GÖDEL’S INCOMPLETENESS THEOREM MAKES THE QUANTUM DOUBLE SLIT EXPERIMENT UNDECIDABLE

Susanna Tall, Arvi Hakanen

Published Mar 6, 2025• 0 citations

Abstract

Kurt Gödel’s incompleteness theorem refers to incompleteness in the sense that there are always statements which can be formulated within a formal system, but which re-main unproved within the system. Gödel’s theorem was first connected with the theory of computability by Alan Turing. Until recently, the inconsistency that Gödel’s theo-rem tackle has not been directly shown to correspond to any physical phenomenon. A recent article showed how to apply Gödel’s theorem in the context of many-body quan-tum mechanical calculations. Even so, it is still not known whether it can be applied to the most primitive quantum physical phenomena. In the present study, we used Gödel’s incompleteness theorem in the case of the quantum double-slit experiment by applying a proof of Turing machine’s halting problem. In addition, we made an analogy between Gödel’s theorem (and Church - Turing theses of computability), and quantum compu-ting by extrapolating the term “computation” as low as to the single-quantum level.

DOI: 10.31219/osf.io/qn6p7_v1

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