Constructibility of the Universal Wave Function

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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.

Original languageEnglish
Pages (from-to)1253-1268
Number of pages16
JournalFoundations of Physics
Volume46
Issue number10
DOIs
StatePublished - 1 Oct 2016

Keywords

  • Constructive existence proofs
  • Dirac’s formalism
  • Hypercomputing
  • Many-world interpretation
  • Mathematical constructivism
  • Physical finitism
  • Potential realizability
  • Universal wave function

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