This is my view as a long-time user, not as a moderator. It's only my perspective and doesn't represent the views of the other mods.
BLUF: We need to grow organically, systematically, and create the environment in which that happens. We need to find the diamonds in the rough.
I think the challenge in these conversations we've had over the years is that we don't really have a consistent definition of what a professional physicist is exactly. Our site is targeted, in part, towards them, but what does it really mean? Is it only research-focused people in "physics?" Is it professors of physics? How many professional physicists are there, really, in the world? And would most physics-oriented people who aren't professors or research scientists in national labs/universities identify as physicists, or would they identify as an engineer or something else more applied?
We often make comparisons to StackOverflow, which has huge popularity and targets professional programmers. And they are held up as the gold standard for how things should work -- there's experts in everything there and you can get some really fantastic answers from famous people in the field. That seems to be what people are looking for here also. But I think we face a lot of different challenges that limit how well that can happen. I'll use StackOverflow and programmers in my discussion, but the same holds for IT admins and ServerFault/SuperUser, etc..
If I am a professional programmer and an absolute beast of an expert in, say, Python -- I will absolutely have used StackOverflow before and I may hang out answering questions because it's fun for awhile. But the nature of the programming field means that I may need to pick up some new tool that I don't know. Maybe I need to build something in Rust, or I have to help out on some web front end project and I need to learn that stack quickly. So I will probably ask some questions outside of my beast-mode area. So I'll be engaged everywhere on the site.
Programmers have a professional need to adapt to new technologies and new areas, and so even if they are the world's best in X, they may be a total beginner in Y. StackOverflow offers engagement on many levels.
Let's contrast that with physics. If I just won the Nobel prize for my contributions to condensed matter physics, it's unlikely that I will need to start asking questions about basic fluid dynamics to get spun up on my next project. And so if I was a user of the site, odds are pretty good that I would only be answering questions in my subject area and have little reason to be asking new questions or learning about things outside of my subject area. My only incentive to learn things outside my expertise is intellectual curiosity, rather than a professional need to keep my employment.
So our type of engagement is different than sites like StackOverflow.
When you're trying to write some code to do something and you get stuck, what's the first thing you do? For me, I head to my favorite search engine and type in some keywords, or I paste in the core error message and hit search. And 9 times out of 10, StackOverflow is in the first few results. And I can poke around and refine the search based on what I see there and I will likely find my answer -- usually on StackOverflow, but even if not, the Q&A has helped refine the keywords I need to search for so I can find what I want. This is true whether I am just starting out learning how to "print('Hello World')" or if I am paid to write software for a living.
It's impossible to use the internet to look for help with programming and not end up on StackOverflow.
Now let's look at what happens when I have a physics question. If you're a new student or a person who has never really studied physics, you do the same thing -- hop on your favorite search engine, type up some keywords or whatever your question is, and hit enter. And you probably end up coming across Physics.SE, although maybe not as prominently and frequently as in the programming example.
However -- this is 100% not how "professional physicists" search for information! Most professionals in the field, and related fields like engineering etc., will be using specialized search engines designed to return scientific information that has been peer-reviewed. If I'm using Google Scholar, there is a ~0% chance I will find something on Physics.SE. The only way I could come across it is if some journal/arXiv paper mentioned it in the citation or acknowledgement list.
So we aren't really discoverable by "professionals" looking for physics.
Tool vs product
When I go to StackOverflow and ask my question about programming, I am asking for help on how to do something very specific. I need to know how to read an XML file. Or I need help on optimizing a particular loop. I need to figure out what the 5000 line compilation error message is saying about my template class. In other words, I am asking about a tool or a building block, not asking about my final product. I'm not asking about my entire software stack, just a tiny, bite-sized chunk of it.
StackOverflow is largely self-contained and managable questions.
