I have a question about the following passage from this article:
Moschidis imagined standing in the middle of AdS space-time, which would be like standing inside a giant ball whose edge or boundary lies at infinity. If you sent a light signal from there, it would travel out and reach the boun...
@MohamedObeidallah When we say that electrons are fundamental particles (in the Standard Model of particle physics) that just means that they aren't composed of simpler particles. In contrast, a proton isn't fundamental because it's composed of quarks.
@MohamedObeidallah Saying that a particle is fundamental does not imply that it can't be created, destroyed, or transformed. However, any reaction that creates, destroys, or transforms particles must obey various conservation laws. Here's an example of a transformation from Wikipedia, which shows what happens when a nucleus captures an electron.
"The leading-order Feynman diagrams for electron capture decay. An electron interacts with an up quark in the nucleus via a W boson to create a down quark and electron neutrino. Two diagrams comprise the leading (second) order, though as a virtual particle, the type (and charge) of the W-boson is indistinguishable."
So in this weak interaction, an up quark is transformed into a down quark, and an electron is transformed into an electron neutrino. Or we could say that an up quark & electron are destroyed and a down quark & neutrino are created.
Note that you can't just have an up quark turn into a down quark, or an electron into a neutrino. Those reactions would break conservation of electric charge. But the combination of the two reactions is permitted.
@ACuriousMind Went to bed and missed your response, didn't realise it was different from regular potential, thanks a lot for your help again. Hope you don't mind the ping while you're not here.
Hey! Is anyone here? I'd like to discuss if someone here knows of how to possibly shift signals without circular shift in matlab. I guess a requirement for fft is that it assumes that it's been given one period of the signal in it's vector? and shifting longer than the time vector with ifft(exp(iomegatau)*fft(signal(t)) wraps around the signal. However, I'd like to not have it wrap around
I guess the problem isn't unique to matlab however
Did i describe the problem well enough btw? Did you "get" the issue? (just asking, wrote a non-coherent question about this in mathematics chat and they didn't get me)
Yeah more or less. I have a time-vector and then a number of different delays i need to execute, but some of the delays are longer than the extent of the time vector, thus a "new" pusle comes in from the other side, which i don't want.
Maybe I could pad a longer signal/time-vector, shift that one, and then cut out the center window ?=
Just use it and remove the frequency associated with the time of the array.
I guess you could squeeze the signal in towards the middle of the array, though that either reduces your frequency resolution or requires a larger array.
A pair of hexagonal lattices with one scaled by the square root of a rational number $r = \sqrt{\frac{m}{n}}$ and then rotated will produce a variety of different coincident points.
For the first lattice let
$$x, y = i+\frac{1}{2}j, \ \frac{\sqrt{3}}{2}j$$
and for the second
$$x, y = r\lef...
I am getting crazy with the QFT book of Itzykson & Zuber. In Eq. 5-173 they have a bunch of terms which are non-zero when the 4-momentum q satisfies $q=pn - (p1+p2)/2$. The momentum $p1,p2,pn$ are time-like. They say that the two terms do not contribute outside a region bounded by the two hyperboloid sheets, that they draw in Fig. 5-8.
They say that these hyperboloid sheets correspond to two different masses $M_+$ and $M_-$ but they don't provide the definition of these masses. Moreover, I have a counter example in 2D, where there are no hyperboloid sheets. For example, $p_n = (1,0), p_1 = (4,3), p_2 = (2,1)$. In this case, $q^2 = 0$ is null. what the hell?
Also, they say that the hyperboloid sheets are centered at $\pm 1/2(p_1+p_2)$ which has no sense since $p_1$ and $p_2$ are vectors... are they talking about the modulus?
Look, I am uploading a picture
This is their Fig. 5-8 instead
These seven lines under Eq.5-173 are driving me crazy
Note that the y-axis there has $q_0$, so I think they're saying the centers of the hyperboloids (the tips of the triangles there) are $(0,(p_1 + p_2)/2)$ and $(0,- (p_1 + p_2)/2)$.
What I think they mean is that the hyperboloids are really higher-dimensional hyperboloids when you draw them in the full $(|q|, q_0,q_1,q_2,q_3)$ space. In that space the center would lie at the vectors they write, but I agree it's sloppy/confusingly worded
Their $\delta$ functions do not vanish when $q$ has a chance to fulfill $q = \pm ((p_1 - p_2) / 2 + p_n)$
And when $p_n \neq 0$, then you get additional term that correspond to a mass (because the mass hyperboloid of a massless particle is the triangle, so the deformation can be interpreted as adding mass)
I don't quite understand what your example is supposed to do - in your case, $(p_1 + p_2)/2 = (4,3)$, so they're not centered at zero
@Slereah if you always keep MTW on one side of your house the weight will make the house gradually tilt to this side. Put a copy of the PDG on the other side and it will restore the balance.
