Is it possible (practically, in real life) to pursue two very distinct research interests (e.g. in AI and theoretical physics)?

It is possible (even “practically, in real life”) to do all sorts of things that are very difficult to do, like: publish five bestselling novels; climb the highest mountain in every continent; win a gold medal in the Olympics; become a successful movie actor; etc etc.

The point is that questions like yours (which seem to get asked here regularly) are very difficult to give a meaningful answer to. We don’t know you and what you’re capable of. Some people can do the thing you’re asking about, others can’t. So just asking “can it be done” is a question that, if interpreted literally, has an easy answer that’s not very interesting or helpful (“yes, it can be done”), and if re-interpreted to mean what I think you really want to know (“can I , the specific person asking this question, do this thing?”), isn’t a question that I or anyone else here have the information to answer.

Perhaps the most helpful way of addressing the question is to look at the number of people who can do the thing you’re asking about. Well, I’ll be honest, that number is extremely small. Most people who want a career in academia already find it challenging enough to do one PhD in one discipline and then pursue a position as researchers in that one discipline. And even from among those super talented people who find it a bit easier than the rest and are smart and hardworking enough that they can realistically contemplate specializing in two very distant disciplines, one of which being as notoriously difficult as theoretical physics and being acquired purely through self-study, only a vanishingly small fraction of that already small group will care to invest the time and energy that it would take to broaden their reach in such a way. For those people it’s not really about a lack of ability - more about the fact that it’s an inefficient strategy for becoming successful and maximally realizing one’s potential; but it kind of amounts to the same thing in the end.

Summary: can it be done? Yes. Is it something that I’d recommend to anyone to have as their career plan? No.

I'd like to address what I see as a misconception in the original question. You wrote,

I have a fairly good foundation on CS because I have been doing competitive programming since I was 13.

But computer science is not the same as computer programming. Here is an analogy: Computer programming is to computer science as elementary arithmetic is to university-level mathematics. When you were young, you learned how to do addition, multiplication, and so on. As a third-year undergraduate, you've surely been exposed to calculus, linear algebra, differential equations, and so on. No doubt you appreciate that being able to add and multiply is quite different from being able to integrate!

Computer programming is a skill that can be applied in many different fields and in many different ways. It can be applied to AI, but also to mobile phone applications, accounting software, controlling traffic lights, streaming movies, and lots of other things. It's a very practical skill, like being an electrician. Computer science, on the other hand, is more about what we can compute, how fast we can do it, what quality of results we can expect, and so on. It's more like being a physicist with a deep understanding of quantum electrodynamics. That physicist may know how electricity works, but you probably wouldn't ask him to wire your house. In just the same way, there are computer scientists who are terrible programmers.

Given your interests, you might find yourself interested in scientific computing at some point: Writing code to predict the weather, determine the strength of a bridge, simulate electrical circuits, and so on. Or not. It can be hard to know where you'll end up. The wise thing to do is to put yourself in a position where you have the flexibility to pursue your interests.

I don't know you or your situation, so I'm not qualified to make specific recommendations. Instead I'll leave you with a question. Suppose you pursue just one field for the length of your career; somehow you never get the chance to contribute to the other field. Forty years later, which will you regret more: Not researching physics, or not researching AI?

I’d like to offer a complement to Dan Romik’s answer. Roughly summarising, that answer points out that this is possible, but is a challenging plan, and (for most people) very difficult to succeed with — all of which I agree with.

But I wouldn’t therefore advise abandoning the plan entirely. Ambition is great! The important thing with such an ambitious plan is just to aim high, but be aware of the difficulty, and make sure you have a good fallback plan if it doesn’t all succeed. The thing to avoid is just staking everything on an ambitious plan, with no fallback.

For instance, if a PhD student told me they wanted to work on a particularly difficult problem, I would make sure they were aware of how difficult it is, and I would strongly advise them to also work on some more tractable problem at the same time, so they don’t risk ending up with nothing. But I wouldn’t discourage them from pursuing the difficult problem altogether.

In your case, the plan you outline has a built-in fallback: you can, at any point, give up on the physics ambitions and just continue with the PhD in AI. So if that’s a fallback situation you wouldn’t be unhappy with, I’d say go for it on your plan — take the PhD in AI, and self-study in physics on the side as far as your time, energy, and interest allow. (And it may not have to be just self-study: you may be able to take physics courses on the side, if your university allows this.) And be aware that it’s unlikely, though not impossible, that you’ll be able to get into pure theoretical physics research this way; but the physics you learn will almost certainly be useful anyway, as having a knowledge of a wide range topics (and not just the obvious ones) is very valuable for researchers in any field.