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So it seems like the general consensus of a "good" question is one that includes adequate research/reasoning to provide context for/justify the question being asked, and if applicable cites sources for research and further reading, outlined on the help page

Yet, there are multiple questions where its greatness or meagerness appears to boil down to nothing more than a mere agreement or disagreement by users. These questions show absolutely no attempt at research and differ primarily in how they appear to the layperson. One question is not even more applicable than another (at least, not necessarily).

What are we as a community looking for in "good" questions? Will we be/are we enforcing these guidelines past a democratic appeal to the false equivalence of popularity to "goodness"?

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It's probably impossible to fully enumerate the characteristics of good questions. For the most part, we rely on people's judgment to determine which questions are good.

That being said, I think there are some heuristics. In my mind, they mostly depend on the idea of a "hypothetical student" who has studied physics up to the topic and level of the question. For example, given a question about general relativity, the hypothetical student is someone who would already be very familiar with Newtonian and Hamiltonian mechanics, electromagnetism, and at least some quantum mechanics, as well as prerequisite math topics like differential equations and linear algebra - perhaps an upper-level undergraduate or beginning grad student. On the other hand, for a simple question about heat transfer involving common objects, the hypothetical student could be a motivated layperson with some mathematical aptitude and the ability to search the web and identify useful sources. (Granted, this is not the most precisely defined concept, but it's a work in progress.)

I expect the asker of a question to have or find resources and education roughly equivalent to what this "hypothetical student" would have access to, and to use those resources and education to make an honest attempt to figure out the answer to the question themselves. As long as I'm satisfied that the asker didn't miss anything that the hypothetical student would have tried, then I'll probably consider it at least a decent question.

Note that I'm not saying the question body necessarily has to include the research/effort that was done. It's possible for a question to be good without describing what the asker checked beforehand. But if I, say, copy and paste the title into Google, I'd better not find that the top result is an answer.

Aside from that, if it looks like the goal of a question is to gain an unfair advantage in any way (e.g. cheating on a homework assignment or exam where outside assistance is not allowed), then I'll definitely consider it a bad question. Same goes for cases where the question appears to come from an educational setting but the asker isn't interesting in actually learning whatever it is they're supposed to be learning. (That being the idea behind our homework policy.)

Also, if a question is something that the "hypothetical student" would consider particularly insightful, i.e. something that students at that level typically wouldn't think to ask, then it's more likely to be a good question.

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What ends up being a good question will inherently be subjective. Good for one person is not good for another. We can point to some objective factors which can help to indicate the quality of a question; but at the end of the day the users here are individuals with their own opinions.

For the three example questions you provided, I can point to several factors that I would assume lead to the main differences in how they are received.

How does light 'choose' between wave and particle behaviour? is a conceptual question; and a quite a significant one in terms of modern physics. There also does not seem to be asked elsewhere on the site, so it is a great resource for us to have.

How do you know when two objects are entangled? is also a conceptual question. Similar to the previous question, it is a really good conceptual question that has importance to modern physics. It's well received, because although the question is fairly straightforward, it does have notable significance in physics. I will say that it does actually appear to be a duplicate of How can we know if a pair of particles are entangled?, so for that reason, I've voted to close it as a duplicate.

Momentum space representation of the hydrogen atom Schroedinger equation is looking for a method to derive an equation. Such a question is generally far less appealing to the broad audience when compared to conceptual questions that are physically significant.

I think at the end of the day though, a lot of it comes down to how "accessible" or "digestible" the question is. I would say a lot more people are willing to think about and read answers relating to the conceptual framework of physics than they are willing to read about the method for deriving a specific equation. You don't need a mathematical understanding to at least get the impression that you've learned something, compared to mathematical derivations, which don't serve much purpose if you aren't doing the math.

The accessible questions (like "How does light 'choose' between wave and particle behaviour?") also get a secondary benefit. If enough people find the question interesting on Physics SE and vote it up, it will become a Hot Network Question, and get exposure to a far broader audience, which almost always leads to more upvotes, and thus more exposure.

At the end of the day, because we deal with people here, questions that ask something people find interesting are more likely to be well received than questions that people don't care about the answers to. That is the driving factor here.

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