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

• URL: http://arxiv.org/abs/2501.19269v1
• Date: Fri, 31 Jan 2025 16:29:16 GMT
• Title: Information Metrics and Possible Limitations of Local Information Objectivity in Quantum Gravity
• Authors: Per Berglund, Andrew Geraci, Tristan Hubsch, David Mattingly, Djordje Minic,
• Abstract summary: Local information objectivity, that local observers can infer the same information about a model upon exchange of experimental data, is fundamental to science. quantum gravity typically violates some of the Cencov assumptions, allowing the Fisher metric and Born rule to vary between observers. We explain these violations, some possible experimental tests, and a new quantum gravity approach based on generally covariant information geometry.
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• Abstract: Local information objectivity, that local observers can infer the same information about a model upon exchange of experimental data, is fundamental to science. It is mathematically encoded via Cencov's theorem: the Fisher information metric is the unique metric invariant under sufficient statistics. However, quantum gravity typically violates some of the Cencov assumptions, allowing the Fisher metric and Born rule to vary between observers. We explain these violations, some possible experimental tests, and a new quantum gravity approach based on generally covariant information geometry.

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