Relational objectivity in presence of finite quantum resources

TL;DR

This paper explores a relational approach to quantum systems that accounts for finite resources, challenging traditional infinite-resource assumptions and aiming to formalize a more realistic quantum description.

Contribution

It introduces a finite-resource, relational formalism inspired by Penrose's spin networks, moving beyond textbook quantum mechanics assumptions.

Findings

Highlights limitations of infinite-resource assumptions in quantum descriptions

Proposes a finite-resource relational framework based on spin networks

Addresses conceptual issues in quantum system and context inseparability

Abstract

The no-go theorems of Bell and Kochen and Specker could be interpreted as implying that the notions of system and experimental context are fundamentally inseparable. In this interpretation, statements such as "spin is 'up' along direction $x$" are relational statements about the configurations of macroscopic devices which are mediated by the spin and not about any intrinsic properties of the spin. The operational meaning of these statements is provided by the practically infinite resources of macroscopic devices that serve to define the notion of a direction in three-dimensional space. This is the subject of "textbook quantum mechanics": The description of quantum systems in relation to an experimental context. Can one go beyond that? Relational quantum mechanics endeavors to provide a relational description between any quantum systems without the necessity of involving macroscopic devices. However, by applying "textbook quantum mechanics" in such situations, it implicitly assumes infinite resources, even for simple quantum systems such as spins, which have no capacity to define an experimental context. This leads to conceptual difficulties. As an alternative, we analyse Penrose's spin network proposal as a potential formalisation of quantum theory that goes beyond the textbook framework: A description in presence of finite resources, which is inherently relational and inseparable in the system-context entity.