Relative Information, Relative Facts

TL;DR

The paper addresses how to interpret quantum theory without committing to an observer-centric ontology by introducing a quantitative relational framework based on relative information. It defines relative information $I_{A|B}$ and relative facts with respect to commuting subalgebras (classical subsystems), showing how these notions reproduce quantum correlations while avoiding absolute, perspective-independent facts. The approach demonstrates that measurements are continuous information-gathering processes and that intersubjectivity arises from the merging of compatible perspectives, even in Wigner-like scenarios. Crucially, the framework remains fully compatible with orthodox quantum mechanics and naturalism, offering a precise, non-ontological account of quantum phenomena and the emergence of classicality from relational facts.

Abstract

We offer a fresh perspective on the relational interpretation of quantum mechanics as a way of thinking about the world described by quantum theory based on quantifiable notions of information. This allows us to provide a definition of a relative fact, with no addition to orthodox quantum theory and no fundamentally special role for observers. By associating perspectives with commutative observables rather than entire quantum systems, several previous problems with the interpretation are dissolved. As a side result, we show how a quantum measurement, properly described, is a continuous process.

Figures (1)

• Figure 1: The increase of the apparatus' information about a system in course of a quantum measurement. Before the start of the measurement, the mutual information $I_{A:B}$ vanishes, it then increases continuously to its maximum value $H_A$ during the duration $T$ of the measurement, at which point the relative information $I_{A|B} = I_A+I_{A:B}$ reaches its maximum value.