Does a solid suspended in beaker filled with Air increase the weight of the beaker?
Which way does the scale tip?
Someone who just thinks they know what they're talking about What is a word or phrase that means a speaker (or writer) is talking about something they know very little about, but they think they know more than they do?  An example: If you read diet message boards, you get dozens of people saying ‘Eat 6 small meals a day,’ or ‘Eat 3 big meals, but don’t snack,’  or ‘Eat more/less protein/carbs/fat.’ Each person is sure they are knowlegable enough to give good advice, but real experts(dieticians or researchers, for example) are rare.  I want a word to describe this attitude.  Bullshit is close, but someone bullshitting usually knows they aren’t an expert, they just want to convince the listener they are.  Also, I’d prefer something politer than bullshit. A projection satisfying $\| Px \| \leq \|x\|$ for all $x$ is an orthogonal projection How to prove that if $V$ is a finite dimensional inner product space and $W$ a subspace of $V$, if $P$ is projection map ($P^2=P$) having $W$ as its range and is such that $\|Px\| \leq \|x\|$ for all $x \in V$, then $P$ is orthogonal projection of $V$ onto $W$. I understand we cannot state with arbitrary precision the position and momentum of a micro-particle as we superpose infinite waves to create a wave packet at the exact position of the particle and hence cannot say which wave is corresponding to its momentum. This is theoretically said. Also some people say that measurement of one disturbs the other and some say it's reality.  Firstly, the theoretical explanation: why should I consider that a wave out of many superposed will give us the momentum or position? We might use another single wave which is not sine in nature and might get the results. Or why won't a single sine wave suffice? This all considers the micro-particle as wave because of de Broglie.  Secondly, the practical thing seems legit.  Thirdly, the electron must have some kinetic energy and position. It is who we are measuring and can't get it exact so why blame the electron as in theoretical concept. How we quantify the uncertainty, it must depend on the measuring device and various other factors.  I might need to edit this post based on your answer so that I can explain more clearly my thinking.  Edit: From here is what gets the measurement problem:        Text: Imagine that you're blind and over time you've developed a technique for determining how far away an object is by throwing a medicine ball at it. If you throw your medicine ball at a nearby stool, the ball will return quickly, and you'll know that it's close. If you throw the ball at something across the street from you, it'll take longer to return, and you'll know that the object is far away.   The problem i­s that when you throw a ball -- especially a heavy one like a medicine ball -- at something like a stool, the ball will knock the stool across the room and may even have enough momentum to bounce back. You can say where the stool was, but not where it is now. What's more, you could calculate the velocity of the stool after you hit it with the ball, but you have no idea what its velocity was before you hit it.   This is the problem revealed by Heisenberg's Uncertainty Principle. To know the velocity of a quark we must measure it, and to measure it, we are forced to affect it. The same goes for observing an object's position. Uncertainty about an object's position and velocity makes it difficult for a physicist to determine much about the object.   Edit: After seeing this answer one of my doubts is very well cleared, the other answers are also written and helpful:        Text: There is a definine velocity and momentum, we just don't know it.   Nope. There is no definite velocity--this was the older interpretation. The particle has all (possible) velocities at once;it is in a wavefunction, a superposition of all of these states. This can actually be verified by stuff like the double-slit experiment with one photon--we cannot explain single-photon-fringes unless we accept the fact that the photon is in "both slits at once".So, it's not a knowledge limit. The particle really has no definite position/whatever. UISearchDisplayController - how to preload searchResultTableView can I put a double 50 amp pole in a 100 amp box What is the correct pronunciation of TeX and LaTeX? Is it tex(tech)? Or Is it tex(like touch)?  Lay-TeX? or La-TeX?  Should I use TeX pronunciation in LaTeX? Implicit conversion issue in a ternary condition Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$ So the question is really hard I think. I tried using a simple way by calculating the probability of each combination that makes a sum divisible by six, but it would take forever. Does anyone have any ideas?  Suppose that we roll a six-sided die ten times. What is the probability that the total of all ten rolls is divisible by six? File access time not updating in ubuntu 12.04 Eeeek! Code blocks are misbehaving! So code blocks in questions and answers on the android app (inline included) seem to be scared of me putting my finger in them. When I poke them, they only move over two columns!  (For clarity, these are the code blocks that overlap the TextArea view because they've been eating too much)  The intended behaviour here is that when I press my finger into a code block, the touch event should register a drag; at current, I try to scroll inside a code block and I end up switching to question or answer view instead, over and over.  EDIT:  Something tells me this is status-bydesign because the text is deliberately cut off (probably inviting you to click on the code block and expand it; UX Decision?): When I visit the reputation tab of my profile, I see a lot of stuff. I can make out some of it, but not all.   What do all the event types mean? Why do some events show an odd reputation gain or not show any reputation change at all? Why are some events sometimes highlighted in yellow? My reputation suddenly dropped, but I don't see anything. What happened? Why do some events disappear from my reputation history? Something special about energy eigenstates when it comes to time evolution? A particle is subject to an infinite square well potential with  $$V(x)= \begin{cases}  0  &amp;   −a \lt x \lt a\\   \infty &amp;  \,\,\,\,\text{otherwise} \end{cases}$$  At a time $t=0$ its wavefunction is given by $$\psi(x, t=0)=\frac{1}{\sqrt{5a}}\cos\left(\frac{\pi x}{2a}\right)+\frac{2}{\sqrt{5a}}\sin\left(\frac{\pi x}{a}\right)$$       (a) What are the possible results of an energy measurement at $t = 0$, and with what probabilities?     Re-writing the terms in $\psi(x,t=0)$ as $$u_1(x)=a^{-1/2}\cos\left(\frac{\pi x}{2a}\right)\qquad \text{&amp;} \qquad u_2(x)=a^{-1/2}\sin\left(\frac{\pi x}{a}\right)$$ such that $$\psi(x,t=0)= \frac{1}{\sqrt{5}}u_1(x)+\frac{2}{\sqrt{5}}u_2(x)$$ with energies $$E_1=\frac{\hbar^2 \pi^2}{8ma^2}\qquad \text{&amp;} \qquad E_2=\frac{\hbar^2 \pi^2}{2ma^2}$$ and probabilities $$P(E_1)=\frac15 \qquad \text{&amp;} \qquad P(E_2)=\frac45$$       (b) If no measurement is performed, what is the wavefunction $\psi(x, t)$ at all times $t$? What are the possible energies and their probabilities if a measurement is first performed at time $t$?     At a time $t$ the wavefunction is given by $$\psi(x, t=0)=\frac{1}{\sqrt{5a}}\cos\left(\frac{\pi x}{2a}\right)\exp\left(\frac{-i E_1 t}{\hbar}\right)+\frac{2}{\sqrt{5a}}\sin\left(\frac{\pi x}{a}\right)\exp\left(\frac{-i E_2 t}{\hbar}\right)$$    The problem is that I cannot answer the second part of the question (b).    The answer states that:      Because the two terms are energy eigenstates, the relative probabilities do not change and are as in the previous part.     I have some questions about the above statement: why does an "energy eigenstate" mean that the probablities don't change with time? Or, put in another way, does a "momentum eigenstate" (for example) have constant relative probabilities when measured at any time?   The answer seems to be implying there is something special about energy eigenstates when it comes to time evolution. The eigenvalues of energy measurements don't seem to change regardless of how many times you measure them, and no matter how long you wait until you measure them. I'm not sure if this is the case, but could someone please explain why all quantum operators (except Hamiltonian) do not exhibit this behaviour. Look at the profile page of , who has just "lost" 100k reputation and all their bronze badges, because of this broken design.  Shouldn't the primary usercard be kept intact no matter how other elements grow?  P.S. So many design bugs these days, did SE do a large CSS refactory?  P.P.S  that squeezes the right pane ( to reproduce) Why does no physical energy-momentum tensor exist for the gravitational field? Starting  with the Einstein-Hilbert Lagrangian  $$ L_{EH} = -\frac{1}{2}(R + 2\Lambda)$$  one can formally calculate a gravitational energy-momentum tensor   $$ T_{EH}^{\mu\nu} = -2 \frac{\delta L_{EH}}{\delta g_{\mu\nu}}$$  leading to  $$ T_{EH}^{\mu\nu} = -G_{\mu\nu} + \Lambda g_{\mu\nu} = -(R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R) + \Lambda g_{\mu\nu}. $$  But then, in the paragraph below Eq. (228) on page 62 of  paper, it is said that this quantity is not a physical quantity and that it is well known that for the gravitational field no (physical) energy-momentum tensor exists.  To me personally, this fact is rather surprising than well known. So can somebody explain to me (mathematically and/or "intuitively") why there is no energy-momentum tensor for the gravitational field? Changing parameter values according to other parameter choice in Processing script using QGIS 3? Can we search posts by number of comments? How can I see the history of stories I've read on Apple News? Sometimes I'll be interrupted in the middle of reading a story on Apple News and later when I open the app, it didn't save the story I was previously reading. I want to be able to resume reading the article, how can I find it again? Can you trip as part of a Tome of Battle Maneuver? Why is Linux reporting "free" memory strangely?