no, the first principles could be reduced to the domain that you're working in, which in this case would be non-relativistic physical optics. that is, the description of electromagnetic waves using maxwells equations. these could be considered true first principles for this problem domain.

you don't need to go to quantum physics or general relativity for everything, that would mean that a description from first principles is impossible for any field that doesn't (yet) directly connect there like biology, psychology, you name it. which may be technically correct but clearly not in the spirit of the idea.

in general this article has a quite surface level focus and narrow scope. there isn't even a description how the most common physical rendering primitive ever, a ray of light, is related to electromagnetic waves in mathematical terms. the article is not very mathematical in general which is disappointing.

I definitely agree with you that the article lacks mathematical rigor, it's something I'll try to improve in the future. Thanks for the feedback!