WannabeNewton said:
My original plan was to dual major in physics and math
Go to a mathematics forum that is akin to this site. You'll inevitably find threads along the lines of "Mathematics BA - is it even worth it?" You could add astronomy to your list to create a triple major in what are probably the three technical disciplines where employability with only a bachelors degree is toughest.
Some people have recommended I try a physics and computer science or physics and engineering double major just to remain "practical" and "employable" in the eyes of potential employers but it seems like doing a comp sci or eng double major with physics would be quite a monumental task that would take away substantially from my self-studying of physics and mathematics (which is honestly the biggest source of joy in my life at the moment).
A physics / engineering double major would be a significant undertaking at Cornell for the simple reason that physics (I'm assuming you're a physics major, not an A&EP major) is in the College of Arts and Sciences while engineering degrees are offered by the College of Engineering. That the two colleges have somewhat orthogonal core requirements is going to make this a rather tough task. Comp sci will be less problematic in this regard because it lives in both colleges. It still won't be easy, and it most likely will add an extra year to your undergrad career.
A much less laborious route would be to minor in one of those other topics. Math would be easy; you're going to come close to the minor requirements for math just by taking the math courses required of a physics major. A minor in some engineering degree might be useful as a backup plan to graduate work in physics, but you're going to be competing with people who majored in that field. Many prospective employers in an engineering field will take the easy way out and put your resume in the circular file.
On the other hand, a comp sci minor would open the door to a slew of technical jobs where the ability to program is an essential but nonetheless secondary job requirement. First and foremost is the ability to reason mathematically and physically. As a side benefit, a comp sci minor could also be of aid should you decide to continue in physics at the graduate level. There are quite a few physics disciplines that require programming as an essential but nonetheless secondary skill.You asked "Can one not just learn programming without all the extra theory?" The answer is yes. You can readily learn to program badly without all the extra theory. I occasionally (with much grimacing) have to look at code written by aerospace engineering or astronomy grad students. It's usually quite atrocious. Unreadable. Unmaintainable. Untestable. Detestable. They learned how to program without any of the extra theory.
Let's flip your question around. "Can one not just learn physics without all the extra theory?" Not really. The same applies to some extent to computer science.
Because programming is a secondary skill in those analytical jobs and in computational physics, you don't need to go whole hog and do a double major in physics and comp sci. Secondary = minor, not major.