Is it possible for one to publish high quality research papers in the aforementioned fields without attending a graduate school? I feel that you can read online material and books about research/graduate school and that would make a satisfactory substitute.
In secondary school (high school here in the USA) and even university, a "research paper" means you come up with a topic and a point of view, go to the library, read a bunch of material, and synthesize a wonderful argument about the topic at hand. This approach has nothing to do with actual research in physics.
For actual research, you need to know what is going on at the forefront of the area. This is not in books in the library, but is some amalgamation of specialized journal articles, seminars with latest results, what you've seen or heard at conferences, and a healthy dose of your own thoughts and experiences. You and your collaborators come up with some new thought, figure out a conceivable way to test that thought, go carry out the experiment (lab work, simulation, theory) to see if you can test it, re-examine your thought since the experiment ended up with a different result than you imagined, and distill it all down into a journal article showing what you did was new information.
The process of doing this is what you learn in graduate school. Everything from getting the needed background, identifying new areas, working with collaborators, doing the experiments, and writing a clear detailed journal article is part of it.
Could you make contributions to physics research without a PhD? Well, yes, I have staff scientists with masters degrees who do quite well, including those who have been named to our Distinguished level. One important thing to note is they got some excellent mentoring early in their careers in how to do real research.
But, no, reading online material and books is no substitute for graduate school. It is but one small part of performing actual research that pushes the boundaries of human knowledge.
As alluded-to in other answers: of course it is possible... but difficult. One thing not mentioned is the "insider information" that, ideally, one gets by being in grad school with a good advisor. Many important, amorphous-but-important ideas exist primarily "off the grid", in the collective minds of experts. You'd miss out on this whole world of ideas if you just look at the more-or-less-formal literature.
For most people it is very important. Graduate school is helpful both in training you as a researcher in some field and in getting your career started through contact with other (expert) researchers. It isn't essential, however, for every individual and it is possible to produce good research output as an independent researcher in some fields.
Graduate school gives you a breadth of knowledge in a general field (math, say) and experience in taking the deep dive into a narrow research area. You learn a lot about what is current and about recent research trends, though in a narrow area.
It is much harder to do this alone. What is available in text books is not usually state of the art. You need to read research papers. But you need to know which research papers are worth the effort.
Having like minded people around in grad school or in an academic (faculty) appointment can be essential for many people to be able to produce. And without a doctorate it is difficult to get an academic appointment.
But, some, a few, people have been successful without doctoral education. Not the easiest or safest path, however. And, again, it is very difficult to actually make a career in research without a doctorate. If you are independently wealthy that may not matter.
Is it possible for one to publish high quality research papers in the aforementioned fields without attending a graduate school?
Yes. A tiny portion of undergraduates do this, so it happens frequently.
Is it possible to get a job paying you to do research in physics without attending graduate school?
Mostly no. The other applicants have PhDs. People with PhDs are available and they are preferred.
You are asking about publishing research, but the title of your question is about PhD. These are two different things. To get a PhD, you complete grad studies by default.
As about studying on your own to the extent that you can produce publishable research, it is possible in principle but highly improbable. Interaction is needed to make sure you got things right.
Finally, it is next to impossible that you will get to publish said research unless you persuade someone (journal editors, arxiv moderators) that you are or were affiliated in some manner with academia.
Edit: It occured to me that "How important is attending graduate school for a PhD" might not mean "Do I have to go the grad school to get a PhD" (which I thought), but "How important are PhD studies for (...)". OP, it'd be good if you rephrased your question in an unambiguous way.
The title doesn't make sense because a PhD is grad school. But sounds like your question is basically "can I do important research without a PhD?" You almost certainly can. There is nothing magical that happens in PhD school. You just get some coaching as you learn all the basic aspects of research: Reading and writing papers, conferences, designing and conducting experiments, applying to research grants, teaching and mentoring junior students.
At its core, research is a simple process:
- Read about field and learn the current state of the art
- Come up with a question that nobody knows the answer to yet (whether it's something they're aware of or not)
- Come up with some possible answer that makes sense
- Prove it according to the scientific method (usually with an experiment)
- Announce it to the world (usually by publishing a paper or presenting at a conference)
You can learn all of these by carefully reading existing publications, and maybe also following conferences and writing letters to the researchers themselves. The problem is that it would be a lot of reading. The average PhD student already reads hundreds of papers and goes to many conferences throughout their education, and they also have lots of professors and postdocs to nudge them in the right direction. You will have to work even harder. I'd say you'd end up reading maybe 1000 papers to get to the level of a PhD, but each paper would also take you much longer to read. And how are you finding time for all this reading? Do you have a day job, and want to get into research on the weekends? Because that will probably not work due to the sheer time and energy research requires. Or are you wealthy and thinking of becoming a gentleman scientist in your own time? That might work - but if doing that, why not just do a PhD and save yourself some trouble?
Learning to do research usually happens under an apprenticeship model. The most typical situation is as a graduate student who works in the lab of an established researcher, who serves as a mentor. In addition to learning the technical aspects of the research methods, a good mentor will teach you how to perform research rigorously, avoid pitfalls (which may not be mentioned in the literature), write papers, respond to peer-reviews, understand the culture of your field, and write proposals for funding. You can also learn by working with more experienced students in the same lab. There are a lot of mistakes that can be made and semi-obvious ideas that many people have tried that don't work, which are unfortunately not recorded in the literature. A mentor will also help you make connections with other researchers, which can help you develop collaborations as an independent researcher.
Could you obtain such mentoring elsewhere? Yes, you might be able to get mentoring in scientific research from a group leader in a government lab or from a manager in private enterprise. You might even find someone who will mentor you just for altruism's sake. However, most research mentoring happens in graduate school because academics are incentivized to train graduate students and there are some checks involved to ensure quality (PhD committees, preliminary exams, thesis defenses). Of course, you can have a bad mentor in academia (or anywhere else) who doesn't do a good job teaching you what you need to know to be a good researcher. So choosing a good mentor is a major factor in whether going to graduate school is worth the investment.
Are there people who can succeed in research without such mentoring? There might be a few, but it is much harder. The apprenticeship model has been used for centuries to train neophytes in fields where obtaining good results requires a lot of experience and nuanced technique. Having someone look over your shoulder while you work (sometimes literally) and make suggestions is often the best way to learn technical skills.
A lot of misreadings of the original question.
Is it possible for one to publish high quality research papers in the aforementioned fields without attending a graduate school ?
Of course it is - if by non-attending grad school you include those jobs in state research labs (that you can get with a good primary degree) which allow you use of specialised equipment. You can even work on an external MS or PhD outside grad school if you have someone there willing to internally supervise.
There's a few people who published after their undergrad degree and without a postgrad qualification. And some notables like Turing who published during their undergraduate studies.
But the question asked by Dan Romik is pertinent here: What do you want to do in future ? To that I'd add, from my own experience, the even more important question - which human environment do you want to work in ?
Just because something is possible doesn't mean that the person knowing it should do it.
Ask yourself where you want to go. Then plan the best route to get there.