Computability at the Planck scale

Details Computability at the Planck scale Computability at the Planck scale

2004-12-15

arxiv.org/abs/gr-qc/0412076v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, misprints corrected, LaTeX version, accepted as contributed paper at CiE 2005

Scientific paper

We consider the issue of computability at the most fundamental level of physical reality: the Planck scale. To this aim, we consider the theoretical model of a quantum computer on a non commutative space background, which is a computational model for quantum gravity. In this domain, all computable functions are the laws of physics in their most primordial form, and non computable mathematics finds no room in the physical world. Moreover, we show that a theorem that classically was considered true but non computable, at the Planck scale becomes computable but non decidable. This fact is due to the change of logic for observers in a quantum-computing universe: from standard quantum logic and classical logic, to paraconsistent logic.

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