It could be theoretical. The high baseline effort and cost to run even a simple experiment would probably preclude empirical work. The theoretical area is probably saturated by now, will be difficult to carve out a niche.

I feel like you could say that about any discipline that any Master's student would embark on just because the state of the art is extremely advanced, no? For example, if you're a chemical engineer focusing on batteries, you could say simple experiments are out of reach too because "simple" has advanced to a point that's extremely complex & expensive. I haven't done a Master's so I don't actually know.

Oh, no I don't think so. High-energy physics has a high cost barrier to entry. Even a simple experiment requires a complex apparatus ex. an accelerator, or a very high pressure vacuum chamber, laser cooling, Bose-Einstein condensates, etc. It's much cheaper to run experiments in chemistry, batteries on the whole are not terribly complicated. We're talking about going from hundreds of thousands of dollars to merely thousands of dollars.

You could go a step further and talk about computer algorithms or mathematics in general. The only cost there is a pen and a piece of paper. The only cost there is your own time. Some experiments and analyses cost more than others, it's just the nature of things.

My point is that when you get sufficiently advanced, you some times require access to resources that aren't just a pen and paper. So sure, some fields of math may still be ok to do with a pen and pencil. It wouldn't surprise me if some require large super-computer style access. Or distributed algorithms that are written by master's & PhDs at massive cloud/internet providers that rely on those large networks to run an experiment. So even in the CS domain I expect there to be Master's thesis that isn't cheap to reproduce.

Similarly, if you're trying to get a novel battery chemistry to outperform a Tesla car battery or generate a completely novel solar cell, you're not going to be able to accomplish that as an IC researcher. As you point out, there could easily be interim projects along the way to identify various interesting properties that might be useful to your long term goal which aligns with my original statement. When that's out of scope you partner with institutions with access to those resources whether those are big corporations, research institutes, or particle accelerators.

Batteries are one I happen to know something about, a startup I worked for hosted $major-university's monthly battery lecture series, we were doing a SaaS business targeted at the vertical. I met a dozen or so grad students doing exactly this.

So, nope, bad example. Taking an existing process and giving it a few tweaks will push it around in parameter space, improving something we care about (number of cycles before 80%, let's say), often at the expense of something else, like you can't apply as many coulombs. Congratulations, you've got a thesis. And there are dozens of basic battery processes.