Quantum Mechanics from Focusing and Symmetry

TL;DR

This paper proposes a foundational approach to quantum mechanics based on focusing on inaccessible variables and symmetry groups, deriving the Hilbert space structure and quantum rules from these concepts.

Contribution

It introduces a new foundation for quantum mechanics using focusing and symmetry, providing clear interpretations and deriving core principles from weak assumptions.

Findings

Hilbert space constructed from symmetry and focusing

Born rule derived from weak assumptions

Quantum paradoxes discussed and addressed

Abstract

A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables - inaccessible conceptually derived variables; several examples of such variables are given. The focus is then on a maximal accessible parameter, a function of the common c-variable. Symmetry is introduced via a group acting on the c-variable. From this, the Hilbert space is constructed and state vectors and operators are given a clear interpretation. The Born formula is proved from weak assumptions, and from this the usual rules of quantum mechanics are derived. Several paradoxes and other issues of quantum theory are discussed.