Quantum Conditional Stochastic Processes

TL;DR

This paper introduces conditional stochastic processes based on real probabilities to derive and interpret quantum mechanics, aiming to clarify its foundational concepts.

Contribution

It proposes a real-number-based framework called CSP and demonstrates its equivalence with quantum mechanics through a formal dictionary mapping.

Findings

CSP can derive quantum mechanics from real probabilities.

Quantum concepts can be obtained from CSP axioms.

The framework provides a new interpretation of quantum phenomena.

Abstract

Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave functions, Born's rule for probabilities and others. If we accept that quantum mechanics is probabilistic, then these concepts can be derived and they become secondary. In this work, we begin with what we call a \textit{conditional stochastic process} (CSP) which is based on real numbers and probabilities. As we shall see, such processes are defined by three simple axioms. We then use CSP to derive quantum mechanics by employing a correspondence called a \textit{dictionary}. We also show that the converse holds. That is, beginning with a quantum system, we employ the dictionary to derive a CSP.