Imagine you have a photon with momentum $p$ which hits a mirror $M$ and is reflected back. Since $M$ is at rest in your frame of reference the total momentum of the system pre-reflection is $p$ and post reflection is $-p$. This seems quite odd to me and a clear violation of conservation of momentum. How this can be resolved: The mirror begins to move/absorbs some momentum after being hit by the photon, but if the photon was reflected with momentum $p$ then we end up having conservation of kinetic energy being violated. The only conclusion that's reasonable is the photon being reflected back has a different (probably lesser) momentum after hitting the mirror and the mirror then picks up some positive momentum, so that the sum of the momenta remains constant and the sum of their kinetic energies remains constant. Is this actually what happens? And if so does that mean that almost all mirrors are heating up when they are reflecting photons?
I was readng Wikipedia article (English one) about radiation pressure because there is something I still cannot figure out. As I understand it, radiation pressure emerges from conservation of momentum. Photons or electromagnetic waves possess momentum and when they are absorbed, reflected or even emitted, the aborber/reflector/emitter experiences a pressure that is proportional to the irradiance (in watts per square meter). OK. In the case of a perfect reflector that does nothing but reflecting incoming radiation, it would seem the reflector is pushed and the radiation is reflected in opposite directions. But the radiation has not lost anything, it has only changed direction. And I do not understand how something can be set in motion (the reflector), which amounts to do work, yet the source of this work does not lose energy. I mean, if the radiation, after a U turn, meets a second reflector, it would have pushed two reflectors a way, yet it would continue in its original direction as if nothing happened...? What am I missing here? Should not photons lose something?
Is it possible to detect 32 bit vs 64 bit in a bash script? I am writing a bash script to deal with some installations in an automated way... I have the possibility of getting one such program in 32 or 64 bit binary... is it possible to detect the machine architecture from bash so I can select the correct binary?  This will be for Ubuntu machines. Adding values to a picklist using apex Do SAS expanders work transparently with SAS controllers? I'm new to SAS expanders and I'm trying to get things right. I understand that SAS expanders, when used with SAS controllers which supports expanders, allows you to utilise the full capacity of supported drives on a controller.  However, say I've got a SAS controller with 4 x SSF-8087 ports, which by itself would support 16 disks. I could then, as far as I understand, instead connect each of these ports to an expander to increase disk capacity.  However, will the SAS controller "see" all disks as if they were connected directly to the controller and not through an expander. Could I look at controllers as switches in a network? Would I be able to create a RAID from a disk on expander 1 and expander 3?  UPDATE:  I don't really have a specific project where I need to use SAS expanders. I'm just curious about how they work, and was thinking about how it would work if I used one or more SAS expanders with a LSI MegaRAID controller (9260-16i) which is running in one of our servers. However, I haven't really put any thought into the distinction between "local" disks and disks in another enclosure. The LSI MegaRAID controller has 4 SFF-8087 ports, which makes it capable of accomodating 16 drives. It is common to see things described as the &quot;gold standard&quot;. It means that something is the best and is the ideal against which other things are to be compared; it cannot be superseded. I often , where a certain diagnostic test (e.g., the nasopharyngeal swab PCR test for infection with the Coronavirus causing COVID-19) is considered the most accurate and then other tests (e.g., cheaper or faster tests) are then evaluated against this benchmark. The etymology is covered in . In short, it is derived from the . Thus gold was the thing against which the value of all other currencies was measured. I don't like this term and would like to avoid using it. First, the desired meaning is not predominant; if you  you will mostly get results for the monetary system, not the more general phrase. Second, the etymology is outdated; the original meaning of the term now has the opposite connotation. The monetary gold standard was abandoned in the 1970s. Economists consider the gold standard to be a bad monetary system. Thus, if you are interested in economics and history, the term &quot;gold standard&quot; actually is associated with being outdated and flawed -- which is close to the opposite of the intended meaning. (Of course, many people are unaware of the original meaning of the term. ) (A note in response to comments: Why I want to avoid this term is relevant, but not essential, to the question. If you don't see a problem with the term, the question can be answered regardless.) My question: Is there a better phrase to use in place of &quot;gold standard&quot;? For example, what term could be used in a medical study comparing a new diagnostic test against the gold standard test? I'm not aware of any good substitute that has essentially the same meaning. Here are two example sentences where I would like a replacement:   A nasal swab is the gold standard for diagnosing COVID-19.     The  served as the gold standard for all scales from 1889 until 2019.   