The uncertainty principle says that $\Delta x\Delta p\geq \frac{\hbar}{2}$. The uncertainty principle is to be viewed as a fundamental fact of nature herself, and the principle has nothing to do with measurement limitations. If such an uncertainty does not show itself in the macroscopic world, it is explained, it is because of the smallness of $\hbar$.  But if one accepts this, then it means that in principle one could make as precise measurements as one wishes by making either $\Delta x$ or $\Delta p$ smaller without bounds. The other will rise without bounds, and at some point must be capable of observation in the macroscopic world, no matter how small $\hbar$ is.   If such a large uncertainty has not been observed in the macroscopic world, how can this be reconciled with the idea described above?
From what I understand, the  states that there is a fundamental natural limit to how accurately we can measure velocity and momentum at the same time. It's not a limit on equipment but just a natural phenomenon.  However, isn't this just an observational limit? There is a definite velocity and momentum, we just don't know it. As in, we can only know so much about the universe, but the universe still has definite characteristics.  Considering this, how do a wide range of quantum mechanical phenomena work? For example, quantum tunneling - its based on the fact that the position of the object is indefinite. But the position is definite, we just don't know it definitely. Or the famous light slot experiment? The creation of more light slots due to uncertainty of the photon's positions?  What I am basically asking is why is a limit on the observer, affecting the phenomenon he is observing? Isn't that equivalent to saying  because we haven't seen Star X, it doesn't exist? It's limiting the definition of the universe to the limits of our observation!
I've always managed my iPhone/iPad/iPod Manually, I recently updated to iTunes 11 and now I can see no way to get my music onto my device.  I used to be able to just drag songs from my library to my device, now there is seemingly no way to do this.  I can view the music on my device by clicking on it on the top right corner of iTunes, but I can't seem to get to a state where I can drag music from my computer onto my device.  I'm using iTunes 11.0.1.12 for Windows if that makes a difference. How do I create tools with multiple properties? I'm trying to create an item that can break certain blocks, but also has a colored name in 1.13.2   Here's the command I'm using.  /give iAugust minecraft:shears{display:{Name:"[{\"text\":\"Arcane Shears\",\"color\":\"aqua\",\"italic\":false,\"bold\":false}]CanDestroy:[minecraft:iron_bars]"}}   But it only has a colored name, and it can't break specific blocks. What are copy elision and return value optimization? How to do relative imports in Python? Imagine this directory structure:  app/    __init__.py    sub1/       __init__.py       mod1.py    sub2/       __init__.py       mod2.py   I'm coding mod1, and I need to import something from mod2. How should I do it?    I tried from ..sub2 import mod2 but I'm getting an "Attempted relative import in non-package".  I googled around but found only "sys.path manipulation" hacks. Isn't there a clean way?      Edit: all my __init__.py's are currently empty    Edit2: I'm trying to do this because sub2 contains classes that are shared across sub packages (sub1, subX, etc.).  Edit3: The behaviour I'm looking for is the same as described in  (thanks John B) Find the infinite sum $\sum_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $ I am facing a problem, where I have to find the partial sum of a sequence/sum and with that, the infinite sum of the sequence.  $\sum_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $   The problem here is that I don't know how to proceed. I would be thankful if someone would steer me in the right direction. undefined reference to `__sync_val_compare_and_swap_4' error at compilation, using gcc 4.1.1 and 4.2.0 for Sparc v8 target How do I reenable Quack Overflow if I disabled it? Term for things like "naughty step" where the step is not what is naughty Can anyone remind me of the grammatical term for the apparent misapplication of an attributive adjective, as in the phrase "the naughty step" (where it is not the step itself that is naughty but the person consigned to it)? I've followed this tutorial to install Ubuntu 15.10:    After restarting my computer I got to the grub menu and chose Ubuntu. Shortly after that I got this error:  /run/lvm/lvmetad.socket: connect failed: No such file or directory WARNING: Failed to connect to lvmetad. Falling back to internal scanning.   These messages keep adding up on a black screen every second. After a while,  I get access to the initramfs ash console.  what am I doing wrong? Is it possible to dual boot two OS's at the same time? Is there a rule of thumb for objective questions asked out of curiosity? Will the Lee 100mm filter holder work with a Samyang 14mm autofocus lens? Will this  work with a ? Which adapter ring would I need to buy for it? Thank you, and apologies if any of this comes across as confusing - I'm very new to filters and what-not. I posted on another account yesterday and received some very useful tips, but had to remove it as it was a duplicate account causing me login issues. Thanks, guys! How to sum $\sum_{x=0}^{N-1} \cos{\left( \frac{2\pi x}{N} \right)}^{2}$? I've tried solving it, but I'm not familiar with these kind of progressions and I couldn't get to a result. Also, I've found that the result is just $N/2$, but I don't get why would that be the answer, as it doesn't work for $N=1$ or $N=2$. Appreciate your help :) Is there any parameter (in terms of physical quantities such as mass, length, charge...) which can be used to decide when to treat a system quantum mechanically and not classically? Use /testfor to make a custom command Basically, I'm trying to recreate the Faction plugins /f map in my single-player without mods as my PC doesn't run them very well. (I know it sounds strange.) I am trying to use the /testfor to test if I have written '/f map' in chat, and if I have, it would show me a custom generated map. I don't know how to word this better xD Essentially what I want is for it to test if I have written a command in chat, and if I have, display something. How to convert image of map into vector format? How can I convert string to datetime with format specification in JavaScript? Sorting citations using \cites command in biblatex I am using biblatex for citations and bibliography. Now I often have lists of multiple citations, for which biblatex has the \cites command. Now I can get citations to automatically sort if I don't want page numbers, but I cannot get it right with page numbers.  What I want is all citation ordered chronological (oldest first). Is this possible, or must I just do this by hand?  Here is an example.  \documentclass[11pt,oneside]{memoir}  \usepackage[     style=authortitle,     useprefix=false,     maxnames=2,     firstinits=true,     sortcites=true,     uniquename=init,     abbreviate=true,     backend=biber,     sorting=ynt ]{biblatex}  \begin{filecontents}{jobname.bib} @book{tom1,   author = {Author, A.},   year = {2001},   title = {This book is from 2001},   shorttitle = {2001}, } @book{tom2,   author = {Author, A.},   year = {1999},   title = {This book is from 1999},   shorttitle = {1999}, } \end{filecontents}  \addbibresource{jobname.bib}   \begin{document} This one is corrent.\footnote{\Cites{tom1,tom2}.} This one is corrent.\footnote{\Cite{tom1,tom2}.}   This one is incorrent.\footnote{\Cites{tom1}{tom2}.} This one is incorrent.\footnote{\Cites[1]{tom1}[12]{tom2}.} \end{document} I've been googling for some time now, and can't find the manual for the TikZ library calc. All I see is people using it. Where can I find the manual or some info?  Is it the same as the LaTeX package calc? The latter doesn't seem to mention TikZ in the manual. How to download all required Ubuntu drivers Is there a package of Ubuntu drivers as driver pack solution? I tried to search for it, but I did not find it. If there is, how can I easily get it?