Fine, but you wrote clearly here that you want your operator to be binary - to take in two vector fields. But in the equation you're feeding it a single vector field, $E_g$.
I am proudly an attention seeker! When I have a non-trivial thought, or want to engage with humans I think might be interested in something I might have to say,
Anonymous
@YuzurihaInori Vector operators are not vectors...
I "seek out" their help and attention. I ask and expect a (polite) response. I want the "attention seeker
" terminology to stop as it seems to me a dirty trick used to attempt to prevent people from opining and conversing. At any rate, the conversation bothers me because I think the Physics community has a general tendency to . . . well . . . to put it colloquially "think some kind of way". It's completely fine to ignore people (actually not really) but name calling sucks.
My question is how should I respond to this kind of thing? It really pissed me off because , I don't even care about that kind of attention. I mean I've lived!!! I don't care for . . . . sigh
@YuzurihaInori well don't follow in my footsteps, I'm strange , lol but you may observe at a distance :P
Anonymous
@Cows SemiC just pointed out that you were writing quite a few long (including some meaningless sentences) aimed at people who were clearly not involved in the conversation. I do agree that calling you an "attention seeker" was a bit over the top, but let's give this line of conversation a rest already.
@Cows You're engaging in a monologue over a public space - that's the chat. That's taking up space where no actual conversation is happening. That's effectively spamming, if not intentionally - which I am perfectly happy to believe.
@Cows For the record: Pinging random people with aimless questions like "You there?" or questions you have no reason to believe they are interested in is considered "spamming the chat" here if done more than once, and especially if you do so after someone asked you to stop.
Responding to people who ask you not to do something here with "This chat is not your property" is not the way to deal with disagreements, there is precedent for that attitude being rather unwelcome here. Instead please figure out what is bothering other people and consider if they do not have a point.
For better or worse, chat is a single stream of messages often containing multiple conversations, which means we all need to use it in a way that does not overly disrupt others' usage of it.
I remember that guy. I enjoyed conversing with him, but he acted viciously when some people pushed back against him posting competition problems here.
@ACuriousMind This goes back to our conversations about what would happen if too many users started using the chat - a desirable alternative for the formality present in the Q&A site counterpart, but renders the chat functionally retarded.
@BalarkaSen Yes, it is feasible for our current volume of chatters if we all try a bit, and I think there would be room for some more, but at some point the concept of a single "bar" for the whole site falls apart. E.g. SO has a model where most large tags/subtopics have their own chat, there's no "general SO chat"
@ACuriousMind you make valid points. I probably should also be more considerate in the chat. I do have a tendency to push the envelop on here. I shall scale back a bit. I do hope people join my convos. I have genuine interests in most things I ask about.
@Cows Maybe this helps to not take it personal: I regularly see posts in here which I'd like to respond to in other circumstances, but which I can't because I'm currently doing something else, or am tired, or already debated a lot and am not looking for another technical conversation, or... Sure, sometimes I'm also genuinely not interested.
Another thing to consider is that conversations will start easier if you offer something: "Talk to me about X!" is very non-specific, and usually will only draw in people currently bored or really excited about X. Asking a specific question about X, or presenting a specific line of thought for discussion usually has a somewhat higher success rate in getting a conversation going.
@ACuriousMind assuming you're either not at work, or are very bored, can you write the EM wave solution of Maxwell's equations in terms of the field strength tensor? If so, does that mean it is in a sense a tensor wave like gravitational waves?
Hi guys, I'm looking into the c theorem and the a theorem (RG flow for CFTs) I have two questions, one about stereographic projections and one about higher dimensional integration The stereographic projection x/a --> tan (x' / a) seems to result into an integral that I can't reproduce, and at some point I have the divergence of a quantity under the integral sign which Zamolodchikov turns into a boundary and a bulk part, but again I cannot reproduce the form of this integral
@YuzurihaInori has been asking about gravitomagnetism, and I was wondering how close the analogy to EM is. If the EM wave can be written as a tensor wave that would make the correspondence very close.