The best substitute I can think of is &quot;official,&quot; as in &quot;a nasal swab is the official way to diagnose COVID-19&quot;. &quot;Official&quot; implies some form of uniqueness. But &quot;official&quot; implies the existence of some authority that gives it this designation (as opposed to scientific consensus). A  asks for a &quot;perhaps humorous&quot; alternative -- the suggestion there, &quot;mother of all&quot;, is not appropriate here. (There is also .)  In response to the answers and comments doubting the premise of this question: I personally have a negative association with the phrase &quot;gold standard&quot; because I know people who advocate for returning to the gold standard or its modern equivalent, , and have discussed the topic at length. Several  US  continue to advocate for a return to the gold standard. Thus asserting that no one will interpret the phrase in terms of monetary policy is simply not convincing. I'm doing some exercises on Apostol's calculus, on the floor function. Now, he doesn't give an explicit definition of $[x]$, so I'm going with this one:     DEFINITION Given  $x\in \Bbb R$, the integer part of $x$ is the unique $z\in \Bbb Z$ such that $$z\leq x &lt; z+1$$ and we denote it by $[x]$.   Now he asks to prove some basic things about it, such as: if $n\in \Bbb Z$, then $[x+n]=[x]+n$  So I proved it like this: Let $z=[x+n]$ and $z'=[x]$. Then we have that  $$z\leq x+n&lt;z+1$$  $$z'\leq x&lt;z'+1$$  Then $$z'+n\leq x+n&lt;z'+n+1$$  But since $z'$ is an integer, so is $z'+n$. Since $z$ is unique, it must be that $z'+n=z$.  However, this doesn't seem to get me anywhere to prove that  $$\left[ {2x} \right] = \left[ x \right] + \left[ {x + \frac{1}{2}} \right]$$  in and in general that   $$\left[ {nx} \right] = \sum\limits_{k = 0}^{n - 1} {\left[ {x + \frac{k}{n}} \right]} $$  Obviously one could do an informal proof thinking about "the carries", but that's not the idea, let alone how tedious it would be. Maybe there is some easier or clearer characterization of $[x]$ in terms of $x$ to work this out.  Another property is $$[-x]=\begin{cases}-[x]\text{ ; if }x\in \Bbb Z \cr-[x]-1 \text{ ; otherwise}\end{cases}$$  I argue: if $x\in\Bbb Z$, it is clear $[x]=x$. Then $-[x]=-x$, and $-[x]\in \Bbb Z$ so $[-[x]]=-[x]=[-x]$. For the other, I guess one could say:  $$n \leqslant x &lt; n + 1 \Rightarrow  - n - 1 &lt; x \leqslant -n$$  and since $x$ is not an integer, this should be the same as $$ - n - 1 \leqslant -x &lt; -n$$  $$ - n - 1 \leqslant -x &lt; (-n-1)+1$$  So $[-x]=-[x]-1$ How is the system call in Linux implemented? When I invoke a system call in user mode,how did the call get processed in OS?  Does it invoke some some executable binary or some standard library?  If yes,what kind of thing it needs to complete the call? Change style of labels of Tikz nodes of a given style Can't install xposed framework I want to install the xposed framework on my Nexus 5 and in the framework, the install/update option doesn't work.  My Nexus 5 runs Android 5.0 (Lollipop). I am working on a game and would like to include a few jump scares. So here is a rather simple question — What makes a good jump scare and when and how should they happen? Are Android OS updates region specific? Well, I have a Galaxy Ace with 2.3.3, build XWKPY and Samsung Kies doesn't show an update to 2.3.4 yet.  I'm thinking of manually updating it through Odin and I need to know if I can just download any Gingerbread 2.3.4 update file or is there anything else that I need to be worried about? Proving that this function is continuous on $G\times G$ Let $M$ be the manifold of real positive definite $n \times n$ matrices, define a mapping $i:A \to \sqrt A$ (where $A\in M$ and $\sqrt A$ means the unique positive definite square root of $A$). Please show that $i$ is smooth. As , the retag privilege serves a lot more confusion and a lot less of its benefit due to the suggested edit system. It must be done away with. It will be done away with. ♪  In light of this decided course of action, we're going to need a new snack for the road between "Create Tags" at 300 reputation and "Established User" at 1000 reputation. We'd like your help in thinking about some ideas on what would be a nice privilege to sit at this level. Since we're... a bit dry on our end.  The primary guideline in deciding what kind of privilege to put here is acknowledging its position in the overall hierarchy of privileges. 500 reputation is an early-intermediate user, one who has started to really get the hang of the site and its function. It can be something that provides convenience in how they currently can act on the site, or it could be some new functionality that fits as an early ability (especially considering there's no new abilities until 2000 reputation's "Edit Everywhat" ability).  I look forward to hearing what creative ideas y'all can provide. How to know if the system console is open? Can we know, with python, if the system console of blender is open? I know that we can open or close it with this function:  bpy.ops.wm.console_toggle()   But it doesn't return the 'state' of the system console like open or closed (True,False).  I want to be sure that the console is open when i execute one of my script. High contrast theme and Firefox-Font colour issues? Show that if m/n is a good approximation of $\sqrt{2}$ then $(m+2n)/(m+n)$ is better If I multiclass into 2 or more classes/subclasses that can cast spells, how do I determine what spells I know or can prepare?  For instance, if I am playing a multiclassed character with 1 level in warlock, 2 levels in bard, and 3 levels in paladin, how do I determine which spells I know/have prepared?    Related: Custom action to set emblem in thunar I assume it doesn't connect to anything (other than the satelite I guess), is this right? Or it does and has some kind of charge? Render looks darker than Look Dev mode