# A Relative Church-Turing-Deutsch Thesis from Special Relativity and Undecidability

arXiv: https://arxiv.org/abs/2206.06419 · HTML: https://mlsanity.com/paper/2206.06419/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 18 references that are in the map.
- First posted on arXiv 13 Jun 2022.

## Builds on (most cited first, 4 of 4)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Brain-inspired computing: We need a master plan](https://mlsanity.com/paper/2104.14517/) (2021)

## Abstract (arXiv)

Beginning with Turing's seminal work in 1950, artificial intelligence proposes that consciousness can be simulated by a Turing machine. This implies a potential theory of everything where the universe is a simulation on a computer, which begs the question of whether we can prove we exist in a simulation. In this work, we construct a relative model of computation where a computable textitlocal machine is simulated by a textitglobal, classical Turing machine. We show that the problem of the local machine computing simulation properties of its global simulator is undecidable in the same sense as the Halting problem. Then, we show that computing the time, space, or error accumulated by the global simulator are simulation properties and therefore are undecidable. These simulation properties give rise to special relativistic effects in the relative model which we use to construct a relative Church-Turing-Deutsch thesis where a global, classical Turing machine computes quantum mechanics for a local machine with the same constant-time local computational complexity as experienced in our universe.