But physics is a little bit different. Most of the time, my bite-sized chunks and my tools I need to make my bigger product aren't physics tools! I may need to know when two operators commute (math), or how to write a for loop (programming), or how to optimize a code to run over 10,000 cores (scientific computing), or how to sample my experimental design space to reduce uncertainty (statistics), or how to write up my equations (latex). None of my tools to build my final product are physics specifically.
So I won't really be here to ask questions that help me in my professional life -- I will be elsewhere on the network.
If you look at the number of professional programmers in the world, it is huge. And they don't get together in person terribly often because it isn't a community that does conferences and seminars and the like. So StackOverflow is in many ways their community. There's so many unknown and untapped people who can help them there.
But in the physics world, it's different. Young folks may not realize this because they don't see inside that world. Earlier when I talked about engagement, I touched on specialization -- I don't need to go learn some new area frequently. And that means I know my area very well, and by extension, I know the community very well.
If I have a question, I know exactly who to ask. And I will see them in person at a conference at least once a year. I travel to conferences all over the world and I would recognize every living giant of my field. And I know the vast majority of professors/active researchers in my field. If I know it will be awhile before I see them, then I will send an email or shoot them a text. And if I don't know somebody personally, I know somebody who can make the introduction. So I don't need this community to learn things directly related to my research, I go right to the source.
What is physics?
I've alluded to this throughout, but it's an important point -- what is physics, really? If you ask a researcher in physics, you'll get a very very different answer than if you ask somebody who is in high school taking a "physics" class. To the high school student, physics is adding vectors and drawing free-body diagrams. But for a researcher, those topics probably wouldn't even be in the top 500 things they use to define physics.
Most of what the beginners are stuck on isn't physics, it's problem solving. Many times, we could replace the "physics" part of the vector addition with some other word problem and it would be the same problem to solve.
And if we go back to discoverability, who is most likely to find out this website exists? The students who think physics == adding vectors. And we see this in the many, many Newtonian mechanics questions we get at the start of every school semester.
How do we grow?
I just listed what I see as the systematic challenges we have here. How do we address them? What can we do to get world-famous scientists involved?
I think first and foremost, we probably won't get today's giants of the fields. There's so many challenges to overcome and they probably aren't going to be interested in the site as it is now, for all the reasons (plus some) above.
In my view, we need to be making sure the giants of tomorrow find us. We need to make sure that the team discovering the major breakthrough 10 years from now has grad students who asked their early questions about physics here. Those folks who hop onto Google and say "what is F in F=ma" and end up on our site. If we look at a lot of our power users now, the folks who are active professors and researchers, they started out on the site years ago as grad students and stuck around. They grew up with the site and continue to contribute to it. But this growth is slow and organic, it can't be forced.
It can't be forced, but it can be fostered. We need to be supportive without compromising quality. We can't let the 50 "plz I need this tmw" questions cause us to lose patience and snap at the 51st, because that 51st might be somebody who goes on to be a physics great as they learn and mature. We have to be polite but firm. But we also cannot allow any of those questions to stick around.
We have to make this an environment that is attractive for others to not just come to ask a question or to answer a random question. It needs to be a place where people come to engage with like-minded people between conferences and those in-person meetings. And that means it needs to be friendly and respectful. Anybody who stumbles upon a place that looks rude, or immature, or annoying, isn't likely to go "Yeah! This is where I want to spend my free time!" It needs to be a place that people want to engage with, not just a place for transactions (i.e. come to ask a question and get an answer, then leave when completed).
I think back to the best instructors I have ever had, and there is a pretty clear trend. They may have been friendly, or they may have been really gruff and unfriendly, but they took their work seriously and they figured out how to motivate me to learn. I could ask my question but they would almost never answer it. Instead, they would help me learn the tools and the building blocks I needed to answer the question. That's what we need to do here as well -- particularly with the huge number of very basic questions. We cannot cast those users off into the internet oblivion, but we also can't hand them the answer. We need to point them to the Q&A here that gives them the tools they need. And we need to help them refine their own toolset.
Ideally, some of those folks will go on to be the next greats. And they will have gone through their journey there with the people here.