@apt45 I think I know what's going on: They wrote $q - (p_1 + p_2)/2 = p_n$ and squared that. This is the equation for a hyperboloid with mass $p_n^2$, shifted ("centered") by $(p_1 + p_2) / 2$.
(In more detail: $q^2 = m^2$ is the usual equation for a mass hyperboloid. Doing $x\mapsto x + a$ is a shift operation that must also shift the submanifold described by this equation by $a$, so $(q - a)^2 = m^2$ is the equation for the same hyperboloid shifted by $a$
But crucially, in the shifted hyperboloid, the "mass" $m^2$ is not the mass of $q$! A "hyperboloid of mass $m$ centered at $a$" does not consist of vectors with mass $m$.
So your example shows nothing - sure, $q^2 = 0$, but the "mass" they're talking about is not $q^2$, so the shape described by the equation is still a hyperboloid with non-zero "mass".
They explain it very confusingly and I think it's poor terminology, but I'd say there's nothing wrong there.
@apt45 Different people look for different things. Weinberg is excellent if you're looking for a comprehensive and comparatively rigorous treatment of QFT that explains most of its steps in exhausting detail (at least at first). Books like I&Z are more "casual", and many people find their intuitions and explanations nicer than the forest of indices Weinberg's equations develop into.
@abhas_RewCie Do not ping random people to answer your questions, especially not when they're just poor photos of exercises. You've been told this before.
@JohnRennie Okay, I'll come to you next time to learn more about Baloch waves, currently, a rough solution will work (specially (d)), you may leave other bits, in case you know the solution...
Hey guys, quick question, practically speaking how do electromagnet strengths compare with rare earth magnets. I dont often see permanent magnets using a unit thats eaasy to compare with electromagnets, or they dont provide strength info per unit mass
@ACuriousMind well technically youd hit the curie limit before that most likely
or was it called curie temp
curie temp
but how do you take the magnetic ffield produced by something like a solenoid and compare that with the magnetic forces characteristic of magnet. Like there should be some kind mass related term for a magnet shouldnt there, but you just see people throw out "this neodynmium magnet is ~1T"
@ACuriousMind I understand what you said. I am still confused by the following thing. If I take $q=p_n -(p_1+p_2)/2$ and square it, I get $q^2 = p_n^2+(p_1+p_2)^2/4-p_n\cdot(p_1+p_2)$. If I draw this contour, I get the orange lines. Instead, If I plot $(q+(p_1+p_2)/2)^2=p_n^2$ I get the blue line. What am I misunderstanding here?
I think I am missing something trivial. The two equations should be consistent with each other, somehow, right?
consider that you initially have an equation that determines $q$ uniquely - it's not an equation with a whole range of solutions, there's *one specific $q$" that fulfills it
yes, I understand this. But then, why I should I trust that their quantity C(q) vanishes in the region outside the blue line but still below the orange line?
I&Z are interested in the blue graph because when you do this for the lowest $p_n^2$ of all the $p_n$, then (for fixed $p_1,p_2$) you know that all the other hyperboloids for the other $p_i$ have larger "mass"
Therefore their blue shapes lie "inside" the hyperboloid for the lowest $p_n$, and therefore no possible $q$ lies outside of it.
Hence $C(q)$ vanishes outside of this hyperboloid for the lowest $p_n$.
yes, I understand their logic. I am trying to understand why what I was doing is not correct. Which mistake I would have made by choosing the orange line?
but you wouldn't have been able to make a nice statement about where the lines for all the other $p_n$ lie, so it wouldn't have told you anything interesting about $C(q)$
I don't use the review queues - they're not that useful for mods
user434058
@ACuriousMind Does anybody ever do that? :P I always thought that Meta was meant for scrounging up already asked questions since every bug that you face would have been discussed about in Meta before.
user434058
@ACuriousMind So you guys have your "VIP review queues"? ;-)
@FakeMod Sort of, but I more meant that e.g. the close review or LQ review queue is not something we're supposed to be doing (since our votes are binding)
user434058
@ACuriousMind Yeah, sure, but not me :-) At least, not now.
user434058
@ACuriousMind Yeah, binding votes need to be handled with special care.
user434058
Is there any way to see how many posts did you VTC or "Recommend Deletion" were really deleted? In other words, the accuracy of your reviewing. SEDE might help, but I don't know how...
@Dair Here's a cute integer thing I noticed a few years ago while messing around with square roots and Pell"s equation. Obviously, 18 - 13 = 5. Not so obviously, 18^2 - 13×5^2 = -1. That is, 18/5 is a good approximation for sqrt(13). I suppose I should do a search to see if there are other numbers with that pattern...
There are other number pairs apart from (18, 13) with that property.
A pair of hexagonal lattices with one scaled by the square root of a rational number $r = \sqrt{\frac{m}{n}}$ and then rotated will produce a variety of different coincident points.
For the first lattice let
$$x, y = i+\frac{1}{2}j, \ \frac{\sqrt{3}}{2}j$$
and for the second
$$x, y = r\lef...
