This question looks in imminent danger of being closed on the grounds that it's a pure mathematics question. This is something that happened a lot when I was more active on the site, and is one of the reasons I'm less so now. I'm wondering (a) whether the on-topicness of maths-as-used-in-physics is something that was ever formally discussed, and (b) whether the current community really finds it desirable to ban such questions.

I realise there's a strong tradition of defining this site's topic as being "only questions about physics." The question is whether "physics" here should mean "what physicists do" or the much stricter (and more epistemologically suspect) "what is in the physical world." The linked question above is a good example, because it's clearly technically about a mathematical concept (Dirac delta functions), yet the topic is also clearly something that was developed by physicists, is taught on every physics syllabus, and is of interest to every physicist.

I also realise that there is a mathematics stack exchange where this would be on topic - but in many contexts it is often said that the existence of other Stack Exchange sites should not affect what's considered on topic, so I think that is not relevant here.

To reiterate, my questions are

  • Was a consensus ever explicitly reached on the on-topicness of such "purely mathematical" questions, and where can I find the discussion?

  • Is it desirable, to the current community, to allow questions about the mathematical concepts on which physics is built?

Edit: Ah, the difficultly of searching meta. I've found a previous discussion on this topic. The accepted answer, with +16 votes, says:

a question which focuses entirely on mathematical details, whilst perhaps appropriate for the mathematics SE, should be kept on the physics SE if it is motivated by physics, even though it may not necessarily be regarding how it is precisely applied to a physics problem.

which would suggest that the linked question is just on topic, period. Still, it seems worth bringing up again to see if that's still the consensus, and perhaps to remind active close-voters that the agreed policy isn't quite as exclusive as they might think.

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    I think the question should be left open because it's the Dirac delta function, and Dirac was a physicist. And it has attracted some serious contributions from the sort of posters this site should encourage, not discourage. – John Duffield Oct 4 '15 at 10:16
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    Since the question currently has 4 close votes and is hence one close vote short of a migration to Mathematics (which it likely will receive in a matter of hours if left unprotected) I have locked the question while the meta discussion is on-going/active. – Qmechanic Oct 4 '15 at 10:57
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    Also keep in mind that some questions that are "about the mathematics" are, in part, questions about "this is what a physicist means when he writes something like that" (e.g. as an outsider looking in, I think physicists almost always mean to take limits in the sense of distributions, rather than pointwise convergence that a mathematician would read it as), and that context would be lost if migrated to math SE. – Hurkyl Oct 4 '15 at 12:06
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    Jamal's answer also states Questions devoid of any physics content (or references to physics), which focus entirely on mathematical details should be migrated to the mathematics SE. So I think many close-voters (myself included) invoke that opening statement as a rationale for migrating math questions to math.se. I don't think the argument of the consensus is quite as clear as you're making it out to be. – Kyle Kanos Oct 4 '15 at 13:01
  • The point @KyleKanos mentioned is why I voted to close. There is no physical content in that question, a Dirac delta function is well-defined in a mathematical context and that is how the question is presented. I first learned of the Dirac delta in a math class, not a physics class, so it's not exclusively (or even primarily) the domain of physicists to understand. For something like this, I don't see how a physicist could provide any extra insight a mathematician could not, except perhaps some examples of uses; but that wasn't asked, the definition was asked. – tpg2114 Oct 4 '15 at 15:22
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    I agree with all the above, yet I would be less strict about closing down mathematical questions for two reasons: 1) physics, especially research in modern physics (QFT, strings, gravity) pretty much comes down to working out the maths, there's not much intuition left; 2) we are discouraging naive questions about "what is the physical meaning of..." (I totally agree) but if we discourage technical questions as well, I wonder what are the actual questions that we are left to ask. – gented Oct 4 '15 at 21:00
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    @GennaroTedesco we don't discourage naive questions about physical meaning, we discourage lazy questions, and we discourage them because they're lazy, not because they're about the physical meanings of things. Actually, asking about the physical meaning of something is quite a good question for the site, as long as it shows some effort and motivation and fits our scope in other respects. (In particular, a question that is literally "what is the physical meaning of [thing]?" is not going to be very well received.) – David Z Oct 4 '15 at 22:20
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    I have a physics-based answer and would like to add it, but cannot since the post is locked. The idea of distributions is that, for any continuous physical quantity, you can never measure precisely its value at a point. Rather, you can only make more and more accurate measurements, by, eg., engineering better equipment. So, thinking of a function in terms of it's values at points is unnatural in physics. Rather, one should think about what could be measured about it. Distributions are the most general framework for such self-consistent systems of measurements. – Nick Alger Oct 9 '15 at 13:42
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    Perhaps, rather than semantically parsing policy, just use this as the criteria: Would the OP get a more useful answer in Physics SE or Math SE? [@tpg2114] – Aabaakawad Oct 9 '15 at 18:57
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    @Aabaakawad that would in itself be a change in policy. I think the problem with it is that like the current policy, it's too much of a judgement call - in this case some might feel that math.SE might give better answers, but others might not, especially given the high-quality answers it's received here. The trouble with judgement calls in this context is that it only takes five votes for the question to be migrated, and there's no way to vote against - that system works much better if the criteria for closing/migrating are very precise. – Nathaniel Oct 10 '15 at 10:44
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    @Nathaniel: and there's no way to vote against Not exactly true; voting Leave Open is a vote against closure and if 3 people vote Leave Open before the fifth Close vote, then the post is removed from the queue (though it doesn't remove the previous close votes). – Kyle Kanos Oct 12 '15 at 12:02
  • @KyleKanos huh, I didn't know that - I always assumed that option just did nothing. But still. – Nathaniel Oct 12 '15 at 12:48
  • @Nathaniel: The page on Close+Reopen vote privileges describes the Leave Open vote in the next to last paragraph. Perhaps a more important key to the system is the need for a larger number of consistent reviewers; currently, it's basically the same 10-15 of us voting daily. I doubt it would guarantee borderline questions remaining here & open, but variety could help those cases. – Kyle Kanos Oct 12 '15 at 12:54
  • I think my answer to the engineering/physics issue applies here. – DanielSank Nov 23 '15 at 1:56

