Complex joint probabilities as expressions of determinism in quantum mechanics

TL;DR

This paper explores how complex joint probabilities can represent quantum states and transformations, revealing a deterministic structure underlying quantum mechanics and explaining the emergence of classical reality from quantum laws.

Contribution

It introduces a state-independent framework using complex conditional probabilities to describe quantum transformations and the emergence of classicality from quantum determinism.

Findings

Complex joint probabilities represent quantum states.

Transformations are expressed via complex conditional probabilities.

Classical reality emerges as an approximation to quantum laws.

Abstract

The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex conditional probabilities that describe the fundamental relation between precise statements about the three different observables. Since such transformations merely change the representation of the quantum state, these conditional probabilities provide a state-independent definition of the deterministic relation between the outcomes of different quantum measurements. In this paper, it is shown how classical reality emerges as an approximation to the fundamental laws of quantum determinism expressed by complex conditional probabilities. The quantum mechanical origin of phase spaces and trajectories is identified and implications for the interpretation of quantum measurements are considered. It is argued that the transformation laws of quantum determinism provide a fundamental description of the measurement dependence of empirical reality.