The Transformation-Response Framework: An Operational Reformulation of Quantum Mechanics

• URL: http://arxiv.org/abs/2606.09000v1
• Date: Mon, 08 Jun 2026 03:55:25 GMT
• Title: The Transformation-Response Framework: An Operational Reformulation of Quantum Mechanics
• Abstract summary: We present the transformation-response framework, an operational reformulation of quantum mechanics.<n>A quantum state is not a Hilbert space object but a catalog of a system's responses to all physical transformations.<n>The framework provides a unified, economical, and falsifiable foundation for quantum theory rooted in operational primitives.
• Score: 0.65268245109828
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present the transformation-response framework, an operational reformulation of quantum mechanics. A quantum state is not a Hilbert space object but the catalog of a system's responses to all physical transformations: for each operation $g$ from the system's local group $G$, an interference experiment gives a complex value $χ(g)$. The collection $\{χ(g): g\in G \}$ is the characteristic function and defines the state. The only postulate is that $χ$ is positive-definite, encoding the requirement that no superposition of transformations yields negative probability. From this single assumption, the entire standard formalism is derived: Hilbert space via GNS construction, Born rule via Bochner theorem, Schrödinger equation from group automorphisms, and especially Feynman path integral as a Trotter limit. The framework is background-independent and time-neutral: time is a coordinate along a one-parameter subgroup of $G$. It also reveals a new physical constraint, product order positivity, which may lead to testable predictions. The framework provides a unified, economical, and falsifiable foundation for quantum theory rooted in operational primitives.

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