A new type of Multiverse, G\"odel theorems and the nonstandard logic of classical, quantum mechanics and quantum gravity

TL;DR

This paper explores a novel multiverse concept linked with Gödel's theorems, suggesting that classical, quantum, and gravitational theories are incomplete and inherently contain undecidable propositions, leading to a three-valued logic system.

Contribution

It introduces a new multiverse framework connected with Gödel's theorems and proposes a nonstandard three-valued logic for classical, quantum, and gravitational theories.

Findings

Classical, quantum mechanics, and quantum gravity are incomplete due to Gödel's theorems.

These theories admit undecidable propositions, implying a three-valued logic system.

The work links multiverse concepts with logical incompleteness in fundamental physics.

Abstract

The problem is posed of establishing a possible relationship between a new type of Multi-verse representation, G\"odel undecidability theorems and the logic of classical, quantum mechanics and quantum gravity. For this purpose example cases of multi-verses are first discussed in the context of non-relativistic classical, quantum mechanics and quantum gravity. As a result, it is confirmed that thanks to G\"odel theorems non-relativistic classical and quantum mechanics, as well as quantum gravity theory are incomplete. As a consequence, they necessarily admit undecidable logical propositions and therefore obey a three-way boolean logical, i.e., a propositional logic with the three different logical truth values true, false and undecidable.