My question is mostly, what should I be looking at if Zamolodchikov;s book doesn't clarify sufficiently (for the second part) and also what's a good start on Stereographic Projections and its application in solving integrals for the first question
@JohnRennie Well, I don't know what a "tensor wave" is but you can certainly write down the solution from knowing the $E$ and $B$ fields since these are just the components of the tensor
It makes sense. Whether it's useful depends on what you want to use it for ;)
Generally the covariant formulation of EM is not terribly useful in solving any actual EM problems, but very useful in getting a simple prototype for covariant field theories
I do know a bit of CFT but I'm utterly lost at RG flows. However, questions about the stereographic projection etc. as such don't really sound as if they are specific to CFT or RG flow, so you could either try to ask them here anyway or ask at math.SE/in the math chatroom
In any case, I intend to spend my day off playing the newly released Pillars of Eternity 2 and not spend overly much brain cells on anything intellectual ;)
@JohnRennie Thanks for taking my topic seriously :) If you don't mind, could you tell me if it is possible to have a momentum continuity equation straight out of einstein field equations? Or sth in terms of like : If energy or mass is flowing out of a region, then the momentum must be flowing out of the region (in analogy with electric charges and currents)
We all know $L^2$ (i.e. magnitude of angular momentum squared) has eigenvalues $0, 1/2, 1, 3/2,...$ in QM. Why then are the legal energy levels for a pair of particles with masses $m$ rotating in $3$ dimensions around a sphere with radius $r=a$ equal to $E_n = \dfrac{\hbar^2 n(n+1)}{ma^2}$for $n=0,1,2,...$??? What happened to the half integers??
@YuzurihaInori To be honest I'm not sure what you're asking. Momentum flow goes into the stress energy tensor, so we normally put it on the right side of the Einstein equation.
@Lozansky The orbital angular momentum (which is $\vec x \times \vec p$, unlike spin angular momentum) does not actually admit the half-integer values.
@ACuriousMind But in the chapter "Angular momentum" (=orbital angular momentum?) Griffiths writes that $L^2 f^m_l = \hbar^2 l(l+1)f^m_l$ for $l=0,1/2,1,3/2,...$ and $m=-l, -l+1,...,0,...,l-1,l$. But then (in the same chapter) he claims that $L^2$ has the eigenvalues $\hbar^2 l(l+1)$ for $l=0,1,2,...$. Since spin hasn't even been introduced, I am wondering how this is consistent?
@YuzurihaInori This is built into GR because the divergence of the Einstein equation is zero, and Einstein's equation equates the Einstein tensor to the stress-energy tensor.
In general, the possible eigenvalues of a quantum mechanical angular momentum are 0,1/2,1,3/2,... But in the specific case of the angular momentum operator acting on complex-valued square-integrable functions, only the integral eigenvalues occur.
The "root cause" of this is that the representation on complex- or real-valued functions is almost "classical", and the half-integral values do not occur classically.
Got it. Well, he mentions the half-integer thing at the end of the section. It's the spin part. The integral ones are the orbital angular momentum solutions.
@AbhasKumarSinha There's plenty of Indian users around here with experience in it, and there's a problem solving room where JEE problems are discussed frequently.
Just like the Pythagorean distance remains invariant in euclidean geometry, the distance formula I mention (I forgot it's name), remains invariant in Minkowskian geometry (flat space-time geometry).
@rob Congrats Prof!😊
@dmckee Any way to read @rob's paper without a nature subscription? :)
Ok .... I'm looking at a student response to a question on a final exam.
I told them that the SHO through a diameter borehole in a uniform model Earth would have a period of 83 minutes and asked for the angular velocity $\omega$.
The intent was that they would find $\omega = 2 \pi / T = 1.26 \times 10^{-3} Hz$.
This student used the formula for the angular frequency of a simple pendulum $\omega = \sqrt{g/L}$ with $g = 9.8 \,\mathrm{m/s^2}$ and $L = R = 6.4 \times 10^6\,\mathrm{m}$ and got essentially the same answer.
I hate it when things "just work out" on test problems.
It's not a coincidence, because for a harmonic oscillator $a_\text{max} = \omega^2 A$, which gives $\omega = \sqrt{a_\text{max}/A}$. And the amplitude is the radius of the model planet...
