Quantum theory as inductive inference

TL;DR

This paper introduces a novel approach to quantum theory and probability based on algebraic integration, information geometry, and maximum entropy, avoiding traditional Hilbert space frameworks.

Contribution

It proposes a new foundational framework for quantum theory using algebraic and information-theoretic methods, bypassing Hilbert space formalism.

Findings

Provides a unified algebraic approach to quantum and probability theory.

Addresses conceptual issues without relying on Hilbert spaces.

Utilizes maximum relative entropy for inference in quantum contexts.

Abstract

We present the elements of a new approach to the foundations of quantum theory and probability theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal with conceptual and mathematical problems of quantum theory without any appeal to frameworks of Hilbert spaces and measure spaces.