Constructibility of the universal wave function

TL;DR

This paper examines the constructibility of the universal wave function in quantum mechanics, arguing that without physical bounds or hypercomputation, it remains non-constructive and symbolically definable only.

Contribution

It offers a constructive perspective on the universal wave function, linking foundational quantum issues with constructivist mathematical philosophy.

Findings

Universal wave function is non-constructive unless physical bounds exist.

Basic operations on the wave function are undefinable without physical bounds.

Constructivist approach clarifies the mathematical nature of the wave function.

Abstract

This paper focuses on a constructive treatment of the mathematical formalism of quantum theory and a possible role of constructivist philosophy in resolving the foundational problems of quantum mechanics, particularly, the controversy over the meaning of the wave function of the universe. As it is demonstrated in the paper, unless the number of the universe's degrees of freedom is fundamentally upper bounded (owing to some unknown physical laws) or hypercomputation is physically realizable, the universal wave function is a non-constructive entity in the sense of constructive recursive mathematics. This means that even if such a function might exist, basic mathematical operations on it would be undefinable and subsequently the only content one would be able to deduce from this function would be pure symbolical.