Information Metrics and Possible Limitations of Local Information Objectivity in Quantum Gravity

TL;DR

This paper explores how local information objectivity in quantum gravity may deviate from classical assumptions, proposing a covariant information geometry framework that could modify the Born rule and be tested experimentally.

Contribution

It introduces a generally covariant information geometry approach to quantum gravity, extending classical Fisher information concepts to account for quantum and environmental effects.

Findings

Deviations from Fisher metric reflect environmental and quantum effects.

Possible modifications of the Born rule depend on observer context.

Proposes experimental tests for covariant information geometry in quantum gravity.

Abstract

Local information objectivity, that local, independent observers can infer the same information about a model upon exchange of independently acquired experimental data, is fundamental to science. It is mathematically encoded via Cencov's theorem: the Fisher information metric is the unique metric invariant under the assumptions of independent, identically distributed sampling and sufficient statistics. However, quantum gravity typically violates these assumptions, permitting contextual deviations from the Fisher metric that reflect the dynamical experimental and environmental configurations. This yields a possible extension of spacetime general covariance to information geometry. Since compatibility with the metric on probability spaces heavily restricts the form of the Born rule for quantum mechanics, deviations from the Fisher metric also can induce modifications of the Born rule, leading it to vary between observers. We explain some possible variations, advocate for experimental tests, and suggest a new quantum gravity approach based on generally covariant information geometry.