Yes, I can’t prove I have pi. But you can’t prove that I don’t. I’m not a physicist I’m a mathematician. Quantum phenomena appear to actually, in reality be “probabilistic” and to actually involve irrational numbers.

If rationals exist in reality and you are comfortable with Graham’s number existing in reality (which has more digits in its base 10 representation than the number of particles in the observable universe) then why not irrationals? They are the completion of the rationals.

Unless you are a finitist.