Is it a good idea to join a second group as an undergraduate researcher if I don't feel challenged enough? I'm currently a second-year undergraduate physics major, and I joined an experimental nuclear physics (astrophysics primarily) group a few months ago. I joined the group wanting to work extremely hard to learn new things, apply them (and my intuition and previous knowledge) to solve problems, and present my findings and progress on a weekly basis, reporting to the group head on a more frequent basis though. It started out like that at first - the head made me solve a problem, write a GUI/applet for it (just to show that I fully understood the problem), and then implement that into a particular framework that would be used for an actual experiment later on down the road. I noticed that the head also didn't like to be a mentor too much - that is, he only liked to tell me what I needed to know for my task and nothing else, leaving extra learning for myself.

The problem with this is I'm left mentally starved. I've been assisting this other person in my group (relatively new graduate) on preparations for that actual experiment that I mentioned earlier, and that feels good. I've learned more of what's going on behind the scenes (significance of the experiment, theoretical implications of the results obtained, detector and equipment [and setup]) through publications, other people within the university, and asking the group head, but all of this was essentially on my own. As a result, I feel that any average joe with minimal work-ethic and intuition could thrive in a group like this. I've learned a lot more about nuclear physics/astrophysics (hence, more about this universe we live in) through sources that I might have otherwise not come across had I not joined the group, so that's good. 

Also, just quick side note, the experiment is coming up soon, and I'm sure I'll learn a whole bunch through that process, and sorting out and analyzing the data after the experiment will certainly put me to work.

I've been thinking about possibly trying to join another research group, just so I can quench my mental thirst. There is a nuclear theory group at my university, and even though I know nuclear theory is probably way over my head, I'm willing to put a lot of time into working hard.

Here is my question: Is attempting to join another group a bad idea? Should I instead tell the group head how I feel, and see where to go from there, or would that be far too disrespectful?

Please excuse any ignorance of mine.
Is attempting to join another group a bad idea? Should I instead tell the group head how I feel, and see where to go from there, or would that be far too disrespectful?


These two options are not mutually exclusive. You can do either, both, or none of them.

As you see it, you believe your choices are


Talk to your current supervisor - You should absolutely do this, regardless of what you decide to do with respect to the other group. Your mentor has no way of knowing what you're thinking unless you tell him; it's up to you to let him know if you need more from the supervisory relationship. Of course, you should do this in a respectful and adult way.
Join a second research group - You should consider doing this if you're interested in the research the second group is doing. As an undergraduate, it's to your benefit to experience different kinds of research, different advising styles, etc, to help you understand what you need when applying to graduate school. Note, however, that research is very time- and energy-consuming, and if you spread yourself too thin, you will experience "research" only on a superficial level and won't get much out of it. Only you can determine whether you really have enough free time and energy to participate in two research groups in a meaningful way.


Finally, I'd like to comment on your statement


  ... all of this was essentially on my own. As a result, I feel that any average joe with minimal work-ethic and intuition could thrive in a group like this.


You seem to think that because your mentor gives you a lot of independence and doesn't tell you exactly what to do, that standards and expectations in the group are pretty low. That's not necessarily the case. 

The ability to work independently is a highly valued skill in supervisees, and it's great that your advisor has given you the chance to show your capabilities in that respect. This means that he'll be able to write strong recommendation letters for your graduate applications - much, much stronger than a supervisor who could only speak to your ability to follow focused, specific instructions.

Research is not like coursework. It's supposed to be highly self-directed. If somebody is telling you exactly what to do and what to learn next at every step, you're not doing research. If you feel like you're not sufficiently challenged by what you're doing now, you are supposed to take the initiative to speed things up.

In other words, don't confuse a hands-off mentoring style with low standards. If the group in general is productive, does good science, and writes solid papers, then standards are what they're supposed to be. From your description, you are learning a lot of new things, starting a new experiment, finding out how research works, and overall describing a pretty excellent research experience.