A categorical framework for quantum theory

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.

Bridging the Gap: Does Closure to Efficient Causation Entail Quantum-Like Attributes?

“…Specifically Small (2006) argued that quantumness can be accommodated by a self-referential logical structure. In an argument partially similar to that of Filk and von Mueller (2010), Small proposed that if the dichotomy between the observer and the quantum system is lifted, so that the observing and observed systems are embedded in a self-referential loop, then critical quantum features, specially entanglement and the measurement process, can be emulated by a causal loop of inferential entailment, i.e. an impredicative model.…”

“…12. Self-referentiality has been invoked in the context of physical quantum theory, specifically for topics such as the measurement problem (Chiara 1977;Breuer 1995), entanglement and the observer/observed duality (Filk and von Mueller 2010), organizational closure in quantum systems (Groessing 2005) and has even been qualified as a central feature of the quantum world (Small 2006;von Stillfried 2010). Specifically Small (2006) argued that quantumness can be accommodated by a self-referential logical structure.…”