Generalized Probabilistic Theories in a New Light

TL;DR

This paper introduces an extended formulation of generalized probabilistic theories that unifies quantum and classical systems, addresses foundational questions, and suggests implications for quantum computing and the nature of physical laws.

Contribution

It presents a new extended operational probabilistic theory framework that applies to both quantum and classical systems, explaining the necessity of complex Hilbert spaces and the universe's non-deterministic nature.

Findings

Unified framework for quantum and classical systems

Addresses measurement problem and Bell's theorem

Suggests a non-deterministic foundation for physics

Abstract

In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend this work to infinite dimensional Hilbert spaces are given. Moreover, this new formulation which will be called as extended operational probabilistic theories, applies not only to quantum systems, but also equally well to classical systems, without violating Bell's theorem, and at the same time solves the measurement problem. A new answer to the question of why our universe is quantum mechanical rather than classical will be presented. Besides, this extended probability theory shows that it is non determinacy, or to be more precise, the non deterministic description of the universe, that makes the laws of physics the way they are. In addition, this paper shows that there is still a possibility that there might be a deterministic level from which our universe emerges, which if understood correctly, may open the door wide to applications in areas such as quantum computing. In addition, this paper explains the deep reason why complex Hilbert spaces in quantum mechanics are needed.