Computability at the Planck scale

Abstract

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.

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

References in corpus (8)

• Spin Networks and Quantum Gravity
• Computational capacity of the universe
• The Holographic Principle
• Introduction to Loop Quantum Gravity and Spin Foams
• From Philosophy to Program Size
• Spacetime at the Planck Scale: The Quantum Computer View
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Cited by in corpus (8)

• Logical Interpretation of a Reversible Measurement in Quantum Computing
• Theoretical Setting of Inner Reversible Quantum Measurements
• I, Quantum Robot: Quantum Mind control on a Quantum Computer
• Quantum Mind from a Classical Field Theory of the Brain
• The Geometry of Jordan Matrix Models
• Quantum Gravity: Has Spacetime Quantum Properties?
• Emergence from Symmetry: A New Type of Cellular Automata
• String Theory - Nomological Unification and the Epicycles of the Quantum Field Theory Paradigm