Observables and Information

Greco, Giuseppe Junior

Across physics, computation, and information science, observation is increasingly recognized as a non-neutral operation. However, a unified formal framework describing how observer-dependent structure emerges from information processing remains lacking. In this work, we introduce Informational State Dynamics (ISD), a substrate-independent framework in which observers are modeled as compression operators acting on an underlying informational substrate . Informational states arise as observer-relative compressions shaped by intrinsic informational loss and structural selectivity. We show that no observer can access a complete or unbiased representation of the informational substrate, and that non-equivalence between observers follows necessarily from asymmetries in compression. ISD is compatible with classical information theory and provides a minimal, falsifiable foundation for analyzing observer-dependent structure across physical systems, artificial agents, and abstract information-processing architectures.

Roderich Tumulka

Gertjan J. Burghouts, Jan‐Mark Geusebroek, Arnold W. M. Smeulders

Greco, Giuseppe Junior

Across physics, computation, and information science, observation is increasingly recognized as a non-neutral operation. However, a unified formulation describing how observer-dependent structure emerges from information processing remains lacking. In this work, we introduce Informational State Dynamics (ISD), a general framework in which observers are formally modeled as compression operators acting on an underlying informational substrate. Informational states are defined as observer-relative compressions shaped by intrinsic informational loss and structural selectivity. We show that no observer can access a complete or unbiased representation of the informational substrate, and that non-equivalence between observers arises as a necessary consequence of compression asymmetries. ISD is substrate-independent, compatible with classical information theory, and provides a minimal, falsifiable foundation for analyzing observer-dependent structure across physical systems, artificial agents, and abstract information processors.

Lev Deych

guobin ouyang

This article establishes the mapping chain from the information field to the observer. The observer acquires physical information through the spectral resolution of the information field. The mapping chain proceeds from the coding weights , through the Born Rule, Algebraic Normalization, and Birkhoff Mixing Matrix, finally arriving at observables. This article derives in detail the complete mapping from coding to observation, analyzes the observable extraction mechanism, and discusses the relationship between the irreversibility of the mapping and the observer's information capacity.