Minimax context principle

TL;DR

The paper introduces the minimax context principle within a topos-based quantum mechanics framework, proposing that the physical space corresponds to the configuration space of a structureless point particle, balancing accuracy and simplicity.

Contribution

It formulates the minimax context principle and defines order relations on contexts, linking quantum structures to classical physical space concepts.

Findings

The minimax context principle captures key features of physical space.

Order relations on contexts are introduced as analogs of daseinisation.

The principle balances maximal accuracy with minimal degrees of freedom.

Abstract

I show how space-like structures emerge within the topos-based approach to quantum mechanics. With a physical system, or, more generally, with an operationalistic setup a context category is associated being in fact an ordered collection of contexts. Each context, in turn, is associated with certain configuration space. The minimax context principle is put forward. Its basic idea is that among various configuration spaces the `physical space' is the configuration space of a structureless point particle. In order to implement it, two order relations on contexts are introduced being analogs of inner and outer daseinisation of projectors. The proposed minimax context principle captures two characteristic features of physical space: maximal with respect to refining the accuracy, and minimal by getting rid of extra degrees of freedom.