The Laws of Observation

Ruth E. Kastner

Greco, Giuseppe Junior

This paper examines the relationship between Informational State Dynamics (ISD) and physical law within an observer-relative framework. Physical laws are interpreted as stable regularities emerging from constrained informational state transitions rather than as fundamental, observer-independent prescriptions. The analysis clarifies how dynamical laws retain predictive power and empirical objectivity while remaining compatible with observer-relative state attribution. ISD thus provides a minimal informational foundation for physical law without modifying existing physical theories.

Majid Mohammady, Takayuki Miyadera

In the quantum regime, the third law of thermodynamics implies the unattainability of pure states. As shown recently, such unattainability implies that a unitary interaction between the measured system and a measuring apparatus can never implement an ideal projective measurement. In this paper, we introduce an operational formulation of the third law for the most general class of physical transformations, the violation of which is both necessary and sufficient for the preparation of pure states. Subsequently, we investigate how such a law constrains measurements of general observables, or positive operator-valued measures. We identify several desirable properties of measurements which are simultaneously enjoyed by ideal projective measurements---and are hence all ruled out by the third law in such a case---and determine if the third law allows for these properties to obtain for general measurements of general observables and, if so, under what conditions. It is shown that while the third law rules out some of these properties for all observables, others may be enjoyed by observables that are sufficiently ``unsharp.''

Stanley Everett Sambey

We present a unified formulation of the Law of Observation (LO) as a structural principlegoverning persistence and emergence in physical systems. Previous work established irre-versible constraint pruning (ICP) as the minimal mechanism by which admissible historiesare reduced, and introduced weighting over histories to account for relative dominance amongsurvivors. Here we show that these components arise naturally as consequences of a moregeneral law: observation corresponds to the progressive restriction of admissible configura-tions under irreversible constraint formation. Persistence arises when alternatives becomeirreversibly distinguishable, while observed structure is shaped by pre-pruning weighting. Inthis way, the Law of Observation unifies conceptual interpretation, structural mechanism,and empirical behavior within a single framework for stable configuration formation. irreversible constraint pruning, law of observation, persistence, distinguishability, constraint density, emergence, complex systems, non-equilibrium systems, structure formation, decoherence

Massimiliano Sassoli de Bianchi