@0celo7 It's because helicity is the eigenvalue of an operator that squares to (a multiple of) the identity, so the only possible eigenvalues for that operator are +1 and -1.
@0celo7 It squares to 1 :D Write out $(\frac{1}{2}\vec p \cdot \vec \sigma)^2$ and use that the anticommutator of Pauli matrices is $\{\sigma_a,\sigma_b\} = 2\delta_{ab}\mathrm{Id}$.
@0celo7 Ah, that - yes, they are, but they are also the actual Lie algebra $\mathfrak{su}(2)$, so their relations are, up to scaling, preserved in all representations.
@DanielSank Are you getting at that the researcher might say that in their case the value lies in actually getting the answer? And that questions should be off-topic for just asking for the results of calculations, no matter the intended goal or "value"?
Given a problem P, whether the answer to P or pedagogical value of solving P is the goal of the poster's pre-post activity seems to have absolutely no bearing on the quality of that poster's post about P.
After reading G. t'Hooft's question, I have just found a way to pick a side when I am not sure about the answer, 1.)I do not know in case I have to get an answer (someone point a gun to my head?) 2.) never pick the side of fundamentalism if there is no fundamentalist, then 3.) pick the big names
@DanielSank OK now that I'm on a computer: there are questions that would qualify as homework-like in one context (e.g. if assigned as a homework problem) but not in another context (e.g. if part of a research project). We can't tell whether those questions are supposed to get the homework-and-exercises tag without extra information about the context. But presumably those questions are a small minority.
And ideally, the issue of whether a question should be closed would be decided independently of whether it is a homework-like question (in the sense of the quote you posted earlier) or not.
Now, in practice we tend to apply a slightly different set of criteria to homework-like questions than to other questions. Specifically, if we (the community) decide that a question is homework-like (again in the sense of the quote), we require evidence of effort to narrow the problem down to a specific conceptual issue. If we decide it's not homework-like, we're somewhat less strict about that requirement.
So our criterion for closing a particular type of bad question is one thing for clearly homework-like questions, a different thing for clearly non-homework-like questions, and interpolates between them for questions which are ambiguous.
(this is my impression of the way things actually work, I'm not saying this is or isn't the way they should work)
Hopefully the two things (i.e. the two versions of the closing criteria, for homework-like and non-homework-like questions) are not too different. Again, ideally they'd be the same, and then the issue of whether to close a question decouples from the issue of whether it counts as homework-like. But in practice the decoupling is only approximate.
I know this is a messy situation but it emerged as a compromise of sorts between people who wanted to allow homework-like questions and people who didn't, or who did only under certain conditions. It's something I would like the community to revisit someday, but it will take a lot of effort to restructure the homework policy properly.
> there are questions that would qualify as homework-like in one context (e.g. if assigned as a homework problem) but not in another context (e.g. if part of a research project).
I'm not a huge fan of that.
I thought we say "homework-like" to indicate that whether or not the problem is actually from a homework assignment is irrelevant.
> We can't tell whether those questions are supposed to get the homework-and-exercises tag without extra information about the context. But presumably those questions are a small minority.
We can't tell, so why try? Why not just hold all questions to the same standards of quality?
@DavidZ This poses a problem. There are specific rules for "homework-like" questions. Therefore, under the site rules, whether or not a question is closed surely depends on whether or not it is homework-like.
Here's what the homework-like close reason says:
> Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better
This has nothing to do with whether or not the question is actually motivated by a homework assignment.
@DavidZ I think I can illustrate the heart of my concern with a simple example.
Consider the following question: Consider a conducting cube with a charge $q$ on it. a. Find the potential at all points on a line which passes through the centers of two parallel faces of the cube. b. Find the electric field near the faces of the cube. An infinite sum representation is acceptable.
That's a homework-like problem. It's bad and should be closed because there's no indication of a conceptual question or any show of effort.
Now consider the same question re-worded: I work at CERN and do experiments wherein high energy charged particles are deflected by electrodes of peculiar shape. We have an experiment involving deflection by a charged cube. What is the potential along an axis passing through two parallel faces of a conducting cube with charge $q$ on it, and what are the surface fields?
That question sucks as much as the first and should be closed.
I think the site meta should reflect this (assuming others agree). It also seems kind of weird that the definitive source for the homework policy is that meta post and the close reason.
@DanielSank well, yeah, but in this case I think it'd be fairly obvious that the question is a homework question in disguise
@DanielSank setting aside the point from my previous message, consider this: how does the site meta not reflect this? Sure, there is the lack of a specific rule equivalent to the homework policy for non-homework-like questions, but does it say anywhere that questions like this example (assuming we accept it as non-homework-like) should not be closed?
@DanielSank BTW we say "homework-like" because the category also includes things like contest questions, self-study questions, review problems, puzzles, and so on.
My future vision for the homework policy is that it will no longer be a homework policy, but rather a policy applying to all questions. But as I said, it's going to be a complicated process to develop a consensus on that.
