Statistical Interpretation of the Procedures Measurement of Physical Quantities

TL;DR

This paper offers a conceptual framework linking algebraic and probabilistic approaches in quantum physics, emphasizing operational measurement procedures and their foundational significance.

Contribution

It reorganizes and synthesizes existing quantum models to clarify assumptions and operational meanings, proposing a path for axiomatic reformulation grounded in laboratory practice.

Findings

Highlights the importance of experimental procedures in defining quantum quantities

Critiques purely mathematical formulations when detached from experimental interpretation

Proposes a reconstruction of quantum theory respecting empirical and conceptual clarity

Abstract

This work develops a conceptual framework for the foundations of quantum physics, linking two main approaches: the algebraic formulation and quantum probability. Rather than proposing new axioms or theories, the text reorganizes and synthesizes existing models, highlighting their assumptions, conceptual structures, and operational significance. The analysis begins with von Neumann's measurement theory and its subsequent developments by Mackey, emphasizing the role of experimentally feasible procedures and the need for a statistical model grounded in laboratory practice. The work adopts an operational perspective, according to which physical quantities are defined solely through experimental measurement methods, and the corresponding probabilistic measures are derived from measurement outcomes. The introduction critically examines the limitations of purely mathematical formulations - such as the algebraic method - when separated from experimental interpretation. The text argues for a clear distinction between axioms, postulates, and presuppositions, and for a reconstruction of quantum theory that respects both empirical constraints and conceptual clarity. Overall, the goal is to provide a coherent path from operational principles to algebraic structures, offering a basis for an axiomatic reformulation of quantum mechanics that remains faithful to physical practice.