I'm reading this paper, and it states that we can define a set of lines on $\mathbb{R}^2$ by $$\mathbb{L}=\{[(a,b,c)]\subset\mathbb{R}^3|(a,b,c)\in\mathbb{R}^3,\,a^2+b^2\neq0\}$$
@HDE226868 Observe that $a^2+b^2 \neq 0$ means just $a\neq 0 \vee b\neq 0$ for real numbers. Now, $[(a,b,c)]$ describes the line $y = \frac{a}{b}x + c$ where $y =c$ if $b= 0$.
@ACuriousMind Ohhhhh. . . I had been trying to prove it from the definition of an affine Grassmanian, i.e connecting the basic description with other properties. I can't believe I overthought it.
@HDE226868 It is sometimes quite challenging to translate abstract mathematical definitons back into something that makes sense, don't worry about it :)
@ACuriousMind I need to write an email to Straumann asking him why these references either A) don't exist, B) don't show at all what they should, C) reference nonexistent chapters
Tell me about it, I almost wrote Witten an email about why the heck he thinks "It can be shown" is an appropriate phrase to use when no one has ever shown that :D
I eventually figured it out, but it was infuriating
@TerryBollinger Apparently FLRW is uniquely fixed by requiring that group of isometries leaving the velocity of a comoving observer fixed contains SO(3)
@TerryBollinger I joined FaceBook under protest, but I discovered that I can keep track of my niece's emotional state by checking once a day. As in: she was posting "not a morning person" stuff and then "my co-workers are idiots" kind of stuff, then "here is whts a chick wants from a guy" stuff then "he broke my heart, I'll dig his out with a rusty spoon" stuff."
This chat room reminds me of that at times.. Only with finer granularity.
@HDE226868 The reasons for various sizes and frequency ranges in information transmissions systems is fundamentally an question of electrodynamics.
The practical aspects are important parts of many experimental physicists' daily lives.
In particular, the choice of coaxial wire as opposed to other shapes and topologies of conductor comes down to interesting questions of the mode structure of those various topologies.
This is the sort of thing that can be far more satisfactorily explained via a physics oriented discussion as opposed to a typically "engineering" style discussion.
As I've argued before, if someone posts a question like that here, they probably want the physics type approach. We should respect that rather than discouraging it.
@DanielSank Also the cross-talk properties. Coax has vanishing cross-talk but it is complicated and expensive compared to, say, twisted pair. SO then you ask how to reduce the cross-talk in twisted pair and maybe come to mutually prime winding numbers or some such.
I'm in particle physics. We often need to run hundreds or thousands of signal from the detector to the DAQ (less so these data, as a lot of CPU has been pushed at of the counting house and into the machine, but still). Hundreds of cables lying side by side of tens or hundreds of meter. Signal transmission between the cables is a risk.
Twisted pair reduces the risk a little, because now it is dipole--dipole, but over long runs it still matters.
You'd be delightfully surprised at how many really complicated things in physics can be understood very intuitively in the context of signal processing.
@DanielSank It's contain some components faster than that, but I suppose that's a good center for the band.
I'm not actually a signal guy. Someone else always worried about those issues (Big Science means you end up specialized), but I've sat through talks about many times.
@0celo7 Lots of people turn in drafts of various sections and a committee dumps most of the work on a post-doc. Then edits and sends them back and send the result out for collaboration approval.
I've been wondering if we should do that too. Our author lists are like 20 folks long. I wonder if we should just throw up a web page called martinis_group_authors.org.
You need a construction crew, a software army, instrumentalists, theorists, and people to make sure all those people's work goes in a coherent direction.
The quantum Zeno effect (also known as the Turing paradox) is a situation in which an unstable particle, if observed continuously, will never decay. One can "freeze" the evolution of the system by measuring it frequently enough in its known initial state. The meaning of the term has since expanded, leading to a more technical definition in which time evolution can be suppressed not only by measurement: the quantum Zeno effect is the suppression of unitary time evolution caused by quantum decoherence in quantum systems provided by a variety of sources: measurement, interactions with the environment...
@bolbteppa : I have seen some of them, and I'm not impressed. Leonard Susskind is the guy who will tell you that the infalling elephant goes to the end of time and back and is in two places at once.
user54412
8:56 AM
Finally got my code paper out. Now I can actually start doing science.
user54412
@ACuriousMind I put in as many indices as I could, just for you ;)
I saw you guys have a lot of awesome CTC discussion in the past 3 days. I wish I will be able to catch up later. My brain resources is currently 99% on my honours project, in particular some spectroscopy stuff
"Solutions of the Cauchy problem for the wave equation on a non-globally hyperbolic spacetime, which contains closed timelike curves (time machines) are considered. It is proved, that there exists a solution of the Cauchy problem, it is discontinuous and in some sense unique for arbitrary initial conditions, which are given on a hypersurface at time, that precedes the formation of closed timelike curves (CTC)."
"We conjecture that this well-posed nature of the initial value problem is true for initial data on a spacelike hypersurface (but not necessarily of data on $\mathcal{I}^-$) not only for our specific wormhole spacetimes, but also for any 4-dimensional, asymptotically flat, classical spacetime with topology of the form $R \times S - {p}$, where S is a closed 3-manifolds,
and we also conjecture that in such spacetimes the initial value problems is well posed, in the same sense as fpr $\Phi$, for all other non-interacting (linearly superposing) fields, classical and quantum"
@ChrisWhite you're joking aren't you? Now you begin answering email about bugs, fixing bugs, and email about how do I install dependency X for your program?