Indeed later in the problem I ask them to find the maximum acceleration and that it comes to $g$ is suppose to be the big surprise.
But any way, their answer differs in the 3rd digit, but then I rounded all the inputs to two digits so that is to be expected.
I just hadn't noticed that particular way to stumble into the right answer. This student is in for partial credit.
This is madness, how can $P_0$ be positive definite :(
Energy doesn't have to be positive, e.g. Hydrogen atom energy levels, and susy is supposed to 'prove' that energy levels are always $\geq 0$, not assume it :(
Basically they want to figure out what the anti-commutator $\{ Q_a^L, \overline{Q}_{\dot{a} M \}$ looks like, where $L, M$ are the indices for the different susy generators, while $a, \dot{a}$ are their components, it must depend on $P_{a \dot{a}} = P_{\mu} \sigma^{\mu}_{a \dot{a}}$, and then some other symmetric matrix $C$ in $L$ and $M$. They prove that the $C$ matrix is Hermitian after 3.30, so they can diagonalize it,
and they can even re-scale the diagonals so that you only have $\pm 1$'s along it, but it takes positive-definiteness to remove the $\pm$ question, and they seem to do this by ending up with the right hand side being $C^L_M P_0$, but this depends on $P_0$ being positive-definite
I'm guessing they probably assume positive-definiteness as an axiom for this theory
Since they're probably doing the free theory?
I think for most reasonable theories you can assume positive definiteness of the Hamiltonian, or at least that it is bounded from below, in which case you can renormalize it to being positive definite
If it's bounded from below by $P_0 > -C$ you can just redefine $P_0 \to P_0 + C$ and the theory will be the same
@JohnRennie sounds interesting, would like to inquire on that myself further, considering similar directions, not an expert on this, but there seems to be some kind of natural math relation between tensor formulations and waves (of all types)... some of this is brought out in one of my oft cited refs in here Tenev + Horstemeyer... suspect this has been studied somewhere... there is probably some ("more") precise way to formulate your question... would seem to require extended analysis/ inquiry...
@YuzurihaInori Nature's rule is that the paper as accepted by them can't appear on arxiv for six months, so you can read it for free eventually. What's new is that this analysis includes our entire data set, with all the hairy corrections and little details. If you just want to know the big idea, you could look at the commissioning paper from a few years back and substitute the new result from the Nature abstract :-)
@Slereah Wess and Bagger's SUSY book, the book which the above argument is taken from www2.ph.ed.ac.uk/~s0948358/mysite/SUSY%20chapter%203.pdf is probably the one susy book one should read, and probably what will get you to the promised land
You hid the questionable part of claiming that this operator can be "diagonalized" in the implicit claim that the "evident eigenvector" is, in fact, a meaningful vector. As they are a Hilbert basis, infinite sums of the basis of energy eigenstates only make sense if the sequence of their coefficients is square-summable, which your sequence of entries in that vector very likely is not. — ACuriousMind ♦24 mins ago
so SUSY is one of those "this model has an infinite parameter space, so you only get to shrink the parameter space down with experimentations" kind of thing?
SUSY is the only known way of going beyond the Poincare group + internal symmetries by the Coleman-Mandula theorem, and making SUSY local gives you supergravity, i.e. quantum gravity, but it's not renormalizable, but you can fix it with strings to get renormalizable gravity, all other paths have gigantic flaws
Hello, apologies in advance for this sort of a question, but I figured this might be a good place to ask. Does a bad semester in undergrad significantly affect the grad schools one is likely able to attend, if the undergrad is otherwise a fine student (3.5-3.7 GPA at application, research, etc.)?
is there a scale at which SUSY would lose it's usefulness...like...the partner particles get so energetic that it messes with the theory's other predictions in some way or other?
