Quantum mechanics from five physical assumptions

TL;DR

This paper derives the core principles of non-relativistic quantum mechanics, including the Born rule, from five fundamental physical and information-theoretic assumptions, reducing reliance on traditional axioms and interpretations.

Contribution

It introduces five physical assumptions that alone derive the formalism and core results of quantum mechanics, simplifying foundational understanding.

Findings

Derivation of the Born rule from physical assumptions

Reduction of interpretative axioms in quantum theory

Justification of Hilbert-space formalism from symmetry and interaction assumptions

Abstract

Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions concern fundamental symmetries of physical interactions. The third concerns the Hilbert-space dimensions and the fourth and fifth the self-interaction Hamiltonians of the systems that function as "observers" within the theory. These assumptions are shown to provide a sufficient motivation for the usual Hilbert-space formalism, and to obviate the observation-related axioms and most interpretative assumptions with which minimal quantum mechanics is typically supplemented.