The presheaf of Quantum Realities and constructions of the space-time from the Space of Ultimation

TL;DR

This paper introduces quantum models using algebraic geometry, representing the universe as a presheaf over the space of ultimation, and demonstrates how classical space-times can emerge from ultrametric spaces.

Contribution

It proposes a novel framework linking quantum models, presheaves, and the emergence of space-time from ultrametric structures.

Findings

Universe modeled as a presheaf on the space of ultimation

Derivation of classical space-times from ultrametric spaces

Models based on algebraic geometry and category theory

Abstract

The paper presents several quantum models constructed with the formalism of algebraic geometry. The Universe is presented as a presheaf on the "space of ultimation" (i.e. the branching future) with values in certain category which enhances the category opposite to C*-algebras. Given models show the possibility to derive ordinary space-times (of both Special and General Relativity) from ultrametric spaces.