To answer the titular question, no, they are not always off topic. But just because a question is about math used in physics does not make it on-topic either. All of calculus is used in physics and I would be hard pressed to say that somebody asking a question about the formal definition of a derivative or a limit would be on-topic here.

However, it is easy to imagine questions that are basically only math but where physicists can provide more applicable information. One example I can think of from fluid dynamics is our somewhat... relaxed... use of Einstein summation notation and things like the Levi-Civita symbol or Kronecker delta. Mathematicians could provide an answer to questions about that, sure, and they would be absolutely correct to boot, but I think many people (myself included) might not understand the answers because the level at which we need to know them and apply them is much more limited in scope.

This is the gist of the selected answer the last time we talked about this. Without some tie to physics (aside from the fact the topic in question is named for a physicist or invented by one -- Newton being a physicist doesn't make basic calculus questions on topic) or without some way that somebody experienced in physics can provide more insight (aside from just giving examples where the thing is used), it just isn't on topic.

The question you linked to about the Dirac delta function just doesn't provide anything that I am aware of that makes it uniquely physics. It has formal definitions, which OP listed in the question, that are based solely on math. It has alternate definitions/approximations, which are based solely on mathematical constructions (Fourier transform, infinitely narrow Gaussian). Just because it is used in physics (system dynamics, quantum mechanics, etc) does not make it on-topic. We use basic algebra operations too and we wouldn't want questions on how to FOIL a polynomial.

That's why I voted to close it.

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    Honestly I don't think that is the gist of Jamal's answer. It doesn't say anything about being uniquely answerable by physicists, but rather it talks about being "motivated" by physics. Admittedly that's hard to judge in this case, so perhaps the problem is that current policy leaves too much room for interpretation. But I don't think the fact that it could be answered on math is sufficient reason for it to be off topic here, either in terms of what was agreed before, or in terms of what's desirable for this site's quality. – Nathaniel Oct 5 '15 at 0:15
  • @Nathaniel I would agree that there is a wide range of acceptability and at the end of the day, it's just a judgement call. I think all of our "policies" (homework, engineering, computational, math) are created because there is still uncertainty about the focus of the site. To me, it all boils down to this question: Is this a site for physicists, or is this a site for physics. I tend towards the latter while it seems others lean more towards the former. But to me, on any given day, to do my work, I might be a member of Physics, Math, CrossValidated, StackOverflow, Academia, Workplace.. – tpg2114 Oct 5 '15 at 1:51
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    Programmers, Space Exploration, Environmental sciences, Computational Science... and maybe some more. And based on my question, I go to the specific site. Others seem to see "Physics.SE" to mean "things a physicist works with" and so any topic a physicist might encounter in their work is on topic here. I think the community as a whole spans the spectrum from "this is for physicists" to "this is for physics only." As a result, many of our policies will have some ambiguity and judgement calls and it might be 5 that close and then another 5 that reopen just by where they fall in that spectrum. – tpg2114 Oct 5 '15 at 1:54
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    All fair points, well taken. Perhaps it's my background though (I've always worked in multidisciplinary environments and never purely been a physicist), but I'm always puzzled by the concept of this thing called "physics" that's distinct from "the things that physicists, as a culture, are interested in." It seems to be defined only on an "I know it when I see it" principle. In this case I do see where it's coming from but in general I'm very confused about what it's really supposed to mean. – Nathaniel Oct 5 '15 at 7:40
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    For me the interesting questions lie precisely in the places where disciplinary boundaries become blurred, and so the general tendency of Stack Exchange sites to define them strictly frustrates me. That's a totally personal view of course. Perhaps it could be solved with a "multidisciplinary science Stack Exchange", but something tells me that wouldn't work out very well in practice. – Nathaniel Oct 5 '15 at 7:49
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    @Nathaniel, imagine doing [exo-]planetary atmosphere chemistry, my base field. Might be physics, might be astronomy, might be geoscience. One could easily think chemistry, but in fact when I try to talk to chemists, I usually get a blank stare. – Aabaakawad Oct 9 '15 at 18:48
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    @Aabaakawad I often have much the same issue. This is a good argument for trusting the OP's judgement about which site is the appropriate one for a given question, rather than migrating 'automatically' based on the perceived topic of the question. – Nathaniel Oct 10 '15 at 10:47

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