@DavidZ Ok, but this is missing the point. Let's try a better example, something I would actually ask as related to my research:
Suppose I have a 2-level quantum system subjected to a Hamiltonian $H = I(t)\sigma_x + Q(t) \sigma_y$ where $I$ and $Q$ are stochastic and independent. What is the probability versus time for finding the system in $|0\rangle$ given that it started in $|1\rangle$?
That's not from a homework assignment, but it's a crummy question.
@DavidZ If that's your vision then we're of a like mind.
I don't see any reason at all that questions generated in a research environment should be considered acceptable if they suffer the same quality problems which happen to be most common in questions coming from homework assignments.
@DavidZ @DanielSank: I agree with DanielSank that the wording of the policy should better reflect that the reasons for asking a homework-like question are irrelevant. The current blurb seems to indicate that questions where the actual purpose is just getting the answer are not homework-like if OP is not actually interested in the method of finding it (which may even be true for actual homework questions :P)
As I see & act, the HW policy applies to any question asking for help on "doing the math" of anything, be it an actual HW question, a research project or a derivation of a line in a textbook
Users who get their questions closed tend to argue on the "I've shown work!" phrase in the close reason
I personally think that "showing your work" probably isn't necessary if the point is we don't solve homework problems
@ACuriousMind Which means to say in effect that the homework policy is to go ? What's the use of changing the wording of the policy if in effect it negates the policy itself by allowing any type of homework question on the site by not questioning it's intent ?
Or at least not needed in the close reason, especially since the HW policy summary starts off with, It's not enough to just show your work and ask where you went wrong
@Gaurav Strange, I read it completely the other way: that the policy is strengthened, not removed
Well, I think the following is necessary for something "homeowork-like", i.e. asking about the result of a calculation, what I would not close: 1. Ask about a derivation *not* found in standard material (and reasonably demonstrate that it cannot be found by googling). 2. Show your work, explain at which point you are stuck. 3. Ask a *specific* question about the point at which you are stuck. Not "how to proceed?". If you can't ask such a specific question, don't ask the question at all.
@Gaurav I want to disallow any kind of homework question by not caring about their intent, not allow them!
@KyleKanos The fact that they often argue is indicative of one fo two things (not exclusive): The wording of the policy is unclear, so they think showing work is sufficient, or they just try to argue with anything they see because they're desperate.
@Gaurav If it does not ask a conceptual question, but merely asks for the result of a calculation, then yes, I think that's the point @DanielSank also was making above - your intention shouldn't matter, asking "Given X, what is the value of the quantity Y?" is just not a good question
@Gaurav They are identified by asking for the result of a calculation without asking about any specific physical (theoretical or experimental) concept.
@ACuriousMind I could consider being more lenient on #1. I think #2 is too related to #3 to really be separate and both are bad reasons for leaving open
@ACuriousMind I'm more worried about the first case than the latter
@KyleKanos I'd not close things because the solution is in some book. But if it is found e.g. on Wikipedia (as it quite often is the case!), then it should be closed. But yeah, I don't mean to be draconian about 1., and you're probably right that 2. and 3. are a single thing.
Would this question be allowed to migrate to Physics.Main?
What are the specs of the components I would need to make a 1050 kph, non-rocket-propelled motorbike?
If I'm allowed to migrate, would/could I get answers like this? Keeping in mind that this is the kind of answer that I want...:
As...
I found it kind of wired.... I asked question quite specific in other sites of SE, but I usually asked question too board in Physics SE, I wonder why. Maybe it takes some more practice in asking well posed physics questions.
@Shing (ref my prev comments) Moreover, I think the problem is more of there being not much questions of a high level physics than there being many homework questions per se.
No offensive meant, but does the whole "question-closing", "upvote, downvote" things work exactly like training pet dogs? If the users behave themselves, then give him some upvotes, if they don't, close their post.
I forget the name for the famous experiment, sorry.
@Shing The SE model is called gamification. It's meant to reward people (with imaginary internet points) for doing things others consider worthwhile - what's wrong with that?
2
And the experiment with the dogs you're probably thinking of is Pavlov and his dogs, although the point of that one was different
@Shing iirc, the Pavlovian dog experiment shows that, if a bell was rung during feeding every time, the dogs begun to associate the bell with food, and began to produce saliva (a reaction to getting food, normally) even if no food was presented to them and only the bell was rung
It shows that it is possible to transfer reactions to certain things by association to other things, to which the reaction might not make sense.
The way votes and closure would condition the behaviour of users is closer to the operant conditioning of behaviorism, championed by Skinner, than to Pavlovian conditioning.
@0celo7 It's quite difficult here to fit other courses into one's schedule, and I usually have enough other things to do so that I have no time for non-physics, non-math courses.
@Shing Well, good answers should discuss more than just giving a one-line answer in most cases, but they won't discuss with you, if that's what you want.
@Shing No, I mean that good answers should do more than just literally answer the question (which could, in most cases, be done in very few sentences)- they should give background, perhaps refer to other questions one might think of, and thoroughly explain why the answer they give is correct.
OP should not pose further questions as comments in the same question, unless they are very closely related - it's preferable to ask a new, follow-up question.
