What question did this study set out to answer?

The research aims to determine the conditions under which fragment-limited observers may exist within quantum mechanics.

March 30, 2026Open Access

Fragment-Limited Quantum Mechanics

Key Points

The research aims to determine the conditions under which fragment-limited observers may exist within quantum mechanics.
Introduced Fragment-Limited Quantum Mechanics to formalize observer constraints.
Derived implications of finite fragment accessibility on standard quantum mechanics.
Established a controlled-imprinting collision model to analyze objectivity and viability thresholds.
Decoherence is crucial for understanding the viability of fragment-limited observers.
Identified a minimum classicality threshold vital for classicality in quantum systems.
Explained the coexistence of macroscopic redundancy with low-access fragments, complicating bounded-error inference.

Abstract

Fragment-Limited Quantum Mechanics (FLQM) is an access-conditioned operational extension of quantum theory addressing a question logically prior to standard measurement theory: when can physically realizable, fragment-limited observers exist at all? Standard quantum mechanics assumes idealized observers with unlimited access to global system states. Real observers are subsystems of the environments they measure, restricted to finite fragments. FLQM formalizes these constraints and derives their consequences within standard unitary quantum mechanics, preserving the Born rule without modification. The framework establishes three interlocking results. The Minimum Classicality Threshold (MCTO) identifies the global information-supply precondition for classicality. The Viability–Objectivity Separation Theorem (VOST) proves that macroscopic redundancy can coexist with regimes where every accessible fragment lies below the Holevo–Fano ceiling, rendering bounded-error inference impossible independent of measurement strategy. Exact viability thresholds and objectivity capacity are derived in a controlled-imprinting collision model and extended to restricted access classes and multi-outcome pointer variables. The paper provides quantitative, falsifiable predictions for minimum fragment sizes required for viable observers on current superconducting, trapped-ion, and photonic platforms. Classicality emerges as a three-part condition requiring dynamical stability, Darwinian redundancy, and fragment-scale viability simultaneously. This work complements and extends: G. Sell, “Minimum Classicality Threshold for Observers” (Zenodo, 2026, DOI: 10.5281/zenodo.15088098); G. Sell, “Objectivity Without Observers: A Viability–Objectivity Separation Theorem” (Zenodo, 2026, DOI: 10.5281/zenodo.15106907); G. Sell, “Accessible Predictive Information and the Limits of Observation” (Zenodo, 2026, DOI: 10.5281/zenodo.15204022). Keywords: quantum Darwinism, decoherence, fragment-limited observers, Holevo bound, Fano inequality, classical emergence, viability threshold, objectivity capacity, quantum foundations

Fragment-Limited Quantum Mechanics

Key Points

Abstract

Cite This Study