As a reference for anyone encountering this discussion, I thought I’d mention Natural Units explicitly. Basically, they are the systems of units that particle physicists use. They are attempts to normalize out as many fundamental constants as possible, exactly as you discuss.
Unfortunately, you can’t build a system that gets them all. You are always left with some fraction over pi, or the square root of the fine-structure constant, or something.
As a reference for anyone encountering this discussion, I thought I’d mention Natural Units explicitly. Basically, they are the systems of units that particle physicists use. They are attempts to normalize out as many fundamental constants as possible, exactly as you discuss.
Unfortunately, you can’t build a system that gets them all. You are always left with some fraction over pi, or the square root of the fine-structure constant, or something.