@ACuriousMind I see, it is kind of an art to answer as well as to ask. I still need more practice. I am so glad to talk with you, but I am sorry I have to leave now. see you :)
@Slereah I think the connection on both comes by considering the tangent bundle as an associated SO or GL bundle, respectively, and then choosing the connection on the frame bundles that is compatible with the Levi-Civita connection on the tangent bundle
There's the theory of associated bundles to principal bundles. You should properly have the "actual" connection living on the principal bundle and induce the connections on all other bundles through the "association process".
I'm afraid I've not seen this actually explicitly done, but that may well be because I haven't actually learned this systematically. Maybe @Danu knows more/other things?
@0celo7 Nah, anyons are things with fractional statistics, you'd see that only if you consider multi-particle spaces and ask yourself what exchanging two particles does
In higher dimensions, there's only two possibilities - either the sign stays the same, or it changes, because the universal cover is only a double cover. In this case, the universal cover is a countably infinite cover, and so one gets more possibilities in which the exchange of two particles can act.
You don't see the anyonic character if you're only examining a single particle
Ah, wait, we see that spin is not quantized, though! We need now projective reps of $\mathrm{U}(1)$ - and what's the universal cover of $\mathrm{U}(1)$?
@ACuriousMind: My combinatorics skills are terrible. How do I quickly verify that the Riemannian curvature tensor has $\frac{n^2(n^2-1)}{12}$ independent components using the skew and interchange symmetry and Bianchi 1?
@ACuriousMind curves which are not homotopic to a point in $S^1$ can be "unwraped" in $\mathbb{R}$ and they define equivalence classes by the wrapping number...maybe
@0celo7: Alternatively, you might just observe that you can choose the charge even not integer, and all you get is that $\mathrm{e}^{2\pi e}$ for $e$ the charge/spin differs by a phase from the identity, so it's an allowed projective representation
@0celo7 Yeah, that's possible. I'd have said that $\mathbb{R}$ is simply connected and that $\mathbb{R} \to \mathbb{R}/[0,1]$ is a covering map onto the circle. By uniqueness of the universal cover, $\mathbb{R}$ is the universal cover.
@ACuriousMind I used the definition given in HE that the cover is a set $(p,[\lambda])$, with the equivalence class of homotopic curves and the only homotopic curves on $S^1$ are the ones with equal wrapping number (this sounds wrong)
Ah, you're using the explicit construction of the universal cover. That's fine, but one need not always do it this way - it's often easier to take something simply-connected and show it covers the space instead of constructing the cover in terms of the curves.
@0celo7 linear complex irreducible reps of $\mathbb{R}$ are just given by a sending $1$ to some phase $\mathrm{e}^{\mathrm{i}\theta}$ with $\theta\in[0,2\pi)$ arbitrary.
Hmm...looking at that, it seems that there are no non-trivial projective reps at all.
@0celo7 Not exactly, but looking at the little group again, I think we're doing nothing wrong - indeed, we need to find projective reps of $\mathrm{SO}(2)$. There's only the trivial projective rep. There's no such thing as "spin" in 2 dimensions...
(Why there is classical angular momentum is related to the fact that the 2D reps of $\mathrm{SO}(2)$ are ot reducible as real representations, only as complex ones
user54412
@Huy Note also "These twenty functions are precisely the 20 degrees of freedom in the second derivatives of the metric which we could not set to zero by a clever choice of coordinates." There is a more geometric way (probably best done in Riemann normal coordinates) at arriving at the same answer.
@0celo7: I think the proper answer is this: The concept of spin is meaningless in 2D, there are no non-trivial representations of the rotation group upon the projective space of states. The concept of statistics is not meaningless, because it relies on the actual linear representation of the universal cover that gives the projective representation, this is where anyons come from.
Oddly enough, I cannot find anything that actually discusses what the actual notion of "spin" is supposed to be in 2D, it seems mostly they just take the 3D system and confine it to 2D, so that there's still the notion of spin from 3D.
@ACuriousMind the reason for the existence of homework in the first place is to help students understand methods. It doesn't matter that the student may only care about the answer; the important fact is that the reason the question was assigned as homework was to help them learn something about the process for doing the question.
@0celo7 Any unitary representation is only ever a phase, and phases are irrelevant, so all projective representations are trivial.
@DavidZ So a problem where it's actually the answer that's needed for something is not homework-like, even if it could be homework or self-study in other contexts? (I think this is also what @DanielSank was talking about=
@ACuriousMind yeah. But it's probably harder than you'd think to come up with an example that's truly ambiguous. They're out there, sure, but they're rare.
I'm usually good at finding stuff, but here there's so much stuff about spin systems in two dimensions that are irrelevant to what we are trying to do that it drowns out anything I could use
user54412
17:57
@ACuriousMind Are you saying in a truly 2D universe electrons wouldn't have spin? But in a 3D universe electrons confined to a 2D surface obviously do?
Perhaps somebody of more authority may know the time (of a specific timezone) where most people are online and offline.
Would this question be allowed to migrate to Physics.Main?
What are the specs of the components I would need to make a 1050 kph, non-rocket-propelled motorbike?
If I'm allowed to migrate, would/could I get answers like this? Keeping in mind that this is the kind of answer that I want...:
As...
