@0celo7 It's just the semi-direct product of the general linear group with the translations, just like the Poincare group is the semi-direct product of Lorentz with translations.
@Slereah I don't care whether it's "gauge" or not, I want to know what exactly you mean by that statement. Do you mean that a diffeomorphism $M\to M$ is equivalently given by a smooth function $M\to\mathrm{GA}(4,\mathbb{R})$?
Something about how for all 1-forms $\sigma$, $\mathcal L_{\xi} \sigma = d(\xi \sigma) + \xi d\sigma$ and the translation is defined by $\rho^a = \xi e^a$ and the rotation by $\tau^a = \xi \omega^a$
not quite sure what $\xi$ is supposed to be wrt the diffeomorphism
@0celo7 As a physicist who's learned some real analysis you just have to know when to translate between $y=C x+O(x^2)$ ($x\to 0$), $dy/dx=C$ ($x=0$), and $dy=C dx$ ($x=0$).
@0celo7 Sure. Take for example that one passage in Arnold of the definition of a functional derivative. The action has units so it means nothing to be small, but you can define an infinitesimal change in action.
The real analysis way to do this is to tack on an $O(h^2)$, with some weirdo epsilon delta meaning
Mathematicians will do the "For all epsilon there exists a delta such that blah blah blah", which is the rigorous way to do it.
Physicists say "it's an infinitesimal. Deal with it."
So just translate between the two
adding a new definition of $+O(h^2)$ wherever needed.
@0celo7 I can always find a smaller lambda to make the statement $h_{\mu \nu}\lambda \ll 1$ true. That's the gist of the "for all epsilon there exists a delta" thing inside the $+O(\lambda^2)$.
@Slereah "To first order", a diffeomorphism is $x\mapsto x+\epsilon \xi(x)$ for $\xi$ a vector field. (The Lie algebra associated to the group of diffeomorphisms is precisely the Lie algebra of vector fields)
Genealogical link between the Queen of England and Mohammed
Via Spanish monarchy, not too surprising
Apparently via Zaida of Seville, the muslim mistress of Alfonso VI
Well, via 5 different lines even
Then again from what I've read, you are basically related to everyone from 1500 years ago in Eurasia
"A descent from Genghis Khan was proposed by Iain Moncreiffe in Royal Highness that requires descent of Thocomerius, Voivode of Wallachia, from Jöchi (presuming parentage from Mengu-Timur, possibly identifying Thocomerius with Toqta, Khan of the Blue Horde[11] or one of his brothers), which is controversial. However, further on, this connection leads to Francis, Duke of Teck (shown in the first chart) through the half-brother of Dracula as proposed by Moncreiffe and Gerald Paget."
Oh god
The Queen is a vampire
Oh Dracula
Such style
it would be fun if they made a Dracula movie where Dracula actually looked like Vlad the Impaler
I know it is not measuring, but I am so seduced to think that hat X has a physics meaning / is a physics process, but I have no idea what exactly it is
When you want to figure out what happens when you measure an observable, the first thing you do is figure out what happens when you act on a wave function with the operator corresponding to the observable
so if I measure a wavefunction it collapse, and then I immediately measure the collapsed wavefunction again, the second action can be thought as the hat X?
See, I had the opposite experience. When they taught us wave functions first, and how we should be thinking of differential operators in linear algebra terms, I found all the calculus stuff to be extra conceptual baggage that got in the way of understanding.
I didn't find quantum intuitive until I saw the linear algebra approach.
Yeah, but I guess what I'm saying is it's a matter of what you emphasize. To me, the fact that QM is about linear operators and Hilbert spaces etc., regardless of whether you're talking about wave functions in some continuous space, is at the heart of it.
And you're not always talking about wave functions. Feynmann manages to get a lot of mileage out of a two-state abstract system.
I heard about a QM book that did everything in terms of density operators, and never asserted that a particle has a quantum state. I never located the book, but it sounds like an interesting approach.
For most serious physicists this site is of no use because 95% of the answers and comments are written by the above mentioned insane man.
However, also they are pure rubbish, the comments of D. T. Sank can mislead high school students who can fail exams because of this monster determined to c...
@Danu &all Good morning. I am not trying to be good friend here. I am just trying to understand things. I think the situation is now, that so far no one has explained the mechanism of Gravity. Only the understanding of it's influences has developed further. This simply means that we should try keep all the options open. Otherwice Le Sage can become new Erastothenes. In some 2000 Years.
Let $P_{SE}$ be the set of all physics stack exchange users, denoted as couples $(u,r)$ where $u$ is the user name, and $r$ is the reputation. The famous $9\cdot 10^3$ relation $\sim$ tells us that $(\forall (u,r)\in P_{SE})(\forall (v,s)\in P_{SE})(u,r)\sim (v,s)\leftrightarrow r\geq 9\cdot 10^3 \land s\geq 10^3$. Of course all the members of the equivalence class $[(DS,9,128)]$ can be thought as equivalent, i.e. the same person.
Therefore ACM, JR, DZ, DMCK and so on are all equivalent to DS, i.e. DS itself.
I once trying to approach the issue of elementary or GUT magnetic monopoles this way, but so far the only thing that can serve as a counterexample is if isolated fractional charges are detected, as according to this PSE discussion: http://physics.stackexchange.com/questions/169903/experiments-or-phenomenon-to-falsify-the-existence-of-monopoles
@yuggib Oh, didn't see your correction. But then your proof doesn't correctly reflect the insanity at work here, users with less than 9k reputation have been claimed to be socks.
@ACuriousMind And I'm reasonably sure various people over the years have written scripts to alert them if keywords are mentioned in chat.
So, @ChrisWhite and all others, where should I look for any ready-made scripts to install if I want to be alerted for if certain words are mentioned on a certain website?
I don't think you can do that for any website. SE offers an API for devs, I think, so there's a premade interface for obtaining the chat messages (and other posts) for those scripts here. I could be wrong, though
Oh. No, I was trying to pose this as a more general question having applications outside of SE, e.g. for setting up my own alerts for certain stuff posted on a website.
e.g. if a website says - Plumber wanted, and if I'm a plumber, I would like to be alerted. (Giving a stupid lowly example, that can be generalized to job-hunting, post-doc hunting etc.)
http://physics.stackexchange.com/questions/220296/what-is-the-medium-of-probability-waves That question reminds me of Something:
As you noted, photons do not need a medium, yet are an electromagnetic wave. Ergo, waves do not need a medium to propagate. In a vaguely similar way, probability is not a physical thing, and does not propagate. Yes, quantum mechanics seems spooky at first - relax and play with it and you will get the feel for it. – Jon Custer 7 mins ago
=========== So when we say probability current, it is just a mathematical formalism, and there's really nothing about a flux of…
For most serious physicists this site is of no use because 95% of the answers and comments are written by the above mentioned insane man.
However, also they are pure rubbish, the comments of D. T. Sank can mislead high school students who can fail exams because of this monster determined to c...
