number, as $\lvert\mathbb{N}\rvert$, then $\lvert\mathbb{N}\rvert = \lvert k\mathbb{N}\rvert = \lvert\mathbb{N}\times\mathbb{N}\rvert$. Then two series with different numbers (e.g. $\lvert \mathbb{N}\rvert$, $\lvert k\mathbb{N}\rvert$) of terms– and so having different limits– paradoxically have same number of terms–and so are possibly formed by the same terms. The paradox could be the fundamental reason. Are there other explanations? Is the use here of 'countably many' is proper? Dropping articles in the title (of an article or a section) or in the caption (of a figure or a table)? What's the general rule? It is said that "To give added punch, articles are often dropped in the titles"  Source:   Is there any general rule or reference about dropping articles, especially in academic research papers? How to add flavouring ingredients to steamed or boiled veggies? Do I need a US visa to transit (or layover) through an American airport? In Europe usually you don't need to go through immigration to change planes (unless you are entering/exiting Schengen). Is it the case in the US as well? May I catch a connecting flight on one of the US airports if I don't have US visa? What are some alternative launchers that can be used to launch programs in Ubuntu's default Unity desktop? I received a table template, which I'm intended to generate dynamically with data using Java. But when the table becomes to large, the compilation with LaTeX fails. The specific about this template is, that it stretches the table width into the maximal page width and has same column widths for all data columns (except the first column).  Here is a minimal version of the full template, that still works fine:  \documentclass[final,authoryear,3p,twocolumn]{elsarticle}  \usepackage{amssymb,amsmath} \usepackage{calc} \usepackage{array} \newcolumntype{L}[1]{&gt;{\raggedright\arraybackslash}p{#1}} \newcolumntype{R}[1]{&gt;{\raggedleft\arraybackslash}p{#1}} \usepackage{eurosym} \usepackage{microtype} \usepackage{needspace} \usepackage{fp}  \usepackage{graphicx} \DeclareGraphicsExtensions{.pdf} \input{pgfexternal}  \newcommand\tabt{\rule{0pt}{2.6ex}} \newcommand\tabb{\rule[-1.2ex]{0pt}{0pt}}  \begin{document}  \begin{table*}[t]     \footnotesize     \begin{tabular*}{\linewidth}{@{}L{2em}@{}*9{R{(\linewidth-2em)/9}@{}}}\hline\tabt $i$ &amp; $1$ &amp; $2$ &amp; $3$ &amp; $4$ &amp; $5$ &amp; $6$ &amp; $7$ &amp; $8$ &amp; $9$\tabb\tabularnewline\hline\tabt $1$ &amp;  &amp; $48.87$ &amp; $0.01$ &amp; $0.05$ &amp; $1.23$ &amp; $0.00$ &amp; $0.20$ &amp; $5.67$ &amp; $2.35$\tabularnewline     \end{tabular*} \end{table*}  \end{document}   But when extending this example by another column, so that the table would look like the following example, it fails:  \begin{table*}[t]     \footnotesize     \begin{tabular*}{\linewidth}{@{}L{2em}@{}*10{R{(\linewidth-2em)/10}@{}}}\hline\tabt $i$ &amp; $1$ &amp; $2$ &amp; $3$ &amp; $4$ &amp; $5$ &amp; $6$ &amp; $7$ &amp; $8$ &amp; $9$ &amp; a\tabb\tabularnewline\hline\tabt $1$ &amp;  &amp; $48.87$ &amp; $0.01$ &amp; $0.05$ &amp; $1.23$ &amp; $0.00$ &amp; $0.20$ &amp; $5.67$ &amp; $2.35$ &amp; b\tabularnewline     \end{tabular*} \end{table*}   This fails, no matter how many columns I add. So far, it seems for me to be a problem with the division by 10. May it be, that LaTeX isn't able to handle that properly by default? How can I solve this problem and make even larger tables work using this template. Or is that to any other problem I don't see yet? Thanks for any help! How to fix soft 404 errors in GWT? In GWT I have been receiving soft 404 errors for some URLs of my online shopping website. Ichecked all those URLs and those pages are looking good and there is nothing wrong in that page. Then why I'm receiving that errors?  