The physical interpretation of daseinisation

TL;DR

This paper offers a conceptual and physical interpretation of the topos approach to quantum physics, focusing on the daseinisation process for operators, bridging traditional Hilbert space formalism with topos-based quantum theory.

Contribution

It provides a physical motivation and interpretation for the daseinisation process within the topos approach, with explicit examples for a spin-1 particle.

Findings

Daseinisation links Hilbert space formalism to topos quantum theory.

Explicit construction for a spin-1 particle's spin-z operator.

Physical intuition behind abstract topos constructions.

Abstract

We provide a conceptual discussion and physical interpretation of some of the quite abstract constructions in the topos approach to physics. In particular, the daseinisation process for projection operators and for self-adjoint operators is motivated and explained from a physical point of view. Daseinisation provides the bridge between the standard Hilbert space formalism of quantum theory and the new topos-based approach to quantum theory. As an illustration, we will show all constructions explicitly for a three-dimensional Hilbert space and the spin-z operator of a spin-1 particle. This article is a companion to the article by Isham in the same volume.