A Categorical Framework for Quantum Theory

TL;DR

This paper proposes a categorical framework that underpins classical and quantum physics, highlighting fundamental conceptual differences, especially regarding the nature of facts and time, to better understand the foundations of quantum theory.

Contribution

It introduces a novel categorical framework for quantum theory that emphasizes conceptual foundations over purely mathematical structures, contrasting with classical physics.

Findings

Classical physics aligns with a categorical framework involving logic, time, reason, and observer-observed dichotomy.

Quantum physics requires a different framework incorporating the reduction postulate and the emergence of facts.

The categorical approach reveals a different notion of time in quantum physics, emphasizing the present.

Abstract

Underlying any theory of physics is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with physical phenomena, but they also constitute our fundamental assumptions about reality. Many of the discrepancies between quantum physics and classical physics (including Maxwell's electrodynamics and relativity) can be traced back to these categorical foundations. We argue that classical physics corresponds to the factual aspects of reality and requires a categorical framework which consists of four interdependent components: boolean logic, the linear-sequential notion of time, the principle of sufficient reason, and the dichotomy between observer and observed. None of these can be dropped without affecting the others. However, in quantum theory the reduction postulate also addresses the "status nascendi" of facts, i.e., their coming into being. Therefore, quantum phyics requires a different conceptual framework which will be elaborated in this article. It is shown that many of its components are already present in the standard formalisms of quantum physics, but in most cases they are highlighted not so much from a conceptual perspective but more from their mathematical structures. The categorical frame underlying quantum physics includes a profoundly different notion of time which encompasses a crucial role for the present.