aiqbench analysis
This paper proposes an operational reformulation of quantum mechanics that derives standard formalism, including the path integral, from a single postulate regarding system responses to physical transformations. By grounding the theory in background-independent, time-neutral primitives, it offers a unified and potentially falsifiable foundation that could yield new testable predictions. The work represents a significant theoretical advance in foundational physics rather than an immediate product or engineering application.
The Transformation-Response Framework: An Operational Reformulation of Quantum Mechanics
arXiv:2606.09000v1 Announce Type: new 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 $\chi(g)$. The collection $\{\chi(g): g\in G \}$ is the characteristic function and defines the state. The only postulate is that $\chi$ 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, Schr\"odinger 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.
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 $\chi(g)$. The collection $\{\chi(g): g\in G \}$ is the characteristic function and defines the state. The only postulate is that $\chi$ 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.
Part I of series work. Comments are welcome!
arXiv:2606.09000 [quant-ph]
(or arXiv:2606.09000v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.09000 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 263 words