Physics and mathematical reality: comments on Aharonov et al, arXiv:1902.08798

Abstract: Do we have two kinds of reality: physical and mathematical? What is the role of mathematics in physics? These fundamental questions have intrigued original and brilliant minds since ancient times. A recent article (Aharonov, Cohen and Oaknin, arXiv:1902.08798) offers a viewpoint on the use of abstract mathematics in quantum theory. They argue that, in some cases, it may result into a paradox focusing on an example in quantum mechanics regarding Aharonov-Bergmann-Lebowitz (ABL) rule. In this comment we discuss three issues: theory reduction and approximation, origin of a paradox, and the reality of time. It is pointed out that paradoxes appear even in mathematics; we explain them as the results of the acceptance of pure logical artifacts. In physics too, the impact of the so called quantum and relativity revolutions, have led to the emergence of counter-intuitive and mysterious notion of the physical reality. The most fundamental change has been on rejecting the reality of time. A radically new perspective that physics is the language of mathematics is suggested. The mathematical reality of the natural numbers manifests in the form of physical time.