This is the notification that I received in my GWT:     Dear owner or webmaster,      While crawling your site, we have noticed an increase in the number of   transient soft 404 errors around 2013-06-30 16:00 UTC (London, Dublin,   Edinburgh). Your site may have experienced outages. These issues may   have been resolved. Pending suggested edit message bug I just tried to edit a post on Stack Overflow but when I pressed the 'edit' button it showed me this message on a white page.    I know what the message means but I don't think it is supposed to show up in a white page. So, is this a bug or is it something else? Why is ++i considered an l-value, but i++ is not? Why is ++i is l-value and i++ not? Expectation inequality for a set and its subset. Given that a function $g(x)$ is a monotone increasing function. Its domain is an interval [c,d]. There are two sets $a_j \in A, j= 1,...,J$ and $b_k \in B,k=1,...,K$  on this interval, which satisfy $c_z \in C = B$\A and $c_z \geq a_j$ for all $a_j \in A$. For example, the interval $[c,d]=[0,8]$,$A=\{0,1,2,3,4,5\}$ and $B=\{0,1,2,3,4,5,6,7\}$. In this case, does the following inequality hold? If yes, could you give me some hints to prove that?  $$\frac{1}{K} \sum_{k=1}^{K}g(b_k) \geq \frac{1}{J} \sum_{j=1}^{J}g(a_j)$$ It is generally believed and claimed that quantum computers can outperform classical devices in at least some tasks.  One of the most commonly cited examples of a problem in which quantum computers would outperform classical devices is $\text{Factoring}$, but then again, it is also not known whether $\text{Factoring}$ is also efficiently solvable with a classical computer (that is, whether $\text{Factoring}\in \text{P}$).  For other commonly cited problems in which quantum computers are known to provide an advantage, such as database search, the speedup is only polynomial.  Are there known instances of problems in which it can be shown (either proved or proved under strong computational complexity assumptions) that quantum computers would provide an exponential advantage? Which is faster/best? SELECT * or SELECT column1, colum2, column3, etc I've heard that SELECT * is generally bad practice to use when writing SQL commands because it is more efficient to SELECT columns you specifically need.  If I need to SELECT every column in a table, should I use   SELECT * FROM TABLE   or   SELECT column1, colum2, column3, etc. FROM TABLE   Does the efficiency really matter in this case? I'd think SELECT * would be more optimal internally if you really need all of the data, but I'm saying this with no real understanding of database.  I'm curious to know what the best practice is in this case.  UPDATE: I probably should specify that the only situation where I would really want to do a SELECT * is when I'm selecting data from one table where I know all columns will always need to be retrieved, even when new columns are added.   Given the responses I've seen however, this still seems like a bad idea and SELECT * should never be used for a lot more technical reasons that I ever though about. How to mount ufs file system under Debian testing? In order to mount my /dev/sda4  under /mnt/ufs_mount on Debian Testing , i have tried the following commands (it works fine under Debian Jessie):  modprobe ufs mount -r -t ufs -o ufstype=ufs2 /dev/sda4 /mnt/ufs_mount   and:  mount -t ufs -o ufstype=ufs2 /dev/sda4 /mnt/ufs_mount   But i get this error:  mount: /dev/sda4 is write-protected, mounting read-only mount: wrong fs type, bad option, bad superblock on /dev/sda4,    missing codepage or helper program, or other error     In some cases useful info is found in syslog - try    dmesg | tail or so.   The output of: dmesg | tail :  [ 1136.965142] ufs: ufs_fill_super(): bad magic number [ 1255.758946] ufs: ufs_fill_super(): bad magic number [ 2098.945757] ufs: ufs was compiled with read-only support, can't be mounted as read-write [ 2098.946045] ufs: You didn't specify the type of your ufs filesystem        mount -t ufs -o ufstype=sun|sunx86|44bsd|ufs2|5xbsd|old|hp|nextstep|nextstep-cd|openstep ...        &gt;&gt;&gt;WARNING&lt;&lt;&lt; Wrong ufstype may corrupt your filesystem, default is ufstype=old [ 2098.967212] ufs: ufs_fill_super(): bad magic number [ 2927.982112] perf: interrupt took too long (2504 &gt; 2500), lowering kernel.perf_event_max_sample_rate to 79750   Edit My sources.list:  deb http://httpredir.debian.org/debian/ stretch main deb-src http://httpredir.debian.org/debian/ stretch main  deb http://security.debian.org/debian-security stretch/updates main deb-src http://security.debian.org/debian-security stretch/updates main   And uname -a:  Linux debian 4.6.0-1-amd64 #1 SMP Debian 4.6.4-1 (2016-07-18) x86_64 GNU/Linux   How to mount ufs file system under Debian testing? What are the different endings in Dishonored? If you have the ability to cast a spell without a spell slot, can you cast that spell using a spell slot? A 10th level Drow warlock (for instance) has the following Drow Magic racial trait (PHB p. 24), in addition to its warlock spellcasting abilities:  You know the dancing lights cantrip. When you reach 3rd level, you can cast the faerie fire spell once per day. When you reach 5th level, you can also cast the darkness spell once per day. Charisma is your spellcasting ability for these spells.  Can the Drow warlock cast faerie fire (which is not on the warlock spell list) using a warlock spell slot? Can it cast darkness (which is on the warlock spell list) using a warlock spell slot?  The  says this about the Magic Initiate feat:  If you’re a spellcaster, can you pick your own class when you gain the Magic Initiate feat? Yes, the feat doesn’t say you can’t. For example, if you’re a wizard and gain the Magic Initiate feat, you can choose wizard and thereby learn two more wizard cantrips and another 1st-level wizard spell. If you have spell slots, can you use them to cast the 1st-level spell you learn with the Magic Initiate feat? Yes, but only if the class you pick for the feat is one of your classes. For example, if you pick sorcerer and you are a sorcerer, the Spellcasting feature for that class tells you that you can use your spell slots to cast the sorcerer spells you know, so you can use your spell slots to cast the 1st-level sorcerer spell you learn from Magic Initiate. Similarly, if you are a wizard and pick that class for the feat, you learn a 1st-level wizard spell, which you could add to your spellbook and subsequently prepare.  But this specifically requires you to pick the feat for one of your classes to be able to cast the spell learnt using your class spell slots, and does not seem directly applicable. A Warlock can use warlock Pact Magic spell slots to cast spells learnt from levels of another spellcasting class, per the multiclass spellcasting rules (PHB p. 164):  If you have both the Spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the Spellcasting class feature, and you can use the spell slots you gain from the Spellcasting class feature to cast warlock spells you know.  Similarly, if the warlock has learnt the invocation Mask of Many Faces (PHB p. 112)...  You can cast disguise self at will, without expending a spell slot.  ...Can the warlock cast disguise self using a spell slot, e.g. to decrease the chance it can be dispelled? How to disable Chrome's Incognito Mode? Let $\Gamma$ denote the positively oriented circle of radius $2$ with center at the origin. Let $f$ be an analytic function on $\{z \in\mathbb{C} : |z|&gt;1 \}$, and let $$\lim_{z\to \infty}f(z)=0.$$  Prove that $$ f(z)=\frac{1}{2\pi i} \int_{\Gamma} \frac{f(\xi)}{z-\xi}d\xi,  $$ for all $z\in\mathbb{C}$ with $|z|&gt;2$.  I have no idea how to even start. Any hint will be appreciated. In the current era of cricket, we see batsmen using switch hits to play a ball. That is, while playing a ball they change their batting side (left to right handed and vice versa) just before the ball comes to them.  My question is, can a bowler bowl a switch ball? Meaning, can a left hand bowler bowl right handed to a batsman? If it is not permitted, then is it not unfair to the bowlers that batsmen can change their batting style but not the bowlers? Or are there are any rules against a switch hit?