@bolbteppa Not an observation, just something people think we should theoretically be able to explain. Very different from the host of unexplained things particle physicists were observing in their colliders that eventually led to the genesis of the Standard Model
@Slereah Dark matter is probably one I'm willing to fully count, but it's not really in the realm of HEP theory. The muon g-factor I'm a bit sceptical about since I never trust perturbation theory so I'm counting it has half an observation ;)
Yeah, but you can't hold back your blame for Democrats either, who mostly deserve it too, but R's deserve it more, this seems to have 'radical-ized' physicists Michio Kaku and Weinberg and the rest to become popularizers of science :p
He did his own version of it, e.g. the First Three Minutes book and atheism and stuff
They have brought up this collider a good few times in interviews on youtube etc
"It was the turning point of the decline of american exceptionalism. It broadcast to the world that America is not ashamed to be number two. An easy decision to make. Absolutely a no brainer."
Hello, apologies in advance for this sort of a question, but I figured this might be a good place to ask. Does a bad semester in undergrad significantly affect the grad schools one is likely able to attend, if the undergrad is otherwise a fine student (3.5-3.7 GPA at application, research, etc.)?
"The SSC meant a great deal to the theoretical physicist Steven Weinberg, who had independently co-devised electroweak theory in 1967 and shared the 1979 Nobel Prize in physics for his contributions to it. In eloquent testimony to Congress and in elegant prose for the public (in a book called Dreams of a Final Theory, published in 1992) Weinberg emphasized that physicists were "desperate" for the machine because they were "stuck" as physicists in their progress toward what he called
"a final theory" of nature-a complete, comprehensive, and consistent theory that would account for all the known forces, fields, and particles in the universe. "
@JohnRennie I asked a physics prof in my department who is on the admissions committee the exact same question and he said if it's in the first few years then it does not matter as long as your grades in your senior courses and other advanced level courses are good.
(A) You'll need a good story about how and why that happened.
(B) You'll want some good letters of recommendation from people who've spent some time with you after that.
(C) It's true for everyone that it is easier to get into merely very good schools than the most elite schools, and that is probably more true after a stumble.
(D) It's help to have something else that makes you stand out from the crowd.
Interestingly the two I've help get accepted to grad schools recently were both "second-time arounders".
@dmckee Then let me ask sth. Suppose I completed First year in a college and wantto apply to Harvard or MIT for a course in Physical Sciences. What's the best possible route?
@bolbteppa I think the SSC was pushing the technology so far that budget an time overruns were inevitable. The LHC had the benefit of another decade of technological development, but even so it overran both its budgets and the schedule. My guess is that the SSC would have drastically overrun.
Maybe, but even as they were planning CERN's collider back then too as that article says, they still felt "The SSC's acceleration energy would be 60 times greater than the CERN collider's, making it by far the most powerful proton accelerator in the world" was a realistic goal even back then, even if it was not 100% possible, a 50 times greater thing would be good too :p
@ACuriousMind for my part, what I found more irritating was the suggestion that people who are not interested in engaging with the preferred topic were 'not capable' of such discussion
Basically SUSY implies the sign of the energy always has to be exclusively positive or exclusively negative, and so if you want a theory with energies bounded from below and not from above you pick the $+$ sign, hmm
@JohnRennie The SSC was already over the proposal budget when it was shut it down, and they hadn't even finished civil construction, much less installed any hardware. Plus the improvement (nearly a breakthrough, really) in magnet technology they had counted on hadn't come to fruition.
The after the fact audits also turned up all kinds of things. Money badly mis-allocated. Money misappropriated (though I never heard of any criminal charges). Money simply lost—there was a lot of money they hadn't actually spent but no longer knew the location of!
The DOE took a long hard look at how big physics projects were managed after than and made some changes.
Mandatory financial and process training for various tiers of project leadership.
More structured accounting rules.
More steps along the road to actually getting traunches of money.
More traunches, each of which has to be qualified for.
The mistake that really blew my mind was that they had bought thousands of workstations for analysis ... years before there was any data.
My grad-school buddies and I inherited five of those machines. By the time we got them, their combined drives and memory made two decent machines.
@dmckee if it were to be built now it would be a straightforward project. The trouble is that enthusiasm for a slightly bigger hadron collider is a bit limited with the failure of the LHC to find anything new but the Higgs.
I'd guess the next collider built will be an electron-positron collider.
