If this represents Peikoff's actual views, he is provably an idiot: quantum mechanics has nothing to do with Kantianism, non-objective art, or "progressive" education, except in the minds of muddleheaded post-modernists who don't understand it and erroneously think of it, on the basis of after-the-fact popularized descriptions, as denying the existence of objective reality.
It was certainly not "given" to us by Kantianism of any sort, but by objective reality itself: it's the best mathematical model we have of how weird matter and energy really are.
Again, assuming Peikoff's views are being faithfully reported, he seems the sort of nitwit who was taken in by Alan Sokal's Social Text hoax article.
So I guess you disagree with Einstein then?
Leonard Peikoff is Ayn Rand without the sense of humor.