why doesn't Heisenberg's uncertainty principle also work for macroscopic bodies which are in-turn made up of quantum-particles?  ps: if proof is provided it will be a lot more useful.
Many introductory quantum mechanics textbooks include simple exercises on computing the de Broglie wavelength of macroscopic objects, often contrasting the results with that of a proton, etc.  For instance, this example, taken from a textbook:     Calculate the de Broglie wavelength for      (a) a proton of kinetic energy 70 MeV      (b) a 100 g bullet moving at 900 m/s   The pedagogical motivation behind these questions is obvious: when the de Broglie wavelength is small compared to the size of an object, the wave behaviour of the object is undetectable.  But what is the validity of the actual approach of applying the formula naively? Of course, a 100g bullet is not a fundamental object of 100g but a lattice of some $10^{23}$ atoms bound by the electromagnetic force. But is the naive answer close to the actual one (i.e. within an order of magnitude or two)? How does one even calculate the de Broglie wavelength for a many body system accurately?
Can this identity be derived from the binomial theorem?  $$n(n+1)2^{n-2} = \sum_{i=1}^{n}  i^2 \binom{n}{i}$$    I tried starting from $2^n = \displaystyle\sum_{i=0}^{n} \binom{n}{i}$ and dividing it by $4$ in order to get $2^{n-2}$. What is the time span of The Last Jedi? I use a Full HD 24" external display besides my 15" MacBook Pro Retina, on which I use the option for most screen estate regarding the Retina display. In the display arrangement screen, the MacBook Pro is therefore a bigger rectangle than the external display. Is there a way to size these rectangles regarding their "real world size" instead of resolution? I'm annoyed by my cursor teleporting vertically whenever I move from one display to another. why can't i select two objects in edit mode?     I am trying to make a face from two different meshes but can't perform the action Do we need inertial frames in Lagrangian mechanics? Can I export Shotwell pictures database saving all the tags? I've imported lots of pictures into Shotwell and spent some time setting tags. Are those tags locked-in in Shotwell or I can export them (and import again or use with other software)? Fatal error occurred, no output PDF file produced in php file We are using following code in .php script for generate .pdf file.  $result1 = exec("R CMD Sweave /var/www/html/r/r_latex_sweave.Rnw");  $result2 = exec("pdflatex /var/www/html/r/r_latex_sweave.tex");   but, we are getting this errors when we are executing .Rnw and .tex files.  ! I can't write on file `r_latex_sweave.log'. Please type another transcript file name:  ! Emergency stop !  ==> Fatal error occurred, no output PDF file produced!  Note: We have .tex and .Rnw folder in /var/www/html folder? What are the minimum root filesystem applications that are required to fully boot linux? I use ssh on a variety of machines, mainly linux. Accounts on these machines vary in naming scheme: if my name is First Last, then I have accounts: first, flast, last_f, lastf, and sometimes I need to log in as root. For each machine I use, I would like the openssh client to know which account to use when I don't specify on the command line.  So the question is: How do I make ssh server Do The Right Thing when a username is not specified? We always change subject and verb positions in whenever we want to ask a question such as "What is your name?". But when it comes to statements like the following, which form is correct?        I don't understand what are you talking about.   I don't understand what you are talking about.      Another example        Do you know what time is it?   Do you know what time it is?      Another example        Do you care how do I feel about this?   Do you care how I feel about this? Similar to Lifepod 1993, but not it Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$ Prove that for any natural number $n&gt;1$, we have $(2n)!&lt;(n(n+1))^n$    I tried using induction, but I failed in that approach, I rather found it was untrue, but on several case testing, I found it to be true. I am out of ideas here, please help. Thank you. Is it possible to assign numbers generated in an Error-Message? Let $P(X)$ denote the power set of $X$ (the set of all subsets of $X$) with a partial order given by inclusion.  If $F: P(X) \to  P(X)$ is monotone (order preserving), then $F$ has a fixed point.  How are we going to prove that without using the term (complete lattice)?! Outline radius? How to filter by messages, not by conversation? I have been emailing my Gmail account error messages from a project I am working on.   I am trying to use Gmail filters/labels to sort out the class of errors.  But because the subject line is basically always the same even if I have a specific filter for 3 known error cases, the label is applied to the conversation, instead of the specific message.  Therefore, all the errors get all the filters.  I do not yet want to delete the errors, but would rather file them separately.   I have not yet used the NOT contains string yet, but that looks to be non-scalable as I get to the fourth or fifth error case I am done with handling.  Is there any option other than turning off Conversations for all my email?  (I guess I could use one of my spare accounts to turn off conversations and do the work there but would be nice to have such an option). Rising edge pulse detector from logic gates The circuits I describe are entirely made of 7400 series logic gates (7402, 7404 and 7408 ic). I'm trying to build a rising (positive) edge pulse detector using logic gates.  The following circuit should work in theory:   (see )  I do not expect the short output to be seen through a LED so, to test it, I make it trigger an SR latch to its up state:    However, it doesn't have effect on the latch. So I added an inductor to delay the input to the NOT gates in the pulse detector circuit and it worked:   But now I can see the short flashing output through a LED which I should not because it would mean it is too long to work with a circuit like that:   Which intends to toggle the D Latch output on each clock rising edge (Note that this is a D Latch not a D Flip-flop)  And anyway there is no place for inductors in integrated circuits so there must be a way to do this only with logic gates. Can someone solve this mystery?  BTW It does not show in my schematics but I did put 10K pull-down resistors where there might be floating pins. I'm trying to make a systemd timer that runs every 15 minutes. Right now I have:     timer-fifteen.timer:  [Unit] Description=15min timer  [Timer] OnBootSec=0min OnCalendar=*:*:0,15,30,45 Unit=timer-fifteen.target  [Install] WantedBy=basic.target    timer-fifteen.target:  [Unit] Description=15min Timer Target StopWhenUnneeded=yes    This runs over and over again without stopping. Does it need to be *:0,15,30,45:* instead? How can I make this work? What are the biggest changes between UA Ranger and PHB Ranger? Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?